Teenager on TiKTok Resurrects an Essential Question: What is Math? (smithsonianmag.com) 160
Long-time Slashdot reader fahrbot-bot shares a story that all started with a high school student's innocuous question on TikTok, leading academic mathematicians and philosophers to weigh in on "a very ancient and unresolved debate in the philosophy of science," reports Smithsonian magazine.
"What, exactly, is math?" Is it invented, or discovered? And are the things that mathematicians work with — numbers, algebraic equations, geometry, theorems and so on — real? Some scholars feel very strongly that mathematical truths are "out there," waiting to be discovered — a position known as Platonism.... Many mathematicians seem to support this view. The things they've discovered over the centuries — that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever — seem to be eternal truths, independent of the minds that found them....
Other scholars — especially those working in other branches of science — view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing "outside of space and time" makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. Platonism, as mathematician Brian Davies has put it, "has more in common with mystical religions than it does with modern science." The fear is that if mathematicians give Plato an inch, he'll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all...?
Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions — what mathematicians call axioms... But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it "fit" so well with what we observe in nature...? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner concluded that the usefulness of mathematics in tackling problems in physics "is a wonderful gift which we neither understand nor deserve."
"What, exactly, is math?" Is it invented, or discovered? And are the things that mathematicians work with — numbers, algebraic equations, geometry, theorems and so on — real? Some scholars feel very strongly that mathematical truths are "out there," waiting to be discovered — a position known as Platonism.... Many mathematicians seem to support this view. The things they've discovered over the centuries — that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever — seem to be eternal truths, independent of the minds that found them....
Other scholars — especially those working in other branches of science — view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing "outside of space and time" makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. Platonism, as mathematician Brian Davies has put it, "has more in common with mystical religions than it does with modern science." The fear is that if mathematicians give Plato an inch, he'll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all...?
Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions — what mathematicians call axioms... But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it "fit" so well with what we observe in nature...? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner concluded that the usefulness of mathematics in tackling problems in physics "is a wonderful gift which we neither understand nor deserve."
TikTok, this story is a crock (Score:5, Insightful)
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Sure, but that was a time before Slashdot. https://en.wikipedia.org/wiki/... [wikipedia.org]
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At one point in time, putting Plato in the headline would have generated more clicks and been more relevant to the story. That time is not now.
So... First Pluto now Plato demoted to a dwarf something-or-another...
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Re:TikTok, this story is a crock (Score:4, Informative)
just no Amazon, please (Score:2)
Re: just no Amazon, please (Score:2)
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I'd recommend the book's publisher, except that most publisher websites are extremely complex to use compared to an Amazon checkout. I've had just this problem several times in the last year trying to send books to family or colleagues.
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Also this book, while flawed, Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being [amazon.com] attempts to answer the question.
> Here's the original TikTok in question. The person is dumb as a brick.
Oh dead god -- is that ever painful to listen to. (I'm suprised that "Air Force" T-Shirt doesn't say "Air Head.") Anyhow, here is like, you know, a transcript of the mp4 [ssstiktok.io] like, you know:
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[1] Saying "I don't think Math is real" is pretty fucking retarded.
But it's not! It's pretty complex at times...
Ba dum tscchhhh
[3] Why does knowing WHO came up with the concept of Algebra or Mathematics matter? It is irrelevant; it won't help you pass Algebra class.
Honestly this sounds like you're saying "shut up and learn only the curriculum". I agree with Paul Lockhard that teaching maths without any of the history, context and human struggle is a mistake.
Furthermore, it is debated whether Mathematics is
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Hang on, you might just have made their point:
e^(i * pi) + 1 = 0.
So - math isn't real, you're working with imaginary numbers!
I prefer Flammable Maths https://www.youtube.com/c/papaflammy/videos [youtube.com], but even less people would enjoy his content.
Re:TikTok, this story is a crock (Score:5, Insightful)
This is a very obnoxious response to a really earnest question. I find it notable that professors of mathematics are delighted, and here you are dumping on a teenager who is voicing some fairly interesting questions that she had but clearly has no outlet for them. Have you considered that perhaps the reason why she's on TikTok asking about this stuff is because our system has failed to answer these questions for her? That nobody ever engaged her or made her consider these things before? Sure, we're mostly tech people here and probably this stuff has gone through our heads at one point or another—or maybe we've just intuited it but never considered it—but I hardly think that's a good reason to be so aggressively patronizing.
Sometimes I sit and contemplate mortality and the universe and I come up with questions and answers that aren't unique, but I wasn't taught existential philosophy in school. Taking a philosophy class beyond logic never occurred to me because people have spent so many years making jokes about philosophy majors, I didn't understand that there was something really interesting going on there. Now I wish I'd taken that as my minor in University. But I certainly wouldn't feel particularly encouraged to continue if someone laid into me, calling me 'retarded' for even wondering out loud about ethics.
I don't know how we got to this place where we pathologize even ASKING questions and engaging in discourse. I really hope she reads some of the friendly answers that come her way.
I hope some of you ask the question, "what does it mean to treat another person well," or, "what kind of philosophy belongs in our curriculum?" It's clear that while some people have some answers in regards to mathematics, they're sorely lacking in some empathy. Maybe bone up on that a bit.
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This is like reviewing Sesame Street like it's some serious maths documentary.
[1] 11 marbles... Ah ha ha! 12 marbles... Ah ha ha!
[1] This count guy is fucking retarded, can't he even count higher than 12!
It's TikTok, get a grip.
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For anyone who cares (Score:4, Informative)
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I'd argue Goedels incompleteness theorem was a bigger blow to the project of formalizing mathematics as a single system of self proving rules. Russels paraddox simply proved set theory wont work.
With all that said I dont REALLY agree with any of the takes offered. I think Maths is simply just a language. A set of symbols used to reason and communicate *stuff* to other humans. Its a very specific language, with very specific laws, what coders would describe as a DSL (Domain Specific Language). Music is too.
Yes, please (Score:4, Funny)
I whole heartedly endorse people who follow this line of thinking. Especially if they endorse the new thinking that match is racist and 2+2 can sometimes equal 5.
The more people that think this way, the better.
My kids are going to need high paying jobs that use math, and the less competition they have, the better.
The world will need unskilled labor and burger flippers- those jobs don't use that nasty, evil math.
Re:Yes, please (Score:4, Insightful)
Are you a bot? Did you read even the summary? Do you understand what it's about? Are you just triggered because the concept of 'TikTok' appeared in the headline?
It's about a question of philosophy and epistemology that has been asked and thought about for hundreds or thousands of years in various forms. If burger flippers continue to exist for much longer, the type of people who will do that job are more likely to be people who lack intellectual curiosity and deep understanding of what little they know. I have a 20-year-old calculator that can do a calculus problem out perfectly in less than a second.
Employers of the future don't need mindless pocket calculator employees who can turn out the answers to math problems. They need people who are capable of thinking deeply, critically, and rationally about problems -- skills they learn when exercising natural curiosity to ask epistemological questions such as, 'how do we know that?' and 'why is it so?'
Yep, that *is* entertaining (Score:2)
> I like to play a game where I fix the issue while they are talking. I then wait for them to finish talking before informing them that its no longer a problem. Happens more than you would think.
Yeah I do that sometimes, because so often certain people spend more time talking about a problem and solution than it takes to just do it. My current boss and my boss two jobs ago were like that. My last boss very much was not. He'd give me a big project, like "write a software development policy for the organ
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Read the history of the calculus sometimes. It took a boatload of deep thinkers before the pieces fell into place. Most of the early thoughts got replaced, but what they were replaced with would have been developed were it not for the early erroneous thoughts.
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I whole heartedly endorse people who follow this line of thinking. Especially if they endorse the new thinking that match is racist and 2+2 can sometimes equal 5.
Well, it can equal 11.
The more people that think this way, the better.
My kids are going to need high paying jobs that use math, and the less competition they have, the better.
The world will need unskilled labor and burger flippers- those jobs don't use that nasty, evil math.
The lack of basic math literacy is frightening. You don’t need to understand diff eq; but at least addition, subtraction and multiplication. How many times have you bought something that cost Y.X, given the clerk a bill equal to Y, they ring it up while you look for C amount of change; when you give them the X change get a blank stare and an explanation that they can’t take it because the register said they have to give you a specific amount of change?
I don’t know w
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Snicker. I was watching one of those Prosperity Preachers on the tele, they are good comedic material. One fellow was opining about the number 1000 and how it comes up repeatedly in the Bible. He informs us that he's a complete stranger to math but he gets the import of the number 1000. The message slowly morphed into 1000 people each sending him $1000 to "continue his ministry". I contend it would "continue his private pool and bathhouse construction." Then the squeeze play, you must sow before you reap an
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Math does not follow from observation. Full stop.
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Some does, some doesn't. Although follow might be too strong a word. Rather, some observation inspires some math. Once a mathematical area gets going though, it seems to generate a life of its own.
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oh, ~2 + ~2 = ~5
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This isn't hard, revolutionary, exciting, profound or interesting. I would really like to know why people are making a big deal of it.
This is completely off-topic, but people are making a big deal of it because a guy named James A. Lindsay who says he's a math PhD is writing 8,000 word essays on how a straightforward understanding of math like the one you've posted is a sign of the death of Western Civilization and the return of mob rule. He's getting impressionable people worked into a froth by saying that it represents "self-interest, cronyism, corruption, and an unstable form of uncivilized might-makes-right that will surely eventually collapse into the more brutal and familiar stable sort in which whomever can kill enough people gets to make the rules."
He says you're either evil or, in your innocent naivete, you have been duped by evil people. You're preparing us to accept death camps by making a point about pie charts.
I know who James A Lindsay is and what he has written and spoken about, like the grievance studies hoax, and "The Two Big Falsehoods of Critical Social Justice". I wouldn't recognize him from your description though.
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Clearly you have not considered that suggesting that 2+2=4 clearly identifies Lindsay as LITERALLY HITLER!!!!!11111OMFG!
Definition (Score:2)
Math is a system by which one can derive information and predictions about a situation by laying out the facts and then taking advantage of the layout to manipulate those facts to extract the prediction or information needed.
And science is (Score:2)
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I thought we left manipulating the fact up to the statisticians?
It's very simple - math is a tool (Score:2)
Math is a tool that most people just use for different purposes - anything from making change to sending people to Mars. A much smaller group of people (e.g. mathematicians) develop and improve math. It's not different than a saw. Most people will just use the appropriate type of saw to cut wood, metal, or other materials. There is a much smaller group of people who develop, improve, or invent new types of saws.
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No maths is an art. You can use art as a tool but that does not make at itself a tool.
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Math is a religion [amuniversal.com].
Re: It's very simple - math is a tool (Score:2)
You can call tool design art if you want. Designing a better mousetrap is art to some.
Re:It's very simple - math is a tool (Score:4, Interesting)
And if we return to Mathematics, it's both invented and discovered, and the debate about how it is more discovered or more invented is akin to the grand debate at the begin of Christianity if Jesus is more godlike, or more human, which led to the big schisms in early Christianity e.g. between Nestorians, Orthodoxy, Catholicism or the Assyrian Church.
As an example: To describe the Real Numbers, different mathematicians in the 19th century invented some nifty methods, like Cauchy sequences, Dedekind cuts, Bolzano-Weierstrass etc.pp.. Each of them can be used to describe a certain property of Real Numbers, their completeness in respect to sequences, which makes them different to Rational Numbers. Each of the methods was invented. But behind them, there is the discovery, that, once you set one of the methods as axiomatically true, you can prove the others as theorems.
The Art of Explanation (Score:2)
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If it has absolutely no real world appliance (Score:2)
If it has it's called "physics". Infidels.
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So cryptography is physics?
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That makes the person giving me my change a physicist.
Maths tied to Universe (Score:5, Insightful)
If mathematics is just something we dream up from within our own heads, why should it "fit" so well with what we observe in nature...?
I used to be amazed by that but after a conversation with a colleague in maths a few weeks ago I'm slightly less amazed. His point was that the rules of maths are set by our universe. For example, the reason we have 1+1=2 is because if I take 1 litre of water and add another litre of water to it I have 2 litres of water. However, if we were in some unfathomably different universe where if I did that I only ended up with 1.5 litres of water then we would undoubtedly have developed some completely different rules on which to base our maths.
It's also even easier to see that our universe has impacted the way that we develop maths. For example, calculus was invented by Newton to describe the behaviour of mechanical systems. Even today the development of maths is being impacted by string theorists who are pushing the development of maths in the direction they need to explain potentially physical theories of the universe.
The thing I find interesting with this line of reasoning as a physicist is that it suggests that maths may not be as fundamental as we tend to think it is and, if it isn't, then it suggests there may be a more fundamental way to approach maths that is not so "our-universe" centric that may suggest new approaches and ideas for getting at really fundamental physics.
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Galois land. Take 1 liter of water, add anotherand you have none (mod 2, different numbers possible).
Re:Maths tied to Universe (Score:5, Interesting)
Such a universe would be strange in even more ways. If it were just water that did that, they'd probably just deal with it the way we deal with any chemical reaction that creates byproducts or consumes reagents. OTOH, I think what you really mean is that in this bizarro universe, *all* additions would have a result that scales down 25%. Snap your fingers and make that happen here, and it's sure death; but since you've posited the notion of higher life forms speculating, this alternative universe has to have something about it that makes the scaled addition survivable. What happens when you have a child? The universe might be populated by a class of demi-beings, and this would be accepted as normal from the very beginning.
As the demi-beings accumulate nutrients and grow, they do so at a slower rate than in our world. Do they eventually become whole beings, or are they always demis? Do new classes of life emerge every time you bear offspring and that has to be survivable and normal too, so everything mates with everything maybe?
But, if Dad is alone and the kid walks in, what's in the room? Then the kid leaves and walks in to Mom's room. What happens? Maybe the rooms get smaller every time somebody walks in!
Then, what happens at the subatomic level when particles collide? Quantum physics in the 1+1=1.5 universe? It would be a fun exercise if we even fully understood physics in our own universe.
We are in that Bizarro Universe (Score:2)
If I'm going 10 miles per hour and double my speed, I can go 20 miles in a single hour. Again, math and reality are in agreement.
If I'm going
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If I'm going .75c (constant for the speed of light) and want to double that, math could arrive at 1.5c but reality prevents us from ever going that fast. At that point, we don't say that math doesn't work or that reality is broken but we do live in a universe where something like simple multiplication doesn't really get us an answer reflecting reality. It's at those intersections that we fall back and say, "huh, that's unusual. I wonder what's going on there." and we begin fleshing out new dimensions for math and science, like relativity.
If you have a 1 gallon container with .75 gallons of water in it and you add .75 gallons of what what do you have? A full 1 gallon container and a wet floor. Your example doesn't break multiplication. It says that multiplication isn't the correct operation to apply there. It says that the rule about what you do with acceleration is more complex than a simple multiplication. There is a ceil operation in there (or something like that)? Math is a modelling tool. Your physics being incomplete or inaccura
The other way around, I think (Score:4, Interesting)
I used to be amazed by that but after a conversation with a colleague in maths a few weeks ago I'm slightly less amazed. His point was that the rules of maths are set by our universe. For example, the reason we have 1+1=2 is because if I take 1 litre of water and add another litre of water to it I have 2 litres of water. However, if we were in some unfathomably different universe where if I did that I only ended up with 1.5 litres of water then we would undoubtedly have developed some completely different rules on which to base our maths.
Those kind of situations happen all the time even in our own world - mix one liter of water and one liter of alcohol and you won't get two liters of liquid. 1+1 != 2 is not unfathomable, it's every day, and that points us to the fact that it's not "math" that magically matches the real world, it's that we add clauses and subclauses and exceptions and decision points until we get a mathematical system which matches our universe and what we want to accomplish in it to a pretty good approximation. Turns out that maybe parallel lines do meet in our universe. Turns out that a quantum particle can be in two places at once without being two particles, and if you counted two particles you'd be wrong even though you see two particles. Or something like that - I don't actually understand the math of quantum physics myself, so I'm just repeating what people have said to try to explain it to dumb people like me.
In a universe with different rules, we'd have to pick a different subset of all possible mathematical rules to describe it. Whether that means that different math would be needed in a different universe is an interesting question that I don't know the answer to.
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And how does that contradict 1+1=2? If you're comparing unlike objects you're already not using the math on its own terms. 5 humans plus 5 grapefruit also do not equal 10 moons. Quantum particles are irrelevant to this, and accounting for them uses a completely different set of concepts, except that you're now saying "we don't know everything therefore math is invalid". Whether or not particle A plus entangled article B equal two particles the very validity of that question proves 1+1=2
I'm not sure where you got "we don't know everything therefore math is invalid" from what I said. 1+1=2 is true in the ideal universe of pure mathematical objects (given all the correct assumptions, of course). Which situations we can apply it to in our own universe of real objects, though, is something we can only figure out the hard way, as you point out with your humans, grapefruits and moons example. Even if you just stick to adding humans it's complicated: Do you count a just-fertilized egg as a hu
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Half-baked theory time: Maybe counting numbers have only become truly useful on a large scale with the advent of mass production and interchangeable parts. Back in the day, if you asked someone to help you fight two guys or lift two rocks or cut down two trees, they'd always ask, "How big are they?" Knowing 1+1=2 was useful, sure, but not nearly as useful as it is in a world where there are 570 grams of Cheerios in every family-sized box.
On second thought, that half-baked theory sucks. It's always useful to be able to count your children, and many animals, not just humans, can do it. Oh well. The theory was fun for the ten minutes it lasted.
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You're either a troll or an idiot.
I'm not sure where you get those two options from. I think these questions are interesting, and I like to think about them. The application of the ideal universe of mathematical objects to the real world of messy and ill-defined objects isn't at all straightforward. We shift between many levels of mathematical sophistication depending on what questions we're asking and how accurate or precise we want an answer to be. 1+1=2 is perfectly adequate in some situations; in other situations the best we can do
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Take 1 litre of water and add 1 litre of alcohol and you no longer get 2 litres.
Math is independent of our universe, because we use it to create all kinds of models of the universe. Nobody said that these models are the real universe. Our models are merely an approximation of our reality and these models keep changing and keep getting adjusted all the time.
Fact is we can use math to create all kinds of models including that of completely different and strange universes.
Math serves us to describe reality in
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For example, the reason we have 1+1=2 is because if I take 1 litre of water and add another litre of water to it I have 2 litres of water. However, if we were in some unfathomably different universe where if I did that I only ended up with 1.5 litres of water then we would undoubtedly have developed some completely different rules on which to base our maths.
We live in such a universe. You will *not* get exactly 2 liters after performing such an operation, due to any number of factors (additional gravity, reduced surface boundary, coming to thermal equilibrium, etc). If you try adding, a liter of alcohol to a liter of water, it will be quit an obvious difference.
But that's also not the standard arithmetic concept of addition. When we say something like "1+1=2" we're really talking about how, if you have some objects, and you make a collection of (say, draw an
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If you try adding, a liter of alcohol to a liter of water, it will be quit an obvious difference.
That's not 1+1 at all. That's more like 1a+1b.
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Any set of observations can, of course, be described using mathematics. But generally you expect your description should be about as complicated as the thing you're describing. If you measure 100 numbers, any description of them should itself involve about 100 numbers.
But that isn't what happens in physics. You measure 100 numbers, and then you find you can reproduce all of them using a very simple description with only 3 numbers. Then you go and collect another 1000 measurements, and find you don't nee
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"I used to be amazed by that but after " ...I was no longer high, I wondered how we possibly talked about that for hours last night.
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"His point was that the rules of maths are set by our universe. "
I take it your colleague is also a physicist? Because a mathematician I think would not agree.
It's certainly true that certain mathematical models are studied and their properties well understood because they are convenient to describe our universe and so there is a lot of practical value in those models. And its probable that if we lived in a different universe with rules we would find exotic, that we'd have created and studied models that we
Formalism (Score:2)
There is also formalism, which is starting from a set of axioms and rules, and seeing what evolves. The starting axioms and rules that most mathematics can be derived from is first-order logic and ZFC set theory. Whether or not you believe the axioms isn't even relevant; it's just a game of mechanically manipulating the symbols in the axioms according to a set of rules.
Mathematicians don't work this way because it's much too inefficient. But just knowing the actual rules and how to start from them can
Mathematicism: alternate to platonism & nomina (Score:3)
I'd like to introduce you all to something called mathematicism -- the view that physical stuff is literally made out of mathematical stuff. And I'd like to discuss it as an alternative position on the topic of the existence or reality of abstract objects, opposite of both platonism and nominalism.
In the same way that when we can construct a series of sets that behave exactly like the natural numbers and so are indistinguishable and thus identical to them, so too can we construct complicated mathematical objects that behave indistinguishably from the fundamental constituents of reality and so are, for all intents and purposes, identical to them.
It's possible to build up complicated mathematical objects such as special unitary groups out of bare, empty sets. Special unitary groups are considered by contemporary theories of physics to be the fundamental kind of thing that the most elementary physical objects, quantum fields, are literally made of. Excitations of those quantum fields, which is to say particular states of those special unitary groups, constitute the fundamental particles of physics, which combine to make atoms, molecules, stars, planets, living cells, and organisms, including us.
This illustrates how, in a very distant way, we ourselves can be said to be made of empty sets. And as all of the truth functions, and so all the set operations, and all the other functions built out of set operations, can be built out of just conegation, and the objects they act upon are built up out of empty sets, everything can in a sense be said to be made out of negations of nothing.
It is not a special feature of contemporary physics that says reality is made of mathematical objects; rather, it is a general feature of mathematics that whatever we find things in reality to be doing, we can always invent a mathematical structure that behaves exactly, indistinguishably like that, and so say that the things in reality are identical to that mathematical structure. If we should find tomorrow that our contemporary theories of physics are wrong, it could not possibly prove that those features of reality are not identical to some mathematical structure or another; only that they are not identical to the structures we thought they were identical to, and we need to better figure out which of the infinite possible structures we could come up with it is identical to. We just need to identify the rules that reality is obeying, and then define mathematical objects by their obedience to those same rules. It may be hard to identify what those rules are, but we can never conclusively say that reality simply does not obey rules, only that we have not figured out what rules it obeys, yet.
The mathematics is essentially just describing reality, and whatever reality should be like, we can always come up with some way of describing it. One may be tempted to say that that does not make the description identical to reality itself, as in the adage "the map is not the territory". In general that adage is true, and we should not arrogantly hold our current descriptions of reality to be certainly identical to reality itself. But a perfectly detailed, perfectly accurate map of any territory at 1:1 scale is just an exact replica of that territory, and so is itself a territory in its own right, indistinguishable from the original; and likewise, whatever the perfectly detailed, perfectly accurate mathematical of reality should turn out to be, that mathematical model is a reality: the features of it that are perfectly detailed, perfectly accurate models of people like us would find themselves experiencing it as their reality exactly like we experience our reality. Mathematics "merely models" reality in that we don't know exactly what reality is like and we're trying to make a map of it. But whatever model it is that would perfectly map reality in every detail, that would be identical to reality itself. We just don't know what model that is.
There necessarily must be some rigorous formal (i.e. mathematical) system or ano
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Thanks!
And Fourier transforms representing complex waveforms is a small piece of what I'm talking about, sure.
What is math? (Score:4, Funny)
Baby don't sqrt() me, don't sqrt() me, no more.
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These guys [youtube.com] have the answer.
The definition is simple (Score:3)
My dad, a PHD Physicist, Mechanical Engineer and Master Machinist taught me that Math is "A language used to discuss relationships." Though I haven't learned anything past Geometry this statement left me never afraid of math from calculating change to Celestial Navigation.
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Reminds me of the story of how Einstein got his interest in math from his Uncle:
"Young Albert did not like algebra, and his uncle is supposed to have aroused his curiosity by telling him to think of it as a detective story, where x was the criminal who had to be identified by following the “clues” in the equations. Once the boy had grasped this idea he never looked back."
Platonism makes more sense (Score:2)
Whether we find some mathematical proof or not, the thing still exists. For example, back in the day, let's say 200,000 years ago, our ancestors had no concept of what stars were, or the motion of planets (or even what a planet was). And yet, all of those things existed despite not knowing what they were. It was only because we evolved and realized those shiny dots in the night sky are stars a long distance away from us, that we live on a planet, and there are other planets in what we later discovered wa
Huh (Score:2)
I've always considered math to be just another language we use to convey information about the physical universe. Where does that lie between these two camps?
Is it invented, or discovered? (Score:2)
Is it invented, or discovered?
Math as a property of nature is discovered.
Math as a symbolic representation of those properties is invented.
Math is a class (Score:2)
some teenagers will fail, because they're wasting time on social media and not doing their homework.
confirmation bias (Score:2)
why should [math] "fit" so well with what we observe in nature...?
That's called confirmation bias [wikipedia.org]. It "fits" so well with our observations of nature because we crafted it to do just that.
Math is a tool we created along the way toward understanding nature and creating society. It's not magic that this tool we created just happens to be valuable not just in counting bits and grains but also planning roads and predicting orbits. We made it that way, and we continue to extend it as needed for work and for play and for wonderment.
Real-world applications of the Pythagorean theorem (Score:2)
Honestly, I think the way I most often use the Pythagorean theorem is when I divide up a slice of cheese when making sandwiches for my kids: because a full square of sliced cheese is just too big, but split the one square slice diagonally both ways so that you get 4 right trigons, then those can be trivially recombined into 2 squares that are each half the area of the original square with no waste.
QM (Score:2)
As you approach the particles in QM, physics approaches pure maths.
Under certain conditions, spin and velocity act as independent particles despite being just mathematical properties.
Ergo, maths and physics are ultimately the same thing.
From a British perspective ... (Score:2)
"Math" is an older English word for the stuff that is gathered from mowing grass or hay. You will find it as part of the word "aftermath".
"Maths" on the other hand, is an abbreviation for "mathematics".
Math is a method (Score:2)
Maths is a language (Score:2)
Maths is a language which only some people learn to speak. It can describe not the appearance of things but how they behave and move through time. It is the scourge of our time that illiterate dumbarses existing in positions of power and authority. I once wrote a brief and provided options based upon very basic maths showing that the costs of doing nothing were increasing exponentially, The managers decided to keep doing nothing, I was stopped a few months later by one of them who complained that the cost o
anyone else now have haddaway stuck? (Score:2)
What's essential about this question? (Score:2)
What has thinking about this question brought in terms of actually usable results?
Who cares? (Score:2)
Whether math is invented or discovered is irrelevant, and like most questions in philosophy, it cannot be answered.
You may as well ask, was the lever discovered or invented? Like math, it is a tool that is able to extend the abilities of humans. While the lever extends the physical capabilities of humans, math extends the mental capabilities.
developed (Score:2)
Re: (Score:2)
Nope. That sort of thinking only leads to perpetual motion machines, over-unity power generators, etc.
(in exactly the same way as "alternative medicine" leads people to believe that dolphins make the best midwives, etc.)
Think: If alternative medicine actually worked we could simply throw a dead badger into the Atlantic ocean and cure all the cancer in the world!
Re: (Score:3)
Think: If alternative medicine actually worked we could simply throw a dead badger into the Atlantic ocean and cure all the cancer in the world!
To be fair, have you actually tried that?
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Think: If alternative medicine actually worked we could simply throw a dead badger into the Atlantic ocean and cure all the cancer in the world!
To be fair, have you actually tried that?
Ya, but it turned out the badger wasn't dead, just resting.
Re:Useful (Score:4, Interesting)
The better way to describe math is to create the comparison, Math vs Physics. Why do math and physics differ so, both numbers and formulas and yet completely different. Physics is meant to be a representation of reality and maths, maths is just a modelling tool, nothing, until it models something and the something is the something and the math is just a modelling tool. Math is nothing until you construct a mathematical model of something else. Maths geeks become infatuated and see things that are not really there, you can not use math to model math, it is just a modelling tool ie you use math to model physics.
Re: (Score:2, Troll)
Nonsense. If you measure the volume of the universe in cubic planck lengths, about 120 digits are sufficient. Physical reality requires no more accuracy than that. Yet we can still prove that pi is irrational.
Math is not bound by physical reality.
Purity [xkcd.com]
Re: Useful (Score:2)
Re: (Score:2)
Ah, the typical Math Major's argument: if the Math doesn't match Reality, it is Reality which is wrong.
Huh?
Maybe you meant something like, "If the (human-created) mathematical model of reality doesn't match Reality, it's the model which is wrong".
Math in itself can't be wrong. Math just is.
Re: (Score:2)
That's just silly.
Certain parts of math are useful in dealing with certain parts of physical reality. Calculus can be used to determine distance from acceleration. Set theory will accomplish nothing for the same problem.
Re: (Score:2)
Why do math and physics differ so
a) They're completely different disciplines. One is pure theory, the other is modelling of a system.
b) We only have a tiny amount of the information needed to develop a model for Physics.
Measuring that tiny subatomic stuff, mesureing the interesting stuff that's on the other side of the galaxy, measuring the stuff inside black holes, etc. isn't easy, if possible at all
eg. Look at how long it took mankind to detect a single gravitational wave.
Re: (Score:2)
A mathematician, a physicist and a biologist observe a house. One man and one woman enters, and some time later three people emerge from the house: The woman, the man and a child.
The physicist stated: We had a measuring error.I
The biologist said: They have procreated.
The mathematician said: If one more person enters the house, it will be empty.
Re: (Score:2)
Ya, group theory was nothing until we discovered it was of use in physics, then it became useful in crypto, then it became not nothing. Go back and hit the bong again, you didn't get enough.
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
You can exactly and precisely express the ratio of the circumference of a circle to its' diameter by using the symbol 'pi' instead of using decimal symbols.
You seem t
Re: (Score:3)
That standards document doesn't actually appear to advocate for not teaching standard mathematical practices, but rather putting them in a social and historical context. It is a curriculum attempting to be math+context, not merely math. Whether that's a more effective way to teach calculation is one thing, but it has a chance of getting more non-white children interested in math and its place in society. The article you shared does not adequately cite the various things it purports to be commenting on, and
Re:Math is racist (Score:5, Insightful)
To the "woke" everything, including science, is a social construct, and by extension, a political construct.
Of course science is a social construct - it's a fucking brilliant one, that allows a bunch of biased, error-prone primates to correct each other's mistakes and work together to build a pretty reliable model of reality.
And, the social construct that is *science* has shown us again and again that literally almost every part of human experience is influenced to some degree by social construct. Language being the first and most obvious... you literally can't think without using a social construct. Color - many cultures never had a concept for "blue". Morality - is human sacrifice good or bad? Depends on if you are an Aztec or not. We perceive things that we have names for, and we name things so that we can perceive and communicate about them. The fact that we can construct these shared hallucinations and represent abstract concepts in a concise way is what allows us to build massive, cooperative civilizations with advanced technology. If understanding that makes you "woke"... well, guilty as charged.