"It's checkable in the small" is a fantastic quote with respect to the huge mathematical edifices we've built

Utterly admirable that she admits that proofs can be pretty much true, not absolutely true.

Good interview

This was great

Does anyone know where I can get that proof of multiplication and simplification that Dr. Kuhn is referring to?

@Evan490BC

4 жыл бұрын

It's probably this: hal.archives-ouvertes.fr/hal-02070778/document

@NewCalculus

3 жыл бұрын

I have no idea what she was babbling about nor do I care. However, if you want to understand the arithmetic operations, you need me because only I understand: kzread.info/dash/bejne/n5Oco8qDZNOan9Y.html

I see some comments above about how math is useless, and I want to say there is something in mathematic pernicious. For example, endless "abstractionization" (or obsessive-compulsive disorder for **extreme clearness**) People always do something with great passion and obsession that eventually turns out to be completely useless(maybe decades later). To avoid it, one must know what is really the target. For me, it is the mathematic phenomenon based on what reality gives us(geometry, number, function)rather than a literal game on the concept. If we can reveal all this wonder in reality without using the mathematic symbols, then we do not need it. Similarly, if we can use symbols perfectly without giving it definition, then we don't need definition. Tell me, does anybody care about the "stark clear" definition of the matrix and the binary operation of it? Maybe we need another Peano here. Do you want to be one wasting all your life on that stark definition?

It is always so odd to me how hostile people can be to the notion of mathematics’ “reality.” Fundamentally, what is mathematics? Obviously this is no mean question and possesses no uncontroversial answer, however I would suggest (and I’d like to think that I’m in good company in doing so) that it is nothing more than the rigorous study of pattern, consistency and relation. Therefore to say that mathematics exists is just to say that our world is one possessed inherently of those qualities and throughout which such qualities run like ontic blood through all things. To have a world of objects - be they traditional objects such as tables and particles, or more likely the foreign yet fairly well understood (mathematically speaking) wavefunctions and spaces of QFT or the like - to have a world of objects is of necessity to have a world of relations, lest we assume that said objects are all individually isolated and unrelated to each other - which in the traditional case would arguably make for the existence of many separate worlds each possessed of a single, solitary object alone in an otherwise empty universe, and in the more modern sense of the word object probably is not even sensible, as interrelated wavefunctions are so fundamentally interdependent through entanglement, etc. To have a world of objects with relations that hold between them can only be sensible in a world which possesses some degree of consistency, else no relations could hold save for the singular relation of being somehow “chaotically unrelated.” To have a world of objects with relations that hold consistently between them, then, is nothing more or less than to have a world of patterns - which is itself nothing more or less than to have a world which can be studied mathematically. Mathematics is the study of structure itself; if we live in a world such as possesses any structure whatsoever (hard to argue otherwise, although I’m always open to a new wild idea lol) then we necessarily live in a world in which mathematics is “real.”

@JamesWebbKilledTheBigBangStars

4 жыл бұрын

Because it's wasting money, talents and time. Just take a look at state of present day cosmology; mostly dominated by people who never even know what a beaker is. Any science that does not butter one's bread is false "science", waste of time and money.

@ihsahnakerfeldt9280

4 жыл бұрын

Great comment.

@TheAgentJesus

4 жыл бұрын

Plastic Kruat to even phrase things as such reveals how ironically out of touch with the broader goals and process of science you truly are. I’m not going to waste a lot of time arguing with you because that will get both of us nowhere, but if you’re even remotely open to revising your views on this I would encourage you to look into the origins of science and the scientific method as they arose in the more abstract pursuits of philosophy and even politics; furthermore, I’d encourage you to read Eugene Wigner’s famous (or infamous, I suppose, depending on your perspective) paper on the “unreasonable effectiveness” of mathematics in the natural sciences for some choice examples of areas in which pure mathematicians developed theories and spaces which turned out to be extraordinarily useful in the physical sciences decades, even centuries down the line (for a specific example that’s one of my personal favorites, look at the origins of the hyperbolic geometries developed by Riemann - working solely in the world of pure mathematics - which ultimately proved indispensable for the formulation of Einstein’s General Theory of Relativity more than a century later). I should note that I’m not necessarily in disagreement that there are at least *some* instances in which pure mathematics has arguably strayed a bit too far afield of reality to ever be likely to prove “useful” in the physical sciences - although, again, it’s truly difficult to ever really know before we know. Would you still say in the light of these examples that pure mathematics is a waste of time and resources? That it provides no insight or utility into the more “productive” fields of physics or other natural sciences?

@TheAgentJesus

4 жыл бұрын

Ihsahn Åkerfeldt thanks!! I’m not sure about that qualification myself, but I’m glad you think so hahaha

@ihsahnakerfeldt9280

4 жыл бұрын

@@TheAgentJesus It's a logical explanation for the "unreasonable efficiency" of mathematics in explaining the natural world.

She is my idol she is so smart love you and congrats on being amazing

why don't the books go all the way to the end of the shelves?

@astonesthrow

Жыл бұрын

Umm..... Math.

Maybe a 500-page proof is "sublime" rather than "beautiful"!

0:09 - That's not... "computer science". It has a name: it's called mathematical logic.

What are these holes in logic she is talking about? Is it nonconstrucatability?

@shoopinc

4 жыл бұрын

Axiom of Choice leads to Banach Tarski paradox. A seemingly contradictory process by which you can turn a sphere with a volume V into two spheres each with volume V.

@pmcate2

4 жыл бұрын

@@shoopinc But a paradox isn't a hole in logic. In this specific case the logic checks out, and the paradox only arises when we choose to interpret it incorrecty. In this case, that would be thinking of the sphere as a physical sphere.

@shoopinc

4 жыл бұрын

@@pmcate2 The supposed hole is in Cantor's work, what Poincare believed was that infinite sets themselves do not exist. Personally I think infinite sets exist, so Banach Tarski is not a problem. But this does have implications in physics. A photon which we generally think of as a little sphere can split into two and sometimes three. Axiom of choice is somehow linked to the nature of quantum mechanics, that's not my specialty. But I would guess the connection is in the nature of hilbert spaces. phys.org/news/2020-02-quantum-photon.html

@pmcate2

4 жыл бұрын

@@shoopinc I also see no problem with infinite sets. Yes, I agree that is a good physical example of the Banach Tarski paradox. Taking that idea even further, the supposed one-electron-universe idea could be another example. Also, I think information in the classical sense resembles the BT paradox. For example: if I read a book, then I have copied that information to my mind, yet it is also still on the page, so that someone else can read it and so on... and then we have infinite copies of that information. I've had this idea for years and have no clue what to do with it lol. Btw, what is your specialty?

@shoopinc

4 жыл бұрын

@@pmcate2 Fluid Mechanics

Computers are great tools for doing math but awful for advance of mathematics, simply because mechanical constructs have no imagination. How machine works, equations are broken down, transistors are charged with electricity, each electronic gate represents some exact value. There are things computers can and can't do, let me explain. Every calculator can multiply by 0. Transistors get charged, jolt is send to some gates and those stay open, no multiplayer means none get closed and charge pass by in another set of transistors without change in original value. But if we ask computer what is something divided by 0, machine simply close all receiving gates, so jolt of electricity has nowhere to discharge. 0 means no gates are open to the other side, this is why most calculators report Error. You can try if you want, some will say cannot divide by zero. Engineers provide some way out of this paradox, they install another transistor, not meant to represent any value, it's just for discharging trapped jolt of power and report computational anomaly back to user. But is it really true, why it would be impossible to divide by 0? Let's see how nature works, all matter is emerged from quarks. All quarks are about the same and it's not clear if they can be broken down, maybe into strings, if they exist. Proton is made from 2 up and 1 down quark. So we deal with a whole split in 3 near "equal" parts. Please mind we are using geometrical terms here, not invisible inner properties of stuff that exist. We can't split a sphere in 3 exactly equal parts, 10 divided by 3 = 3,33..., it's never 3,4. There are only 2 kinds of quarks in a typical proton, up and down, those are slightly different. Let's say value of up is 3, so two of them makes 6 geometrical units, so down quark must be 4 units. Neutron is other way around, it's made from 2 down quarks and one up. Here's a problem, down quark is 4 and they are two, so both are 8. But we said up quark is 3, therefore neutron equal to 11 parts. Except this can't be true, if we could split both proton and neutron into quarks, there would be 3 up and 3 down quarks, nothing else. How can same quarks equal 10 in one combination and 11 in another? People might say, quarks are not tinny spheres, they have no exact geometrical properties, so there's nothing to compare. Does this mean universe can't have any distinctive volume or finite amount of charge, since we don't know how much protons and neutrons are out there? More over, if proton loose a quark, it became neutron. Something got exchanged in an equation and mathematical axiom suddenly doesn't apply anymore, like universe must bound to some other number theory just because of simple mathematical operation. One more thin is worth mentioning, smallest atom in existence is a hydrogen atom, but it doesn't need to have a neutron also, it can be only a proton and an electron, except it can obviously be much more and there are many varieties of quarks. My point is, it is possible to divide by 0 somehow, maybe this is what makes dreams work.

The "laws" of the universe are not based on mathematics. Math can only describe what we see. You see a group of rocks on a beach, you name them 1-10. It is no different if you see the moon going around the Earth and find the numbers that correlate with that motion. That is the real world. Mathematics is a mental construct we use to describe the real world. If you believe otherwise...that all we see is based on mathematics...you will have to allow for the possibility of an intelligence using mathematics to construct the universe, which is fine with me. Either view neither proves nor disproves Intelligent Design nor a godless universe.

I thought it was Mrs Doubtfire 😳

@vonBottorff

2 жыл бұрын

Classic KZread comment....

Mathematics is adding and subtracting, nobody ordered multiplications. Why is adding numbers so different from simple multiplication, first difference we can spot is in number of ways both methods reach same result. We can add numbers and count each step, but if we multiply some amount, we do all those steps in a single stroke of geometrical magic. We don't really know if multiplication is correct because it's derived from balance. Except multiplication is also adding, it add how many times we want to multiply some mathematical entity. Here's a trick, 1 + 1 +1 = 1 x 1 x 1. There are two solutions to this problem, both are nonsense. We could just say 1 is 1 on both sides since no matter how many steps we count on left side of equation, we can always multiply result by 1 and get same answer. Or we can be exact and say result is 1 (+2), since we must also count how many times 1 was added to a set on the left side. How about 1 + 1 = 1 x 1. It this scenario we took 1 and add another 1, those makes two of the same. But if i try to multiply 1 with another 1, i didn't do anything really. Is 2 same as 1? It works only after we add 3 number entities, doesn't make sense with less than 3. It's because there must be hidden path how one was duplicated into 2 same and closed values. Answer became clear only once we deconstruct number theory, it is possible to balance any object at two exact half's, except there could be infinite amount of numbers between one and two. Multiplication can't distinguish why something is like it is, multiplication is counting number of steps, not things in themselves. It depends what we're asking, it's like walking to a mountain trough a forest could take infinite number of steps or we can just fly there in a straight line.

Mathematics is the language of God, this is why it’s consistent, logical and true and stands the test of time. All of God’s laws are mathematical.

@johnbrzykcy3076

4 жыл бұрын

Hey Heath... I agree with your statement.

@johnbrzykcy3076

4 жыл бұрын

@Jay Tee I agree mathematics is the language of the Universe. But my assumption ( leap of faith) is that God created the Universe. So.... are they God's law? Just laws of chance? I'm knocking on the door of the universe. Who will open ?

@johnbrzykcy3076

4 жыл бұрын

@Jay Tee Jesus is knocking on your door (NOT hell ). I think there are laws of chance and laws of perfect prediction. Seeking meaning to existence does seem futile... yet I think most people want some kind of meaning. Otherwise.... what is the meaning of Love? Consciousness? Even Math?

@johnbrzykcy3076

4 жыл бұрын

@Jay Tee Jesus does not want our money... just our hearts!

@soulspacehomestead4941

4 жыл бұрын

Jay Tee You are correct, if you do not have a relationship with God then you do need faith. You only need faith in something when you don’t know it to be true. For example, the Wright brothers had faith that they could create a machine that would fly, once they did, they no longer needed faith. God has imparted intelligence in the entire universe in every creation and the language of that intelligence is mathematics.

True is not the right word.

@marielizysurourcq

4 жыл бұрын

Yeah, right. Chess is "true" too.

@brianbob7514

4 жыл бұрын

@@marielizysurourcq good one

Mathematical demonstration is sublime but irrelevant if it does not prove anything in real world . Quantum mechanics is real and many of the experiments proves that, unfortunately mathematics can't handle it so well . Physicists will use the mathematical instrument as long that is useful for them even if it doesn't look to beautiful.

@benedictus5657

3 жыл бұрын

excuse me what Physicists were astounded by what experimentation into quantum mechanics showed them, the maths behind it was consistent. Just look at the riemann hypothesis and the odd little proof that the sum of all natural numbers is -1/12. Absolutely counter intuitive, but accurately describes part whats happening in what we call the casimir effect

@mksensej8701

3 жыл бұрын

@@benedictus5657 Yes, they just found a mathematical formulation that fits almost %100 .

Since it's a double-edged sword, if mathematics does not correspond to physical reality and observations it's junk; useless, no matter how 'elegant' it is.

@xspotbox4400

4 жыл бұрын

Mathematics is true because it can help us understand material world we live in and it's beautiful because it can make our imagination come true.

@globaldigitaldirectsubsidi4493

4 жыл бұрын

false, reality is merely an illusion. Uninteresting, random and not exact. Mathematics is superior to physics.

@shoopinc

4 жыл бұрын

Anti-matter was predicted off pure mathematics, Dirac saw a possible negative solution and bam turned out to be correct. Maxwell found the wave nature of light from pure mathematics. Distribution of heat on a ring is a convolution. The universe must be intrinsically mathematical, or we have found many many coincidences in a row - not likely.

@metakatana

3 жыл бұрын

Mathematics is both a formal science and an art. However, it is *NOT* an empirical science and thus it should not be treated as though it were. Mathematics does *not* need to "correspond to physical reality", whatever that means, in order for it to be useful. I hope you know that mathematics *can* be used to describe physical reality -- without it we wouldn't have computers or rockets.

@jhonybraavo

2 жыл бұрын

What is useless?

Nothing beautiful about math.