Is math real?

For the discussion of math. Duh.

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Mega85
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Is math real?

Postby Mega85 » Tue Feb 23, 2016 9:32 pm UTC

Is math a real thing or is it a human invention?

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Re: Is math real?

Postby ConMan » Tue Feb 23, 2016 10:08 pm UTC

Probably. Have you read much about the philosophy of mathematics?
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Re: Is math real?

Postby wumpus » Tue Feb 23, 2016 10:09 pm UTC

Math is complex. If you ignore the imaginary parts you are missing too much math.

Of course, there is a famous quote that says "god made the integers. All else is the work of man..."

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Re: Is math real?

Postby Mega85 » Tue Feb 23, 2016 10:47 pm UTC

I'd say that math is real, and that saying it's a human invention is just as incorrect as saying that time is a human invention.

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Re: Is math real?

Postby Flumble » Tue Feb 23, 2016 11:28 pm UTC

Mega85 wrote:I'd say that math is real, and that saying it's a human invention is just as incorrect as saying that time is a human invention.

But there's no one who can verify or falsify that there was time before we had an idea of time.

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Re: Is math real?

Postby Sizik » Tue Feb 23, 2016 11:37 pm UTC

How Can Math Be Real If Our i's Aren't Real
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Re: Is math real?

Postby Cleverbeans » Wed Feb 24, 2016 12:32 am UTC

Defining "real" is philosophical difficult, and must be established before we can determine if math can be categorized as such. For example a unicorn is not real as a thing that exists in the material world but you can argue it's real as an idea or concept. Personally I'm of the opinion that math is a useful fiction like money.
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Re: Is math real?

Postby doogly » Wed Feb 24, 2016 3:22 am UTC

Provide a list of five or so different things that you consider to be "real." Then we can decide if math should also be on that list.
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Re: Is math real?

Postby Mega85 » Wed Feb 24, 2016 2:11 pm UTC

doogly wrote:Provide a list of five or so different things that you consider to be "real." Then we can decide if math should also be on that list.


Trees
Dogs
Water
Gravity
Fire

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Re: Is math real?

Postby doogly » Wed Feb 24, 2016 2:15 pm UTC

Hmm. What are some things that aren't real?
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Re: Is math real?

Postby Nicias » Wed Feb 24, 2016 3:47 pm UTC

I personally think that math is realer than all of those things you named.

All of the items you named are contingent on the physical laws of the universe.

To me, math is independent of that. I'm somewhat of a Platonist in terms of math.

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Re: Is math real?

Postby Mega85 » Wed Feb 24, 2016 8:19 pm UTC

doogly wrote:Hmm. What are some things that aren't real?


Dragons
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Planet X
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Re: Is math real?

Postby PsiSquared » Wed Feb 24, 2016 8:20 pm UTC

Mega85 wrote:
doogly wrote:Provide a list of five or so different things that you consider to be "real." Then we can decide if math should also be on that list.


Trees
Dogs
Water
Gravity
Fire


I'll say that mathematics is no less real than gravity is.

Both are not material things. You cannot see, hear, smell, taste or touch gravity. You can see an apple falling down and record the orbits of the planets, but attributing these things to "gravity" is a human-made abstraction.

Moreover, this human-made abstraction called "gravity" includes quite a great deal of math. So I really don't see how a person who accepts the premise that "gravity is real" can claim that "F=GMm/r2" (Newton's Law of Universal Gravitation) isn't real.

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Re: Is math real?

Postby doogly » Wed Feb 24, 2016 9:48 pm UTC

Yeah, math is much more like your real list than your unreal list.
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Re: Is math real?

Postby ConMan » Wed Feb 24, 2016 11:10 pm UTC

I mean, what even is gravity? Many great minds failed to guess that maybe the reason things on Earth fall down is the same reason things in the skies go back and forth. Then someone (or two someones) had to invent calculus to work with the model that let those two things work together, but even that model had its flaws. Now we've decided that in fact nothing is falling, or going back and forth - in fact everything is going in a straight line, but heavy things can change what a straight line is. And someone had to invent ridiculously crazy geometry and calculus to work *that* out. And when things do change what straight lines are, they do it in a ripple that spreads out everywhere, and it's taken us the better part of a century to show that the ripples really exist and weren't just a convenient fiction to make the previous model work. And despite that, we still reckon there's an even deeper model that we haven't worked out properly yet. So if you want to claim that gravity is real then (1) you're going to have to define what gravity is, and (2) odds are you'll be wrong.

Then to ask whether mathematics is real, and I highly recommend you read the Wikipedia article I linked to see what some of the big schools of thought are on that topic, you first have to work out what mathematics is. Pretty much all mathematics we work with these days is based on axioms - i.e. statements of what we're going to believe is true - and sets of rules that determine how you can construct new ideas from existing ones. Not every mathematician uses the same fundamental axioms, or the same rules for manipulating mathematical objects, and even then it's likely that there are systems that we haven't even considered yet, not to mention things that must be true but that we know we can't prove. And yet, when we use the bizarre set of rules we've come up for ourselves to estimate how to build a bridge that won't fall down, or a rocket that will make it to another world, it seems to do pretty ok. So in conclusion, who knows?
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Re: Is math real?

Postby PsiSquared » Thu Feb 25, 2016 12:07 am UTC

ConMan wrote:...Now we've decided that in fact nothing is falling, or going back and forth - in fact everything is going in a straight line, but heavy things can change what a straight line is. And someone had to invent ridiculously crazy geometry and calculus to work *that* out...


Actually, there was no need to invent any new mathematics, because the mathematician Brenhard Riemann already invented that "ridiculously crazy geometry and calculus" in the mid-19th century.

And interestingly enough, this is a very typical case. Nearly always, when we unravel a new secret of the physical universe, we find that the mathematical framework needed to quantify it already exist. Cases like Newton having to invent calculus before formulating his theory of gravity are the exception, rather than the rule.

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Re: Is math real?

Postby Cleverbeans » Thu Feb 25, 2016 12:29 am UTC

Mega85 wrote:Trees
Dogs
Water
Gravity
Fire


All of these can be observed directly or indirectly with your senses, so math is not real.

Also, sorry for the late edit.

PsiSquared wrote:And interestingly enough, this is a very typical case. Nearly always, when we unravel a new secret of the physical universe, we find that the mathematical framework needed to quantify it already exist. Cases like Newton having to invent calculus before formulating his theory of gravity are the exception, rather than the rule.


I would argue instead that when we develop new models in Cantor's Paradise it's that the math simple becomes a better tool. Is it any surprise that right after we invent statistics it describes the statistical parts of the world more accurately? Or that when we build mathematical models for computation that mimic practical problems like cryptography or technical drawing which have ancient mathematical roots that we do in find ways to do them? Mathematicians come through, hallucinate the world is some way, or describe some internal workings of mathematics and the scientists come along in their wake and go "Oh! I found some piece of the world that looks a lot like what that mathematician did." Here, now where we give the Fields medal for papers on Percolation theory I feel at though Hilbert was right.
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Re: Is math real?

Postby ConMan » Thu Feb 25, 2016 1:30 am UTC

PsiSquared wrote:
ConMan wrote:...Now we've decided that in fact nothing is falling, or going back and forth - in fact everything is going in a straight line, but heavy things can change what a straight line is. And someone had to invent ridiculously crazy geometry and calculus to work *that* out...


Actually, there was no need to invent any new mathematics, because the mathematician Brenhard Riemann already invented that "ridiculously crazy geometry and calculus" in the mid-19th century.

And interestingly enough, this is a very typical case. Nearly always, when we unravel a new secret of the physical universe, we find that the mathematical framework needed to quantify it already exist. Cases like Newton having to invent calculus before formulating his theory of gravity are the exception, rather than the rule.

That is true. I think I should have more accurately said something like "we had to go and borrow what had originally seemed to be a physically irrelevant and ridiculously crazy geometry and calculus". I mean, it's not too crazy if you don't look too closely at it, but I solved the differential equations for the time-variant Schwarzschild metric once and I still shudder at the thought of all those tensors.
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Re: Is math real?

Postby PsiSquared » Thu Feb 25, 2016 2:47 am UTC

Cleverbeans wrote:
PsiSquared wrote:And interestingly enough, this is a very typical case. Nearly always, when we unravel a new secret of the physical universe, we find that the mathematical framework needed to quantify it already exist. Cases like Newton having to invent calculus before formulating his theory of gravity are the exception, rather than the rule.


I would argue instead that when we develop new models in Cantor's Paradise it's that the math simple becomes a better tool. Is it any surprise that right after we invent statistics it describes the statistical parts of the world more accurately? Or that when we build mathematical models for computation that mimic practical problems like cryptography or technical drawing which have ancient mathematical roots that we do in find ways to do them?


Indeed, neither of these things is particularly surprising.

What is surprising, is that things like Riemann's non-Euclidean geometry turn out to be a 100% accurate description (as far as we know) of the way curved spacetime behave. And what's even more surprising, is that you can summarize all of Einstein's general relativity with a single tensor equation:

Rμν−(1/2)gμνR =8πGTμν/c4

This short equations tell you - exactly - everything you ever wanted to know about gravity.

Mathematicians come through, hallucinate the world is some way, or describe some internal workings of mathematics and the scientists come along in their wake and go "Oh! I found some piece of the world that looks a lot like what that mathematician did."


When this "piece of the world" is a universal law which describes how gravity works everywhere, and when "looks a lot a like" means "this short equation, without any need of twéaking, gives a complete an accurate description of" then yes, this is pretty d**n impressive.

And an even more striking example of this is quantum mechanics: The quantum world behaves in ways which completely defy common sense, and no pre-20th century scientist (or mathematician) could have possibly guessed that our universe actually behaves in this completely crazy way. Yet, the entire mathematical framework for the theory was perfected many decades earlier, by pure mathematicians who couldn't care less about practical applications (and certainly didn't have anything remotely resembling a picture of a quantum mechanical universe to guide them)

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Re: Is math real?

Postby jestingrabbit » Thu Feb 25, 2016 9:51 am UTC

PsiSquared wrote:
ConMan wrote:...Now we've decided that in fact nothing is falling, or going back and forth - in fact everything is going in a straight line, but heavy things can change what a straight line is. And someone had to invent ridiculously crazy geometry and calculus to work *that* out...


Actually, there was no need to invent any new mathematics, because the mathematician Brenhard Riemann already invented that "ridiculously crazy geometry and calculus" in the mid-19th century.

And interestingly enough, this is a very typical case. Nearly always, when we unravel a new secret of the physical universe, we find that the mathematical framework needed to quantify it already exist. Cases like Newton having to invent calculus before formulating his theory of gravity are the exception, rather than the rule.


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Re: Is math real?

Postby PsiSquared » Thu Feb 25, 2016 12:20 pm UTC

Can you name a single example of a classical mathematical construct which didn't become useful by the dawn of the 21st century? Because I can't think of a single one.

But even if your description of the situation were accurate and only 1% of all mathematics had any relevance to the physical world, it wouldn't have mattered. Even a success rate as low as 1 in 100 would still be miraculously high, given that "success" means that century-old mathematical concepts can single-handedly explain universal laws such as relativity or quantum mechanics.

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Re: Is math real?

Postby Cleverbeans » Thu Feb 25, 2016 6:34 pm UTC

PsiSquared wrote:Yet, the entire mathematical framework for the theory was perfected many decades earlier, by pure mathematicians who couldn't care less about practical applications (and certainly didn't have anything remotely resembling a picture of a quantum mechanical universe to guide them)


It's interesting that you point out quantum mechanics in particular, which has multiple mathematical interpretations. Also, the first model used matrix arithmetic introduced by Caley who was a pure mathematician I find it completely unsurprising that someone found applications for linear equations. In some senses those are the only equations we know how to solve.
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Re: Is math real?

Postby Cradarc » Thu Feb 25, 2016 10:53 pm UTC

Is logic real? Math is just structured logic and abstracted objects.
The fact that equations can explain physical phenomena is more about the human mind than it is about nature. There are no equations in nature, but we perceive them there because it makes more sense to us. It allows us to generalize and make connections between different events.
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Re: Is math real?

Postby PsiSquared » Thu Feb 25, 2016 11:14 pm UTC

QM doesn't have "multiple mathematical interpretations".

It has multiple formulations which are mathematically equivalent to one another.

On the other hand, funnily enough, QM does have multiple physical interpertations. Actually, nobody really knows what is really going on in the quantum world. The only thing we do know, is that our mathematical models give the correct results. And when I say "correct result" I mean that they allow us to accurately predict things like the electron magnetic moment to 12 decimal places.

And you don't find that surprising... Well, fine.

Anyway, I've never claimed that math is necessarily "real". I actually don't like debates of the sort of "Is X real?" because the word "real" means many different things to different people. What I am saying is that once you accept the reality of abstract concepts like "gravity", it makes no sense to claim that math is any different.

Let me ask you this:

What is the difference between mathematics and gravity in your view? Why do you regard mathematics as "nothing more than a useful tool", but regard gravity as "real"? It seems like a double standard to me.

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Re: Is math real?

Postby PsiSquared » Thu Feb 25, 2016 11:30 pm UTC

Cradarc wrote:Is logic real? Math is just structured logic and abstracted objects.
The fact that equations can explain physical phenomena is more about the human mind than it is about nature. There are no equations in nature, but we perceive them there because it makes more sense to us. It allows us to generalize and make connections between different events.


But nature didn't have to be logical.

Just because the human mind really wants nature to make sense, doesn't mean that the universe is obliged to cater our whims. Yet, somehow, when we try to use logical abstract concepts to make sense of nature, it works.

And this is a fact which requires explanation.

Case in point: Religion also stemmed from basic needs of the human mind. But religion didn't help us unlock the mysteries of the physical universe just because our ancestors really really wanted it to (religion may be useful for other things, but this - again - points to the way the universe really works rather than the way we would like it to work).

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Re: Is math real?

Postby Carlington » Fri Feb 26, 2016 1:33 am UTC

I am dangerously underqualified and will happily bow out if necessary, but surely that's begging the question, PsiSquared? Logic is built by the human mind, but the human mind is built to make sense of concepts based on the conditioning it has received. That conditioning comes from interaction with our universe, so if the universe was radically different then we would be conditioned differently and different things would make sense. (Is this just the weak anthropic principle in a funny hat? I think it might be.)
What makes sense? Well, we see objects fall to earth, so it makes sense that something causes objects to fall to earth. In a universe where things didn't fall to earth, it would make sense that things didn't fall to earth, and so we'd make use of mathematical constructs that explained that nicely.
Is math real? In some sense, math is a formalised metalanguage for all possible universes and a bunch of concepts besides. So I would say that math is real in the same way that natural language is real, which I think is an open question. Language is real in some sense, in that it has direct and measurable effects in the world around us (that's its entire purpose), but whether it has a physical manifestation (handwave cough quantum states within electrons traversing neural pathways blather) and what that might be can't be determined reliably yet, and I would apply the same reasoning to the question regarding maths.
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Re: Is math real?

Postby Cradarc » Fri Feb 26, 2016 3:19 am UTC

PsiSquared wrote:Just because the human mind really wants nature to make sense, doesn't mean that the universe is obliged to cater our whims. Yet, somehow, when we try to use logical abstract concepts to make sense of nature, it works.

It has nothing to do with how much we want something to be true. It has to do with how our environment influence our perceptions.
When a group of ancient people did a rain dance, it rained. To them, the rain was the result of their dance. Is the connection between their rain dance and the rain real? "Of course not", we scoff. "They simply could not observe the complex dynamics that were happening on a molecular level". But, we can't either, since it happened so long ago. The only thing we can be certain about is that these ancient people thought they explained why it rained after they did their dance, just like how we think we know what causes rain.

It's interesting how we formulate mathematical "laws" for nature. These laws are all created in hindsight. It's like observing cars on a freeway, and setting the speed limit to the fastest speed ever recorded. To what extent is this speed limit "real"? There's nothing to enforce it. The speed limit is just an abstract summary of all the data we took while observing cars.
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Re: Is math real?

Postby PsiSquared » Fri Feb 26, 2016 9:42 am UTC

Carlington wrote:Is math real? In some sense, math is a formalised metalanguage for all possible universes and a bunch of concepts besides. So I would say that math is real in the same way that natural language is real, which I think is an open question. Language is real in some sense, in that it has direct and measurable effects in the world around us (that's its entire purpose), but whether it has a physical manifestation (handwave cough quantum states within electrons traversing neural pathways blather) and what that might be can't be determined reliably yet, and I would apply the same reasoning to the question regarding maths.


Yes, that's a very good analogy.

Take, for example, the word "dog". It is a man-made artificial construct, not only because English is a man-made language but also (and more importantly) because humans have a very complex mental model of what "the dog category" really is.

Yet, the word "dog" also refers to a very real thing that exists in the physical world.

And the same is true for mathematics. Yes, the exact way we define things and the exact symbols we use are human-made artificial constructs. But it is also clear that these mental models have close analogues in the real world, or else math wouldn't be so useful and so successful in explaining the world around us.

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Re: Is math real?

Postby jewish_scientist » Fri Feb 26, 2016 2:44 pm UTC

PsiSquared wrote:Moreover, this human-made abstraction called "gravity" includes quite a great deal of math. So I really don't see how a person who accepts the premise that "gravity is real" can claim that "F=GMm/r2" (Newton's Law of Universal Gravitation) isn't real.


You could define gravity as the force that causes attraction between everything that has energy. It is important to note that that definition does not require gravity to behave such that it can be modeled mathematically. If a force attracted all object that had energy and randomly changed its strength between random objects, then it could not be modeled mathematically; however, it would still satisfy this definition of gravity. Someone could argue (although I would not) that gravity is real, and it is only a coincidence that it can be modeled mathematically.

PsiSquared wrote:Can you name a single example of a classical mathematical construct which didn't become useful by the dawn of the 21st century? Because I can't think of a single one.


I can think of several modern mathematical things that have no (current)physical applications. For example, if x = 1+2+4+8+16+...+2^n then x > 2*x.


My belief is that some non-physical objects exists (e.g. numbers, functions, polygons, sets, infinities), and some actions (e.g. adding, rotating, limiting) can be preformed on, to and/or with these objects. I would call these objects mathematical objects (I am fairly sure that is actually a term), and these actions mathematical operations (again, I am fairly sure that is an actually term). A weak point in this philosophy is that this means that the sentences, "I put an infinite sum into the campfire," and "I need to take the third root of my car," are logically and grammatically valid even though they are really confusing/ meaningless.

Regarding 'imaginary' numbers; I vote that we replace every instance of i with √-1, and refer to numbers with √-1 in them as complex numbers.
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Re: Is math real?

Postby doogly » Fri Feb 26, 2016 4:05 pm UTC

jewish_scientist wrote:You could define gravity as the force that causes attraction between everything that has energy. It is important to note that that definition does not require gravity to behave such that it can be modeled mathematically. If a force attracted all object that had energy and randomly changed its strength between random objects, then it could not be modeled mathematically; however, it would still satisfy this definition of gravity. Someone could argue (although I would not) that gravity is real, and it is only a coincidence that it can be modeled mathematically.

You would need a non mathematical definition of "force" and "energy" if you thought that there could be a nonmathematical "gravity." And good luck with those.

And on the other hand as well, randomness isn't something we can't handle in math. At all. We do this a lot, all over the place, and in mathematical physics too.
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Re: Is math real?

Postby aph » Fri Feb 26, 2016 6:29 pm UTC

Real:
Mega85 wrote:Trees
Dogs
Water
Gravity
Fire

Unreal:
Mega85 wrote:Dragons
Unicorns
Fairies
Planet X
The Counter-Earth

Of the real things, you can see (or perceive trough other senses) a dog or a body of water. You can't see a dragon or a unicorn.You can count imaginary dogs just like you can count imaginary dragons, or imaginary field functions or whatnot. So, math is more abstract than any of the things on the lists, and the category of 'real' does not apply.

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Re: Is math real?

Postby PsiSquared » Sun Feb 28, 2016 4:05 am UTC

jewish_scientist wrote:You could define gravity as the force that causes attraction between everything that has energy. It is important to note that that definition does not require gravity to behave such that it can be modeled mathematically. If a force attracted all object that had energy and randomly changed its strength between random objects, then it could not be modeled mathematically; however, it would still satisfy this definition of gravity. Someone could argue (although I would not) that gravity is real, and it is only a coincidence that it can be modeled mathematically.


That would be a really strange statement.

If something is a universal law which is true everwhere, how can it be a "coincidence"? In the same vain, I could argue that gravity itself isn't real and it is only a coincidence that things fall down.

Besides, without quantifying gravity, the statement of "there is a force which causes attraction between everything that has energy" rests on very shaky grounds. What about two equal electric charges? Or two magnets which face one another at the same pole? Where is that force that attracts every object to any other object in that case, hmmm?


And what about two pieces of paper which are glued together? Or an apple which is attached to the branch of a tree? Here's a force which attract two objects. Would you call it gravity? If not, why not?


A weak point in this philosophy is that this means that the sentences, "I put an infinite sum into the campfire," and "I need to take the third root of my car," are logically and grammatically valid even though they are really confusing/ meaningless.


I don't really see this as a problem.

Just because mathematical objects are not physical objects, does not put their reality in to question.

Besides, you can't put gravity in your car either (not directly, anyway).

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Re: Is math real?

Postby SuicideJunkie » Mon Feb 29, 2016 6:18 pm UTC

PsiSquared wrote:
jewish_scientist wrote:You could define gravity as the force that causes attraction between everything that has energy. ...
That would be a really strange statement.

If something is a universal law which is true everwhere, how can it be a "coincidence"? In the same vain, I could argue that gravity itself isn't real and it is only a coincidence that things fall down.

Besides, without quantifying gravity, the statement of "there is a force which causes attraction between everything that has energy" rests on very shaky grounds. What about two equal electric charges? Or two magnets which face one another at the same pole? Where is that force that attracts every object to any other object in that case, hmmm?


And what about two pieces of paper which are glued together? Or an apple which is attached to the branch of a tree? Here's a force which attract two objects. Would you call it gravity? If not, why not?
The "the force" part should be taken as not meaning that there is only one force period, but that there is only one force that cares only about objects having energy. There could still be other forces that care about things having electric charge.

That said, "energy" would lose meaning if you had a truly random gravitational force.


Perhaps the question should be "Why are the rules of the universe so simple?" It took a LOT of work to get to where we are, but everything about the universe keeps boiling down to equations you can write on a T-shirt.

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Re: Is math real?

Postby doogly » Mon Feb 29, 2016 6:31 pm UTC

We develop mathematical language based on what's important. I can write gravity as G=T and electromagnetism as d*F=J because we have loaded a whole lot into these symbols. There's no surprising simplicity here. All they have to do is follow some sort of pattern, and math can talk about it, because math is just about patterns. Random, statistical patterns? We got those too. There's really no feasible way for it not to be mathematical.

Try to write down a non mathematical description of bizarro-gravity. There really are no alternatives, except for there being nothing that could be meaningfully grouped into a coherent thing to be named "gravity" at all.
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Re: Is math real?

Postby PsiSquared » Mon Feb 29, 2016 8:41 pm UTC

doogly wrote:We develop mathematical language based on what's important. I can write gravity as G=T and electromagnetism as d*F=J because we have loaded a whole lot into these symbols.


Fair point.

But still, even if you incorporated all the defintions along the way, I doubt the resulting statement would be more than a few pages long. And since these few pages describe the rules of operation of the entire physical world, the simplicity and compactness is still very surprising.

It certainly didn't have to be that way.


Try to write down a non mathematical description of bizarro-gravity. There really are no alternatives, except for there being nothing that could be meaningfully grouped into a coherent thing to be named "gravity" at all.


Well, to be fair, as long as the notion of gravity is limited to "what makes things fall down", you don't really need mathematics to talk about it. People have been doing that for thousands of years. Only when Newton extended the notion of gravity to "a universal force", this was no longer possible.

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Re: Is math real?

Postby jewish_scientist » Tue Mar 01, 2016 1:57 pm UTC

PsiSquared wrote:
A weak point in this philosophy is that this means that the sentences, "I put an infinite sum into the campfire," and "I need to take the third root of my car," are logically and grammatically valid even though they are really confusing/ meaningless.


I don't really see this as a problem.

Just because mathematical objects are not physical objects, does not put their reality in to question.

Besides, you can't put gravity in your car either (not directly, anyway).

What I mean is, if I were to play Devil's Advocate and argue against this position, this is the area I would attack.

doogly wrote:We develop mathematical language based on what's important.

In 100 C.E., did calculus exist? No one knows about it; no one has even heard the word. I am very curious as to what your answer will be.
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Re: Is math real?

Postby doogly » Tue Mar 01, 2016 2:31 pm UTC

No. Did you?
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Re: Is math real?

Postby LaserGuy » Tue Mar 01, 2016 7:59 pm UTC

jewish_scientist wrote:In 100 C.E., did calculus exist? No one knows about it; no one has even heard the word. I am very curious as to what your answer will be.


Yes. Elements that make up modern calculus can be traced to ancient times. They didn't necessarily have all of the tools or language to describe it that we do today, of course, nor did they have a formalized system to describe all of the concepts.

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Re: Is math real?

Postby doogly » Tue Mar 01, 2016 8:10 pm UTC

Sure but he might as well have picked a million years ago, the specific date doesn't really matter.
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Re: Is math real?

Postby aph » Tue Mar 01, 2016 8:42 pm UTC

PsiSquared wrote:Just because mathematical objects are not physical objects, does not put their reality in to question.

I find it interesting that even when we are talking about physical objects, we are referring to our sensory events or perceptions. The 'mental image' of a dog is just as real as the mental image of the number three. It also seems that these mental images are arranged in a hierarchy - you can perceive a color without perceiving a surface, but you can't perceive a surface without being able to perceive colors and edges. Or you can perceive a dog or the number three, but you can't count them without understanding the concept of counting. Mathematical concepts seem to be in this realm of abstractions, grounded in sensory experiences, but more general and abstract.

---

On another note, we know there is something in the nature, outside our senses, that causes us to perceive a dog, but are there [i]integers[i] in nature, or are they just our perceptions? Interesting discussion: http://www.damtp.cam.ac.uk/user/tong/talks/integer.pdf


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