Steven Weinberg - Is Mathematics Invented or Discovered? 

It's when he gets into God then it becomes frustrating - very biased towards Christianity & seems totally clueless that other religions exist Never asks these religious people uncomfortable questions - stops being a Journalist and becomes a biased believer Questions like: 1. What does one DO In Heaven? Any work? Why would an all-powerful being need to get any work done? Which means billions of people are just sitting about doing nothing, an idle, lazy, useless and pointless existence for eternity! And that is why he does not ask such questions

Yes, indeed!!!

He's an old white dodecaphobe.

Anything that starts out with a frame isn't good when you get to this guy's level. Words trap us, words aren't true, really- because we can call something by a different name and not realize we're talking about the same thing. You have to open up

not all questions are practical questions. In actuality, he didn't answer the question, likely because he has no answer, or isn't philosophically equipped to do so.

It's certainly not possible for conscious, well-organized, intelligent people to pontificate over the meaning of mathematics without a coherent, orderly Universe which one exists in. Regularities are necessary to have a whole and mathematics is, indeed, a study of coherent absolutes and regularity.

Same here. Listening to this interview, I found myself thinking how wonderful it would be to learn physics from him!

Principles that guide mathematics are not mathematics

exactly

quantities describe sets, and sets are invented. KEvron

But discovered first.

@@KEvronista no sets exist in nature.

@@ursulagwozdz1955 nature is the only place sets may exist. learn to read, dunce. KEvron

proteusx, your comment suggests you will not be doing anything useful for humanity.

@End_Sensorship sure, but philosophy isn't a science, and I was only referring to scientific methods. what do you mean by "positive"

@End_Sensorship Thank you for saying this. Rare though it is someone sees this dualistic dynamo over the tip of the iceberg science that others declare is all there is, who when they discover more along the way further incorporate it but pretend each new increase is the new all there is. I deplore such dismissiveness as that. Those are are the sort of minds who uphold some immaculate conception of birth whereas in reality its a competition for zygote formation with only a few victors with extinction of one's potential kindred at conception. The same minds who focus only on the visible spectrum's ongoings as if nothing else happened...Hopefully you won't mind me perusing your channel's liked videos to look for corresponding impetus.

@End_Sensorship I'm also very critical of philosophy. Why? Essential because of 4 things (I will outline 3 - the last one needs a long explanation): 1. I see no non-trivial result about anything. And philosophy is a very old discipline. It should have produced something non-trivial. But it didn't. For every scientific discipline I'm interested in, I can name several non-trivial statements. From philosophy none. And I'm interested in philosophy in the sense that I'm interested in philosophical questions. 2. Some statements (like the impossibility of infinite regress) are wrong. But they circulate around as valid arguments. 3. Philosophy plays with words. It is not precise enough for a deeper discussion. It seems to me it is a rhetorical rather than knowledge building discipline. More learning an argumentative strategy. And that is for me the difference between "philosophy of possible worlds" and mathematics. Mathematics is precise in the description of the worlds. Philosophy is not. And over the years many sciences emancipated from philosophy. And I think it is because of 3. And 1 and 2 is a practical consequence of that which enabled that emancipation. I know philosophers which are scientifically literate and can contribute to science. And I know philosophers who are trying to be precise and work in parts like ethics which is not yet emancipated. But they are critical of today's philosophy. Especially 3. Philosophy claims to strengthen critical thinking. But I often see the contrary aspects. Rhetorical arguments and misrepresentations of science (especially QM). ps: Your positive-negative description is for me of that rhetorical kind. In the first part positive is the descriptive part instead of the thing itself. In the last part negative parts are the aspects of reality science has not have had a interest in yet (or split into different disciplines). What you mean is perhaps (?) "positive" in the sense of *positivism* . The only thing one could object to positivism is if one has a strange definition of the scientific method or reality (rhetorical misrepresentations). The precise formulation of the scientific method is proven (mathematically) to be the best reality approximating strategy without presuppositions. pps: Mathematics is not build on set theory (ZFC). It is only the basis of most subdisciplines.

@@guineapig55555 I agree with you. ps: And there is a reason for the effectiveness of mathematics. And it is ingrained into the scientific method. The best (mathematically proven) strategy to approximate the truth is by collecting enough data (...) and finding the simplest model consistent with this data (Ockham's razor). Simplicity in the sense of easily describable (Kolmogorov complexity). But that means that one has to calculate the high number of consequences of a scientific model by a low number of describing assumptions. That is especially what mathematics does (the science of structures or simple models). What remains is why mathematics arrived there before physics. I'm not convinced that this is the case. Rather physics and mathematics stimulate one another. And then it is natural that sometimes one is ahead of the other. Today physics is ahead. Mathematics does not know how to formalize the standard model. And the analysis of pseudo-Riemannian manifolds is rudimentary. Newton needed calculus way before it was formalized. So physics is ahead sometimes. And sometimes mathematics. Hilbert spaces and Lie groups were introduced because of physical reasons by mathematics to understand the equations of physics better. And sometimes (like in this case) the simpler descriptions are more robust to changes (classical -> quantum).

@@tofu-munchingCoalition.ofChaos I don't know about any of the types of logic you listed there, but I think that in the end it mostly reduces to semantics, like many things in life. What is the true delineation between physics, math, statistics, and logic? If math is The overarching explanation for everything, then wouldn't it make more sense to simply characterize it as "Logic"? At what point does Logic "devolve" into math and physics? At what point does physics devolve into statistics, or the other way around? Maybe I was wrong, and math, physics, and statistics are all intertwined into one complex logic of multiverses. I dunno

This is neither math nor physics question . It is not even philosophy . It is religion

I believe you cannot over estimate the importance of Mathematics. If I had to judge, and of course I'm swimming in deep water, I sould say that Dirac and Roger Penrose are more accurate than Weinberg. If one has to chose between Nobel Prize winners that is.

@Pedro Miguel de Almeida Areias expand please.

@@SandraWantsCoke what?

I like the way you put it. The world doesn't look anything like mathematics, it can be described with that language, but in some ways a spoken language fits better. There is a deeper "language" underlying all of this that we aren't capable of understanding let alone have any access to yet. A few billion years of AI should fix that. Whether there will be any biological component to consciousness then is...immaterial...but then nothing was material in the first place.

@Taqifsha Nanen your as sincere as a dog pissing on a carpet. We seek truth, not to be rude. This question is 2500 years old, with A LOT of valid points on both sides. If you had the answer why not write a massive book about it and call out all nominalists, formalists, fictonalism and semi platonists. I mean you have the answer right?

Whats your major?

@@michaelking8391 Aerospace Engineering with a minor in math.

Absolutely! And I'm a humanities prof, not a scientist.

The characters of Verne never put a foot on Moon, no footprint.

@@massecl exactly, thats the actual point.

One analogy to this that I thought of is when you build a building with legos. You can describe the building mathematically if you know the parts used to make it, but without the knowledge that you are using legos then your math is meaningless. The mathematics only describe the interaction between the parts, it only makes sense if you have something non-mathematical (an idea about an object and knowledge of how it works) before you can make sense of it mathematically. But you cannot describe the legos themselves mathematically - unless you can break them up into parts (such as atoms), the point being that if there is a smallest building block and you can't break it up any further, then your math becomes useless. Because fundamentally you are only describing interaction when you use mathematics, and that only works if you are talking about distinct parts of something.

+John Doe Bravo, John Doe! I had not thought of that before. Yes, that seems right on....all math operators are verbs that describe action upon nouns, or objects. Once the smallest object is in hand there are no verbs available to define it further. All the verbs that may define what the object can do will have already been known in the process of identifying that basic building block. But...if the verbs are energy and the nouns are matter then if a particle can convert to energy then I don't know what to do..does that math become verbs operating on verbs or nouns operating on verbs?

Math is an abstract generalization of the empirical (real) world. Nobody has ever seen a perfect circle. The sun and moon were real world inspirations for the concept of a circle. The "invention" of PI as a constant, is only possible because our generalization (circles) of what is physically real (sun and moon) carries certain consistencies. In other words, because we consistently define circles as being perfectly round, the constant of Pi can emerged. Circles and Pi are not part of some platonic truth that we don't have physical access to, but only part of an invented model of the universe around us. Mathematical abstractions are ultimately rooted in the empirical world, and the empirical activity of mixing elements together, and then imagining what happens in and between. Essentially what an artist does on canvas, mathematicians do in their mind, and instead of with paint, with numbers, lines, circles, and other abstract figures.

Ztech Hi! If I may opine, anything said about the empirical world is "a posteriori", meaning details that are added to Platonic concepts. The Platonic concepts are the templates into which sense datum must fit in order to come into consciousness. Datum that does not fit templates seems confusing, like the double slit experiements, or else it could be that we never even become conscious of who knows what. Friedrich Nietzsche even commented (parapharasing): "that a deaf man, who was allowed to see Chladni's sound-vibration sculptures on plates of glass and metal, and who was given an education in wave propagation and mixing, would still not know what sound is." However if he was a good student he would be able to do the maths and talk all about sonic vibrations with Platonic certainty. For that man, the empirical observation of sound is not possible. You wrote: "Mathematical abstractions are ultimately rooted in the empirical world, and the empirical activity of mixing elements together, and then imagining what happens in and between. " Even if one accepted the first half of that sentence, the second half can't be said to be empirical, rather it is Platonic. Immanuel Kant said:"Thoughts without content are empty, intuitions without concepts are blind."

rh001YT "Even if one accepted the first half of that sentence, the second half can't be said to be empirical, rather it is Platonic" Yes, I tend to agree. And as you seem to imply, some have considered our freedom to select and arrange objects, part of our ability to "reason", as opposed to being an empirical process. For example, in cognitive science, the heurisitic-analytical theory reasoning was put forth in the late 70's, and more recently, Mental model theory. Plato himself believed in the value of thought experiments, and it is rather impossible to do a productive thought experiment, without free selection.

Yep. 'There are lies, damned lies, and statistics'. - Or maybe we should be saying, 'statisticians and the opportunists who use them' ;-)

@Leo Juan This is obviously phishing dude. There are no password hackers in real life because encryption exists. These sites likely just steal data by key logging or directing you to fake sites

Mathematics is hammered into us by nature. It's just as much an invention as a discovery. Or as Sagan put it: The exploration of the cosmos is a journey of self discovery.

Doesn't that apply to EVERYTHING? We can't even invent something that is not in nature, can we? How about poetry - they are using words that are already there

dude youre so right happy idiots ignorance is bliss smart people can struggle too smart for their own good smarties can drive their self crazy i totally agree w you

But these smart minds are what lead to the progress of humanity and better the society!

Why? What did you hear in this discussion of mathematics and its role in physics that you felt is conduce to war and other kinds of destructive or aggressive behaviours?

So do I

yes i agree, axioms and rules of deduction are invented to deal with the platonic forms

+LegendLength +Ran Shoham In math, the question is invented, the answer is dicovered. What i mean is this: Let us ask what is relation between sides of triangle? The answer depends on what you mean by triangle and you say, it is closed geometrical object created by 3 different straight lines. Now what is straight line? And how is this object created? In what kind of space? Is it continuous space, or discrete? And on and on you go. Basicly, you must define all the information you need to get the answer. In this case, there are 5 informations - 5 euclid postulates. Those are invented and then answer is hidden somewhere in them, you need to find it. Without those five postulates, you wont get pythagorean theorem, f.e. without fifth euclidean theorem you get lobachevsky geometry that is quite different from the euclidean, high school one and the answer will be different - there is no pythagorean theorem in lobachevsky geometry. Another thing might be considered to be discovered is what kind of postulates actually work together, i.e. what kind of postulates you can postulate so that they are consistent with each other. F.e. you cannot postulate that fifth euclidean postulated doesnt hold and at the same time first four euclidean postulates hold and also the pythagorean theorem. These kind of "input" informations wont work together. So you are inventing questions and then you need to discover wheter the question makes sense, and then you need to discover the answer. But because not every question is permitted, in certain sense you can say whole math is just discovery - you are discovering which questions makes sense, you are not just randomly inventing them. But thats actually job of every inventor - the guy who invented car also needed to discover something that works, he didnt just put it randomly together as he wished. I think the whole confusion is linquistic and not really very fundamental. Discovering something should mean, that it is there somewhere and you just need to find it out (am i right?). But what is that "there"? When you seek the answer you are seeking it in the question. The question is the "there". When you are seeking which questions make sense, you are seeking through the world of all possible ideas. This is the "there", but it is other world from the first one. And if you seeking new species of frogs, you are looking in the jungle. That is the "there" which is again very different from the first two. So it all depends from what kind of world you are asking the question wheter postulates of mathematics (i.e. input informations) are discovered or invented. Personally, i think whole controversy is simply because different people ask the question from the position of different world.

@@michalmaixner3318 Good explanation. I agree. It is only a rhetorical/linguistic problem. The mathematical question is discovered (interpreting "there" the right way) and invented (in some weak creative but limited sense) and the answer is discovered but has a very similar weak but creative component (how the actual proof works - which is also limited) to it.

The questions are in the interview and answered so, I think you mean the question in the video title which seems a bit sloppy.

@Chipmunk Assuming you're talking about formulas that relate physical quantities, the problem is that any such formula is a model. The accuracy with which any model predicts is dependent on its assumptions and they always turn out to be insufficient as better models are inevitably invented. Your comment reminds me of a painting I once saw. A big circle roughly drawn with a thick brush in black ink. There was a statement written next to it, "I am arguably a perfect circle". For at least the artist who painted the circle, he saw perfection which I think is just as legitimate as the "truths" we find in mathematics.

+DP ie Most modern day mathematicians believe that math is invented, clearly as does Weinberg in this clip.

+DP ie - I agree with Tegmark. I believe the universe is made up of mathematical objects. There's nothing special about that, it's just the way things are. Maybe a non-mathematical universe could exist, but what it would be like seems hard to imagine.

Ponder, Could you be an algorithm inside math witnessing all the relative different algorithms such as particles and space ? If someone was to look inside into the universe from the outside would they just see all possible math axioms rather than objects...

Math is invented as much as any structure is invented over chaos and time. Such things eventually harmonize and as a byproduct of our own sentience, we are able to successfully formalize a description of the nature of the world around us. Math doesn't perfectly represent the nature of reality however. There is always a bit of noise that corrupts the end state but math is a beautiful approximate and we may grow closer to the truth as time goes on. Or at least, I hope so.

@@xit1254 how many possible dimensions would exist there? It is hard to imagine any existence without dimensional form.Therefore a world without maths is unimaginable.

afaik, he first speak about the guys experience that there are no beautiful explanations for this part of physics. then he went on with the beauty thing. useful in this case means useful as in an explanation. ofc its useful when you calculate the aerodynamics but useful as in understanding you need beautiful math because that shows us the math works and is properly built

+Jeff Harper I give you an example: Einsteins special relativity has 2 postulates - constancy of speed of light (c) and principle of relativity. From this it follows that there is time dilatation: t´=t/Sqrt(1-v^2/c^2) On the other hand, you might not know about these postulates but some observations will force you to admit, there is some time dilatation. Then you need to work out some model that works to required accuracy, because you need it to solve some technical issiues. So let us seek the answer as power series: t´=a*t+b*t^2+c*t^3+d*t^4+... where a, b, c, d and all the rest are constants, that are supposed to be determined by experiment. Now, you dont know wheter those are true constants, perhaps they depend on where exactly in the space you are, so they perhaps depend on space coordinates. Also, perhaps they will depend on temperature, who knows? You need to determine all this by experiments. In the end, you will find those constants dependent only on the speed of light and speed of the "spaceship" or whatever. But you dont know why and you wasted a lot of funds doing experiments to determine this. Obviously this is no explanation and it predicts very little with a lot of input from experiments. You dont want this kind of model in fundamental science. Luckily, we are rewarded for seeking better exlanations by actually finding them. The einsteins explanation is much more beautiful just two postulates and everything follows! You almost dont even need any experiment to fix the theory. Nature is good to us:) Now, why in plasma physics the simple model is probably wrong is because the system itself is very complicated. So much can happen when all those particles interact and it in fact does happen. On the other hand, how much can happen when you scatter one particle of the other and just probe the fundamental nature of interection of just these two particles? The system is very simple, so the answer should be simple. If the system is complicated (like plasma, or, god forbid, living organisms) the answer is most probably complicated too.

Are there 2 people in the video? Isn't that certain?

I slightly disagree only in the sense that it is a tool created in reality that is able to precisely measure itself therefore it has to be as any tool is bound by the laws that allow it to measure anything in the first place. If our observable universe doesn't allow a tool for reading inside a black hole because it's outside of our observable universe then there is no tool to make within observational value to us about that inside and Mathematics has observational value that is defined to it by our observations of either our universe or the mathematics our universe allows

George Thomas : Mathematics is Deductive, by virtue of which, allows for certainty, but does not Of Itself say anything about phenomenal reality. By contrast, knowledge of phenomenal reality (science), is Inductive, by virtue of which, can only attain at best a degree of probability, and therefore can not attain certainty, even as expressed in the language of mathematics. The quote wasn’t referring to counting, but instead epistemology.

His talk has gone over your head. And to answer your question, it's invented

@@unholy1771 well no because the interviewer has asked the question of other people. The others actually answered the question. Here there was no answer. The conclusion is we dream of beautiful math. What does that even mean? The others fairly clearly stated their position. The other physicist said math is discovered and the mathematician that created the company Wolfram Alpha and the product mathematica say invented. The tally I have so far is 1-1 with one Pat Buchanan. I am a computer programmer and thus a scientist that primarily uses math for my job. I can tell you math itself is only discovered.

but they talked about beauty, hopes and dreams, those ones are some solid scientific arguments. .. no, wait.

@@Falkdr yeah, no. Maybe @Steve Jobs would know this if he listened to what was said and used the principle of science to evaluate what was said. But, I am saying that even with beauty, hope, and dreams, those are an answer to some question, but they are not even bad answers to the question is math invented or discovered. Those are non answers to the question.

I agree. Only the term 'believe' was lacking to make it pseudo science. Dr. Sabine Hossenfelder wrote a whole book about beauty in physics ('Lost in Math') and how it is distracting from the scientific method.

You almost sound like Plato right there :)

I don't agree. The constant pi has always been there. We gave the shape of the sun and moon a name, circle, but we didn't come up with the shape. That is impossible. Therefore, pi has always been there. As a matter of fact most equations that are not circle have pi in it. The constant pi has a way bigger role in mathematics than you think. It be really hard for to explain pi outside of just circles, but look up videos. I only know because I'm in college and next semester I'll be taking calculus 3

Granted that we have never had an experience of a perfect circle or a perfect square; it does not mean that Mathematics is necessarily rooted in experience. If Mathematics was an empirical practice then we would have to refer to reality to find proofs of its theorems or propositions; since we do not it is clear that Mathematics is closer to Logic than empirical reality and hence closer to the faculty of pure reason than to experience, per se. It is important to distinguish between the origin of an idea and the content of the idea; some feature of reality may lead to the formation of an idea, but that does not mean that the idea itself conforms to reality. On another note; your hypothesis is very well suited to explaining the origin of geometrical intuition; but I doubt it can apply to Algebra or number theory; for it is difficult to see the feature of reality of which the integer is a perfect model; if the word perfect can be applied at all.

I wonder if he studied the more abstract mathematics involved leagues above physics. Algebraic Topology, for instance, rarely (if ever) finds application in the physical sciences.

@@SandraWantsCoke He'll have to use braille?

Beauty to me means something that leaves us in awe, surprise, or delight. But that probably is subject to vary if you come from a different background. What you don't know will seem beautiful, or what wraps different ideas that seem useful to you will seem beautiful. If there is a point of convergence for all or most people that we would reach, given enough time, to agree on what beautiful is, or what truth is, or how to describe things and the world, is unknown by me. And even if we did, it would not necessarily mean it is true, possibly. Only that our ideas converge there. So I am not sure how useful this talk of Beauty is. What could happen, is that people use this word, Beauty, to refer to properties of equations or of thinking, that we can't quite express with words, eg: very well defined, concrete, etc, but we just don't know the exact words for it. However, a Mathematician could know what another Mathematician means when talking about Beauty, because we sometimes pick up patterns, that we can't put into words. So one person started the bubble and does certain things and calls it Beauty, and another can pick up what the first one probably means by Beauty, even if the first didn't put into words what he was implying by Beauty. So we use words sometimes to refer to abstractions of the word that would be worded into many words. For example, love is such a broad concept: Where is the limit to consider something love, or what is the minimum? Is it love assessed by the giver, and if they care, or by the actions, if they fit our views of caring and loving, and what actions are included? The way I see it is we do some processing but doesn't always get to consciousness, even if we want to access how we evaluated something, and why we labeled it as Beautiful, or Love, consciousness doesn't get to access it: That kind of hints me that we are viewers of the world, rather than taking action ourselves (by ourselves, mean consciousness)

The Lagrangians are perhaps not elegant. But the principles from which one derives the Lagrangians are elegant. It's like the explicit formula for the mathematical pendulum. This formula is ugly. But the differential equation it is based on is not. Many beautiful equations in differential geometry become ugly if one wants to explicitly calculate something. This is very similar. The Lagrangian of the four forces is ugly because it is expressed in such a way one can start to calculate things.

@@carnap355 completely disagree, it was a discovery within the scope of the initial rules.

Nice, I like your interpretation

or Barney the purple dinosaur

You've not understood at all. He's not saying the physical content of the theory has been anticipated by the mathematics in which the theory is ultimately expressed.