I make excuses for miniaturizing particle colliders in the sense they could be used to create antimatter for a matter antimatter propulsion. Even at 1% efficiency to thrust if its designed in such a way that the energy it produces converts the next ion to anti-matter, (like net gain in fusion so it repeats the process), one could get to mars in 24 days with 50 tons and 10 ton of hydrogen for collider to convert to matter antimatter process. Real kicker with this is that as a space ship goes fast, the conversion to anti-matter contains more energy, to help offset relativistic drag at high speeds. Huge deal if this is possible within the next 1000 years, because it means difference if aliens can efficiently hop stars systems or not.
Non-mathematicians beware. Saying real numbers are infinite decimals is not sufficiently rigorous to do mathematical proofs. They are actually defined as Cauchy sequences or Dedekind cuts, neither of which is a walk in the park. Making rigorous the infinitesimals dx that many physicists are fond of is also quite difficult. Ironically, the calculus of infinitesimals arises quite simply in constructivist mathematics.
I would be happy to watch a debate between Cauchy and Cantor!! By the way, even in the Cauchy's view you can construct real numbers if you have infinite time, which makes it non-constructive in my view, so a lot of "rigorous mathematical proofs" are not rigorous in my humble opinion!
Well, infinite decimal is nothing more than than a Cauchy sequence of finite decimals. It is as rigorous as the other definitions (of course you identify 0.(9) = 1 etc)
I don't know the details of Gisin's arguments but I did my graduate work on constructive mathematics, specifically a constructive variant of the type theory. What I understand from intuitionistic logic is that the core difference is that the law of the excluded middle is not accepted, in other words, for any hypothetical proposition p, the truth value of p \/ ~p is not known (in classical logic it is always true whether or not you know the truth value of p. In intuitionistic logic, you MUST know the truth value of p otherwise you can't evaluate p \/ ~p. You also can't say ~~p = p. This has huge impact on "existence" proofs that used in mathematics, specifically proofs by contradiction will no longer be valid without admitting this law of the excluded middle. The core of non-determinism in this context is that we can't say p is either true or false but we don't know which. You must know what the value of p.
When cutting a piece of wood I talked with my dad about how long it needed to be. "Is it just shy of 457mm or just over 457mm? I asked. He said "Either is near enough." I think my dad used maths entirely the right way.
I have studied propositional logic and axiomatic systems, generally considered the foundation of mathematics, and I have to strongly disagree with the notion that math is just a human construction. High level concepts in math might seem arbitrary on the first pass, but logic itself is in some sense inevitable, it follows from an exhaustive review of all possible ways that information can be combined. The structures that emerge from a system of axioms are unavoidable. In my view, logic is the foundation of reality, and concepts exist independently of the conceiver. The abstract notion of a circle exists and existed long before any physical manifestation of it, or any human mind evolved to write down the definition in a hundred languages.
As a college dropout, you might say my whole life has been lived intuitively. So my intuition tells me that, while the next digit in a real or irrational number is unknown, it is not in a superposition of [0|1|2..|9> (or whatever the notation is) until it is calculated. The next digit will always be what the next digit is. So it could only be in such a superposition if the number itself can't be calculated with the next iteration through the Turing or Von Neumann machine. Ergo superpositions are non-computable. To quote an ancient movie: "This is this [what it is]... This ain't something else"...
The comparison of Peterson to fundamental cosmic phenomena has me imagining Peterson as the avatar of a Great Old One, who we can’t understand because to understand would shatter our psyche, and that thought makes me chuckle.
Jordan Peterson isn't difficult to understand. It's just that understanding his conclusions requires knowledge of multiple disciplines since what he talks about is ultimately multidisciplinary in nature. They being: psychology, philosophy, mythology, religion, literature, and sociology
The problem with quantum isn't math - its data; specifically that we are not permitted to see it: not clauser, not aspect, not Zeilinger... And when we do finally get data, we can see that it is filtered for effect. The data on its own is quite classical - its only by filtering the data can you violate bell.
I feel like the real number argument might be extended to say pi doesn't have any digits past the 2 trillionth (or whatever the current record is) because we haven't calculated them yet, so therefore pi is not really real. Is that a fair extension, or are we only talking about real numbers as they are attached to real world quantities, like the mass of an electron?
In the philosophy of mathematics there is this old discussion about the "actual infinite" and the "potential infinite". This question seems to be an example of it.
Whole quantum mambo jambo begun when some of the greatest authorities didn't understand what was going on in the double slits experiment. The mystery of this experiment is all about the scattering of light. It's called the Compton effect. Very simple explanation without any complex jambo mambo mechanics.
Intuitionist mathematics doesn't go nearly far enough. Classically trained mathematicians continually mistake infinite limits for realities, yet there is no indication that is true in the physical universe. Since the physical universe was the model for math in the first place, I think we should be listening more carefully. Reality is algorithmic with amazingly useful limits. If we keep focusing only on the limits, as if there's no problem or cost in getting to them, we’ll never figure out the deeper structure of the universe.
As a mathematician I have had debates about this with my colleagues for decades. The problem is not math itself. The problem is in people's way of thinking and their attitude towards math, And I am pretty sure it will be the same in physics.
I believe that Sabine misunderstood what exactly intuitionist mathematics is. Intuitionism is one of many interpretations of constructivist mathematics. Constructivist mathematics rejects non-constructive proofs (such as those that assume the existence of objects and make proofs by contradiction) and only accepts proofs where it is possible to explicitly *construct* the object. Constructivist mathematics is *not* limited to finite numbers or with finite precision (except perhaps the finitism school). The numbers thar are possible in classical mathematics and not in constructivist mathematics are abstract and generally involve scenarios with infinity. Constructivist mathematics is not a different type of mathematics, but rather a subset of classical mathematics. Basically, it asserts fewer things than classical mathematics. Fear not, actually all the mathematics we use in science and engineering is purely constructivist. Classical mathematics is only necessary in highly abstract proofs with little to no practical use, such as properties of infinite spaces and sets. However, even though we do not use classical mathematics in science and engineering, we still use the logic of classical mathematics (which leads to "platonic reasoning"). In this context, I imagine that the interpretation of what he is saying is something like: In order to affirm that it will or will not rain in exactly 1 year in the future, it is necessary to prove that it is at least possible to build an "oracle" that predicts this with arbitrary certainty. If this construction is not possible (physically speaking, not technologically), it may be an extrapolation to say that the answer to this question is something determined/defined.
Reality is not Schoedinger's cat. The height of egoism tells you that if you don't recognize it, it is not manifest. The Universe IS whether you 'are' or not. You have been busy today!
if your in the middle of reviving a cat and its heart is stopped at the time but u later manage to revive it was it alive or dead? alternatively if you ultimately fail to revive it? :P
Real numbers have an influence on reality and are real, because WE are intelligences that can encapsulate the concept in our physically based neural network models, and then make decisions based on them. For example, you could say "if my friend Bob picks a number that is equal to the number I choose, which his 10/3 (real) then I will jump, otherwise I will not". Physics can compute with real numbers. Aside from that, we have no idea of what the fabric of reality is and whether continuous or discrete (or some unconceivable alternative) is used. So to throw "abstract" ideas out the window makes no sense.
As a really bad calculator, allow me to express a mathematical intuition / vision: There are two kinds of 0 : 0 as information: "0" (0 is not really nothing because it is information) and 0 without information, symbolized by an empty space: " ". I really do feel a difference there.... Thank you for this interesting video!
Constructive/intuitionistic logic is more rigorous than standard math, for this reason it is used by computer languages for writing math proofs, like agda
I tried to wrap my had around intuitionist mathematics a while ago until I discovered that the law of ecluded middle which intuitionist mathematicians don't except is equivalent to the statement that subsets of finite sets are always finite. And not accepting that subsets of finite sets are finite is definitely too much for me.
There's an extremely interesting phenomenon in mathematics: the fact that a lot of actual mathematical theory doesn't really depend too much on the foundations. A lot of algebra, topology and geometry work pretty much the same regardless of which version of logic, set theory or type theory you build it on. Particularly this applies to the parts of math that are relevant to physical theories. There's no known property of black holes that depends on the validity of the law of excluded middle.
As a computer scientist frustrated that you cannot do algebra woth floating point numbers (they're not associative) I have long believed that real numbers aren't real. Instead of indeterminacy and measurement I think it would be interesting to reformulate physics with rational numbers only.
Intuitionist mathematics leans towards an appeal to authority fallacy. Using mathematical proofs helps us level the playing field and forces someone to have a reason and not just a feeling about an answer. I agree there are some bad theories out there that tend towards impossible infinities, but that is more an indicator of a incomplete theory without a proof.
That reminds me of the dome paradox. How does a ball on top of a dome decide which way it's going to roll down the hill? Up and Atom did a great YT video on that one. I dare say mathematicians could care less, but it keeps physicists up at night. There's a great comment on that video: "If it moves, it's biology, if it smells, it's chemistry, if it doesn't work, it's physics."
The transition from past to present and from present to future that are implicit in the use of formulas that include time as a variable, apply very well to formulas that describe at a macro level what is happening in the world of matter, but apparently at a micro level, where Planck time operates, is where these formulas do not operate. There is nothing strange about the above if we consider that the material world only exists in the Present, and what "separates" the present from the immediate past or the immediate future operates on the Planck time scale.
The issue is language if all data needed is available. A clue is in the ontology. Instruments are tools we make. The symbols we use, also tools. I think he's correct to a point. The issue does appear to be with a tool we use.
From a German Idealist perspective (think Kant, Fichte and Hegel) the jump from intuition to "so let's stick to what we can actually make ourselves" is a type of category error. The professor's ideas assume intuition to be a thing which takes as it's object some real thing external to the mind which is perceived. From this perspective, various infinities must be disallowed, for no human can perceive infinity (whatever that means). The assumption about intuition need not be accepted. German Idealists argued that intuition can also take as it's object thoughts themselves. Indeed, this is the brilliant feature of our minds that makes self-consciousness possible (how can one be conscious of the self having sensations if one can only have intuitions about things outside of that self? No intuition of hot or cold applies to the idea of the self). If we can take thoughts as objects for intuition, then infinities can be allowed. For example: thoughts about numbers and their usefulness yields intuitions about addition; working with addition over time yields intuitions about continuing addition; continue addition enough and you have intuitions about [countable] infinities. On a practical note, I'd argue that intuitions about our self are the source of empathy and compassion (it's the intuitions we have about our own internal life that spurs recognition of and care for the internal lives of others). And I'd argue that the analytic understanding of intuition has manifested itself in modern society as coldness and hostility. For anyone who read this and thinks I'm being way too loose with the word intuition, I understand the concern. I tried to use the word in a way consisted with how various philosophers have used it, but I didn't try to define it myself. Apologies.
I find myself in a very odd position. I agree completely with Sabine that maths are not real; they describe reality. Yet, I can't help but feel that Gisin has described a key idea about how the universe works at its most fundamental level even if the connection to the maths is false.
Nazaré Tedesco has become a classic meme! If there were an Oscar for acting in Brazilian soap operas, this actress would have won it for this character! In short, she plays a sociopathic character with borderline tendencies who kidnapped a baby from a poor family. The poor family becomes rich through hard work, and the daughter grows up, slowly discovering that her mother is not her real mother and is both evil and crazy.
Are fetal cats alive or dead? Are unconscious cats alive or dead? Are brain dead cats alive or dead? Are cats that have stopped breathing but have brain function alive or dead?
Quantum Mechanics is EXACTLY how reality works. Our problem is a failure to understand it properly and a desire to force it into the mold of Classical Physics in which it cannot possibly fit. Properly speaking, there is no such thing as "Wave Function Collapse" which was a convenient way to describe observations that we did not understand at the time (1930s). More properly, the so-called "Wave Function Collapse" is simply another way of saying "Entropy Increase" or "Irreversible Thermodynamic Event".
Of course Sabine is correct. I’m surprised (well. Not really.) somebody took the trouble to perform a useless analysis of all the useless cases in which useless math is invalid because it makes assertions or predictions about abstract ideas. Because that’s useless? But what really confuses me is how that guy got published!?!?
I think we simply don’t understand quantum phenomena well enough. Mathematics is merely a description of phenomena, like language, but more precise, focused, and rigorous. not in topic .The infinite degrees of freedom in quantum perturbative gravity precisely correspond to the degrees of freedom of the energy-momentum stress tensor of various fields. Attempting to eliminate these degrees of freedom is fundamentally incorrect because vacuum fluctuations inherently include the vacuum corrections of all fields. These vacuum corrections naturally carry the combinations of all possible degrees of freedom, which are formed by all fields and their combinations. Furthermore, all these degrees of freedom automatically correspond to the increased degrees of freedom at each loop of quantum perturbative gravity. Attempting to eliminate degrees of freedom is equivalent to claiming that the vacuum field lacks the corresponding fields and their associated gravitons. However, the vacuum inherently cannot consist of corrections from only a single field; it must involve corrections from all fields and their combinations. When the vacuum fields and their combinations interact through coupling, they precisely correspond to the existence of the infinite degrees of freedom of gravitons. Gravitons correcting themselves may introduce corresponding ghost fields. However, this can be addressed through interactions with curvature fields. For example, the scalar curvature field R^2 can be constrained via the energy-momentum stress tensor T^munu to derive a scalar field. The degrees of freedom of this scalar field can then absorb divergences. Additionally, the energy-momentum stress tensor T^munu inherently contains the degrees of freedom of all energy fields and their combinations. From this perspective, one can deduce that the corrections of all quantum fields in the vacuum precisely correspond to the infinite degree of freedom corrections of gravitons, further substantiating the validity of quantum perturbative gravity. In other words, we should first identify all vacuum corrections of energy fields and their combinations. Once these are identified, all possible degrees of freedom will naturally be included. These degrees of freedom will be absorbed into the corresponding physical quantities and will align with the infinite degree of freedom combinations of gravitons.
In terms of math, I may say look at sets and those sets the self repeat tend to grow linearly where those sets of mixed complexity grows factorially. With enough complexity, its almost all probability distributions and almost all measures that the optimal point exists in complexity. However science tries to force it into simplicity because of false ideals like Occum's Razor. But one simply counts strings that self repeat and strings that contain complexity, complexity set is just so much more larger. People see complexity in nature, but it could just be random because most observations will likely be in complexity because there is just so much more of it than self repeating strings. People see it and think Gaia theory, but it maybe just the expect observation. But its also the worst solution exists in that area of complexity as well, which human bias can quickly pick up optimal solutions or negative solutions in complexity. Because its so much larger its both going to exist in there. This has huge amount of to do with like future of human food production in space. NASA or sci-fi shows tend to show the food selection in the simplistic range, some kind of monoculture, when just simple counting of elements of simple and complexity, its very likely the optimal solutions exist in complexity. There could be distributions where its not, but if there a bit of randomness, just a slight bit of randomness of optimal point, it will end up in complexity almost all the time.
FWIW, I think there is a fundamental problem with applying 'imaginary numbers' - you know, the sqrt(-1) variety, to physics problems. It 'simplifies' the maths but creates a legacy of discontinuities that crop up at the boundary conditions. We play free and lose with conservation of everything by assuming stuff 'pops into existance then annihilates' because.. reasons.
What my father always says; “if you can’t dazzle them with your foot work then baffle them with bullshit”. So it Looks like there dancing skills are lacking
Mathematics is not the crutch through which physics can limp ahead. Mathematics is at best like a sidey or a main character's best friend but ultimately it has to be physics that has to take the call.
very cool! To me this is such a philosophic dilemma as it comes down to how much we believe we are good at generalizing reality. Isn't math coming into existence to rationalize the observable reality around us? If so, how can we rely on it to describe and predict other phisical domains? And is it because of these crippling doubts that i fail to be thrilled when Brian Cox talks about how you would experience walking on the event horizon of a black hole?
Sabine you mentioned something like Quantum mechanics is useful but fundamentally not how reality works, this leads to the question In your opinion what is your gut feeling for how reality work?, I have worded that badly but I hope you can see through the bad wording.
Yes, I wish I knew how reality worked... More seriously, my issue with quantum mechanics is that it's incompatible with Einstein's theories. I think that resolving this tension is a good way to make progress. That doesn't mean that I know how to do it.
@@SabineHossenfelder Yet there is a way to connect them and eliminate many of the current issues in physics; one of course, MUST use existing concepts and never use speculation or 'out of whole cloth' ideas to fix it. Current quantum is correct as is GR. Expressing GR in QM terms, appears rather straight forward if one accepts the basics of Field Theory. So, that is what I am working on (yes, I am a physicist and not playing games in fields I never had training; maybe totally wrong but so far, its working ...time will tell. lol.)
17 годин тому
As "not a physicist" I always get a feeling that quantum mechanic (and everything up from it : QCD, QED, etc.) is just a mathematical hack (as in: dodgy workaround). We know it works pretty well and 100 years later we have built an entire system on top of that hack.
If I understood this argument correctly, then there's nothing wrong with asking questions, hypothesizing, and then getting it shot down... That is the scientific process. There is probably some value in questioning the assumptions. Even if it goes down a blind alley, perhaps something new is discovered, even if it is conventional maths that were overlooked.
I have similar ideas about all numbers being truncated in that the way we conceptualize numbers is rooted in set theory. I think we embed logical fallacies into math by assuming that any thing is a thing. One whole, distinct thing. We created zero, but we created one first and based every other number on the idea of grouping or dividing ones. Zero is just "but what if one... minus one?" In real life everything happens on a gradient that can be infinitely sliced. The universe doesn't think in things, it thinks in events. There's never a point at which .999999 becomes 1.0000000 without another 1 somewhere at the end. "Whole numbers" are just a matter of convenience in accounting.
He sounds like the people I knew (not me, no, NOT ME) who didn't want to do the homework to get a correct answer in either his math or applied-physics classes, and felt insulted when his professors graded his work appropriately. I have been trained that answers with uncertainty calcs, as appropriate, are really necessary. I'd suggest he be required to furnish appropriate theory-based uncertainty calculations to show his work is actually useful instead of assigning a 'ghost in the math' hypothesis. You know, asserting that it's QM level effects in the brain cells that 'create' consciousness, which conveniently side steps having to be the systemic analysis of neural networks. WOW, you actually ended up in the same place I did!! Wrote that Penrose allusion before you got to it in your presenta6tion, so in terms of local time and variables, so I claim local credit for it! Unless you were psychically willing me to converge on your conclusion?!
Yes physics always comes before maths.... also... the little known fourth law of thermodynamics concerning intensive and extensive properties needs to be used to make the math obey the laws of phyics.... the Sky Scholar you tube channel makes it so so clear
I remember a lecture from Feynman who mentioned Babylonian Math and Greek Math, and was a proponent of this very idea. It seems we have physics seems more in the Babylonian phase trying to use Greek Math.
Haven’t watched it all the way through but isn’t that why we use Planck’s constant? It’s the fudge factor for all the things we can’t figure out? Or are we not using that anymore?
How is having to postulate that the present moment is special a problem. Propositions that are deemed to be obvious but not derivable from more fundamental propositions are precisely what postulates are supposed to be.
This is actually not surprising at all, in some sense. Mathematics are just another language. Language is the very substance of *culture*, which dictates certain paradigms and viewpoints. If you want to see things from another culture's point of view, you have to learn the language, because of the memes it conveys. If you are looking to gain perspective in a useful way that let's you see things from *outside* of the current framework, or better, from a completely different framework, then working strictly within the current paradigm and framing is a sure way to fail. The fact is, outsider thinking is needed, but the disciplines involved have become an exclusionary priesthood, that very specifically weeds out any such thinking along with those who engage in it, defeating themselves utterly.
I mean, the question of intuition is present in philosophy since early modernity, considerations by Hume and Kant notably about mathematics, this is indeed nothing new and I don't think a platonician conception was necessarily dominant either.
So he actually means digits, as in digits after the (arbitrary) decimal place, not *significant digits* as in numerics? Maths has been a quite successful problem-solving tool in the past 5000 years it would seem, I wouldn't ditch it too fast...
isn't what we call time just change..we measure time or change in our local standard in reference to time on earth and the sun.. but outside of that context.. time is just a construct.THERE IS JUST CONSTANT CHANGE IN 3 STATES PAST PRESENT AND THE FUTURE. TIME IS JUST A MEASUREMENT..
computers also do not know nothing about measurements. Binary Digits are just codes in GF2, and sometimes in others GFs. You then with some sort of calibration have to convert it into a some kind of measurement, if the codes are still valid of course
I'm very thankful for having constructs like the Dirac Delta Distribution, or White Noise in the Schwartz Space.. One might not be able to construct them, but they do come up rather "naturally" trying to simplify calculations. No, they are not of this world, and they are mere fantasy,, I think, but I can start with something "real", use such constructs to ease my calculation, can come out at something "real" again. "Real" meant in the sense that I can relate it to seomething I can perceive in the world. . I can dive underwater, catch a fish, and climb out of the water again. Yes, I was "under the surface" for some ttime, but now I hava a fish I can eat ...
I remember a particular actor saying the same. something about one plus one is one and what not. let us just ignore the inconvenient fact all that faulty math's seem to be working so well.
Sounds like another excuse for a bigger particle collider.
I make excuses for miniaturizing particle colliders in the sense they could be used to create antimatter for a matter antimatter propulsion. Even at 1% efficiency to thrust if its designed in such a way that the energy it produces converts the next ion to anti-matter, (like net gain in fusion so it repeats the process), one could get to mars in 24 days with 50 tons and 10 ton of hydrogen for collider to convert to matter antimatter process. Real kicker with this is that as a space ship goes fast, the conversion to anti-matter contains more energy, to help offset relativistic drag at high speeds. Huge deal if this is possible within the next 1000 years, because it means difference if aliens can efficiently hop stars systems or not.
John, you are spot on!
Non-mathematicians beware. Saying real numbers are infinite decimals is not sufficiently rigorous to do mathematical proofs. They are actually defined as Cauchy sequences or Dedekind cuts, neither of which is a walk in the park.
Making rigorous the infinitesimals dx that many physicists are fond of is also quite difficult. Ironically, the calculus of infinitesimals arises quite simply in constructivist mathematics.
thank you for pointing that out
Yeah. That's what I was about to say.
But plank lengths imply there are no irrational numbers
I would be happy to watch a debate between Cauchy and Cantor!! By the way, even in the Cauchy's view you can construct real numbers if you have infinite time, which makes it non-constructive in my view, so a lot of "rigorous mathematical proofs" are not rigorous in my humble opinion!
Well, infinite decimal is nothing more than than a Cauchy sequence of finite decimals. It is as rigorous as the other definitions (of course you identify 0.(9) = 1 etc)
I don't know the details of Gisin's arguments but I did my graduate work on constructive mathematics, specifically a constructive variant of the type theory. What I understand from intuitionistic logic is that the core difference is that the law of the excluded middle is not accepted, in other words, for any hypothetical proposition p, the truth value of p \/ ~p is not known (in classical logic it is always true whether or not you know the truth value of p. In intuitionistic logic, you MUST know the truth value of p otherwise you can't evaluate p \/ ~p. You also can't say ~~p = p. This has huge impact on "existence" proofs that used in mathematics, specifically proofs by contradiction will no longer be valid without admitting this law of the excluded middle. The core of non-determinism in this context is that we can't say p is either true or false but we don't know which. You must know what the value of p.
That's what I told my math teacher all the time but he didn't want to listen.
When cutting a piece of wood I talked with my dad about how long it needed to be. "Is it just shy of 457mm or just over 457mm? I asked. He said "Either is near enough." I think my dad used maths entirely the right way.
I was very confused the first time I went to Home Depot to buy a 2x4…..
@@scytobyup, it’s a dirty lie
I have studied propositional logic and axiomatic systems, generally considered the foundation of mathematics, and I have to strongly disagree with the notion that math is just a human construction. High level concepts in math might seem arbitrary on the first pass, but logic itself is in some sense inevitable, it follows from an exhaustive review of all possible ways that information can be combined. The structures that emerge from a system of axioms are unavoidable. In my view, logic is the foundation of reality, and concepts exist independently of the conceiver. The abstract notion of a circle exists and existed long before any physical manifestation of it, or any human mind evolved to write down the definition in a hundred languages.
As a college dropout, you might say my whole life has been lived intuitively.
So my intuition tells me that, while the next digit in a real or irrational number is unknown, it is not in a superposition of [0|1|2..|9> (or whatever the notation is) until it is calculated. The next digit will always be what the next digit is. So it could only be in such a superposition if the number itself can't be calculated with the next iteration through the Turing or Von Neumann machine. Ergo superpositions are non-computable.
To quote an ancient movie: "This is this [what it is]... This ain't something else"...
The comparison of Peterson to fundamental cosmic phenomena has me imagining Peterson as the avatar of a Great Old One, who we can’t understand because to understand would shatter our psyche, and that thought makes me chuckle.
shub-niggurath
Jordan Peterson isn't difficult to understand. It's just that understanding his conclusions requires knowledge of multiple disciplines since what he talks about is ultimately multidisciplinary in nature. They being: psychology, philosophy, mythology, religion, literature, and sociology
Peterson was only one made sense. In order to think you have to risk being offended
@@TechnoMinarchistPeterson knowledge on philosophy is childish.
@@TechnoMinarchist "If you think you understand Jordan Peterson, you don't understand Jordan Peterson." - Richard Feynman.
Sounds like this guy might need to meet Terrance Howard.
I'm not convinced that time physically exists. How is time not an explainable illusion with motion alone?
The problem with quantum isn't math - its data; specifically that we are not permitted to see it: not clauser, not aspect, not Zeilinger... And when we do finally get data, we can see that it is filtered for effect. The data on its own is quite classical - its only by filtering the data can you violate bell.
I feel like the real number argument might be extended to say pi doesn't have any digits past the 2 trillionth (or whatever the current record is) because we haven't calculated them yet, so therefore pi is not really real. Is that a fair extension, or are we only talking about real numbers as they are attached to real world quantities, like the mass of an electron?
Yes, I think this would be one of the implications. On a similar note, perfect circles aren't real, etc.
In the philosophy of mathematics there is this old discussion about the "actual infinite" and the "potential infinite". This question seems to be an example of it.
Whole quantum mambo jambo begun when some of the greatest authorities didn't understand what was going on in the double slits experiment.
The mystery of this experiment is all about the scattering of light. It's called the Compton effect. Very simple explanation without any complex jambo mambo mechanics.
Intuitionist mathematics doesn't go nearly far enough. Classically trained mathematicians continually mistake infinite limits for realities, yet there is no indication that is true in the physical universe. Since the physical universe was the model for math in the first place, I think we should be listening more carefully.
Reality is algorithmic with amazingly useful limits. If we keep focusing only on the limits, as if there's no problem or cost in getting to them, we’ll never figure out the deeper structure of the universe.
2+2 does not equal 4 because we can’t even get to 2, there are an infinite number of decimals after 1 and we can’t count them to get to 2 😢
As a mathematician I have had debates about this with my colleagues for decades. The problem is not math itself. The problem is in people's way of thinking and their attitude towards math, And I am pretty sure it will be the same in physics.
1x1=2 right?
I believe that Sabine misunderstood what exactly intuitionist mathematics is. Intuitionism is one of many interpretations of constructivist mathematics. Constructivist mathematics rejects non-constructive proofs (such as those that assume the existence of objects and make proofs by contradiction) and only accepts proofs where it is possible to explicitly *construct* the object. Constructivist mathematics is *not* limited to finite numbers or with finite precision (except perhaps the finitism school). The numbers thar are possible in classical mathematics and not in constructivist mathematics are abstract and generally involve scenarios with infinity.
Constructivist mathematics is not a different type of mathematics, but rather a subset of classical mathematics. Basically, it asserts fewer things than classical mathematics.
Fear not, actually all the mathematics we use in science and engineering is purely constructivist. Classical mathematics is only necessary in highly abstract proofs with little to no practical use, such as properties of infinite spaces and sets.
However, even though we do not use classical mathematics in science and engineering, we still use the logic of classical mathematics (which leads to "platonic reasoning").
In this context, I imagine that the interpretation of what he is saying is something like: In order to affirm that it will or will not rain in exactly 1 year in the future, it is necessary to prove that it is at least possible to build an "oracle" that predicts this with arbitrary certainty. If this construction is not possible (physically speaking, not technologically), it may be an extrapolation to say that the answer to this question is something determined/defined.
Why did she misunderstood? this video was about Gisin´s way tto connect it with QM and the measurement propblem.
Reality is not Schoedinger's cat. The height of egoism tells you that if you don't recognize it, it is not manifest. The Universe IS whether you 'are' or not. You have been busy today!
if your in the middle of reviving a cat and its heart is stopped at the time but u later manage to revive it was it alive or dead?
alternatively if you ultimately fail to revive it? :P
the problem is not to claim that "Reality is not Schoedinger's cat. " but to prove it. can you?
Real numbers have an influence on reality and are real, because WE are intelligences that can encapsulate the concept in our physically based neural network models, and then make decisions based on them.
For example, you could say "if my friend Bob picks a number that is equal to the number I choose, which his 10/3 (real) then I will jump, otherwise I will not". Physics can compute with real numbers.
Aside from that, we have no idea of what the fabric of reality is and whether continuous or discrete (or some unconceivable alternative) is used. So to throw "abstract" ideas out the window makes no sense.
You know a guy has no idea what he is talking about when he only states the problem, but presents zero solutions to it.
As a really bad calculator, allow me to express a mathematical intuition / vision: There are two kinds of 0 : 0 as information: "0" (0 is not really nothing because it is information)
and 0 without information, symbolized by an empty space: " ".
I really do feel a difference there....
Thank you for this interesting video!
Math kind of has that, in the form of 0 and undefined. At least if im understanding you correctly.
I think the real problem is this: too much thinking, not enough loving.
We can do both😉
Mathematics is a social construct and everyone should choose their maths whatever they identify with.
"I like my mathematics traditional - well done." Might not have that quote exactly correct, but I love that idea.
2:13 this made me remember a physics teacher that told us "in the human reality, numbers have like 4 o 5 decimals"
Constructive/intuitionistic logic is more rigorous than standard math, for this reason it is used by computer languages for writing math proofs, like agda
I tried to wrap my had around intuitionist mathematics a while ago until I discovered that the law of ecluded middle which intuitionist mathematicians don't except is equivalent to the statement that subsets of finite sets are always finite. And not accepting that subsets of finite sets are finite is definitely too much for me.
There's an extremely interesting phenomenon in mathematics: the fact that a lot of actual mathematical theory doesn't really depend too much on the foundations. A lot of algebra, topology and geometry work pretty much the same regardless of which version of logic, set theory or type theory you build it on. Particularly this applies to the parts of math that are relevant to physical theories. There's no known property of black holes that depends on the validity of the law of excluded middle.
“All models are wrong…but some are useful.”
Is there any tie in to Gödel’s incompleteness theorem? There are limits on logic and limi5s on math?
Yes there is! That's where it gets *very* fascinating. (y)
The mess at the foundations of physics is probably rooted to the mess at the foundations on Mathematics
As a computer scientist frustrated that you cannot do algebra woth floating point numbers (they're not associative) I have long believed that real numbers aren't real.
Instead of indeterminacy and measurement I think it would be interesting to reformulate physics with rational numbers only.
Indeed!
Even with my surface level understanding of maths, number theory calls out
Intuitionist mathematics leans towards an appeal to authority fallacy. Using mathematical proofs helps us level the playing field and forces someone to have a reason and not just a feeling about an answer. I agree there are some bad theories out there that tend towards impossible infinities, but that is more an indicator of a incomplete theory without a proof.
That reminds me of the dome paradox. How does a ball on top of a dome decide which way it's going to roll down the hill? Up and Atom did a great YT video on that one. I dare say mathematicians could care less, but it keeps physicists up at night. There's a great comment on that video: "If it moves, it's biology, if it smells, it's chemistry, if it doesn't work, it's physics."
Sounds like an “Unreasonable Effectiveness of Mathematics….” Type question. Above my pay grade.
The transition from past to present and from present to future that are implicit in the use of formulas that include time as a variable, apply very well to formulas that describe at a macro level what is happening in the world of matter, but apparently at a micro level, where Planck time operates, is where these formulas do not operate. There is nothing strange about the above if we consider that the material world only exists in the Present, and what "separates" the present from the immediate past or the immediate future operates on the Planck time scale.
I like math raw. With some onions, salt and pepper as a Mathbrötchen.
The issue is language if all data needed is available.
A clue is in the ontology.
Instruments are tools we make. The symbols we use, also tools.
I think he's correct to a point. The issue does appear to be with a tool we use.
From a German Idealist perspective (think Kant, Fichte and Hegel) the jump from intuition to "so let's stick to what we can actually make ourselves" is a type of category error.
The professor's ideas assume intuition to be a thing which takes as it's object some real thing external to the mind which is perceived. From this perspective, various infinities must be disallowed, for no human can perceive infinity (whatever that means).
The assumption about intuition need not be accepted. German Idealists argued that intuition can also take as it's object thoughts themselves. Indeed, this is the brilliant feature of our minds that makes self-consciousness possible (how can one be conscious of the self having sensations if one can only have intuitions about things outside of that self? No intuition of hot or cold applies to the idea of the self).
If we can take thoughts as objects for intuition, then infinities can be allowed. For example: thoughts about numbers and their usefulness yields intuitions about addition; working with addition over time yields intuitions about continuing addition; continue addition enough and you have intuitions about [countable] infinities.
On a practical note, I'd argue that intuitions about our self are the source of empathy and compassion (it's the intuitions we have about our own internal life that spurs recognition of and care for the internal lives of others). And I'd argue that the analytic understanding of intuition has manifested itself in modern society as coldness and hostility.
For anyone who read this and thinks I'm being way too loose with the word intuition, I understand the concern. I tried to use the word in a way consisted with how various philosophers have used it, but I didn't try to define it myself. Apologies.
I find myself in a very odd position. I agree completely with Sabine that maths are not real; they describe reality. Yet, I can't help but feel that Gisin has described a key idea about how the universe works at its most fundamental level even if the connection to the maths is false.
Nazaré Tedesco has become a classic meme! If there were an Oscar for acting in Brazilian soap operas, this actress would have won it for this character! In short, she plays a sociopathic character with borderline tendencies who kidnapped a baby from a poor family. The poor family becomes rich through hard work, and the daughter grows up, slowly discovering that her mother is not her real mother and is both evil and crazy.
Are fetal cats alive or dead? Are unconscious cats alive or dead? Are brain dead cats alive or dead? Are cats that have stopped breathing but have brain function alive or dead?
Quantum Mechanics is EXACTLY how reality works. Our problem is a failure to understand it properly and a desire to force it into the mold of Classical Physics in which it cannot possibly fit. Properly speaking, there is no such thing as "Wave Function Collapse" which was a convenient way to describe observations that we did not understand at the time (1930s). More properly, the so-called "Wave Function Collapse" is simply another way of saying "Entropy Increase" or "Irreversible Thermodynamic Event".
Of course Sabine is correct. I’m surprised (well. Not really.) somebody took the trouble to perform a useless analysis of all the useless cases in which useless math is invalid because it makes assertions or predictions about abstract ideas. Because that’s useless? But what really confuses me is how that guy got published!?!?
I find the inexorable move from empiricism, to nominalism, to self-refuting attacks on reason, so very interesting.
I think we simply don’t understand quantum phenomena well enough. Mathematics is merely a description of phenomena, like language, but more precise, focused, and rigorous.
not in topic .The infinite degrees of freedom in quantum perturbative gravity precisely correspond to the degrees of freedom of the energy-momentum stress tensor of various fields. Attempting to eliminate these degrees of freedom is fundamentally incorrect because vacuum fluctuations inherently include the vacuum corrections of all fields. These vacuum corrections naturally carry the combinations of all possible degrees of freedom, which are formed by all fields and their combinations. Furthermore, all these degrees of freedom automatically correspond to the increased degrees of freedom at each loop of quantum perturbative gravity.
Attempting to eliminate degrees of freedom is equivalent to claiming that the vacuum field lacks the corresponding fields and their associated gravitons. However, the vacuum inherently cannot consist of corrections from only a single field; it must involve corrections from all fields and their combinations. When the vacuum fields and their combinations interact through coupling, they precisely correspond to the existence of the infinite degrees of freedom of gravitons.
Gravitons correcting themselves may introduce corresponding ghost fields. However, this can be addressed through interactions with curvature fields. For example, the scalar curvature field R^2 can be constrained via the energy-momentum stress tensor T^munu to derive a scalar field. The degrees of freedom of this scalar field can then absorb divergences. Additionally, the energy-momentum stress tensor T^munu inherently contains the degrees of freedom of all energy fields and their combinations.
From this perspective, one can deduce that the corrections of all quantum fields in the vacuum precisely correspond to the infinite degree of freedom corrections of gravitons, further substantiating the validity of quantum perturbative gravity.
In other words, we should first identify all vacuum corrections of energy fields and their combinations. Once these are identified, all possible degrees of freedom will naturally be included. These degrees of freedom will be absorbed into the corresponding physical quantities and will align with the infinite degree of freedom combinations of gravitons.
I can't imagine the headache you had when trying to make sense of his word salad. Thanks for taking one for the team!
Terrance Howard just got excited by your title. 🤣
In terms of math, I may say look at sets and those sets the self repeat tend to grow linearly where those sets of mixed complexity grows factorially. With enough complexity, its almost all probability distributions and almost all measures that the optimal point exists in complexity. However science tries to force it into simplicity because of false ideals like Occum's Razor. But one simply counts strings that self repeat and strings that contain complexity, complexity set is just so much more larger. People see complexity in nature, but it could just be random because most observations will likely be in complexity because there is just so much more of it than self repeating strings. People see it and think Gaia theory, but it maybe just the expect observation. But its also the worst solution exists in that area of complexity as well, which human bias can quickly pick up optimal solutions or negative solutions in complexity. Because its so much larger its both going to exist in there. This has huge amount of to do with like future of human food production in space. NASA or sci-fi shows tend to show the food selection in the simplistic range, some kind of monoculture, when just simple counting of elements of simple and complexity, its very likely the optimal solutions exist in complexity. There could be distributions where its not, but if there a bit of randomness, just a slight bit of randomness of optimal point, it will end up in complexity almost all the time.
FWIW, I think there is a fundamental problem with applying 'imaginary numbers' - you know, the sqrt(-1) variety, to physics problems. It 'simplifies' the maths but creates a legacy of discontinuities that crop up at the boundary conditions. We play free and lose with conservation of everything by assuming stuff 'pops into existance then annihilates' because.. reasons.
Hard topic explained in a simple fashion. Thanks! Cool video!
What my father always says; “if you can’t dazzle them with your foot work then baffle them with bullshit”. So it Looks like there dancing skills are lacking
Mathematics is not the crutch through which physics can limp ahead.
Mathematics is at best like a sidey or a main character's best friend but ultimately it has to be physics that has to take the call.
very cool! To me this is such a philosophic dilemma as it comes down to how much we believe we are good at generalizing reality. Isn't math coming into existence to rationalize the observable reality around us? If so, how can we rely on it to describe and predict other phisical domains? And is it because of these crippling doubts that i fail to be thrilled when Brian Cox talks about how you would experience walking on the event horizon of a black hole?
Interessant! ich bin auch nicht überzeugtt!
Sabine you mentioned something like Quantum mechanics is useful but fundamentally not how reality works, this leads to the question In your opinion what is your gut feeling for how reality work?, I have worded that badly but I hope you can see through the bad wording.
Yes, I wish I knew how reality worked... More seriously, my issue with quantum mechanics is that it's incompatible with Einstein's theories. I think that resolving this tension is a good way to make progress. That doesn't mean that I know how to do it.
@@SabineHossenfelder Also, measurement is ill-defined.
@@SabineHossenfelder Yet there is a way to connect them and eliminate many of the current issues in physics; one of course, MUST use existing concepts and never use speculation or 'out of whole cloth' ideas to fix it. Current quantum is correct as is GR. Expressing GR in QM terms, appears rather straight forward if one accepts the basics of Field Theory. So, that is what I am working on (yes, I am a physicist and not playing games in fields I never had training; maybe totally wrong but so far, its working ...time will tell. lol.)
As "not a physicist" I always get a feeling that quantum mechanic (and everything up from it : QCD, QED, etc.) is just a mathematical hack (as in: dodgy workaround). We know it works pretty well and 100 years later we have built an entire system on top of that hack.
Same
Jurden Patterson was the only person who sense
But the undetermined number doesn't changes its state with all other 9 digits. 3:17
When I was in school they told me the square root of -4 was 2i = i=imaginary number. I was like-thats stupid.
If I understood this argument correctly, then there's nothing wrong with asking questions, hypothesizing, and then getting it shot down... That is the scientific process. There is probably some value in questioning the assumptions. Even if it goes down a blind alley, perhaps something new is discovered, even if it is conventional maths that were overlooked.
I have similar ideas about all numbers being truncated in that the way we conceptualize numbers is rooted in set theory.
I think we embed logical fallacies into math by assuming that any thing is a thing. One whole, distinct thing. We created zero, but we created one first and based every other number on the idea of grouping or dividing ones. Zero is just "but what if one... minus one?"
In real life everything happens on a gradient that can be infinitely sliced. The universe doesn't think in things, it thinks in events. There's never a point at which .999999 becomes 1.0000000 without another 1 somewhere at the end. "Whole numbers" are just a matter of convenience in accounting.
In the existing Universe, with the uncertainty principle, exact math or infinite digits really do not make sense. So, they have a point.
He sounds like the people I knew (not me, no, NOT ME) who didn't want to do the homework to get a correct answer in either his math or applied-physics classes, and felt insulted when his professors graded his work appropriately. I have been trained that answers with uncertainty calcs, as appropriate, are really necessary.
I'd suggest he be required to furnish appropriate theory-based uncertainty calculations to show his work is actually useful instead of assigning a 'ghost in the math' hypothesis. You know, asserting that it's QM level effects in the brain cells that 'create' consciousness, which conveniently side steps having to be the systemic analysis of neural networks.
WOW, you actually ended up in the same place I did!! Wrote that Penrose allusion before you got to it in your presenta6tion, so in terms of local time and variables, so I claim local credit for it! Unless you were psychically willing me to converge on your conclusion?!
The only solution for reality and the EPR paradox, is that one of Bell's assumptions is wrong and that is statistcal independence :)
Math frequently comes up with solutions that don't apply to reality.
Like dividing by zero, Schwarzschild
Every flashdrive is evidence that quantum physics works the way we calculate it
Yes physics always comes before maths.... also... the little known fourth law of thermodynamics concerning intensive and extensive properties needs to be used to make the math obey the laws of phyics.... the Sky Scholar you tube channel makes it so so clear
I like maths the way we do it. You know, so that planes fly, boats float etc. etc.
Some mathematicians are using the computer as a model way too much. Don't map everything onto the computer.
I remember a lecture from Feynman who mentioned Babylonian Math and Greek Math, and was a proponent of this very idea. It seems we have physics seems more in the Babylonian phase trying to use Greek Math.
If you go looking for "write-downable" rational math, including trigonometry, on UA-cam, you'll find some interesting stuff
Honestly, his concept seems delusional.
5:45 Yes, and the math is missing some factors.
Jordan Peterson can be like getting hit over the head with a dictionary at times.
Haven’t watched it all the way through but isn’t that why we use Planck’s constant? It’s the fudge factor for all the things we can’t figure out? Or are we not using that anymore?
It feels like we're trying to use digital numbers to represent an analog world.
So my zeros in math at school should be 10 now.
Doesn't his idea also mean there is freewill? Because we can't predict the future until we determine it.
It is not true mathematics is difficult. Because there are only 3 types of people in this world. Those that can count, and those that can't.
How is having to postulate that the present moment is special a problem. Propositions that are deemed to be obvious but not derivable from more fundamental propositions are precisely what postulates are supposed to be.
Quantum physics is an emergent property of Europeans learning Vedic philosophy.
This is actually not surprising at all, in some sense.
Mathematics are just another language. Language is the very substance of *culture*, which dictates certain paradigms and viewpoints. If you want to see things from another culture's point of view, you have to learn the language, because of the memes it conveys.
If you are looking to gain perspective in a useful way that let's you see things from *outside* of the current framework, or better, from a completely different framework, then working strictly within the current paradigm and framing is a sure way to fail.
The fact is, outsider thinking is needed, but the disciplines involved have become an exclusionary priesthood, that very specifically weeds out any such thinking along with those who engage in it, defeating themselves utterly.
I mean, the question of intuition is present in philosophy since early modernity, considerations by Hume and Kant notably about mathematics, this is indeed nothing new and I don't think a platonician conception was necessarily dominant either.
So he actually means digits, as in digits after the (arbitrary) decimal place, not *significant digits* as in numerics?
Maths has been a quite successful problem-solving tool in the past 5000 years it would seem, I wouldn't ditch it too fast...
The fact that there's loss of information in maths means it can never describe the universe.
isn't what we call time just change..we measure time or change in our local standard in reference to time on earth and the sun.. but outside of that context.. time is just a construct.THERE IS JUST CONSTANT CHANGE IN 3 STATES PAST PRESENT AND THE FUTURE. TIME IS JUST A MEASUREMENT..
Anyone who calls it 'Maths" can find a rock to hide under...
Just like engineers, don't get hung up on to many decimal points
I think the argument against real numbers is very strong. However I truly do not see how that has much bearing on quantum mechanics.
computers also do not know nothing about measurements. Binary Digits are just codes in GF2, and sometimes in others GFs. You then with some sort of calibration have to convert it into a some kind of measurement, if the codes are still valid of course
I'm very thankful for having constructs like the Dirac Delta Distribution, or White Noise in the Schwartz Space.. One might not be able to construct them, but they do come up rather "naturally" trying to simplify calculations.
No, they are not of this world, and they are mere fantasy,, I think, but I can start with something "real", use such constructs to ease my calculation, can come out at something "real" again. "Real" meant in the sense that I can relate it to seomething I can perceive in the world. . I can dive underwater, catch a fish, and climb out of the water again. Yes, I was "under the surface" for some ttime, but now I hava a fish I can eat ...
Sounds like a crank.
I think opinion will be divided.
I remember a particular actor saying the same.
something about one plus one is one and what not.
let us just ignore the inconvenient fact all that faulty math's seem to be working so well.
Physicist can hardly be called reliable on mathematical matters. I prefer american actors in all honesty.
The question is, discussions about the meaning of QM are finite or infinite?
I am very interested in how intelligent beings on other worlds explain scientific problems and how their technology developed.