Transcendental Mathematics (1 Viewer)

[Captain pi]

Why Transcendent Mathematics Is Just As Antiscientific as Radical Postmodernism

"Consider the radical form of postmodernism which claims that mathematics is purely historically and culturally contingent and fundamentally subjective. This is an a priori philosophical view. Scientific evidence is seen as irrelevant. No evidence from any science, including congnitive science, is given priority over that a priori view. Arguments based on empirical evidence which have no weight for someone who comes to the discussion with such an a priori view.

Now consider the radical version of the transcendent mathematics position. It adopts the Romance [of Mathematics being objective in any realm, even transcendental realms] as a fundamental, unshakable truth. It accepts as an a priori philosophical position that mathematical entities have a real, objective existence and that mathematics is objectively true, independent of any beings with minds.

This, too, is an a priori philosophical view. Scientific evidence is seen as irrelevant. No evidence from any science, including cognitive science, is given priority over that a priori view. Arguments based on empirical evidence have no weight for someone who comes to the discussion with such an a priori view."¹

¹George Lakoff & Rafael E. Núñez, Where Mathematics Comes From: p. 305 (if I remember, I saw it November)

Captain pi requests your thoughts:

 

[shannonm]

what the heck?

go get a maths textbook and enjoy learning, dont dwell on this philosophical bullshit

 

[Trev]

haha hugh, please dont ruin maths by introducing english to it

 

[Captain pi]

what the heck?

go get a maths textbook and enjoy learning, dont dwell on this philosophical bullshit

(1) I have enjoyed, and still enjoy doing mathematics. This enjoyment comes as much from exploration as from solving problems.

(2) It's damn important to know if we are capable of determining whether mathematics is as powerful as some (I, included) believe.

 

[shannonm]

and how will a discussion re this philosophy shit allow you to find out whether make is as powerful (ROAR) as you believe

 

[Slidey]

Can postmodernism build civilisation? No? Then mathematics and science win.

I like philosophy, but postmodernism is just bullcrap which I won't even touch with a ten-foot pole. I'd need at least a 20.

 

[illucid]

Well well well......

Ever heard of the Chaos theory?.... It sort of (and i emphasise sort of) voids postmodernism stipulating that everything is in a pattern, just not a nice linear one, that could theoretically be expressed in a mathematical equation but would require some kind of overhaul of how we think about maths at the moment... Theoretically society itself seems to undergo the progression from modern to post modern to "postmoderne" (i have no idea how it is spelt but it means past both of them)..... I'd love to hear a little more from the guy that has Schroedinger's kitty cat mentioned in his sig.... Surely someone with any knowledge of quantum physics would be interested in things such as the chaos theory or even something as base as, say, philosophical nihilism.

Also as a weird question what kind of music are people interested in?....

(i'm my schools resident freak child, i enjoy 4u maths and 4u english... Only one ever from out in the western suburbs i think...)

 

[Captain pi]

Also as a weird question what kind of music are people interested in?....

Not at all.

Schöenburg. (no, I can't back that up.)

Shostakovich.

Beethoven.

Bach.

 

[illucid]

well... Have a look at some chaos theory stuff. An interesting thing is that no one has exactly a neat definition of what the chaos theory is.... I'd point you in a direction but i am yet to find any nice resources on it.
but the idea is that a small change (read: minute) in initial reading varies the output of this magic equation hugely....

You aren't studying 4u maths and 4u english like me per chance?

(i like your music... Says a lot about you)

 

[Slidey]

Chaos theory? How's this for a definition:
Point 1: It is NOT about chaos, but about levels of complexity which appear to be chaos to humans.
Point 2: It states that simple causes do not have simple effects, counter intuitively - we often think "if I do this, that will happen".

Obviously from this it follows that simple causes have complex effects and that an interplay of myriad simple causes will have superbly extremely humongously complex effects - what we'd casually call chaos, because there is seemingly no relation of the effect back to the cause.

Actually, I am analysing Henri Poincare's chapter from On Giant's Shoulders at the moment. You could, and I would, say that he is the inventor/discoverer (I would maintain discoverer as I believe maths is platonic) of Chaos Theory.

I'm afraid I do not know much about philosophical nihilism, but you surely can enlighten me.

 

[illucid]

the nihilism thing was kind of my petty joke (sorry )... It is actually a "thing" (don't have an apt term for this) but it sort of renounces every single idea we take for granted. Even the most base one of existence itself. (Do we exist? Are you all here as figments of my imagination, or i yours?) Stuff like that.

I like your chaos theory information. I am a mathematical n00b compared to the people in this forum i'm sure. I am hoping to rectify that over the next few months.

So how do you describe this kind of pattern?
And you haven't read the play Arcadia have you? (or are you one of those, linguistically insalubrious types that only did advanced.. If you did extension 1 and 2 are much more fun, just like in maths)
(and doesn't it seem to follow that then postmodernism is really a sort of ultra-modernism.. Scary when things fall prey to such a paradigm shift like that)

 

[Slidey]

I am interested in philosophy, however, I have not much exposure to it. I find it fun to ponder and pose questions such as "do we exist" but I only do so half-heartedly. Cognition and meaning/lack of meaning do interest me, though.

I typically have a high lexical density, so I wouldn't define myself as one of those 'linguistically insalubrious types'. I only do Advanced, though. There is only so much HSC English I can stand. I love linguistics. I even like analysis in English. I don't like it when politics or religion is dragged into English, which my teachers inevitably do.

How do I describe that pattern? Well, that's what chaos theory is about! Chaos Theory is the study of complexity. I personally think optimisation is more interesting, however. Heard of P=NP, or that a polynomial is complete in non-polynomial time?

Try a google search on chaos theory and introduction, or chaos theory and explanation. It's interesting stuff. Feel free to discuss what you read here.

 

[illucid]

I have done the google thing for Chaos theory... Except no one seems to be trying to make the Chaos theory more than groundless conjecture. I want someone to say "i'm developing an equation for the movement of a fly using every imaginable factor... In accordance with the chaos theory" or something like that. That would really get me interested in it. I haven't heard of the P=NP thing. I will look for it now i didn't seriously think that you were an idiot because you don't do ext. 2 English, but the advanced course does suck something fierce if you like to think, i think they should totally restructure that course.

Two questions.... What kind of music do you like and are you left or right handed?

 

[Slidey]

I've grown to be right-handed, though I didn't favour either hand when i was younger. I like all sorts of music. As a rule, I hate R&B, country, rap, metal.

Chaos theory is used in weather forecasting... among other things.

P=NP is about being able to do algorithms or computations in a shorter amount of time than currently is possible. IF you can prove a polynomial is complete in no-polynomial time, then things such as timetabling issues would not be a problem. Do you know why time-table issues generally exist? Because to make a perfect time-table would take longer than the universe has existed for. That's a long time. If this time could be shortend dramatically, it'd be great. And if P=NP can be proven true in just one case, that will be sufficient. If you can figure out P=NP, then you could probably create an algorithm which quickly tests prime numbers with 100% accuracy... which would mean encryption is out the window.

I personally think the Advanced course is OK. Hated it in year 11, but I'm coming 1st now, and I can honestly say I enjoy it. For me, it's about picking the best of my multitude of ideas swirling in my head and putting them on paper seriatim to create a well-flowing synthesis. Though if I ever get a dodgy text (Shakespeare... *cough*), I'll be pissed.

 

[KFunk]

Check out this (Is Chaos Theory Postmodern Science? http://www.reconstruction.ws/044/mackey.htm). A bit of philosophical (perhaps more social) nihilism is present in some of nietzsche's work so have a read of him. A lot of great thinkers have been philosophers, mathematicians (and physicists)... true polymaths really. I see a lot of the higher level philosophical thinking to be quite similar to pure maths. An example is Kant's 'Critique of pure reason' (which I'm slightly into at the moment) where he basically establishes the fundamental axioms from which he will atempt to prove that 'a priori' judgements and conclusions can be made and come to, respectively. Not to dissimilar to proving that 1+1=2 really.

I read Arcadia for ext.1 english and, as a result, Stoppard would have to rank up there on my list of favourite writers. He's wonderfully witty. He does some very clever things in incorporating mathematical elements such as chaos theory, fermat's last theorem and the laws of thermodynamics into the structure and content of the play. That chaos element of sex will always create entropy.

[Sorry about the fractured nature of this post. It's just a collection of some of things that your dialogue has brought up in my mind]

 

[Estel]

postmodernism is just bullcrap which I won't even touch with a ten-foot pole.

Go shoot yourself.

 

[withoutaface]

As a rule, I hate...metal.

Go shoot yourself.

 

[Templar]

IF you can prove a polynomial is complete in no-polynomial time

I don't get what you're trying to say there.

If you can figure out P=NP, then you could probably create an algorithm which quickly tests prime numbers with 100% accuracy... which would mean encryption is out the window.

There is a way to quickly test whether a number is prime or not, without proving all NP problems are in fact P problems.

 

[Slidey]

Go shoot yourself.

I feel the hate, pomo boy.

Go shoot yourself.

There are always exceptions to the rule.

There is a way to quickly test whether a number is prime or not, without proving all NP problems are in fact P problems.

It's not a test of primality; it is a test of the likelihood of primality, unless you're referring to an algorithm which tests via brute force... which is NOT quick.

http://www.claymath.org/millennium/P_vs_NP/
http://en.wikipedia.org/wiki/Complexity_classes_P_and_NP

 

[fitz33]

It's not a test of primality; it is a test of the likelihood of primality, unless you're referring to an algorithm which tests via brute force... which is NOT quick.

http://www.claymath.org/millennium/P_vs_NP/
http://en.wikipedia.org/wiki/Complexity_classes_P_and_NP

actually a polynomial time primality test was discovered in 2002
http://mathworld.wolfram.com/AKSPrimalityTest.html