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Does mathematics really exist in nature or not?


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I propose the exact oppposite. Declaring that math is subjective is tantamount to declaring the infallibility of human perceptions. My problem with the idea that math isn't objective is the fact that we don't get to determine any of it's rules. Some people want to claim we invented math, but if we did we had NO SAY in how it happened, including the inventors. Inventors decide how their inventions come together and work. No one ever had that choice with math. We didn't get to decide right answers. Math would objectively tell us we are wrong. So the idea that it's a man made system that functions perfectly and describes the universe anywhere equally well seems absolutely ludicrous.

If you mean the exact opposite of what I just wrote, then I don't see it in what you wrote. Moreover, for all the yammering it doesn't make one whit of difference in either how math is done or applied, or in how the universe operates.
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Sorry I was responding to Sciwiz comment. I should have been clear about that. I am not yammering. This is an important point. Nobody invented math. We discovered it. If we discovered it it's an objective part of reality because we didn't make it.

Roger Sciwiz. I tend to agree that it's objective, but as I said, it doesn't count one whit of difference whether math is invented, discovered, or any other nuanced or diced appellation folks care to apply. IIRC correctly I entered the fray on the subject of animals counting and gave evidence that they do. As there is no indication the yammering isn't over on that or the invention/discovery meme, I'll excuse myself until or unless some other factual error or baseless claim is introduced. (Or the mood strikes me of course. :P ) Yammer on!
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Math most definitely exists in nature. The proof of this exists not only in the geometrical and fractal structures exhibited by natural arrangements of matter, but also in describing the behavior of matter and energy. The fact that matter arranges itself into structures demonstrates the mathematical properties and rules it must obey. To argue that mathematics is a man made concept is akin to stating that the universe exists and behaves the way it does because we invented a language to describe mathematics, which is utter nonsense. These mathematical structures and behaviors exist whether we exist or not and regardless of any language that must be invented to describe it. In essence, our mathematical language is a result of studying how nature behaves and is structured.

Edited by Daedalus
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Well I'm going to only address Bill Angel's post because in replying to the other two posts I would do little but repeat myself. The refutations there are at best flimsy and nothing I haven't already from a certain perspective (mine if nothing else) addressed and I don't see that conversation going anywhere but in a complete circle.

 

As far as the fermions go, however, that's an interesting point. Would that be similar, in principal to quantum entanglement? I'm sorry for my ignorance on the subject I just haven't had the time to explore the subject as deeply as I would like so I would defer to your experience in the matter.

 

Never mind, I see that electrons are classified as fermions so I suspect this is the case.

 

Well by your logic what I said must still hold true. For all fermions if they share a spatial probability distribution then they cannot have all of the same properties. I fail to see how that would invalidate my claim.

 

To be clear, I reasoned that if you abstract away the property of an object the property is unmoored from objective reality on the premise that the objectivity of the property rested in its relationship to other properties of the same object.

 

Now I suppose that you were attempting to argue that fermions all share these particular properties thus no property of any individual fermion was tied to its objective identity so much as to the abstract principal, if so that fell rather flat, or I missed something in your explanation.

 

I'm not sure what you were attempting to prove, but assuming the Pauli exclusion principal and Fermi-Dirac statistics hold true then on what foundation, from what premise would you disagree?

 

If two fermions occupy the same probabilistic distribution space, which I take to mean they have the same statistical probability of being at any given location within the same space upon examination, then they cannot share all properties in common, there must be at least one property difference such as spin, they cannot share the same characteristics unless they find themselves in separate probability space distributions.

 

I mean like I said, maybe I'm missing the crux of your argument, but I fail to see how your contention is relevant to my claim except possibly by way of affirmation.

 

 

Sorry, one final point as more responses seem to have entered the fray which both disappoint and upset me. What is upsetting here isn't that you disagree, but that your contentions are so flimsy and baseless. I've heard better arguments from Christians concerning the objective existence of God, from whom you seem to be taking a page.

 

Your general methodologies seem to be to declare that your position is true, offer fuzzy logic along with some highly questionable claims, and you seem to be content with your matter of fact dismissals.

 

I mean it's a pretty lamentable affair to say the least. Really? Animals can count? And that's been proven beyond the shadow of a doubt? Down to the single celled Eukaryotic life, if it technically qualifies as an animal it has the capacity to count?

 

It's just really sad, this is a forum dedicated to science, yes? You are all highly intelligent rational human beings, correct? Don't insult my intelligence with such poor and meandering rationale, if you're really going to show that math is objective in nature you can do a much better job of it I should hope. I mean it's to the point that most of the comments aren't worth addressing because they don't entertain the force of a proper refutation. Either seriously address the points that have been made or concede the point, but why on earth would you expect anyone to be persuaded by such unsound arguments? Would you allow yourselves be persuaded by your own arguments? If so I would really call your rational faculties into question. Seriously, do better, it's not a huge request.

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if you're really going to show that math is objective in nature you can do a much better job of it I should hope. I mean it's to the point that most of the comments aren't worth addressing because they don't entertain the force of a proper refutation. Either seriously address the points that have been made or concede the point, but why on earth would you expect anyone to be persuaded by such unsound arguments?

 

Let's attack the argument from the angle of geometry. If our goal is to show that mathematics is inherent to nature, then all we have to do is look at the geometric arrangments of matter, which can only be described mathematically. In order for physical things to exist, the atoms that comprise their structure must be arranged in a very specific way. Not only must the atoms exist in a specific arrangment, but each atom must be linked to specific atoms that comprise the molecules. If mathematics did not exist in nature, then it would be impossible for atoms to be grouped together and form geometrical structures because there is no other way to describe geometry except with math. Because atoms are arranged into geometric structures, we had to invent the language of mathematics to describe it. This is no different than inventing a word to describe an apple or an orange. We are simply identifying things that already exist in nature.

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Daedalus: That was a really solid effort, literally from a certain perspective, I commend your attempt at rigor.

 

Still the contention makes a few assertions that, A:lack imagination and B: as far as I'm aware have no basis in truth other than the fact that you said it was so. For instance: "geometric arrangements... Can only be described mathematically". Now if you said "can" be described mathematically I would have agreed but you've given no proof of the only part of your claim beyond asserting that such is the case.

 

If that were true it would be impossible for me to describe in plain English the atom at every location by name and position according to some reference point without the use of numbers. As it so happens such a feat is technically possible, "there is a carbon atom to the left of the reference, below the reference, and positioned at the leading edge" you get the idea. Now I may take an absurdly long time to describe the geometry in this way but it could in theory be done.

 

This once more alludes to the problem I mentioned previously, most of these arguments follow the form: "math is real because obviously math is real. Therefore P=NP QED"

 

You get the idea, it proves nothing, it only reiterates that the physical universe can mostly be described fairly accurately in most respects through the use of math.

 

Again it's like Christian logic: "God is real because you can only describe the universe because God made it that way. Do you see how everything in nature works, it couldn't work that way if an intelligent designer hadn't intelligently designed it that way."

 

You know, actually that's a good way to test your argument. Whatever you are about to say, imagine the people you think are the most misguided applied the same logic to prove a ludicrous claim. If you would tear it apart if it were used against you, don't bother saying it. If you can conceive of no sound way to refute it I will entertain the notion.

 

Also, in response to TheGeckoMancer: I mean I suppose I can say, and in fact have already said pretty much the same of you. Honestly I don't know why you would waste the time it takes to type out a response just to basically say:"I know you are, but what am I?"

 

Perhaps you felt offended by my previous post, perhaps you really and truly feel I made no relevant points worth discussing, in which case I really don't know what to tell you, because having seen your arguments I am lead to conclude we must occupy different realities where logic and reasoning have developed in entirely different and diametrically opposed fashions. Just as you declare my suppositions and contentions to be fluff so too would I regard your contentions to be weak and severely lacking in substance and merit. I mean I'm sure you're a good person, and I'm sure you know how to form a solid and robust argument, clearly in this case you have not done so.

 

I mean if you decide it's worth the time to really throw down the gauntlet and prove before all witnesses the incontrovertible objective reality of mathematics, I would invite you to do so. I am by no means invested in the idea that math isn't objective beyond the fact that I see no compelling reason to believe otherwise. I mean honestly you'd be doing me a favor, sparing me a trip down the existential rabbit hole.

 

However if you find that you cannot mount a truly solid defense of your position, I would encourage you that least entertain the notion that the mathematics that we employ is not objectively true, but founded on human perceptions which are subjective according to what senses are available with which to abstract and develop a formal system, which by a recursive process of observation and revision can be addended or modified to asymptotically approach objective truth without ever being truly able to reach it.

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My first post was meant to mimic yours, and while only a partial argument it does underlie the flaws in yours.. Nothing you have to say takes that many paragraphs. I don't like reading excessively windy things. It bothers me because you may have really solid ideas under all the fluff but I don't want to dig through it. I literally didn't read what you put up. Just that my name was in it. Don't use 2 words where 1 is sufficient I guess. And if you really feel thats the MINIMUM number of sentences you can use to phrase your arguments, lay it out clearer.


So I will present my argument really clearly and in very few sentences.

 

There are only 2 things that exist. Things we make. And things we discover.

 

Things we make can be objective or subjective.

 

Things we discover are objective. Unless they are false.

 

I don't think you can disagree with anything I said. Maybe you can posit a third category of things that are but that is an uphill battle because you are already adding needless complexity.

Edited by TheGeckomancer
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A perfect circle doesn't exist in reality, there's no such thing, its an abstract concept based on a locus. Things like [math]\sqrt{1}[/math] doesnt exist either, it's a concept made up so we could explain a particular phenomena. Again mathematical dimensions don't physically exist, and again then will use this mathematics in string theory or such. But the dimensions are hypothetically based on the laws of maths, not the laws of physics. There are plenty of things within the realms of maths that don't physically exist.

 

However contrary to the hypothetical maths is a distinct set of laws that when applied to the right Physical being, force, or space give us precise answers explaining how the given being or force react. This isnt a coincidence, so maths must be tied to nature in some way.

 

The answer is, some very specific maths exists within nature. The rest are "possibilities" that are not tied to our physical reality, but only exist within the realms of maths.

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Things we make can be objective or subjective.

 

Things we discover are objective. Unless they are false.

 

I don't think you can disagree with anything I said.

 

I don't really understand this. I don't know what you mean by "make" vs "discover". And I'm not really sure what you mean by "objective" and "subjective".

 

For example, colour is subjective but would you claim that we "make" the perception of colour? Or do we open our eyes and discover it?

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No. We make definitions for colors. Colors are objective they are wave lengths of light with measurable differences. The definitions we make are subjective, such as how one color appears to a person vs a different person, but the thing we discovered, that wave length of light is objective. Discoveries are objective, things we make can be either objective or subjective.

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Daedalus: That was a really solid effort, literally from a certain perspective, I commend your attempt at rigor.

 

Still the contention makes a few assertions that, A:lack imagination and B: as far as I'm aware have no basis in truth other than the fact that you said it was so. For instance: "geometric arrangements... Can only be described mathematically". Now if you said "can" be described mathematically I would have agreed but you've given no proof of the only part of your claim beyond asserting that such is the case.

 

If that were true it would be impossible for me to describe in plain English the atom at every location by name and position according to some reference point without the use of numbers. As it so happens such a feat is technically possible, "there is a carbon atom to the left of the reference, below the reference, and positioned at the leading edge" you get the idea. Now I may take an absurdly long time to describe the geometry in this way but it could in theory be done.Really? Please, by all means, describe the arrangement of atoms in allene and propyne without referring to any mathematical terms whatsoever... These molecules have the exact same number and type of atoms.

 

It is impossible for you to describe the arrangements of atoms, and your example proves it!!! "There is a carbon atom to the left of the reference, below the reference, and positioned at the leading edge." You are referencing mathematical terms that describe position. The term "reference" itself means origin point within a local coordinate system, which is purely mathematical. You seem to think math is concerned with only numbers, but you are seriously mistaken in your assumption. Stating direction such as left or below is no different than stating [math]a_1.x < a_0.x[/math] and [math]a_2.y < a_0.y[/math]. Just because you decide to use algebraic description of position and arrange the statement as a word problem does not result in you successfully describing the arrangment of atoms without using math. For instance, try comparing the size of the Earth to the size of the Sun without any mathematical concepts whatsoever... It's impossible. Sure, you could say the Sun is bigger than the Earth, but that is a mathematical relationship that can be expressed in an extension of our language which uses mathematical symbols and expressions such as [math]S > E[/math]. Just because you use words to describe something doesn't mean you did a comparison without using math. Size is a mathematical relationship and we do not need exact numbers to compare the sizes of the Earth and Sun as my example has clearly shown. So... no, you cannot describe the arrangment of atoms without referring to position, size, or any other mathematical relationship, regardless of how abstract you wish to make the comparison. Mathematics isn't just about numbers because it exists in nature and cannot be so easily explained away.

 

So, I reassert my statement. Define the arrangment of atoms without referring to any mathematical terms. This includes relative terms such as left, right, top, bottom, front, or back, which are nothing more than words used to represent mathematical language. Do you know why we invented less than < , greater than > symbols or any mathematical symbol? It's so that we don't have to write a paragraph of words to describe the same thing that the symbols represent. So, you cannot simply use mathematical terms such as left, right, top, bottom, etc... and claim they have no basis in mathematics because each of those words describe a relative position.

 

This once more alludes to the problem I mentioned previously, most of these arguments follow the form: "math is real because obviously math is real. Therefore P=NP QED"

 

You get the idea, it proves nothing, it only reiterates that the physical universe can mostly be described fairly accurately in most respects through the use of math.

 

Again it's like Christian logic: "God is real because you can only describe the universe because God made it that way. Do you see how everything in nature works, it couldn't work that way if an intelligent designer hadn't intelligently designed it that way."

 

Mathematics is nothing like Christian logic, and such a comparison truly demonstrates your ignorance of what mathematics really is. We cannot physically see God, and our belief or disbelief in him is not required for the universe to exist. Mathematics, however, can be seen and exists regardless of whether we believe it does or not. Most everything around you exists as an arrangment of atoms and has mathematical properties such as position and size. We didn't invent these mathematical properties. They already existed. It really doesn't matter what we call them, whether or not we use symbols or words (groupings of symbols) to define them, or how we form sounds using our lips and vocal chords to communicate these mathematical terms with each other. We can clearly see that these mathematical relationships such as position and size exist. However, if we wish to communicate that one cave is bigger than another, then we would have to invent words (bigger) and symbols (>) to describe this to each other. Eventually, it became important to give better and better descriptions. So, we inventented more words and symbols such as inches and meters that would allow us to describe position and size more accurately.

 

So, let's talk about numbers, which seems to be what you think mathematics really is. Numbers would not exist if they didn't occur in nature. It has nothing to do with philosophy or religion. Because we physically observe size, position, and quantity, we invented symbols and words in our language to describe them. I have one tree in my yard, but my neighbor has two trees. My tree is bigger than both of his trees. How much bigger is my tree to his tallest tree? Now, I have to use numbers to be able to answer this question and communicate it with my neighbor. I could use feet or meters. Both terms describe a predefined length. Did we invent these terms? We sure did. However, these lengths exist regardless what we call them or which unit of measurement we use to describe them. In fact, we can compare both trees in units of their heights. His tree is 3/4 the size of my tree or my tree is 4/3 larger than his. That statement is true regardles which unit of measurement we use to measure the trees. If these mathematical relationship did not exist in nature, then trees would not have a size to compare and, therefore, would not exist.

 

If that's not enough to convince you, then tell me how many people are on Earth without using any mathematical terms or relationships.

 

You know, actually that's a good way to test your argument. Whatever you are about to say, imagine the people you think are the most misguided applied the same logic to prove a ludicrous claim. If you would tear it apart if it were used against you, don't bother saying it. If you can conceive of no sound way to refute it I will entertain the notion.

It seems to me that you should practice what you preach.

Edited by Daedalus
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^There is no non mathematical way to describe relationships of size, position, orientation, velocity, or mass accurately. It doesn't matter if you explicitly use numbers. In fact a lot of equations ARE sentences, just written with symbols because mathematicians and logicians LOVE simplest possible expressions.

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That statement is also true. It doesn't detract from the truth of my statement lol. Actually, I think by my definition reality would fall under things we discovered :D.

 

We can't experience reality directly therefore things we discover are merely the effects on experiment we percieve as models.

 

I'm not even sure what you mean by "things we make". The sun is in all probability a part of reality yet I don't see how we made it. The unified field theory probably "exists" (has a referent) in nature yet we've neither made nor discovered it.

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.... Are you trolling me right now?

 

Would you prefer me to say things humans create? We did not make the sun, we discovered the sun. It is an objective part of reality. Granted we did not have to work hard to discover the sun.

 

We discover these underlying principles to the universe through indirect observation and mathematics. We then create (something that can be subjective or objective) mathematical predictions based on our observations.

 

Also, would it be clearer to you if I said that we are still discovering reality day by day?

Edited by TheGeckomancer
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We discover these underlying principles to the universe through indirect observation and mathematics. We then create (something that can be subjective or objective) mathematical predictions based on our observations.

 

Also, would it be clearer to you if I said that we are still discovering reality day by day?

 

This is the subject of the thread. You are merely assuming the conclusion by saying "we create mathematical predictions". These "predictions" are derived from models developed from experiment and then the logical structure of nature which we call "math" is applied to these models to make prediction. We aren't really "discovering" or "making" anything but rather describing the effects of

reality on experiment. This is a remarkably narrow view of reality but people can't see that because of metaphysics and the nature of language. Humans are merely actors within the greater reality who can build on the knowledge of previous generations through language and its handmaiden; modern science.

 

If you could stepoutside of what you "know" this would be painfully obvious to you. But the only thing people can see is what they know. This too is a form of assuming the conclusion.

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Then how come math has been used to accurately predict the existence of real things decades before we were able to test it, such as particles? That seems to be a direct violation, that is not building on knowledge, that was something entirely hypothetical and mathematical in nature applied to reality and turned out to be true.

 

To me there is not logical stance to take that says math is not a part of the natural world. Some try the argument that math is a language we use to describe the world and we refine that language to make more and more accurate statements. That actually makes sense except for the predictions problem. Which is a huge one. If math not a part of the natural world then we could not use it for predictions about unknowns. If we observed any system long enough we would be able to describe it perfectly mathematically and make perfect mathematical predictions about it because the universe is constant. But that would be the end.

 

There would be no reason for one mathematical system to be applicable anywhere else. In fact it's illogical for it to do so. That's one of the things that gives real credence to the "universe is a computer simulation" theory. It explains why math is a fundamental part of the nature of the universe.

Edited by TheGeckomancer
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To me there is not logical stance to take that says math is not a part of the natural world. Some try the argument that math is a language we use to describe the world and we refine that language to make more and more accurate statements. That actually makes sense except for the predictions problem. Which is a huge one. If math not a part of the natural world then we could not use it for predictions about unknowns. If we observed any system long enough we would be able to describe it perfectly mathematically and make perfect mathematical predictions about it because the universe is constant. But that would be the end.

you're confusing the mathematical model with the actual phenomenon. maths doesn't have to be fundamental to be useful.

 

for example, language is not a fundamental part of the natural world but it can and has also been used to describe and predict phenomena (though not as precisely as maths).

 

i'm not sure what you mean when you say "the universe is constant;" what about the universe is constant?

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you're confusing the mathematical model with the actual phenomenon. maths doesn't have to be fundamental to be useful.

 

for example, language is not a fundamental part of the natural world but it can and has also been used to describe and predict phenomena (though not as precisely as maths).

 

i'm not sure what you mean when you say "the universe is constant;" what about the universe is constant?

 

 

 

I am not confusing any phenomenon. Non mathematical language is NOT used to predict phenomenon, unless you mean "I reckon the sun will rise tomorrow" that is not even a prediction that is a prediction of a basic absolutely repeating pattern, that is the most sophisticated predictions standard language can make. I mean the universe is constant as in we can wake up today and expect everything to still be behaving the same way it was yesterday.

 

Actually a better way of saying this is. Standard language cannot predict things we haven't observed. Math can, and perfectly accurately. That is a HUGE problem to resolve before saying math is something we made up. We also made up english but it does NOT allow us to do that.

Edited by TheGeckomancer
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Here, let me use more formal logic.

 

If a system is objectively real, then we will be able to observe any aspect of that system in nature.

 

If an element of a system does not and cannot exist in nature, the system cannot be objectively real.

 

Imaginary numbers cannot exist in physical reality and do not exist in physical reality.

 

Imaginary numbers are a necessary element within our mathematical system.

 

Thus mathematics contains elements which cannot and do not exist within nature, and because systems whose necessary elements do not exist within nature cannot be objectively real, mathematics cannot be objectively real.

 

There, formal logic. Either show that imaginary numbers exist, show that systems which necessarily contain non-real elements can still be objectively real, or show that imaginary numbers are not necessary to a complete understanding of mathematics.

 

Alternatively concede the point.

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