I don't know anything about math because I am from the opposite field of sciences; social science. But one thing I see from the several lectures of Prof. Lakoff, he is a genuine, and not a snob or so arrogant scholar. He is the real kind teacher. I love how he gives lectures. This is a respect from Thailand.

Very nice explanation of negative x negative -- as rotations -- most insightful I've ever heard.

One of the better explanations in this series.

@jjt1881

2 жыл бұрын

Disagreed!

@hipsabad

Жыл бұрын

definitely!

@santacruzman

Жыл бұрын

@@jjt1881 On what grounds? Unless you have grounds, your "disagreement" is merely a misuse of termenology.

In most pre-college classrooms, the word metaphor is a word that describes something in terms of something else. I can understand that mathematics puts quantities in terms that add a new understanding to their relation with other quantities, which means that it uses numerical and other symbolic metaphors. So mathematics in that sense puts quantities and their relationships with one another into a form that makes them easier to manipulate in our minds, so it is a discovery that helps humans to make new discoveries about our existence. For instance, we did not invent gravity, but calculating the gravitational constant makes it easier for us to understand how and why planets and galaxies, and falling apples, do their thing!

@kundakaps

Жыл бұрын

A constant has no explanation. That's why it's a constant.

@Also.Sprach.Zarathustra

2 ай бұрын

I agree Roberta. Very nicely explained. I would only add that mathematics is not a discovery, they are more like a "property" or capacity of our dear human mind.

That part at 8:17 was brilliant. I’ve had this thought before but couldn’t articulate it quite like George did.

Thank you for introducing me to George Lakoff and his body of work.

Awesome explanations, I really wish that more mathematicians knew how to articulate their discipline with linguistic and social sciences in the epistemological level like Dr Lakoff does...

@santacruzman

Жыл бұрын

We would all be enriched if this were the case. In actuality he is just taking the scientific method to heart. His collaborative book, Where Mathematics Comes From..." is well worth a read.

A lot of people in the comments seem to be missing that Lakoff's contention is that The relationship between mathematics and reality is not an either or relationship. The two fit together as part of one whole that the brain puts together. There is no mind independent mathematics because it requires a mind. At the same time, the universe is always already out there to be seen as mathematical and can be seen as mathematical even if we are not actually looking at anything. Mathematics is surely a construct and assistive symbols just like any language.

I would like to dig deeper into Lakoff's and Nuñez's work. I do not know how metaphors work in cognitive linguistics, so I'm not even sure how they could be as precise as mathematical notions. I also do not know how metaphors could capture completed infinities and other mathematical oddities. Furthermore, his improvised answer to the "unreasonable effectiveness of mathematics in science" was unsatisfactory, but perhaps he has done better in written work. Finally, the whole discussion about mathematics being or not being in the world would become interesting only if made more precise. My own opinion about the latter problem is this. There is a pretty clear sense in which (some) mathematics is in the world: physical objects bear relations among themselves which bear some morphism to some mathematical structures. Here is an example. The particles in helicoidal nebulae bear spatial relations which are (at least approximately) monomorphic to an ideal helix. That should suffice, should it not?

11:05 "We create mathematics that fit". Couldn't agree more. Based on our limited human comprehension. IMHO, "The language of Math" is dictated by the physical laws that pre-existed and is the language we use to interpret them. If the physical laws were different, then the math may be as well.

@HorukAI

4 жыл бұрын

I do not agree completely. Mathematics can describe almost any universe, even chaotic one. What's important is that mathematics is abstractly about structure (fundamental similarities), quantities (fundamental differences), change (in any space), space (in any number of dimensions and definitions of distances, even without all those, like Hilbert spaces, or with spaces with regions without space or abstract topology which is built on open sets). What I want to say is yeah mathematics or more precisely aksioms of parts of it wouldn't be thought of without natural phenomena, but any deducting system working on given set of aksioms would discover pretty much the same theories even without any understanding of the substance. That's how we got into weird parts of mathematics without any connection to the real world. Basically mathematics for me is a logic applied to any set of consistent aksioms. What is logic then - that's a real question. Even logic can be vastly different, just look at fuzzy or modal, or quantum logic as described by Von Neumann. It also depends on its dictionary of possible formulas and rules (like modus ponens) which are really it's own aksioms. In the end we come to the point where it's not possible to know because in the end it might be some platonistic Logos or String Theory Landscape and connected anthropic principle or something else that is responsible for us to be able to deduct, which gives your assesment some weight.

@massecl

4 жыл бұрын

@@HorukAI Nay, mathematics describe our models of the Universe.

@deldia

4 жыл бұрын

zildyanVH wrong. You’re only calling something “logical” because that activity yields human value in the real world. If it didn’t the other wouldn’t be “true” in any sense.

@shaunmcinnis1960

4 жыл бұрын

@@deldia Couldn't your own limited comprehension be a major factor in how we interpret these questions?

@deldia

4 жыл бұрын

Shaun mcinnis no - just because we can find answers that are ever more correct and may never find the ultimate correct answer due to cognitive limitations it doesn’t mean that the answers we have or had weren’t true or correct - they were valuable. Newtonian physics is still true - there’s no definition of truth that makes sense if we can’t label superseded ideas as still being true in some sense.

I think it's a great contribution to how mathematics is learned but not to what mathematics really is or what kind of reality they have if any. That means that it offers great insights into cognitive ways of knowing, clarifying, learning, and developing mathematical concepts but not a single insight about the interactions between mathematical structures with the real world. e.g. what Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" If mathematics is simply a human construct, it makes no sense that it applies to our best theoretical insights about how the world works beyond our simple, biased and incomplete perceptions of it.

George Lakeoff said that "the marvelous thing about mathematics is that we can create mathematics with our brains that fit phenomena in the world remarkably." But Robert's question was " there was a time when there was no human minds but the physical world worked and that physical world seems to be described by mathematics." The question was not answered.

@davidwright8432

2 жыл бұрын

When there were no humans (or their equivalents elsewhere) there were no descriptions of anything - assuming descriptions require a describer. The universe simply 'is'; we come to discover and describe certain aspects of that existence, but our descriptions are not what's out there.All there is 'out there' (which of course includes us and our interior life!) is, in Newton's phrase, 'Natura naturans' - in English, 'Nature naturing' - just doing its thing. It doesn't require our knowledge of it, or permission, to do thhs.

@davidwright8432

2 жыл бұрын

' " there was a time when there was no human minds but the physical world worked and that physical world seems to be described by mathematics." ' The reason that wasn't 'answered' is that it isn't a question. It's a statement.

Lakoff's argument takes off when he mentions metaphor.

Interesting that it takes a linguist to give us a satisfying understanding of this question about mathematics.

@estuchedepeluche2212

3 жыл бұрын

True, very true. Sometimes people are so deep into their fields, they lose the capacity to elucidate general ideas and basic concepts in simple terms. Plus, maths are languages, and Lakoff is an extraordinary thinker beyond linguistics that can explain complicated phenomena in understandable terms.

@chrisjackson3759

2 жыл бұрын

Makes perfect sense to me.. since math ultimately is a type of language

@edwardmurdoch5070

2 жыл бұрын

He, and Johnson, are also philosophers, linguistic philosophers... and that question is not in the realm of mathematics but of philosophy.

@santacruzman

Жыл бұрын

Ultimately, Lakoff is a gifted thinker. Linguistics is merely one domain rewarded by his attention.

Bang on!!!!

As Maurice Merleau-Ponty wrote: "perception is a nascent logos"

Lackoff clearly ignores the opening question. Instead, he talks about the psychological, cognitive and (to some extent) the neurophysiological and evolutionary processes that seem to be involved in acquiring our concepts of number and learning mathematics. This is very interesting and important stuff and we need not deny a word of it, but it does not show that, say, the number '3' is neither (in some sense) invented nor discovered. Lackoff seems just to confuse talk about the _nature_ of mathematics with talk of _thinking_ about mathematics as we learn it - the category mistake of all psychologisms.

@ASLUHLUHCE

4 жыл бұрын

Is he actually showing that maths is 'invented'?

@theophilus749

4 жыл бұрын

Anonymous No! Nor that it isn’t. What he says is interesting but simply irrelevant to the question of whether maths is or is not invented.

@ASLUHLUHCE

4 жыл бұрын

@@theophilus749 If he's saying mathematics fundamentally exists in our minds and isn't drawn from some other 'reality' (platonic idealism I think it's called), doesn't that mean it's 'invented'

@theophilus749

4 жыл бұрын

@@ASLUHLUHCE Platonic Idealism is indeed the expression. However, even if mathematical concepts are in the mind, this would no more imply, all by itself, that mathematics was invented than the fact that the concept of an atom was in our minds implies that atoms were invented. In general, if concepts are 'in the mind' (whatever quite that means) perhaps what puts them there is just our recognition of the shared features of entirely non-invented things. That said, there is a big problem with locating concepts (any concepts at all) in our minds and that is that it would make concepts individual. My concept of an apple would be something in my mind and yours something in your mind. This would make understanding each others concepts problematic to say the least. We could have no shared public understanding of what 'apple' meant or what apples are. But since we do have such understanding, I suggest that he concepts are not in our minds. Minds latch on to concepts, they do not accommodate them. However, this is an added issue.

@ASLUHLUHCE

4 жыл бұрын

@@theophilus749 Interesting, thanks for the response. I've just started reading the wiki page on 'philosophy of mathematics'

The discussion (as is so often the case) is about definitions. The philosophical term is A Priori - that which has "existence" independent of experience. How we come to be aware of this realm does not necessarily define the realm itself. Plato got a bit carried away in imagining that "the forms" were truer than the world of experience, when it is better to understand the a priori as different to, not realer than, the world of experience. Obviously, we invent the things that we discover, and vice versa.

Although he beautifully explained how math was invented, I'm still not sure if he fully answered the question. At the end he says the log is in our mind, not in the spiral galaxy. But that log perfectly explains the spiral galaxy so in that sense the log IS in the galaxy, therefore math was also discovered.

@shaunmcinnis1960

4 жыл бұрын

Agree.

@tacopacopotato6619

4 жыл бұрын

are the constellations in the stars or in someone's head

@cyberpiok439

4 жыл бұрын

Under his explanation, the statement that log is in the galaxy does not follow from the statement that log explains spiral galaxy, no matter how "perfect" that explanation is from us human's perception. That's the whole point.

@thegaygammaguy5604

4 жыл бұрын

Its called GOD. He creates this and all things discovered by scientist. Stop this nonsense haha

@magnusjonsson7303

4 жыл бұрын

If there is no differens between invented or discovered then math is (like reality).

I knew it! It (mathematics) is just our way (and the best way) of understanding and defining the nature of world around us.

@puma7171

2 жыл бұрын

As we discover the world around we also discover the underlying maths. So there is no invention but a relationship between both kinds of reality.

@faismasterx

2 жыл бұрын

It's our use of language to understand and express the logic. Math is the language of reality, but it isn't reality itself.

@yubz1496

2 жыл бұрын

no. The 36+ constants are exact mathematical principles created in the fabric of space time at the start of the universe. The universe is proven to be more ordered at the beginning

@dhireshyadav1783

2 жыл бұрын

@@yubz1496 Those constants aren't just mathematical jibbrish, they correspond to the real physical laws, otherwise they wouldn't even be relevant. It's the reality and physicality that's primary, the mathematical descriptions are just a way to put them into one of our frameworks. Mathematics is just an emulation of the Physical reality into our languages and ideas. It's not the Physical reality itself. Our brains don't even need to understand all of what reality is, it takes whatever is necessary to survive or exist. It just needs to imitate, and can only imitate. It's an evolutionary phenomenon. That's all.

@yubz1496

2 жыл бұрын

@@dhireshyadav1783 No its not. God created the constants there is no other explaination for it. You think all the contants and matter came about by chance ? That is almost impossible

Very nice. I think a more didactic response to clarify the presenter´s confusion at the end, when he tries to refute Lakoff, would be to explain that ¨thinking Math was in the world before humans¨ would be similar than bees thinking infrared optical shapes were in the world before they existed. It is their visual capacity what makes them see the world as it is for them (infrared images with different intensity); in the same way our logical capacity and interaction with the environment make us see math everywhere (create metaphors). It is not fundamental to the universe, not created by us. But emerging from us, just like other capacities, like our quality to see or hearing.

@Also.Sprach.Zarathustra

2 ай бұрын

Bravo, beautifully expressed.

I tend to agree with him. We are just doing the math to correspond with what we see in nature. That nebula is not attached in any way to a real math, but rather this language of mathmatics we construct gives a real picture of the natural event. The difference is between making a knife fly through the air, & describing the math that predicts its eventual trajectory. One is happening, the second is a description of what is happening. You discovered a way to describe what is, but math is not this entity out there that you discover parts of. This was a real pleasure to hear. He was a great speaker & clearly bright. He also was one I agreed with on this subject oddly enough.

Cool, it took Lakoff 2 minutes and 8 seconds to say, "Metaphor". Anyway, Mathematics as Metaphor is an interesting twist.

@puma7171

2 жыл бұрын

The metaphors explain how we come to an intuitive understanding of maths, they don't explain maths themselves, including its mind blowing properties and implication and, most importantly, how they fit the real world in areas where our intuitive understanding fails.

@KEvronista

2 жыл бұрын

he probably meant "simile".... KEvron

The interviewer made a good point about “math” applying even where there a no minds to create symbols and calculations. The scientist basically said No, but his example seems to say Yes.

@dfhwze

4 жыл бұрын

His example showed us that math's purpose is to comprehend reality, using models, metaphores and approximations.

@scienceexplains302

4 жыл бұрын

@@dfhwze The purpose of the symbols, etc, is such. But one plus one equals two in nature whether anyone is there to comprehend it or not.

@dfhwze

4 жыл бұрын

@@scienceexplains302 I believe even the most fundamental arithmetic, like the incrementation as you describe, are artificial constructs to help us understand reality. Our strong intristic beliefs about such logic are not an absolute proof of what reality is.

@scienceexplains302

4 жыл бұрын

@@dfhwze You seem to confuse the symbols for the reality. An increment is not artificial by any means and they happen. The act of increase has nothing to do with helping us understand anything. Please demonstrate a possible way in which an increment of one, say, planet in a lifeless solar system, does not increase the count of planets by one in that solar system.

@dfhwze

4 жыл бұрын

@@scienceexplains302 I cannot demonstrate this as I too believe incrementation reflects reality. My point is not that there may or may not be an empirical way to prove otherwise, but that whatever we think we know, boils down to beliefs and assertions rather than universal truth.

But that's the mystery -- the math does "fit the phenomena remarkably" -- yes math is not "in the world" -- math is in some thought-world, or abstract world, or other-world -- and it sits there as the underlying architecture of that world -- and, it is a metaphor for the real world --- math first, world second -- or is it -- world first, math second. Either way, math is playing in the big leagues when it comes to theories of the universe.

@BugRib

3 жыл бұрын

Well put!

@Cssaarr

2 жыл бұрын

hmm I think it fits phenomena perfectly because it was built to fit; you take relationships that exist, translate them to symbols and relationships amongs them (at this point, nothing misterious) and then you deduce the missing parts from what you already have (like when your brain sees part of an image and completes what is missing); everything you deduce, is derived from the first basic representations of the world; you could probably describe the world in other ways different to math and in the opposite way, when you describe the world in math, you let many things out (in that sense math is a very basic, simplistic, incomplete description of reality, so that some aspects of reality can fit our basic brains)

Mathematics is a certain type of language used to describe the relationship between aspects of the physical world, both observed and non observed.

Here's a thought: does a sphere actually exist as a platonic mathematical object, or is it merely a cognitive metaphor? Spheres are useful in that they can, for example, help describe some of the properties of subatomic particles and fundamental interactions, as well as resulting macroscopic phenomenon like the shape into which an idealized lump of uniformly distributed matter would coagulate under its collective gravitational field... yet, does that make the sphere a real object, even in a platonic sense? Certainly, as a metaphor, it is essential to our ability to understand and predict nature/reality. In that sense one could argue that mathematical objects might be understood to exist as abstract transformations that function within the context of the software of our mind, yet contain some descriptive or generalizable qualities with respect to the aspect of 'objective reality' that the brain needs them to act upon.

@parker5944

4 жыл бұрын

I always have trouble when we privilege some things as real and other things as unreal. In a pragmatic universe, real is what real does. Everything has an action/movement to it that effects the sense of reality to varying degrees. Here it seems we are calling metaphor unreal while simultaneously it is what we utilize to describe/manipulate/and get perspective on the world. The sphere is like the engine that powers the various theories it helps formulate. I suppose I subscribe to the Buddhist idea that reality is essentially interconnected and eternally in flux. I have yet to decide whether that rules out the idea of a singular reality which is objective and outside and which we all interpret or that we are all jointly creating the sense of objectivity through some sort of consensus. The latter seems counterintuitive but subjective/objective seems to me to be another false dichotomy; Consciousness is fundamental as our experience of anything at all, “inward or outward”, is based on it. What consciousness is, in itself, non-confined to human intelligence is yet to be discovered or verified as real or unreal and I suppose that sort of thing may come down to all of our individual (or pseudo-individual) experience. I guess that is ultimately what all religion is attempting to describe (w varying degrees of success) at base; the ocean underneath the wave. Perhaps the sphere is the platonic/oceanic concept which manifests (or just describes?) waves of imperfect spherical objects. IMO, it is all real but, at least on this human plane, everything exists on a spectrum according to how our various senses are able to interpret it; somethings are seen and somethings are apprehended. I don’t think that necessarily makes me dualist. What do you think?

@melgross

4 жыл бұрын

I’ve never believed in the concept of the platonic ideal as “somewhere” where these shapes exist. We can imagine these ideals, but that’s about it.

@melgross

3 жыл бұрын

ThotSlayer they don’t have to come from anywhere independent of human needs. Just because we can imagine a shape doesn’t mean that that shape has to exist somewhere. A sphere is an easy shape to talk about because gravity tends to have all conglomerations of large mass attempt to be as close to the center of gravity as possible. In other words that shape is the result of the least amount of energy that that mass can result in. But choosing a shape that doesn’t exist in nature is much more useful to consider. A chair, for example. Are you saying that you actually believe in the discredited concept of ideal shapes?

@melgross

3 жыл бұрын

ThotSlayer that’s a contradiction in terms. You’re either one or the other. You can’t be both.

@melgross

3 жыл бұрын

ThotSlayer in addition to fixing your spelling, maybe you should.

where we get the metaphor of rotation? Lakoff is a great cognitive scientist and was a staunch adherent of logic to AI but change his mind. I am sure in his theory there are building blocks or atomic metaphors. I read him 20 years ago. I wonder how his theory is standing the test of time. Any one knows?

I cannot wrap my head around with very last statements George Lakoff made at the end of this video.

In Sir Roger Penrose's " Is Mathematics Invented or Discovered?" he claims that Mathematics is discovered and I find Sir Penrose's argument very hard to debate. In essence, he reminded us that there are examples of physical theories (he mentioned the general theory of relativity) which, at the time of their formulation, gave predictions that were many orders of magnitude more precise than the accuracy of the available observations and so observation could not have had any effect on the predictions of the theory. Certainly, the available observations act as a guide in designing the theory in such a way as to agree with the already available observational data. Many years later, when the accuracy in the observations had improved sufficiently, the new, more accurate observational data turned out to verify/agree with the predictions of the theory. It is in that sense that he assigns an independent reality to mathematics which is reflected in the physical world and I find this argument extremely convincing. Is it however safe to follow and trust the conclusions drawn by a mathematical physical theory blindly until the very end i.e. to arbitrary large energy scales way beyond the ones we have already probed with experiment or at least we have the potential to probe in the near future? Probably not, since history has revealed that theories that give accurate descriptions of reality in certain energy scales have to be replaced by more accurate theories to describe phenomena in higher energy scales. This fact however does not in my opinion invalidate the former argument about the independent reality of mathematics it only indicates that this mathematical reality is more elaborate than our currently best theories and a refinement of the latter is necessary in order to encapsulate the mathematical/physical reality. TDP.

So, is there no objectivity in this world? From physical sense and philosophical point of view, do we just apply metaphors from our understanding of the world to derive patterns, constants and limits which essentially have no real meanings? Is he trying to suggest that as we are part of the nature, we understand the working of it naturally (but by using mathematical metaphors we break down it systematically in logical formats, as our mind seems to work in this way) ? Well, I would love to watch a debate between George Lackoff and Max Tegmark.

To add to this something that I’m not sure was said, mathematics has to be a universally agreed upon language in order for it to have any meaning or utility for all people. There are an infinite set of systems we could have built to describe the universe we see, but we decided on this one and universally hold to the same basic tenets. It strikes me more as a system, that was invented by a small subset of individuals who decided to systematize their observations, that was then agreed upon by the rest of the world as the standard. There’s no reason corolation and causation have to be the same thing…

@MrJacko1946

2 жыл бұрын

Mathematical notation is an invention, just as writing and musical notation are.

@anthonypolonkay2681

2 жыл бұрын

Your confusing the idea of symbol convention with the idea of math as a concept in itself. Nobody disputes thag we invented the symbol conventions for math. But to argue we simply made up a system that works out to describe things like the orbits of planets, the way gravity acts, the theory of relativity, and eigenstates is rather ridiculous. That akin to saying we got to make up the lore to our own universe, and it actually coming true to whatever we came up to.

@MrJacko1946

2 жыл бұрын

We made,up everything!, gods concepts language music love life laughter maths and physics,and chemistry. In the entire unfeeling freezing oblivious vacuum out there we made it,all up. And when we're gone ....?????

Two features of math are often conflated. The first is the 'true by definition' aspect of math. The concept of 1 or infinity existed before humans started using it, just as the concept of a door, or a flower, or the Statue of Liberty existed before we used it. The second is the ability to derive new facts from some other facts and basic axioms. This is simply logic at work, nothing specifically about math. The problem is when the two features are conflated and we attribute something deep and mystical about the ability of math to describe the world.

@vladoh2011

3 жыл бұрын

@Riz Raw Concept of door is intangible and it has always been here and will always be here. And there and everywhere... Only actual doors are tangible.

Brilliant.

Does anyone think the origin of mathematics is similar to that of physics? Our brains have a capacity to abstract reality with mathematics however we can also do just that through explanations and physics. Both are imperfect. Both a testable, physics by evidence and mathematics by proof...

I'm not a big math guy, but I'm into big ideals, and this whole ideal of math being discovered or Invented is very interesting indeed, my first thought was that it was invented to describe the physical world, then the one fellow said something along the lines of regardless of humans there is no highest number, and I thought to myself, true enough, and thought to myself well it must be discovered then, then I watched a few more videos nothing very convincing either way then, I watched this one and didn't think much of anything this guy was saying, it all seemed to be valid, but said nothing to change my mind until he said "the math is not in the spiral its in your brain" boom! so back to math was invented to describe the physical world around us

My problem with this explanation, and I agree with his anti-Platonic argument, is that to me, his position doesn’t fully explain the fact that there are underlying structural reality’s in nature that are described by mathematics. I’m referring to such phenomena’s as Fibonacci sequences, and fractals. These phenomena’s belie the speakers argument because, though they are described by our cognitive abilities, they exist in nature apart from them.

At 10:06 he is saying a spiral formula can be used to explain the motion of a spinning nebula, but the spinning nebula is unaware of the formula and it's the human mind that attaches the spiral equation to the motion of the spinning nebula. But that doesn't answer the question. The question is: does the spiral formula (or math in general) exist if humans didn't exist. What he said was that it's the human mind that attaches the math of spirals to the physical event of a spinning nebula. We still don't know if the spiral formula exists only in the human mind when it's attached to the spinning nebula or if the human grabs it from the outside world and attaches it to the spinning nebula.

@smittymcjob2582

Жыл бұрын

To make it simpler, let's stick to simple math: I say if two apples drop from a tree and then two more apples drop from a tree we then have four apples on the ground even if no human ever existed. It is true that it's the human that assigns names to counts (one two three....) and objects (tree, apple).. but conceptually, even if two and four were never named, we would still have four apples on the ground. So math has to be there even if people weren't there to use it. Please rebut my point is you believe I'm obviously wrong.

mathematical statements being true regardless of physical reality to apply it to or not is another question to whether reality consists of mathematical attributes....i.e. pattern, quantification, order, similarity and difference in whole, collective or individual attributes etc. 2 is greater than 1 (regardless of language/symbol used...as the concepts the symbols/language represent is not nonsensical and false) is true, even if there is nothing to apply it to and even if there is no-one to think about it. Fundamental truths that are definite. This refutes a basis of secular science philosophy, that nothing is definite and nothing is ultimately knowable to the point of certainty. Certainty, positive and negative is a reality, just as doubt is a reality and probability a reality... This means there are degrees of knowledge and degrees in reality (and its measurement), just as there is equality/similarity and difference/opposite.

As deeply insightful as this research is, it seems to merely set up a formal system of representation (albeit a physical one) consisting of conceptual primitives (definitions and axioms, if you will). That you can map mathematical concepts to neurological primitives is a demonstration of representational capacity, of mapping, or at most, of equivalency between two representational systems). Analogously, that mathematics can be founded on set theory didnt answer the question whether mathematics is real or not. It served only to provide a rigorous foundation of what we construed as math. It is too broad a claim to infer ontological primacy of a given formal system of representation even if it happens to be the foundational one of a particular ‘entity.’ Can you imagine computers eventually suggesting that there is no “reality” or higher concepts to be discovered as it’s only a matter of 1’s and 0’s and conclude that taking the world literally is the mistake of taking representation literally. With computers we readily agree that their representation is only a digital approximation of what we think of as the physical reality. As such we won’t settle the question of the ontology of reality or mathematics in this way. I read Lakoff here as making a leap from metaphysical positions he isn’t articulating.

I look at mathematics like the Anthropic principle. Mathematics is based off of the way we experience the universe and so of course it would be right, because it was just a notation to describe observably true things. That we deal with things like limits and infinities and undefined numbers, things that really only gain their meaning in a transitive way when used for various calculations, that we can abstract principles from multiple sets of mathematics in physics and apply these mathematical abstractions to other systems that then allow for testable discoveries, I think is evidence of the limits of mathematics as a simply self-fulfilling prophecy that results from deriving a system of logic from the universe. There is plenty of evidence that Mathematics can only describe the universe to a... limit.

FINALLY!!! - At least someone out there has a brain! Lakoff is 100% accurate on his final conclusion. I'm glad to see at least someone doesn't make a religion out of the question of mathematics being invented or discovered! Finally! Take THAT, Penrose!! lol

@ibdaramy7261

Жыл бұрын

@Divided_And_Conquered - you just turned the discussion into an anti-religious sentiment. But we can forgive you for that :-) In all seriousness, the fact that Mathematics is discovered should not strike you as odd. Computer programs produce results. One may be able to reverse engineer the results to discover the algorithm whose creator is a human being. The human body is without doubt a sophisticated machine that is orders of magnitude more complex than any automobile. Why should it not have a creator and by extension the universe also? Let us not try to fit out theology into our morality and scientific or intellectual world view.

Mathematics is present in the very fabric and workings of the Universe, and we the mathematics romancing creatures happen to be a part of the Universe, too. So invented or discovered, the real question is: Do we even have a choice in the matter, when the mathematical code is already entangled with our very existence? In fact, for many of us, if we had to venture a bit we would place our chips on mathematics being all that there is.

Quantum matter, splitting things at exact half's, action reaction principle, mirroring, perfect balance at tiny edge, center of the mass, all those physical phenomena are bases of number theory and mathematics, they are consistently and definitely real and not a subject to our imagination. Problems arise when we try to move beyond capabilities of our minds, when results are so complicated, temporal and machine assisted groups of people can't follow any common reasoning. Problem is, we can understand everything even without any math.

@kristine8578

4 жыл бұрын

Can I borrow your statement for our debate 😃, it would be a great help if you would agree

@xspotbox4400

4 жыл бұрын

@@kristine8578 Why not, math students love it :)

@goe54

4 жыл бұрын

@box "Problem is, we can understand everything" Oh common man!

@xspotbox4400

4 жыл бұрын

@@goe54 There's a glitch in the matrix.

I was thinking of it in terms of this: That spiral nebula in question, before man was around to perceive it or assign any math to it, still existed in spite of not being perceived. This of course, is an assumption, but logic tells us every assertion must have at least one assumption, and I think this is a fairly safe assumption. Then along came man and developed the ability to see the spiral nebula, and felt it was the god of whatever. Along w/other stellar bodies like planets or constellations who were of course other gods. But it wasn't really the god of whatever, that's just a metaphor man made in its best effort to understand what they saw. As wrong as they were, if you were to go back and ask them, they'd be incredulous if you were to suggest maybe their idea was just a metaphor. After all, their metaphor worked. They were able to chart the movement of these gods, accurately enough to accurately predict their future behavior. If the model could accurately predict events in the future, how could it just be a metaphor? That nebula and those constellations must be gods! Then man developed the ability to see things a bit further and a bit more clearly and realized this nebula was this big thing in space very far away. The entire thing. Not a god. We realized it was this thing out there that exuded light, which we could see at a great distance. Perhaps a star. Like our sun. W/basic math we slowly were able to figure out some of its properties even, like that it was far away. But we were still wrong. It isn't one solid thing w/these few properties, it wasn't a star like we perhaps thought at one time, even though at low resolutions it looked like a blob of light to us just like stars do etc... But we weren't wrong entirely, it does exist, even if its not a singular 'it' at all, it is far away, it does emit light, but that was just our best effort at describing it through the best metaphor we could come up with, even if the metaphor was now taking the form of what we now call 'math', and even if it was finally what we would call accurate as far as it went - but since our metaphor wasn't complete, it was still wrong, still 'merely' a metaphor, unassociated w/reality enough to lead us in to incorrectly believing that a nebula was a star. Then man developed the ability to understand this star wasn't a star at all and was made mostly of gas and how it had come to be shaped in a spiral. Could figure out its history. Still using this metaphor which had become so sophisticated that we were discovering all sorts of ways our prior versions of the same metaphor had been wrong. Math. Working so well, so defined, so sophisticated, so accurately predictive, that it starts to seem like reality itself. But woefully incomplete. Always glossing over the bits we don't understand. Improving our picture of what is actually there, but never giving a complete picture of what is there, due to how imperfect our metaphor still is, though we every improvement we marvel at how much more complete our picture is and imagine we are finally 'there'. We are now at the pinnacle, as we see it, of the development of this metaphor, of our 'math', so we don't yet see what future generations will see w/the benefit of having even better defined this metaphor that we use as a tool beyond the level we have defined it now- that is from their perspective, it'll be obvious how wrong we are at present in our interpretations due to the flaws we have yet to iron out of our metaphor. I would put it like this: Math is our attempt at describing reality using a method that we consciously put effort into trying to make as accurately corresponding to reality as possible. Ever more successful. But until it is perfectly successful, both in accuracy and also in completeness, then it is just a metaphor. The goal is to improve math so that it becomes less and less a metaphor, and more and more an accurate and complete representation of what 'is'. But as quantum mechanics shows us, we are only just beginning down this road, no where near able to refer to math as more than just a metaphor yet, we now know it has much more refining it yet needs. We once thought a man was a thing. Then we realized the idea of a man as a singular thing was a metaphor because in reality a man is made up of smaller things. Its still a useful metaphor to think of a man as a singular thing, but it just a metaphor. Then we realized the idea of these things, organs, were a metaphor because those organs were made up of smaller things, atoms. Now we realize atoms are a metaphor, because they are actually made up of smaller things. etc... etc... etc... Now we're down to what, plank lengths? Vibrations in fields or strings? We now examine even what we used to think of as nothingness itself, the vacuum, and realize even it isn't what we thought w/our incomplete metaphor. Remember, accuracy is not enough. Using the metaphor of 'gods' to accurately predict the movement of Mars across the sky, while accurate and predictive, is a metaphor woefully incomplete allowing for the mistaken belief that Mars is a being rather than a planet. After all, I can use the secrets taught to me by the priests of Mars to accurately predict where he'll be on the night sky every night for the next year, so it must all be true. I've tested it, the secrets work! All praise to Mars! Even today w/our unprecedented refined level of our metaphor 'math', its no where near complete, so we are still doing the equivalent of calling planets gods, even if not so anthropomorphic - fumbling around w/a dozen wildly contradictory 'theories of everything', each of which fits our current metaphor, but which are mutually exclusive from each other, and possibly even all incorrect if no one has even theorized the correct 'answer' yet, but in the very least, due to their mutual exclusivity, all but one of them must be wrong - yet they all fit our current metaphor - math. If our math was more than a metaphor, such wrongness would not be able to fit w/in it. There would be no room for mutually exclusive theories, for it would be accurate and complete. But our metaphor, math, is a very useful tool. We make the metaphor. We compare it w/reality through experimentation. When it fails to compare, this is a success because then we can refine it until does compare w/reality. Making it slightly less a metaphor. TLDR: In conclusion, I think math could potentially be more than merely a metaphor. And that this is the goal, and that we are making good progress toward this goal. But I also think quantum physics is showing us that we aren't anywhere as near to that goal as we thought we were say 100 years ago. We are only just beginning to understand how precious little we know and how much our math, so far, is merely a metaphor, though an ever more useful metaphor as we try to make it more and more an accurate and complete description of reality.

@shaunmcinnis1960

4 жыл бұрын

Nice; you talk sense! No mystical bullshit.

@goe54

4 жыл бұрын

Mutually exclusive theories are not math, so their existence do not prove that math is only a metaphor.

To answer interviewer's question at 10min nature doesn't use math or computation. It is the principle of least action. Math is our math and it's an abstract covering tool.

@KEvronista

2 жыл бұрын

bingo! stars don't carry the one in order to form. KEvron

The question perhaps would be better posed in the active form, ie ' Did humans invent or discover mathematics ?' And perhaps instead of the words 'invent' or 'discover' we could replace them with or add in the terms 'utilise ( wittingly or unwittingly ) ' and 'identify patterns of'. So, now we have ' Did humans utilise ( wittingly or unwittingly ) ' and 'identify patterns of' mathematics ?' And the anwer is 'yes to both'. Just as we we used stones as tools, our understanding of the properties of stone and our analysis of it developed through use, consideration and labelling. Same with fire, geology, geography etc . And of course all these things would exist without humans around anyway. And maybe, just for fun, we could ask 'did humans invent or discover language that allowed them to ask daft questions such as 'is mathematics invented or discovered ?' ?

Mathematics is nothing unless you speak/think/write in math. This is also true of quality English/French/etc. You can write formulas endlessly, only some small % of them will actually describe some real part of nature, the rest will be mathematically consistent but have no important value. This is also true of English; you can write endlessly in proper grammar and only some small % of it will be magical. Is poetry invented or discovered? Neither, it's created out of existing lesser parts. It's an extension of understanding. You don't invent or discover a perfect vase, you create it out of material and skills. The vase is still just clay & process but it has the special quality of being very well organized. Same with math, the rare part that appears magical is no different than the endlessly numerous valid equations that have no magic at all. You could imagine a planet with life that created math as fine as ours, but never associated it with nature, in that case it would be a form of poetry without analogy to reality and the notion that it was there to be discovered would not never come to mind.

Logarithmic spiral is not the nebula it's in your understanding. If one did not understand how the logarithmic mathematic works, will he or she be able to produce spiral galaxy, in other words, can intellect come from chaos? Can I code a program to do spiral without ever knowing how to apply logarithmic mathematic to spiral ? I know the answer is no. Therefore one can arrive at an understanding only an intellectual mind can produce intellect, chaos produces more chaos.

Consider two categories, mathematics (M) and reality (R) Theorem: There is an isomorphism from (M) to (R). Proof: Refer to comments below.

I understand what he's saying but how then mathematics can predict the unobserved or unknown?

Sylvan Tomkins found that this specific question is highly predictive (0.3) of the two character structures that dominate the West: Humanism, versus the Normative (which Prof. Lakoff calls "authoritarianism"). (See Ch. 24 in Vol. III of Affect Image Consciousness, for reconceptualization of a study Tomkins did in the 1960s.)

It seems that everything is in some kind of proportion to everything else. Mathematics is a symbolic language for expressing that. I think.

@KEvronista

2 жыл бұрын

*"It seems that everything is in some kind of proportion to everything else."* that's set theory in a nutshell. minds arbitrarily, yet reflexively, create sets, and minds assign values. KEvron

Next debate would be " Are natural laws invented or discovered?"

@wade5941

3 жыл бұрын

Fair question. Surprised that did not get more response.

@edwardmurdoch5070

2 жыл бұрын

What natural laws... the ones in classical mechanics, general & special relativity or quantum mechanics? (You have your answer within my question) :P

@KEvronista

2 жыл бұрын

like math, if they describe, then they are invented. KEvron

@santacruzman

Жыл бұрын

Yes. Ultimately the same answer. Regularity is a pattern and then it is described in as general a way possible so as to include all relevent phenomena. The 'it is discovered' hypothesis is really just a naive form of platonism. But as realists we know there is no 'realm of the forms' except in the minded confines of rational creatures.

Embedded experience as sense is mathematical. Mind and brain is extended by experience and doing as a metaphor for numbers collection of objects. Move steps to tell one and one is two. Space Metaphors that are created through experience. Metaphor gives you going back negative numbers. Mental rotation that leads to imaginary numbers. Define what is going on as concepts clear once grounded the answer. Metaphor are needed points in number line. It’s a metaphor that is our mathematics. Infinite set of numbers we have two concepts of infinity. A complete set of all metaphor. Actual infinity , mathematics metaphorical It’s not in the world. Spiral mathematics. Constant rotation we put the out there. It’s in your understanding. We can see the world and category it. It’s not ou there in the world. Downey California

Maybe I'm just not smart enough, but I feel that Lakoff didn't really answer the last question. Sure math is in our head, and the spiral nebula is out there. But "something" IS controlling the behavior of that nebula. That THING is math (maybe its not called math in nature, maybe that is just our name for it, but IT is there).

Not convinced. From a disinterested perspective, it appears that Lakoff is merely recycling, Hume’s constant conjunction without the implication that it bears. What is metaphor in this case other than a Priori knowing? This merely kicks the can down the epistemological road. And, ignores the metaphysical and ontological conclusions … And more likely the metaphysical and ontological presuppositions.

There's only one thing known with certainty to exist, and it's also the one and only thing known to exist that can't be described by math, even in principle. Any guesses what it is? Any theories about why it's the one thing known to exist that can't be described by math, even in principle?

@garythibault8032

3 жыл бұрын

Conciousness.

-×-=+ proof does not use rotations, It is proven with basic math, To formally rotate you also need this, not the other way around

Is math "objective"? As I understand it, human experience of the world is that of the subject, we are the subjects of our lives. Is the experience of mathematics the subjective experience of understanding the world?

Chuckling. I’m not sure the nebula is out there. Why? Because it’s most pronounced in George’s circular reasoning. It is very difficult to see how George misses how he consistently begs the question. Ugh. So he bases his understanding of the Cosmos on the difference between the Classic syntactical difference between the perfect and imperfect verb constructions. By this reasoning, the Aorist verb tense lead to the big bang. Nice try.

Certain objects of mathematics and the language is created but the structure is obviously not created. No one created the *platonic solids* . If you could just create more, we would but by necessity those are the only ones that can exist. We didn't create that rule or limitation. We discovered it.

Isn’t the question creation or happenstance?

@scienceexplains302

4 жыл бұрын

Chris young No. For example, chemical reactions are predictable. So when a chemical reaction (or bond, for that matter) occurs, the process is not happenstance, and there is no need for a conscious agent to explain the interaction.

"The map is not the terrain" Sun Tzu. I'd say the answer to the question is both. The emerging patterns of mathematics are discovered. The concept of mathematics is invented.

Makes no sense, "the flowers fit certain types of series, the series are not in the flowers." Who says? What about an automobile? It obviously contains mathematics in its design which - based upon his explanation is not in its design but on one's cognitive ability to perceive the mathematics. The world behaves as if it was designed using mathematics that was created for its design; in other words, to enable its design.

Mr. Lakoff is expanding on Immanuel Kant's claims in his book "The Critique of Pure Reason" and without having read that book one will not find his short explanations convincing. Kant's "CPR" very much influenced Friedrich Nietzsche, particularly in this essay, which explains better than Lakoff in this interview what is meant by metaphor here: oregonstate.edu/instruct/phl201/modules/Philosophers/Nietzsche/Truth_and_Lie_in_an_Extra-Moral_Sense.htm And yet Nietzsche's claims in that essay will still not be completely convincing or well understood without reading Kant's CPR. Kant did not claim to know why the human brain/mind was built the way it is, but described it's possible modes of thinking or conceptualizing about the world. He narrowed it down to 12 modes or concepts, which have sub-levels, that by themselves or in combinations describe any and every thought you can possibly have including every kind of fantasy, like unicorns. Then, through experience with the world we mark as real those fantasies for which there is evidence and call that knowledge. Kant declared math to be apriori thinking. Some misinterpreted Kant as meaning apriori was magical. By apriori Kant meant that there was no way to find a deeper ground making it seem like it was a foundational mode of thinking but it may not be....no way to tell. Apriori math is like a ruler measuring itself and declaring itself to be accurate. Someone once said (maybe Nietzsche, or influenced by him) that everything....the universe and everything in it...is like an explosion in a fireworks factory. If one zooms in and freeze frames a moment of that explosion then one can describe that little bit with maths and declare it all to be deterministic cause and effect, but the whole picture of that explosion will be chaos. Humans, because of how the brain is built, will imply or make a solid seeming metaphor for just a little bit and then use that to explain more stuff resulting in a vast construction built of metaphor. In fact, if it's all perfectly random then every possible interaction of matter and movement would have to be included at least once, else it's not really random but instead there is selection favoring some interactions more than others. But it seems that with all of what we think of as time in the denominator it will turn out to be random and logic and reason and maths will be, as Nietzsche opined, a vanity, and thus human, all too human.

@vladoh2011

3 жыл бұрын

Apriori thinking and apriori math are two different things. Unless you mean apriori square thinking

I guess I don't know what a metaphor is :) .. incomplete infinity ... interesting .. what primitives need to be in place for metaphors to take hold ..

"The flowers may fit certain kinds of series, but the series are not in the flowers." I guess that depends on your point of view.

If America was discovered multiple times (it was), this would be the same America. The name would be different, but the name isn't an inherent part of the continent(s). But if the cellphone was invented twice, these would be radically different. This is what differentiates discovery from invention. But for a technique to be useful in mathematics, there needs to be a proof that requires that technique. This means that this technique has to be discovered. I mean, it is not like this is hard problem... I find it really obvious.

If this is true then how is possible that humanity wield such immense power over nature, and I mean only humanity. This only brings more questions to evolutionists. We certainly could live without this knowledge, like animals do, but we could consider ourselves humans? Why nature gave us, and only to us, such immense power? Or is it perhaps that we humans are meant to discover nature? If so is this a conscious act?

I don't see how you can create math out of something that is already there? I would guess that everything is the way it is and was always going to be that way.

I'm leaning on a side that it's a human invention. I don't think in any reality without human mind there are 2 exactly the same things at the same time so you could even call them two. Let's say 2 atoms to make it very simple. They can never be exacty the same at least they have to occupy different position so that makes them different.

@HorukAI

4 жыл бұрын

I think you've misinterpreted the measurement problem if you are referring to everything being just a probability wave until 'observer' comes and collapse it. Of not them your claim can be extended to the old - does moon exist if we are not looking at it (or existing at all). I tend to accept that it does.

So, in imperfect Man's efforts to explain the infinite, beautiful mind of the Almighty Grand Creator, we see tht He placed universal patterns n His Creation thru designs tht we can accurately formulate thru consistent interpretation, using Math as our tool to get the most basic, slightest, infinitesimal undrstnding tht our limited minds could process & reason on?? Hmph. AWESOME!

@roqsteady5290

3 жыл бұрын

yawn

@jayl7920

3 жыл бұрын

@@roqsteady5290 so U don't believe n God? big whup. who cares? won't miss ya whn U're gone. LOLOL

@thbmatrix

2 жыл бұрын

That's the punishment for learning to read...

My view is that math is a language used to describe structure and casual relationships in reality. You can say that the new term to describe something is being invented, and what is being described was discovered. The question is whay the structure and design and associated laws exist in a manner that allows it to be captured using the language of mathematics. The theist would say God.

Waoo....waoooo.....waoooo!!

And this is the reason philosophers do not require waste paper bins.

Maths I remember a story before numbers existed where animals were represented as stones. When a sheep went through a gate a stone was put to one side. If there were some stones left over the person knew there was some sheep missing. Sometime later the brain evolved and we were able write down and record stuff and numbers were invented. Even now babies brains need to develop and learn to read, write and count. Even today mathematicians have invented numbers and equations to describe things they don't understand such as 0 and infinity. This stuff is not natural and needs to be learnt.

@somexp12

Жыл бұрын

Only the language used to describe mathematics is invented. When you run into issues like Russell's paradoxes or Godel's Incompleteness Theorems, these are issues found in the artificial conventions that people like the logical positivists used to structure mathematical knowledge. Mathematics, itself, however, comprises those preexisting laws that *force* mathematicians to limit their output. The reason we can understand mathematics is because it is the structure of reality. Our thoughts and imaginations are part if reality (though they can represent unreal things), and, therefore, are *incapable* of imagining true mathematical contradictions. You can say the words "square circle," but you cannot create a mental image of a circle with angles. Nor can you draw a picture of one. This is because both pictures and imaginations are part of reality and must follow the rules that structure reality. This is why mathematicians are able to know when they've proven or disproven a theorem. If these rules were invented, mathematicians could churn out any old "theorem" and decide (by virtue of their authority) that it were true. Mathematics would be completely useless if this were the case. Kind of a strange thing, though. I've actually encountered people who would *rage* at you for suggesting mathematics were anything but an invention. I don't know what threatens them so much about the opposing view, but it does make a lot of sense that they would be the type to think they can alter the truth through the force of their personality.

@dmitriy4708

9 ай бұрын

@@somexp12 Math is an invention based on our basic observations and inborn systems in our brain (like distinguishing space, time, directions etc.). So, it is an invented language used to create some models of reality that is based on what we know about reality. No wonder it works in reality, we created it based on reality. So, saying that math is discovered makes no sense, it is not math that is discovered, it is regularities in nature that are discovered and used to create a toolbox like math to predict more about reality which sometimes work and sometimes fail, we dismissed not working parts and created the set of rules based on what works so we can use it. And some predictions were true as a result, yay! We used the result of centures of trial and error to establish a language system to help us find new regularities in nature based on already known regularities and evolved invented rules. Simple, isn't it? And there are a lot of areas in math that are useless or not applicable to reality, we are just not very interested in them. Is it strange that the tool we invented and perfected for thousands of years to work in reality works in reality?

can't agree with any of that!

Mathematic is a consequence of the Eternal Life-Structure, mirror'ed in the structure. Specific the Intelligence, (Logic/Order) and the Perspective-Principle, (all relations relationship) According to the Life-Renewing-Principle, Developing-Circuit's, and the Developing-Spiral. Mathematic and Language get's re-invented and re-new'ed endless. Language without Mathematic, is No language, and Mathematic without Language is Not Mathematic. Just short, but Basic 'Mathematic' of the Mathematic, (and Language)

I wouldn't say it's that remarkable to pluck a string it rings harmonically and we place a fret there and it happens to be exactly 1/2 the distance. Nature exists, the harmonic exist, independent of the fret or math or the human brain the Same exact thing. I love math a lot great tool like a stick, I just don't get to obsessed with my stick philosophically that's wierd.

@vincentzevecke4578

5 ай бұрын

Read Kant, First 😊

His replies/explanation have no relationship to the question.

all reasoning hide the most fundamenral question:why did we evolve to understand mathematics? Was it a coincidence?

a circle is a circle. a right triangle is a right triangle. the properties and proportions are the same in America, Africa, or Andromeda. the only thing we invented are the symbols we use to describe them.

How about Christian's core theology is 1+1+1=1?

This would’ve been better if the camera man wasn’t over doing

Do what now what did you say to me ?

So, uh, this is *everything*! Peace out Platonism! Nice to know you ‘radical’ constructivism! Gosh. Wow. Thanks for this.

Mathematics is a perspective

@bradmodd7856

4 жыл бұрын

oh my god, you have said nothing, congratulations on that

@bradmodd7856

4 жыл бұрын

I'll add that if we are discovering numbers, we are discovering everything....it is all coming to us from somewhere else. This is the only metaphysical duality I can envisage, I cannot see a division between matter and ideas, only between ideas we have and those we have not yet got access to. Where they are coming from is the mystery.

@millerfour2071

4 жыл бұрын

Taqifsha Nanen The natural numbers, more specifically 1, has certain properties, there is a corresponding set associated with 1. Different ways viewing the number 1 gives a perspective. Only in relation to the logical thinking structure arising out of human brain, can math make sense. For a child, there are two physical things. For a mathematician, there are abstract quantities. It’s all a matter of perspective.

@bradmodd7856

4 жыл бұрын

@Taqifsha Nanen this might hurt to hear this but 1 does not exist, nor any of the other numbers, at least not in the physical world. Everything is different and changing from moment to moment. So we have discovered a code, that exists in consciousness that looks like our sense data, but it doesn't correspond exactly.

@millerfour2071

4 жыл бұрын

Taqifsha Nanen Clearly you are on the side that math is discovered and is independent of of the human mind. Best way to test out your assumption is to see what mathematical results a person who cannot see, touch, head will produce.

If I have 2 apples and "multiply" by 2...?

Stewart Lee has really let himself go!

spiegandomi come se legessi un giornalino di ALAN FORD............IL PESO ATOMICO DEI NUMERI DA 012345678 A 9 realizzano "nel tempo" tutte le "sostanze" neccessarie ad appropriarsi dell'infinito al fine di ottimizzare l'equilibrio cosmico cioe' delle galasssie pianeti stelle nebulose ecc....in parole piu' semplici man mano che lo spazio-tempo si impadronisce dell'infinito gradualmente si affinano tutte le creature (gas) presenti nel cosmo E' SISTEMATICAMENTE AUTOMATICO CHE IL NUMERO ATOMICO DEI NUMERI NON E' UN DATO FISSO......ALTRIMENTI NON RIUSCIREBBERO A CREARE L' "EQUILIBRIO" DEI GAS......!! se sei 1 laureato in fisica mi hai capito benissimo......saluti............18.01.2020 mauro STOKY SPIEGANDOMI MEGLIO A MIO PARERE...................il peso atomico sempre variabile dei numeri da 012345678 a 9..............REALIZZANO colori REALIZZANO fonte di calore REALIZZANO chimica..............QUINDI SONO PURE LETTERE !!!!!!!!!!!! forse mi sto' sbagliando ma non credo proprio....!!!!!!!! saluti stoky 18.01.2020

Great job on handling the old and tiring question "Did Mathematics exist before humans?". It did NOT. What existed were processes in the nature that we today characterize, or describe, in terms of mathematical concepts we developed. The crocodiles - as physical entities - existed before humans, but the description of the crocodile, in terms of proper vocabulary and grammar, did not. That's all there is to it.

Mathematics was developed! Nothing DEEP about it as Kuhn would like to see it!

@daithiocinnsealach3173

4 жыл бұрын

But it _feels_ deep. Like religion. Like a good novel.

We discovered that we can measure stuff and we invented how to do it so it's both.

@KEvronista

2 жыл бұрын

measurement requires the establishment of sets and valuation, both of which are products of the mind. KEvron

Ham egg and chips, peas on the side.

So your essentially saing math is in our DNA? INTERESTING. So we are born with the ability to understand that if you have a object and add another the amount present is more. But who give that a number 2?

The opposite to infinity is 0

What west is dicovering , asking question in 19th , 20 th centruy .. Ancient India has answered all , from comology to mathematics .. Time is not same , was told 5000 years ago in ancint India ..concepts of universe , Multiverse all explained in ancient Indian texts

sounds like he's saying the math is invented. but he doesn't want to say it.

Fucking genious