0435: "Purity"

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greenblob
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Re: "Purity" Discussion

Postby greenblob » Wed Jun 11, 2008 11:43 pm UTC

I just noticed something. There's more than one definition for "purity."
And yes, mathematicians are the most "pure."
The alt-text is more appropriate than usual.
Last edited by greenblob on Thu Jun 12, 2008 3:00 am UTC, edited 1 time in total.

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fenrir_darkwolf
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Re: "Purity" Discussion

Postby fenrir_darkwolf » Wed Jun 11, 2008 11:54 pm UTC

Schaard wrote:As all sciences were created by humans, I'm not sure how any one of them can claim to be pure - they are necessarily as conditioned as we are. Each is a system for the interpretation of natural phenomena, and any scientist/mathematician/chemist who thinks he's dealing with objective truth needs a reality check and probably a little ego deflation.

Scientific theory is a contrived foothold in the chaos of natural phenomena. - Wilhelm Reich

Alternate thread title : Plato vs. Nietzsche


The basic rules and axioms of all sciences are created by humans, but the remainder of our knowledge has been gathered by studying nature. So yes, sciences and especially mathematics and physics can be considered "pure."
"You're gonna have to learn everything anyway, so which is first is not essential."
-Richard Feynman

marginally_stable
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Re: "Purity" Discussion

Postby marginally_stable » Wed Jun 11, 2008 11:58 pm UTC

I wonder how replacing "pure" by "poor" will change the picture. Haha!

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DougBTX
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Re: "Purity" Discussion

Postby DougBTX » Thu Jun 12, 2008 12:00 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.


I don't understand your jump from step 3 to 4. Just because you can describe something doesn't mean that the description exists. The Ancient Egyptians described the sun as a god riding across the sky in a chariot, you might even say that the sun has the behaviour of a sun god riding across the sky. But the thing which actually exists, the sun, doesn't change when we change our description of it.

I like this line from Diadem:

Diadem wrote:- Mathematics is the study of patterns and structure.


We use maths as a language to describe patterns and structure, but there has to be someone doing the describing. Maths is a human construct to understand patterns.

Unless you are saying that the patterns themselves are Maths, and we just happen to describe them using mathematical notation. That's an interesting idea, which I've not thought much about yet. Will get onto it.

gendou
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Re: "Purity" Discussion

Postby gendou » Thu Jun 12, 2008 12:16 am UTC

DeadCatX2 wrote:
gendou wrote:The laws of physics cannot be derived from mathematical reasoning.
Experiment is necessary! This is a very important distinction!

I'm not disagreeing with you. What I'm saying is this.

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.


Sure, I agree that math exists even when you remove all observers.
That's not my point. Sorry that I was confusing/confused.

The comic suggests that all the depicted sciences, including physics, can be reduced to mathematics.
I don't agree.
Physics is not reducible to math.
Rather, math is a tool used in physics.

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fenrir_darkwolf
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Re: "Purity" Discussion

Postby fenrir_darkwolf » Thu Jun 12, 2008 12:21 am UTC

marginally_stable wrote:I wonder how replacing "pure" by "poor" will change the picture. Haha!


Hey, there are plenty of mathematicians with high paying jobs, like... uhhh... ahhh... touche...
"You're gonna have to learn everything anyway, so which is first is not essential."
-Richard Feynman

sgware
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Re: "Purity" Discussion

Postby sgware » Thu Jun 12, 2008 12:35 am UTC

Image

Too bad mathematics is just applied Philosophy. gg.
One day, I hope to change the world. Now if only they would give me the source code...

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Syphon
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Re: "Purity" Discussion

Postby Syphon » Thu Jun 12, 2008 12:42 am UTC

sgware wrote:Image

Too bad mathematics is just applied Philosophy. gg.


As I stated earlier, too bad philosophy is just applied agriculture.

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Chevron
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Re: "Purity" Discussion

Postby Chevron » Thu Jun 12, 2008 12:45 am UTC

It is entirely likely that someone has already said this in one of the 8.5 forum pages I haven't read of this thread, but I decided to post it after I saw how long I'd have to search to see if this was indeed the case.


Was anyone reminded of this when reading this comic?

Image
Image

Dawudd
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Re: "Purity" Discussion

Postby Dawudd » Thu Jun 12, 2008 1:18 am UTC

When I studied Biology in 9th grade, I thought, ‘this is fundamental’. Then came Chemistry in 10th grade, and I thought, ‘no, this is fundamental’. Then I took Physics in 11th grade, and I concluded, ‘it can’t get more fundamental than this’. But then came calculus in 12th grade, and I discovered, ‘all those other subjects are merely universe-specific; Mathematics is truly the fundamental subject’. Then I took a Computer Science class, got momentarily intrigued, but moved on, because it’s—gasp—applied. Then I took Logic in college and realized, ‘wow, there is something that is fundamental to Mathematics!’. Then I took Philosophy, and I saw, ‘Logic is merely an application of Philosophy’. I did not find anything more fundamental, so I I continued studying (Analytic) Philosophy. But, then, I accidentally solved all the fundamental philosophical problems. And I was bored. So I returned to Logic. But that wasn’t relevant enough, and Computer Science started to be more interesting.

Where am I headed? Sociology?!

MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 1:21 am UTC

while I believe that philosophy is on the purer end of things, maths does not seem to be applied philosophy. both maths and philosophy have the exact same approach and do the exact same things, just in different subjects. and I'm talking about philosophy at its best in its purely logical format (like descartes), not the heavily applied version (like, I dunno, marx)

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pliny
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Re: "Purity" Discussion

Postby pliny » Thu Jun 12, 2008 1:59 am UTC

Syphon wrote:
pliny wrote:
DeadCatX2 wrote:





Define "define"

Or fuck you, and all people who are pedantic about things that are common knowledge.


Don't get angry at me, I was poking fun at an earlier post asking me to define "exist".

People really ought to read threads before posting.
Don't look behind you.

It doesn't like to be seen.

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pliny
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Re: "Purity" Discussion

Postby pliny » Thu Jun 12, 2008 2:02 am UTC

Syphon wrote:
sgware wrote:Too bad mathematics is just applied Philosophy. gg.


As I stated earlier, too bad philosophy is just applied agriculture.


The concepts and ideas found through philosophical thought and study were used to found and develop mathematics.

The ideas and concepts of agriculture were not used to found and develop philosophy. Philosophy is the study of the fundamental nature of knowledge, reality, and existence; we were studying all of those long before we settled into agricultural societies, anyway.
Don't look behind you.

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pliny
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Re: "Purity" Discussion

Postby pliny » Thu Jun 12, 2008 2:07 am UTC

Let me get out another idea: mathematics is not the philosophia perrenis. When you bring our established "truths" of mathematics into contexts far enough removed from the ones they were developed in, they collapse.

I don't mean to say this doesn't hold true for other disciplines; in fact, it holds true for all the ones in the comic, and practically every other field, study, or subject. One aim of philosophers is to find something that does not collapse under a sufficiently exotic context.
Don't look behind you.

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MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 2:20 am UTC

pliny wrote:Let me get out another idea: mathematics is not the philosophia perrenis. When you bring our established "truths" of mathematics into contexts far enough removed from the ones they were developed in, they collapse.


eh? where does this come from?

also try not to double/triple post ... looked down upon, I think

EtzHadaat
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Re: "Purity" Discussion

Postby EtzHadaat » Thu Jun 12, 2008 2:25 am UTC

I'm gonna have to disagree with the assertion that psychology is applied biology. I think it could be, but it appears to be applied...uh...intuition. The neurological basis for psychology seems to have little impact. Also I'd like the "logy" to be taken off the end. I wouldn't include it on this scale, or I'd have the distance between it and biology greater than the distance between physics and math.

Also I don't think you can say philosophy is pure. Descartes' proof of God is accepted by some philosophers and not others (I don't think any accept it today, but...) Being convincing is more important than being right, because there's no way to determine who's right for real.

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fenrir_darkwolf
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Re: "Purity" Discussion

Postby fenrir_darkwolf » Thu Jun 12, 2008 2:38 am UTC

sgware wrote:Image

Too bad mathematics is just applied Philosophy. gg.


You're forgetting Descartes was a mathematician. :mrgreen:
"You're gonna have to learn everything anyway, so which is first is not essential."
-Richard Feynman

Schaard
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Re: "Purity" Discussion

Postby Schaard » Thu Jun 12, 2008 2:54 am UTC

fenrir_darkwolf wrote:
Schaard wrote:As all sciences were created by humans, I'm not sure how any one of them can claim to be pure - they are necessarily as conditioned as we are. Each is a system for the interpretation of natural phenomena, and any scientist/mathematician/chemist who thinks he's dealing with objective truth needs a reality check and probably a little ego deflation.

Scientific theory is a contrived foothold in the chaos of natural phenomena. - Wilhelm Reich

Alternate thread title : Plato vs. Nietzsche


The basic rules and axioms of all sciences are created by humans, but the remainder of our knowledge has been gathered by studying nature. So yes, sciences and especially mathematics and physics can be considered "pure."


They cannot be considered pure in any objective sense, and such a sense is implied in the usage of the word. They are only pure once you accept that all perspective, and thus all truth, is conditioned, and thus subjective. There are no facts, only interpretations.

This essentially comes down to how much of a platonist you are. If you believe that human beings discovered mathematics, a thing that was existent before human perception, you are essentially agreeing with Plato in the idea of Forms (one, two, good, beautiful - perhaps nix the last two). If you rather believe that human beings created mathematics, you are agreeing with Nietzsche (and not only him) in his assessment of the situation. 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. Scientific discoveries are meaningful, useful, but we must not mistake the map for the territory itself. Sure, 2+2 is the same on Earth as it is on Mars.. but this doesn't mean that mathematics is some sort of grand universal yardstick. It just means that an arbitrary set of arbitrary symbols that we use to interpret natural phenomena is very useful and widely applicable.

In science, we have a bad habit of hiding truth behind a bush and then praising ourselves for finding it.

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Syphon
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Re: "Purity" Discussion

Postby Syphon » Thu Jun 12, 2008 2:57 am UTC

pliny wrote:
Syphon wrote:
sgware wrote:Too bad mathematics is just applied Philosophy. gg.


As I stated earlier, too bad philosophy is just applied agriculture.


The concepts and ideas found through philosophical thought and study were used to found and develop mathematics.

The ideas and concepts of agriculture were not used to found and develop philosophy. Philosophy is the study of the fundamental nature of knowledge, reality, and existence; we were studying all of those long before we settled into agricultural societies, anyway.


No we weren't, 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.

ARVash
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Re: "Purity" Discussion

Postby ARVash » Thu Jun 12, 2008 3:12 am UTC

Schaard wrote:As all sciences were created by humans, I'm not sure how any one of them can claim to be pure - they are necessarily as conditioned as we are. Each is a system for the interpretation of natural phenomena, and any scientist/mathematician/chemist who thinks he's dealing with objective truth needs a reality check and probably a little ego deflation.

Scientific theory is a contrived foothold in the chaos of natural phenomena. - Wilhelm Reich

Alternate thread title : Plato vs. Nietzsche


Unless of course a theology were infallibly true, at which point, Sacred doctrine would be the most pure science; then Mathematics, etc etc. and this list would be official :P

I personally like the list a lot, and being a Catholic I have to say I believe the list to be objectively true. :P
Hey!

doctor_kiwano
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Re: "Purity" Discussion

Postby doctor_kiwano » Thu Jun 12, 2008 3:44 am UTC

As a professional mathematician (at least for the time being), let me assure you that what we actually do in these situations is sit down for a pint with some philosophers and alternate between snickering at everyone else, making cracks about sciences being "upstart young disciplines without even half a millenium of history to them", and complaining that all those other (better funded) departments not having any respect for the disciplines which spawned them, and upon which they still depend.

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Incompetent
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Re: "Purity" Discussion

Postby Incompetent » Thu Jun 12, 2008 3:46 am UTC

I would argue that if we are to posit an external reality, accessible to us via our thoughts, it makes more sense to regard mathematical insights as 'real' or 'true' than sensory experiences. Proving > seeing and hearing.

In other words, I'm OK with people saying maths is all invention, with no claim to truth or reality, but one could equally say the senses are all hallucination, and I think the latter is actually a more reasonable hypothesis than the former. People's fantasies can match and surpass 'real' sensory experiences, which suggests we are perfectly capable of hallucinating the whole lot, whereas mathematicians prove results that are far more intricate than anything anyone has ever taken out a patent on.

As for philosophy being to the right of maths on some 'application' scale, there are various kinds of philosophy.

Formal logic and mathematics are pretty much different words for the same thing.

Ethics, aesthetics and so on are formally unrelated to science and maths, though in practice they may be a source of inspiration or motivation.

Ontology underpins physics and everything to the left, but I wouldn't say it's necessary for mathematics or vice versa (though maybe I'm missing something here).

The one branch of philosophy I'd put clearly to the right of mathematics is epistemology (study of knowledge), a field which underpins all intellectual discourse.

aristotle2600
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Re: "Purity" Discussion

Postby aristotle2600 » Thu Jun 12, 2008 3:51 am UTC

Was looking for the following:
Psychologists think they're experimental psychologists.
Experimental psychologists think they're biologists.
Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think they're physical chemists.
Physical chemists think they're physicists.
Physicists think they're theoretical physicists.
Theoretical physicists think they're mathematicians.
Mathematicians think they're metamathematicians.
Metamathematicians think they're philosophers.
Philosophers think they're gods.

And found also this:
Users think they're software developers.
Technicians think they're hardware engineers.
Developers and engineers think they're computer scientists.
Computer scientists think they're philosophers.
Philosophers think they're God.
God thinks he's a system administrator.

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scowdich
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Re: "Purity" Discussion

Postby scowdich » Thu Jun 12, 2008 4:07 am UTC

I'm just gonna jump in here to highlight 2 things:
1) The lack of love for engineering, which I'll say is a mix between applied math and applied physics
2) The philosopher looks almost exactly like me. It's spooky.

Rinso
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Re: "Purity" Discussion

Postby Rinso » Thu Jun 12, 2008 4:18 am UTC

It's mathmagician, thank you!

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Spazikstan
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Re: "Purity" Discussion

Postby Spazikstan » Thu Jun 12, 2008 4:40 am UTC

Rinso wrote:It's mathmagician, thank you!


And math + logic = magic :D

Also, as a future psychologist, I am....mildly offended :p
My current sociology professor is a bit nutty so its all good.
Where do anthropology people fit in?

IabMichael
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Re: "Purity" Discussion

Postby IabMichael » Thu Jun 12, 2008 5:29 am UTC

Does that mean sociology is the greatest, mind-blowing orgasm a human is capable of attaining?
If so, as a biologist, I'm strangely ok with being somewhere in the middle ;)

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Claren
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Re: "Purity" Discussion

Postby Claren » Thu Jun 12, 2008 5:33 am UTC

I searched the thread, and can't believe I'm the first to bring up Dick Feynman's thoughts on the matter (especially given the mouse-over text about physics + sex):

"Physics is like sex: sure, it may give some practical results, but that's not why we do it."

I must have missed something when I searched. :D

MysticTerminator
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Re: "Purity" Discussion

Postby MysticTerminator » Thu Jun 12, 2008 5:37 am UTC

ayup

he sure did like comparing physics to sex, huh.

AvalonXQ
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Re: "Purity" Discussion

Postby AvalonXQ » Thu Jun 12, 2008 5:37 am UTC

Math is pure because it is entirely constructed, with no basis in reality.

Cenyu
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Re: "Purity" Discussion

Postby Cenyu » Thu Jun 12, 2008 5:48 am UTC

Chemistry is sex, physics is masturbation and math only provides the porn dialogues everybody tries to skip anyways. :D

Hello xkcd.

Patren
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Re: "Purity" Discussion

Postby Patren » Thu Jun 12, 2008 5:53 am UTC

Spazikstan wrote:Where do anthropology people fit in?


It has been determined that anthropology people are floating above it all in a hot air balloon watching everything with a telescope. There is also at all times a person manning the water balloon cannon to shoot at sociologists.

EtzHadaat
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Re: "Purity" Discussion

Postby EtzHadaat » Thu Jun 12, 2008 5:57 am UTC

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.

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

Also anthropologists aren't clearly distinguishable from sociologists on the way way left.

muzar
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Re: "Purity" Discussion

Postby muzar » Thu Jun 12, 2008 5:59 am UTC

I've read through a lot of the posts in this topic, and have yet to see the "classic" series I encountered many years ago:

Biology is applied Chemistry.
Chemistry is applied Physics.
Physics is applied Mathematics.
Mathematics is applied Logic.
Logic is applied Biology.

Has the appeal of circularity, and is no less accurate for it, IMHO.
Please note that regardless of whether "maths" or "logic" exists without humans, our use of the principles of these fields is an application of the grey matter - that is to say, biology.

chocolate thief
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Re: "Purity" Discussion

Postby chocolate thief » Thu Jun 12, 2008 6:25 am UTC

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.

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


I'd have to say that human observation is required for things like shapes and quantities to exist. We have no way of observing a world without observing it; therefore, I don't know if we can reach a conclusion on whether shapes and quantities exist objectively.

If you can imagine not being a person, try to describe something like quantity or shape in purely objective terms. this exercise is impossible.

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Re: "Purity" Discussion

Postby pencilears » Thu Jun 12, 2008 6:29 am UTC

oh come on,
everyone knows sociology is just anthropology with no science in it at all.

also the idea that math is some how a gift from angles on high irks me a little, along with the semi "ascent of man" look to this comic.
but then, I'm into geology and anthropology which are apparently like Paranthropus or heidelbergensis and too out there to even count on the timeline.

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Re: "Purity" Discussion

Postby pencilears » Thu Jun 12, 2008 6:42 am UTC

EtzHadaat wrote:
Also anthropologists aren't clearly distinguishable from sociologists on the way way left.


hey now thats not fair, sociologists ask people questions about what they think they are thinking about and what they think they are doing or going to do. then they have numbers they can wave around like "73% of the natives of bongo bongo think this survey is demeaning" that kind of stuff.

anthropologists go out there and watch people and try to get inside their heads from an outsiders perspective. to try and see what they really do and why they really do it.

the natives of bongo bongo may say they don't eat their grandmothers on the survey they hand to the white guy in the suit from the government but they might include the anthropologist who's lived there for years in a little endocannibalistic funeral if they think old grandmom would have been cool with it.

Hell, I'd say anthropologists also beat out psychologists on the front of actual scientific study of humans.

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HPDDJ
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Re: "Purity" Discussion

Postby HPDDJ » Thu Jun 12, 2008 7:25 am UTC

Scigatt wrote:I really want to invoke Godwin's law on this one...


There should be a Godwins law for invoking Godwins law out of context.

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HPDDJ
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Re: "Purity" Discussion

Postby HPDDJ » Thu Jun 12, 2008 7:27 am UTC

Syphon wrote:
sgware wrote:Image

Too bad mathematics is just applied Philosophy. gg.


As I stated earlier, too bad philosophy is just applied agriculture.


Isn't agriculture just applied reproduction, and ultimately, sexual intercourse?

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The Rumpled Academic
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Re: "Purity" Discussion

Postby The Rumpled Academic » Thu Jun 12, 2008 7:33 am UTC

EtzHadaat wrote: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.


DeadCatX2 wrote:helium atoms will always have two protons whether or not anyone knows what helium, atoms, two, or protons are.


Don't you see that while you are contemplating a Universe prior to human consciousness, you're still applying your own notions of numbers to it? If you really try and think about the Universe without using any pre-existing human concepts... well, it's very difficult, for starters, but there certainly exists absolutely no impetus for anything to be defined as seperate to anything else. Matter is existing and chemicals are interacting, but without a conscious observer dividing and seperating the Universe into pieces, numbers have no existence.
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.

Not to say, of course, that mathematics isn't admirable. But it is just, as Schaard put it, "an arbitrary set of arbitrary symbols that we use to interpret natural phenomena [that] is very useful and widely applicable." My only issue is with the case that mathematics is somehow 'purer' than the rest of the disciplines and activities that frolic on the earth's surface. It's no closer to a 'pure truth' than interpretive dance is - everything is filtered through our human eyes and brain; including the notion that the great singularity of the universe divides naturally into pieces.

(Tangential note: all this is what makes the Buddhist concept of nirvana so goddamn intoxicating. For those who don't know, the idea of nirvana is to try and attain (mostly through meditation) a mental state in which one can view the Universe without human eyes, or conceptions, or any attachment to the human condition at all. To see the essential suchness of the Universe without automatically breaking it down in pieces and numbers and subjective sensory data. Of course, those Buddhist monks who do claim to have reached this state of enlightenment can't tell us anything about it, because the very instant you apply human language to the Universe, the purity is necessarily shattered.)
(Just like it is whenever we try and describe the universe in any terms - the mathematical included. Like I said before; the thing to do is to forget this doomed striving after fact-purity, and revel in all this glorious subjectivity! Again, like Schaard noted, once you've accepted that all observable truth is necessarily conditioned by the particular perspective of the observer, it lends *everything* a kind of purity.)

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.


This doesn't work. The jump from 3 to 4 is entirely without ground. I could describe the movements of the planets completely consistently using something impossible to prove existent (specifically, say, a system of invisible and impalpable strings linking all the planets a gigantic celestial yo-yo), but that would not even remotely imply that this system would exist in reality even if all observers were removed. Rather, while I was thinking about it, this tool for thinking about the Universe exists in my mind. Maths exists in a similar way: in our minds, as a very useful tool for thinking about the Universe.
Yes: mathematics is (maybe a shade ^_^) more believable than my yo-yo theory, but the parallel holds nevertheless. Just because the things we observe through our eminently trickable senses can be interpreted using a certain set of principles does not mean that they would exist (in any sense) if the observer was to disappear. Prior to that disappearance, the set of principles exists in the observer's mind, but after that, the Universe continues as it ever has; placidly, without need for the division and differentiation of itself into numbers.

To paraphrase Pliny the Much-Much Younger, if the "pen" of mathematics breaks (with ZF/ZFC spilling everywhere), the Writer can certainly find another method of writing. It wouldn't mean that the Universe is broken - just the pen.

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. The Neolithic/Agricultural revolution actually gave the average person less free time. Farming processes did produce more food than nomadic processes, but this didn't immediately translate to more free time for the farmers, as they were suddenly involved in the production of surpluses (for trading), rather than just what they have to eat right now. Much more was produced, but it took much more time to do it. I read an anthropology paper only about a month ago that estimated that the average nomadic pre-agricultural hunter-gatherer only needed to work for about 3 hours at most to obtain the food necessary for their survival. With only some part-time exceptions, the rest of the day was free time. In comparison, the agriculturalists had to work truly dreadful hours - and so do we today. :P

Plus, it won't do to deny the philosophical breakthroughs of pre-writing man. The fact that by the time we had paper and pens at all, we already had a deeply-ingrained set of ideas about the fundamental qualities of reality for the credited philosophers to pick at and argue over shows that there must have been a fair bit of thought about basic philosophy before writing and, yes, before agriculture.

(*Disclaimer: I'm not an anthropology student. I'm just interested in stuff.)

SolkaTruesilver wrote:I hope I have not offended you.


Not even a little bit. I'm enjoying this discussion immensely. :D


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