0435: "Purity"

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MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 11:11 pm UTC

nope, that's physics. math, as people have pointed out, doesn't require the existence of the universe in order to say meaningful things

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Re: "Purity" Discussion

Postby JET73L » Thu Jun 12, 2008 11:16 pm UTC

Have you (can you have) ever seen a quantum variable? What about a microcosmic string dimension? Or even anything that even implies the existence of such things?
http://www.xkcd.com/171/
(that link may not be perfectly relevant, but it's interesting)
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Re: "Purity" Discussion

Postby Sungura » Thu Jun 12, 2008 11:28 pm UTC

Xalerwons wrote:On a more whimsical note:
Math is just applied philosophy.


Thank you! (What I said in a prior post, much shorter put) lol. Yet the mathematicians will fight this one I bet haha. Yet, what has this thread digressed into but a philosophical conversation? Case in point. :P
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Re: "Purity" Discussion

Postby Troz » Thu Jun 12, 2008 11:30 pm UTC

Elfer wrote:Way over to the left, there ought to be an engineer.


Ah, but I can top that. At least twice as far as the engineer there ought to be a plumber/other skilled trades.
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 11:34 pm UTC

amysrabbitranch wrote:
Xalerwons wrote:On a more whimsical note:
Math is just applied philosophy.


Thank you! (What I said in a prior post, much shorter put) lol. Yet the mathematicians will fight this one I bet haha. Yet, what has this thread digressed into but a philosophical conversation? Case in point. :P


no, I think we're fine with it. I'm not sure whether I would go as far as to say that math is applied philosophy in general, as there are some branches of philosophy far less pure than math, but the broad sentiment seems to sit well with us

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Re: "Purity" Discussion

Postby pliny » Thu Jun 12, 2008 11:40 pm UTC

MysticTerminator wrote:...

I'm not entirely sure I understand your objection


My objection is that "supposing you have to electrons in a box" is irrelevant, because you can't have two electrons in a box, because then you would know where the electrons are, meaning you don't know how fast they are moving, meaning they are out of the box. That, and there is no way for you to know two and just two electrons are in the box.

Regardless of the size of the box.
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 11:44 pm UTC

pliny wrote:because you can't have two electrons in a box, because then you would know where the electrons are, meaning you don't know how fast they are moving, meaning they are out of the box.



this is just incorrect. I did not say the box has zero width or anything silly like that.

I also don't see why I can't have a theoretical system that consists of a box with two electrons in it. If I wanted, I could corroborate that there are two electrons by measuring the total charge or something.

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Re: "Purity" Discussion

Postby malik » Fri Jun 13, 2008 12:32 am UTC

Math is rigourous philosophy. Thoughts described with symbols. Also, note that this could be a circle instead of a line. Is sociology just applied philosophy (Ethics by Aristotle)? Probably not, but it almost fits.

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Re: "Purity" Discussion

Postby ParanoidDrone » Fri Jun 13, 2008 1:41 am UTC

Only on xkcd will a discussion about a comic devolve into a philosophy/math debate. :D

Regarding the alt-text: If Physics is to Math as masturbation is to sex, then is Sociology a full-blown orgy?
Insert witty phrase here.

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Re: "Purity" Discussion

Postby atalanta » Fri Jun 13, 2008 3:01 am UTC

Just wanted to say... the squirming octopus held by the biologist is an AWESOME visual touch. Nicely done (and so cute)!

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Re: "Purity" Discussion

Postby william » Fri Jun 13, 2008 4:29 am UTC

MysticTerminator wrote:
pliny wrote:because you can't have two electrons in a box, because then you would know where the electrons are, meaning you don't know how fast they are moving, meaning they are out of the box.



this is just incorrect. I did not say the box has zero width or anything silly like that.

I also don't see why I can't have a theoretical system that consists of a box with two electrons in it. If I wanted, I could corroborate that there are two electrons by measuring the total charge or something.

Besides, usually when they put those electrons in boxes they make them cyclical or some weird shit like that.
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Re: "Purity" Discussion

Postby nonorganon » Fri Jun 13, 2008 4:50 am UTC

You can bullshit your way through any of these fields, to a point. It isn't a hierarchy, it's a row of ladders of equal lengths but with differing heights of the bottom rung. Art has an extremely low entry level while math has a higher barrier of entry, but those at the top of their fields are all reaching towards the same unknown with the same rigorous approach in their fields. Genius is genius is genius and divisons like this are counterproductive. Cultivate an interest outside of your favorite field.

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Re: "Purity" Discussion

Postby ASW » Fri Jun 13, 2008 5:09 am UTC

JET73L wrote:
space_raptor wrote:Anyways, theferrymantune wins the thread.

Agreed.

Hmmm, this is interesting. There seem to be several divisions amongst the participants of this conversation, most "groups" having their own separate definition of maths, and arguing based upon that. Thus, no real way to identify who is correct, even philosophically (which is what some people have nearly used for proof.") Chaos reigns. A/=/A when the definition of A is abstracted. I love pointless arguments between other people with no possibility of resolution with both keeping their basic assumptions. It's like watching a boxing match with whole fish instead of gloves. Makes no sense, but it's fun to watch.

By the way, i still xconsider math to be the language that descibes the ____ness (countableness? nah, that's not it) of the universe for which, to my knowledge, humans have no word, and simply use math in its place.


OK to preface, I have a bit of bourbon in me and I am watching old episodes of Roswell ;)
However, there is a relation to the subconscious that I have been aware of that is inexpicable. You know, the thought behind thought, the preface to the linguistics you use for cognition. Sit in the quiet sometime and try to distinguish the two, I find it facinating to try to listen to the non "English" thoughts I have, the thoughts that form my linguistic thoughts. This is the "____ness" to which you refer. I dont know the psychological term for it though, just a simple IT guy here ;) But I have always seen it as pure logic. Math is the only way we can express it; logistics. We then define math in terms of what it is explaining. Thus the reason that everyone defines it differently, we all have different sets of logic. If it is explaining organisms then biology, if chemical reactions, then chemistry, if physical reality, then physics....understand? It doesn't matter if we have a PHD in math or not, we still have a certain ____ness that we need to explain in some method. The problem is, the discussion revolves around people weighing the description of these events rather than thinking of them just as definitions. But math is independent of the all, which in essence makes it pure, and a good way to define our thoughts and give a indistinguishable truth to them.
But, like you, I find discussions of these nature entertaining and edifying in that they make you think about things that you don't get into conversations about normally with people about you.

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Re: "Purity" Discussion

Postby Patren » Fri Jun 13, 2008 6:51 am UTC

ParanoidDrone wrote:Regarding the alt-text: If Physics is to Math as masturbation is to sex, then is Sociology a full-blown orgy?


Earlier on someone put up a chart showing that the full-blown orgy is most likely occurring in the art studio. Also, there may be a semi-full-blown orgy going on in the anthropology lab. Appropriately enough, these two places share the same building at my college.

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Re: "Purity" Discussion

Postby pliny » Fri Jun 13, 2008 7:51 am UTC

ASW wrote:
JET73L wrote:
space_raptor wrote:Anyways, theferrymantune wins the thread.



Sit in the quiet sometime and try to distinguish the two, I find it facinating to try to listen to the non "English" thoughts I have, the thoughts that form my linguistic thoughts. This is the "____ness" to which you refer. I dont know the psychological term for it though, just a simple IT guy here ;) But I have always seen it as pure logic. Math is the only way we can express it; logistics... But math is independent of the all, which in essence makes it pure, and a good way to define our thoughts and give a indistinguishable truth to them.


I disagree with you on the basis that I think it is entirely impossible to render unstructured pre-linguistic thought through mathematics. I do not go through a system of axioms and proofs and equations before reaching a worded or wordless conclusion.

On a related note: to all you people who keep saying "what is this? Maths isn't _______(insert: number, equations, formulae, all the things people said)", please tell me what it is. Obviously I have a flawed understanding of what mathematics is, because so many people are saying "no, that's wrong!". I think it would facilitate discussion if we defined "mathematics". This isn't a joke, I'm really curious as to how our definitions differ.
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Re: "Purity" Discussion

Postby DrimeR » Fri Jun 13, 2008 9:58 am UTC

pliny wrote:
ASW wrote: Sit in the quiet sometime and try to distinguish the two, I find it facinating to try to listen to the non "English" thoughts I have, the thoughts that form my linguistic thoughts. This is the "____ness" to which you refer. I dont know the psychological term for it though, just a simple IT guy here ;) But I have always seen it as pure logic. Math is the only way we can express it; logistics... But math is independent of the all, which in essence makes it pure, and a good way to define our thoughts and give a indistinguishable truth to them.


I disagree with you on the basis that I think it is entirely impossible to render unstructured pre-linguistic thought through mathematics. I do not go through a system of axioms and proofs and equations before reaching a worded or wordless conclusion.

On a related note: to all you people who keep saying "what is this? Maths isn't _______(insert: number, equations, formulae, all the things people said)", please tell me what it is. Obviously I have a flawed understanding of what mathematics is, because so many people are saying "no, that's wrong!". I think it would facilitate discussion if we defined "mathematics". This isn't a joke, I'm really curious as to how our definitions differ.


I disagree with ASW in that the "___ness" is pure logic, as logic is not innate but something we learn later... just try to follow a 6-year-old kid's path of thought. There is also a simple psychological test "free association of ideas" (not sure if the english name is exactly that one) which uncovers the complex structure of our inner mental processes, in which one must respond as quickly as possible with the first idea that comes to mind when listening to a word. The results are anything but pure-logic related. (Of course, there are more complex test that elude the impact of language but they are not so easily performed.)

On the other hand, i feel the same thing than pliny that my thoughts are much more complex than any mathematical entity can describe. And i mean describe, because i understand mathematics just as another language, a very wird one, with a very very very complex grammar, but very very very concise. As many others have pointed out before, mathematics can exist on their own. Of course, as any other language, it is based on part of our natural experience, in this case numbering (natural numbers) and a set of rules based on experience of these numbers; but then these rules and concepts have been extended, for instance introducing the number zero, or negative numbers (they do not exist but they are the way we represent certain aspects of nature), and from there on... mathematics is just a very precise language which rules do not allow ambiguities.

If our words in the spoken languages were concise in their meaning, and the rules allowed a better description of relationships between concepts (in this sense German has got a better structure than other western languages, maybe that's the reason why the greatest philosophers are Germans) we could arrive to sounder conclusions that we usually do.

Of course mathematics is the only language that allows quantification (but after several years of learning algebra and geometry and other obtuse areas of maths i also know that numbers is just a tiny portion of it, mostly used by physicist and economists (and widely despised by true mathematicians). But also, we can achieve complex tasks (like intercepting balls midair without using any mathematical trick (the brain region related to maths remains deeply inactive while playing sports ;) and the way we do it might be described by a math model someday, but it will be nothing more than a description of how things work.

the answer resulted longer that i wanted (i like concise, but never achieve it), hope it is not just babble to you.


PD: some politicians in fact never do learn logic though, in fact i suspect it is a kind of secret requirement for any power position

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Re: "Purity" Discussion

Postby Warped_Jack » Fri Jun 13, 2008 10:56 am UTC

pliny wrote:My point about things not being fundamental is that you don't have a definite number of anything unless each "one" is indivisible.


But if something is fundamental, it is indivisible.

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Re: "Purity" Discussion

Postby Sungura » Fri Jun 13, 2008 12:13 pm UTC

MysticTerminator wrote:
amysrabbitranch wrote:
Xalerwons wrote:On a more whimsical note:
Math is just applied philosophy.


Thank you! (What I said in a prior post, much shorter put) lol. Yet the mathematicians will fight this one I bet haha. Yet, what has this thread digressed into but a philosophical conversation? Case in point. :P


no, I think we're fine with it. I'm not sure whether I would go as far as to say that math is applied philosophy in general, as there are some branches of philosophy far less pure than math, but the broad sentiment seems to sit well with us


Yes that may be true. I'm a biochemistry major with a mathematics degree as well. Plus I love philosophy. So I'm all over this little chart. And I'm totally off the chart too - art is another passion although now I tend to use that for science because it's hard for companies to find a designer that can understand what they are trying to say. My own little "niche". So while I guess it is a line like the comic - it's also more like a graph with multiple vertexes interconnecting. I'm not sure it would be a complete graph though.

All in all though - I've been disappointed lately with the comics - this one is by far the best in a long time!
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Re: "Purity" Discussion

Postby ASW » Fri Jun 13, 2008 2:25 pm UTC

pliny wrote:
ASW wrote:
JET73L wrote:
space_raptor wrote:Anyways, theferrymantune wins the thread.



Sit in the quiet sometime and try to distinguish the two, I find it facinating to try to listen to the non "English" thoughts I have, the thoughts that form my linguistic thoughts. This is the "____ness" to which you refer. I dont know the psychological term for it though, just a simple IT guy here ;) But I have always seen it as pure logic. Math is the only way we can express it; logistics... But math is independent of the all, which in essence makes it pure, and a good way to define our thoughts and give a indistinguishable truth to them.


I disagree with you on the basis that I think it is entirely impossible to render unstructured pre-linguistic thought through mathematics. I do not go through a system of axioms and proofs and equations before reaching a worded or wordless conclusion.

On a related note: to all you people who keep saying "what is this? Maths isn't _______(insert: number, equations, formulae, all the things people said)", please tell me what it is. Obviously I have a flawed understanding of what mathematics is, because so many people are saying "no, that's wrong!". I think it would facilitate discussion if we defined "mathematics". This isn't a joke, I'm really curious as to how our definitions differ.


I don't know, as I said, I think that math is a direct function of the thoughtless nature. We came up with a set of characters to describe the way things are. There is only one way to interpret them, which is where we differ from traditional linguistics.
I always thought of my "prethought" processes as my pure logic before it is broken down in to a transferable state to external sources. neurons fire in my brain responding to other stimuli to form a reaction, then another set of neurons translate that to something in a store able state. So I always saw my brain thought as a result of a series of functions much the way transistors and gateways work on computing. It just so happens that our brains are a teeny bit more complicated. Also, my ideas are tainted by me being a CS Grad ;) But as I said before I think everyone sees math/logic different.

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Re: "Purity" Discussion

Postby The Rumpled Academic » Fri Jun 13, 2008 3:02 pm UTC

JET73L wrote:There seem to be several divisions amongst the participants of this conversation, most "groups" having their own separate definition of maths, and arguing based upon that. Thus, no real way to identify who is correct, even philosophically (which is what some people have nearly used for proof.") Chaos reigns. A/=/A when the definition of A is abstracted. I love pointless arguments between other people with no possibility of resolution with both keeping their basic assumptions.


Hey man, that ain't fair - this whole thread, I've been using and problematising the definitions of math offered by my opponents! None of them have been shown to exist outside of the minds that conceive them.

MysticTerminator wrote:math, as people have pointed out, doesn't require the existence of the universe in order to say meaningful things


How can math say anything at all without someone to say it?
No, really. Your use of that verb is really interesting - how can that 'saying' possibly exist in a universe without consciousness to perform and receive it?

MysticTerminator wrote:Rumpled Academic, I'm trying to understand your reasoning. Are you saying that if I have some quantum mechanical system with two electrons, that the only reason I'm saying there are two electrons there is because I'm fundamentally assuming that (a) the two electrons are different from everything else in the system, which is the only reason I'm able to talk about them as separate from everything else in the first place, and (b) the two electrons are fundamentally the same type of thing, which is why it makes sense to say there are two of them as opposed to just some stuff ?


That's pretty much the reasoning. The differentiation you make between these things, however intuitive it is, is part of a system of classification that you are applying to the Universe.

MysticTerminator wrote:...It seems like both of these assumptions do hold here.


Of course it seems like they do! Mathematics wouldn't be the most respected language for observing and explaining natural laws if it didn't do so well. The important thing is that (as you recognise) these are only assumptions: unprovable assumptions we tacitly accept only because of their intuitive nature. The assumption that there are two electrons there (as opposed to there being merely matter, and everything being a causal part of everything else) involves applying a human concept (that of plurality; of matter being divisible - but only finitely) onto a Universe that doesn't require it to function.
(Needless to say, intuition alone can't be enough to prove any point absolutely. If everything naturally intuitive given the information given to us by our senses was absolutely true, then (along with a great deal of other exciting things) the world would be flat as a pancake.)

Every example that has been raised ('suppose there are K atoms in the Universe', etc) presupposes that each of the things being counted are actually differentiated, in some absolute way, from the rest of the matter making up the universe.
I suggest that they are only differentiated in our minds, working as they do with sensory information.
I mean, I know it makes intuitive sense to say that here is a tree and there is another tree (and together they make 2!), but what are we basing that on, really, other than the fact that they look and behave similarly, and that there's air between them? Why should such arbitrary distinctions mean anything in an unobserved Universe? The trees are matter, and so is the air between them. What possible purpose could numbers have for existing in the Platonic sense when the differentiation between some matter from other matter just takes place on a supremely arbitrary perceptive level? Because, as had been said, the possible division doesn't stop - 1 world is populated by 6 billion people, comprised of some ungodly number of cells, comprised of atoms, and so on; 'til we reach whatever small level of existence our current scientific equipment enables us to see - which is by no means necessarily the smallest).

Warped_Jack wrote:...As far as I was taking the chemistry point, an enzyme has a specific shape for one (well as far as my knowledge of them go anyway) purpose. It binds to a specific molecule, and catalyses a reaction, perhaps breaking it down into two smaller pieces. So, for example, enzyme A would bind to molecule A, because molecule A can bind with enzyme A. Molecule A gets broken down, and the pieces fall away from the enzyme. Molecule B on the other hand, has a different shape, so the binding process couldn't happen...


I hear what you say (and I appreciate you taking the time to explain some of the scientific stuff), but really, all I could see in all of your examples was the presupposition of these things (an enzyme, a proton, a quark) having a seperate identity to other things similar to them, and working from there. Quarks "only coming in threes" only has numerical significance if the quark is seperable from the rest of the Universe in anything aside from a conscious mind contemplating it in isolation, and in comparison with other divisions that it has made.

There's a few other points I would like to address, but I really need to sleep. Goodnight, internet.

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Re: "Purity" Discussion

Postby MysticTerminator » Fri Jun 13, 2008 3:43 pm UTC

ok, so suppose I just have a simple system, two electrons in a box. Then it's not strange to differentiate them from the rest of the universe, I think, since there is no "rest of the universe" -- this is the entirety of the system. That's it. The two electrons. Then does it make sense to count them?

edit:

pliny - http://en.wikipedia.org/wiki/Mathematics

as a very, very abbreviated description, one might say "the study of structure". Hence equations, formulae, whatnot, are things we use to talk about structure of whatever we're investigating, be it an algebraic concept, physical system, blah

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Re: "Purity" Discussion

Postby UberN00b » Fri Jun 13, 2008 6:53 pm UTC

aliosha wrote:Heya; I'm not a maths uni student, but I am doing the most advanced ("pure") maths that I can at secondary school. And I have things to say (more things).

A couple of people have argued that maths must be imagined to exist; that is, that it is a construct of the mind. Now, I loved what someone had to say about imperial and metric measurements. They said, I have a ruler, it says 1in. However, on another ruler, it says 254mm. Therefore, the definition of number has changed, so maths has changed, so two different observations of the same thing differ. Therefore, maths is subjective.

Thank you! Btw to bad my secondary school doesn't do just pure maths, but i got a guy who went to cambridge to teach me A-level pure maths lol he's a priest (it makes no sense)

We have all agreed that Maths is applied Philosophy but Maths itself is just Philosophy which is then proved by Physics after this Physics is given a reason of being important by the others after it. it is like the hyararcy (spell check) triangle. The reason Maths is made important is because it is applied! The good thing is more people would like to use applied sciences rather than pure.

Others are saying that Maths is definite without man or not well as i said before you can change distances by swaping between metric and imperial. The Maths suggests it was the same distance all the time BUT we as Man (general term women please don't be offended) created this distance, though it was the same all the time we made the distance (this isn't quite right but i'll say it anyway:) mean something. :|

(ATTACK MY VIEW WITHOUT MERCY it is the only way I can learn new things)

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Re: "Purity" Discussion

Postby Warped_Jack » Fri Jun 13, 2008 7:59 pm UTC

I don't think the fact that things can be measured in different units has any grounding whatsoever. It doesn't make it subjective at all, it's just another way to compare x amount of something to y amount of something else.

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Re: "Purity" Discussion

Postby strix99 » Fri Jun 13, 2008 10:04 pm UTC

This is random but it reminds me of a scene in "Jesus Camp" where they show a snippet of an evangelical Christian child being home schooled with creationist leaning/orientated textbooks. The young mind says, "I like where it says that science can never really prove anything." It had me yelling at the TV how nothing can prove anything except for math, and thats only if you buy in to those damn satanic axioms :)

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Re: "Purity" Discussion

Postby Frankablu » Fri Jun 13, 2008 11:37 pm UTC

I put CS above EE in abstraction -- CS is applied EE, which is applied physics.


I disagree,

CS doesn't really relay on EE or physical computers for that matter,
they are tools which we can use, (though a common misconception of non cs students)

At higher levels it's pure/applied maths, just a different part of maths then the other subjects tend to use.
We run off Turing machines (mathematical concept) just as well :)

If P = NP for example, We can solve maths.

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Re: "Purity" Discussion

Postby BlueNight » Sat Jun 14, 2008 3:01 am UTC

You all have it ALMOST right. So close, too.

The study of Logic is itself the most pure field. From it derives Philosophy, Math, and Physics.

Math is impure in this way: it is Logic applied to numeration.

Physics is impure in this way: it is Logic applied to the physical realm. Math is its primary tool.

Philosophy is a label applied to structured thought, but structure is applied Logic.

Logic is structure; structure is Logic. It is the one fundamental thing without which we cannot study anything. Axiomatic systems come and go, but in the end, A=A.

The Logician is off the right edge of the panel, smiling knowingly, but not mockingly. He knows they will, eventually, realize the truth.

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Re: "Purity" Discussion

Postby Serifus » Sat Jun 14, 2008 6:47 am UTC

how long until someone makes a mobius strip out of it?lol, if no one does i will

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Re: "Purity" Discussion

Postby Warped_Jack » Sat Jun 14, 2008 9:27 am UTC

Already done, go back a few pages. Some people disagreed, lots.

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Re: "Purity" Discussion

Postby Serifus » Sat Jun 14, 2008 10:23 am UTC

I have a question: since in some physics observation sometimes changes the outcome, does that apply to maths aswell?

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Re: "Purity" Discussion

Postby Warped_Jack » Sat Jun 14, 2008 10:57 am UTC

Serifus wrote:I have a question: since in some physics observation sometimes changes the outcome, does that apply to maths aswell?



In statistics I suppose, when there's actually something to observe. (Like a population or sample) But otherwise, in say pure maths, what is there to observe? Your calculations are either right or wrong. There's no middle ground that I know of. (But then, I only study A level maths)

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Re: "Purity" Discussion

Postby Furiae » Sat Jun 14, 2008 1:47 pm UTC

I have printed this and will go in early to my Psychology class on Monday and tape it to the front wall. It is an elective for my Engineering degree/s as I like both. -.- I could do it for one of my Math classes but I have the habit of getting to them at the exact minute they start. Pedantic, anyone?

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Re: "Purity" Discussion

Postby The Rumpled Academic » Sat Jun 14, 2008 2:04 pm UTC

BlueNight wrote:You all have it ALMOST right. So close, too. The study of Logic is itself the most pure field.
From it derives Philosophy, Math, and Physics. Math is impure in this way: it is Logic applied to numeration.
Physics is impure in this way: it is Logic applied to the physical realm.
Math is its primary tool.
Philosophy is a label applied to structured thought, but structure is applied Logic. Logic is structure; structure is Logic.
It is the one fundamental thing without which we cannot study anything. Axiomatic systems come and go, but in the end, A=A.

The Logician is off the right edge of the panel, smiling knowingly, but not mockingly. He knows they will, eventually, realize the truth.


Oh, dear - another shipper of yet another field of human thought claiming to be the purest. Sigh.
Logic is just a human concept (based, like they all are, on intuition and sensory information) that we apply to the Universe to help us try and understand it. As someone already pointed out, A doesn't equal A when the meaning of A is abstracted. It may seem like the statement that A=A is as fundamental and absolute as it is possible to be, but it still rides on the back of a number of unprovable assumptions. Namely: the assumption that A exists, coupled with the assumption that such an existence can be accurately described in any language (lingual or mathematical).

To bring up Descarte's Evil Demon once more: contemplate for a moment the possibility that everything you can sense is an elaborate illusion designed to trick you. A 17th-century Matrix.
Add to that the notion that all of the ideas in your head (borne as they inevitably are from the data retrieved by your senses) are similarly false.
Think, also, about the relative likelihood, if this demon-illusionmaker did exist, of him choosing to provide you with a fake Universe that conformed to all of the true rules of the real Universe - which would provide you the systems of logic and thought necessary to (potentially) understand your predicament. To truly trap you inside your illusory cage, surely the best option would be to make the fake Universe operate by a different system of logic - but one that would seem perfectly natural and self-evident to those who've grown up in a Universe that sees it acted out.
Now, given the possibility of this being the case* (however ridiculously minute), is the statement that A = A unequivocably, 100% true? Of course not. Our very most fundamental ideas about logic could themselves be part of an illusion, just like our sensory data could.
A equalling A is almost certainly true - but that isn't quite the same thing, is it? To claim a discipline that uses this as a basis as absolutely 'pure' and truly indicative of the truths of the Universe just doesn't hold water - it's filtered through our senses and human conditioning; just like everything else.

*I probably don't need to point out that there's no possible way to disprove this scenario - if it were true, your life would be exactly as it is now, after all.

MysticTerminator wrote:ok, so suppose I just have a simple system, two electrons in a box. Then it's not strange to differentiate them from the rest of the universe, I think, since there is no "rest of the universe" -- this is the entirety of the system. That's it. The two electrons. Then does it make sense to count them?


Your 'system' is intrinsically hypothetical, which makes it a construct of the mind. If you've constructed a system with 'two electrons in a box' (I don't actually know whether that's possible, but I'll assume that it is), then the electrons - and whatever surrounds the electrons, and the box itself - are still part of the Universe. If you are looking at the system in complete isolation to the rest of the Universe, then, well, that's fine; but the isolation only really exists (conceptually) in your mind. Therefore, it makes sense that the concepts derived so easily from this system (like, say, '2') are as well.
Mind you, I'm not saying that it doesn't make sense to count them (counting has obviously led to enormous technological improvements and wellbeing, etc) - but it is just a human tool. My point, rather than any disparagement at all of mathematics, is just that it's false (not to mention a little vain) to say that numbers and mathematics have a 'pure' and 'absolute' existence outside of human conceptions of them.

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Re: "Purity" Discussion

Postby MysticTerminator » Sat Jun 14, 2008 3:13 pm UTC

the box isn't a part of the universe -- the box is the universe, and the electrons are the particles in this universe, with no other particles around, so there isn't a sense in which it's isolated since it's the only thing there. so, in a universe of this type, it makes sense, and more to the point, is fundamentally a pure and intrinsic notion, to count these electrons?

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Re: "Purity" Discussion

Postby Warped_Jack » Sat Jun 14, 2008 4:56 pm UTC

The Rumpled Academic wrote:To bring up Descarte's Evil Demon once more: contemplate for a moment the possibility that everything you can sense is an elaborate illusion designed to trick you. A 17th-century Matrix.
Add to that the notion that all of the ideas in your head (borne as they inevitably are from the data retrieved by your senses) are similarly false.
Think, also, about the relative likelihood, if this demon-illusionmaker did exist, of him choosing to provide you with a fake Universe that conformed to all of the true rules of the real Universe - which would provide you the systems of logic and thought necessary to (potentially) understand your predicament. To truly trap you inside your illusory cage, surely the best option would be to make the fake Universe operate by a different system of logic - but one that would seem perfectly natural and self-evident to those who've grown up in a Universe that sees it acted out.
Now, given the possibility of this being the case* (however ridiculously minute), is the statement that A = A unequivocably, 100% true? Of course not. Our very most fundamental ideas about logic could themselves be part of an illusion, just like our sensory data could.
A equalling A is almost certainly true - but that isn't quite the same thing, is it? To claim a discipline that uses this as a basis as absolutely 'pure' and truly indicative of the truths of the Universe just doesn't hold water - it's filtered through our senses and human conditioning; just like everything else.

*I probably don't need to point out that there's no possible way to disprove this scenario - if it were true, your life would be exactly as it is now, after all.


No there is no way to disprove the argument, BUT all of your arguments appear to be based on the idea that nothing around is 'true.' (It could be just an illusion of very well thought out logic, but not the real logic of the universe.)

Now imagine that I create life in a box, where up is down, and down is up, (ie gravity is reversed) also that this little life form is sentient, maybe even human if you like, and has free reign to do what they like, except leave the box. It's in his own little universe if you will. Imagine that they carry out research, and form their own physical laws for inside their box universe.

Now, for their perceived universe their assumptions and laws may be perfectly correct, even though they would be entirely wrong to the 'real' universe (ours). I mean, gravity is working in the wrong direction! However, for all intent and purpose for the lifeform, their laws are correct.

At this point, I'm not sure if I've made a point in favor of your argument or against it. :wink: Since this scenario could be applied to the human race as 'in the box' and the outside 'real' universe being entirely different.(ie, Matrix style scenario) HOWEVER, my point is, does it really matter? If we cannot escape the box (our universe) should we just accept that our laws are as true as we currently know them to be, and that A does equal A?

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Re: "Purity" Discussion

Postby MysticTerminator » Sat Jun 14, 2008 6:07 pm UTC

Warped_Jack wrote:At this point, I'm not sure if I've made a point in favor of your argument or against it. :wink: Since this scenario could be applied to the human race as 'in the box' and the outside 'real' universe being entirely different.(ie, Matrix style scenario) HOWEVER, my point is, does it really matter? If we cannot escape the box (our universe) should we just accept that our laws are as true as we currently know them to be, and that A does equal A?


well, leaving aside the philosophical question of whether it matters if the end results are exactly the same (to which I have decided on an answer yet), one could also introduce a slight perturbation -- suppose that once every trillion years, the master race (the guys outside the box) flips gravity for a couple seconds in the box universe or something like that. Then no, the civilizations that work upon the idea of gravity being up wouldn't be right. eh?

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Re: "Purity" Discussion

Postby K^2 » Sat Jun 14, 2008 7:07 pm UTC

I don't think that spectrum is quite fair.

First of all, what are we considering the purity in terms of? All of these fields are part science part engineering. Physics is, without a doubt, the purest science. But it employs engineering only for hypothesis testing. While entire branches of chemistry are essentially all about engineering on some level. Consider biochemistry, for example. Some of it is research, but most of the work done to achieve something new is still just finding new ways of putting things together using well known rules.

Math is an odd one out all together. Pure mathematics is not most certainly not a science. And I mean it in a good way. Science is about designing a model that fits the real world. We have no way to prove that anything in the world actually works the way our models do. Best we can do is find models that make better predictions and give us more tools to modify the world around us. These tools will be used by engineers to actually make something new.

Mathematics doesn't concern itself with precision, fitting the model to the experiment, or anything like that. It is taking a set of axioms and constructing sets of rules based on these. Whether these axioms have anything to do with real world or not is of no concern. Granted, physicis will use the results, by simply substituting for axioms some rules that were experimentally derrived. But that hardly makes mathematics a science of any sort.

Then there is applied mathematics, of course, but I would think of it more as a form of engineering. Just like an experimentalist might occasionally need engineers to design some equpment, a theorist will occasionally need tools built by applied mathematitians.

The actual spectrum would probably need to be constructed from projections on 3 principal axies: engineering, experimental science, and theoretical science. Then we could fit all of the extra fields mentioned, like CS, electrical engineers, etc, as well as expand this into branches.

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Re: "Purity" Discussion

Postby UberN00b » Sat Jun 14, 2008 7:14 pm UTC

BlueNight wrote:You all have it ALMOST right. So close, too.

The study of Logic is itself the most pure field. From it derives Philosophy, Math, and Physics.

Math is impure in this way: it is Logic applied to numeration.

Physics is impure in this way: it is Logic applied to the physical realm. Math is its primary tool.

Philosophy is a label applied to structured thought, but structure is applied Logic.

Logic is structure; structure is Logic. It is the one fundamental thing without which we cannot study anything. Axiomatic systems come and go, but in the end, A=A.

The Logician is off the right edge of the panel, smiling knowingly, but not mockingly. He knows they will, eventually, realize the truth.


SORRY logic and MATHS has nothing to do with each other. Look at Xeno's paradox:

Let us assume that Achilles can run ten times as fast as the tortoise, and that the tortoise gets 100m headstart.

Now, by the time Achilles covers 100m, the tortoise will have travelled a further 10m. When Achilles travels that 10m, the tortoise will have moved another 1m. And so on and so forth. Achilles will never catch the tortoise, beacuse every time he gets to where his opponent was, the tortoise will have moved a tenth of the distance away.

And that is essentially Xeno's paradox, as we know that in actuality Achilles could easily outrun the tortoise, but the maths doesnt quite add up. Logic proves the Maths wrong BUT if we think Philosophicaly if logic is a part of our human interface with the world, the fact is in a certain circumstance this outcome can happen.

WHICH IS WHAT MATHS IS ABOUT!
Last edited by UberN00b on Sat Jun 14, 2008 7:22 pm UTC, edited 1 time in total.

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Re: "Purity" Discussion

Postby MysticTerminator » Sat Jun 14, 2008 7:21 pm UTC

doesn't all maths follow from some logical principles? the way to prove most things in maths is "suppose p, show (by some other logical means) that p implies q, hence q" or whatever; we of course also have proofs by contrapositive or contradiction as well. as your example shows, maths doesn't follow from incorrect logic (obviously the argument in the putative paradox above is wrong), but it does follow from logic.

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Re: "Purity" Discussion

Postby bigglesworth » Sat Jun 14, 2008 7:51 pm UTC

Can't the Achilles thing be solved on a graph? Correct me if i'm wrong (I gave up maths at a level, and sorry for these axes), but Achilles beats the tortoise at about 110m.
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Re: "Purity" Discussion

Postby user42 » Sat Jun 14, 2008 9:36 pm UTC

Please forgive me if this has already been covered or if I'm breaking any rules. As a physicist I felt the need to add something to this comic.
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