0435: "Purity"

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P_M_D
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Fixed it for you.

Postby P_M_D » Thu Jun 12, 2008 7:54 am UTC

Image

:D
Aren't you all entitled to your half-arsed musings.You've thought about eternity for 25 mins & think you've come to some interesting conclusions.I couldn't give a ha'penny jizz for your internet assembled philosophy.

DrimeR
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Re: "Purity" Discussion

Postby DrimeR » Thu Jun 12, 2008 8:10 am UTC

DeadCatX2 wrote:1) Things exist without our observation.
2) These things have behavior.
3) This behavior can be described mathematically.
4) = math exists even if you remove all observers.


There is a small mistake in your reasoning, substitute "mathematically" by the name of any language, existing or fictious (e.g. "in english"), and therefore you conclude that any language must exist independently of who is/was/will be around.

Nature is. Independently of who's there. How Nature is described depends on who and how a description system has been developed. Mathematics is limited by its own grammar as Goedel nicely demonstrated.

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The Rumpled Academic
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Re: "Purity" Discussion

Postby The Rumpled Academic » Thu Jun 12, 2008 8:28 am UTC

DrimeR wrote:
DeadCatX2 wrote:1) Things exist without our observation.
2) These things have behavior.
3) This behavior can be described mathematically.
4) = math exists even if you remove all observers.


There is a small mistake in your reasoning, substitute "mathematically" by the name of any language, existing or fictious (e.g. "in english"), and therefore you conclude that any language must exist independently of who is/was/will be around.


That's a far more elegant way of expressing what I was trying to with my Cosmic Yo-yo shenanigans. If you could, dear reader, kindly mentally substitute the language example for the yo-yo one in my above post - much better and clearer.

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Re: "Purity" Discussion

Postby scarletmanuka » Thu Jun 12, 2008 10:09 am UTC

DrimeR wrote:
DeadCatX2 wrote:1) Things exist without our observation.
2) These things have behavior.
3) This behavior can be described mathematically.
4) = math exists even if you remove all observers.


There is a small mistake in your reasoning, substitute "mathematically" by the name of any language, existing or fictious (e.g. "in english"), and therefore you conclude that any language must exist independently of who is/was/will be around.


This is not necessarily an unreasonable conclusion, if you consider "exists" to mean the same kind of conceptual existence used for the mathematics version of the argument. Or do you believe that English would not even conceptually be a language if nobody alive spoke it? I think that depends on what we consider a language to be; if we define it as a structured set of rules for making statements, the position that the language is independent of the presence of observers is a reasonable one. This sort of language is not useful in any practical sense because it is all a syntactic game: you can say what sentences are valid, but you can't communicate with it.

Where it gets tricky is if we require the statements of a language to have fixed meanings. It's quite reasonable to require this of a language, and for a given statement to have a fixed meaning (or set of meanings) implies that we're considering this against the background of various entities interpreting the statement. So interpretation is innate to language, in this definition, and therefore language obviously cannot exist without a background of observers.

So I think the parallel with language is not exact, because there's no compelling reason why mathematical statements need to be interpreted; mathematics can be reduced to a syntactic game and still remain valid as mathematics. Indeed, that is often the point.

LouisAdam
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Re: "Purity" Discussion

Postby LouisAdam » Thu Jun 12, 2008 11:16 am UTC

Purity is fairly worthless, fashion students will be reaching out to infinite impurity but I'm willing to bet they tend to enjoy themselves =]
OH. And HI.

PILLOSOFY. These schools tend to be based on numbers while philsophy should be on a scale for language based schools. In my opinion. Innit.

Philosophy = Physics - Maths + Language - any half decent way of testing theories.

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The Rumpled Academic
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Re: "Purity" Discussion

Postby The Rumpled Academic » Thu Jun 12, 2008 11:39 am UTC

scarletmanuka wrote:This is not necessarily an unreasonable conclusion, if you consider "exists" to mean the same kind of conceptual existence used for the mathematics version of the argument. Or do you believe that English would not even conceptually be a language if nobody alive spoke it? I think that depends on what we consider a language to be; if we define it as a structured set of rules for making statements, the position that the language is independent of the presence of observers is a reasonable one. This sort of language is not useful in any practical sense because it is all a syntactic game: you can say what sentences are valid, but you can't communicate with it.


How could language possibly exist, even conceptually, in a world where it isn't being conceived of? If it only exists in the minds of those who use it, and all of those minds (in this example) are dead, it surely follows logically that the language cannot exist anymore. From my point of view, neither definition of language could allow it to exist absolutely without an observer, seeing as both only exist inside minds. For a structured set of rules to have even conceptual existence, someone/thing/Thing has to be conceptualising them, surely?

scarletmanuka wrote:So I think the parallel with language is not exact, because there's no compelling reason why mathematical statements need to be interpreted; mathematics can be reduced to a syntactic game and still remain valid as mathematics. Indeed, that is often the point.


Given that the very notion of numbers is just a human conceptual tool, mathematics is already a form of interpretation.

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Re: "Purity" Discussion

Postby asad137 » Thu Jun 12, 2008 12:17 pm UTC

blazillian wrote:I study both, and there are a lot of times that chemistry is more fundamental than physics


[Citation Needed]

Asad

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JET73L
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Re: "Purity" Discussion

Postby JET73L » Thu Jun 12, 2008 12:57 pm UTC

fix'd for content and spoiler'd for size
Spoiler:
Image

Thought I'd already posted this, but I hadn;t, so it gave me a chance to make this addition in visual format.
Ought to tick off pretty much everyone here, judging by the conversations.
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Re: "Purity" Discussion

Postby ShaKri » Thu Jun 12, 2008 1:24 pm UTC

equations and numbers AREN'T maths.... they are our sybolisation of maths. our way to describe and calculate it.

so our way to show maths may be linguistics .. but maths its self is not linguistics.
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JET73L
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Re: "Purity" Discussion

Postby JET73L » Thu Jun 12, 2008 1:31 pm UTC

Yeah, I worried about the exact phrasing. Maths as we know it is, as I see it, technically linguistics as applied to the universe, writing out how things are described via numbers and calculations. There is no word for the actual -ness of the universe, which is what is described by maths. Thus my reasoning for "linguistics as applied to the universe."
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Re: "Purity" Discussion

Postby theferrymantune » Thu Jun 12, 2008 1:43 pm UTC

^_^
Spoiler:
Image
Did you mean to search for: spidurs

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Re: "Purity" Discussion

Postby Warped_Jack » Thu Jun 12, 2008 2:04 pm UTC

The Rumpled Academic wrote:No one on the side of pure maths has yet answered this argument of mine:
To say that there are two stars makes necessary a division from those stars to the rest of the matter in the Universe. If there wasn't some good reason to think that these two stars were the same kind of thing, but different things, then how does it make sense to differentiate them into numbers? In the end, though, aren't these differentiations made by us arbitrary, based on our mental and perceptive faculties making sense of the world? We choose two speak of basic math in terms of 'two apples' plus 'three apples' - a distinction which does seem intuitively true and normal from a human standpoint - however, what I'm saying is that these distinctions are based entirely on conditioned human mental processes, which would have no cause to exist even hypothetically in an unobserved world. What possible cause could this differentiation of matter from matter have for existing in a universe without a consciousness trying to make sense of it by reducing it into understandable and regulatable pieces? Even the very most fundamental differentiations we make (between the apple and the earth, between you and me) have no real basis in 'pure' nature, and are based on subjective human perception. Just because it seems intuitively reasonable true to us that here is an apple and here is another apple, and to deal with the Universe with those ideas, does not in any way make it (or anything derived from it) absolute truth - any more than it does any other field that is based on subjective human ideas and sensory perceptions; which is to say, all of them.


Hmm. Well differentiating one object from another is hardly something that only humans do, is it? Animals will eat the food they know is good for them, and not eat that which is bad. Similarly, a female lion or somesuch, with cubs, appears to know if a cub has gone missing (Which implies the ability to recognise a difference in the quantity of her cubs present)

So, I would argue that although yes, we would say "two stars" another life form/observer could easily do the same. An imaginary microscopic sentient observer may even say there were not two stars, but instead several millon atoms in two large clumps, if your catch my drift. So, to re-state, the counting of similar objects isn't intuitively true for just humans, I think.

Oh wait, I totally didn't finish my point here :oops:
Nature does differentiate between objects. Even with no observers at all, forces still act differently on different objects. For example an magnetic field will have no effect on an uncharged/polarised molecule. Or enzymes only bind to substrates with a shape complimentary to their binding site.

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The Rumpled Academic
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Re: "Purity" Discussion

Postby The Rumpled Academic » Thu Jun 12, 2008 2:53 pm UTC

Warped_Jack wrote:Hmm. Well differentiating one object from another is hardly something that only humans do, is it? Animals will eat the food they know is good for them, and not eat that which is bad. Similarly, a female lion or somesuch, with cubs, appears to know if a cub has gone missing (Which implies the ability to recognise a difference in the quantity of her cubs present)


I suppose I can't really expect every contributor here to have read (let alone remembered) all of my posts, but I have already addressed this exact objection. To reiterate what I said then: I say 'human consciousness' just because we are the species who has taken the notion of numerical reasoning processes further than any other species that we know of. It makes the discussion much more natural than if I were to be speaking about abstract, hypothetical, floating consciousnesses, or animal ones - though of course the same principles I've been talking about do apply to all of these varieties of consciousness. The issue isn't humanity so much as it is consciousness. That doesn't damage any of my arguments, as far as I can see.

Warped_Jack wrote:Nature does differentiate between objects. Even with no observers at all, forces still act differently on different objects. For example an magnetic field will have no effect on an uncharged/polarised molecule. Or enzymes only bind to substrates with a shape complimentary to their binding site.


Ah, now this is interesting! Why is it that you say that the workings of atomic-level chemical reactions serve to prove that numbers exist outside of the human mind? Why aren't the mathematical explanations we use to explain these phenomena defined as merely that: not as platonic truths that apply from-high to everything, but human explanations of existing phenomena that are widely applicable?
...Look; as someone with only very limited knowledge of these fields, could you possibly explain these phenomena in greater (...and layman-expressed) detail? Together with how you think they prove the unobserved existence of numbers as absolute truths, keeping in mind that I don't deny the empirical existence of matter or of chemical reactions?

I'm no polemicist arguing his point without actually listening to the arguments of his opponents - if there is genuine scientific examples relevant to this discussion that I'm unaware of, I'd love to hear about them. As I say, though, I've studied very little in the area (preferring to just look at the fields in very generalised, abstract terms), so you may have to walk me through anything remotely technical.
Last edited by The Rumpled Academic on Thu Jun 12, 2008 3:09 pm UTC, edited 1 time in total.

Elfer
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Re: "Purity" Discussion

Postby Elfer » Thu Jun 12, 2008 3:05 pm UTC

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

(Flexing.)

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Re: "Purity" Discussion

Postby space_raptor » Thu Jun 12, 2008 3:11 pm UTC

Actually, in the spirit of the alt text, I believe the engineer should be lying in a pool of sweat with various and sundry people, animals, and objects covered in bodily fluids.

Anyways, theferrymantune wins the thread.

Arguing over whether something exists outside the human mind or not seems kind of pointless to me, but I guess that's why I'm not a philosopher!
The drinking will continue until morale improves.

Patren
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Re: "Purity" Discussion

Postby Patren » Thu Jun 12, 2008 3:21 pm UTC

The Rumpled Academic wrote:
Syphon wrote:nomadic humans studied nothing. Without the power of agriculture freeing people up to do nothing, they'd never have had time to sit and think. The concept of agriculture was permanent settlement and communities, which yes, was the driving force behind philosophy.


This isn't strictly true.


I'm sorry, I'm going to have to disagree with you Rumpled Academic on this one.

It isn't that it isn't strictly true, it's that it isn't true is the least bit. At all. Agricultural is yes, the driving force behind philosophy students sitting in starbucks and discussing philosophy until their shift starts at starbucks(we anthropology people do this too), but it isn't the driving force behind philosophical thought.

Let's see, what else was there before agricultural *ponder*.
Art
Religion
Biology
Chemistry
Physics
Image
Math
So I am pretty sure there was probably philosophy.

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Re: "Purity" Discussion

Postby Chrysalis » Thu Jun 12, 2008 3:36 pm UTC

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age." [Lovecraft]

plad
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Re: "Purity" Discussion

Postby plad » Thu Jun 12, 2008 4:18 pm UTC

After a short discussion with a friend we've arrived to the following conclusion:

Mathematics is just applied Philosophy.

Theology is just applied Sociology.
Philosophy is just applied Theology (I really did talk to someone who tried to make this claim so I think it is legitimate).

And thus we've completed the circle.

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Re: "Purity" Discussion

Postby Warped_Jack » Thu Jun 12, 2008 5:00 pm UTC

The Rumpled Academic wrote:
Warped_Jack wrote:Hmm. Well differentiating one object from another is hardly something that only humans do, is it? Animals will eat the food they know is good for them, and not eat that which is bad. Similarly, a female lion or somesuch, with cubs, appears to know if a cub has gone missing (Which implies the ability to recognise a difference in the quantity of her cubs present)


I suppose I can't really expect every contributor here to have read (let alone remembered) all of my posts, but I have already addressed this exact objection. To reiterate what I said then: I say 'human consciousness' just because we are the species who has taken the notion of numerical reasoning processes further than any other species that we know of. It makes the discussion much more natural than if I were to be speaking about abstract, hypothetical, floating consciousnesses, or animal ones - though of course the same principles I've been talking about do apply to all of these varieties of consciousness. The issue isn't humanity so much as it is consciousness. That doesn't damage any of my arguments, as far as I can see.


Yeah, I did think of that as I wrote it, but thought I'd chuck it in anyway on the offchance. I've been reading this topic on and off the last couple of days between revising for my A levels, so yeah, sorry about missing a couple of the posts addressing it.

The Rumpled Academic wrote:
Warped_Jack wrote:Nature does differentiate between objects. Even with no observers at all, forces still act differently on different objects. For example an magnetic field will have no effect on an uncharged/polarised molecule. Or enzymes only bind to substrates with a shape complimentary to their binding site.


Ah, now this is interesting! Why is it that you say that the workings of atomic-level chemical reactions serve to prove that numbers exist outside of the human mind? Why aren't the mathematical explanations we use to explain these phenomena defined as merely that: not as platonic truths that apply from-high to everything, but human explanations of existing phenomena that are widely applicable?
...Look; as someone with only very limited knowledge of these fields, could you possibly explain these phenomena in greater (...and layman-expressed) detail? Together with how you think they prove the unobserved existence of numbers as absolute truths, keeping in mind that I don't deny the empirical existence of matter or of chemical reactions?

I'm no polemicist arguing his point without actually listening to the arguments of his opponents - if there is genuine scientific examples relevant to this discussion that I'm unaware of, I'd love to hear about them. As I say, though, I've studied very little in the area (preferring to just look at the fields in very generalised, abstract terms), so you may have to walk me through anything remotely technical.


Hmm. I think originally my point was to express that nature does differentiate between things, hence there need not be an observer to 'split' things into quantifiably groups for counting.
However, the ability to be counted wouldn't necessarily prove the existence of numbers, simply that it could be done.

Then again, there are some things where nature does seem to 'count' the pieces involved. Taking quarks for an example, the fundamental (as far as we know) chunks that make up protons and neutrons in the nucleus. They are discrete blocks, and as far as protons and neutrons are concerned, only ever come in threes. Ever. At the moment, you will never find a quark on it's own. You may find it in a pair, but with an anti-quark, and those don't exist for any significant length of time (I believe)

Now, I think that shows how nature does sort of show numerical patterns. Especially as when the quarks combine in the necessary way to make a proton, the charge is the equal and opposite charge to that of an electron. Without that necessary fact, the universe would be entirely different. Down to massive consequence or divine intervention, I couldn't tell you, BUT to me it shouts that there is a clear numerical relevance here.

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.

The way atoms arrange when they bond is based on the number of bonds and lone electron pairs around each atom, and this decides the overall shape of each molecule, and each enzyme. SO, the fact that these angles between bonds all align and match up to make a molecule which will be complimentary to another molecule implies the existence of number again to me. Since, if the angles between bonds was unmeasured and didn't matter, molecules would take all manner of different shapes, and the chance of another molecule coming into existence which exactly fitted it would be even more minute.

And, just to add, the bonding angles between atoms is sort of a 'built in' thing if you like. Like the shape of a water molecule is always the same, that sort of thing.

Hmm. I hope I answered your question here. Took me awhile to get the thought-process back though, so I hope it makes sense

plad
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Re: "Purity" Discussion

Postby plad » Thu Jun 12, 2008 5:08 pm UTC

I'm having a big problem with what the Rumpled Academic tries to say.

As far as I understand it, the claim is that "Math does not exist without consioucness to perceive it".

If I've missed the point, ignore the rest of the post.


The question that I have in regard to this claim is "What is existance?".
What does it mean that math exists or does not exist?

In a universe without any consioucness there are still K atoms, organized in some specific pattern (well, probably).
Does that mean that the number "K" exists? because if it does, any fact you say will give you more and more applications of math to the existing universe.
Let's assume that all the physics law "exists" in this sense. Does that mean that math exists?

This raises the second question - What is math?
Is math the collection of all the numbers and the facts related to them (the fact that if you have 2 apples, and 3 apples that you have 5 apples)?
Because on the one hand, this is the most common perception of math, on the other hand, it is very close to physics (If you have 2 apples moving at 0.5c to one direction, and 3 apples moving in the direct opposite direction at 0.5c, then they're moving at speed ? in relation to one another).

On the other hand, if math is the concepts and generalizations, then of course it cannot exist without a conciousness (concepts by definition need perception).
I don't think someone claims that there are finite-fields floating around in the universe, with a "physical" existance (and if you want to define other form of existance - return to the previous question).

So, the way I see it, math - as the scientific field - does not really exist without conciousness.
But in the same way, physics does not exist - if you percieve physics as the field of modeling the universe, and not as the collection of phenomenon that sometimes behave according to some obscure rules (In a way what I'm saying is that pure-physics does not exist in our world, and everything in "practical" physics is an approximisation of the universe/theory - depends on which side of the experiment are you on).

On the other hand, I'm still not sure how to define existance without consioucness (and I'm not really sure how to spell consioucness), so I'm not sure the question have any meaning.

Bummer.

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Re: "Purity" Discussion

Postby Oorang » Thu Jun 12, 2008 5:42 pm UTC

I enjoyed the inference that "more pure" was somehow "better". I think from a very pragmatic way of thinking you could state that the value of endeavor is at least somewhat correlated to the results (or use) that said effort produces. The more application a given science has, the more use it has. Therefore the more application that a science has, the greater its value.

Or to say it another way... No one will give a crap about your science unless you can make it do something useful :mrgreen:

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Re: "Purity" Discussion

Postby pminva » Thu Jun 12, 2008 6:00 pm UTC

Within the Math cult - Pure means unapplicable - eg - Applied Mathematics is a derivative (derisive) act to "Pure Mathematicians". So - they make no distinction between Pure Math and Philosophy (Bertrand Russell, Nagel, Goedel). That is the joke I am seeing.

And all of the prior perceptions in postings are basically true to their authors' perspectives (and the real world) - but the Math ego lives in the Hilbert Cube, which basically claims to be homeomorphic to everything and is of no other real use.

Math models things. One discovers - then there is a math model for it. It is only syntax and logic - when applied. The quest of the pure mathematician is to derive pleasure from the unapplicable.

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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 6:08 pm UTC

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 ? It seems like both of these assumptions do hold here.

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Re: "Purity" Discussion

Postby UberN00b » Thu Jun 12, 2008 7:07 pm UTC

UBERN00B wrote:
EtzHadaat wrote:
Schaard wrote:
fenrir_darkwolf wrote:Much in the same way that there is no such thing as a second, a minute, or an hour, but these are useful abstractions that human beings have agreed to conform to, there is no such thing as a wavelength, electromagnetism, or mitosis - these are names that we have given to segments of natural processes that are neither independent nor objective. Therefore, to say that math is objective or "pure" is a little silly.

Which side are you on? Obviously waves existed and had lengths long before humans were aware or gave them names. Is your point that Nietzche and friends are ridiculous people?

Math is clearly not a human construct. The word "math" is a human construct, and so are our words for numbers, our words for sums and such, but quantities are real things, shapes are real things, and they behave in predictable ways you can uncover by looking at them. Two plus two did equal four long before the first human noticed it was such.

IMPORTANT PART wrote: Humans have no control over how math works. Finding and naming things is not the same as creating things.


A perfect example of how wrong you are is the change of the Imperial measurement to the Metric measurment! Sorry :| (btw I like the quote bubble)

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El Cool
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Re: "Purity" Discussion

Postby El Cool » Thu Jun 12, 2008 7:08 pm UTC

Wow. I just came from lying inside my car thinking about how math is the basics for all.
And yes, God is a mathematician.

I've thought about this before too. Its very interesting that you made a comic about it.
Now I can just link the picture in conversations for a win. :)
- There are 10 types of people in this world: those that understand binary and those that don't -

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Re: "Purity" Discussion

Postby Aurora Firestorm » Thu Jun 12, 2008 7:09 pm UTC

Nothing wrong with applied stuff. Heck, I hate doing math just to be doing math (gasp!) -- I like to know I'm doing something with my math.

It's ridiculous how many times I've discussed this exact comic topic with other people. :) On the tiers so far, we have:

Sociology, Most Humanities (social sciences, literature, etc.)
Psychology
Biology, Neuroscience, Computer Science
Chemistry, Electrical Engineering
Physics
Math
(I start with math; we can go to Logic or something else down here)


I put CS above EE in abstraction -- CS is applied EE, which is applied physics. Neuro is also applied chemistry plus applied EE; it's different enough from usual bio that I wanted to put it up there. Humanities tend to be (pardon the stereotype, but it's just my opinion) sometimes fluffy, usually stretched applications of psychology that range from the many times clear and accurate (analyzing history in social studies, etc.) to the really variable (modern art interpretation, etc.)


If you think about it, physicists aren't 'on top' in some situations -- I like to think about it in levels of abstraction, and in terms of that, they're pretty low on the abstraction chain (and thus are the ones doing the really complex stuff most people don't need to know). Why should I, an Electrical-E freak, get my hands dirty in the physics when all I need to do is know how to hook up my components, not their physics equations (beyond, say, Ohm's and other one-level-up-from-physics formulas)? In terms of application, it seems to me that the higher your abstraction, the easier (relatively) and more workable things become. This is why math-physics majors are masochistic ;) and the rest of us don't touch the stuff. It's highly unnecessary to know the assembly code when you have Python, not to mention assembly is a pain to code in. I prefer simpler explanations for things, and if I can skip the inner workings that are really, inordinately complicated, I'll do so. Lazy college student, I am, but it saves me a lot of neuron death :-P


My boyfriend likes to loop it: Biology is chemistry is physics is math, is logic is psychology is...so no one's on top, kind of like those Escher (sp?) staircases.

UberN00b
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Re: "Purity" Discussion

Postby UberN00b » Thu Jun 12, 2008 7:11 pm UTC

Another thing I don't like the idea that maths is a way of seeing pattens in things that's stats. But there is stats and pure in maths and stats is just applied (just applied) (everything can be made into and proved by stats). Philosophy is thought, Maths is truth and down to biology you have a form of truth but after that you have constant lies. (If you disagree with the last bit your lying)

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Isn't math applied logic?

Postby alexlesuper » Thu Jun 12, 2008 8:01 pm UTC

I think he could have put that in there. Then again, there aren't that many logicians...

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I are back.

Postby pliny » Thu Jun 12, 2008 9:39 pm UTC

We can all agree bagels wouldn't exist without people?

I think making the distinction between maths and everything else people have invented is a rather arrogant move by mathematicians, and I think that it makes much less sense than they seem to think it does.

The existence of numbers would require, eventually, the finding (or existence of) a basic unit which cannot be subdivided. "Atom" means "no-cut" because it was hypothesized to be the smallest thing possible. Then we found that it was made of smaller bits, and went "these must be smallest" but then surprise! Protons and neutrons are made of quarks! I wouldn't be at all surprised if we managed to find a way to look inside quarks somehow that they turn out to be made of something smaller.

There is a flaw inherent in saying something like "two apples"; each apple may look similar on a macroscopic scale, but zoom in any large amount and you will see that each is vastly different from another, with things in different places, things structured differently, and things moving differently.

Calling it "two apples" is just simplifying it. I don't believe in numbers because I don't think there is a way to have a certain number of things.

Especially not things as complex as apples.
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Re: I are back.

Postby MysticTerminator » Thu Jun 12, 2008 9:47 pm UTC

pliny wrote:We can all agree bagels wouldn't exist without people?

I think making the distinction between maths and everything else people have invented is a rather arrogant move by mathematicians, and I think that it makes much less sense than they seem to think it does.

The existence of numbers would require, eventually, the finding (or existence of) a basic unit which cannot be subdivided. "Atom" means "no-cut" because it was hypothesized to be the smallest thing possible. Then we found that it was made of smaller bits, and went "these must be smallest" but then surprise! Protons and neutrons are made of quarks! I wouldn't be at all surprised if we managed to find a way to look inside quarks somehow that they turn out to be made of something smaller.

There is a flaw inherent in saying something like "two apples"; each apple may look similar on a macroscopic scale, but zoom in any large amount and you will see that each is vastly different from another, with things in different places, things structured differently, and things moving differently.

Calling it "two apples" is just simplifying it. I don't believe in numbers because I don't think there is a way to have a certain number of things.

Especially not things as complex as apples.


so how about substituting "electrons" for "apples". see above.

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Re: I are back.

Postby pliny » Thu Jun 12, 2008 9:54 pm UTC

MysticTerminator wrote:
pliny wrote:Calling it "two apples" is just simplifying it. I don't believe in numbers because I don't think there is a way to have a certain number of things.

Especially not things as complex as apples.


so how about substituting "electrons" for "apples". see above.




Somehow I doubt electrons are fundamental, indivisible particles. Call it a hunch, if you must.

Besides the fact that it's pointless to say "I have these two electrons" when any electron can be literally anywhere in the universe at any given time. You can say "it is likely that there are at least two electrons in this vague space" but I don't call that counting, myself. Or numbers, for that matter. For it to be a number it must be definite and quantifiable.
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 10:06 pm UTC

eh, I think it's popular in the nonscientific community to say that oh man look how we continue to break things down forever and ever it's obviously never going to stop, but I'm not sure how much, if any, basis this has. I think it's been agreed upon for a while that electrons are probably fundamental. Anyway, this isn't terribly crucial to the argument itself, just a side note.

so, pliny, suppose you have two electrons in a box. standard quantum mechanical example. they are then, in fact, in the box. they're right there.
Last edited by MysticTerminator on Thu Jun 12, 2008 10:21 pm UTC, edited 1 time in total.

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Re: I are back.

Postby Warped_Jack » Thu Jun 12, 2008 10:15 pm UTC

pliny wrote:
MysticTerminator wrote:
pliny wrote:Calling it "two apples" is just simplifying it. I don't believe in numbers because I don't think there is a way to have a certain number of things.

Especially not things as complex as apples.


so how about substituting "electrons" for "apples". see above.




Somehow I doubt electrons are fundamental, indivisible particles. Call it a hunch, if you must.

Besides the fact that it's pointless to say "I have these two electrons" when any electron can be literally anywhere in the universe at any given time. You can say "it is likely that there are at least two electrons in this vague space" but I don't call that counting, myself. Or numbers, for that matter. For it to be a number it must be definite and quantifiable.



What, you'd say that 6billion people on this vague region of space called Earth, isn't counting? Don't be silly.

Also, whether or not electrons are fundamental is beyond the point. Imagine you have the most indivisible, fundamental particle that matter is made of. Therefore, if you have two of them, there are still two. Going back to quarks, that would be a good example. Surely if quarks are made of something smaller, then those smaller bits must be within the quark. Therefore:

- You know where they are
- You should know many

Hence, definite and quantified.

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Re: "Purity" Discussion

Postby Feirgon » Thu Jun 12, 2008 10:16 pm UTC

MysticTerminator wrote:eh, I think it's popular in the nonscientific community to say that oh man look how we continue to break things down forever and ever it's obviously never going to stop, but I'm not sure how much, if any, basis this has. I think it's been agreed upon for a while that electrons are probably fundamental. Anyway, this isn't terribly crucial to the argument itself, just a side note.

also, suppose you have two electrons in a box. standard quantum mechanical example. they are then, in fact, in the box. they're right there.


Until you open the box and try to observe it. Shrodinger's cat would also leap out of the box.

But this arguement boils down to two schools Platonism (math is a universal constant) and Intuitionism (math is purely man made).
Platonists would say that the Universe was always divisible by all its parts even before each subsequent part was discovered (a discoverable universe).
Intuitionists would sat that the Universe is a whole and only through observation does a divisibility arise (a describable universe).

Neither side of these arguements (I think) will ever converge. Hopefully, though, people can at least understand where each is coming from.


As for me, I believe it is a little from column A and a little from column B.
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Re: "Purity" Discussion

Postby pliny » Thu Jun 12, 2008 10:21 pm UTC

MysticTerminator wrote:
also, suppose you have two electrons in a box. standard quantum mechanical example. they are then, in fact, in the box. they're right there.


The problem with that quantum-mechanical example is that it never happens.
Edit: also, they won't be in one place for an observable amount of time.

Warped_Jack wrote:What, you'd say that 6billion people on this vague region of space called Earth, isn't counting? Don't be silly.


That's entirely different, people do not exist as a probability cloud in the manner electrons do.

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

Postby MysticTerminator » Thu Jun 12, 2008 10:28 pm UTC

...

I'm not entirely sure I understand your objection

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Re: "Purity" Discussion

Postby aliosha » Thu Jun 12, 2008 10:33 pm UTC

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.

However, let us consider it thus: I have a square. I measure the side to be 5in. Therefore, the area is 25in^2. However, on my other ruler, I see that the area is 1270mm^2. However, the mathematician says "for any square of side A, where A is a number, the area is A*A". Thus, the mathematician sees that both of these are true WITHOUT USING ANY NUMBERS. For a mathematician, numbers follow from maths, not vice-versa.

And so, we can make some definitions.
AXIOM 1: A = A. Now, A could be anything. A could be a matrix of side 4. A could be a vector, or a surd, or an integer, or a complex number. It doesn't matter. All we have done is set down an axiom that a number is equal to itself.
Now we define our first number.
AXIOM 2: 0 = A - A, where the "-" operator takes the removes a "thing" from another "thing" leaving a third "thing".
Also, 0 = nothing, i.e. for any size, there is a smaller size, apart from for 0. (By size, I mean modulus. How big it looks, feels, how much it weighs, and so on).

Now, hopefully it follows that A*0 = 0.
This is because:
A=A
A - A = 0
A*0 = A * A - A * A = 0 (because of axiom 2).

I'll leave it with that.

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Re: "Purity" Discussion

Postby sgware » Thu Jun 12, 2008 10:40 pm UTC

Spazikstan wrote:And math + logic = magic :D
Math - logic = ?

As for the chicken/egg question:
aliosha wrote:However, let us consider it thus: I have a square.
Note that before you even start doing that math problem, you've engaged in ontology. Philosophy ftw.

I'm of the opinion that we discovered math. Math "itself" can be thought of as totally pure, but then so can any sort of theoretical discipline. The study of math probably came after the study of philosophy, so again, Philosophers ftw.
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Re: "Purity" Discussion

Postby aliosha » Thu Jun 12, 2008 10:53 pm UTC

sgware wrote:
aliosha wrote:However, let us consider it thus: I have a square.
Note that before you even start doing that math problem, you've engaged in ontology.

I'm of the opinion that we discovered math.

I hadn't started doing maths at that point, I was still doing physics (measuring things and working stuff out using that). The maths started later.

As for discovering maths, yes.

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Re: "Purity" Discussion

Postby JET73L » Thu Jun 12, 2008 11:08 pm UTC

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.
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