0435: "Purity"

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Realist
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Re: "Purity" Discussion

Postby Realist » Wed Jun 11, 2008 5:12 am UTC

Mathematics is just applied biology.

Since you do it with living brains.

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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:13 am UTC

pliny wrote:And what will become of them?
The idea was that that stage will never be reached, because emergent complexity is by its nature something which is too complex to model from the ground up.
Drake Zure wrote:same mathametician.
I think that's a bit unlikely. There's no evidence whatsoever that Randall bothers with continuity outside of story arcs.
Various people effectively wrote:Maths isn't real.
This is another of those meaningless semantic debates. What does "real" mean? Every tool we use to analyse the Universe in which we live is in a sense an invention of ours; does that make it any less significant? Maths uses logic to show that certain theorems necessarily follow from certain axioms, regardless of other details about the way the world is. In that sense, Maths really is "true" outside of the physical universe. You can argue either way, because the terms aren't sufficiently well-defined. You prefer to think of things as only being "valid", whatever exactly that means, if they can be applied to something "in the real world". That's fine, but please recognize that it is not the only meaningful position that can be taken.
timt wrote:Funny, where i live your be riddled for doing the subject with the least amount of applicability as they are less effective in the "real world".
This also has a ring of truth to it. People pride themselves on what they're good at: hence, mathematicians and the like place stock in the ability to think abstractly, independently of the real world, while engineers ridicule them for wasting their time. That is, until they come up with something which turns out to help the engineers.

There has actually been an increasing amount of interdisciplinary traffic in recent years, with experts contributing ideas to each other's fields. This, in my view, can only be a good thing.
mjkuhlman2000 wrote:On a random note, how are math/physics dual majors able to sleep at night? How can you be entrenched in different fields that use opposing methods of reasoning? Inductive (sensory evidence) and Deductive (absolute proofs)?
I prefer to think of these methods as complementary, rather than opposite per se. For a start, Physics itself actually uses both: Theoretical Physics uses plenty of deductive reasoning to work out the consequences of a proposed theory.
Tirian wrote:Agreed that pure math is applied philosophy.
What does that even mean? Philosophy, considered as an entire field as opposed to specific subsets of it, is so poorly-defined, and has such loose, nay nonexistent, standards for logical rigour that to claim that maths is "applied philosophy" has no clear meaning at all.
McCarthy1 wrote:Math is theoretical and there's no reason for it. ($5).
If you meant this at all seriously, it might be worth observing that without Maths, none of the other fields would exist in anything remotely resembling their current state.
pliny wrote:Now, this is just me, but my mind rejects basing such complex systems about things we consider to prove themselves.
You use exactly the same argument I have heard put forward dozens of times, which is based on a fundamental misunderstanding of what axioms are and how Maths work. This has been discussed to death in other threads, but I'll summarize. To elaborate on what AstralRunner said, because to say that axioms are "taken for granted" is to look at them in the wrong way: axioms are not taken to "prove themselves". The meaningful objects in Maths are theorems, which are basically of the form "If (this set of conditions) holds, then (this set of consequences) follows". The axioms are simply conditions which are used often enough, which is why you get, for example, the "axioms of group theory" which basically define a group. "If (the axioms of group theory, plus a few other commonly-used axioms which are required for the axioms of group theory to even have any meaning) hold, then (various theorems) follow" is a meaningful statement which can be proven using only logic. To say that the axioms of group theory "proved themselves" would be both ridiculous and meaningless.
dancuzz wrote:Also, I tend to think there should be an applied mathematician much closer to the physicist, with the pure mathematician further off. Though this of course would necessitate a disparaging reference to physics as "applied applied mathematics," which is just awkward and silly.
Quite. The joke loses its humour if it stops being concise.
mealone wrote:without math, physics would be t3h suxxzors.
Actually, I seem to recall reading about someone who developed Physics to a respectable level without Maths. I can't remember the details at all, but I'll post again if I refind it.
MysticTerminator wrote:the one problem with the argument that "without math, physics would be sux0rz" is that without physics, math would be pretty sux0rz too. pretty much all development in analysis was spurred on by a long time by physics, and differential geometry is just general relativity.
For a long time, yes, Maths and Physics fed naturally into each other's development, because the two were barely considered distinct. For a long time, for that matter, Maths, Science and Philosphy were seen as the same thing. Since then, however, the subjects have gone, to a great extent, their separate ways: there are now vast swathes of analysis and differential geometry that have nothing to do with Physics.
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Re: "Purity" Discussion

Postby GodShapedBullet » Wed Jun 11, 2008 5:15 am UTC

I don't think couch potatoes are constructing any theories.

Maybe like a "I should probably shower" theory.

But they never test their hypothesis so nothing gets done.

MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:16 am UTC

of course; I didn't mean to imply that the entire extent of those subfields were proper subsets of physics (although it does seem that I meant that), rather, as you seem to agree, that neither analysis nor geometry would be near the level of sophistication at which they now lie were it not for the great deal of physical intuition and motivation for the two fields

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Re: "Purity" Discussion

Postby AstralRunner » Wed Jun 11, 2008 5:18 am UTC

pliny wrote:So you accept (admit) that the maths are essentially unprovable, and there is no more reason to believe them than Scientology besides "intuition"?


That only follows if you have a pathological desire for certainty, and equate everything that is not absolutely certain forever with everything else that is not absolutely certain forever, regardless of all other attributes of the systems in question.

Or, as a quote I've forgotten the source of goes, "People who believe the Earth to be flat are wrong. People who believe the Earth to be a sphere are also, strictly speaking, wrong. But if you think that they are both equally wrong, then you are more wrong than both of them put together." Or something like that.
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MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:18 am UTC

upon reflection, pliny, while I agree that the void is indeed perfectly pure, I think I would have to advocate maths as equally pure. everything in maths is true, without question. you may raise the point that there are axioms, and so forth, but we realize that: all of our statements are along the lines of "given ZFC, such and such is true, without any possible impurities in this observation". (well, some areas of math don't use ZFC, of course, but whatever).

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Re: "Purity" Discussion

Postby gormster » Wed Jun 11, 2008 5:20 am UTC

With the exception of sociology, you can apply Money Made in the opposite direction.
Eddie Izzard wrote:And poetry! Poetry is a lot like music, only less notes and more words.

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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:21 am UTC

by the way, I must also point out that I am uncomfortable with the idea that "good sex requires a lot of masturbation"

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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:21 am UTC

@Mystic Terminator:
I find a difference between truth and purity.

@AstralRunner:
But the world is flat.
Edit: but you are right. Maths has helped the world brazilians of times more than Scientology, besides.
Last edited by pliny on Wed Jun 11, 2008 5:23 am UTC, edited 1 time in total.
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Loki
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Re: "Purity" Discussion

Postby Loki » Wed Jun 11, 2008 5:22 am UTC

Aww, its sad that psychology is so far down on the list.

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Re: "Purity" Discussion

Postby Logodaedalus » Wed Jun 11, 2008 5:24 am UTC

I suppose I have to jump on the relationship of psychology to biology -- well, cognitive science to neuroscience, anyway. I, for one, consider all those people who study the brain to just be looking at one physical implementation of the pure informational system that I study as a cognitive scientist. I guess I'm a Marrian in that way... the computational level is the most interesting (and, in some sense, "pure"), followed by algorithmic, then implementation last. I guess from that perspective, it would go: math -> cognitive science -> biology -> chemistry -> physics, at least if you ignore all the other parts of the latter three that don't have to do with cognition. But then, since even math is an epistemological construction, who cares about anything that doesn't take minds into consideration? :-)
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MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:24 am UTC

pliny wrote:@Mystic Terminator:
I find a difference between truth and purity.

@AstralRunner:
But the world is flat.
Edit: but you are right. Maths has helped the world brazilians of times more than Scientology, besides.



...brazilians?

so, what would you describe as purity, then?

RojSmith
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Re: "Purity" Discussion

Postby RojSmith » Wed Jun 11, 2008 5:24 am UTC

About this maths business:

Yes, maths is the purest of all science. It is not hampered with mundane, day-to-day stuff such as... I don't know... realiy... :P

Sorry about that, but someone has to go against the flow. :)

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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:27 am UTC

What?

Maths is not a science in any meaningful sense. It does not rely on logical induction or the scientific method.
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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:27 am UTC

I think one way to articulate what I meant about maths is that it is precarious. All of these mathematical truths we have, lots of them are grouped together, yes? Often a group of these truths might be grouped together by the axioms necessary for their truthiness, yes? What, then, happens if we so much as disprove (perhaps accidentally) one little axiom that helps to form the basis of an entire branch of maths?

I don't know much, I'll admit; I have yet to finish high school.

More than anything I want to be proven wrong.

Edit: I have yet to finish tenth grade.
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MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:29 am UTC

then that area of math will be inconsistent. so? how does this affect purity?

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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:30 am UTC

MysticTerminator wrote:then that area of math will be inconsistent. so?


What is its value outside of its consistency?
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shpax0r
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I've never posted here before

Postby shpax0r » Wed Jun 11, 2008 5:30 am UTC

But I needed to say that, as a biologist with an affection for cephalopods, it made me happy to see my ilk represented as "people holding octopuses."

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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:31 am UTC

MysticTerminator wrote:then that area of math will be inconsistent. so? how does this affect purity?


Never mind, I'm too tired and sleepy to articulate what I mean on this point.

I concede it.
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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:33 am UTC

Mystic Terminator wrote:then that area of math will be inconsistent.
More to the point, you cannot "disprove" an axiom in and of itself. It is possible that the axiom is self-inconsistent, though really that will only happen if there are other axioms that it's being used in conjunction with - in which case it is just a false statement given the other axioms that you're using.
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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:36 am UTC

Robin S wrote:
Mystic Terminator wrote:then that area of math will be inconsistent.
More to the point, you cannot "disprove" an axiom in and of itself. It is possible that the axiom is self-inconsistent, though really that will only happen if there are other axioms that it's being used in conjunction with - in which case it is just a false statement given the other axioms that you're using.



Ok, ok, maths is da bomb, you win.

I am going to sleep.
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mudge
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Re: "Purity" Discussion

Postby mudge » Wed Jun 11, 2008 5:39 am UTC

Re: the alt text, the physicists have it half right. Pure math is autofellating, applied math is masturbation.
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Re: "Purity" Discussion

Postby akashra » Wed Jun 11, 2008 5:39 am UTC

Bahahaha, I used to be exposed to the fights/arguments between the chemistry and physics teachers at high school, and know a few Maths/Physics PhDs, so immediately found this hilarious :)
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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:39 am UTC

pliny: I'm not trying to "win", I'm trying to explain how maths works so that you understand.

But I sense I'm only going to annoy you further, so I'll just let you get to sleep. My apologies.
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mudge
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Re: "Purity" Discussion

Postby mudge » Wed Jun 11, 2008 5:42 am UTC

pliny wrote:
Roun wrote:Going farther to the left, we have Economists, then Business majors, then Business Administration, then Philosophy, followed by writers and artists.


Philosophy trumps maths.

We had to conceive of numbers before we could fiddle with them.


Philosophy is masturbating without an orgasm.
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pliny
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Re: "Purity" Discussion

Postby pliny » Wed Jun 11, 2008 5:45 am UTC

Robin S wrote:pliny: I'm not trying to "win", I'm trying to explain how maths works so that you understand.

But I sense I'm only going to annoy you further, so I'll just let you get to sleep. My apologies.


You aren't annoying me; I just need to sleep.

I dismissed my part in the conversation because I don't think in my present state you could get me to understand anything.

I do understand it in the way that maths is at least a little bit like "all dogs have tails. Fido is a dog. Therefore, Fido has a tail", in that it may or may not be consistent with observations of the world, but either way it is consistent within itself.

Though if I had more energy I would mention that you're headed for dangerous territory saying that something can't be disproven.

I don't, though, so goodnight.

Edit: also, no need to apologize, none at all; at the very least I should apologize for assuming I understood things I did not.
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Re: "Purity" Discussion

Postby Thesea » Wed Jun 11, 2008 5:47 am UTC

pliny wrote:I think one way to articulate what I meant about maths is that it is precarious. All of these mathematical truths we have, lots of them are grouped together, yes? Often a group of these truths might be grouped together by the axioms necessary for their truthiness, yes? What, then, happens if we so much as disprove (perhaps accidentally) one little axiom that helps to form the basis of an entire branch of maths?


For when you come back to this in the morning:

I can think of an example of something like this happening in Geometry: Euclid had a set of five axioms that are the basis of Euclidean Geometry (most common), I'm sure you could look them up.... one axiom states that lines that are parallel are always the same distance apart, ie, never intersect. However, further in history it was discovered that parallel lines do intersect-- at infinity-- for instance when projected into infinity. (picture railroad tracks disappearing into the distance) This divergence from Euclid's axiom led to Non-Euclidean Geometry, of which one branch is Projective Geometry. The axiom was not completely disproved, so there was simply a separation between types of Geometry based on how the axiom is interpreted. (I think there may be some religions that are separated in a similar way?)
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and I don't know what I am.
I know that I am not a category.
I am not a thing -- a noun.
I seem to be a verb,
an evolutionary process --
an integral function of the universe."
-- R. Buckminster Fuller

rcf1105
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Re: "Purity" Discussion

Postby rcf1105 » Wed Jun 11, 2008 5:47 am UTC

Image

AstralRunner
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Re: "Purity" Discussion

Postby AstralRunner » Wed Jun 11, 2008 5:49 am UTC

Some physicists bring the Physics Department's requested research budged to the president of their university, which totals in the area of 26 million dollars.

"Damn, physics is so expensive," says the president. "Why can't you guys be more like the Math Department? All they ask for are pencils, paper, and wastebaskets. Or even better, why can't you be like the Philosophy Department? They don't even ask for the wastebaskets."

Thesea wrote:However, further in history it was discovered that parallel lines do intersect-- at infinity-- for instance when projected into infinity.


That's wrong. Learn to math.

What happened is that the parallel axiom could not be proved from the other 4. Latter, it was discovered that this is because it is independent of the other 4, and in fact there exist alternate versions of the parallel axiom that produce spherical and hyperbolic geometries. Euclidean geometry was always, and still is, self-consistent.
Last edited by AstralRunner on Wed Jun 11, 2008 5:52 am UTC, edited 1 time in total.
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Robin S
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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:51 am UTC

In the projective plane, parallel lines do actually intersect at a point at infinity corresponding to their direction.
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Patren
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Re: "Purity" Discussion

Postby Patren » Wed Jun 11, 2008 5:52 am UTC

And we anthropologists are not even on the purity scale. We're just flying above it in our hot air balloons watching all of you with telescopes.

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Re: "Purity" Discussion

Postby Robin S » Wed Jun 11, 2008 5:52 am UTC

Bumped into Cory Doctorow recently?
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Re: "Purity" Discussion

Postby borborygmus » Wed Jun 11, 2008 5:53 am UTC

Huh. I read the alt-text and thought back on college...I must not have fully appreciated sociology. Dang. [or should I call it...sociolorgy! :wink: ]

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Re: "Purity" Discussion

Postby MysticTerminator » Wed Jun 11, 2008 5:54 am UTC

Robin S wrote:In the projective plane, parallel lines do actually intersect at a point at infinity corresponding to their direction.


I think AstralRunner was taking issue with Thesea's logical exposition, but yes, I think the point in question is roughly valid.

Patren
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Re: "Purity" Discussion

Postby Patren » Wed Jun 11, 2008 5:54 am UTC

Robin S wrote:Bumped into Cory Doctorow recently?


Occasionally. He has slightly better equipment so he is usually above us.

Thesea
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Re: "Purity" Discussion

Postby Thesea » Wed Jun 11, 2008 5:55 am UTC

AstralRunner wrote:That's wrong. Learn to math.


It is not wrong it is just different from common math. Learn to branch out.

http://en.wikipedia.org/wiki/Non-euclidean_geometry
"I live on Earth at present,
and I don't know what I am.
I know that I am not a category.
I am not a thing -- a noun.
I seem to be a verb,
an evolutionary process --
an integral function of the universe."
-- R. Buckminster Fuller

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Re: "Purity" Discussion

Postby squishycube » Wed Jun 11, 2008 5:55 am UTC

Aw, damn being on UTC+1, all the good gags have already been made when I read the comic...

As a philosophy student I was going to say that philosophy should be on both sides of the scale.
My usual approach is useless here

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Re: "Purity" Discussion

Postby theferrymantune » Wed Jun 11, 2008 5:56 am UTC

What came to my mind was the idea of the sociologist saying something like:"math is just a social phenomenon." And it would go round and round.
Well... english not being my native thats the best i could come up with.

squishycube wrote:As a philosophy student I was going to say that philosophy should be on both sides of the scale.


Yeah or something like that. ^_^
Last edited by theferrymantune on Wed Jun 11, 2008 5:58 am UTC, edited 2 times in total.
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Re: "Purity" Discussion

Postby Salaric » Wed Jun 11, 2008 5:57 am UTC

GuitarFreak wrote:Alt text: On the other hand, physicists like to say physics is to math as sex is to masturbation.


My god How I agree!! Maths might be the purest, but Physics is sooo much more fun!!

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Re: "Purity" Discussion

Postby sk8ingdom » Wed Jun 11, 2008 5:58 am UTC

I wonder where computational linguistics and semiotics fall...


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