This Physicist Says We’re Using Maths Entirely Wrong
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Intuitionist mathematics is the idea that the entire discipline of maths is a mental construct based on human thought rather than a platonic realm of eternal truths. According to physicist Nicolas Gisin, one of this idea’s biggest proponents, that maths is based on human intuition is the reason why quantum mechanics seems so strange. Let’s take a look.
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Small clarification: in intuitionistic logic, the axiom of the excluded middle is replaced by weaker axioms, and it all amounts to this: given a proposition p, the propositions p, not(p), and not(not(p)) are distinct, but stacking negations further reduces to either not(p) (for an odd number of negations) or to not(not(p)) (for an even amount of negations). Intuitively (pun intended) it all means that the notion of truth is split into two: constructive truth - p, and irrefutable truth - not(not(p)). In this framework, true implies irrefutable but not vice versa. This allows one to track "constructiveness" of proofs explicitly in a consistent way. The classical logic thus **embeds into** intuitionistic logic - by only looking at statements of the form not(p) and not(not(p)).
Now the reason why analysis becomes freaky in this framework is because lots of statements about real numbers that are classically true are merely irrefutable in the new framework. For example, given an arbitrary pair of real numbers x and y (defined as Dedekind cuts), the proposition "not(not(x = y))" means "there's provably no way to prove that x != y", but "x = y" means "here's an algorithm that certifies that each digit of (x - y) is zero". In general, most statements about equality of certain real numbers from analysis (without any degree of precision baked in) are going to be irrefutable but not constructively true. Sheafification of G has a good video on this topic.
There is an entirely new way of conceptualizing analysis that comes from this called smooth infinitesimal analysis. It ditches classic epsilon-delta analysis in favour of constructing a version of real numbers with infinitesimals that are irrefutably zero but still not constructively zero, and then using them to reason about analysis in a way that's arguably closer to the traditional (pre-rigorous) methods of calculus. The upside is that it's very clear conceptually, and it allows algebraic geometers to use their favourite tool of nilpotents in the analytic category :) The downside is that it's entirely incompatible with classical analysis, because none of the results of the smooth infinitesimal analysis survive the passing to the irrefutable (since infinitesimals are irrefutably zero). This is in contrast to the nonstandard analysis, which is very much non-constructive but introduces infinitesimals in a different way that's entirely compatible with classic analysis. I'm not an expert on these topics, but IMO there's little value in this theory for practical applications (because numerical methods aren't going to look any different, and physicists probably don't care about the true/irrefutable distinction in the first place), but others like Terry Tao have found it a useful tool for theory building. FWIW I don't think that quantum uncertainty (coming from non-commuting linear operators) has anything to do with the uncertainty coming from certain important statements about Dedekind cuts being merely irrefutable. This whole thing smells of topos theorists trying to get funding (which isn't a bad thing in the current academic environment), IMO this is taking it too far.
Damn what a mind blowing idea.Showing me new way to learn real numbers that I studied in my graduate studies.Can u refer me where to learn more about this logics? I 😅 know just basic notions of logics and set theory that anyone studies in undergraduate studies.
Physicists who care about reaching a fundamental understanding of neurobiology care, because the distinction between objectively provable and irrefutable is extremely important in any psychologistic system, and has huge downstream consequences, like being able to map cosmological and quantum categories correctly based on whether you know beforehand which conclusions are a result of evolved physiology, and which are so universal as to be regarded as embedded in the laws of nature. If we ultimately fail to distinguish between the laws of nature and phenomena, and we lose a consistent relational viewpoint, then both scientific methodology and the principle of non-contradiction will vanish, and both technology and laws will stagnate and degenerate as they do in all such cultures historically. It is only the ontological separation of phenomena, law, and observer, that resulted in science, and if that collapses into monism again, as it did in every ancient culture, science will necessarily disappear, and magical thinking will become policy again.
@ What in God’s holy name are you blathering about?
@noobyfromhell Contributing to your informative post. Very disrespectful and uniformed reply.
Bro got high and forgot he wrote that 😂@@johannpopper1493
“All models are wrong…but some are useful.”
The question is correct & Answer correct
The question is correct & Answer incorrect
The question is incorrect & Answer correct
The question is incorrect & Answer incorrect 🙂
And the process of building structures that can be used in models _can't_ tell you which model is applicable or what range of situations it will be applicable in (because the same process can build an endless number of logical structures that _won't_ work to model any given situation).
(This is the position that math is neither subjective nor an underlying reality to the universe -- it's effectively the branch of logic that deals with developing logical structures and figuring out their relationships to each other, with the choice of structures and relationships being explored often but not always motivated in part by what may be useful for modeling phenomena in the material world.)
Alternatively, one might say, "All models are of lower than ideal resolution."
Everything flows.
@@Alan-zf2tt Said one Qbit to itself!
Sabine needs to be more intellectually careful since intuitionism/constructivism does utilize real numbers it's just the treatment is different. Constructivism/Intuitionism challenges the classical concept of real numbers as a completed, uncountable infinity, arguing instead that only numbers with explicit constructions or algorithms should exist. This avoids reliance on abstract, non-constructive proofs, like the existence of arbitrary real numbers that can’t be explicitly defined. By focusing on computable reals, constructivism aligns math with concrete processes, ensuring direct applicability to physics, where measurable and finite representations are essential for empirical work. This approach keeps math closer to the physical reality it aims to describe, avoiding metaphysical assumptions about infinite sets or unobservable entities.
Where do transcendental numbers fall in that I wonder? I'm not sure what the intuitionist/constructivist way of building the real numbers is. Also when you say complete do you mean the mathematical definition of complete for metric spaces. Complete with regards to what?
Stop confusing a set of the world with reality. The problem with that is that it falls under the fallacy of begging the question.
@@devinwilliams5960Transcendental numbers can be computable, such as e and pi...
> arguing instead that only numbers with explicit constructions or algorithms should exist
What word "exist" means here? I can argue number 3 "does not exist", since it's just an abstract concept of "three objects".
You can see three objects, so the number is instantiated.
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!
Why not study cosmic rays?
Or a number collider.
Hadrian's Big Colliderscope
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
Maths is based on measure, so this is an excellent use of it..
@@scytobthey are made from a 2"x4" after milling and drying it will be about 1/2" less both dimensions.
Sounds like Robert Frost
Good blocks of beech it was I split
Yeah Imma dork
Perhaps the most fundamental idea of Intuitionistic Mathematics is the rejection of the Law of the Excluded Middle; i.e. the assumption that a statement is either true or false. The Law of the Excluded Middle is used in many proofs by showing that the supposition that a statement is false leads to a contradiction, so that the statement must be true. Intuitionistic Mathematics rejects such proofs. Gisin's ideas about existence -- at least as they are described here -- seem closer to Constructive Mathematics, which insists that proofs of existence must provide a construction for them. For example, an irrational real number should be described by a process for *constructing* the next digit, together with a guarantee that the next digit is correct.
"A remarkable recent development in mathematics is the refounding, on a rigorous basis, of the idea of 'infinitesimal quantity, a notion which, before being supplanted in the nineteenth century by the limit concept, played a seminal role within the calculus and mathematical analysis."
-From the preface to the book A Primer of Infinitesimal Analysis by John L. Bell. In the introduction, Bell gives us good reason to pay 'a certain logical price', and one is 'forced to acknowledge that the so-called law of excluded middle ... cannot be generally affirmed within smooth worlds'. In my view, physics attempts to describe a smooth physical world. I highly recommend this very approachable book to all mathematically inclined people, including physicists.
Bringing us to the alignment & bias challenge...right ? I think.
@@DLCaster I think this is a novel perspective. There is something to having to settle with finite things in the real-world and how finite things tends to engender "roughness". Infinities do tend towards smoothness like taking any limit to infinity of some function, in the grand scheme of things- things do smooth out from a more global view as things extend further and further away from the more local initial run of a function. But there also are some infinities that seem rough at any level, I think there's a kind of fractal that maintains roughness at every level. However, fractals like this are pretty unique, I think one of them is like the Koch Snowflake. I would wager if infinity actually was a thing in the universe it would be something like these rough-at-every-level fractals.
@@DLCaster Thanks. There are so many publications achieving nothing much today that it’s always useful to have an informed recommendation.
Interesting, what I’ve seen that excluded middle used invalidly most is when someone fails to conjecture alternative explanations to the two they claim are the only possibilities. And in my experience, it’s usually the alternative explanation which can be proved that the person says is so absurd it’s not worth considering.
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 is.
Yup
I've never really understood the justification for intuitionism, but your comment helped me figure it out! The law of the excluded middle is perfectly fine in logic, but math is not logic and can't be reduced to it. As Quine said, if you deny the excluded middle you are have just changed the subject from logic to something else. The thing is: Math generally denies it, just not systematically. It invokes it for some proofs, but then forgets about it in other contexts, such as getting around the incompleteness theorem.
It's this inconsistency that intuitionism addresses.
@@darkwingscooter9637There are many flavors of logic. Mahayana Buddhists had 4-state logic millennia ago.
@@darkwingscooter9637 How exactly is math not logic or can't be reduced to it? Every proof I have seen or done boils down to demonstrating that what you want to proof logically follows from axioms or from statements which have previously shown to follow from axioms.
@@murphyslaw3483 Infinite numbers for example are NOT logical. Nothing has ever been measured or observed as infinite so the concept of an infinite value is not logical......yet it's quite common.
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'll refine your criticism: it's that platonism in mathematics, where mathematics is the gold standard instead of computability in most fields, has led to disaster in applied mathematics especially in physics. Economists are using the wrong calculus but at least they understand the problem. I work in the epistemology of universal commensurability and testifiability and so understanding that computability (operationalism, intuitionism, realism, naturalism) has surpassed mathematics as a logical foundation for applied mathematics is a natural consequence of that work. We can (we are working on it) naturalize mathematics rather easily and the discipline would change little other than in basing itself on solid foundations.
I think it could well be that the laws of physics have been written in form of a computer program that simulates reality. If you look at it that way the laws of physics might really seem to be written in the language of mathematics to us, but the aren't. They are just approximated mathematics generated by software.
@@TheNaturalLawInstituteI would disagree that they have “surpassed” platonic mathematics. I think that you can get a decent enough framework for most purposes without recourse to platonic mathematics. However, it is a bit arrogant to assume that it can be done away with entirely, where, what I see as the main justification seems to be “naturalism looks pretty to most scientists and scientismists”, so it is true and should be true in all contexts. I simply find naturalism to be a bit arrogant in general, and it is made doubly so by the supposed “obviousness” of it.
What Gisin seems to be doing in practice is to try to study how different numbering systems affect quantum mechanics. His numbers with known and unknown digits are exactly that - a new number system. Constructivist, sure, but making a new number systems is not a revolution by any means. From the fundamental point of view quantum mechanics just needs a Hilbert space, the question being can we rip off real numbers from it completely. The video of Sabine does not explain what should be the actual profit of all of this.
@@TheNaturalLawInstitute Depends on what you mean by "Platonism". The actual historical Platonism as the ontological and methodological paradigm of Plato''s Academy is quite different from the "Platonism" of Gödel and Penrose, who postulate "timeless being" outside of mind. The Greek ontological term Nous is mental qualia, as is also definition of mathematics as the dianoetic science transmitting between Holistic organic order of Nous and particulars of external sense percepts.
Rather that "surpassing mathematics", computability is taking pure math back to constructivism from the post-Cartesian bumb on the road that messed up many heads.
Computability is of course not restricted to what mechanical von Neuman machines can do, but very much includes also ideal dianoetic computing, without which pixels on a screen don't make any coherent sense.
Sorry Sabine but this is a very shallow reconstruction of what Gisin said. It would be long to explain why in details, it's enough to say right now that the irrationality of real numbers is not the cause of indeterminism, it's connected instead to what a measurement is. Such irrationality could be seen as the power of resolution of the measurement (have a look at the place in 'conversations at Vienna circle' where wittgenstein talks abou pi). And you and the others who underestimate the importance of this debate about intuitionistic and constructive mathematics can maybe have a look at 'mathematical intuitionism' by Posy (who is cited by Gisin) and 'elements of intuitionistic logic' by Dummett. Also the blog of Andrej Bauer can help a lot in terms of understanding why this debate is important in linking constructive math to applied sciences (like Physics).
Hahah, of course its shallow, 316,000 people have seen it. That makes it a brilliant reconstruction. Its a video. It's less than 10 minutes. Does anyone think that Sabine thinks she reconstruct Gisin in 10 minutes. Of course not. The law of the excluded middle is this... there are 50 maths people who agree, 75 maths people who disagree, and 315,875 people in the middle who appreciate the conversations created, her way of presentation, and oh by the way, she is getting rich for it.
@fraugger7583 no doubt she's getting rich, good for her. I just don't find very pleasing to see hundreds of thousands of people getting misinformed and being happy of it. Not all Sabine's content is like that though, that's the point. Even in such a context some consistency across the subjects would be nice.
@@nm800 I didn't find her analogy about logarithms convincing. The issue should track to discrimination, not representation. If she's presenting measurement in a representational mode, she can't be headed in a good direction. She had many of these small lapses in the first months of her channel, and she's been much better since then. I would count this episode as an unfortunate regression.
On the flip side, 315,000 people have now heard of Gisin who hadn't previously known about his work, and no one who is likely to make any actual use of this philosophy will stop here.
Veritasium screwing up how he explained the transmission of electrical energy was a far more severe matter, and that one went out to multiple millions.
You are right, Sabina is wrong about it, and that for someone who tries to solve the measurement problem. With misrepresentation of Gisin she will go nowhere, except making more youtube clips as confusion is a strong motor to make more.
Thanks for the recommendation. This video is the first I’ve seen on intuitionist logic, and it sounds very interesting. I am a bit confused on something though, from the video it sounds like our math for quantum physics is confusing because the math should only be “constructable” once the measurement occurs… and it makes it sound like we can only correctly describe the past with intuitionist math because the future is indeterministic with this kind of logic.
I think I must understand that part wrong, because I don’t think such math would allow for people to make predictions, and making and testing predictions is an important part of science. Also, current quantum mechanics describes the possibility of multiple states already, so it’s “kind of” describing something that isn’t determined yet anyway, so it’s not clear to me from just the information in this video why current quantum mechanics doesn’t follow intuitionist logic.
Fully understanding this probably requires going down a long rabbit hole of math philosophy, but if you’re able to enlightened me a bit on the subject I’d appreciate it.
Terrance Howard just got excited by your title. 🤣
He is going to retweet that 💯
😂😂😂😂😂
HA
The great Terrance!,I thought this was based on his ideas...
Mathematics is not a tool of physics, it is a language for describing ideas. Physicists and engineers use it as if it is a tool that is supposed to serve their ends. Perhaps understanding the ideas represented by a piece of math might go a long way to helping physicists to get some clarity in representing the ideas they are trying to articulate.
There are few mathematicians who believe real numbers are completely unnecessary construction. One of them is N J Wildberger here on TH-cam.
The best we can do with mathematics is much like understanding the engineering of nature's ways around us. Anyone that tries to design things soon find that it is only an estimator of what will likely happen. Too many minute factors can get in the mix to have a real solid answer established. So the inherent diversity of views of what is going that can generate something of a usable results that are of value, if you can find our where they work to do so. [Like, get that cat out of that box as quick and safely possible or it will surely die.] All one is doing with Intuitionist mathematics is noticing an effect and applying that behavior even where it is not readily measurable. When you throw a lot of these together, you might notice that some things that appear illogical on the surface have viable ways of happening. It is just we are not likely going to be able to measure it doing so with a high assurance. Like, where there is notion of virtual space [there is energy there we cannot note that can make unstable virtual particles pop in and our of existence], then there are ways for enough energy to show up and pull off a stunt that doesn't otherwise make sense. Or like perhaps the real reason that combining black holes seem to loose mass is that some of it is getting folded into an area where time is real slow under the combined surface, that otherwise still does emit gravity, and that which is then deeper ceases to be detectable.
Does quanta incorporate the discrete value of number or the absolute? I can give you the count of 10 and arrive at 9, or 10 depending whether the count starts at zero, or at one... if the count must use a real value (eg.the number of apples to buy) doesn't matter. Interval is discrete, so no zero value for the first Apple, or include the possibility of a zero apples origin and start counting from nothing, for if I gain the whole world of apples but lose count what have I truly gained ..something something: physics!
Exactly. Math is anthropocentric, applied formal logic with inspiration drawn from physics, counting, and problems resulting from trying to draw inference given knowledge about physics and counting, and then became very rich due to inspiring itself by trying to find generalizations, searches for esthetics, and trying to find better models for more advanced physical phenomena. For some reason, the exact opposite of this idea is taught in high school and even in higher education; they make it seem like mathematics is a transcendental gift from the Gods and that it's "unreasonably effective" in describing physics. As if it's some sort of coincidence, when the entire point of physics is to formally describe the obvious laws that we can observe and that hold everywhere. It's not "unreasonably effective". It's effective because we did our best to make formal models to succinctly capture the rules we observe in nature.
Not seeing it like that, and seeing it through a platonist lens is a terrible take on it, and disencourages people from really understand what it is and how they should use it, and invent similar useful things.
Mathematics is not a language, its a measuring stick. There is no oral component, there are no sentences or conjugations. You cannot express any idea that pops into your head, it can't be translated into another language. It has no flexibility to be changed by the people who "speak" it on a whim. How would you express envy in mathematics, without using English or other actual language?
The idea that there is a reality independent of human awareness is one of the fundamentals of how the human mind works, and it is not possible to not believe it, though sometimes people mistakenly believe that they don't believe it. Also, the belief that there is a reality independent of what we know directly is one of an interconnected network of various types of finitude that compose human reality and in which we try to live as best as we can.
The best explanation (as an engineer who studied Pure Mathematics) I’ve heard: We live in an analogue world, but attempting to “digitise” this - convert it to mathematics - unless we have an infinite number of bits we will introduce quantisation distortion or errors. If the true meaning of time/matter/life etc exists within the “lost” data, we will never understand it.
If all we have is one bit for our digitisation, Schrödingers cat can only be alive or not - it cannot be unwell, injured or any other state. Just as at one time in our history we only had 4 elements (earth, air, fire & water) until we better understand the practical aspects of sub atomic physics, attempting to digitise (convert) this into mathematical form risks losing important data; without which our understanding becomes (at best) a “good guess”.
Yeah. Analogue continuous directed movement can be "digitized" by a change of direction, and that is sufficient - and what also these electronic machines are actually doing behind the images of "0" and "1".
Numbers as such lose data, they are inherently entropic when compared to computing. With binary alphabet symbolizing arrows of time (and relational operators etc.) we can write number 1/0 as both < and >, 0/1 as concatenation and 0/0 as concatenation >
If all we have is one bit for our digitisation, Schrödingers cat can only be alive or not - it cannot be unwell, injured or any other state."
But isn´t that mixing up contraries with logical contradictions? When we speak about the cat`s life, we only want to express if it lives or does not live. The disease of the cat, the injury of the cat, the happiness of the cat, goes into a whole other direction, which must be expressed anew from the get go.
@@PandaPanda-ud4ne Yeah. It's really just the animistic cat metaphor that has been keeping Schrödinger's metaphor alive.
When we ask the underlying math question by undressing it to the bare mathematical minimum of imaginary "1-bit machine", or temporal analog of closed loop without any input of output, we have the mathematical answer.
No, asking the "state" of a non-interaction is not really a mathematically meaningful question. Closed loop (closed even to the Halting problem!) does not exist in any genuine mathematical sense, and neither does pure either-or as such, except as self-annihilating contradiction.
Contrary oppositions, different story. They are "creative contradictions" that can generate structure from themselves, inside the interval of a contrary. At least when speaking of a temporal contrary. Lets mark arrows of time with < and >. In our contrary analog qubit, time can now move both outwards < > and inwards >
< >
< >
< >
etc.
Let's make it more fun and pose a homework question instead of spilling the goods. How can we interpret the operator language, so that Stern-Brocot type construction of measurement/number theory comes out of it, ie coprime fractions in their order of magnitude?
@@santerisatama5409 *runs way from santerisatama5409, screaming and crying and wiping his nose, trying to put as much distance as he can to the TH-camr´s comment*
@@PandaPanda-ud4ne ???
What is this? The movie version where the protagonist says "I can't handle the truth!"?
If so, PandaPanda is the Yin-Jang Panda in motion and much stronger than the original movie character who could not face the truth but only to project his fear to others.
If so, the moment of recognizing the truth, that behind all the language games, the simple truth that mathematical truth actually exists, is a moment of beauty and courage and hope, with all the terror involved.
Thank you for being, friend!
Thanks!
See Norman Wildberger. He's had this concern about the real number system for years. My favorite of his examples is a particular curve in the x/y plane. I don't remember the functional form right now, but at any rate the point (1, 1) is on that curve. And EVERY other point on that curve has either x or y irrational. So Wildberger notes that if you're asked to supply 1 million points on that curve for a graph or something, you can't do it. Because you can't write the necessary numbers down, or represent them in a computer, or whatever. Not correctly, at least - all you can do is approximate them.
What Wildberger really thinks is that this need for approximation should be more formally recognized in our mathematical reasoning. For example, if you asked me to give you a million points that were within some epsilon of that curve, I could do that just fine, and in theory you could make epsilon as small as you liked - I'd just have to work harder the smaller you made it. It would become a rigorously specified problem, instead of a hand waving business. All of those points would, of course, be RATIONAL numbers, which are the numbers Wildberger regards as "real" (in the sense of reality).
What Wildberger does NOT do, though, is question the utility of mainstream math to science, engineering, and so on. He makes it very clear that his quibbles are strictly theoretical and not germane to most practical applications. So I don't think he would be in this boat of trying to say that our struggles in physics are due to anything mathematical per se.
1:03 he's a Swissysicist
👏🏻
😂😂😂
Einstein also went to university in Zürich
Jesus loves you❤✝️Repent and God bless
The cat is alive until it is dead.
That's what I told my math teacher all the time but he didn't want to listen.
Send him his paper on the topic, lol.
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.
I heard that 4/8 of the people in the world are unable to simplify fractions
LOL!!!😅🤣
@@stefanogandino9192 😉
I love it. I remember my mathematics professor calling me to his office, and he posed urn and similar probability problems. I had never really learned about factorial at that young age, so I worked out verbal algorithms to compute those problems. He showed me factorial and binomial coefficient as symbols for those methods of calculating. But "counting" is not really as simple as what we learn at a very early age. The indeterminism implied in this statement above is beautiful. But there really are fuzzy boundaries between people who can't count, people who can't "count", and people who can nail these problems. And then to truly understand QM, maybe we need another level?
One and one is so much more than two. 😉
Thank you for being so outspoken on these topics. Makes me feel like I'm not taking crazy pills
Intuitionist math reminds me of a Dilbert cartoon where he has to visit the accounting department where the hooded witch-like figures and their trolls explain that numbers don’t merely reflect reality but create it. In order to escape a life of eternal torment in accounting he erases their budget causing them all to vanish.
How considerate of him.
I agree with you, Sabine. I was listening to his theories, and i like the math we have. It's hard to understand because when we see it, it goes against everything we think. But that math explains why it's there, and it's thrilling to even hear it explained.
That's what I said that's probably why everybody thinks I'm crazy,I told you them,That everything doesn't always add up .
Not sure why people still hang on to the "non deterministic" view. Much like (good) encryption, you simply don't know the state of (everything). Worse, unlike (good) encryption, you don't even know what the transformation function is... But just because we don't, and maybe can't, know neither the state nor the function, does that mean we write it off as "non deterministic" instead of just "WE can't determine it"? Did we trade "God of the gaps" for "God of the (nano) gaps"? Are we so full of ourselves that we've reverted to "we can't tell thus it must be non deterministic, there's no way we simply reached OUR limit".
Good point: take your egos out of the discussion!
Simple. Because there's no reason that reality should have been deterministic other than God said so in the Bible. Not exactly a scientific endorsement. And if you can't prove reality is in fact deterministic and have to reference the old testament, it's quite reasonable for an atheist to decide that reality is probably non-deterministic.
@@TysonJensen Objectively wrong. First off, when you zoom out to a more macro level, what do you see? Oh, determinism. Zoom in a bit. Oh, still determinism. Some more. Oh... who would have thought. Still determinism. Until you reach a point where... WE can't determine any more. But, back in the stone age you could determine even less. Then you got better. And better.
That's the "God of the gaps" type argument, attribution to divine power that which we couldn't explain. And the gaps became ever smaller and well... that God is still getting squeezed.
Logic suggests that, if up to a point we have NOT seen non determinism, that would suggest that past that point we should bias towards it STILL being deterministic past it, not the other way around.
The main issue is, if it is deterministic, there's no such thing as free will. You just do what you're supposed to do, just another cog in the machine doing its turn. And that, to most humans, is unthinkable, insufferable. Thus, every chance we get, we kick that can down the road again, which let's us keep humoring the notion that our "fate", while unknown, is neither pre-determined nor inescapable.
p.s. You're wrong about the Bible, as it states the other way around, because of the free will concept. In it, men was given free will, which immediately removes determinism (at that scale), as its mutually exclusive. Events at a macro level could be "foretold", but not the details on how to get there, because there was the (small scale) non determinism, aka free will, to contend with.
Because that is what experiments have led us for now. Sure, there is still the possibility of non local interactions faster than light speed and other workarounds but it is the current simplest explanation: if there is no limitation between options, the universe just chooses one ( or all at the same time in parallel universes)
_"Is Auntie Sabine well?"_
_"I don't know, I haven't seen her in a day or two."_
_"But she could be dead?"_
_"Yes, but she could also be alive."_
_"Let's phone her to find out then."_
Undecidability is not necessarily quantum. When the measurement or decision is made, it is not necessarily persistent. The means of measurement may or may not permit accuracy. But you have to apply the theory or the formula to the real world in order to find out something.
I find the inexorable move from empiricism, to nominalism, to self-refuting attacks on reason, so very interesting.
I don't think mathematics represents reason, so much as it represents coherent communication.
Most reasoning capacity seems to be evolved, rather than learned.
There are reasonable non mathematicians, and unreasonable mathematicians.
Though, the mathematician has an advantage in precise communication.
Now I have to go watch those! Thanks, now I won't get anything done today as I go down yet another rabbit trail!! 😂
A professor once told me, that his institute uses a self-developed version of Pascal, which always outputs two values for each result, and the real value is somewhere in between. The usual single results, he said, are deceptive, because you don't know how many of the given decimal places are actually correct. In extreme cases, all of them can be wrong, and you really have no idea. At that time, I was working as a student on a topic, that involved computationally intensive numerical integration. The number of iterations determined the accuracy of the result, and I couldn't estimate the additional errors the computer makes, e.g. due to rounding errors or calculations with differences of very large numbers with many matching decimals from the starting point. So I decided to run the calculations on different machines and also with the special Pascal that the professor made available to me. It was very enlightening, and I still wonder to this day, why you can even do physics and engineering without doing this.
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.
This could explain why my drummer's concept of a 4 beat bar seems to be different to the generally accepted norm. He's not a bad drummer, he's just using his own maths.
No, I suspect he's a bad drummer. Unless you enjoy playing with him.
Great one. Would never hear about this stuff without this show. The exponential thing comes up in computer science, you have this situation where you need need to get b from a*10^20 + b*10^-15 - a*10^20, but b has disappeared in the floating point arithmetic. I think this guy is asking the right questions in terms of finite information and quantization. When you really into fast code, like for games, its about realizing the output is gonna be in this quantized space of 0-255 color values. Once you do that, you see that, the solutions aren't well defined. for instance, look at Fast Inverse Square root algorithm, just some slop that outputs the right math faster than inverse square root within a quantization limit. In physics that translates to situations where the "wrong" math can always output the right answers within limits of quantum observation.
just because it's called a "real" number doesn't mean it's any more real than imaginary one, it's just a name and mathemathicians are just as bad at naming things as regular scientists
" it's just a name"
With a meaning. Imaginary numbers cannot be expressed on a number line from minus infinity to plus infinity. Real numbers can be located on a number line.
@@thomasmaughan4798 think about it...
SO WHAT
number - no matter what kind - is still the same kind of abstract thing as every other one
worse even - it's just as abstract as every other thing in math
@@Cashman9111 They're not equally abstract at all. Can you give me $i?
@@gw7624 I can't give you $(1/3) either. Or $0.005 for that matter.
@@gw7624 can you give me $π?
It kind of makes sense to me. In a computer, the accuracy of a value is based on the size of the data. The larger the value with variations, the more space required to store it. When space is limited, the number is an approximation of the real number but not the real number itself. Without an infinite amount of space, or an infinitely accurate way to measure, the number stored are never going to be fully accurate or "real". Maths itself may not be the problem, but the ability to measure and store that information is. The best example I can think of is Pi. There is no way to store it accurately as it has not been fully measured. Then humans make mathematical models based on not real measurements but approximation (excluding absolutes), when the output is an approximation with less accuracy than the inputs. This is then tested to prove the model works with some level of accuracy or inaccuracy. The output can never be the "real" number because the inputs were not "real".
That's like saying circles aren't 'real' because all material manifestations of circles are imperfect. Which is true in a narrow definitional sense but not in reality. Material circles and triangles have the same properties you would expect them to have based on their Platonic ideals.
Essentially the difference between Pi accurate to 30 decimal places and Pi accurate to infinite decimal places is negligible for almost all applications. We still use our approximations to build bridges and send rockets throughout the solar system without inaccurate results.
@@langov3 You would then have to prove that a material manifestation of a circle was perfect to an infinite measurement and also represent that which is impossible. I agree that approximations are acceptable. The problem starts when you create a model based on a relationship between an input and an output value. If the accuracy of those values cannot be infinite, then a created model is susceptible to that accuracy. At that point the model becomes best fit based on available input and output data over a dataset. Overall, it's not maths that is the problem though. It's not "human intuition" either as A.I. training data generates complicated mathematical models that are "best fit". Maybe there is a missing property on data like adding an extra dimension. Going from just value and units, and adding accuracy to that.
Do the digits of Pi beyond the boundary of a Plank length have any relevance for our Universe? Should Pi calculated for resolutions far beyond a Plank Length have any relevance in our Universe? It is irrelevant.
The same applies for the fractals of the Mandelbrot set or the bifurcation diagram, or other infinities. Any resolution of calculation beyond the Plank's Length make little sense in our Universe.
@@taedian9346 My point was that there are no perfect manifestations of circles or spheres but the imperfect manifestations we do have share the same properties as their gometric ideals.
A triangle with sides equal to 1m and a tolerance of 1cm will not be weaker than one with a tolerance of 1x0^-15mm and will not manifest novel properties at different accuracies. In the same way we shouldn't have to calcualte Pi to infininte decimal places to enable us to do quantum physics. 34 decimal places should be enough.
I wouldn't describe models as best fit either. An AI uses a dataset of accurate results to reference against its outputs whereas a mathematical model uses a dataset and a theory to make a prediction. An Ai can generate results but it's solution will be inscruitable. A mathematical model IS the solutiion wich generates a result,
Greater levels of accuracy are only relevant for chaotic models
@@langov3 AI uses a dataset to train with which creates a mathematical model. It's that mathematical model that is used to take inputs and generate outputs. Some of the internal output stages can be used to feedback into earlier stages to adjust how the model behaves. It doesn't use the dataset once it is trained. New input data is presented to it to give an output.
Now the term "accurate results" used as input comes back to data only being accurate to a certain level. I've already stated that we cannot measure values to infinite accuracy or store them with infinite accuracy. So any data is only accurate to a certain level. If someone determines that data isn't accurate when creating a mathematical model because it doesn't fit their expectations, then isn't that intuition?
This reminds me of a joke: Engineer thinks his formulas are approximation of reality, physicist believes reality is approximation of his formulas, and mathematician does not care.
Pi has entered the chat.
The reason I don’t understand Jordan Peterson is because I spend most of my time looking up the words he says in the dictionary.
I live when Sabine brings the hammer down on theories and papers
When I write the equation, special case of Euler's pearl, e^(i*Pi) = -1, this is only exactly true when Pi = Pi, not an approximation to Pi. Further, when one write Pi as an infinite series, this is equivalent to telling someone that you can always find the next term in the series, and the math for this is very neat as discovered by Newton, a generalization of the binomial theorem.
If one wants rigor in Calculus, Weierstrauss is good enough for me with his for every epsilon, there exists a delta. I think this is entirely standard math from the 1800's; so are Gauss and Riemann.
Also, after Godel and especially Turing, we know that any mathematical system is inadequate and incomplete. I like the Law of the Excluded Middle, used in reductio ad absurdum proofs, but if you find a place where this does not work, you have found something very valuable. Or as Ralph Waldo Emerson said earlier (1850's): "There is a crack in everything God made."
Also, the equation above, with e, i, and Pi is only exactly correct when e = e, and not an approximation to e.
Also, everything that includes Pi is just an approximation.
Like... everything with a curvature...
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"...
Right, I don't understand how it is non-deterministic when it is literally always the same, it is determined . . . what am I missing?
@@AndroidPoetry unobsorved does not seem to be equal to undetermined. While pi has all the digits it has, we don't know all of them. Yet, they are not determined by observation, but uncovered. Numbers do not live in a quantum state, imho.
the next digit "will be" what it "is"
You refer to it in a present tense and a future tense in order to define it. That seems questionable
Digits are abstract, so if we don't know what a digit is and thereby we can't think of it, then how can it already exist?
Ur defining a digit right after defining it as undefinable.
@@AndroidPoetry......that Mathematics is not a Science
@@buckets3628 The point is that there are no probability associated with the "next digit" problem if it always result the same next digit regardless of computational method or device. Equavating it with super position is like saying apples are kinda oranges, sure we can find some common property but equivalance is not shown rigorously.
It only could ever work this way if you can also prove that the randomness of QM is not inherent (which I belive Sabines view anyway) but simply our way to handle our ignorance about the system, using math. As far as I know that is not excatly the mainstreamm interpretation of quantum "randomness".
We could do quantum mechanics using z=a+ib, where a and b are rational numbers instead of real numbers.
Alternatively, we can continue using real numbers, acknowledging that they inherently involve infinities without any direct physical meaning. Indubitably, a real number can be seen as a ratio of infinities: r=∞/∞.
Yeah, that sounds good until you actually learn something about numbers in middle school. ;-)
At 0:10, _"I don't know about you, but I quite like my maths the traditional way, well-done."_ -- it's among the best math quips ever. :) Brilliant!
I like it medium rare.
@@GiovannaIwishyou i would say the proper term is median rare!!
No not brilliant.
@@NathanDean79 yeah, forgive us non-native low-threshold newborns :).
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.
What's "really real" is a matter of pointless pseudo-philosophy. Pi is definable in an abstract way, it has absolutely nothing to do with real physical space and circles in it. We don't need to compute its digits to work with it. In fact, its list of digits is probably the least interesting and important thing about it.
@Math-Phys-Space "Solve for x = 1+2+3+ ... " Almost everyone would say, "x = infinity" but it does not. Infinity is not a number therefore an invalid use of the equal sign. I've seen non-mathematicians argue and argue that it does. (There are some good videos on TH-cam explaining this in detail.)
Are you simply stipulating that infinity is not a number or is that the result of some calculation (asks the non-mathematician)?
It isn't unusual to see physicists arguing things like inf-1=inf
Or 1/inf=0
but maybe they are misbehaving?@@douglaswilkinson5700
The definition of existence is ambiguous.
If there are too many didgets for me to count, it doesn't exist.
I'll definitely be explaining this to my math teacher...
If he doesn't understand this intuitively, I'll have to tell him maths isn't for him.
@0:50 Sabine, you need to clean your room, carry daily the heaviest object you can carry around, and then become an improbable monster. Only after you've slain the dragon of your fears atd metamorphosed into an eternally improving existentiality will you be able to understand Peterson, LOL
She should delete her math books while she's at it. Because the math's wrong lol
The guy has saved hundreds of thousands if not millions of individuals from themselves, also improved a lot of young men's lives which were in need of attention since the past 10 years the left have been doing nothing but shitting on them.
How odd, my high school math teacher also said I was using math wrong. Perhaps I'm a physicist in drag?
"New Math" ~ Tom Lehrer
My teacher in university used the following example: "The quadrillionth digit of pi is a 1". Most people would say the statement is either true or false, we just don't know which of the two. An intuitionist would say that that statement has no truth value, until we have a definitive proof showing which of the two it is.
But everyone I talked to that actually worked with intuitionist mathematics had a much more pragmatic view: they viewed it as useful for type theory, and proof assistants like Coq, and they didn't necessarily care about the philosophical implications all that much.
The answer to your maths teacher is that maths (as in fundamatal behavior of the universe) has a value for the quadrillionth digit of pi but the maths (as in communicated human statements) has no value for the quadrillionth digit of pi.
That is similar to my own position: not all aspects of a mathematical theory can be treated as "real" unless it has actually been _realized_ in some physical _context._ For example, in special relativity you define a reference frame based simply on coordinates, but it is impossible to actually confirm the predictions of special relativity unless you actually have a physical object located at those coordinates, and so you could only actually assign ontological reality to reference frames which have objects at their center and would have to treat the other kinds of reference frames as purely metaphysical despite being parts of the theory, because there is no real _context_ in which they could be _realized._ Adopting this position actually allows you to interpret quantum mechanics in local and philosophically realist terms (similar to Rovelli's solution in his paper "Relational EPR"). Similarly, we shouldn't treat the quadrillionth digit of pi as _real_ unless you can conceive of some sort of real-world context whereby it wold actually have relevance.
This discussion is beautiful
I am glad to have discovered it. Too beautiful for words really. Relativism abounds wherever humanity exists. And does that imply functional realism?
@@Alan-zf2tt Functional realism seems very similar to contextual realism. Both are attempts to revive direct realism by taking relativity/relationalism/contextualism into account. These views seem to be rather fringe for some reason, but I've never seen good argument against them.
@@amihartz I used functional realism in a sorta math sense.
There is an event
it has am initial frame of reference (domain/pre-image)
It has a destination frame of reference (codomain..range/image)
And something happens that is generally predictable but not very accurately so
I accept your comment that these are similar.
Maybe "functional" in math sense and "contextual" sense in general.
A topologist might assert these are equivalent? It is the same beast but in a different jungle
I’ve been saying for years the issue is how physicists do the math, but my argument has been from a different angle.
I’m currently pursuing my PhD in mathematics and in my time in academia have come across a handful of physicists and physics students. One glaring thing as a mathematician in training is the amount of approximating that happens. That’s ok, I get it, when working with a model you have to balance the amount of detail it captures with the ability to actually analyze the model and obtain something useful. What strikes me is how many in the physics departments seem to either willfully ignore or are just plain ignorant to the possibility that these approximations may lead to a cumulative error in certain contexts. The math physicists do just has to be “good enough” to describe whatever they are observing. They tend to then take the discrepancies across descriptions and models to be an indication of something in need of a new theory, rather than it possibly being due to a cumulative error of comparing models that are inherently just approximations of what we observe.
You just described a cowboy ,,, in the building trades a person who does a job that looks done but in reality has mistakes in it
The total error can't be more than the product of total errors (and often is just the sum of errors). If a deviation is seen greater than the total errors, the hypothesis is disproven (p=0). 1st year physicists know this; its not a matter of them misunderstanding mathematics.
Dealing with error margins and uncertainty is fundamental to physics.
@thebeesnuts777 I had a 4x4 deck post that was rotten, so I bought another. Strangely, when in place, the deck rails didn't reach it. Turns out it was 3.5x3.5. The timber vendor claimed that the wood had shrunk in drying. I said maybe that tree wasn't big enough so the sawyer just moved the blades a bit: but in any case, it wasn't a 4x4. I was advised to "shim it", or buy new deck rails. Theory vs reality. Computation vs observation.
@@rustybayonet Nowadays, all “4x4” are actually 3.5”x3.5”.
The theory about mathematics not being abstract, is well studied and explained by Dr C K Raju in his classic work "Cultural Foundation of Mathematics". It took me a long while to understand him, but now it makes complete sense. The reason we have baloney paradox such as Banak Tarski sphere, is precisely because of this "pure" math. Anyone interested should definitely read his book.
3:51 thank you for letting cat live 😭
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
@@violetquinnlawVets tend to reserve these philosophical points until after the owner has paid the bill.
The number of digits needed IS defined - naturally one can take any result and compress it down to the same fixed length of digits, no matter what way it’s written. It’s not the actual digits, it’s the information in them…
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. Granted, in weaker logics it can be tricky to figure out the "correct" generalizations of classical results, but the amazing fact is that these generalizations exist at all. 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.
We need close observation of black holes. Will you go? ;-)
It is a good point you make! Math has it's own Darwinian tree of evolution. But did math exist only to be discovered OR did it only appear once it had been invented?
@Alan-zf2tt Why did the quaternion cross the product? ;-)
@@williambranch4283 The fact that math helps to model reality is miraculous and long may it be so.
But does this mean math has great insight bearing in mind that some pure math becomes applied math after a century or so.
@Alan-zf2tt Famously, British mathematician Hardy said, his field of number theory would never be useful ;-)
Very interesting and surprising discussion.
Theoretical Physicist: If you try to reach a pretty girl standing nearby by taking each step 1/2 as long as the previous step, you'll never be able to reach her. Lowly Engineer: I can get close enough.
Management Expert:
Neither of you will reach the pretty girl. I just made one leap and took her with me. 😎
@@Prof-Joe-H 😄
Epsilon trauma unlocked.
A salesman; has an apple cart. He starts with 4 apples. He adds 4x as many apples, as he started with. 4x4. He now has 16 apples.
A sneaky kid steals 4 apples. His sneaky friends join in, stealing a total of 4 times as many. -4 x -4 = - 16 apples. The result is NOT 16!
Me as a kid: Teacher, math is wrong. I'm not. Don't tell me about integers, or about "concepts" or whatever you're going to say to say this is correct.
I can prove I'm right, by moving apples around on a table. He marks me wrong, and says "I'm right" by drawing numbers on a paper.
"Oh but, multiplying a negative takes us further back towards positive-" YEAH ON YOUR IMAGINARY LINE!
Math - should reflect reality. Math, should be a way we interact with, and describe, real events, objects, and things. Reality.
I don't give a **** what that means for your integers, or theoretical crap.
When I reached Geometry - teacher, I'm sorry, there's no such thing as infinity. Neat idea. But since it doesn't exist, why are we talking about it? Oh, so there's supposed to be a line, with zero in the center, and it goes with positive numbers infinitely to the left, and negative, infinitely to the right. Sorry - the only line that can exist with no end - is a circle. (Or a shape where the line connects back to itself.) Reality. I can prove that. I can make you a line without end. I can draw geometric shapes!
But the teacher puts his mythical, imaginary and cute idea of a line, with zero in the center, on a chalkboard, with infinity symbols on each end. Nice IMAGINARY thing!
I think the problem with math is it's designed to reflect things that are not real, cannot be real, and will never be real.
"But you don't understand, negative numbers are not supposed to mean negative objects!"
Then why do I give a **** about them, son? Sounds like something that doesn't exist.
Why on God's green earth DON'T negative numbers represent the absence or loss of REAL things?
Edit: And before you start arguing with me - read the last sentence again. I GET what negative numbers are SUPPOSED to be. I challenge that very notion.
I say, negative numbers should reflect LOSS or ABSENCE of real things. The imaginary line of positive/negative numbers is JUST THAT. So we shouldn't give a damn about moving integers around on it.
First, math has always started with the Conjecture where the Proof or dis-proof follows after much work. In this way, all math is grounded in human intuition. However, all this stuff about not using Real numbers is ludicrous. That's like saying you can't talk about what you are thinking because thoughts don't exist in physical reality. Math is a language for describing relationships (between things real, things imagined or just relationship's in general). It's always human constructed, but what it describes is not. The relationships are part of shared reality, but the language is made up. The problem that people get tangled up in is treating the structure of the math as a necessity to the relationship it describes, but we can only describe what we experience (physically and mentally) and our math only applies to our experience. There are relationships which will never pop out of our math because we haven't noticed them yet, or haven't found a way to describe them in a formal system. And, any formal system are only ever partial descriptions of anything (e.g., Gödel and Turing).
Well, yes; but relationships between what and what? And if we 'don't really need to know' the answer to that, what are we talking about? This is a nontrivial question.
@@davidwright8432 Relationships between anything and anything. Language is always an abstraction. Math describes relationships not things.
I'm not convinced that time physically exists. How is time not an explainable illusion with motion alone?
First define "exists" and "illusion" in a falsifiable manner then you will likely have an answer, or at least a better question.
"Time is an illusion. Lunchtime doubly so." - Douglas Adams.
"Reality is merely an illusion, albeit a very persistent one." - Albert Einstein
Motion requires time. Time is changes of state. Motion is a change of position, thus can't happen without time.
We have the time which is day morning, afternoon and night and repeat the same cycle. As far as clocks, month and year are concerned then it is creation just to get the idea not real.
@@Hazara26 there's time, and measurement of time. Both are called time, but you're talking about the latter.
LOL. What you do with the example of the Schrödinger Cat, and the logical mistake you always do in quantum physics, is to use a Stochastic Proxy Observer . Instead of observing the cat, which you can't , so you observe the proxy observer, which tells you "to me, it could be dead or alive, 50% of chance". This is the reaction of quantum physics to the principle of indetermination: since the phenomena is too small for being observed, then let's put a Stochastic Proxy Observer, which is computing some probability, and then observe the proxy observer, until we can open the box, and see the cat. Then, we switch from the proxy observer to observing the actual thing. We don't know where the particle is, precisely? No problem. Put a proxy observer and observe the proxy: the proxy will tell us "look, the particle could be here or there, no idea, same chance". And now this is the state of information of the proxy. But, at a certain point, we observe the particle, just because now we can, and we say : entanglement!! Entanglement!!!", where actually we should say "we stopped to observe the proxy stochastic observer, and now we start observing the particle".
I like maths the way we do it. You know, so that planes fly, boats float etc. etc.
Then you like constructive maths.
Would you have said this before Newton & Leibniz invented the differential?
Put another way: Yes, but the warp-drive doesn't.
Where is your sense of adventure?
Math doesn't make boats float or planes fly. Math just tries to measure their functions
@ Maths allows us to design boats and planes. And pretty much everything else. Without the maths, which works, nothing else would. The age of Trial & Error, or build by experience, passed a very long time ago. I assume you know this.
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.
As an undergraduate I made an effort to learn mathematics (was one or two classes short of a double major). When I talk to my fellow phizBroz they think they know math... they don't even know what they don't know... same thing about physics with my mathbroZ... very silly. Then there's the comp Sci ppl who don't understand how to CALCULATE and the numerical physicists that don't know how to computer... especially when "boltzmann" machining....finally there's the engineers who know that I'd it doesn't work when you set sin = 0 and cos = 1... then it's probably a bad idea to build it.
I like this blouse better than the pink and gray.
I was kind of liking the woman ranting in a pink shirt😂
We should start using colliders to launch numbers at each other..
I’d pay to see that.
CERN
Even the smallest of children can use and understand 1/3, butit has an infinite string of nonzero digits.
A fraction really doesn't have an infinite string of digits. "Decimal numbers" don't really exist in pure mathematics, because coherent arithmetic can't be defined for them.
Trust the smallest of children, not dishonest language games of dishonest adults hypnotized and desensitized by imaginary ownership of numbers called "money".
Constructive/intuitionistic logic is more rigorous than standard math, for this reason it is used by computer languages for writing math proofs, like agda
It's not more rigorous, it's just a more expressive language. Proof assistants can use any formal langauge whatsoever, but people usually use type theory because it's a language with good computational properties. You can always get classical mathematics out of it by adding the law of excluded middle and the rest of the fluff as additional axioms.
@@AlexanderShamov I argue that it is more rigorous. I think the most rigorous theory of math is automata theory. Because you have to determine explicitly the behavior of every object you are working with, all the possible states. I want a body of mathematics that has the same property.
@@joaquincapellancruz7402 wouldn't Turing machines be more rigorous and expressive than automatons?
@therealjezzyc6209 Every finite computation can be modeled by some finite automata. Turing machines have infinite memory. Same issue.
@@AlexanderShamov by 'more rigorous' I mean 'a tad more rigorous' - in constructive mathematics a distinction is made (between constructive and non-constructive proofs), where in classical mathematics it is "neglected", but I agree that otherwise everything is the same. My point is that constructivism is not some kind of weird idea, as portrayed by the video
The mess at the foundations of physics is probably rooted in the mess at the foundations on Mathematics
The phanton of Gödel! 👻👻
There is no "mess" at the foundations of physics. The "measurement problem" was solved by decoherence. Sabine's "rebuttal" to this is that "decoherence doesn't explain why we observe one outcome rather than another!" That is just complaining about nondeterminism. Why should we expect the outcomes of experiments to have explanations for why we observe one outcome rather than another? Maybe it's just random. As Bohr said, "stop telling God what to do." Sabine thinks there is a "mess at the foundations of physics" only because she is a strict determinist.
@@amihartz humm... good point...🤔🤔
To be fair, that actually depends on what the definition of the word "is" is.
@@logangodofcandy yeah … what is an object …. I like category theory reasoning … although I think it still needs further maturity
Also the fact that so many paradoxes or deeply unintuitive results actually derive from the reals in some way
Imagine math is your fav subject and after 12/13 years of school you fail horribly at university studying mathematics (were 2 years studying) and then later watch a 3min video about the imaginary unit on TH-cam (after having eaten liver) and are like "yea that's ez af", but it's the first time sb ever told you "it's like a rotation of 90° of a number, like imagine how it can be negative - that's 180 degree, the opposite direction, but it can also be 90° (like pushed into or pulled outside) the layer of observation, that's 'i' plus a value of how much".
Yea sure, makes sense. NOOOO W8 OMG! NOW THIS ACTUALLY MAKES SENSE.
W8... WHY DIDN'T I GET THE WHEN GOING TO UNIVERSITY FOR 2 YEARS?! WHY DID I NOW GET IT IN 3MIN?!
They using/teaching math wrong.
Now check this out: you the type of nerd that trys to know 4d shapes of 3d shadows (that's possibly also just a way of knowing karmic laws in time too)?
Well that imaginary unit "it's... just precise 3d" not 4d, that's actually nothing hard.
It's just what a computers graphics card and processor calculates when opening a game like Minecraft.
But doing this as a human feels like being a slave.
Dude every 4-6 year old with a pc knows how he can move in Minecraft and starts building his world with placing individual blocks, why you gotta do express yourself so weirdly with the imaginary unit like it's really complicated?!
It's NOT, it's just 3D that is not even 4D.
However current usage of mathematics like we learn it in university is like "the system of symbols that are used are so overcomplicated... In order to write down all the blocks that 4yo has placed in his 1h old world, it would take you 5 lifetimes with the imaginary unit notation and explaination expressed in university math talk terms".
See where I'm going here? You start a system of learning to precisely calculate things, but your usage of that language itself has the effect of everything you come up with and imagine outruns inside of your thoughts and imagination or inside of the computers game physics, everything you could ever write down on a piece of paper.
You putting then a pen down on a piece of paper making use of thee math terms with imaginary unit is kinda identical to signing that you lost against Infinity "as if you were verifying how a b*llet penetrates your brain" that you were never able to outrun/dodge or avoid, cos... You played that game.
Now try to see the big picture: the 20yo(s) stop playing Minecraft and it takes the 4yo(s) 16 years to reach that point and the first day he started playing it were actually 3 or 5h and not just 1.
But 1h is alrdy 5 lifetimes worth of calculations on paper, just to keep up.
Now express all of one persons 16years worth of multiple worlds on paper in "imaginary unit notation terms" in how many human lifetimes?
And I didn't even take into account redstone mechanics (which are ez, diagrams too), but they then also need to be linked to the blocks and grids and chunks on paper with "i" too.
See nobody cares.
Why? Because the brain and information interface with a pen and paper and the current mathematical expression may in some senses like "minecraft worlds" be alrdy outshined by a monitor, mouse and keyboard and headset, and that's just one of many.
Elon Musk's NeuraLink Brain implant might be fixing exactly that problem.
And then you can think of sth and just "beam it to the pc or sb else", now we don't need "complicated i - terminology anymore", however...
Lot's of things might still be "chasing sb else's idea", when you wanna do your own.
Hehe
5:20 Gisin mistakes ðe Bivalence Principle, which indeed fails, wið ðe LEM, which obviously holds. How many make ðat simple mix-up! 😞
Gisin is correct, in as much as he points out that 'accuracy' of our mathematical models when presented in reality can ultimately only be as precise as the data we can feed them. In the case of the real world, that also means how complete are the values we can actually feed it etc. I.e. we can represent the relationship between the diameter and circumference of a circle, but we cannot represent that with complete accuracy. So in reality, mathematical formulae are an expression of notional relationships which 'would be' completely predictive 'if' we could feed them with complete and perfectly defined values - and crucially we have no choice but to accept that. In reality they are more like recipe's which one can show are ideal with quantised value input, but the outcome depends completely on what actually goes into the mix..
So in effect the mathematics and formula are actually 'statements of belief' in relationships between 'factors of reality' which 'would apply' if we had complete representation of the data to the n'th degree of accuracy. We can prove the notional math with more notional math and forcibly quantised and notional values - and how the outcomes are entirely correct and indeed become laws. But at the limit, that does not mean we can verify it all with actual real world data, particularly when we enter the vagaries and random properties of the vanishingly small and largely statistical quantum world.
So as you rightly point out, the risk is that developing mathematics itself in isolation to represent the unresolved world at the quantum level, can end up at the limit with as much random formulae (and thus theories) as there are uncertainties in the quantum world itself. This means that we naturally end up with multiple and often incompatible 'math' theories for various proposed 'realities' - where none of them can ultimately be proven to represent a complete solution. I have no idea how it could be otherwise - I mean what other choice do we have?
Sounds more like philosophy than physics
Plausible, if you remember that Brouwer found much to admire in Kant.
It is philosophy and not physics. It is philosophy of maths, though, and I for one (like many) agree with Gisin. However, how does this translate into maths application to physics is a totally different matter. There I disagree with Gisin. But I am not a pro in these matters.
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 accept 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.
Maybe some proof of it, but the concept definitely does not.
@@joaquincapellancruz7402 I don't understand what you are saying. What is "it" and what concept?
@@svenglueckspilz8177 "It" refers to the equivalence between EM and the finite subset theorem.
@@joaquincapellancruz7402 So you are saying even if there is a correct proof that LEM and the finite subset statement are equivalent, they are still not equivalent?
@svenglueckspilz8177 A correct proof in which system? The theorem of finite subsets is valid in constructive mathematics, which rejects LEM. In fact, in classical mathematics (Set theory+classical logic) you can proof TFS independently of LEM. Look for it.
As I understand this, mathematics is a model of something, including virtual reality (i.e. your computer games). The fun math puzzle of a hotel with infinite rooms and "How do you place people?" is a 'Linked List' in computer science: The link list has a linear search function (decent, not the best) and a horrible sorting function (don't use Bubble Sort). Moreover, math is used for difficult problems by adding to the rules, such as Virtual Numbers (i.e. e^j = 1 + j). Mathematics have the power of modeling our reality and our dreams, so we get better answers, that is all it can do. Mathematicians know how to make anything difficult; I want to go back to high school and memorize my algebra and trigonometry books with all their rules: I went for years believing that dividing by zero meant 'infinity' was the answer, when the true answer is 'undefined'.
Mathematics is not a model. It's an abstract extrapolation. We find five stones on the beach and we learn to count them. Then we count a bag full of rice and it's boring like heck. We say "F it!" and postulate that no matter how big the sack would be, we could always assign a number to its contents. THAT is how math is born. At some point you just give up looking at the real world and you say to yourself that you have enough evidence to just go with a simple rule. The intuitionist, however, goes one step further and says that "We don't know unless we do.". The little problem with that is that every time we do, we find that the intuitionist was just a drunken guy who was full of it and we could have saved us a lot of work because nature ALWAYS gives the result that ordinary logic predicts. In other words, that drunken a-hole made us run around for nothing. ;-)
@@lepidoptera9337 Mathematics is neither a model nor an abstract extrapolation. We can do mathematics perfectly well - and even better - without postulating any "mathematical objects".
Mathematics is empirical science based on empirical methods of intuition and constructibility. Source of intuition is the whole that is present in each part. Intuition alone is not sufficient for scientific truth, we need also contructibility for proofs by demonstration that can be verified by peer-review by fellow sentient beings.
Biggest issue with a purely constructivist mathematics is that it does not allow for proof by contradiction, which is used for many results such as there being infinitely many prime numbers. Perhaps there may be an infinite subset of the prime numbers that can be enumerated somehow, but I’d rather just accept the law of excluded middle and save the trouble.
The prime number thing is just one example, but there are other foundational results that, to our knowledge, require contradiction, such as the Hahn-Banach Theorem, Baire Category Theorem, or the uncountability of the reals.
Edit: I see now from one of the replies that I misunderstood constructivism. You can still use proof by contradiction, but only in settings where a sufficient condition for double negation elimination can be proven. This does in fact hold in the case of proving there are infinitely many primes (where the proof involves constructing a new “prime” number under the assumption that there are finitely many primes).
If you can't practically factor large integers into two primes, does it matter how many primes there are?
@@williambranch4283 yes it does, its a core result to mathematics. most of mathematics do at least implicitely rely on that.
@snack711 Aristotle and law of excluded middle? Depends on context. There are cases where a binary result is the only possibility, but this isn't true in all cases. Sometimes the coin lands on edge ;-)
@@williambranch4283🗿
This is not true. Constructive mathematics does use proof by contradiction. This is a common misconception. There are in fact two kinds of proof by contradiction. The first one is "assume p, reach contradiction, therefore not p". This is constructively valid. What is also constructively valid is "assume not p, reach contradiction, therefore not not p". What is not constructively valid is to then prove p from not not p because double negation elimination does not hold constructively in all cases (this is the classical proof by contradiction). So long as you can prove double negation elimination for your particular proposition then you can use contradition in any direction. If you can't then you can only use contradiction in one direction, so to speak. In particular, if you can prove "P or not P" for a given proposition P then "not not P implies P" is also true constructively hence both proof techniques are equivalent.
The proof that there are infinitely many primes is actually constructive. Given any finite set of primes you can literally construct a larger prime from following the reasoning in the damn proof.
Furthermore, for numbers the law of excluded middle does hold, this is because constructivists typically take "m=n or m≠n" to be true because both m=n and m≠n are decidable in finite time for integers and rationals. So all number theoretic results are perfectly constructive because they are algorithmic.
As a computer science graduate whose primary interation with mathanatical proofs has been through proof assistants, which typically are based on intuitionistic type theories, I definitely have a preferance towards constructive mathematics. I rarely need to assume the law of excluded middle to prove anything I care about, and think the nice computation properties are more valueable, so we should avoid it for most use cases. For example, if you avoid the LEM, a proof of existence immediately gives you the value that exists, which is really nice. How much we need computability to consider the universe, I have no clue, but I think computability is the more practical thing to keep. (Though as CS guy, that is certainly because I like programming and computation) I do want to note note that LEM (forall P, P or not P) is logically consistent with most type theories, it just doesn't have a computational meaning, so if your proof really relies on it, you can assume LEM and get classical mathematics as the result.
Freewill is how cold butter looks at a knife. Freewill is also how a cold knife looks at hot butter💀
@4:00 nope? The "act of measurement" makes the superposition _in the model_ "go away". But the superposition was never really physically there in the first place, except for entanglement structure. The whole Cat is never in superposition, only the elementary particles can be in effective superposition by virtue of monogamous entanglement (and there is a _realist_ gravitational model for that, ER=EPR). You should also check out Jacob Barandes' framework for QM, it is "radically conservative" but clearly shows that superpositions and Hilbert space are _convenient_ fictions, and what is base marble is something like entanglement. Barandes does not know what this "entanglement" is physically/ontologically, but his non-Markov transition matrix formalism clearly establishes what superposition of macroscopic objects *_does not have to be taken literally._*
> The whole Cat is never in superposition, only the elementary particles can be in effective superposition
This has proven to be false. Systems much larger than an elementary particles were put in a superposition. IIRC someone did that with a fullerene molecule.
Besides, Schrödinger created the tale to highlight the core difficulty in QM: it cannot be restricted to fundamental particles, as it is possible to create a macroscopic system that depends on microscopic outcomes. This is the purpose of the radioactive decay in the cat experiment @denysvlasenko1865
This sounds like a philosopher pretending to be a physicist. But what do I know? Maybe I'm not real either or my math hasn't come into being yet.
Great movie.
Oh Sabine is already starting hot:" I like my Maths the traditional way ....well done." You know this video is going to be good.
The problem Gisin has raised goes much further: real numbers describing position or time demand that every point in space or time contain infinite information, which is either impossible or necessitates totally different cosmology.
Yes, in particular, in order for a particle to contain infinite information of its position and momentum it would require infinite energy to store it.
Does it though?
Why couldn't a real number be just one information?
@@mathieuaurousseau100 Do you mean by "one information" an answer to a "yes or no" question, a binary 1 or 0?
If you point to an arbitrary point in space and use a unit that produces a real number as an answer, trouble ensues.
simplest example, you pointed to a point in space and say "from me to this point is now 1 unit of length". So you can now define a square with a side of 1, fine. But the diagonal of that square is square root of 2 and THE UNIVERSE IS NOT BIG ENOUGH TO ENCODE ALL THE DIGITS OF THIS NUMBER IF YOU USE 1 ATOM PER DIGIT. Unless we assume that the universe is spatially infinite, but even then you already used up 1 universe to write 1 number. What about π?
@@mentalitydesignvideo Why do I need to be able to encode all the digits of this number? I encode it as sqrt(2).
@@mentalitydesignvideo Either way assuming a continuous universe doesn't lead to infinite entropy, and therefore it doesn't require an infinite amount of information
Sounds like pure sophistry... which is a fancy word for clever bullshit
There's a big difference between 40 and infinity. infinity is incalculable, but I've calculated to more than 40 DP many times.
Example would be the halting problem, who's "solution" requires an instance of infinity. So this would suggest that we shouldn't put any value in the output of that thought experiment because it requires "using maths that isn't real"... and I agree...
A couple of years ago, I conceptualized the Observer Calculus which shows standard Real Numbers can't complete the continuum.
That both the continuous and discrete cannot be reconciled.
There is no value exactly almost zero.
No such value exists.
There is no end to an unending line.
And a line (curved or straight) is not a collection of points as sometimes referenced.
There simply is no "every"...an abstract version of Thesseus' Ship.
And the Observer Calculus points to physical space-time (not only in the mathematical realm) as being truly continuous and not purely discrete.
The concept starts out by proving (1/2)^n cannot converge to zero and .999... is not exactly equal to 1.
One of the notions is abandoning the concept of infinity as some ultimate value, and instead, replacing that concept with the idea of "never". Never arriving.
And so, if Zeno, never finishes that famous garden walk of nested halves, then how do any of us cross the road, short of asking the chicken?
Smooth (un-evaluated) continuous pushes across an interval.
The moment we stop to check the value. There it sits as if it always existed there, some eternal flag, its shadow waving under a never-setting yet ever-moving sun.
< creation | annihilation >
Reminiscent of that familiar cat-in-the-box.
The moment a gap exists between any two points unending divisibility exists...and the moment they touch...zero divisibility exists.
The gap cannot be bridged both discretely and continuously simultaneously.
Like some moments flash that must remain ever hidden from our perifral view.
I call this this the threshold of the Observer.
What do you mean by "can't complete the continuum"?
The idea that a value approaches infinity, or zero (1/infinity) (asymptote) and just filling in the gap without proof, comes from the fact that for practical purposes, accepting a little error, it works! Take for example a transformer. one could use the same thing as a voltage transformer, or as a current transformer. Both calculations are different, but theoretically the same, IF no details are left out. but in practicality they are simplified, and therefore the correct one has to be used. Lets say you divide a current bij 1000 with a 1:1000 turn ratio. it would be impractical to measure an sufficiently accurate voltage across the 1 primary turn, but the current model works. Could is be that in mathematics, for these cases there is also another (undiscovered) model that has no infinite value / asymptote?
@@d.j.wiendels6572 yes, sort of "undiscovered". I developed the concept after a heated debate over .999... and 1.
So the idea of an asymptote. Some value approaching division by zero.
The value in the denominator will not reach zero, without a deformation. In other words, simply making the value zero. Not discretely and continuously simultaneously.
A value cannot "approach" infinity. Every arbitrary large value (even values too large to write down ) don't "approach" infinity.
We can say "As the value grows without bounds." Or "As the value gets arbitrarily large. "
But (1/n )^p cannot converge to zero.
Regardless of the size of p or n.
We can say it "tends towards" zero as n, p "tends towards" infinity.
But changing the viewpoint of infinity to the concept of "never ending" or "unbounded" gives a better overall picture.
@@m3bmuadib a line is not a collection of points. Rather it can be "a collection" of subintervals with > 0 lengths. But there is no "the collection" of subintervals.
There is no "every".
Much like Thesseus' ship.
Notice how this has started us on that "slippery slope" towards possible randomness needed for quantum processes. At least where the position of some particle is concerned in continuous real-time
Even with my surface level understanding of maths, number theory calls out
Normal mathematics uses things like the law of excluded middle to do proof by negation and this is one of the issues, and why they want to have only constructed objects
Because a lot of unintuitive objects can be constructed by proof by negation
In logic some people solve paradoxes by using paraconsistent logic that don’t explode when you have contradictions, so it’s not necessarily crazy to get rid of law of excluded middle
So you might at least expect that if you are going to produce non intuitive results you should at least be able to do it relying on only other axioms that are less contentious potentially
I like math raw. With some onions, salt and pepper as a Mathbrötchen.
Crystal Maths...
That's like saying PI doesn't equal PI until all digits have been calculated. But PI can be written with just one symbol and it equals exactly PI.
I'm sure this has been studied and I am not a mathematician but: surely we could device a math system where irrational numbers can be worked with with infinite precision, say instead of saying 1.41159... we write, IDK, say SQRT(2) and computer could implement this.
Pi tells us things about circles. But do circles exist in the real world?
The Pi symbol is just like infinity symbol. A cheat, that bears no resemblance to anything in reality. It's imaginary. The only time it will ever be relevant, is when you're calculating something that exists, or you can build, in reality. Going too far into the calculation with numbers is meaningless. (Like building an anchor chain so long it's longer than the deepest part of the ocean.)
Math should reflect reality. Currently, it reflects fantasy and imaginary concepts. (Like straight lines without end.) Sorry, infinity doesn't exist. Stop cheating, and you'll get real results. (I like how pi keeps going. It represents, to me, that circles can keep expanding, and keep getting larger. But, there's no point in continuing that number past something that can physically exist, or we can build.)
@daanschone1548 not until you measure one with exact precision
@@slo3337 exactly. Plato did believe perfect mathematical shapes do exist, but we can only see imperfections with our minds. I think that is a fantasy.
Sounds like something I would say to a maths teacher in school. Real numbers do not exist, have you ever seen one?
The maths tries to be elegant, not correct.
0:41 Except everyone can make sense of Jordan Peterson...
Jordan Paterson can't make sense of Jordan Paterson
Except... nope. Even Jordan Peterson has a hard time making sense of himself... hence how he constantly misses the point of discussion, contradicts himself often, says meaningless phrases or is ambivalent to leave wiggle room so that later he can say "that's not what I said"... and of course hecan't answer a simple question sensibly because when people challenge him on his statements he can interpret what he said to suit the situation.
😂😂😂😂😂😂
Excellent video. This type of more philosophical discussion of maths and science stimulates the mind.
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Does the guy know that squirrels compute in order to leap from post to post? Physical systems implement computation during interactions. Penrose may be thinking that the persona, of Marilyn Monroe, would be not computable, it being a qualia like the color red. A qualia is not computable because it is complicated to describe mathematically. The color red can't be described by words or math. These are too complex for anyone to compute which doesn't mean they're not computable by the brain? Computing is arriving at some information by starting with some other information.
Yes but ultimately the words are arranged so that other humans may read part if they wish and discard then move on to something else if the human wished to.
Rest of known world does not seem bothered too much and a bookworm might wonder how well the words tasted|?
Red is a wave length, wave lengths are computable.
@@denism4227 who will compute them on surface of the sun or center of sun?
@@denism4227 tastes, sounds and colors are qualia computed by brains.
Intuitionist astronomy: All the small moons of Jupiter and Saturn did not exist until we found them.
6:09 Intuitionist Maths is
Ramanujan Mathemathics
The Professor " But I hadn't completed that proof ... How did you know ?"
Srinivasa " I dont know , I just do. "
( lines from the mivie )
He is referred to as Ramanujan, never "Srinivasa"
@no-one-in-particular somewhere in time, he was no one in particular ; just like when Albert was a clerk.
@@TheStudioManila What are you talking about? Srinivasa is a patrynomic, it's not a "first name". Indian names are different, Ramanujan is the given name, and he should be referred to as such.
The Professor :
Srinivasa :
Is there any tie in to Gödel’s incompleteness theorem? There are limits on logic and limi5s on math?
No. The theorem merely states that second order logic is strictly more powerful than first order logic and that, in particular, there exist theories formulated in second order logic that have no formulation in first order logic equivalent to the second order theory. The "complete" part means that every theorem in the second order theory should be provable in the corresponding first order theory, and the "consistent" part means that every theorem valid in the corresponding first order theory should be valid in the second order theory. Peano's axiomatization for arithmetic (which consists of 4 first-order axioms and a second-order axiom) is the key case in point discussed by Gödel Theorem.
In later years, Gödel and many others forayed into higher order logic, trying to establish tractible axiomatizations for large useful subsets thereof. The two that Gödel developed were Dialectica and System T. There are lots of higher order logic formalisms now (in addition to those that Gödel laid out), many of which can be arrayed into The Lambda Cube. Martin-Löf's stands out, and it's used as a core of one of the validation systems: Coq. Hindley-Milner, which lives lower on the Lambda Cube, is another well-known higher order logic that is also the basis of C++'s template-based type-checking system. There are even theorem provers, now, for higher-order logic - most of them are AI-based.
Gödel's second theorem is that there is no complete and consistent formulation of higher order logic - at least not one formulated in first order logic. (Curiously, it makes no similar blanket statement about higher order logic formulations of higher order logic, except for the case of the formulation of such a logic within itself.) This was partly what motivated Gödel's excursion into higher order logic.
Every theory formulated in first-order logic can be reformulated, equivalently, as an algebra; if necessary, by adding a "boolean" type and converting predicates into boolean-valued operators. An example is an affine geometry, A, over a field, F (of size > 3), which can be written as a ternary algebra, with a single operator: a,f,b ∈ A×F×A ↦ [a,f,b] ∈ A, with the following axioms: [a,0,b] = a, [a,1,b] = b and [a,rt(1-t),[b,s,c]] = [[a,rt(1-s),b],t,[a,rs(1-t),c]]. So, in reality: a first-order theory is just a fancy name for an "algebra" and "first-order logic" = "algebra".
Theories that are formulated on higher-order logic have at least one "transcendential" axiom that goes beyond algebra. The archetype is calculus, with the relevant axiom being The Axiom Of Completeness for the underlying real number system. Other higher-order theories may, likewise, be called "calculii"; an example being the Lambda Calculus (the beta rule is a higher-order axiom and the substitution operation referred to by the beta rule is intrinsically a higher-order concept). You might even consider the higher arithmetic / number theory as "Diophantine Calculus". So, in essence: the main statement of Gödel's theorem is that Calculus Transcends Algebra.
You just said, "we cannot measure anything to infinite precision", very true. Does this mean that we will never be able to measure anything related to, in what we call Quantum Physics?
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TIL that mathematicians can have even crazier theories than physicists.
Crazier?
We, math people, are not bound to measure anything with cumbersome instruments. Our theories are fine, not crazy.
Renormalization or collapsing waves all over, those are crazy.
One of my greatest realization was tha tthere are things than cannot be known, measurements that can't be taken, proofs that can't be solved. Many more things can, but there are a "stubborn" sub-set that can not.
As somebody heavily influenced from the philosophy of Nietzsche I agree with the idea that there are no eternal ideas AKA "true world" beside ours