How does mathematics relate to the physical world?

[dmtlunatic]

So mathematics is a language; with learned, human-rules, of when I can and cannot use certain terms correctly?

 

[sssssssssss]

Well to use the operator =, you have to abide by its equivalence relation properties. so yes lol

 

[dmtlunatic]

So maybe my "proof" was "grammatically incorrect"?!

From 'remarks on the foundations of mathematics':

Imagine calculating with SQRT(-1) invented by a madman, who, attracted merely
by the paradox of the idea, does the calculation as a kind of service, or temple ritual, of
the absurd. He imagines that he is writing down the impossible and operating with it.
In other words: if someone believes in mathematical objects and their queer
properties--can't he nevertheless do mathematics? Or--isn't he also doing mathematics?

Also (unrelated - but highlighting the same point): http://en.wikipedia.org/wiki/Surreal_number

They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first presented in a work of fiction.

These are starting to come into use in the financial world, as game theory becomes ever more popular. Simply: the language that is being used changes; just as it does with "normal" human language -- nothing is static; except that which is thought to be being described -- except: we can't ever describe it; because we're describing a description!

 

[P A]

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.

As I already explained, it's not a matter of authority nor of rigor. If someone doesn't know what they're talking about, I reserve the right to let them know - especially if I possess some measure of qualification in the field that is being discussed. Also, this is basically independent of my role as a moderator here. I'm a Bluelighter too, you know, same as anyone else. If, like Psyduck et al., you want to take my isolated, one-off pieces of commentary to heart and internalize them as the 'tone' that is being 'set' for this subforum, that is certainly your prerogative.

 

[rangrz]

No reference was made to physical constants.

No,but he claimed it permeated the physical world. I noted that is not a physical constant, nor have I ever found it during rigorous study of the physical world.

 

[Roger&Me]

ALet 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.

You took the thought right out of my head and phrased it better than I could have. I see this all the time in psychedelic users: they sense science and math as being some sort of constriction on their "anything wacky is possible" mentality and so they align themselves in opposition to it. And I guess what I'm trying to say is, who cares? Most of these people haven't even taken a basic calculus course, so what do they know about real math or what it entails or says about physical systems? Intuition about mathematics is gained by actually working problems of many different types, in many different subfields of mathematics, over and over again until you can see the subtle analogies that exist between axiomatic systems, and even analogies that link together those analogies.

I hope that made sense, I haven't had my coffee yet this morning so I'm having trouble gettin' those thoughts out :D

 

[Sodacrates]

First off, to yougene. You mention Godel, Einstein and Cantor, and they all did dabble in Platonism (I really disagree with your use of the word mysticism. I think metaphysics or just Platonism would have been better. Plato thought his way to his understanding of the world, and that particular primitive man's understanding of the world, the majority of us still learn from despite the fact that many modern three year olds have a better grasp of the inner workings of the world than he did. Mysticism seems to be implying his ideas as religious which they are distinctly not). I think you could mention almost any 19th century mathematician and that statement would stand true, but today, Roger Penrose is a Platonist. And I would bet that if you spoke enough about metaphysics to Witten or any other big String Theorist they would have very Platonic views, if not being Platonists themselves.

Slimvictor, this is the first time I have ever been discussing this and someone brought up my view before I did. I didn't even know Lakoff had the same view as I did (I never thought I came up with this view as I once heard a teacher argue with a student about whether math was representative of the natural world and the teacher took this view; it did't convince me then as my view was probably far closer to Platonism back then, but after a few more years I understood what my teacher was saying). We interact with world through our senses and reason. When you hear 1+1=2 you have an emotional response telling you that it makes sense and it's correct. Experience may be a prerequisite for that feeling, but you only need at most need a limited experience showing that basic math is true before you can understand all of it. If I say 1,000,000,000,000+1,000,000,000,000=2,000,000,000,000, most of us have never seen a trillion things added with another trillion things and seen two trillion as a result, but it still yields the emotional response of making sense. Our reason creates a representation of the world which operates based on Mathematics. Our reason is astoundingly accurate, allowing us to slam things as small Protons together at the speed of light, so we have at least a mostly accurate picture of the world in our head, but is it perfect? Well, by definition, no.

In advanced mathematics when we prove things, we use our emotional reaction of "making sense" as guidance about what is mathematically correct. Is it possible that we could see math that we can prove is correct yet isn't representative of reality? All it would take is the model of the world found in our head not being perfectly representative of reality. If you assume a naturalistic standpoint, than it's safe to assume the most accurate model of the physical world in our heads was selected for, and that would mean it's safe to say we have an almost perfect model of the world in our mind.

When using math to calculate complex physical systems like rockets leaving orbit, or particle colliders, our best simulations are never perfectly correct. We tend to blame physics and chemistry for margin of error, but I believe math, itself, may be a culprit as well. I know that a lot of people will find that ridiculous and it may ridiculous, but I don't see any huge fault in my reasoning.

 

[-=SS=-]

..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.

Golden ratio discovered in a quantum world
http://phys.org/news182095224.html

I don't understand what they're saying so much but I thought it was worth mentioning here.

 

[yougene]

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.

I believe Lakoff doesn't take a stance on Platonic Realism. His point is whether or not mathematics signifies something "out there", it's simultaneously a human experience. That to understand the how and why of math you have to dig into biology and phenomonology.

Mysticism seems to be implying his ideas as religious which they are distinctly not

Religious implies a dogma. Mysticism implies an experience. It's accurate to say many great minds weren't just Platonists but Platonic mystics with "an eye to see". It's not a given these experiences carry validity but to characterize mysticism as religious belief would be inaccurate.

 

[alasdairm]

if we just made up maths Why is the physical world so amenable to mathematical description?

alasdair

 

[P A]

I see this all the time in psychedelic users: they sense science and math as being some sort of constriction on their "anything wacky is possible" mentality and so they align themselves in opposition to it. And I guess what I'm trying to say is, who cares? Most of these people haven't even taken a basic calculus course, so what do they know about real math or what it entails or says about physical systems? Intuition about mathematics is gained by actually working problems of many different types, in many different subfields of mathematics, over and over again until you can see the subtle analogies that exist between axiomatic systems, and even analogies that link together those analogies.

I hope that made sense, I haven't had my coffee yet this morning so I'm having trouble gettin' those thoughts out :D

Exactly. Forget the coffee - I couldn't have said it better myself. There seems to be an unfortunate undercurrent of anti-intellectual/anti-science sentiment that pervades a few drug subcultures, most prominently the more hallucinogenically-inclined ones.

 

[rangrz]

^
Agreed. I have difficult time interacting with psychedelic users. It seems anything based on logic and empirical observation provokes hostile responses.

 

[slimvictor]

if we just made up maths Why is the physical world so amenable to mathematical description?

alasdair

Lakoff isn't saying we just made up math. He says the foundations are innate.
But he does say that higher math is extrapolated from those foundations based on the processes of human cognition.

I clicked on the link in your post, and liked what Ebola said there:

Our engagement of the world (a way in which the universe folds in on itself, partially perceiving and acting upon itself in time in the way we do) implies the project of mathematized concepts produced in this interaction. What is description other than rendering parts of the amorphous whole into comparable, discrete, static units amenable to quantification? This process is the order arising of chaos, to return to the latter at some point.

While we know not the universe 'as such' (for we encounter nothing of the sort), it's not just cognitive imposition going on here; the act of creation is at once an act of discovery, two sides of the same coin. This could account for why the universe 'for us' is amenable to mathematization. We 'discover' the creations wrought of the conditions of possibility for our investigation, in our case mathematized.

Edit: Why are the three of you insulting psychedelic users? Seems like stereotyping people in this way cannot be a good thing, especially on a website devoted to issues surrounding drugs. It smells of small-mindedness and bias to me. Mainstream society stereotypes drug users, then different factions of drug users stereotype each other. Reminds me of African Americans who insult each other for having darker skin.

Together we stand, divided we fall.

 

[Sodacrates]

I strongly disagree. "An eye to see"? I don't see why the word mystic is necessary. Perhaps using religious was wrong, but you do seem to be implying some sort of spirituality behind certain humans being really smart. Why is mystic not superfluous this situation?

There are always people that are going to be suspicious of science. Lots of people struggle with basic scientific and mathematical concepts, and when you tell them even though they don't understand, such and such is proven, they, often times, remain skeptical because they don't understand the concepts.

 

[Foreigner]

I took math to the university level along with the biological sciences. I find math beautiful and seamless in the way it describes things, at least at the non-theoretical levels. To me it's just a way of describing the world and identifying patterns. I've seen math in different expanded ways while on psychedelics, so while I understand the prior mentions of psychedelic anti-intellectualism, that has not been my experience. Psychedelics seem to amplify whatever your experience already is. If a mathematician does a psych then they are probably going to gain some further axiomatic knowledge into math through the experience.

The other thing that's important to note is that not everyone is wired to grasp math, but that does not make their experience or their interpretion of it any less authentic. I agree that people's egos can be hard to deal with but c'est la vie... I don't think that should denegrade maths, sciences, or "mystical" and intuitive approaches. They're two sides of the same coin really.

 

[P A]

Edit: Why are the three of you insulting psychedelic users? Seems like stereotyping people in this way cannot be a good thing, especially on a website devoted to issues surrounding drugs. It smells of small-mindedness and bias to me. Mainstream society stereotypes drug users, then different factions of drug users stereotype each other. Reminds me of African Americans who insult each other for having darker skin.

And this just smacks of fashionable, off-base PC-liberal sanctimony. If a rigorous sociological study investigating the prevalence of anti-science attitudes among heavy psychedelic users were to discover that what I said was true, would my characterization still be perceived as 'insulting' and 'small-minded'?

Or to put it another way: If I were to claim that African Americans generally listen to more rap music than rock'n'roll, would you consider this evidence of my stereotypical-racist bigotry? Or would I just be making a casual, probably accurate social observation? I think you might want to reread my post and reconsider what exactly you mean by 'stereotyping,' since, by your implication, it would appear that anyone who says anything whatsoever about a particular social group as a whole is nothing less than bigot scum. How about this: As a group, psychedelic users are more likely to have visionary experiences. People who work in grocery stores are more likely to come into contact with food products. People who commit 'crimes of passion' often feel guilty after the fact. Such bias! Such petty small-mindedness!

 

[rangrz]

slimvictor: I insult them because I get tired of having my research (and the research of my forerunners and peers) consistentally misinterpreted and dismissed by people with no clue of what it even means and who do so based on nothing but aberrant brain function.

I have never gained any insight into mathematics or physics based on psychedelic use myself BTW.

 

[sssssssssss]

Slimvictor, this is the first time I have ever been discussing this and someone brought up my view before I did. I didn't even know Lakoff had the same view as I did (I never thought I came up with this view as I once heard a teacher argue with a student about whether math was representative of the natural world and the teacher took this view; it did't convince me then as my view was probably far closer to Platonism back then, but after a few more years I understood what my teacher was saying). We interact with world through our senses and reason. When you hear 1+1=2 you have an emotional response telling you that it makes sense and it's correct. Experience may be a prerequisite for that feeling, but you only need at most need a limited experience showing that basic math is true before you can understand all of it. If I say 1,000,000,000,000+1,000,000,000,000=2,000,000,000,000, most of us have never seen a trillion things added with another trillion things and seen two trillion as a result, but it still yields the emotional response of making sense. Our reason creates a representation of the world which operates based on Mathematics. Our reason is astoundingly accurate, allowing us to slam things as small Protons together at the speed of light, so we have at least a mostly accurate picture of the world in our head, but is it perfect? Well, by definition, no

Does this relate to what I said earlier:
1 + 1 = 2 is more like 1 + 1 = 2 +/- u where u accounts for human error since the element 1 is the mean of actually having the value to be exactly one with a normal distribution.
So its like adding two random variables X,Y~N(1,1) where the curves converge to 1 (since if the mean is one, taking the the mean of the results of n experiments where n is large also = one) aka, they are limits.

or am i just talking out of my ass lol

 

[Roger&Me]

Edit: Why are the three of you insulting psychedelic users? Seems like stereotyping people in this way cannot be a good thing

If you read my post carefully, you'll see that I never insulted anyone. I merely made an observation, which I feel that I'm in a good position to make because I have been a psychedelic user myself, have know many of them IRL, and have been a regular in the PD forum for years. Such thought patterns as I described in my earlier post are commonplace in that community, as they are a direct side effect of the drugs.

 

[Sodacrates]

Why would you assume you were talking out your ass unless you didn't understand what you were saying?

I don't think you can account for the human error as a human. Perhaps if you had some other being or machine that interacted with the physical world more closely than humans could, you could account for human error, but I don't think human error exists until you reach complex math. Perhaps when we think the value of something is 1 we could be off by a little, but it's pretty hard to imagine on a macroscopic scale of adding one object to another and coming up with anything but 2 objects. And that would be our senses that were misleading not our reason. When math becomes complicated, we believe we use simpler math to "prove" it, and we do, but we are proving laws that our brain's model of the world follows, not that the actual world follows. It could be possible that some part of math makes sense and works with our reason and we can prove it, but our reason does not match up with reality at that point.

What you would see is the physical world giving back different results than we had planned. In every complicated physical system from rockets, to gravity calculations, to high end computers, we can not make perfectly accurate predictions, even if we believe we understand them completely. Like rockets. The path of rockets has to be readjusted quite a bit every time we send rockets any distance at all. Usually people attribute this to us not understanding physical systems well enough to make accurate predictions, which might be true, but it also might be that our reason does not add up with reality and that mathematics itself isn't accurate. So I don't think what you and I are speaking of is the same, but I don't think you are talking out of your ass (unless you do).