Infinity is fake | Jordan Ellenberg and Lex Fridman
Вставка
- Опубліковано 13 чер 2021
- Lex Fridman Podcast full episode: • Jordan Ellenberg: Math...
Please support this podcast by checking out our sponsors:
- Secret Sauce: wondery.com/shows/secret-sauce/
- ExpressVPN: expressvpn.com/lexpod and use code LexPod to get 3 months free
- Blinkist: blinkist.com/lex and use code LEX to get 25% off premium
- Indeed: indeed.com/lex to get $75 credit
GUEST BIO:
Jordan Ellenberg is a mathematician and author of Shape and How Not to Be Wrong.
PODCAST INFO:
Podcast website: lexfridman.com/podcast
Apple Podcasts: apple.co/2lwqZIr
Spotify: spoti.fi/2nEwCF8
RSS: lexfridman.com/feed/podcast/
Full episodes playlist: • Lex Fridman Podcast
Clips playlist: • Lex Fridman Podcast Clips
SOCIAL:
- Twitter: / lexfridman
- LinkedIn: / lexfridman
- Facebook: / lexfridman
- Instagram: / lexfridman
- Medium: / lexfridman
- Reddit: / lexfridman
- Support on Patreon: / lexfridman - Наука та технологія
"I'd like to ask you an absurd question" -- "Of course!" -- I like this guy.
Ridiculous**
This comment will go places
Right?
Infinity: the total amount of USD that can ever be created.
no because u would run out of material when all matter would disolve in a few trilion years.....so u could not make no stuff anymore
Good one
I think you meant LSD
@@bobancikic7458 the value of blackholes would be denominated in USD until the universe died of heat death.
this is a good thing.
Chuck Norris counted to infinity... Twice
Divided by zero
Chuck Norris is infinite
Counting his birthdays
Eleventy five days after his death
Wtf loll😂😂😂💯🍻
This argument could go on forever....... Or could it? (twilight zone theme)
*VSauce theme
@@danceswithstone hello
@@danceswithstone the actual word for this comment is "infinite regress"
hahaha
Engineer from first principles until you talk to a mathematician in which case you use the engineering approach: "I don't know what I did but it's working now. Ship it."
I feel like you give me a voice! I appreciate your videos very much and I’m very thankful to live in an age where I can see this type of content consistently. 🖤
'Ghosts of Departed Quantities' - nicking that, title of my first solo album.
Lex, I have also struggled with the concept of infinity. At a young age, 2 years old I would get extreme anxiety and take off running when I thought about "forever" As I got older, I realized that time is a construct that we are experiencing as beings in the 3rd dimension. And that our human brains cannot fathom what the 4th dimension is like, just how a 2D being can't imagine 3D.
Man, as a kid I would lie in bed and think about like, what it meant to live in "heaven, *forever* " and when I thought about the longest period of time I could imagine, then multiply it, forever... and in a moment I could almost "conceive" what infinite meant, and my heart would drop in my chest and I would jolt up in my bed like "fuck, I dont wanna think about that again, anymore."
I dunno, just something that stuck with me when I was a small kid.
The real question is: Is mathematics manufactured for our consensuses to make sense of numbers? Infinity doesnt work in our brains comprehension of math. Why did we choose to recognize numbers in 10's 100's 1,000's We could have learned it in evens, odds, or maybe left or right. We are training ourselves to think a certain way, then we dont understand how to think about a concept of infinity, but infinity never made sense to me.
It’s like the null pointer exception
I like Aristotles answer to this. The distinction between potential and actual infinity.
Potential infinities exist. This is the kind we find in mathematics. The mental process is non-terminating. Take adding numbers no matter how big you can get you can always add 1 and get something bigger without any end in sight. However, notice whatever number you get to it is something specific, finite quantity, and this is the actual.
Actual infinities don't exist, either in mental process nor as a thing in reality. One of the implicit laws of his is law of identity, every thing you come to know is something specific that has identity, it can't have that identity while being something else contra to that identity at the same time in the same respect. To be specific is to have a unique set of finite properties. Because if it didn't, how would we know if it's unique or not? The properties would actually go on without end. So now let's take actual infinity. Let's say it has a specific identity, but if it's actual infinite it has no finite set of things, therefore it can't be uniquely identified. Therefore it has no identity. Therefore it doesn't exist.
Also don't mistake actual infinity for eternal. These are not the same thing.
This is an issue that is close to the heart of many of the really greats in Physics(1890's). The problem at the time was believed to be an ontological problem and is now understood to be a epistimological problem. There is a beautiful book by Erret Bishop that rewrites much of useful mathematics into terms that allow any proof to be constructed. The issue is largely moot with Goedel's theory, which shows that we largely misunderstood mathematics and logic up until that point.
love how lex learned how to write catchy names for the yt algorithm
It’s more about engagement. Google wants to give you content it believes is highly engaging. So more catchy titles = more engagement = more exposure from said algorithm.
@@John_Doe742 The sweet irony, that he added so much more than you did. You just missed the point. He was talking about the more intricate values behind the algorithm in an attempt to help you understand it better. I think his comment added value to the conversation even though you didn't think so. Sure it wasn't anything I didn't know already but it doesn't make it incorrect.
On the flip side, that comment was lol's and well placed, so from a joking perspective you got a laugh outta me if that was the goal :P
Lex interviewing Nate Diaz would be epic!!!
No it wouldn’t
Nate wouldnt be a good person to interview on a podcast about diverse topics of life. He is probably a humble guy with a good outlook on fundamentals of life but IMO he might struggle to dive deep into certain subjects
Yh what they gonna talk about nate can barely hold a conversation and speak fluent English
...they have almost the same diction 😀
I understand almost nothing of which they speak but I listen because it tingles my smooth brain.
Ur brain isn't wrinkly like mine?
People are infinitely stupid. Debunked!
Hey Lex, maybe you should get this guy NJ Wildberger to come on your podcast. He has videos on his channel, Insights into Mathematics, where he speaks about this topic quite extensively.
Infinity is as simple as moving the goalpost
Nice watch
the theory that posits there are no integers, no "values" as such is something I want to understand better. Seems very pertinent to the underlying geometry of reality
if you find infinity in a confined space then we must have infinity in a maximum space, not being comfortable is your own barrier. its beautiful when you can precisely define the edges but genius is seeing beyond
the theory positing there are no integers, that there are no "values" as such. That is something I want to understand better. Seems very pertinent to the underlying geometry of reality.
Infinity is a direction, not a destination. Saying "infinity" isn't real is like saying "backwards" isn't real.
Sound, logical arguments can be constructed for any/all/infinite opposite/antithetical points of view …. Maybe, sound, logical arguments mean nothing in terms of the truth? Thank You for these videos!🌀♥️🌀
The truth that can be spoken in not the ultimate truth. It is unknowable by the human mind, which is a product of ultimate truth.
the "infinity" within Calculus that "works" works only in conjunction with the infinitesimal derivative in the definition of the limit - which itself is not a literal value, but rather hand-wavy method based on intuition. so it's not fair to use Calculus as a case-in-point for where mathematical infinities comply with the real world. as it should be understood, all of mathematics is as abstract as its infinities, and so the goal posts for what is and isn't consistent is relative to the system its defined in.
If I remember my analysis book correctly, the point of infinity is to make good approximations of quantities that wouldn't be as easily done without it (if at all).
infinity - along with its counterparts singularity and eternity - is the source from which there enters an element of newness to structures that inherently terminate - love your ability to reason and love lex and your conversations, thank you for sharing
I’m uncomfortable with entropy/chaos…on a mental level. Has Lex done a podcast re: entropy?
Why are you uncomfortable with it?
I immediately agreed with Cantor's diagonalization proof. Then I realized I didn't understand it, so I didn't believe it. Then I understood it and didn't believe it. Then I understood it and believed it. But I remain nevertheless unconvinced.
Lol ,
You nailed it..!😂😂😂
I've been thinking about this recently... except I think the counting numbers are fake, too. The only numbers we should accept are the handful of constants in geometry and physics: pi, phi, e, etc.
Have a shot of whiskey every time you hear the word "like".
My liver just failed
Like they said in the video, in Newton's calculus the concept of infinity (both the infinitely large and the infinitely small) is not super precisely defined (later on mathematicians did try to precisely define calculus, and all of that is encapsulated in a branch of math that we call "mathematical analysis"), but it is a tool we can use to effectively do calculus and specifically calculate limits and derivatives and integrals. In that version of calculus, in my opinion, infinity simply represents the idea of observing what happens to certain situations when numbers get very small or very large. Is that such a foreign concept in real life? Personally, I don't think it is. I don't see why we're having philosophical arguments that lead nowhere. Calculus clearly works... and actually describes a lot of real life phenomenon very accurately.. to me that settles any sort of philosophical debate.
Philosophers still argue if chairs exist. Im not surprised they are not convinced by your argument.
Infinity is the hobble of humanity. It is obviously existent in the irrationality of existence, yet we humans are creatures who are deprived of the understanding of this must. Our lack of understanding is our lack of perception of this obvious truth.
Infinity is impractical and should never be used as a variable in math equations. The number of atoms in the universe or some other ungodly large number should be used instead. At the heart of it, infinity is not a number, but the never ending nature of numbers.
SSS🌙 if infinity was a place, there’d be no room for you to exist.
I'm 1:09 into this video... never heard of the concept of 'infinity being fake'..... and upon hearing the qualifiers... I 100% believe infinity is fake. But I also believe in the concept of robust mathematical tools. Infinity just happens to be like this super amazing substitute for "we dont have the logic to understand the deepness of this yet"
1 can be an infinite number if you take infinite as immeasurable. If you had a single object in space it would be immeasurable because you need something else to define it. It can't count itself and so is immeasurable. It's relative. I think if the universe as being both finite and infinite. Finite because there is a definite amount of stuff in it. And infinite because it will always be at least one bigger than can be measured or counted. Like a string of pearls. Take one pearl and use it to count all the others because you need one thing to count another. At the end the pearl you used has nothing left to count itself and so the actual number of pearls is unknowable. Like the uncertainty principal there will always be some information that is ultimately unknowable.
if infinity is fake, what is at the end?
Lex, get Wildberger on and see if he's a quack or not.
@@pdutube Yep, he has an issue allright!
A lot of people feel uncomfortable about infinity because they have received bad/incomplete teaching about subsets like real numbers/calculus. It has nothing to do with infinity itself. I have heard people saying stuff like "you can arrive to all sorts of contradictions if you assume infinity" which is totally wrong for example. We learn about real numbers without a construction, like Dedekind cuts, which might be reasonable but the result is that we feel the uncomfortable feeling that something is not completely explained there. I guess a lot of people assume there is no further explanation and reals are just not well defined. Of course there are those who know and yet propose we should do things differently.
I mean.. when you Stop counting??
The singularity of a black hole, when mass reaches infinity? I have tbh, I almost spit up my drink when I first heard that as if it was so obvious that his understanding had failed him at that time. That was my 'intuitive' take.
I don't know what to believe. But then again, I have about as much interest in math as I do accounting or business.
maybe a physical infinity. but certainly counting numbers you can go on forever
Where is this art from? (On your UA-cam listing for this clip). GRACIAS!! 👊
There is a hypothetical finite highest countable number for any sentient being to count to, before they expend all energy available to them in the universe.
@@TheGubernatis Nope. The tools of computation, also, have their limits.
@@TheGubernatis They take energy, too.
Why would infinity as a "useful hack" be any less real than complex numbers, or even real? What hierarchy/ordering of "realness" are you imposing on abstract concepts in order to rank or compare them?
Infinity is irrational.
If infinity is fake, is a circle then fake?
Holy shit, I've been thinking about that lately for the last year or so and I didn't know it was a thing. Maybe I'm just part of the hive mind.
seems like our minds always kind of follow some general trends of thinking in society, I doubt much of us have any really original thoughts, but it always feels like we do
Maybe it’s just media conditioning?
The limit does not exist. Shoutout to anyone who knows where that came from
I just watched a video that mentioned something from old India writings that if the entire books of math were obliterated…math would happen again 🤓👉
Maths.
Mathematics.
I have a very strong intuition that the universe can't be finite. But it also can't be infinite. From a logical perspective existence seems to be an impossibility. The more you think about it, the more you realize there can be no possible coherent explanation for it. Conceptual thinking so not the right tool for the job.
I have the same opinion. There are a lot of contradictory things in the universe, wave/particle duality, uncertaintly principle, quantum entanglement to name a few. I think it is possible we will come to the conclusion that the Universe is both infinite and has a beginning. I also like Roger Penrose's ideas about a cyclical universe and also the idea that universes are born and re-born and evolve, which makes sense, just not testable. :)
I've always thought that there is no such thing as a realized infinity. The potential for infinity exists, yes, theoretically the whole numbers are infinite, but you're not going to count to infinity just to prove it, because you'd be counting forever... Infinity exists as an idea of what something potentially is, but can never be realized.
That's because you don't think outside the earth. The universe could be infinite itself or be eternal o the process that brought the universe into existence is infinite.
@@artbar6 But that's not based on actual science or evidence. Infact, the theoretical concept of infinity doesn't have a sound mechanic whether imagined or not. It's just wishful thinking.
@@davidw2433 If one thing is true it is that either things are finite or they are not finite. Show me a proof of something that is not finite. Cantor failed and you seem to not even understand basic facts of logic.
@@davidw2433 no shit. Proof not finite
@@davidw2433 No it doesn't. And it isn't the inverse, it is the denial. Either you are right, or you aren't. Either the sky is blue, or it isn't. Either the sun will rise tomorrow, or it won't. Either 1+1=2 or it isn't. Either things are finite, or they aren't. Taking both positions is by definition a contradiction and illustrates a complete lack of understanding of logic on your part.
Zero defines the end. 1 isn't 1 with a decimal point and an infinite amount of zeros, it's just is 1, the end.
Show me proof of something that is not finite.
Infinity and zero have a lot in common, lets get rid of both of them!!
Lex - *sarcastically* Bro i'm basically an expert
Me - Sounds about right
They took infinity shots of vodka
Finitism should be taken seriously, because: no infinite set of anything has been observed in the physical universe; infinites are only known to exist as abstract ideas. And we do get into trouble when expecting to have an actual set of infinite things in physical existence, and theoretical physics of the origins of the universe is a good example. Various multiverse theories posit an infinite regression of prior events into the past. Logic itself gets violated, for if there are an infinite set of prior events, how could the present even come into being?
This video make me think of discrete math
Infinity is possible outside of this universe.
This can be proven simply by definition. Science is based off of what is measurable. Infinity is immeasurable. Therefore it is impossible to physically prove that infinity exists in the real world. The only question is what does mathematics tell us about the existence of infinity?
Yes, the question is whether or not infinity is a useful concept.
@@williamolenchenko5772 it is for us, since our perceptions of reality are so small.
There's no instruments capable of measuring infinity. Moving goalposts doest make infinity go away.
turing machine does not need infinity
sometimes are mind cant rap your head around these big Q>A what you do not understand or no youjust dont no
Maybe it’s double slit’ish. Numbers don’t exist until they are observed
The arguments that support infinity break down if you only think about it for more than one second. For instance, the argument that you can always add one to any finite number, sure you can do this but nomatter how many times you do this the result will still be a finite number. And if you say "but what if you do this an infinite amount of times", than you're supposing the presupposition of what you're trying to conclude. It's an obvious fallacy in logical thinking. The argument that you can always divide a number is the exact same fallacy, because the result will always be finite unless you presuppose that you can do this an infinite amount of times.
@guy man reality
@guy man Are you serious?
@guy man How oes your exaple result in ininity
Uhm, doesn't Pi have an infinite number of digits?
Energy is infinite soooo
I like Lex because he never tackles complex subjects. /sarcasm
Maybe the idea of finity is because of the end? At leat that is our conecpt of things. Endings and all that's our conception and only that of something inhuman. Infinity is the same. How can we know if things have no end? It's a philosophical question after all. And it's not bad. I guess.
I think what people really want to know is if we've been here for an infinite amount of time..like how many iterations of humans could there have been? I don't like the idea of infinity either because it makes the idea of time obsolete. How do you keep track of the date when the clock runs for an infinite amount of time?
@@HigherPlanes you just pick a point in experience and then arbitrarily decide that it is this time. That is exactly what we did. (but we decided that it should be based around the rotation of earth and it's rotation around the sun)
@@zookabazooka6472 I guess it serves the function for everyday life.
@guy man Nothingness is Nirvana, or annihilation.
@@HigherPlanes Care to elaborate what you mean by annihilation?
Not all real numbers are accessible/computable.
If we lived in an infinite universe we could not exist, as any part of infinity can be divisible/multiplied by infinite. This would therefore provide no reference point for reality or relativity to exist in. There would be no reference scale. Existence could be infinitely small and infinitely large at the same time. That is my opinion on the matter and I do not think you need to be a doctorate in math's or physics to work that out.
What this comes down to is, while 1/3 + 1/3 + 1/3 = 1, Mathematicians have decided to accept that .3 repeating + .3 repeating + .3 repeating also equals 1. The problem is that it is not. There are no amount of 3s you can add together to make it true, but in the limit, WE have decided to ACCEPT that it is TRUE because it allows Mathematicians to invent useful tools that Engineers & Scientists can then use to make excellent approximations. Because the Large infinity can be used to fool you that this is True (again, it is not, we have just decided to state that it is true to go from there to invent useful mathematics), the Small infinity that is more understandable to the human mind is Zero. Just like 1/3 + 1/3 + 1/3 = 1, we can show Mathematically, that 1/3 * 1/3 * 1/3 * 1/3 * .... (infinitely times) is equal to 0 (BY DEFINITION). If you think what this is saying, that you can take 1/3rd of a piece of pie, cut it into 3rds, and then do this again, and again, and again, and again, ..., then Mathematically, you will end up with ZERO pie to eat. This type of infinity mathematics 'tool' can be used to make 2 full pies when you only started with 1 pie - and is a famous mathematics problem. Infinity isn't real, but invoking it allows us to do real useful calculations. Once you accept the religion of Infinity, you then get introduced to the Imaginary World of (i) - which I personally think is far more understandable to humans once you grasp that a 'number' can have more than 1 part to it to represent that there are numbers both above and below the numberline.
This is a common misconception, the 1/3=.3333... is just an artifact of notation. There's no sense in which the .333... needs to end, it's just an artifact of converting 1/3 to decimal notation. In actuality it's as simple as 1/3+1/3+1/3=3/3=1; nothing left over. This is especially true since our choice of a decimal number system is arbitrary. If we used a ternary number system instead, the "decimal" expansion of 1/3 would simply be 0.1; 2/3 would be 0.2, and 3/3 would be the usual 1; no repeating decimals.
Haha “lex” we’re “1” it’s “xeno” I would love to speak in depth about this.
I'd love to be worthy to be on Lex's podcast, I don't think he has vacancies for armchair enthusiast about everything that's written nothing!
So, i) there is an objective aconceptual reality which nonetheless our purely conceptual mathematics perfectly describes, and ii) the concept of the number 1, for instance, is part of this description but not the concept of infinity because it does not reflect our conceptual experience of this aconceptual objective reality even though that concept of infinity may allow for much more powerful conceptual tools to enable us to describe it.
Nahhhhh.
Existence would be the only infinity available
Not only does infinity exist, but multiple infinities exist
The universe doesn't end with infinity?
how can space stretch beyond Planck length...apparently leads to tiny black holes..
honestly none of us no for sure of infinity exsept for the fact that the very word exsist like nobody knows what happense when you die the dead cant talk unless you die and come back to life common sense says most dead people dont talk
Why does he say that it makes him think of ‘The Netherlands in the 1930’s’?
Calculus only works on our scale
I always thought that infinity was a concept, not a fact.
Do also believe numbers are concepts , what about emotions??
@@Daithi_mk why id that?
@@Daithi_mk define concept
The now ....flow of the tao is the flow of the infinite present ...
doesnt infinity also imply that there must be infinite energy, because how could you even get to infinity if you run out of energy at some point? so hows infinity even real if something like the principal of energy conservation exists? so there will ever only be theoretical infinity in natural numbers because you would need infinite energy to count infinitely.
Infinity doesnt exist anywhere, you can count forever or make a computer Who Will (x)*(x)*(x)... they computer Will run out of time the number Will be enormous but not infinite
Anything that the human brain can think of is possible
Check out new calculus
If infinity is not real, then nothing is, obviously..
Its basically, do we live in a discrete digital type universe or an analog universe. Maybe we escape this problem with the multiverse where they both exist, where ours is more akin to digital.
That side angle makes me think those are the worst fitting glasses I've ever seen.
Great...!
First Pluto isn't a planet ..
And now you take away infinity..!!!
..eeh... infinity is very real and you are it
With all my respect to both of you .
I do not agree on that with you .
Just think clearly for one moment ...
How can infinity be fake ?
When whoever studied physic in school and knows the basic of it - knows that one of the fundamental laws of physics says that energy is never lost in nature .
Correct, numbers are a made up concept - infinity does not exist. Just like 0 does not exist.
And what do we have to thank for this myth? The nefarious machinations of Big Infinity
Get 2 mirrors and you can see infinity in the real world
cow ku russ make head big ouch
From a pure numbers perspective you can always add another zero. Simple. Now from a physics perspective, yes singularities are an issue.
daithi Logical existence doesn't need a human brain to exist. It exists necessarily.
@@Daithi_mk To add, just because we can't count outer space rocks beyond say 100,000 that we only found, does Not mean that 100,001 thousand rocks in outer space don't exist.
Infinity is fake...
Of course, I'm not going to NOT click.
Science and philosophy are TERRIFIED of infinity. It’s ridiculous.
561 to 303. A.C.I.'s finest