Nice presentation, well beyond my math understanding. A question, maybe you can do a presentation on the coriolis effect. Does it affect the planets in orbit, how about star systems orbiting in galaxies? How about dimensions?
I find it easiest to think of infinity as a process rather than a number. Its a process that discribes a neverending chain of numbers or events or whatever you wanna plug into it. This works with how some infitities are "larger" than others.
Great video. I recently noticed an example of infinity (or division by zero) arising in an everyday mathematical formula. When I am driving my car, the dashboard displays the current fuel efficiency that the car is getting in litres per 100 km. It shows it as a bar that gets longer or shorter as the car consumes more fuel or less fuel per unit distance. When I bring the car to a stop (to stop at a traffic light, for example), the bar becomes as long as the display will allow, and then suddenly disappears. This is just how the indicator handles the division by zero issue, since when your car is stopped but the engine is still running, it is consuming fuel but not travelling any distance, and therefore has a momentary fuel efficiency of "infinity" litres per 100 km.
@@tinkeringtim7999 how much milk do you have if you have 0 liters of milk? How fast do you go when you go 0 km/hour? When the value reaches 0, the property stops existing other than that we can talk about it.
@@daarom3472 If you are using existence in a colloquial sense, please explain in what sense. If you mean existence as in predicate logic, I can't see a way to express that consistently so perhaps write what you mean by that in a concrete unambiguous way. I suspect you will struggle to, because the whole point is these things are incredibly difficult (maybe impossible) to pin down from the perspective of numbers. We've been trying to figure it out since Euler looked at the primes through sequences and polynomials. If it's just simple and self evident in your view, then all you're telling me is you don't actually know what is going on when one litre of milk is "added" to another and the result shown to be consistent with our counting system. In other words, if you think you know what numbers mean/do and you haven't studied number theory from the perspectives algebra/topology/analysis then you have only proved you can fool yourself. I don't see how anyone who has studied even one of those perspectives to a significant degree of apprehension could've entertained such a facile thought for long enough to type it but I'm open to the idea it's possible.
Me: *about to type "Technically, you would need a limit for those divisions to be true."* Dr. Hossenfelder: "I hope there are no Mathematicians watching..." Me: :)
@@shoopinc once you get the ball rolling with non standard analysis, it can be extremely intuitive, however, to make it rigorous requires a ton of heavy machinery to be developed. Whereas using the standard real numbers, a close to fully rigorous treatment can be done in first year.
I swear I would've said similar, upon being a disabled person and waiting on the g-d damned government to getting around the agree to the obvious while you're sitting in homeless shelter waiting on subsidized housing shoulder to shoulder with convicted murderers that are completely oblivious to the idea that upon finding out their names that you can check their criminal convictions on a damn smartphone. The DMV? Yeah. Even just renewing a state ID; time slows down and yet somehow you age faster!
When you get a number and they skip your number and you have to get a new number but they say you just didn't hear your number. No lady you all skipped like 10 numbers.
That really blows my mind away, what a masterpiece of didactics! Sabine is the absolutely best teacher, I've ever met. Read a whole book (by John Barrow) about this, but didn't understand half of what she explains in ten minutes. I'm so thankful for this
Thank you for a useful discussion of infinity. I have been tangled up in this for a while, and this clear summary of the mathematical and scientific interpretations was just what I needed to get past my current block! I am really enjoying your channel.
@@DheerajBhaskar Ha-ha-ha, this happens when I think there´s nothing gayest than what we already had... Well I opened a comment (see the last), just for gay comments.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
@@alexleibovici4834 Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations about "something" and talk about it....
@@YT8699 > Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations No. There are objects out there and the concepts are the representations in our brains of those objects out there.
@@alexleibovici4834 I am also a realist who believes in the existence of stuff out there. However, our entire knowledge or understanding of any particular "object" is contained within our "concept", and it appears that our attempts to form coherent concepts from our observations of objects almost always involves the use of "mathematical realities". If fact our attempts to "prove" (another loaded word...) that any particular object actually exists also depends upon the usage of these mathematical realities. So when the distinction between "mathematical realities" and "physical realities" (or objects and concepts) is reduced to the notion that only "physical realities" exist....then we're faced with admitting that our knowledge of that which "exists" is dependent upon that which "does not exist". Of course, some consistent naturalists identify "concepts" as nothing more than a particular set of chemical reactions among the organized elements of the human brain. Thus making concepts into objects...
@Goran Vukovic but but but, was it the story of Socrates or Aristotle that he's the most smart person? He heard people were saying he's the smartest person in the city. So he thought he'd go out to see if that's true. He went out and ask many smart people questions after questions. At first they answered the questions but then in end they ran out of answers. At the end of the day he had found out nobody really didn't know. But he already knew that that he didn't know. And everybody thinks they knew when they didn't know but he knew he didn't know. That means he said he is the most smart person in the city. Then was he wrong?
I am at the end of my physics bachelor (actually I'm doing QFT now, so that was a fun shout out), and there was a lot of new stuff for me in this video. I'm surprised by the amount of material you managed to get in her, because I would think it is also possible to grasp most of what you say with much less of a mathematical background. You inspire me as an educator!
@@daarom3472 No, because pi and e are not infinite in magnitude. Pi is less than 4 but more than 3, that's not infinite. It just has infinite digits in it's decimal representation
So do other numbers depending on how you represent them by the way. 1/3 is 0.33333... on and on forever when represented in it's base 10 decimal form for example. Pi just doesn't have a nice pattern like that, it's irrational
Serendipity. I was just thinking, a month or two ago, that mathematicians should not be using infinity because it's not real, it's not understandable, and makes for possible misunderstandings in the calculations. Now I see this. Did the universe give me you because it thought I was ready? I have not studied maths or physics, but I think about these things. I thought I was really smart. You guys have already worked all this out. Well, I'm glad to have found you, at last. Too late, but I can die in some peace!! Thanks again! 🙂
I'm a Democrat and a Socialist. We don't let the laws of economics get in the way of progress and doing what's right for the common good of society. I'm just sayin'
The videos on this channel consistently progress from stuff I know comfortably to stuff I *don't* know, usually at about the 75% mark. It's a rare and wonderful thing. Thank you.
Her first “examples” definitely raised my eyebrows but when she hit her groove the examples turned out to be “bait” for the grand finale. Her completely approachable explanation of the epistemological difference between physics and mathematics is just brilliant. Entire college courses don’t do any better.
Unfortunately not. More bullshit. Physics with infinity are just mathematical abstractions to try to approximate the observable. There are theories to state even time in not infinite divisible. At this time, there is no concluding evidence that infinite is real. It sure exists in math, in our minds, but not in the observable universe.
@@miguelandrade5964 Actually ? Do NOT exist, in math ! Must use them, to express them ! Each, is an "infinite Limit" ! X^Infiity = Infinity 1/X as X aproaches infinity, aproached 00 ! 00 +/- Any/Every possible number, is NOT 00 ! IF can add any number to Infinity: then previous number IS NOT Infinity !
@@miguelandrade5964 Our minds, can understand the concept of always. Our minds, can not understand what is an Infinite amount. (One of definitions, of infinity)
@@dirktween244 In math (and in our minds), for something to exist all it needs is to be defined. If you like math a little, you maybe want to search some stuff from Cantor. It's fascinating and a bit funny.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
Nonsense. It was completely correct. Sabine was leaving it as an exercise to the viewer to determine what the limit would be if x tended to infinity! Pure magnificent pedagogy!
I am mathematician and I enjoyed watching this video. In optimization we consider extended valued functions and make up such rules for playing with the infinite.
Infinity is a Platonic or mathematical concept! Platonic forms are dual to to particulates -- Plato. Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant. Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein. Synthetic a priori knowledge == space/time -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality. The future is dual to the past, we remember the past and predict the future -- Time duality. My absolute time is your relative time and your absolute time is my relative time -- Time duality. Length, distance or space is defined by two dual points -- space duality. Absolute space is dual to relative space -- space duality. Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality. Space duality is dual to time duality. "Always two there are" -- Yoda.
@TheAbstraction The big bang is a Janus point (two faces) = duality! The future is dual to the past -- time duality. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Apples fall to the ground because they are conserving duality. Potential energy is dual to kinetic energy. The force of gravity is scientific or empirical proof of duality!
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion
Really concise summation of the gap between mathematics and phenomenology. You cannot measure infinity because its value will always be greater by at least one unit than what you have measured.
I appreciate your commitment to the proper use of mathematics in physics. Can you make a video, about some examples of improper use of mathematics in mainstream science?
@@SeanPeckham-xe2gt Yes this also reminds me that I used to call complex numbers "circular numbers", I don't know where this "complex" or "imaginary" comes from but this is really sad. A bit like Pi which should have been 2Pi (the ratio circumference/radius instead of circumference/diameter), That's what the Tau Initiative is about. If you replace Pi by Tau in equations, everything becomes way more intuitive. With Tau, the Euler's identity is even more interesting because instead of tracing a half circle and landing on -1 you make a full circle and come back to 1... tauday.com/tau-manifesto#sec-euler_s_identity Unfortunately I didn't get a proper education in maths so I'm in the process of relearning the base concepts such as the one you described: turn concepts into a physical representation involving the senses (visual, kinesthetic, etc...) and develop an intuitive "feel" instead of applying rules and hoping for the best... This is the kind of thing that you either develop by chance when you are a child and then you become "good at math" or that you don't and then, since school doesn't teach you how to conceptualize and create mental models, you become stuck with the wrong/impractical models in your brain until you decide to take the mater into your own hands... With that in mind I'd be interested if you could share your mental model of the natural logarithm or exponentiation!
Very good discussion of that may be seen here: ua-cam.com/video/T647CGsuOVU/v-deo.html (Disclaimer, I have no association with Welch Labs, the producer of the video.)
Totally agree with this. When I was an undergraduate physics student, I always felt that assumptions were being made whenever I saw a limit as a variable tended to infinity or 0 - fine as an approximation, but it shouldn't be taken as a final model.
I too love, Dr. Sabine, though I counter some of her videos (the flaw is always on assumptions). I hope there'll be a debunking between nuclear physicist Thunderfoot (is that the same as particle physicist?) and theoretical physicist Dr. Sabine, not coz' of dislike but because the exchange between minds who are experts in their fields, is an inspiration and a great example for everybody. God bless, Revelation 21:4
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion
As a published PhD Mathematician, physicists (both theoretical AND the experimentalist ones who criticize theorists) annoy me. We mathematicians have no problem amongst ourselves. Conflicts between different subsets of physicists do not concern us mathematicians. We are quite a happy open-minded bunch.
Great video! I always nitpick whenever people talk about black holes and singularities and their infinite densities; I just could never believe in Infinities in nature. I submitted a question about this to some subreddit, and someone wisely replied to me that they agreed that the densities of the singularities at the hearts of black holes were not infinite... they were just COLOSSAL.
Yes e.g. while reading Hawking I've been thinking the same thing, & he never seems to mention the issue. This is the first time I've seen it mentioned at all (much like the bogus characterizations of fusion achievements).
@@purpleglitter9596 . "Do not exist in science" means [omit 3/11: "not known to exist", ie.] "not known to exist in nature". . Imo, strictly speaking, infinity doesn't exist in math either.
@@red-baitingswine8816 Science is not nature. Its an attempt to explain nature. But nature is nature. Otherwise why would she need to specify that it doesn't exist in science if she meant nature. Infinity does exist in math. Mathematics is pattern identification. Infinity is a pattern. If it didn't exist in mathematics they wouldn't have to keep finding ways to avoid it.
I recently learned some of the Haskell programming language... it is a language deeply concerned with repeating processes and "types"... the idea that Infinity is a 'type' and not a value just makes so much sense to me right now. Thankyou for the awesome video :)
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
"In science, we can always replace infinity with a very large number, we don't do this, but we could." -- We do it all the time in numerical simulations, by replacing the infinite dt's in any integral with a large number of delta t's.
Why is it that Ms. Hossenfelder is the only UA-camr that forms her words so perfectly that I never miss one? The slight German accent doesn't hurt, it may even help. Subscribed!
It's because they speak like they learned from the book. No slang, no dialect. My first spanish teacher was German. She almost never talked german to us, but we understood everything. Years later, when I wasn't a beginner any more I had a teacher from Bolivia. We just didn't understand a word, so he tried to explain in German. We still didn't understand anything.
Yes, but in that explanation we forgot the finite speed of light, so it can't move infinitely fast. For that in reality infinity in the real world is not infinite. 😁
u know ure a genius when u explain highly complex subjects without animation, just speech without any flashy video editing and effects. ure a genius and i love ur videos u are a scientist and a writer sabine
I love how whenever there is a conversation about an expression of 0 becoming solution everyone freaks out because they think somewhere in the world they’ve just given a mathematician a aneurysm lol
The ideas of infinity and an end came into my head when I was 8 years old and lying in my bed going to sleep. In the form of trying to imagine it in space, not in the form of mathematical equations. It was so unimaginable that I finally started crying. It just blew my mind. So here I am over 50 years later thinking maybe I will be able to get 2 hours sleep and this pops- up. Great.
@@mathfincoding It really is. How anyone can accept ' the soup' as an ultimate answer to origins is beyond me. Or that mathematical equations are equivalent to comprehending eternity, an end, or nothingness.
infinity is like a shorthand for "as big as you want". Like saying something equals infinity is just saying that it keeps going, like you'll never run out no matter what you do, unless you use the infinity to destroy the infinity. And putting infinity inside an expression is like saying you're interested in what happens as you keep going, and if things ever stop happening, or if they all would hypothetically cancel out. so saying infinity+1=infinity for example is just saying something like, "if I will never run out of apples, and you give me an apple, I will never run out of apples" or "if I started counting my apples I would not be able to finish (this is not the same as uncountable infinity), and if you gave me another one, I still wouldn't be able to finish counting them" 2*infinity = infinity is like "I'm never gonna run out of apples, and you're never gonna run out of apples, and if you gave me your apples I would still never run out of apples" infinity^2/2^infinity = 0 means like if my friends start cloning themselves, and I buy square grid of apples each time all my friends (including their clones, and their clones' clones, etc.) have had a turn in the cloning machine with a side length equal to the number of times they've been cloned, and split them between everyone, as time goes on each person will get less and less, and in fact if you pick a really tiny (positive) number, at some point each friend/clone will get less than that amount ok that actually probably made it sound more complicated than it is, so dropping the apple analogy, if you start squaring really big numbers, and raising 2 to the same really big numbers, the numbers in the second group will be many times bigger, and in fact, with a big enough number, bigger by an amount bigger than any (finite) amount you want. the last bit of that is sort of the crucial part. Because things that approach 0.0001 or a gazillion without going any smaller/bigger respectively exist, which are in many ways similar to being 0 or infinity, but are crucially distinct. Like you can count a gazillion apples, and see that it is distinct from having a gazillion and one apples.
"There are infinitely many types of infinity" - Terrific. Are there countably infinitely many types or are there even more infinitely many types of infinity?
look at wikipedia: Cardinal number, large Cardinal number, huge Cardinal number, List of large cardinal properties Other infinity concept is : Surreal number also kown as Convay numbers. an other concept is: Hyperreal number. Adding one point to a space to make the space kompakt is called Alexandroff extension .Example for Alexandroff extension is adding infinity to the the complex numbers equals a sphere. All thess can be done in Settheory called ZFC, ZFC is defined by using FOL (first order Language). Every Theory in FOL has a countable Model. Looking from outside we have only countable many set, but looking from inside we see uncountable sets. This is not a contradiction, because the map which makes a set countable is not a Member of the Model.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion
Thank you for your videos, Sabine. I would like to hear your opinion of the mass equation of special relativity. I assume that the singularity at the speed of light indicates that the Special Theory of Relativity is incomplete in the same way that the singularity at the centre of a black hole indicates that the General Theory is incomplete. What does the Standard Model of particle physics have to say about this?
Also true in philosophy: potential infinities vs actual infinities. In math we can say that up to roughly the 20th century we were only dealing with potential infinities, while later we got tools to deal with actual infinities (set theory etc). Infinity also is a strange thing in logic like omega inconsistent theories and also the Skolem's paradox. In particular, the different sizes of infinities is a finicky thing: the relation between the size of sets heavily depends on the axiomatic theory you consider. Personally, it makes me think that infinite sets are not a thing that actually have properties like a size, but some abstract construct to which we assign a concept of size that depends on the theory. The relation between these sets actually tell more about the expressive power of the theory than about the sets themselves. And just a last thing to really insist that in mathematics infinity isn't an obvious thing, in the ZF set theory, the existence of infinite set is an axiom. If we remove ot from the theory we can't prove they exist 🙃
In most practical areas, "infinity" is "take some arbitrarily large number" followed by "define this number as infinite". This also includes floating point math on computers, where, say, with 'double' the 'infinite' value is essentially 2^1024 (with some special case handling to make the math identities hold; zero is another such special case, otherwise it would have been 2^-1023).
@@BGBTech The IEEE/IEC floating-point formats do allow for denormalized values, signed zero, etc. However, there is a fundamental difference between asymptotic (limit) values and true infinitesimal type. A problem with a brief presentation like this one is that a lot of important information gets omitted, leaving the audience with misconceptions. For example, about five years ago the Numberphile UA-cam channel posted a couple of "astounding results" that resulted from not explaining precisely the importance of absolute convergence, and hence produced such errors as the claim that the sum of all natural numbers equals -1/12. The "controversy" caused by that has continued ever since (and I suggest it not be allowed to infect this channel).
@@douggwyn9656 As can be noted, they exist, and are handled specially by the hardware, but exist as definitions and special-case rules applied to the largest and smallest exponents, as opposed to some entirely different type of entity.
@HenryDavidT Yep. Can also note that "in practice" says little about either theory or physical reality, but rather "things done in the name of making it work". I have also seen enough code with things like: # define INT_INFINITY 1999999999 presumably because it is easier to type than 2147483647 or similar... Meanwhile, Windows Calculator seems to be able to go up to 10^9999 for whatever reason (this is outside the range of the usual IEEE formats), ...
In my student days, some 50 years ago, we learnt that mathematical constructs could be equally proven with or without the assumption of infinity. Has this now moved on?
Infinity is a Platonic or mathematical concept! Platonic forms are dual to to particulates -- Plato. Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant. Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein. Synthetic a priori knowledge == space/time -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality. The future is dual to the past, we remember the past and predict the future -- Time duality. My absolute time is your relative time and your absolute time is my relative time -- Time duality. Length, distance or space is defined by two dual points -- space duality. Absolute space is dual to relative space -- space duality. Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality. Space duality is dual to time duality. "Always two there are" -- Yoda.
Fascinating stuff Sabine! The conclusion I come to is that no matter how large the magnitude of a number that we can compute, there must logically always remain an infinity of numbers of greater magnitude which are un-computable. The set of un-computable numbers is necessarily infinitely larger than the set of computable numbers.
Further to this - A perfect circle is infinitely round, however no examples of perfect circles exist in the universe. One of the roundest object available - a neutron star is close but not perfectly round. Perfect circles only exist in the human imagination. So computing numbers with idealized functions such as pi and infinity does not reflect the universe as it actually is.
Thanks for clarifying the distinction between the existence of infinity in the mathematical and scientific sense! It helped me understand the concept of "infinity" better.
Infinity is a Platonic or mathematical concept! Platonic forms are dual to to particulates -- Plato. Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant. Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein. Synthetic a priori knowledge == space/time -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality. The future is dual to the past, we remember the past and predict the future -- Time duality. My absolute time is your relative time and your absolute time is my relative time -- Time duality. Length, distance or space is defined by two dual points -- space duality. Absolute space is dual to relative space -- space duality. Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality. Space duality is dual to time duality. "Always two there are" -- Yoda.
A very nice presentation. It reminds of my first calculus class given by a Bell Labs instructor at a remote University of Hawaii location. His introduction paraphased: .." the most difficult concepts to grasp are the terms infinity and infinitesimal. His explanation of infinity was similar to yours. His explanation of iinfinitesimal, was; you can describe you walking towards a point, dividing the distance in half continually. The infinitesimal is that moment you cross that point." Probably, as you explained zero and may be has a real meaning in the universe. It's amazing how infinity applies to mathematics, but not anything real in the universe. Or perhaps the universe is infinite, but I even find that difficult to believe. If it's an everlasting expanding and contracting universe, I contend the universe is finite of particles/energy. If it's infinte in particles/energy, who knows what to think. In either case, we will only be able to explain those two terms mathematically. Thanks so much for the details in your presentation.
Just started watching. Really hope this mentions Brouwer's Free Choice Sequences, albeit I fear-despite Sabine's brilliance-it won't. Edit: Yeah, it doesn't. Sad. Missed opportunity. Doubly so since it's THE avenue for formulating physics 'without' 'infinity'.
I remember having seen an interview where she was asked about non-classical logics and her reaction was that she was aware of quantum logic but she didn't seem to tie it to Heytings intuitionistic logic, let alone intuitionism. Despite this, much of this video concerns a Cauchy-like approach to infinity. Indeed, here in this video she tends to zoom in on extension of arithmetic by infinite object, while much of the controversies regarding foundations with infinities concern more general objects. To your final outlook, I think with the rise of type theory, a more computable perspective on math in the future is inevitable at that point.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion
What great topic ! Thanks Sabine. The standard cosmological model includes a spatially infinite universe, and it seems to attract little attention how strange indeed it would be! I've only found an obscure paper by Ellis. Thanks also for mentioning others in physics are concerned by this or related issues. It's a shame you didn't mention Hilbert's Hotel. That really drove the point home for me and carries the weight of a great mathematician.
You're swaying between two sides here. On the one hand you take the position that infinities in math are a most useful tool and ostensibly "easy to work with", but then you also warn that too strong of an axiom set might spoil possibility for interesting models. And indeed, you might fall for a trap if you recite insights derived in very strong axiom sets. Not all the fuss about infinite sets is merely the discussion of Cauchy sequences in fields like R or smaller ones, or the extension of its arithmetic by single elements that are "infinitely big" with respect to the total order of R. You blend these notions with cardinality claims known from ZF and it's also worth noting that this video doesn't discuss use of uncountable ordinals and transfinite induction much. I suppose your use for infinity ends somewhere around |(R->R)->(R->R)|, which is of cardinal size of a set given by a finite number of applications of the power set operation on N. I.e. it's tiny from a set theorist perspective. As a side note, if you do not adopt the Law of Excluded Middle and the Powerset axiom, then it's consistent that there is a subset S of N, such that there is a surjection from S to N^N, the uncountable set of functions from N to N. The issue here is that Excluded Middle blends the notions of subcountable with the potentially non-effective classical notion of countability. So claims of assumed necessity will be relativize once you take a step back and throw our some unneeded axioms.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion
Her explanations always trigger me and make me think she's wrong, then I slowly catch up to where I kind of sort of follow what she's saying and I realize I have looked at it wrong my whole life. I love the fact she respects her audience's intelligence enough to really did dig in to some of the more technical side of physics and math.
If you want to dig a little deeper, you could look into the work of Georg Cantor. He was a 19th century mathematician who was the first to prove that the real numbers were a different kind of infinite than the integers. He came up with what is called the diagonalization method to show this. I didn't appreciate its rigor the first time I encountered it, so I encourage people to take the time to work through it.
@@josiahslack8720 and if you want to go even deeper than Cantor without getting mad then you should take a look at John Conway's Surreal Number which goes an order of magnitude further and it's beautiful... He got the medal Fields for this work. Take a look at this conference by him ua-cam.com/video/1eAmxgINXrE/v-deo.html if you loved Cantor, brace yourself for a mind big bang!
True story: I was a high school physics student and our course had progressed on to the general topic of electromagnetism... One morning our lecturer began with some basic principles of electromagnetic field theory, starting with, "OK, let's suppose we take a piece of super-conducting wire of infinite length..." I raised my hand. "Yes?" ... "Doc, if you had a piece of wire of infinite length and you cut it in half, what would you get?" ... "Get out..." In the subsequent detention period that is the only just outcome for being a smart-ass in class, we had a really excellent discussion about the principles and problems of infinity. Looking back, it's probably fair to say that the one hour of detention completely turned around my appreciation of physics, from something that I "took to complement the chemistry and math", turning it in to a field that still delights me, 40 years later. Thanks, infinity...
mathematician here 😁 wanted to point out, that the one-to-one (injective) mapping is not enough for countable infinity, the mapping must also be surjective (and thus bijective)
math teacher only want proofs that you did understand to do math they way he teached you not any other way of math so I guess you failded .So you can have twice his iQ and you still fails -since you could not repeat his teaching ok thats how it is
Are you trying to use oo as *the infinity symbol ∞* ? There are ways to type it, and you may be able to see the result of what I did, which was to go into the Character Map program in Windows and search for *infinity* (Note that you may have to select the right character set in order to find it. I found it in the DOS set for United States and in Unicode ∞∞.) My web browser is showing me both, but YMMV.
@@eljcd I also have a tiny file with interesting characters I find here and there, which I can then use as needed by copy-n-paste, such as this Character to Replace Colon in Filenames ։ (Armenian Full Stop) and this unicode character to put a sort of question mark into file names, the interrobang ‽
0:47 there are different types of infinity. The amount of natural numbers, 1,2,3 and so on is just the simplest type of infinity, called "countable infinity". And the natural numbers are in a very specific way equally infinite as other sets of numbers, because you can count these other sets using the natural numbers. Formally this means a set of numbers is similarly infinite as the natural numbers, if you have a one-to-one map from the natural numbers to that other set. If there is such a map, then the two sets are of the same type of infinity. For example, if you add the number zero to the natural numbers - so you get the set zero, one, two, three and so on - then you can map the natural numbers to this by just subtracting one 1:312:10 The real numbers, that contain all numbers with infinitely many digits after the point, is however not countably infinite. You could say it's even more infinity than the natural numbers. There are actually infinitely many types of infinity, but these two, those which correspond to the natural and real numbers, are the most commonly used ones. Now, that there are many different types of infinity is interesting, but more relevant for using infinity in practice is that most infinities are actually the same. AS a consequence of this, if you add one to infinity, the result is still the same infinity. And if you multiply infinity with two, you just get the same infinity again. If you divide one by infinity, you get a number with an absolute smaller than anything, so that's zero. 2:59 But you get the same 5:49 But is infinity real? Does it exist? Well, it arguably exists in the mathematical sense, in the sense that you can analyze its properties and talk about it as we just did. but in the scientific sense, infinity does not exist. That's because, as we discussed previously, scientifically we can only say that an element of a theory of nature "exists" if is necessary to describe observations. And since we cannot measure infinity, we do not actually need it to describe what we observe. In science, we can always replace infinity with a very large but finite number. We don't do this. But we could. 6:29 Here is an example
Infinity and zero bring in infinite assumptions into an equation. It's a delicate topic with science to point directly to the fact that we're making assumptions about things we don't really know other than it acts like this or that. But that's science right? My favorite quote, paraphrasing, in this clip is: mathematicians understand Infinity very well, you just have to be very careful to know where your Infinity comes from". Mysterious paradoxes. Infinity is everywhere as we calculate it out as practically as we can. Quanta certainly points to some lack of basic understandings. I particularly enjoy Sabina's tone like: look this is how it is. The beauty is that if you approach her explaining the math by not calculating out each equation but seeing how the equations go together it's easier to grasp larger concepts. She consicely points out how the math is derived. The math isn't gobblygook though. It's godlygood as translated in touchscreen slide keyboard and philosophically, to notice much deeper how everything/Infinity is. Okay sometimes it's like a refreshing stroll she pulls it off so well.
@Goran Vukovic If I'm understanding correctly, mathematics only _describes_ the universe, but does not _control_ its behavior (probably). As long as mathematics _continues_ to produce valid predictions about how various parts of the universe behave, it is deemed to be "correct" (or at least "correct enough"). If/when mathematics predicts one thing, and observable reality does a _different_ thing, then the mathematics (either the axioms or the formulas) are deemed "incorrect" and must be changed to fit. The side effect is that the universe _appears_ to follow mathematical laws - but only because the accepted "mathematical laws" have been iteratively customized to fit our observations about the universe. It might be more correct to say that mathematics imposes an artificial structure on how we observe and understand the universe, rather than on the universe itself.
@@HaloInverse Yes. You clearly stated it. However if we are not realist enough or at least a bit then we end up believing in guys like Sheldrake. So Maths might convey truths about the universe instead to be only a tool of the human mind in a dual reality or a glorified way to plot a curve fitting. www.sheldrake.org/reactions/tedx-whitechapel-the-banned-talk
Always go with intuition where the nature of your own existence is concerned...because that's where 'intuition' comes from.. People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. So, in terms of 'numbers', infinitude can only ever be 'one'.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
We have a potential ‘infinity of possibilities’ formed by spherical geometry. We have an infinite number of line symmetries within a sphere as long as it is expanding. In this theory, this represents an infinite number of time line for potential future possibilities. In the equation (E=ˠM˳C²)∞ the brackets represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. The spontaneous absorption and emission of light is continuously forming a probabilistic future by changing photon ∆E=hf potential energy into the kinetic Eₖ=½mv² energy of electrons.
One reason you should not write such equations, at 3:19, is that (obviously) if you divide a positive number by "positive infinity", the result is also a positive ... but zero is neither positive or negative, which is a contradiction. To avoid such contradictions, "Division By infinity" is defined to be a Limit, as if one were in a "never ending" process of dividing the numerator by a larger and larger denominator. Great fun. Zero is "the Limit" of that process if zero is the largest number that's never reached. And one could argue that's why zero must be neither positive or negative, and why -1 must be larger than -2. The definition of a "Limit" was generalized to handle more complicated formulas.
So the general question may be: “is an all powerful entity able to create something it can’t have powers upon?” That shows something all powerful doesn’t make sense.
I guess I'd call that an infinitely understandable clarification of infinities.
I think you will like this -> ua-cam.com/video/Uj3_KqkI9Zo/v-deo.html
So true 🤓
Teachers pet/ asss kisser
I come for the physics, but i stay for the dresses
Nice presentation, well beyond my math understanding. A question, maybe you can do a presentation on the coriolis effect. Does it affect the planets in orbit, how about star systems orbiting in galaxies? How about dimensions?
I find it easiest to think of infinity as a process rather than a number. Its a process that discribes a neverending chain of numbers or events or whatever you wanna plug into it. This works with how some infitities are "larger" than others.
I’m infinitely grateful for this video. Fin.
I have zero disagreements with this.
Great video. I recently noticed an example of infinity (or division by zero) arising in an everyday mathematical formula. When I am driving my car, the dashboard displays the current fuel efficiency that the car is getting in litres per 100 km. It shows it as a bar that gets longer or shorter as the car consumes more fuel or less fuel per unit distance. When I bring the car to a stop (to stop at a traffic light, for example), the bar becomes as long as the display will allow, and then suddenly disappears. This is just how the indicator handles the division by zero issue, since when your car is stopped but the engine is still running, it is consuming fuel but not travelling any distance, and therefore has a momentary fuel efficiency of "infinity" litres per 100 km.
That's one instance where "km per liter" would be a better metric, since it would just be "0" in that case.
I'd say its simply an invalid measure, it doesn't make sense to measure X to Y when Y doesn't exist.
@@daarom3472 it's not that simple, as pointed out above the inverse relation exists and is well defined therefore both relations must exist.
@@tinkeringtim7999 how much milk do you have if you have 0 liters of milk? How fast do you go when you go 0 km/hour? When the value reaches 0, the property stops existing other than that we can talk about it.
@@daarom3472 If you are using existence in a colloquial sense, please explain in what sense.
If you mean existence as in predicate logic, I can't see a way to express that consistently so perhaps write what you mean by that in a concrete unambiguous way.
I suspect you will struggle to, because the whole point is these things are incredibly difficult (maybe impossible) to pin down from the perspective of numbers. We've been trying to figure it out since Euler looked at the primes through sequences and polynomials.
If it's just simple and self evident in your view, then all you're telling me is you don't actually know what is going on when one litre of milk is "added" to another and the result shown to be consistent with our counting system.
In other words, if you think you know what numbers mean/do and you haven't studied number theory from the perspectives algebra/topology/analysis then you have only proved you can fool yourself.
I don't see how anyone who has studied even one of those perspectives to a significant degree of apprehension could've entertained such a facile thought for long enough to type it but I'm open to the idea it's possible.
Aleph-null bottles of beer on the wall
Aleph-null bottles of beer
Take one down
Pass it around
Aleph-null bottles of beer on the wall
Great song for when that car trip takes forever.
@@frechjo Well it certainly beats "Are we there yet? Are we there yet? Are we there yet? ....." :)
thats how you catch the covid
The first beer goes to Mr. Hilbert.
Nope, Aleph broke because of Zeta!
4:41 I think there’s a correction necessary. Shouldn’t x tend to infinity? Something like this:
lim
x → ∞
I noticed that too, thanks for pointing it out!
Yes, lim x → ∞ makes sense and Sabine says ∞ at 4:42.
Yes, sorry. I have put a note on this in the information below the video. Thanks for being so observant!
@@SabineHossenfelder limit_{x -> \infty} x^2/e^x: the limit OF ex squared over ee to the ex squared AS ex approaches infinity
The limit as written is still equal to 0).
No one else explains these concepts so clearly like you do
Me: *about to type "Technically, you would need a limit for those divisions to be true."*
Dr. Hossenfelder: "I hope there are no Mathematicians watching..."
Me: :)
to be fair there surely are some algebraic definitions where that would make sense haha
@@yyeeeyyyey8802 the thing you are looking for is called a wheel
I got a laugh at that too
Nonstandard analysis in my opinion is superior to Cauchy's limit idea. It allows you to do this arithmetic with the transfinite and infinitesimal.
@@shoopinc once you get the ball rolling with non standard analysis, it can be extremely intuitive, however, to make it rigorous requires a ton of heavy machinery to be developed. Whereas using the standard real numbers, a close to fully rigorous treatment can be done in first year.
If you've ever waited at the DMV here in the states, you know infinity is real.
Especially when you are trying to register your new infinity. Those infinities are different types though.
The fact that you can report on it means it wasn't infinite. It's over.
I swear I would've said similar, upon being a disabled person and waiting on the
g-d damned government to getting around the agree to the obvious while you're sitting in homeless shelter waiting on subsidized housing shoulder to shoulder with convicted murderers that are completely oblivious to the idea that upon finding out their names that you can check their criminal convictions on a damn smartphone. The DMV? Yeah. Even just renewing a state ID; time slows down and yet somehow you age faster!
When you get a number and they skip your number and you have to get a new number but they say you just didn't hear your number. No lady you all skipped like 10 numbers.
Not just in the States. Vehicle registration and driving licences work the same way in Australia too. And don't even start on social security.
That really blows my mind away, what a masterpiece of didactics! Sabine is the absolutely best teacher, I've ever met. Read a whole book (by John Barrow) about this, but didn't understand half of what she explains in ten minutes. I'm so thankful for this
Thank you for a useful discussion of infinity. I have been tangled up in this for a while, and this clear summary of the mathematical and scientific interpretations was just what I needed to get past my current block! I am really enjoying your channel.
Same
There's another infinity - Sabine's variety of cool clothes
The perfect gay comment...
Also, her nail polish matches her outfit. An even more perfect gay comment.
She's likely using a clothes rental biz. That seems like a smart move for anyone
@@DheerajBhaskar Ha-ha-ha, this happens when I think there´s nothing gayest than what we already had...
Well I opened a comment (see the last), just for gay comments.
But this dress does not look to be topologically impossible, unlike some others we have seen...
Thanks Sabine, you made me see the difference between mathematical reality and physical reality. 🙏🏻
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
> the difference between mathematical reality and physical reality
That is between concepts and objects
@@alexleibovici4834 Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations about "something" and talk about it....
@@YT8699
> Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations
No. There are objects out there and the concepts are the representations in our brains of those objects out there.
@@alexleibovici4834 I am also a realist who believes in the existence of stuff out there. However, our entire knowledge or understanding of any particular "object" is contained within our "concept", and it appears that our attempts to form coherent concepts from our observations of objects almost always involves the use of "mathematical realities". If fact our attempts to "prove" (another loaded word...) that any particular object actually exists also depends upon the usage of these mathematical realities.
So when the distinction between "mathematical realities" and "physical realities" (or objects and concepts) is reduced to the notion that only "physical realities" exist....then we're faced with admitting that our knowledge of that which "exists" is dependent upon that which "does not exist".
Of course, some consistent naturalists identify "concepts" as nothing more than a particular set of chemical reactions among the organized elements of the human brain. Thus making concepts into objects...
@4:42: There is a mistake in the formulat. Under the limit the formula should have x->∞, not x->0.
As usual, I don't really understand, but my lack of understanding is less infinite than it was before. Thank You.
@Goran Vukovic Oh no, the aleph number of Grok Effer's lack of understanding decreased.
What Grok Effer said!
Well, if she/he took away 1, it may still be infinte, but less so. Because, 1 still was removed.
@@Aurinkohirvi nope
@Goran Vukovic but but but, was it the story of Socrates or Aristotle that he's the most smart person?
He heard people were saying he's the smartest person in the city. So he thought he'd go out to see if that's true. He went out and ask many smart people questions after questions. At first they answered the questions but then in end they ran out of answers. At the end of the day he had found out nobody really didn't know. But he already knew that that he didn't know. And everybody thinks they knew when they didn't know but he knew he didn't know. That means he said he is the most smart person in the city. Then was he wrong?
“Is it just something that we get when we divide something by zero”
Careful there, thats fighting talk.
Thank you Sabine, i’m gonna sound like a broken record but all,you vids are great and much appreciated. 😍
Thanks, I appreciate the feedback. Keeps me going :)
@@SabineHossenfelder Hello Sabine , From All your knowledge and intelligent, What are you Stand for Atheism or God's follower.... ????????
Well, this went south quickly..
@@bmoneybby well it sure did 😂
@@Honestandtruth007 From her scientific presentations, and body language. She is likely agnostic.
I am at the end of my physics bachelor (actually I'm doing QFT now, so that was a fun shout out), and there was a lot of new stuff for me in this video. I'm surprised by the amount of material you managed to get in her, because I would think it is also possible to grasp most of what you say with much less of a mathematical background. You inspire me as an educator!
Just wondering, since some physicists want to practice physics without using infinities, would this mean that Pi and e would no longer be usable?
@@daarom3472 No, because pi and e are not infinite in magnitude. Pi is less than 4 but more than 3, that's not infinite. It just has infinite digits in it's decimal representation
So do other numbers depending on how you represent them by the way. 1/3 is 0.33333... on and on forever when represented in it's base 10 decimal form for example. Pi just doesn't have a nice pattern like that, it's irrational
Serendipity. I was just thinking, a month or two ago, that mathematicians should not be using infinity because it's not real, it's not understandable, and makes for possible misunderstandings in the calculations. Now I see this. Did the universe give me you because it thought I was ready? I have not studied maths or physics, but I think about these things. I thought I was really smart. You guys have already worked all this out. Well, I'm glad to have found you, at last. Too late, but I can die in some peace!! Thanks again! 🙂
Your voice is very enjoyable!
I did economics at uni, no infinity there, everything is scarce!
Hyperinflation on the other hand... :P
lol
I'm a Democrat and a Socialist. We don't let the laws of economics get in the way of progress and doing what's right for the common good of society. I'm just sayin'
@@GregoryTheGr8ster - the "common good" - used to excuse infinite human suffering throughout the ages.
@@GregoryTheGr8ster A Democrat and a Socialist? Sorry Greg, they're mutually exclusive
The videos on this channel consistently progress from stuff I know comfortably to stuff I *don't* know, usually at about the 75% mark. It's a rare and wonderful thing. Thank you.
Thank you for adding much clarity to this topic!
Her first “examples” definitely raised my eyebrows but when she hit her groove the
examples turned out to be “bait” for the grand finale. Her completely approachable explanation of the epistemological difference between physics and mathematics is just brilliant. Entire college courses don’t do any better.
Ok, I stopped watching and I as was about to call bullshit and leave, now I have to watch that part.
Unfortunately not. More bullshit. Physics with infinity are just mathematical abstractions to try to approximate the observable. There are theories to state even time in not infinite divisible. At this time, there is no concluding evidence that infinite is real. It sure exists in math, in our minds, but not in the observable universe.
@@miguelandrade5964
Actually ?
Do NOT exist, in math !
Must use them, to express them !
Each, is an "infinite Limit" !
X^Infiity = Infinity
1/X as X aproaches infinity,
aproached 00 !
00 +/- Any/Every possible number,
is NOT 00 !
IF can add any number to Infinity:
then previous number
IS NOT Infinity !
@@miguelandrade5964
Our minds,
can understand the concept of always.
Our minds, can not understand
what is an Infinite amount.
(One of definitions, of infinity)
@@dirktween244 In math (and in our minds), for something to exist all it needs is to be defined. If you like math a little, you maybe want to search some stuff from Cantor. It's fascinating and a bit funny.
Best and most straightforward explanation I have ever heard. Made me see it clearly the first time.
A typo. At 4:44 there should be lim_{x->+inf}, not lim_{x->0}
You are right, of course. Sorry about that.
The physicist would say infinity is roughly zero anyways
It doesn't matter! It is zero any way.
@@SabineHossenfelder You might want to make this go to the top so everyone sees it.
Ah a new Sabine video, just what I needed. THANK YOU!
One of the most valuable educative and well-made videos in the whole UA-cam and maybe to infinity and beyond... 👌
It would take me an infinite amount of time to fully grasp your explanations, but I am finitely better informed by each of them. Thank you!
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
@@fluentpiffle I was using those metaphorically.
Thanks Sabine, that was immeasurably informative.
3:10: "I hope there are no mathematicians watching this"
Me: Too late muahahaha
Awesome video, thank you Sabine. I just report a little typo at 4:41 with the limit.
Thanks, you are right. Sorry for the blunder!
How could you pay attention to that and notice it, while Sabine was on the screen?
Nonsense. It was completely correct. Sabine was leaving it as an exercise to the viewer to determine what the limit would be if x tended to infinity!
Pure magnificent pedagogy!
No no no. It is right in both senses! Zero or infinite. Sabine never mistakes! LoL
I love your videos because you explain things and I immediately have questions but then, like you're reading my mind, the question gets answered.
I really enjoy your videos.. you explain models and theory's in a way I can follow..your videos give me food for thought..thank you Sabine.
I am mathematician and I enjoyed watching this video. In optimization we consider extended valued functions and make up such rules for playing with the infinite.
Glad I didn't commit any major blunder! It's been a while since my math classes.
Just take your right frame.
Infinity is a Platonic or mathematical concept!
Platonic forms are dual to to particulates -- Plato.
Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant.
Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein.
Synthetic a priori knowledge == space/time -- Immanuel Kant.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality.
The future is dual to the past, we remember the past and predict the future -- Time duality.
My absolute time is your relative time and your absolute time is my relative time -- Time duality.
Length, distance or space is defined by two dual points -- space duality.
Absolute space is dual to relative space -- space duality.
Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality.
Space duality is dual to time duality.
"Always two there are" -- Yoda.
@TheAbstraction The big bang is a Janus point (two faces) = duality!
The future is dual to the past -- time duality.
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Apples fall to the ground because they are conserving duality.
Potential energy is dual to kinetic energy.
The force of gravity is scientific or empirical proof of duality!
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
"Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon..
Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science."
spaceandmotion
Really concise summation of the gap between mathematics and phenomenology. You cannot measure infinity because its value will always be greater by at least one unit than what you have measured.
I appreciate your commitment to the proper use of mathematics in physics. Can you make a video, about some examples of improper use of mathematics in mainstream science?
Can you next time talk about complex numbers and it's physical meaning, please..
Thanks for the suggestion, I will keep this in mind!
Personally, i see complex numbers as 2 dimensional numbers, so they are useful to describe or model things that need 2 dimensions instead of one.
@@SeanPeckham-xe2gt Yes this also reminds me that I used to call complex numbers "circular numbers", I don't know where this "complex" or "imaginary" comes from but this is really sad. A bit like Pi which should have been 2Pi (the ratio circumference/radius instead of circumference/diameter), That's what the Tau Initiative is about. If you replace Pi by Tau in equations, everything becomes way more intuitive. With Tau, the Euler's identity is even more interesting because instead of tracing a half circle and landing on -1 you make a full circle and come back to 1... tauday.com/tau-manifesto#sec-euler_s_identity
Unfortunately I didn't get a proper education in maths so I'm in the process of relearning the base concepts such as the one you described: turn concepts into a physical representation involving the senses (visual, kinesthetic, etc...) and develop an intuitive "feel" instead of applying rules and hoping for the best... This is the kind of thing that you either develop by chance when you are a child and then you become "good at math" or that you don't and then, since school doesn't teach you how to conceptualize and create mental models, you become stuck with the wrong/impractical models in your brain until you decide to take the mater into your own hands... With that in mind I'd be interested if you could share your mental model of the natural logarithm or exponentiation!
@@2072 a proper education in maths
ok nigel
Very good discussion of that may be seen here: ua-cam.com/video/T647CGsuOVU/v-deo.html
(Disclaimer, I have no association with Welch Labs, the producer of the video.)
Totally agree with this. When I was an undergraduate physics student, I always felt that assumptions were being made whenever I saw a limit as a variable tended to infinity or 0 - fine as an approximation, but it shouldn't be taken as a final model.
There are always assumptions and there is no such thing as a final model
Sabine explains difficult concepts with such ease :)
"If you can't explain it simply, you don't understand it well enough" - A.E.
@@v3le Einstein never said it btw
@@vikraal6974 from the memes
It must be R.F.!
I too love, Dr. Sabine, though I counter some of her videos (the flaw is always on assumptions).
I hope there'll be a debunking between nuclear physicist Thunderfoot (is that the same as particle physicist?) and theoretical physicist Dr. Sabine, not coz' of dislike but because the exchange between minds who are experts in their fields, is an inspiration and a great example for everybody.
God bless, Revelation 21:4
At 4:50 it should be the lim as x goes to infinity. This was a nice explanation of dealing with infinity
Noticed that too.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
"Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon..
Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science."
spaceandmotion
As a published PhD Mathematician, physicists (both theoretical AND the experimentalist ones who criticize theorists) annoy me.
We mathematicians have no problem amongst ourselves. Conflicts between different subsets of physicists do not concern us mathematicians. We are quite a happy open-minded bunch.
Great video! I always nitpick whenever people talk about black holes and singularities and their infinite densities; I just could never believe in Infinities in nature. I submitted a question about this to some subreddit, and someone wisely replied to me that they agreed that the densities of the singularities at the hearts of black holes were not infinite... they were just COLOSSAL.
Yes e.g. while reading Hawking I've been thinking the same thing, & he never seems to mention the issue. This is the first time I've seen it mentioned at all (much like the bogus characterizations of fusion achievements).
But she didn't say they don't exist in nature. She said they don't exist in science.
@@purpleglitter9596
.
"Do not exist in science" means [omit 3/11: "not known to exist", ie.] "not known to exist in nature".
.
Imo, strictly speaking, infinity doesn't exist in math either.
@@red-baitingswine8816 Science is not nature. Its an attempt to explain nature. But nature is nature. Otherwise why would she need to specify that it doesn't exist in science if she meant nature. Infinity does exist in math. Mathematics is pattern identification. Infinity is a pattern. If it didn't exist in mathematics they wouldn't have to keep finding ways to avoid it.
@@purpleglitter9596
.
Straw man I didn't say science is nature.
.
(but please see my revision of my previous comment)
How she blitzed in the ad was definitely infinitely German. 😂 God, I love her videos. Please don't ever stop. 😊
Sabine, I love your talk. Post-science, which I founded, believes that we live in the infinite future because our universe has an infinite future.
I recently learned some of the Haskell programming language... it is a language deeply concerned with repeating processes and "types"... the idea that Infinity is a 'type' and not a value just makes so much sense to me right now. Thankyou for the awesome video :)
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
"In science, we can always replace infinity with a very large number, we don't do this, but we could." -- We do it all the time in numerical simulations, by replacing the infinite dt's in any integral with a large number of delta t's.
Why is it that Ms. Hossenfelder is the only UA-camr that forms her words so perfectly that I never miss one? The slight German accent doesn't hurt, it may even help. Subscribed!
It's because they speak like they learned from the book. No slang, no dialect.
My first spanish teacher was German. She almost never talked german to us, but we understood everything. Years later, when I wasn't a beginner any more I had a teacher from Bolivia. We just didn't understand a word, so he tried to explain in German. We still didn't understand anything.
The laser dot explanation blew my cats tiny mind 😻💥 Thank you
Yes, but in that explanation we forgot the finite speed of light, so it can't move infinitely fast.
For that in reality infinity in the real world is not infinite. 😁
0:04 Instantly upsets all the mathematicians.
I'm an engineer, so I don't mind XD
Yep, we do this all the time, no big deal 😂
@Shadman Shahriar: You should talk to Sheldon Cooper (Tv series "The Big Bang" NBC if I'm not mistaken).
Infinity is untestable and unobservable ergo its not scientific.
@@theobolt250 Sheldon despites experimental physicists, so i wouldn't start a debate with him xD
I'll gladly take that infinity, divide 3V by it, call the result -90dBm and point thermal camera at a colleague who just entered the room.
u know ure a genius when u explain highly complex subjects without animation, just speech without any flashy video editing and effects. ure a genius and i love ur videos u are a scientist and a writer sabine
I was going crazy before she mentioned the technicality at 3:16 ...😅 Thanks . Great video 👏
I love how whenever there is a conversation about an expression of 0 becoming solution everyone freaks out because they think somewhere in the world they’ve just given a mathematician a aneurysm lol
I did cringe a little
The ideas of infinity and an end came into my head when I was 8 years old and lying in my bed going to sleep. In the form of trying to imagine it in space, not in the form of mathematical equations. It was so unimaginable that I finally started crying. It just blew my mind. So here I am over 50 years later thinking maybe I will be able to get 2 hours sleep and this pops- up. Great.
Had a similar experience. I ended up puking because it was just overwhelming.
@@mathfincoding It really is. How anyone can accept ' the soup' as an ultimate answer to origins is beyond me. Or that mathematical equations are equivalent to comprehending eternity, an end, or nothingness.
Wait, we do know Chuck Norris counted to infinity. Twice.
While doing so he discovered
- the last digit of Pi.
- that e is periodic.
- a numerical value for i .
Excellent Programme
infinity is like a shorthand for "as big as you want".
Like saying something equals infinity is just saying that it keeps going, like you'll never run out no matter what you do, unless you use the infinity to destroy the infinity.
And putting infinity inside an expression is like saying you're interested in what happens as you keep going, and if things ever stop happening, or if they all would hypothetically cancel out.
so saying infinity+1=infinity for example is just saying something like, "if I will never run out of apples, and you give me an apple, I will never run out of apples" or "if I started counting my apples I would not be able to finish (this is not the same as uncountable infinity), and if you gave me another one, I still wouldn't be able to finish counting them"
2*infinity = infinity is like "I'm never gonna run out of apples, and you're never gonna run out of apples, and if you gave me your apples I would still never run out of apples"
infinity^2/2^infinity = 0 means like if my friends start cloning themselves, and I buy square grid of apples each time all my friends (including their clones, and their clones' clones, etc.) have had a turn in the cloning machine with a side length equal to the number of times they've been cloned, and split them between everyone, as time goes on each person will get less and less, and in fact if you pick a really tiny (positive) number, at some point each friend/clone will get less than that amount
ok that actually probably made it sound more complicated than it is, so dropping the apple analogy, if you start squaring really big numbers, and raising 2 to the same really big numbers, the numbers in the second group will be many times bigger, and in fact, with a big enough number, bigger by an amount bigger than any (finite) amount you want.
the last bit of that is sort of the crucial part. Because things that approach 0.0001 or a gazillion without going any smaller/bigger respectively exist, which are in many ways similar to being 0 or infinity, but are crucially distinct. Like you can count a gazillion apples, and see that it is distinct from having a gazillion and one apples.
"There are infinitely many types of infinity" - Terrific. Are there countably infinitely many types or are there even more infinitely many types of infinity?
look at wikipedia: Cardinal number, large Cardinal number, huge Cardinal number, List of large cardinal properties
Other infinity concept is : Surreal number also kown as Convay numbers.
an other concept is: Hyperreal number.
Adding one point to a space to make the space kompakt is called Alexandroff extension .Example for Alexandroff extension is adding infinity to the the complex numbers equals a sphere.
All thess can be done in Settheory called ZFC, ZFC is defined by using FOL (first order Language). Every Theory in FOL has a countable Model. Looking from outside we have only countable many set, but looking from inside we see uncountable sets. This is not a contradiction, because the map which makes a set countable is not a Member of the Model.
According to the continuum hypothesis, the answer is either yes or no.
infinte types of infinity
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
"Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon..
Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science."
spaceandmotion
I Always waiting for your new ones ..
Thank you for your videos, Sabine. I would like to hear your opinion of the mass equation of special relativity. I assume that the singularity at the speed of light indicates that the Special Theory of Relativity is incomplete in the same way that the singularity at the centre of a black hole indicates that the General Theory is incomplete. What does the Standard Model of particle physics have to say about this?
In other words, in the realm of measurable, "arbitrarily large" is not the same as "infinite". Fair enough.
Also true in philosophy: potential infinities vs actual infinities.
In math we can say that up to roughly the 20th century we were only dealing with potential infinities, while later we got tools to deal with actual infinities (set theory etc).
Infinity also is a strange thing in logic like omega inconsistent theories and also the Skolem's paradox.
In particular, the different sizes of infinities is a finicky thing: the relation between the size of sets heavily depends on the axiomatic theory you consider. Personally, it makes me think that infinite sets are not a thing that actually have properties like a size, but some abstract construct to which we assign a concept of size that depends on the theory. The relation between these sets actually tell more about the expressive power of the theory than about the sets themselves.
And just a last thing to really insist that in mathematics infinity isn't an obvious thing, in the ZF set theory, the existence of infinite set is an axiom. If we remove ot from the theory we can't prove they exist 🙃
In most practical areas, "infinity" is "take some arbitrarily large number" followed by "define this number as infinite". This also includes floating point math on computers, where, say, with 'double' the 'infinite' value is essentially 2^1024 (with some special case handling to make the math identities hold; zero is another such special case, otherwise it would have been 2^-1023).
@@BGBTech The IEEE/IEC floating-point formats do allow for denormalized values, signed zero, etc. However, there is a fundamental difference between asymptotic (limit) values and true infinitesimal type. A problem with a brief presentation like this one is that a lot of important information gets omitted, leaving the audience with misconceptions. For example, about five years ago the Numberphile UA-cam channel posted a couple of "astounding results" that resulted from not explaining precisely the importance of absolute convergence, and hence produced such errors as the claim that the sum of all natural numbers equals -1/12. The "controversy" caused by that has continued ever since (and I suggest it not be allowed to infect this channel).
@@douggwyn9656 As can be noted, they exist, and are handled specially by the hardware, but exist as definitions and special-case rules applied to the largest and smallest exponents, as opposed to some entirely different type of entity.
@HenryDavidT Yep. Can also note that "in practice" says little about either theory or physical reality, but rather "things done in the name of making it work". I have also seen enough code with things like:
# define INT_INFINITY 1999999999
presumably because it is easier to type than 2147483647 or similar...
Meanwhile, Windows Calculator seems to be able to go up to 10^9999 for whatever reason (this is outside the range of the usual IEEE formats), ...
In my student days, some 50 years ago, we learnt that mathematical constructs could be equally proven with or without the assumption of infinity. Has this now moved on?
Do you mean some form of mathematical finitism?
Go get some Kurt Gödel from your library, mathematics itself is either unprovable or incomplete.
@@onecowstampede9140 or is not the right frame.
Wow, was that statement ever standard?
Infinity is a Platonic or mathematical concept!
Platonic forms are dual to to particulates -- Plato.
Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant.
Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein.
Synthetic a priori knowledge == space/time -- Immanuel Kant.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality.
The future is dual to the past, we remember the past and predict the future -- Time duality.
My absolute time is your relative time and your absolute time is my relative time -- Time duality.
Length, distance or space is defined by two dual points -- space duality.
Absolute space is dual to relative space -- space duality.
Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality.
Space duality is dual to time duality.
"Always two there are" -- Yoda.
Fascinating stuff Sabine! The conclusion I come to is that no matter how large the magnitude of a number that we can compute, there must logically always remain an infinity of numbers of greater magnitude which are un-computable. The set of un-computable numbers is necessarily infinitely larger than the set of computable numbers.
Further to this - A perfect circle is infinitely round, however no examples of perfect circles exist in the universe. One of the roundest object available - a neutron star is close but not perfectly round. Perfect circles only exist in the human imagination. So computing numbers with idealized functions such as pi and infinity does not reflect the universe as it actually is.
3:10 Thanks for this. The math side of my brain was getting a bit squeamish a few seconds earlier.
I hope you do a video on normalization of infinities in physics as a followup.
Thanks for clarifying the distinction between the existence of infinity in the mathematical and scientific sense! It helped me understand the concept of "infinity" better.
I waited soooooo hard for a Video which has infinty as topic in this "direction" thank you Mrs Hossenfelder great inspiration.🙏
Hey, buddy, you call her DOCTOR Hossenfelder!
(see: "hey lady you call him DOCTOR Jones +Temple of Doom" to see humor)
I've often thought that renomalization, while it works, means that physicists don't understand how quantum mechanics works at all
Infinity is a Platonic or mathematical concept!
Platonic forms are dual to to particulates -- Plato.
Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant.
Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein.
Synthetic a priori knowledge == space/time -- Immanuel Kant.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality.
The future is dual to the past, we remember the past and predict the future -- Time duality.
My absolute time is your relative time and your absolute time is my relative time -- Time duality.
Length, distance or space is defined by two dual points -- space duality.
Absolute space is dual to relative space -- space duality.
Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality.
Space duality is dual to time duality.
"Always two there are" -- Yoda.
But at least they admit they don't. However, for now: it works.
I absolutely trust what you tell me. I can’t think of any other channel that I do that for
Another great video, Sabine. That is a very nice outfit you are wearing today!
Chuck Norris counted to infinity, twice.
He didn’t though, did he?
He also started the sun.
@@markthebldr6834 And he‘s also going to stop and finish the 🌞.
A very nice presentation. It reminds of my first calculus class given by a Bell Labs instructor at a remote University of Hawaii location. His introduction paraphased: .." the most difficult concepts to grasp are the terms infinity and infinitesimal. His explanation of infinity was similar to yours. His explanation of iinfinitesimal, was; you can describe you walking towards a point, dividing the distance in half continually. The infinitesimal is that moment you cross that point." Probably, as you explained zero and may be has a real meaning in the universe. It's amazing how infinity applies to mathematics, but not anything real in the universe. Or perhaps the universe is infinite, but I even find that difficult to believe. If it's an everlasting expanding and contracting universe, I contend the universe is finite of particles/energy. If it's infinte in particles/energy, who knows what to think. In either case, we will only be able to explain those two terms mathematically. Thanks so much for the details in your presentation.
I sometimes think myself unfortunate for not being proficient in math. I mostly think myself lucky for the same reason.
Just started watching. Really hope this mentions Brouwer's Free Choice Sequences, albeit I fear-despite Sabine's brilliance-it won't. Edit: Yeah, it doesn't. Sad. Missed opportunity. Doubly so since it's THE avenue for formulating physics 'without' 'infinity'.
I remember having seen an interview where she was asked about non-classical logics and her reaction was that she was aware of quantum logic but she didn't seem to tie it to Heytings intuitionistic logic, let alone intuitionism. Despite this, much of this video concerns a Cauchy-like approach to infinity. Indeed, here in this video she tends to zoom in on extension of arithmetic by infinite object, while much of the controversies regarding foundations with infinities concern more general objects. To your final outlook, I think with the rise of type theory, a more computable perspective on math in the future is inevitable at that point.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
"Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon..
Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science."
spaceandmotion
What great topic ! Thanks Sabine. The standard cosmological model includes a spatially infinite universe, and it seems to attract little attention how strange indeed it would be! I've only found an obscure paper by Ellis. Thanks also for mentioning others in physics are concerned by this or related issues. It's a shame you didn't mention Hilbert's Hotel. That really drove the point home for me and carries the weight of a great mathematician.
You're swaying between two sides here. On the one hand you take the position that infinities in math are a most useful tool and ostensibly "easy to work with", but then you also warn that too strong of an axiom set might spoil possibility for interesting models. And indeed, you might fall for a trap if you recite insights derived in very strong axiom sets. Not all the fuss about infinite sets is merely the discussion of Cauchy sequences in fields like R or smaller ones, or the extension of its arithmetic by single elements that are "infinitely big" with respect to the total order of R. You blend these notions with cardinality claims known from ZF and it's also worth noting that this video doesn't discuss use of uncountable ordinals and transfinite induction much. I suppose your use for infinity ends somewhere around |(R->R)->(R->R)|, which is of cardinal size of a set given by a finite number of applications of the power set operation on N. I.e. it's tiny from a set theorist perspective. As a side note, if you do not adopt the Law of Excluded Middle and the Powerset axiom, then it's consistent that there is a subset S of N, such that there is a surjection from S to N^N, the uncountable set of functions from N to N. The issue here is that Excluded Middle blends the notions of subcountable with the potentially non-effective classical notion of countability. So claims of assumed necessity will be relativize once you take a step back and throw our some unneeded axioms.
Did not notice on time your comment!
The problem is that nature appears more like a enormous but finite set made of Plank units, rather than a transfinite number.
@@myt-mat-mil-mit-met-com-trol Don't hurry :)
Good name, btw.
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
"Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon..
Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science."
spaceandmotion
I'll need to watch this again... After more coffee.
Idd sugest some canabis
I never watched any of Sabine’s videos one time
I binge watch your videos because I love your demeanor. You are so cool!
Her explanations always trigger me and make me think she's wrong, then I slowly catch up to where I kind of sort of follow what she's saying and I realize I have looked at it wrong my whole life.
I love the fact she respects her audience's intelligence enough to really did
dig in to some of the more technical side of physics and math.
She's a paradox because many of her arguments are based on assumptions but her conclusions always seem correct.
I didn't follow this, but I'm happy to take her word for it... :)
just got to take a shot come on see it more times.
If you want to dig a little deeper, you could look into the work of Georg Cantor. He was a 19th century mathematician who was the first to prove that the real numbers were a different kind of infinite than the integers. He came up with what is called the diagonalization method to show this. I didn't appreciate its rigor the first time I encountered it, so I encourage people to take the time to work through it.
@@josiahslack8720 and if you want to go even deeper than Cantor without getting mad then you should take a look at John Conway's Surreal Number which goes an order of magnitude further and it's beautiful... He got the medal Fields for this work. Take a look at this conference by him ua-cam.com/video/1eAmxgINXrE/v-deo.html if you loved Cantor, brace yourself for a mind big bang!
this has got to be the most stop, think about it and play channel i have ever seen so far :)
True story: I was a high school physics student and our course had progressed on to the general topic of electromagnetism... One morning our lecturer began with some basic principles of electromagnetic field theory, starting with, "OK, let's suppose we take a piece of super-conducting wire of infinite length..." I raised my hand. "Yes?" ...
"Doc, if you had a piece of wire of infinite length and you cut it in half, what would you get?" ...
"Get out..."
In the subsequent detention period that is the only just outcome for being a smart-ass in class, we had a really excellent discussion about the principles and problems of infinity. Looking back, it's probably fair to say that the one hour of detention completely turned around my appreciation of physics, from something that I "took to complement the chemistry and math", turning it in to a field that still delights me, 40 years later. Thanks, infinity...
mathematician here 😁 wanted to point out, that the one-to-one (injective) mapping is not enough for countable infinity, the mapping must also be surjective (and thus bijective)
6:09 'Scientifically, we can only say that an element of a theory exists if it is necessary to describe observation'. I like that idea
Machian myopia.
@@alfredttarski4521 Maybe. Or Occam's Razor
@@beatricechauvel8237 Which of its almost infinite number of versions?
Yes! Because Chuck Norris has counted to infinity .... TWICE!
The second time was to count backwards from infinity. And he finished in time for dinner!
@@anotherdamn6c Nope, he got beaten by Mr. Rodgers... www.newgrounds.com/search/summary?suitabilities=etm&terms=The%20Ultimate%20Showdown
"oo is not a number".
I suppose that explains all the zeros in my Math tests!
Another thing you never get explained in school! Thank you!
math teacher only want proofs that you did understand to do math they way he teached you not any other way of math so I guess you failded .So you can have twice his iQ and you still fails -since you could not repeat his teaching ok thats how it is
Are you trying to use oo as *the infinity symbol ∞* ? There are ways to type it, and you may be able to see the result of what I did, which was to go into the Character Map program in Windows and search for *infinity* (Note that you may have to select the right character set in order to find it. I found it in the DOS set for United States and in Unicode ∞∞.) My web browser is showing me both, but YMMV.
@@YodaWhat Thank you for the tip!
Alas, I am using an Android device with google keyboard and his demented autocorrecten...
@@eljcd I also have a tiny file with interesting characters I find here and there, which I can then use as needed by copy-n-paste, such as this Character to Replace Colon in Filenames ։ (Armenian Full Stop) and this unicode character to put a sort of question mark into file names, the interrobang ‽
Finally, a good explanation of the distinction between infinity as a concept mathematically (all it is) and it's non-existence in reality.
Thank the GODDESSES for Saint Sabine.
Absolutely, the moment that I first beheld Sabine I finally understood the meaning of love at first sight.
If infinity isn't real, then calculus isn't real
You're right. It ain't
@@thibaudhope2856 It is 😅
And because calculus is not real, you are not 😂
0:47 there are different types of infinity. The amount of natural numbers, 1,2,3 and so on is just the simplest type of infinity, called "countable infinity". And the natural numbers are in a very specific way equally infinite as other sets of numbers, because you can count these other sets using the natural numbers. Formally this means a set of numbers is similarly infinite as the natural numbers, if you have a one-to-one map from the natural numbers to that other set. If there is such a map, then the two sets are of the same type of infinity. For example, if you add the number zero to the natural numbers - so you get the set zero, one, two, three and so on - then you can map the natural numbers to this by just subtracting one 1:31 2:10 The real numbers, that contain all numbers with infinitely many digits after the point, is however not countably infinite. You could say it's even more infinity than the natural numbers. There are actually infinitely many types of infinity, but these two, those which correspond to the natural and real numbers, are the most commonly used ones. Now, that there are many different types of infinity is interesting, but more relevant for using infinity in practice is that most infinities are actually the same. AS a consequence of this, if you add one to infinity, the result is still the same infinity. And if you multiply infinity with two, you just get the same infinity again. If you divide one by infinity, you get a number with an absolute smaller than anything, so that's zero. 2:59 But you get the same 5:49 But is infinity real? Does it exist? Well, it arguably exists in the mathematical sense, in the sense that you can analyze its properties and talk about it as we just did. but in the scientific sense, infinity does not exist. That's because, as we discussed previously, scientifically we can only say that an element of a theory of nature "exists" if is necessary to describe observations. And since we cannot measure infinity, we do not actually need it to describe what we observe. In science, we can always replace infinity with a very large but finite number. We don't do this. But we could. 6:29 Here is an example
I've been saying that forever.
so you mean, for a infinite amount of time ?
Well, Naturally...
I'm sure zero people listened to you
Q: So if you have been saying that forever and zero people listened, does that mean your impact is undefined?!
@@ypey1 It's irrational and uncountable
Sabine, I used to think I was smart and now I definitely know that I am not. Sincerely, thank you for that.
Infinity and zero bring in infinite assumptions into an equation. It's a delicate topic with science to point directly to the fact that we're making assumptions about things we don't really know other than it acts like this or that. But that's science right?
My favorite quote, paraphrasing, in this clip is: mathematicians understand Infinity very well, you just have to be very careful to know where your Infinity comes from".
Mysterious paradoxes. Infinity is everywhere as we calculate it out as practically as we can. Quanta certainly points to some lack of basic understandings.
I particularly enjoy Sabina's tone like: look this is how it is. The beauty is that if you approach her explaining the math by not calculating out each equation but seeing how the equations go together it's easier to grasp larger concepts. She consicely points out how the math is derived. The math isn't gobblygook though. It's godlygood as translated in touchscreen slide keyboard and philosophically, to notice much deeper how everything/Infinity is.
Okay sometimes it's like a refreshing stroll she pulls it off so well.
This video shows how science’s use of mathematics in describing natural phenomena imposes its own, artificial structure on the universe.
@Goran Vukovic If I'm understanding correctly, mathematics only _describes_ the universe, but does not _control_ its behavior (probably). As long as mathematics _continues_ to produce valid predictions about how various parts of the universe behave, it is deemed to be "correct" (or at least "correct enough"). If/when mathematics predicts one thing, and observable reality does a _different_ thing, then the mathematics (either the axioms or the formulas) are deemed "incorrect" and must be changed to fit. The side effect is that the universe _appears_ to follow mathematical laws - but only because the accepted "mathematical laws" have been iteratively customized to fit our observations about the universe.
It might be more correct to say that mathematics imposes an artificial structure on how we observe and understand the universe, rather than on the universe itself.
@@HaloInverse Yes. You clearly stated it. However if we are not realist enough or at least a bit then we end up believing in guys like Sheldrake. So Maths might convey truths about the universe instead to be only a tool of the human mind in a dual reality or a glorified way to plot a curve fitting.
www.sheldrake.org/reactions/tedx-whitechapel-the-banned-talk
Always go with intuition where the nature of your own existence is concerned...because that's where 'intuition' comes from..
People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable..
Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily..
So, in terms of 'numbers', infinitude can only ever be 'one'..
All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective.
'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness..
Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..
Who needs to be first or second?! I am 42!!!! :)
be the six with you as your rute to go life.
We have a potential ‘infinity of possibilities’ formed by spherical geometry. We have an infinite number of line symmetries within a sphere as long as it is expanding. In this theory, this represents an infinite number of time line for potential future possibilities. In the equation (E=ˠM˳C²)∞ the brackets represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. The spontaneous absorption and emission of light is continuously forming a probabilistic future by changing photon ∆E=hf potential energy into the kinetic Eₖ=½mv² energy of electrons.
I'm a recovering MetaMathematician, from the CyberWars. No Joke.
These Battles are why I'm a Mere Sephardic Ethicist Mystic.
& an UltraFinitist observant Shinto who has beef with the Yamato.
& yeah, I was Borne to the Tribes of Tiempo. I grok purpose, yon plebes.
She lost me at infinity
You went to infinity, so you were everywhere.. :)
She cost me an infinity... That´s what he said...
She had me at infinity.
One reason you should not write such equations, at 3:19, is that (obviously) if you divide a positive number by "positive infinity", the result is also a positive ... but zero is neither positive or negative, which is a contradiction. To avoid such contradictions, "Division By infinity" is defined to be a Limit, as if one were in a "never ending" process of dividing the numerator by a larger and larger denominator. Great fun.
Zero is "the Limit" of that process if zero is the largest number that's never reached. And one could argue that's why zero must be neither positive or negative, and why -1 must be larger than -2.
The definition of a "Limit" was generalized to handle more complicated formulas.
Theoretically God could always create an even heavier rock. Even so, he could never create a rock that was so heavy that he could not lift it.
Something You Said yeah but that's just a theory...
So the general question may be: “is an all powerful entity able to create something it can’t have powers upon?” That shows something all powerful doesn’t make sense.
An entity having a potentially infinite strength could lift any weight. Even so, any weight that it would lift necessarily would be finite.