My congratulations to numberphile for making a philosophy of mathematics video. In my opinion, this is a very interesting side of math that gets almost completely overlooked and it should get more attention

@head4shot

5 жыл бұрын

gijijijijijijijijijijji so efin true!

@AshokKumar-os6vo

5 жыл бұрын

Ya I'm also work on mathematics related to philosphy

@mansiveer3231

5 жыл бұрын

@@AshokKumar-os6vo what work you do?

@nothinghqppened5519

4 жыл бұрын

so true..

@TerrelleCheers1

3 жыл бұрын

!!!

He starts with "we are gonna be thinking about three different schools of thoughts on this"! So he believes that the number 3 exists!

@b4theflood422

4 жыл бұрын

Nice! 🔥 Which means theres a 2 and 1

@davejacob5208

3 жыл бұрын

no, he just uses the word. also, he uses it like an adjective for a thing that is not part of mathematical language ("different schools of thoughts")

@user-el4np5xt8c

3 жыл бұрын

@@davejacob5208 that word implies a quantity. No matter how you turn it around its a word that describes a quantity. He's referring to the quantity of ideas he will talk about. So I knew I would get one more than 2 different ideas to listen to. With his words in a non mathematical sentence he conveyed mathematical info to me. So yea still numbers. In case you want to argue further, the dictionary states the word is a number. So yea still numbers.

@andersbendsen5931

3 жыл бұрын

@@user-el4np5xt8c he also states that he's essentially a nominalist. So perfectly in line with the argument, he hasn't used the number in a platonically mathematically sense. Either way, does it really matter? 🤷‍♂️

@BrazilianImperialist

2 жыл бұрын

@@davejacob5208 Someone here no humor

I've told my bank I'm a mathematical fictionalist... they looked at my account and agreed, but still expect my bills to be paid on time.

@larsthomasdenstad9082

5 жыл бұрын

Banks are assholes.

@stevenpdxedu

4 жыл бұрын

@@larsthomasdenstad9082 I told my bank I'm a mathematical fictionalist . . . they told me that they told me they had known that for quite a while, but didn't want to tell me and risk interrupting the cash flow from my overdraft fees.

@pasquino0733

5 ай бұрын

I told my bank I was a mathematical Platonist. In an abstract realm my wealth is numerically limitless.

@wellesradio

3 ай бұрын

You joke, but the idea of economic wealth is a fiction used to leverage power. Think of the Great Depression. Did natural resources and labor suddenly disappear? No, it was all there. In a very real sense, people starved to preserve the status quo of a clever lie.

Easter Egg: In the thumbnail: RIIDIICIIIPO R2-D2 and C-3P0

@ahmedelhori6009

6 жыл бұрын

Canal do Sky what do they mean

@thlrock

6 жыл бұрын

Ahmed Elhori, R2-D2 and C3PO are android autonoton or 'Droid' characters in George Lucas's Star Wars film franchise

@FunkyEspelhoCat

4 жыл бұрын

Wut? They must have changed the thumbnail then, i don't see anything.

@nanamacapagal8342

4 жыл бұрын

@@FunkyEspelhoCat they must have, I remember seeing those numbers there 8 years ago.

This guy (who I'm assuming is a professor) is really knowledgeable about the subject. This video is the only place on the entire internet that explains the Platonist/nominalist/fictionalist battle concisely and well. Thanks, Numberphile!

This was one of the most fascinating videos I've watched in a long time. Thank you so much @Numberphile.

I ended up from A4 paper sizes to the square root of 2 to whether numbers even exist..i love youtube

@stevehardwick8453

4 жыл бұрын

I just made this same journey today, so I guess KZread is using the same algorithm as they were three years ago...?

@RazorM97

3 жыл бұрын

4:40 * camera awkwardly stares at square root of minus one * "Wtf is dis ".

@eyelockedpro3203

3 жыл бұрын

@@RazorM97 i

“All models are wrong, but some are useful” - George E. P.

@nonyobussiness3440

4 жыл бұрын

Models aren’t real. They’re a tool to help us mentally understand or see something that might be unreal. They’re a medium that describes something like a surrealism painting but they don’t define what they’re trying to describe,

@talastra

5 ай бұрын

I just quoted that :)

I used to be a nominalist before I entered university. Then linear algebra started, and this is when nominalism totally collapsed for me. It was a momentary aha moment. All it took was to reflex on the axiomatic definition of what a vector is. Vectors aren't unique concepts in this manner, but it was the thing that striked me. Vectors and vector space create a world completely detached from reality. You don't need anything real to define vector space, and you actually can't use anything real to define a vector. Some vectors can be discribed using numbers and some basis, but vectors aren't those sequences of numbers. And there are vectors that can't be fully described using numbers, for example vectors in spaces with infinite dimensionality. And everything can be a vector if operations are defined. Vectors are literally "anything, for which operations of addition and scaling is defined and well behaved". Look, I say, that I define operation multiply(my bed, any number) = my bed; add(my bed, my bed) = my bed, vector space = set, containing only my bed. Now my bed (a literal physical object that I am sitting on right now) is a vector, because it satisfies all the axioms of vector space! Not a description of the bed, not a representation of the bed, but the bed itself is a vector. And no, it's not like some vector is used to represent my bed, but my bed IS a vector in this context.

@vhawk1951kl

Жыл бұрын

Is it not plain to you that universal can only possibly be imaginary or images in the dreaming or associative apparatus - they clearly cannot be directly immediately personally experienced, or do you suggest otherwise? You could rephrase the question two numbers exist as do descriptions exist - numbers are a form of description are they not not?

@vhawk1951kl

Жыл бұрын

Seemingly a " nominalist" embraces those like me and your former self that take the view or merely observe that all universals are imaginary in the sense that they cannot be directly immediately personally experienced other than as images or symbols in the associative or dreaming apparatus or mind. If we rephrase the question into a form that makes some sense, might we not ask can numbers be directly immediately personally experience other than as proxies or symbols conjured up by the dreaming/associative apparatus or mind. Probly best just avoid blaubs like exist, or just recognise that they are blaubs-pronounced blorbs

@pyepye-io4vu

9 ай бұрын

This is similar to what is sometimes called "structuralism", look up Stewart Shapiro.

@IroAppe

9 ай бұрын

My stance on this is, and I can't believe it hasn't been brought up - that Mathematics describe the relationships and laws of things in our universe. In some way. We can say anything, for example "let there be i=sqrt(-1)". However, simply by ensuring that the implications of that claim are consistent and without contradictions to itself and anything earlier, we derived a new and true relationship of our world. We might not understand, how exactly the physical world works in its most fundamental way, there are many ways to formalize things. But eventually - by ensuring those rules - we see, that left and right claims of Mathematics appear to be particularly useful in the physical world, and make claims that hold true in observation. That's why I don't think, all those things are existing, abstract objects in their own. I think, that all those concepts we have in Mathematics relate to physical relationships in one way or another, we just have no way to discover what they actually relate to fundamentally. We only observe at the very end, that all the logical conclusions we've made line up with the observed reality of our world, and so all the logical steps must somehow be true, how the world works. It's like closing your eyes and driving for 30 minutes, only by exact data where your start position is (assumed perfection) and logical deduction. Somehow those deductions tell you all the actions you have to perform. Then you open your eyes, and you are actually where you worked out you must be theoretically. In the end, observational evidence shows it's all true. But we have no idea, what exactly happened in between, fundamentally, with all the details. It's a model of the world. And the more accurately we can model it, the more accurate our predictions are. But the relationships and laws in mathematics themselves seem to be universally true, since they don't change, they are always the same for every calculation. We found a way to work with the most fundamental laws of how our universe works, without having to understand it. We just worked out the logics, what happens in between, and it works out in the end - and in my opinion - because it actually relates in one way or another, to how the physical world works.

@luck3949

9 ай бұрын

@@IroAppe this is an approach from reality to math. In the approach you describe, math seem to be rooted in reality and is checked by it. This is intuitive. But the most fascinating thing about math for me is the fact that it can be based entirely on itself, without any connection to reality. It reverses the conclusions, not "math is correct, because it passes the reality check", but "reality is correct, because it passes the math check". This empowers me, because it gives to me an even stronger instrument, than reality check.

I really like the talks about the philosophy of numbers. I feel they could go in depth about each one and more about where it's troubles are, and maybe even how they've gone alone historically (with more resolution). It's an interesting topic.

@vhawk1951kl

Жыл бұрын

"I feel .... " Feel meaning what or what do you seek to convey by the word "feel"?

Brilliant. Thank you Dr.Tallant. This is a fascinating lecture that clarified some questions I had about the subject. Although there are concerns and issues with each of the three philosophies, I am leaning towards nominalsim at this point.

This video made me think about this more than I thought I would.

Do ideas exist? Is existence dependent on materiality? What defines existence?

@aleksapetrovic7088

4 жыл бұрын

I define existence.

@aleksapetrovic7088

4 жыл бұрын

@Orson Cart You might've outsmarted me this day, but who defines defining? That should keep you busy for a while.

@aleksapetrovic7088

4 жыл бұрын

@Orson Cart thats who defines who not who defines defining

@Bratjuuc

4 жыл бұрын

@Orson Cart Don't you guys have anything better to do with your brain other than causing useless argues that noone can win?

@maximusgarahan2066

3 жыл бұрын

I can render a rather subtle Socratic argument as follows: The standard way this is cashed out in analytic philosophy goes back to Frege (although it has its roots much deeper than that). The idea is that thoughts are not public. You cannot have my thought; thoughts are metaphysically private. However, the contents of thoughts are not private. Although you cannot have one and the same thought as me, you can have a thought with the same content as me. We can both think about the proposition 2+2=4. So thoughts essentially belong to the minds that think them, and are private to those minds; but the contents of thoughts (propositions, i.e. "ideas") do not belong essentially to minds and are not private. The proposition 2+2=4 doesn't need me or you (or anyone) to be thinking it for it to be true, or for it to exist. If minds suddenly disappeared from the world, so to would all thoughts. But the things that thoughts are about (propositions) didn't depend on any particular mind, and it doesn't follow that if minds disappeared then propositions would too.

Thanks for this channel. I'm very interested in Maths, so this channel is the best opportunity. But my english isn't so good at all so I'm training with your videos my english to. The prounciation of all Numberphile members is very good/perfect. So I have no problems with searching for a translation if there is a vocab which I don't know. Thanks for all :*

excellent intro to philosophy of mathematics, or rather to the different views on it!

Mathematics is just the study of abstract ideas, the properties and facts of abstract objects that obey axioms. The subject emerged out of studying physical objects, and in modern times, has now been generalised to study abstract problems. Mathematics exists in the realm of thoughts.

@frtard

8 жыл бұрын

+Alq I consider it to be the study of _relationships of quantity_.

@AlqGo

8 жыл бұрын

frtard Relationship is just one of many Mathematical objects.

@AlqGo

8 жыл бұрын

irving c I don't think you've ever studied pure maths.

@irvingc4508

8 жыл бұрын

Alq No, I'm studying to be an engineer. Applied mathematics is the only thing I've studied. Did you read the paper? They derived Wallis' pi formulation from a hydrogen atom... It shows a relationship between pure mathematics and the physical world. Maybe your abstract world is a representation of a real mathematical property of the Universe.

@AlqGo

8 жыл бұрын

irving c It is certainly true that Mathematics used to be inspired by Science, where many of the insights in Mathematics came from observations in Science. However, in modern age, Mathematics has been largely independent of Science. Take for example, the space R^k where k is an arbitrary positive integer. Is there any physical space in the real world where k is, say, 50 million? Another example is a ball or other geometrical objects defined in that very R^50,000,000 space! Can you find such objects that are tangible in the real world? The answer is obvious. Mathematics is abstraction, a huge part of which is a study of the properties of Mathematical objects. It is difficult to explain what "abstraction" is (or, rather informally what "generalization" is) to someone who hasn't been exposed to such topics as Abstract Algebra, Analysis, Topology, etc.

That portrayal of mathematical fictionalism was very far from neutral.

@raykent3211

8 жыл бұрын

Agreed.

@Nukestarmaster

8 жыл бұрын

It's more neutral than I could have ever managed.

@Zebo12345678

7 жыл бұрын

He just seems to lack an understanding of it. It's not about calling mathematics false. It's about calling mathematics a human construct. It's a system we created to govern how we do things. No, numbers do not exist. Not as abstract objects, and not as properties of objects. They only "exist" as concepts, that humans have created. I can say 1+1 = 2. That's not something determined by nature, that's something determined by humans. *We* created numbers, and yes, they are helpful. No, they don't physically exist.

@AnalyticalSentient

7 жыл бұрын

Zebo12345678 They have a referent; the structural configuration of physical objects. Which is not irrelevant. Depending on the arrangement of physical substances, for instance, distinct forms of matter result. What exists is not only about material composition; it's also about structural 'shape' or form _of_ said material.

@Zebo12345678

7 жыл бұрын

But what does that have to do with numbers? Yes, we use human-made numbers to reference natural phenomenon. When two hydrogen atoms and an oxygen atom join to make a water molecule, that isn't because numbers said 2H + 1O = H2O, it's because that's just how atoms work. Humans are the ones who decided to label the components from their number variable. It's humans who created the numbers to do that.

The problem with nominalsim is, even for simple concepts like the number 3, if you have 3 apples on one hand and 3 oranges on another, what do these two sets of fruits have in common? Would we say they have the same quantity, but that there's no such thing as quantity?

@Voshchronos

4 ай бұрын

Quantity is a characteristic about sets of objects. That characteristic exists. However, the number three does not always indicate quantity! The same number three could be ordinal, and describe the order an object or a person is in a line. What is the "threeness" in common in these two uses of the word "three"? It's an abstract concept that has no real counterpart in the world. We have created that concept, it's an idea, and ideas do not exist in the same sense as material objects or entities do.

I have a pencil. I have another pencil. Oh, two pencils!

I think the (truncated) platonist idea is that numbers have properties-like primeness-independently of how you conceive of them-hence you can misconceive of a number-and therefore they have mind independent properties. As such, they exist.

It's fascinating as well as depressing to see something so much powerful and magical can't even define it's existence.

This is extremely interesting from a self examination standpoint. With my very limited mathematical background (I watch these KZreads out of interests, not application), I strongly relate to Nominalism (how I learned math) yet Platonism seems impossible to grasp. This helps explain why I can't warp my mind around there being 'imaginary' numbers or even something life infinity. For me, a nominalist, I need a real number to exist in my mind; for a Platonist, that number does exist regardless. VERY interesting indeed. PS I'm a soccer coach... math plays very little in my profession. I just enjoy Numberfile and Sixty Symbol videos a lot! thank you.

@mytriumph

Жыл бұрын

may i redirect you to a youtuber named "another roof"? they have an *amazing* series about how the numbers are defined, which without getting too deep into the philosophy of anything, is really interesting in it's own right

@Tankej0527

6 ай бұрын

Do squares exist? Do they have properties? What are they made of… Are they made of only matter in squares, and were there no matter there cannot be squares, or do they still exist then too, ‘outside’ space and time

this is such a mind blowing concept

Excelent presentation!

loved, loved, loved! just thanks!!!

Right. Got it. Abstract, outside of space and time. Yup, I got a term for that. Imagination.

@Maxb49

3 жыл бұрын

What do you think about the (real) possibility that spacetime isn’t fundamental? If true, how would that change your analysis?

Very well explained and entertaining

I’ve gone down the rabbit hole and it’s now after 7am. Night spent well.

This was a terrific video with a terrific interviewee. Thank you! I want to point out that (being something closer to a mathematical fictionalist myself) that part of the problem in explaining these things has to do with confusion between the words being used, namely "true," "exist," and (barely used here at all) "real." These all stand to be delineated from each other to prevent probably equivocation (a logical fallacy) due to their colloquial synonymy. true ≠ exist ≠ real It's worth taking the time to parse these out. A fictionalist indeed won't agree that numbers offer "true" descriptions of things, but that's in part because of one of two things (depending on the sort of fictionalism you belong to): (1) nothing is real anyway (a.k.a. "anti-realism," which I do not endorse), or (2) what is real is impossible to access directly by any means available to humans and non-humans alike (a.k.a. speculative realism). As a speculative realist, the problem around numbers is that they exist (notice by saying they exist, I'm not necessarily saying they're true nor that they're real) as a type of intentional objects (which has a specific meaning derived from medieval philosophy and, more recently now, phenomenology) which give literal descriptions of real *qualities* of objects (real ones), without actually being real objects themselves nor able to "tap into the truth" of real objects. It would take a whole other video or essay to really get into this, but I think it is inaccurate to say that fictionalism is necessarily extreme. What's extreme to me would be denying that numbers exist at all (which as I've indicated, isn't what all fictionalists would argue) or that they are "merely useful" as opposed to being both useful and aesthetically interesting in their own right.

@sehr.geheim

2 жыл бұрын

yeah, I think I am believe what you believe

I don't agree with any of those completely, but I see pieces of each. Math doesn't really exactly describe objects. If you have 2 apples, those 2 apples are different, therefore you don't have an exact two apples, you have two sets of mass that are separate from each other that are relatively the same. And therefore an approximation of what you actually have. There is no physical depiction of a circle that has a surface, volume, or area that can be accurately calculated by pi. In fact, a circle itself is just another abstract object. I don't have a circle for a mirror, I have a mirror shaped approximately like a circle. Mathematical objects are just tools, like a hammer. The hammer strikes a nail, but the full surface of the hammer doesn't meet the full surface of the nail, there are grooves that hide surface away from each other, but at the end of the day, the job is done just as well.

@MrCrazytodd

9 жыл бұрын

Lee Louviere Either way it's still two apples, much like a truck and a van are still two vehicles.

@XaadeTheBlade

9 жыл бұрын

But the idea that two dissimilar things count as two of something, is completely abstract. There is nothing in reality that can be measured from those two things, and equal two.

@MrPigeonTeeth

9 жыл бұрын

Lee Louviere I don't think that it is really necessary for two things to be the exact same to be counted as two things, even different in some ways.

@sinprelic

9 жыл бұрын

Lee Louviere i like the way you put it! interesting follow up question: do you think ideal cubes absolutely cannot exist in nature, or do you think that the reason we dont see them is because of the nature of measurement (i.e. uncertainty)? those are (very arguably) two different things.

@sinprelic

9 жыл бұрын

i'm a biologist, but i know a little bit of physics and i think of it in this way: sinusoidal waves depend on circles and pi and all that jazz. a wave (which we can observe in nature in the form of light or sound or vibrations or oscillations) has a wavelength/frequency, which are related to energy (energy = planck's constant * frequency (a property directly related to wavelength). however, the uncertainty principle in physics dictates that there is a time-energy uncertainty relation, so the only way we can know a wavelength with absolute precision is to observe it for an infinitely long duration of time (roughly speaking) which is impossible; this is why measuring a perfect circle by extension is impossible. but the nature 'behind' the uncertainty follows mathematical laws where waves interfere to cause the uncertainty. this means that these waves really could be governed by what you might call the platonic circle. perhaps someone could correct me or explain if i'm reasoning incorrectly. cool things to think about, huh :-)

This channel is awesome.

Very interesting. It also helps explain, why students have great difficulty calculating with negative numbers, with fractions, etc. They are very abstract indeed [unless you mind-numbingly just manipulate the symbols]

I like Seven Up, more than I like sprite

@thallium200

8 жыл бұрын

+Miguel Almeida If Sprite was called 8up I may like it better as well. So I like Mountain Dew. Caffeine.

@matthewgrimm9036

8 жыл бұрын

best comment

@dontreadmyprofilepicture1357

8 жыл бұрын

CERTAINLY.

@redsalmon9966

7 жыл бұрын

7 likes for you

@scribesforsubscribers8027

4 жыл бұрын

Passionate Blow with a Right Jab to the abdomen of (what is analytical in relation to logical).

I'd rather see numbers as the linguistic filter through which humans interpret their physical reality. If that makes sense to anyone else? Doesn't make mathematics "absolutely true" or "absolutely false". Since they occur to us in our thoughts, numbers are conceptually true, but since they are physically intangible, they can just as easily be called "false", if you wish to see it that way.

@raykent3211

8 жыл бұрын

It makes sense to me! I was surprised when he said something like fictionalists say that mathematics is false. I know nothing about "mathematical fictionalists" (perhaps they just make themselves up ;) ", but writers of fiction tend to speak of fictional truth, and rarely about falsehood. And I'm not happy about him mixing up the concept of mathematics with the concept of number.

@ianmoore5502

8 жыл бұрын

@Zousteen From Holland how about this one man

@okuno54

6 жыл бұрын

Maxime Boileau If I had to invent a name for this stance, I would call it idealism, and this is definitely where I come from. I would however say _a_ rather than _the_ linguistic filter. Mathematics sets itself apart from natural languages like English in that mathematical languages are carefully defined to be able to express with great specificity, and mathematicians all agree on the definitions. Finally, since I'm a physicalist, I'd say our thoughts (being patterns of neuron-firings) actually are physical entities, and just as "real" as eddies or storms. If you aren't a physicalist, then that might not follow.

@litigioussociety4249

6 жыл бұрын

I believe you just described nominalism. For example, in the case of the square root of negative one, that can be explained by breaking it down into its fundamental parts: one, square root, and subtraction, and those are all things that can be related to the real world. Even in the case of higher dimensions in mathematics, they can be used to relate to physical properties that have more than three variables, such as elements.

@moreofthesame

6 жыл бұрын

Your identity (your memories, emotions, feelings) aren't physical either. Should I assume that you're also 'not real'? How will that impact my ethics?

well done on breaking down these viewpoints into a digestable form for ppl like me.

I always have this video playing while writing a paper late at night.

Numbers, letters, and symbols are all abstract units we have devised over the ages to better communicate and rationalize about the world as we experience it. Language is one of the earliest attributes we developed, but it took a while before we started writing down what we thought our language sounded like. How we decided to represent the sounds of our language in symbols draws from our creative faculty, which is linked to our senses and perception, which differs from person to person. Words are special concepts we recognize and associate with objects, ideas, emotions, etc. Numbers are a lot like words in that they allow us great freedom in describing the world; on the other hand, whereas numbers are infinite, our ability to communicate ideas, and especially to convey an experience, is limited. Our use of language as a primary means of communication is still far from perfect. Language is only our best attempt at conveying our thoughts and emotions. For example, you cannot absolutely convey your current state of being using language. Likewise, you cannot concretely define 'happy'. Granted, there are some experiences that a majority of us can agree we would say tend to make us 'happy', but 'happy' is just a string of letters. That's it. It's an identifier, and just like any other word we readily recognize, it points us to number of other things stored in our memory banks that we associate with the term. But what about when we see a word or symbol we don't recognize? It has little or no meaning at all to us, and no switches in our mind are tripped because we don't have any images or experiences to attach to the word. On the other hand, we aren't restricted by the inherent obstacles of language when engaging in mathematics. Numbers can completely and absolutely describe any physical quantity we would possibly want to record to any degree of precision we want, and then some. Numbers are only as ugly as we need them to be, but the more beautiful side of mathematics lies in an ideal world where we can say that we have a circle of radius 4 or an infinite sum of integers or even such abstract concepts as dividing zero objects among zero recipients. However, in the real world, it means very little to me if someone says they measured a sandbox to be 6 feet by 8 feet with a depth of 6 inches, so they know they can fit exactly 24 cubic feet of sand in it. The molecular make-up of the sandbox tells me that the width varies microscopically due to the uneven surfaces, and no matter how precise a measurement you give me, I can always go one decimal place further, and we can play that game on and on. Though really we're limited by the tools we use to measure said quantities, but I think we can all agree that there comes a point where a measurement is "close enough" for our purposes. We could instead say that there's a certain maximum amount of sand particles we could fit in the sandbox. It turns out that units of measure are ideal, fixed quantities we can envision, and we apply them to the best of our ability, but they really don't "fit" in the real world though they've worked wonders for us throughout many fields of study. Likewise, numbers exist in theory and are at the core of science, but the way I see it is that number is a property that describes either the ordinal ranking of something, or how many of something there are. That is, . Anything beyond that and you're treading in the hypothetical land of mathematics, where solids have faces that are perfectly flat, and we can say we know a quantity exactly. There's only so far you can go applying mathematical principles to the world we live in. As far as numbers existing, they all exist in theory: the imaginary unit, i, Euler's number, e, pi, the golden ratio, even the Fibonacci sequence, prime numbers, perfect numbers, real numbers, infinity, one, zero, rational numbers, irrational numbers, etc. They are all at the root of many natural phenomena and play major roles in many applications, but I truly believe that only natural numbers can be seen as tangible, existing concepts in the real world. I can hold three bricks, sixty thumbtacks, one shovel, and I can be number 1 in a list, number 5, number 1000000, etc. I cannot hold zero staplers or be number zero on a list. Neither of those statements makes sense. Using a number outside the natural number set, or using natural numbers for anything other than ordinal ranking or counting is to apply abstract concepts from an ideal world to a world that's not ideal, and there are plenty implications to consider when making such a move.

@klinchrx

3 жыл бұрын

Mucho texto

Well isn't mathematics sort of a language? A language can't be true of false, its type isn't a boolean far as I know. It can be used in any environment to "describe" a problem and build up frameworks to generalize and simplify the system we interact with (which could be real life, a computer program, observations basically anything we can study and break down), this is how I interpret mathematics, many toolsets within mathematics lets us express ourselves better than we could do orally. Neither of these philosophical statements proposed on the video make any sense.

@aeroscience9834

9 жыл бұрын

Math is not 'just a language'. Languages are arbitrary, and math is logic based. Can you give me a logical reason we call cups "cups"? Probably not, it's just convention. You can, however, PROVE mathematical concepts

@gfetco

9 жыл бұрын

Aeroscience we call cups "cups" because that's the notation, then we can use further observation and define what a cup is mathematically and other tools/languages such as physics, chemistry even biology. Etc. the geometry of the cup and the elements it consists of. Basically every observable entity that defines a cup we can write in a "language". Or brain has this infrastructure to generally define the geometry of a cup and then recognize it with the notation or word "cup". If you've ever studied very basic programming it would be suitable to say that "cup" is a map pair with the geometry. Is that so difficult to comprehend? I wouldn't say that the properties of a cup is equal to any specific "concept" as you yourself phrased it. Our entire written and spoken language is just a huge dictionary mapped to structures. The KEYS can be meaningless (sometimes not, if they are based upon another key such as different suffixes or prefixes). But the structure or pattern the keys is mapped to are certainly not arbitrary, in most languages the keys even have history thus they are not as random as you might think.

@aeroscience9834

9 жыл бұрын

What I'm saying is, you can't prove anything in regards to language, as it is not logic based, unlike math.

@gfetco

9 жыл бұрын

Aeroscience You need to provide me with examples, sorry if I was to harsh in my preceding comment (my digital tongue is a bit demeaning). No one has been able to define mathematics clearly it's a collection of different subjects. But it is still a unified universal language. A language that is mainly used to express your logical conclusions and/or observations. I kind of get it though you can't go about saying mathematics is a language that's the same as saying programming is a language (which is clearly is not). Mathematics, Programming are the same as "talking" in a "specific manner : a language" to describe logically drawn observations to a specific demographic or interpreter, to explain how or why something works or is or should be constructed. Maybe a bit to explicit as it is more generic than that of course but I hope you understand why I could see this video as and its propositions as complete rubbish. It feels as his logics are applied to mere arithmetics which is just a very small part of of a much larger scheme.

@aeroscience9834

9 жыл бұрын

But making divide by 0=1 does not make logical sense. You can't prove it with conventional mathematics, so you would have to add it as an axiom. The problem is, there is nothing in nature to support that axiom, so it not valid.

Through my "career" as a elementary school kid, to A-levels and now university I've went through all three stages of maths and now at the end of my bachelors degree/soon starting masters degree, I'm switching through all three every few weeks xD

This is super interesting! as some one qualified in nothing my thoughts tend towards maths been a language.

Is 'blue' real? One can define a range of frequencies as being blue - but that definition would be arbitrary; that is to say that if some children were raised without being told that frequency range, and then asked to define blue, they likely would not come up with the same range. Blue is just a concept we use to encapsulate a commonly perceived phenomenon. Are our perceptions 'real'? Let the ontological debate begin!

@nasiraliclark

9 жыл бұрын

Heather Spoonheim True, if an experiment could be conducted on that I'd be very interested to see the results. You could even go as far to say the colour I have assigned to my perception of the wavelength that corresponds to "blue" might be different to yours. We both recognise that it is blue, but what do we really see? Is it the same perception?

@NoriMori1992

9 жыл бұрын

Stark Clark That question is the root of the concept of _qualia_. It's an awesome concept, if you haven't already you should read all about it. :D

@HeatherSpoonheim

9 жыл бұрын

NoriMori Yeah, I have encountered it - and it was sort of what I was trying to introduce here. To me, numbers are just adjectives - the way we describe quantity to each other, or even to ourselves. If no one is counting, numbers do not exist.

@NoriMori1992

9 жыл бұрын

Heather Spoonheim It makes me think about things like, how different cultures and languages have interpreted and defined colours over the millennia. There are languages that don't distinguish between blue and green. And when you think about it, you could draw the lines between colours anywhere. We consider a wide range of different shades to be variants of "brown", but if we wanted we could consider some of those variants to be distinct colours, in the same way we consider pink to be distinct from red even though pink is just red with white added. In English, at least, this is not symmetrical with blue, which we still consider to be "blue" (even if we can call it something else, like "sky blue") if we add white to it. We could demarcate colours however we want!

@HeatherSpoonheim

9 жыл бұрын

NoriMori Every culture distinguishes between green and blue - you might be thinking of Vietnamese where they are in one group that is further delineated by a prefix - because leaves and the sky have always been delineated by humans. Red is a big one as well because blood - but, yeah, pink, purple, orange and yellow can get rather squiggly in many languages.

0:13 plato's theory of forms

Great work people. Could you people do a video about the Euler's formula and the transformation between imaginary and real numbers. Ontological mathematics.

Nominalism is the one I agree the most. We start mathematics describing simple things that exist in the concrete world and the more complex numbers, like the irrational or the complex themselves are just descriptions of things we cant measure (like Pi), things in more than 2 or 3 dimensions, or just descriptions about abstract concepts that are not concrete, but depend their existence from beings that think or believe is such concepts.

I seem to be somewhere between Platonism and nominalism. I do like the notion that numbers are mathematical objects, which did start off as interpretations of real phenomena but aren't restricted to it. The fact that numbers can only interact with each other in a finite number of ways, to me, seems eerily similar to how physical objects too can only interact with each other in finite ways. That doesn't mean that numbers exist like physical objects. But they're different from simple abstractions because they're not subjective. Does that make sense?

Platonism: mathmaticians are so reliable because unlike all of us in different realms, they have thoughts that are pretty clear in each step, there is no use of the subconscious mind, you might intuitively get a correct math answer but not always and the same is for all kinds of thinking (math or others) but we still use intuition in others.

@GallumArtemi

2 жыл бұрын

yea, yet intuition can do complex calculations like 'where to place my hand to catch a moving object in space.'. it just can't deal with the abstraction of numbers. it is better at dealing with the world of mathematics directly without going through the proxy of abstraction.

What is the name of the branch of math which studies this particular question please?

I personally adopt a stance of mathematical nominalism and only dabble in mathematical Platonism when it aids me in learning new concepts/ideas. It is much easier to treat a new thing with old rules than learn new rules and all that entails.

What strikes me, having just watched this again, is that all these theories are based on a correspondence theory of truth. They are true, and they are criticised, based on how well they refer to the world. Even the fictionalist's argument is based on a concept of true= referring to 'the world'. I've started to consider maths as being an example of a coherence theory, where something is true because it is consistent with the other statements in the set. Of course this comes to problem of 'if there is an infinite number of numbers, can we ever check that every number is coherent with any other'. The answer, of course, is no. But in broad terms, maths seems to work because statements are consistent with each other. Disproving a mathematical theory involves finding it to be inconsistent with other, accepted, theories. It's is probably true that nominalisation brought maths about, but for these abstract terms it seems more prudent to focus on it's consistency.

@starfishsystems

2 жыл бұрын

I agree on all points. It's natural enough to understand the origins of mathematics in correspondence with objects or features of the physical world, and likewise our initial sense of utility in mathematics lies in its application to the physical world. But it doesn't take long before we begin to see places where that correspondence and utility break down, in a direct sense of "√2 cows" or "π/4 wheel rotations." And that breakdown is where mathematics becomes interesting in its own right, because it starts to tell us about itself. It turns out that this self is remarkably rich. Despite having no physical existence, it does have its objects and measures and properties and so on. Some of what we can develop within mathematics indeed tells us about the physical world, and that's nice, but not strictly required. But what seems most fundamental is, as you say, the principle of coherence. It would be hard to work with an axiomatic formalism that allowed incoherence. As a practical matter, it would be hard to get anything out of it. It would also be a limiting feature of a formalism if it produced incoherence. It's not hard to devise trivial examples of incoherent formalisms. It can't be used for much. But then what's the first thing we do? Try to develop a formal account of how incoherence arises, in such a way that the account itself is coherent. Then we've got something. Gödel undecidability is such an account, not of outright incoherence - a true statement that a given system is incoherent - but of proving the existence of systems the truth of whose coherence can't be decided. Isn't that interesting? I think it's interesting. And it's interesting long past the point of counting sheep, in other words concerns over what "existence" means, philosophically, with respect to these abstractions. Existence, as defined by the abstraction, is sufficient to make it interesting.

@vhawk1951kl

Жыл бұрын

I would refer you to the story of the man in Ireland who asked how you get from X to Y and his interlocutor replied: "if I were you sir, I wouldn't go there from here. Perhaps if you asked yourself what do I mean by numbers and just remained with that question without answering it or killing it.

I've discovered that I was fundamentally a mathematical nominalist, in the sense that I always thought numbers were descriptions of concrete objects. Explains why I've been so baffled by imaginary numbers and irrational numbers. Thanks, Numberphile!

@vhawk1951kl

Жыл бұрын

Would it help if you understood imaginary to convey cannot be directly immediately personal experienced other than as an image or symbol/proxy in the dreaming/associative apparatus or mind? If you can directly immediately personally experience numbers, what exactly do you experience if you do directly immediately perorally experience when you do experience numbers if you do indeed experience numbers as directly immediately and personally as you experience or *Know, pain? So simple yes or no question:*Do* you or can you directly immediately personally experience numbers as directly immediately and personally as you experience pain or the thing on the end of your left leg as your left foot? Yes or no, and if yes, what exactly are you experiencing? Numbers or just multiplicity? Numbers are a form of description are they not?Probly (sic-because it pleases me) best avoid the question : "Do descriptions exist?" Can a mirror reflect itself? While we are at it: Where is the where the where the where?

Nominalism supplemented by substitution of the concept of truth by a state of being uncontradicted should bring it closer to everyday life practice. That can shed light on the interaction of the conciseness of models of thought and the fallibility of the mind.

Complex numbers are very useful describing and handling the properties of dynamic systems in which there is an internal delay in response to stimuli, so they describe real characteristics of real objects. It just so happens that at times the mathematics is found before meeting the objects it describes... which would be troublesome, if we did not live in an universe where this kind of things tends to happen on a constant basis (see the single photon diffraction experiment, with the later choice addendum).

Numbers is just a language used to define logic. Is language non-existent too?

@TheLililitu

9 жыл бұрын

***** Grunting? When I type, I don't make any noise at all. When I read, the words don't grunt in my head.

@TheLililitu

9 жыл бұрын

You know, I went to community college and there are, most certainly, "real" numbers. Haha. Anyways, there's a subtle difference between 'real' (as in reality) and existing (existence) -- although these words are used interchangeably in every day contexts. Reality refers to perceptions, senses, and even beliefs. It's actually a very loaded word that holds human interpretations of existence. You have your reality; I have mine. Someone might say "these are the realities children in (insert third world country here) face everyday." In America, middle class families live in different economic and social realities. People come from 'different' worlds, so to speak. Existence, on the other hand, tends to be more concrete. For instance, France -- its people, geographical land marks, etc-- exist. You and I can not only feel and sense objects in France, these things exist even if we can't sense them. Deaf, blind, and physically insensitive people aren't evidence the Eiffel Tower doesn't exist. They exist because objective standards allow us to verify their existence in physical reality. We can measure (use standards) the Eiffel Tower, a thing that exists, but we can't measure (at the moment) people's differing perception on artwork, love, or lifestyles. Are numbers real? Yes. Do they exist? hmmm. Standards like meters, grams, etc, which comprise of numbers help us verify if objects are actually in existence. After all, if everyone objectively measured the Eiffel Tower in meters, we'd all agree upon some accepted value in meters. However, what standards do we use to ensure that numbers actually exist?

@blackflash9935

7 жыл бұрын

qwerty222999 Well it's possible that, since logic is a concept that living beings create trough pattern recognition in their brain, maths is based on a human concept.Our recognition of patterns makes us want to name and symbolize those patterns that we see.So if you had the time you can pretty much find the logic behind every equation and prove that that equation is based on human understandings of the world.To summarize my opinion is that maths is the language of the universe from the living beings's perspective (mostly humans or only humans), since there is a lot of evidence that caters towards that, although I don't really think that this could be the most correct point of view describing maths.

@TheCinnaman123

7 жыл бұрын

qwerty222999 Of course languaged don't exist, in any objective or concrete sense. Its an emergent property of minds, and if you remove the minds, your remove the language. Languages are a way of communicating ideas, but they along with math are no more real than chess or mancala...

@pepii755

7 жыл бұрын

qwerty222999 whoa dude

I think the 'discovery' of mathematics is like the creation of a language, albeit one that's a lot more rigorous (i.e. logically deductive) in its creation than that of a spoken language. And it's a language for describing the patterns/ structures we can see or imagine. I don't think we know enough about the conscious mind to understand what it means for a structure/pattern to be mathematically describable by it (and not just by our mind, but one that's maximally 'intelligent').

I am just appreciating how polite comments were 8 years ago

This has a tremendous potential to help us promote Intellectual Nutrition thanks!

Numbers exist, the very act of knowing about it maintains it's existence so it really doesn't matter if they're a metaphysical object or just an abstract fiction it doesn't change the fact that the idea of them exists. So I guess I'm a Platonist?

I think the fictionalism is the most accurate, since Mathematics are simply models of the things we consider true… Mathematics uses true logics, but isn't always using accurate representation of the true world… Mathematic is a platonic/nominalist science. Real sciences are connected to the real world, not to fictional models.

@rumfordc

7 жыл бұрын

im confused. is 1+1=2 fiction?

@markhaus

7 жыл бұрын

From my understanding of fictionalism 1 and 1 is 2 is just a piece of our construct of the universe that makes sense to us. But math is made of axioms that are described by other axioms within that same construct so there isn't an absolute truth to nail that construct down to. Personally I think fictionalism lacks the rigor of realist views of mathematics and if you can't stay grounded within the axioms we have (at least until they're disproven) then you just get stuck in solipsistic loops where you can't really refine anything with thinking. But I'm no expert and I've heard wiser people than me argue it both ways.

@deeptochatterjee532

7 жыл бұрын

Marcus Grant Well it doesn't change if you call the numbers anything different. If you make 1 tau and 2 Mao then tau+tau is still equal to Mao and Mao is still Mao times tau. In this universe that remains constant.

@deeptochatterjee532

7 жыл бұрын

SymbolX Our sciences are dependent on three things: mathematics, the scientific method, and logical reasoning. If you take aways any of those three we will end up with much less scientific knowledge.

@_WhiteMage

6 жыл бұрын

_>is 1+1=2 fiction?_ By that same token: "Elves have pointed ears," "Leprechauns wear green," "Unicorns have horns." So it basically depends on whether you believe "true" statements can be made about fictional things. Perhaps "canon" is a better word to describe it.

Ironic that all the other videos shown in the beginning of this video are ones I watched in this binge session.

MORE OF THIS!!

How about nothing but numbers exist? Basically, every particle has its values, its location, its properties etc. All the numbers we make up are ways to connect those values. Numbers don't exist in the sense of 1, 2, 3 but as relations. So this is twice that, and this is 3 times that and so on. The complex numbers like phi are simply infinitely long connections. In the end, if we'd take away the human interpretation of the universe, it's all just trillions times trillions times trillions times trillions of data points with interaction with one another. Just my view on the topic, be welcome to share your thought.

@NoConsequenc3

9 жыл бұрын

How can you, a human, theorize what the universe is like in the absence of yourself?

@TheDebries

9 жыл бұрын

Pseudo Arch Because theorizing is just that, theorizing. I might be fundamentally wrong, but it is just a theory. Unless you have strong reasons/proofs of me being wrong, it will be a theory. Also, just because we are humans doesnt mean we cant think or theorize about things beyond the human ways, even though we cant fully comprehend it. If I get data on a piece of paper and I know enough formula's, I could do massive calculations on everything without ever needing to see what exactly I'm calculating. So up to a point, the universe is just raw data that changes itself (in a way, just not sure what to think of quantum physics in this)

@ishankashyap3350

9 жыл бұрын

Thats a bit like nominalism, which I support!!!!

@Devilofdoom

9 жыл бұрын

I actually agree with you. My own personal theory is that all of reality is in fact a quantum bit. And by that I mean a piece of information that equals both zero and one at the same time (not that I consider time to even exist at this point, I just used it for lack of a better word). So ultimately this means that all combinations of the two must exist making all of reality just a product of infinity. First thing people ask me when I try to explain this is usually "How do you get from numbers to physical things?" and I tell them to look at a 3D game. You can see that you are playing within a world of seemingly solid objects but at the end of the day you could take the machine code, convert it to decimal and what your left with is a number. A number that contains all the information needed to create a 3D world. If you think of just enormous infinity actually is would it be any surprise that somewhere in there is the code for Earth and the rest of the universe?

@George4943

9 жыл бұрын

Devilofdoom Since the observable universe is finite there is a number encoding all of it. The unobservable universe, if any? It may be infinite in which case no finite code exists.

i (as a student of math) agree most with Fictionalist but what annoys me is that existing and being true or false is getting mixed up here. for me they are totally independent...

Is there a practical limit to the accuracy of pi? At what point would there be no useful need to continue fine tuning the approximation. If we could know the maximum dimensions of the 'cold death' of the Universe, what would be the cutoff for calculating relationships between the diameter of the universe to the Planck length?

You should make some calculus videos, or ones about vectors. Those are interesting.

Plato to the core!

Numbers are similar to language, intellectual property, thoughts, ideas, memories, and other brain states. In this regard, they are as real as the concepts of a chair, a bed, or a house. These are different from the objects (chair, bed, and house), but the concepts (i.e. brain states) are needed for humans to construct chairs, beds, and houses from real resources (wood, plastic, cotton, etc.). This does not imply that people could not sit on rocks, sleep on the ground, or live in caves without these concepts, but we would not be as comfortable doing so. We can extend this logic to another level. Wood, for example, results from Nature's DNA memory of how to grow and to reproduce trees. Rocks result from Nature's memory that SiO2, Al2O3, etc. can form crystalline grains and that gravity and rain can pack these grains together into dense solids. There is a theory, in fact, that the fundamental physical particles are merely the knowledge of how to form these superstring states from space-time fabric. Given these facts (I know the theory is not a fact..) it is reasonable to ask which is more real? Is the chair more real or the knowledge of how to build a chair and the knowledge of how it will make us more comfortable?

Couldn't you describe pi to someone as the ratio of diameters of a circle to the circumference? And isn't the square root of negative 1 used in oscillation/rotation in electric currents? Are there other numbers difficult to explain through nominalism?

Correct me if I'm wrong, but wasn't Pi first conceived as a ratio, not necessarily a number to be used abstractly on its own? If so, it could fit perfectly within Nominalism as representing the proportion between a real circle's circumference to its diameter.

Can't we just say that "mathematical truth" is derived from the set of axioms what we've defined which are the rules of the game? It's really no different to chess it seems like. No one would seriously claim that chess moves exist outside of space and time, there are a merely a set of rules which govern the game. So the case of irrational or imaginary numbers... they just emerge from the rules of the game. The epistemology here is Mathematics and the truth or any mathematical claim is then determined by verifying it against the axioms of the epistemology... no?

@pharder1234

9 жыл бұрын

exactly, it was kind of weird that they were conflating, truth as in correctness through a set of axioms, and truth as in a universal law in reality.

@bpansky

9 жыл бұрын

Yes you are on the right track. The rule of the imaginary number is simply declared "it is a number which you can multiply by itself to produce negative one". It's simply true by definition, just like saying "all bachelors are unmarried" is simply true by definition.

@NoConsequenc3

9 жыл бұрын

bpansky Such gives rise to the practicality of language. It's kind of like how many times we will know a word and exactly how to use it and the meaning it's suppose to convey, and yet when called upon to define it we just can't find the words. Sometimes, it's the word itself being used that is it's definition.

@bpansky

9 жыл бұрын

"Sometimes, it's the word itself being used that is it's definition." That sounds like complete nonsense. Do you have an example?

@NoConsequenc3

9 жыл бұрын

bpansky I mean this in a certain way and within a certain context I know that I, in the past, knew how to use a word and what it implied within a context, but when asked what it meant I didn't know how to describe it but only how to use it. This is what I mean by "the word itself is the definition"

Seeing a lot of passionately written walls of text, but not seeing anything that does not fall into one of the three philosophies described in the video.

@AnalyticalSentient

7 жыл бұрын

Booga .Boo What is your position on the subject?

this video made me sub to this channel a few years back... lol

I think it is more useful to think of wherefrom the truth of mathematical statements come. Immanuel Kant says a great deal about this but strict quantitative relations are analytic (counter to what Kant thought). However when we state things such as "the area of a circle is equal to the radius squared times pi" it becomes synthetical. However the quantitative relations are strictily define by us. It depends on our definition of quantities and such. And as such Mathematics is true but only as so far as the statement is synthetical or as so far as we define the outcome.

I'm with plato on this one

Two plus two is four minus one that's three quick maths

I love it when he says nominalism breaks down because, how in real terms can we describe "imaginary" numbers!

I think this is similar to asking: Does beauty exist? Does justice exist?

DEEEEP. give this man a cookie :D

why didn't he mention Rorty and pragmatism when he was talking about fictionalism. which reminds me of bentham idea of truth as a fiction or as an agreement.

@clive1611

8 жыл бұрын

Mostly because I didn't have very long. Stacks of stuff I'd like to have talked about that I didn't, but only so much time. :)

@David-sp9vd

8 жыл бұрын

Thank for the video and response. I guess I left it brief as well. I will just quote the Stanford Enclyopedia of Phil. : "Bentham's analytical and empirical method is especially obvious when one looks at some of his main criticisms of the law and of moral and political discourse in general. His principal target was the presence of "fictions"-in particular, legal fictions. On his view, to consider any part or aspect of a thing in abstraction from that thing is to run the risk of confusion or to cause positive deceit. While, in some cases, such "fictional" terms as "relation," "right," "power," and "possession" were of some use, in many cases their original warrant had been forgotten, so that they survived as the product of either prejudice or inattention. In those cases where the terms could be "cashed out" in terms of the properties of real things, they could continue to be used, but otherwise, they were to be abandoned." However, considering Rorty, where the possibility of change becomes politically impossible, or not possible even in the spectrum of reasonable argument, where we only refer to concrete-tangible things, Rorty concludes, since we cannot reach agreement in principle with platonists, but that it maybe be possible to simply validate their truth on a term or a proposition's effective usefulness (pragmatism.) Anyways, feel free to make any corrections here in my description, if you have the time. I am also being far too brief here. Thanks for taking the time to do the video, and to respond to my comment. It was interesting to someone, like myself, who has studied philosophy on my own and is working towards an Economics-Mathematics degree.

when we talk about i, I think we also need to know with respect to what multiplication, and that there can be multiple possible i's in terms of what we define to be 1, depending on what kind multiplication we are talking about

Great video.

For something to exist outside space and time seems to be like saying something exists no where and never.

@jeroenverschaeve3090

8 жыл бұрын

+Kelbie The fourth dimension exists, except we just can't imagine it since we look in three dimensions. Surely numbers can exist in that was as well.

@kelbs_ow

8 жыл бұрын

Jeroen Verschaeve For what you said to mean anything you actually have to provide evidence and not just say that they exist as i can change one word in your sentence from "numbers" to "flying spaghetti monster".

@kelbs_ow

8 жыл бұрын

***** Thats what i said isn't it?

@kelbs_ow

8 жыл бұрын

***** Haha its okay:)

@nychold

8 жыл бұрын

+Jeroen Verschaeve The fourth dimension does exist in physics, but it is considered spacetime and can be shown to curve using general relativity (which, for the most part, has been demonstrated to be correct). Existing close to a gravity source will cause time to move slower than further away; ie: clocks on orbiting satellites have to be adjusted in order for GPS to work. Another extension of three dimensions into 4 dimensions could also just be time. You can create a 4-dimensional "graph" of an object's position, and watch it change throughout time. Even objects which pop into and out of reality (ie: virtual photons) would have a graph, albeit not a continuous one. In a mathematical sense, the fourth dimension does exist, as it requires 4 "dimensions" in order to perform linear algebra transformations from one three dimensional vector space into the same three dimensional vector space. Within just three dimensions, you can get rotation and scaling, but not translation. If you want to talk about the fourth dimension as some additional physical dimension, then you would need some pretty amazing evidence to back that up.

If you asked me, "What is the most absurd combination of three words you can make in the English language?" I would have to say it'd be, "Math is false."

@balsoft01

7 жыл бұрын

Does Rassel's teapot sound familiar to you? If yes, than you should proof that math is true before you state that. Let me guess, you don't have a single proof.

@Adam-rt2ir

7 жыл бұрын

I feel more like math is a big concept that we follow, that is nor true nor false. Like, say, what is circle for example? I don't mean that i don't know what that is, but in "real" world does it even exist? What's a line? Does that exist? A square? It may not exist but it has it's aplications. And math certainly doesn't lie. It's just the world that we exist in isn't the same as we think it is.

@steliostoulis1875

6 жыл бұрын

Александр Бантьев Read Gödels Theorem

You can think of 42 as the product of 6 and 7. Pi is simply the quotient of the circumference and diameter. We may not know its exact value, but it does have one that can be represented in mathematics.

The numbers in our maths are logical concepts which at first best described the physical world around us and the abstract understanding is developed and refined over time. However, those numbers have original ties to the physical world and then became abstract describing reality that may or may not exist. At the end of day, they are just representations and not the actual thing being represented. Also, human concept of numbers might be totally alien to another creature and that creature might say, ""Wtf are you are guys talking about, there's a more logical and easier way to represent these things" Like numbers, truths are concepts -- something that we've agreed on over time.

I'm pretty sure mathematics is a language- a system used to describe the relationship between different elements. The number one is no more or less real than the word "one", it's just more flexible as a tag. Irrational numbers are just hypothetical relationships that are not logical, and do not exist in our world.

@hannahsypniewski7356

9 жыл бұрын

I've always wondered whether it was a universal language: if there was another way people could have come up with it, or if there was no other way to describe those relationships. We've sent prime numbers into space thinking that math would be universal but it's interesting to wonder if our math it would be as different to aliens as speaking another language.

@ultimatenoob3

9 жыл бұрын

If the aliens had 8 fingers, then they may be using a different base, such as octal. We have only 10 words to describe our numbers because we had 10 fingers to count and had to repeat after 10 counts. Other than all our mathematical relationships describe the behaviour of the universe, and there is full reason to beleive that they might also have discovered maths the same way as us

@AlecBrady

9 жыл бұрын

Sinclairelim "Irrational numbers are just hypothetical relationships that are not logical, and do not exist in our world." Quantum theory relies on imaginary numbers. They are perfectly logical and if any numbers exist, imaginary numbers exist too.

@Sinclairelim

9 жыл бұрын

No, the numbers describe something, that something is real, the numbers are not, they are just a description of the relationship between different elements of a given system.

@JuvStudios

2 жыл бұрын

Almost all measurements in the real world are irrational, we just approximate them.

Fascinating!

for a nominalist, sqrt(-1) is the solution to the equation x^2+1=0, which is equivalent to the question: if you have x^2 objects arranged in a square with lengths x, and you add 1, what length is needed so that the resulting number of objects is equal to zero?

Fantastic video! I think I’m on the end of Fictionalism in general but never considered it before now. Thanks for putting in the effort of making great videos 😁

What do you mean by "fictionalists" think math is false? That seems to imply that they think it's incorrect in some way. By false do you mean not real? or do you mean incorrect? I'm leaning to think that numbers aren't real. They're just a concept we humans use to explain things. And with things like Pie and square of -1 we are beginning to see our concept, aligned with proper logic, has the power to show us things we don't understand and will never be able to. I think the very fact that imaginary numbers exist and we can prove it with math proves that there are certain un-explainable things that exist somewhere outside of our reality.

@MrCrazytodd

9 жыл бұрын

Mike Y That's what I wanna know. he said they say that math's false however very useful / helpful, however never specified in what way math is "false", as if they knew what "correct" were :p

@KillianDefaoite

9 жыл бұрын

Mike Y "Pie" LOL It's spelled "Pi".

@mikeya2384

9 жыл бұрын

:p

The philosophy of mathematics. *Mind Blown*

(Cont.) and it is because you have a universe to play with which contains a lot of concepts that can easily relate with physical reality and therefore be used as a model(A natural number represents a quantity, a rational number a fraction, a complex number a rotation in the plane, a vector bundle the configuration space of a particle, ecc...)

0:29 "so [numbers] don't exist in the same way that tables and chairs do" 1:37 "so in the same way a table exists, a chair exists, a number exists" Talking about Platonism both times -_-

@aditichegu1951

3 жыл бұрын

there's a difference between just existing and existing in the *same* way 😂

@sehr.geheim

3 жыл бұрын

@@aditichegu1951 „so numbers don't exist in the SAME way a table exists“ „so im the SAME way a table extists, numbers exist“

"What use....."? Was my question. I know the answer but I get the feeling you are maybe missing the point buddy?

I think of numbers as just tools in a method that allow us to apply that method ( the method being mathematics ) in order to interpret anything , we can rely on these numbers as tools and nothing more (they're not objects that exist somewhere, nor are they anything more than what we perceive certain phenomenons as )

Please do a video on complex numbers!

Numbers are Binary Code for our Universe if you want put it that way

@xvipes

9 жыл бұрын

So we are digital in the end?

@XelaShade

9 жыл бұрын

Particles are digits basically and we consist from them

@xvipes

9 жыл бұрын

And how many particles we have?And this goes on and on... sadly :/

@borilboyanov5544

9 жыл бұрын

Thanos Densoulew The Universe have three (3) particles: 1 "Head", 1 "torso", and 1 "set of appendages"... everything else is debatable LOL

@TheToXeye

9 жыл бұрын

Giorne Ganz I would agree that any theory which describes the universe is better than any ignorance which does not describe it. Therefore, atoms exist just as much as quarks exist. Somehow, quarks would contradict atoms in the greek philosophy, but we know that atoms exist. Chemistry is a tangible and very real science. And then there's the "binary code" in genomes.

If I draw the blueprints for a house that hasn't been built, are those blueprints "false"? Certainly the house doesn't exist, but nor is it an abatract name for houses. If I were to build a house, I could use those blueprints I carefully planned out and thought about, but the blueprints do not become "true" if I build a house closely resembling the abstraction I put on paper. So my position is that numbers are not real, they are a mental tool, but that doesn't make math somehow "false."

@MountainBlade100

9 жыл бұрын

+Ryan N Yea , it only makes it "probable" .

@rumfordc

7 жыл бұрын

+MountainBlade100 ... no. It's just true. 1+1=2... PROBABLY?! lol only the symbols are probable here, not the numbers nor their relations, which is math.

7:35 ah, I finally hear it outside my head

Can you do a video where the math and physics professors weigh in?

Isn't existing outside space and outside time a bit of a contradiction? As what you are really saying is that they exist at no place and at no time. Which is the same as they do not exist at any place and do not exist at any point in time. Which start to sound an awful lot like the definition of not existing.

@Devilofdoom

9 жыл бұрын

But what its the other way round? Lets say numbers don't exist within space and time, rather space and time exist within numbers.

@Devilofdoom

9 жыл бұрын

Tethloach Kingofreason Yet nothing is a flawed concept. It can't exist because if it does then it is something. I've always thought its that very paradox that created reality.

@TheToXeye

9 жыл бұрын

It kind of makes sense to make use of the tools we are given. Math is a tool. It would not make sense to throw it away in favour of some incoherent mysticism. So in a sense it exists to us and us only. It is our own creation and ours to use. It is not a creation of some mystical being, it is a creation of logical thinking. It is a tool for logical reasoning. And sometimes, logic is the least logical thing you can imagine. At least by the definition of "logical" being that it makes sense. Hence why logic itself has led to many paradoxes. But when you realize that you are wrong, perhaps you will learn a better way. And every time you encounter a paradox, it might be a moment to learn something. For example: "I know that I know nothing" is just a way for Socrates to brag about his knowledge. Ironic, isn't it?

@borilboyanov5544

9 жыл бұрын

Devilofdoom OK. Universe "has" time-space so it could be said Universe "is like" a Number... What's the value of the Universe then? :)

@Devilofdoom

9 жыл бұрын

Boril Boyanov I would say thats impossible to know. It also depends on how you define "universe". If you mean all that is, then i guess the value is infinity. But once you define a finite amount of space-time, such as the observable universe then it will have a finite value.