Does mathematics really exist in nature or not?

[arc]

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. . . . . . . .

 

 

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.

 

Bold mine

 

You have disproved your own argument;

 

Did you ever have the thought when watching a show like the original Star Trek, and think to yourself?

 

“You know it’s funny, no matter where they’ve gone in the universe, every advanced alien civilization they meet speaks English.”

 

Well, we know without even having to do any statistical analysis that this would not occur even once in a million encounters with an unknown advanced alien civilization.

 

Do you think mathematics would suffer the same fate? Do you think their preliminary and advanced mathematics would have differed greatly from ours?

 

They would not because they are derived by a system of logical deduction that would be an unavoidable requirement to allow any civilization to advance to the level of interstellar travel. This means of course mathematics is intrinsic to the universe and is revealed though logic based systematic discovery.

 

You would actually need to prove they experience a different physical reality than we do to claim they would not discover similar mathematical concepts to ours.

[andrewcellini]

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 simply not true https://en.wikipedia.org/wiki/Drive_theory https://en.wikipedia.org/wiki/Terror_management_theory

 

as well as carl roger's theory of self

 

i already acknowledged that language is not going to produce as good of predictions as a mathematical model. this could be do to numerous reasons, lack of clear agreed upon definitions for example.

 

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.

which is an approximation that is suitable for us for now. obviously the earth is not going to be suitable for life when the sun engulfs it in about 7 billion years (and earth may be uninhabitable before then, i'm not totally sure on that).

 

or when the universe is inhabitable after that.

Edited November 27, 2015 by andrewcellini

[sciwiz12]

Also fine, if you want to declare any words I use to belong to some branch of mathematics I should tell you there's a completely non-mathematical way to describe the shape of any object: I can draw it. No mathematical terms are required, just a paint brush, or I could sculpt it in clay.

 

 

 

Also it's faulty reasoning anyway. Even if I needed math to describe an object I need English to describe the world, that doesn't make words real, nor even that which words describe. For instance, I need words to describe the color of the ocean as blue, and you might argue that the oceans would be blue regardless which technically wouldn't be true because oceans aren't really any color,I digress.

 

So you could apply the same reasoning you've applied to math. Words describe things in nature, I had to discover those things, thus words are objectively real.

 

However I can also describe an invisible pink unicorn. Now if words were objectively real, since I described an invisible pink unicorn with words, it must therefore be real.

 

"Hold on!" You might counter, "you're just using objectively real words to describe something that doesn't exist, that doesn't make words not real!" To which I say: blhkrjgfla. It is a word that refers to a specific object that by definition can't be described and doesn't exist but isn't nothing.

 

"You just made that up!" You may counter. In fact I did, I made up a thing and a new word to describe it using the same "objectively real" system by which I can describe the color of the ocean, the feeling of the soil, and the taste of chicken.

 

I really don't know how else to get this accross, your arguments are invalid. That's what I'm saying here, words can fit just as easily into most of your arguments. Words describe things that are real and it's almost impossible to describe certain things without words, but just because it's useful for describing things doesn't make it objectively real. My words aren't bound to the same rules of nature as the objects they describe, neither is math which follows its own rules, at times in spite of knowing that it's concepts cannot exist. If it were objectively real it would be bound to the same rules by which all objectively real things are bound, but is not. I really don't know what more I can say on the subject.

[DevilSolution]

Complex and

 

 

Bold mine

 

You have disproved your own argument;

 

Did you ever have the thought when watching a show like the original Star Trek, and think to yourself?

 

“You know it’s funny, no matter where they’ve gone in the universe, every advanced alien civilization they meet speaks English.”

 

Well, we know without even having to do any statistical analysis that this would not occur even once in a million encounters with an unknown advanced alien civilization.

 

Do you think mathematics would suffer the same fate? Do you think their preliminary and advanced mathematics would have differed greatly from ours?

 

They would not because they are derived by a system of logical deduction that would be an unavoidable requirement to allow any civilization to advance to the level of interstellar travel. This means of course mathematics is intrinsic to the universe and is revealed though logic based systematic discovery.

 

You would actually need to prove they experience a different physical reality than we do to claim they would not discover similar mathematical concepts to ours.

 

Actually YES, a measurably more intelligent ET race would certainly have a different mathematical system to ours.

 

The aspects of maths we use is massively flawed, not that its not useful, but for most purposes its "if the shoe fits" and in some cases (I.E "some" theoretical physics) they will force the shoe to fit.

 

We draw laws up ourself, why should brackets superseded addition? I think they would have a much more refined system.

 

What if mathematics fundamentally exist as 4 dimensional waves and everything we understand of maths are just a subset of the way these waves flow? An ET race could have comprehension or even see things in this dimension, while we are stranded looking at 2 dimensional circles that give infinite decimals.

 

We only have 2 basic operators in maths, addition and subtraction and even subtraction is an illusion of sorts, all the rest of the operators are derivatives of these operators. Do we therefore presume the universe is an extension of 2 operators?

Edited November 27, 2015 by DevilSolution

[sciwiz12]

Arc, you simply declared that alien races would use the same system of mathematics because they must adhere to the same physical laws. I cannot accept this claim at face value until you prove that any sufficiently intelligent race under the same physical laws regardless of sensation and communication must necessarily develop the same systems of formal logic and mathematics. I'm not saying you're definitely wrong but you've declared it very matter of factly without showing why this should necessarily be the case. Under the same logic why wouldn't they all speak English? I mean they exist in the same universe under the same physical laws.

[TheGeckomancer]

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.

 

 

My point this whole time has been to say numbers are real nonphysical objects. You are asking me to counter my own argument to provide you evidence of something I don't think is there. We cannot directly observe everything. We use indirect observation for a LOT of science. Dark matter is a perfect example. If I asked you to bring me a cup of dark matter you would not really be able to. That doesn't mean it isn't there.

[Daedalus]

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.

 

Sciwiz12, your statements have already been shown to be bs. Let's see... The color green and horses exist... so... how about green horses? Nope... they don't exist. Since green horses don't exist, then I guess green and horses aren't real.. Your logic is clearly flawed.

 

How about you try answering the questions I asked and give a credible repsonse to my last post #117: http://www.scienceforums.net/topic/92115-does-mathematics-really-exist-in-nature-or-not/?p=894225

Edited November 27, 2015 by Daedalus

[TheGeckomancer]

Lets try this. Answer my question. If math is not a fundamental part of nature, how can we make predictions of a mathematical nature in a vacuum about the real world and have them be perfectly accurate?

[DevilSolution]

Lets try this. Answer my question. If math is not a fundamental part of nature, how can we make predictions of a mathematical nature in a vacuum about the real world and have them be perfectly accurate?

 

If you submit to this conclusion you must admit that the universe is an extension of 2 mathematical operators. Is that true?

 

Or does something exist beyond those 2 operators and our comprehension?

[TheGeckomancer]

It wasn't a conclusion it was a question. One I genuinely want the answer to. If you are using a socratic style here thats cool but I don't fully understand your question. Are the operators + and -? And why would I have to conclude that is the entire universe? Maybe I am missing it but this makes a lot of leaps.

[DevilSolution]

It wasn't a conclusion it was a question. One I genuinely want the answer to. If you are using a socratic style here thats cool but I don't fully understand your question. Are the operators + and -? And why would I have to conclude that is the entire universe? Maybe I am missing it but this makes a lot of leaps.

 

A few small leaps for man, one huge leap for mankind.

 

The premise it simple, + and - derive every other operator in mathematics, using these operators we create relationships between entities and forces etc that explain how the physical universe works. Therefore everything in the universe can be explained via these 2 operators, meaning the maths not only exists within nature it defines it. By that token the universe is simply an extension of + and -

 

Im sure you understand. But then we can only understand logic, so anything beyond that is beyond our comprehension anyway.

 

goodnight x.

[TheGeckomancer]

I am genuinely not sure about this question. I would say most if not all things in objective reality are defined by math. Our perceptions though, are not rooted in objective reality and has lots of non quantifiable elements to it.

[sciwiz12]

I give up. This is the same head bashing I would expect to encounter in a religious debate, not on a scientific forum such as this. I simply don't have the patience nor the energy to continue to engage in such a fruitless endeavour. You can go on believing whatever you want.

 

I'm really not trying to be an elitist or take any sort of high ground, I simply see a lot of unsupported declarations and lack of logical standards. Maybe from your perspective I'm guilty of the same crime, I hardly see how that is the case as I've attempted to avoid matter of fact declarations and holes in logic but at this point I simply don't have the mental energy to keep bashing my head against this proverbial wall.

 

However, I would propose the following: I will review philosophical, formal, and mathematical logic as well as techniques of proper argumentation, sound rebuttal, and fallacies.

 

I don't believe I've committed any logical errors but I'm sure you seem to think that I have done so. Here's my counter ask however. Please, for the love of there is no God, review logic and the principals of sound argumentation as well as possible fallacies.

 

I'll admit I'm a bit rusty, but you must admit that if I can seem entirely sound and flawlessly rational from my perspective yet somehow flawed and misguided from your perspective and vice versa that it is entirely possible that either of us may be in error.

 

So I would urge you to please review your stuff and practice making sound and concrete arguments. I would really hate to cross your paths again and be subjected the the same unsupported matter of fact declarations. I guess I must just be delusional or something because it really does seem like your arguments take advantage of serious leaps in logic.

 

Anyway, please do that, and if you refuse that's on you but if you do refuse you really can't pretend to claim a rational and intellectual high ground.

[TheGeckomancer]

Again. You have used WAY more words than necessary. Stop with the fluff man. I can sum up your entire post in the following sentences. "I am tired of arguing, in what I feel are circles, and I am not an elitist. (I apologize for this part but I don't know a nice way to say it.) And since I could not establish myself as the clear winner of this conversation that means there is an equal likelihood you are as wrong as me."

 

I asked a straight forward question. Give me an answer to it that doesn't require wittgenstein himself to decypher and I will admit you have made a huge step toward debunking my argument.

[cladking]

Lets try this. Answer my question. If math is not a fundamental part of nature, how can we make predictions of a mathematical nature in a vacuum about the real world and have them be perfectly accurate?

 

Math reflects the exact same logic as the basis of reality. Reality asserts itself through experiment and our models and understanding derive from experiment. Of course there is a correlation between reality and math.

 

It doesn't have to be this way but language defines science and science and reality set the parameters for math.

[TheGeckomancer]

 

Math reflects the exact same logic as the basis of reality. Reality asserts itself through experiment and our models and understanding derive from experiment. Of course there is a correlation between reality and math.

 

It doesn't have to be this way but language defines science and science and reality set the parameters for math.

 

 

Language does not define science. I do not have to be able to even use language to perform science, I can still observe the world, form hypotheses about the universe, establish tests, verify my results and reach my conclusions without language. It would be harder but I can. And I would not be able to share that information with anyone but it wouldn't be less true.

[andrewcellini]

Lets try this. Answer my question. If math is not a fundamental part of nature, how can we make predictions of a mathematical nature in a vacuum about the real world and have them be perfectly accurate?

the premise seems to be contentious.

 

are they "perfectly accurate," and what do you mean by that exactly? are you sure they're not accurate within some bounds?

[TheGeckomancer]

the premise seems to be contentious.

 

are they "perfectly accurate," and what do you mean by that exactly? are you sure they're not accurate within some bounds?

 

This is a fair point. But what happens to my question if we add the word "nearly" before "perfectly accurate"? Does the validity drop to 0? I don't think so.

[andrewcellini]

 

This is a fair point. But what happens to my question if we add the word "nearly" before "perfectly accurate"? Does the validity drop to 0? I don't think so.

certainly not, but it's always good to have clearer questions.

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

certainly not, but it's always good to have clearer questions.

 

Not going to argue that.

[andrewcellini]

the one thing that isn't clear (for me at least) is how something (an abstraction) that is useful to describing and predicting phenomena must be fundamental?

 

your earlier posts seem to boil down to a reification fallacy.

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

It is not useful for predicting phenomena. Useful implies that it's accuracy has limits, knowing card counting and statistic is useful for cheating at poker but it doesn't guarantee wins. Whenever a prediction is not correct it's human error, not a flaw in math. I do not know about reification fallacy, I will look into this and get back to you. I may be. Not sure.

[andrewcellini]

It is not useful for predicting phenomena. Useful implies that it's accuracy has limits

i thought we established its accuracy has limits.

 

also take newtons theory of universal gravitation for example. the model can only be used accurately for certain situations, such as small massive objects near larger planet sized massive objects, or orbits of planets in the solar system (without mercurys precession).

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

I can think of situations where mathematical predictions CANNOT be perfectly accurate. I can also think of mathematical predictions I can make that are perfectly accurate. The ability to be perfectly accurate is.......Well kind of insane. But sorry, going to look up the fallacy thing now.

[andrewcellini]

I can think of situations where mathematical predictions CANNOT be perfectly accurate. I can also think of mathematical predictions I can make that are perfectly accurate. The ability to be perfectly accurate is.......Well kind of insane. But sorry, going to look up the fallacy thing now.

so is your actual claim that only certain mathematical entities are fundamental (the ones that are perfectly accurate and relevant for physics models)?

Edited November 27, 2015 by andrewcellini