How does mathematics relate to the physical world?

[Sodacrates]

I find this question pretty interesting. Take for example, Platonists, depending on their exact view, they often believe math is a window into a more perfect world and our Universe operates in regards to mathematics rather than mathematics being descriptive of the physical world. I think the most important question regarding how math operates is, "Is math always correct?" Virtually every mathematician has very platonistic views (but the majority would not be platonists) and believe that math is a perfect system which guides the properties of the physical world. I find this view to be beautiful, hopeful and somehow redeeming that humans have some glimpse into perfection, but unfortunately (and I mean that sincerely) I do not think it's correct. So what do you think? Is math always correct? Is it descriptive, prescriptive or something else?

 

[Psyduck]

If you want an advanced academic book on the subject. Check out:

http://www.amazon.com/Imagination-Geometry-Ontology-philosophy-mathematics-Philosophy/dp/075461574X

Your library might have it.

 

[-=SS=-]

Basic mathematics is always correct.. it is universal too. Ratios and proportions are found throughout nature and beyond also, the biological domain is rife with it; the golden ratio is present in your hands, your arms, legs, face, body as a whole.. you'll find it in nearly every living organism, although it's most obvious in snail shells, pinecones, sunflower heads etc. Geometry is also present everywhere, which arises from mathematics (ratios in space).

I wouldn't say maths is a window into a more perfect world. Reality is perfect already, maths is just the foundation or matrix of the system that's all. You couldn't ask for a more clear sign of intelligent design than maths in nature really.. it's everywhere if you have the eye to see it. I'm amazed that people can just brush it off as nothing.. well not really, most people are walking dead xD

 

[P A]

You couldn't ask for a more clear sign of intelligent design than maths in nature really.. it's everywhere if you have the eye to see it.

As an aspiring mathematician who, I'd wager, knows more about most mathematical concepts than you do, I'm going have to strongly disagree. And if I don't 'have the eye to see it,' then who possibly could? A scientist? Most of them are atheists. Let me guess - mathematically uneducated buffoons who have ingested one too many hallucinogenic fungi in their time, right? They're the ones with the insight, and everyone else falls under your sweeping indictment as the 'walking dead?' What a crock.

 

[-=SS=-]

What's your problem P A ¬_¬ Whoever appointed you to be the moderator of this forum made a big mistake, you're clearly not someone of philosophical or spiritual bent.. you're a scientific materialist, one of the most notoriously difficult people to discuss these subjects with incidentally.

But on your post:

Richard Dawkins is an incredible genetic biological whatever the fuck he is, academically he knows his shit.. but yet is a total retard when it comes to seeing past his academic education in relation to the bigger picture. I suggest you are of the same variety. You've got some mathematical paradigm going in your head that has got the blinders on you, so actually whilst you should be the kind of person to understand what I'm refering to ironically you're probably less likely to get than anyone else due to your education. Same with Dawkins when it comes to understanding why biological life is being driven, and not accidental mutation and survivalOTF.

Yes, you probably know a shit load more mathematical concepts than I do. And I couldn't care less. It means nothing. Nature and the Universe doesn't give a shit either. Wave your credentials with pride, I really don't give a fuck. But if you do know so much about mathematics then perhaps you'd like to explain WHY we find the golden proportion in all scales of natural systems, from embryonic cell division all the way up to spiral galaxies. And don't just say it's a coincidence ¬_¬

 

[P A]

What's your problem P A ¬_¬ Whoever appointed you to be the moderator of this forum made a big mistake, you're clearly not someone of philosophical or spiritual bent.. you're a scientific materialist, one of the most notoriously difficult people to discuss these subjects with incidentally.

What subjects? Subjects on which you and I disagree? The funny thing is, I'd be willing to wager that I know more about philosophy proper and (perhaps even) religion than you do, too. See, unlike you and PiP et al., I don't tell people with whom I disagree that they suck at doing X, Y, or Z simply because they happen to disagree with me. The joke's on you, kid.

Richard Dawkins is an incredible genetic biological whatever the fuck he is, academically he knows his shit.. but yet is a total retard when it comes to seeing past his academic education in relation to the bigger picture. I suggest you are of the same variety.

1) Who said anything about Richard Dawkins?; 2) How could you possibly demonstrate that what you're saying is true to any disinterested party?

You've got some mathematical paradigm going in your head that has got the blinders on you, so actually whilst you should be the kind of person to understand what I'm refering to ironically you're probably less likely to get than anyone else due to your education. Same with Dawkins when it comes to understanding why biological life is being driven, and not accidental mutation and survivalOTF.

Again, how could you possibly prove this, given that you lack the very education that you are so quick to deprecate?

Yes, you probably know a shit load more mathematical concepts than I do. And I couldn't care less. It means nothing.

Listen to yourself, man. Whether you understand the subject matter (i.e., know what you're talking about) or not means everything in this context.

Nature and the Universe doesn't give a shit either. Wave your credentials with pride, I really don't give a fuck. But if you do know so much about mathematics then perhaps you'd like to explain WHY we find the golden proportion in all scales of natural systems, from embryonic cell division all the way up to spiral galaxies. And don't just say it's a coincidence ¬_¬

Now you're just coming off as crude and bitter. I don't need prove a damn thing to you. You were the one who suggested evidence of 'design,' whatever that means. Since you appear patently incapable of expounding any further on the matter, I'll assume that this little spluttering fit is a product of your impotent polemical frustration with those who may, in fact, know better than you.

 

[Psyduck]

What subjects? Subjects on which you and I disagree? The funny thing is, I'd be willing to wager that I know more about philosophy proper and (perhaps even) religion than you do, too. See, unlike you and PiP et al., I don't tell people with whom I disagree with that they suck at doing X, Y, or Z simply because they happen to disagree with me. The joke's on you, kid.



1) Who said anything about Richard Dawkins?; 2) How could you possibly demonstrate that what you're saying is true to any disinterested party?



Again, how could you possibly prove this, given that you lack the very education that you are so quick to deprecate?



Listen to yourself, man. Whether you understand the subject matter (i.e., know what you're talking about) or not means everything in this context.



Now you're just coming off as crude and bitter. I don't need prove a damn thing to you. You were the one who suggested evidence of 'design,' whatever that means. Since you appear patently incapable of expounding any further on the matter, I'll assume that this little spluttering fit is a product of your impotent polemical frustration with those who may, in fact, know better than you.

I have to agree with SS and others that you set the wrong tone for this forum.

The discussion becomes a power struggle of knowledge when you enter the conversation. Just look at some of the sentences I emphasized above. Such phrases show off your highly analytic and scientific approach to philosophy. Of course, I don't blame you for taking such an approach to philosophy. Neither do I doubt your expertise and enormous amount of knowledge. But I do think, as a moderator dealing with people of different backgrounds and educations, you should widen your perspective and be more open to other ways of doing philosophy.

Philosophy originally, with Plato, was about having a proper dialogue between mutual parties. The goal of a Platonic dialogue was not per se to come to a definite conclusion, to prove something, or to be right... Of course, you will say, eventually philosophy should be about the truth, and Socrates does undermine the false opinion of the opposing party. But Socrates does this by i) having a conversation, ii) listening to the other person, iii) and asking him questions. His dialectical method doesn't want to dominate the other person for the sake of being right. First of all he wants to listen to the other person and by having a dialogue "they" incidentally arrive at truth. Truth basically lies in the conversation itself for Plato. A proper conversation shouldn't be like some kind of scientific experiment where we can "test" who is right and who is wrong. Human conversation has much more potential.

 

[P A]

I have to agree with SS and others that you set the wrong tone for this forum.

Interesting - you're the first Bluelighter to publicly take me to task without first having disagreed with me on one pertinent issue or another. So, what have we here?

The discussion becomes a power struggle of knowledge when you enter the conversation. Just look at some of the sentences I emphasized above. Such phrases show off your highly analytic and scientific approach to philosophy. Of course, I don't blame you for taking such an approach to philosophy. Neither do I doubt your expertise and enormous amount of knowledge. But I do think, as a moderator dealing with people of different backgrounds and educations, you should widen your perspective and be more open to other ways of doing philosophy.

When it starts as a passive-aggressive pissing match (the 'walking dead'?), a 'conversation' is highly unlikely to develop into anything of philosophical merit. I do what I can. The irony here is that someone strolled into a thread and dropped an unqualified opinion, appending a cheeky little insult for whomever happened to disagree with him...and I'm the closed-minded one.

Philosophy originally, with Plato, was about having a proper dialogue between mutual parties.

Exactly my point. If you want to talk specialized concepts with the confident air of someone who knows the territory, either wave your credentials at the door or get ready to be challenged. I have no doubt in my mind, that, had some random rube popped his head into the Academy and tried to forcefully (and insolently; insultingly) propound philosophical/mathematical postulates with one of the tutors, he'd be treated with the exact same degree of 'mutual respect' that I extended to SS.

Of course, you will say, eventually philosophy should be about the truth, and Socrates does undermine the false opinion of the opposing party. But Socrates does this by i) having a conversation, ii) listening to the other person, iii) and asking him questions. His dialectical method doesn't want to dominate the other person for the sake of being right. First of all he wants to listen to the other person and by having a dialogue "they" incidentally arrive at truth.

Sorry to disappoint you Psyduck, but I am not, in fact, Socrates of Athens.

The goal of a Platonic dialogue was not per se to come to a definite conclusion, to prove something, or to be right... Truth basically lies in the conversation itself for Plato. A proper conversation shouldn't be like some kind of scientific experiment (!) where we can "test" who is right and who is wrong. Human conversation has much more potential.

I never proposed any such thing. The 'proof' and 'demonstrations' that I requested were to be delivered in print, not by way of empirical investigation, and therefore had basically nothing to do with science proper. On the other hand, it's funny that you mention my 'analytic' approach - philosophy of mathematics is an analytic topic par exellence. When it comes to snide know-it-alls with unfounded opinions re. topics in which they are not well-versed in the first place, human conversation has little potential indeed.

 

[Busty St Clare]

Basic mathematics is always correct.. it is universal too. Ratios and proportions are found throughout nature and beyond also, the biological domain is rife with it; the golden ratio is present in your hands, your arms, legs, face, body as a whole.. you'll find it in nearly every living organism, although it's most obvious in snail shells, pinecones, sunflower heads etc. Geometry is also present everywhere, which arises from mathematics (ratios in space).

I wouldn't say maths is a window into a more perfect world. Reality is perfect already, maths is just the foundation or matrix of the system that's all. You couldn't ask for a more clear sign of intelligent design than maths in nature really.. it's everywhere if you have the eye to see it. I'm amazed that people can just brush it off as nothing.. well not really, most people are walking dead xD

Maths isn't a truth, it is simply a palate in which artists try and paint the world and it's actions. It is mans way of trying to put onto paper what he sees around him. Just as artists struggle to accurately capture the view from their eyes, so do scientists struggle to explain everything they see with just numbers and equations. Simple math may be a truth (a triangle has three sides whose internal angles all add up to 180 degrees) but as you dive deeper into the quantum abyss our understanding of the world has to be bent to fit. Even then we have to fill in the blanks that no amount of scribbling on a chalk board can accurately describe.... for now.

 

[alasdairm]

You couldn't ask for a more clear sign of intelligent design than maths in nature really.. it's everywhere if you have the eye to see it.

when all you have is a hammer...

I'm amazed that people can just brush it off as nothing..

which, in common with most things, says so much more about the subject than the object.

What's your problem P A ¬_¬ Whoever appointed you to be the moderator of this forum made a big mistake...

i was one of the people who appointed him to moderate this forum and i'll agree to disagree with you.

there's a long-standing rule at bluelight that we don't drag threads off-topic with these kinds of issues. if you have a problem with PA's moderation, there's a mechanism. please use it.

alasdair

 

[dmtlunatic]

it's everywhere if you have the eye to see it..

Or the ear to hear it*, through the cochlea:

Oral transmission of information is much older than the written word.
"We don't see/hear things as they are. We see/hear them as we are."

Ways of seeing are inseparable from what we are told is important to look at. This is how we learn language.

*I'm talking about the "golden ratio", by the way.

 

[rangrz]

Speaking as a physics grad student, none of the fundamental dimensionless physical constants are the golden ratio. In fact, I've never encountered it anywhere in physics. Try harder SS.

That.said, mathematics is an excellent tool to describe physical systems, but ultimately it is an abstraction created by humans, and these physical systems have existed for billions of years prior to math.

 

[P A]

^I had suspected as much, but I refrained from commenting with authority because, in truth, I wasn't certain. You see, SS and Psyduck, my reluctance to engage the matter directly was a result of my acceptance of the fact that some people have different and/or more extensive credentials than do I, the acquisition of which credentials constitutes the sufficient condition whereby someone could acquire knowledge of the technical variety on display above; knowledge which, incidentally, proved crucial in the comprehension of SS's statement (re. the natural pervasiveness of the so-called 'golden' ratio), which statement, in turns out, was basically false. To append rangrz's commentary with some of my own pedestrian knowledge, it seems that humans find the golden ratio to be absolutely lovely, and tend to find it in many odd places. It doesn't take a whole lot of cognitive effort to wonder whether these 'findings' could have arisen as a result of an aesthetic/sensationalistic bias, as discussed here.

 

[yougene]

Here's my take on Platonism and Math. Math is a language. It consists of signifiers and referents. It's something that happens in the minds of humans. Not something that's "out there" in nature. But the referents of this language are "shadows" of transcendental "forms".

This isn't unlike our experience of physical objects. While looking at your computer right now, you're not directly experiencing your computer but a mental representation of it. It's a signifier of what exists beyond your mind. The relationship of mental representation of computer to "actual" computer is analogous to experience of mathematical abstractions to ingraspable "forms".

Mathematical Platonism provides logical consistency across two opposing views here. Math as a reality outside of you vs. a nominal human experience of strings manipulated according to rules.

if I don't 'have the eye to see it,' then who possibly could? A scientist? Most of them are atheists.

Countless mathematicians have dabbled with Platonic mysticism. Godel, Einstein, and Cantor are notable ones that come to mind.

I'm not sure what SS meant by "Intelligent Design" though. Intelligent Design is a specific argument to Judeo-Christian Creationism. I have a feeling he's taking the term to have a different meaning but I can't speak for anyone else.

Let me guess - mathematically uneducated buffoons who have ingested one too many hallucinogenic fungi in their time, right? They're the ones with the insight, and everyone else falls under your sweeping indictment as the 'walking dead?' What a crock.

I think you're taking your "authority" a little too seriously. You moderate a forum of drug users who like to throw ideas around, not a peer reviewed journal.

 

[yougene]

Speaking as a physics grad student, none of the fundamental dimensionless physical constants are the golden ratio. In fact, I've never encountered it anywhere in physics. Try harder SS.

No reference was made to physical constants.

 

[MrGrunge]

Mathematics is used to describe certain aspects of the physical world but it is in no way universal or absolute. As has been discussed earlier, there are physical systems at play in the Universe far beyond our current ability of comprehension, which have existed for billions of years. To say that our description of these systems is 100% accurate seems arrogant to me. The purpose (if you can really call it that...) of mathematics is to predict likely outcomes, not to perfectly quantify the physical world.

We assume that 1 + 1 = 2 only because we've never seen it equal 3.

 

[slimvictor]

George Lakoff argues in "Where Mathematics Comes From" that mathematics results from human cognition, and can only be understood through an understanding of human cognition.

He analyses mathematical ideas based on human experience and human cognitive processes such as metaphor.

For example, he says that four basic metaphors structure our understanding of arithmetic: collecting things, building things, using a measuring stick, and moving along a path.

So, to answer the main question in this thread (how does math relate to the physical world), I believe he would say that math relates to the physical world via human per/conception/reasoning.

Note that he does not deny the inherent ability of humans to perform mathematical tasks - he goes into detail about recent research e.g. on infants that shows that they look longer when one object is placed behind a screen, and then one more, but when the screen is removed, three objects are sitting there. Tiny infants (just weeks old) somehow know that this is impossible. This line of research suggests that we come into this world pre-programmed to count, add, and subtract numbers/objects from 0 to 4 or 5.
Lakoff argues that more complex mathematics is ultimately founded on this simple math, and is accomplished via cognitive processes such as metaphor.

He rejects the Platonistic idea of mathematics, saying that all mathematics that we can ever know comes from human cognition. Instead of seeing mathematics as transcendent, he says that it is the result of human culture and intelligence.

The connection between mathematics and the physical world is not what it seems.
The connection between mathematics and our experience of the physical world is mediated through our minds.

I have actually not read the book (after all this!), but heard him (and his coauthor, Nunez) talk about it once.
What he said seemed to make sense to me, but I do not have the background to really judge.

Let me guess - mathematically uneducated buffoons who have ingested one too many hallucinogenic fungi in their time, right? They're the ones with the insight, and everyone else falls under your sweeping indictment as the 'walking dead?' What a crock.

I think people above were trying to say that you might have expressed your message in a more kind or gentle way, PA. This quote seems quite confrontational and angry, and it was from the beginning of your back-and-forth.

 

[sssssssssss]

I'm no scientist or anything, but here's my thoughts.

Sure 1 + 1 = 2 in a perfect sense, but really 1,1, and 2 are all limits for f(x), a function approaching 1,1 or 2.
because by the archimedian principle, for every real number x, there exists a natural number n such that x < n... i think.

 

[dmtlunatic]

Proof that 3 = 9
Multiply both sides by 0
3 x 0 = 9 x 0
Therefore: 3 = 9

 

[sssssssssss]

Proof that 3 = 9
Multiply both sides by 0
3 x 0 = 9 x 0
Therefore: 3 = 9

Zero isn't part of the real numbers with respect to multiplication because it's inverse is undefined.