16:27 -!- Irssi: Starting query in freenode with Huber
16:27 <Huber> hi
16:32 <Utopiah> hi?
16:34 -!- Huber [n=rnotmani@pool-71-163-205-242.washdc.east.verizon.net]
16:34 -!-  ircname  : nvl8hg2
16:34 -!-  channels : ##philosophy 
16:34 -!-  server   : irc.freenode.net [http://freenode.net/]
16:34 -!- End of WHOIS
16:34 <Utopiah> how may I help you?
16:36 <Huber> oh, i'ts me... sorry
16:36 <Huber> hmm wagner? what nick do i usually use
16:36 <Huber> (i'm on a different computer and irc client)
16:38 <Utopiah> ah ok
16:38 <Utopiah> (I wonder because of "washdc")
16:38 <Huber> yes, it's me
16:38 <Huber> what is new with you?
16:39 <Utopiah> I suddently found number theory interesting
16:39 <Utopiah> at least more interesting than before
16:39 <Huber> really-- tell me more, i have some interest in it
16:39 <Huber> btw, do you know who the mathematician conway is?
16:40 <Utopiah> cellular automata?
16:40 <Huber> John H. Conway
16:40 <Huber> well, he has done so many thing
16:40 <Huber> i guess he is most known for dense packings of spheres in higher dimensions
16:40 <Utopiah> http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
16:40 <Huber> but he invented the game of life
16:40 <Huber> Yes, a year or two ago, i downloaded several programs
16:40 <Huber> for playing the game of life
16:40 <Huber> some of those programs are totally amazing
16:41 <Huber> anyway, what's your new interest in number theory?
16:41 <Utopiah> CA are rather famous in CS (even if Stephen Wolfram think he invented it,like anything else ;) thanks to Von Neuman I guess, so yes I know a bit about Conway from CA
16:41 <Utopiah> well I wouldn't call it an interested but let's say that until few days ago I thought
16:42 <Huber> von neuman designed a machine which could build itself
16:42 <Utopiah> "number theory... well it's nice but sounds more like numerology than anything else, a la Pi the movie"
16:42 <Huber> you can download a realization of that machine from the net and watch it do that, build a copy of itself
16:42 <Utopiah> so I found it a curiosity rather than a "real" field
16:42 <Huber> oh
16:43 <Huber> ok, and what do you think now about number theory?
16:43 <Huber> here is a statement by a guy who i knew in high school
16:44 <Huber> he is the one i mentioned who made his career translating top french mathematicians lol
16:44 <Huber> "My specialty is algebraic geometry. This means, roughly, the study of the geometric properties of solutions of systems of algebraic equations. What I love about this subject is the interplay among geometry, algebra, analysis, and number theory. "
16:44 <Huber> http://math.berkeley.edu/~ogus/
16:44 <Huber> i generally refer to this person as the 'boob from berkeley'
16:46 <Utopiah> but now
16:47 <Huber> now?
16:47 <Utopiah> because of an older interest in crypto{graphy,analysis} and hardware computation (CPUs, FPGA, ...)
16:47 <Huber> ?
16:47 <Utopiah> I find it much more... "practical"
16:47 <Utopiah> I know it sounds like a bad word ;)
16:47 <Huber> hmm
16:48 <Huber> well, yes, these days parts of it are very practical
16:48 <Utopiah> but I mean it's useful there so because of the potential usage I find it way more exciting, because Im able to see part of the consequences
16:48 <Utopiah> I guess it's giving me an affordance to it.
16:49 <Huber> well, you should also look into it in relation to quantum computers (and the algorithms for them)
16:49 <Utopiah> yes
16:49 <Huber> that is where the action really is, most of which is classified
16:49 <Utopiah> but that I already looked into
16:49 <Utopiah> from a more physics viewpoint actually
16:49 <Huber> well, i've looked at it from a philosophical point of view also
16:50 <Utopiah> I want to be able to leverage the adapted algoritmss the day quantum computers will be available
16:50 <Huber> to refute Deutsch
16:50 <Utopiah> (but that links back to crypto too)
16:51 <Utopiah> manyworlds?
16:51 <Huber> i ran into some insane person on the net claiming to be 30 years old, but apparently he has done some original work in such algorithms
16:51 <Utopiah> ?
16:51 <Utopiah> (prefer http://en.wikipedia.org/wiki/Quantum_Darwinism )
16:52 <Huber> deutsch argues that the fact that quantum computers can apparently do many simultaneous computations forces the conclusion that these computations are each done in a different world
16:52 <Huber> proving many worlds
16:52 <Utopiah> :/
16:52 <Huber> (or illustrating many worlds)
16:53 <Huber> i argue that only follows if one trys to retain a classical standpoint while trying to talk about quantum phenomena which don't fit with a classical view
16:53 <Huber> etc.
16:55 <Utopiah> Im really not a fan of manyworlds
16:55 <Huber> good
16:55 <Utopiah> but it's rather an intuition than an ability to build a solid proofs against it ;)
16:56 <Huber> right
16:56 <Huber> anyway, so are you following any url's on your new interest in number theory
16:56 <Huber> or was it just an idea that came to mind
16:57 <Utopiah> I checked Berkeley and ENS courses to find online material
16:57 <Utopiah> I mean podcast or videos first
16:57 <Utopiah> but didnt find anything relevant
16:57 <Huber> what subject were you searc hing for exactly?
16:58 <Utopiah> nothing really, more of an overview of number theory, history and gradual advances in it to get a coherent basis then how it goes, subfields of it, recent discoveries, etc
16:59 <Utopiah> (quickly checked the last thesis about it too at
16:59 <Huber> hmm... that princeton book we talked about would probably help you there
16:59 <Utopiah> oh good idea
16:59 <Utopiah> didn't think abou tit
16:59 <Huber> yup
17:00 <Huber> i have been reading some of their sections on that
17:00 <Utopiah> http://www.numbertheory.org/ntw/N5.html
17:00 <Utopiah> I obvisouly can't fully enjoy most (or any? ;) of those but it gives me a view of what is happening
17:01 <Huber> what is the ENS site for lectures?
17:02 <Utopiah> http://www.diffusion.ens.fr/
17:02 <Huber> thanks
17:02 <Utopiah> they have an RSS feed 
17:02 <Huber> in my opinion, you have the right idea, i myself believe it is possible
17:02 <Utopiah> very nice to stay updated
17:02 <Huber> to get an overview of these fields (in math, for example)
17:02 <Huber> but it seems impossible if you start from lists of dissertations, etc.
17:02 <Huber> yet, i believe there is an overview
17:02 <Huber> look, i have an idea
17:03 <Huber> i mentioned perhaps that i was speaking with this teenaged math genius
17:03 <Huber> last year, on irc, for several months
17:03 <Utopiah> yes
17:03 <Huber> It would benefit both of us to get into contact with him again
17:03 <Huber> he is able to get that overview of fields, and he's in the process of doing that 
17:04 <Huber> his ability to do that is one reason he's such a genius, in my opinion
17:04 <Utopiah> yes
17:04 <Huber> (asperger's genius for math, esp. geometry it seems)
17:04 <Huber> esp=especially
17:04 <Utopiah> (btw I remember your wikipedia advice so I checked its number theory portal few days ago)
17:05 <Huber> one key is 'universals'--
17:05 <Huber> for example, in some sense the famous 'cantor set' turns out to be a 'universal'
17:05 <Huber> any set in any way resembling it turns out to be essentially equivalent to it
17:05 <Huber> at first it appeared as just a freaky example of an strange and odd set
17:05 <Huber> yet now it is known that it is not a freak example, it is a 'universal'
17:06 <Huber> in the sense that it is the essentially unique freaky example of its kind (and no other thing but it)
17:06 <Huber> if you get my drift..
17:06 <Huber> On a more general level, Bourbaki claimed they were 'structuralists'
17:06 <Huber> but of course, the couldn't give a definition of 'structure'
17:06 <Huber> admittedly they had something in mind
17:07 <Huber> but for practical purposes what they did amounts to trying to put all of math in the form of category theory (which at least, is something which is mathematically definite)
17:07 <Huber> etc etc.
17:07 <Utopiah> well it's always about finding patterns or structure, isn't it?
17:07 <Huber> well, but you can't define those terms
17:07 <Huber> in practice, bourbaki reverts to set theory as the basis
17:08 <Huber> (ok, you don't have a definition of 'set' either, but you do have the axioms for set theory-- there are no axioms for "structure theory")
17:08 <Huber> and then, on the basis of set theory, he in effects does math in the style of category theory
17:08 <Huber> (as you can read several articles coming to this conclusion, as i did recently)
17:08 <Huber> are you still there, i think i can help you with your overview
17:09 <Utopiah> Im here yes
17:09 <Huber> if you have just a few minutes for me to continue
17:09 <Huber> ok
17:09 <Utopiah> but
17:09 <Utopiah> Ill have to go soon though
17:09 <Huber> ...?
17:09 <Utopiah> (prefer to warn you now)
17:09 <Huber> ok
17:10 <Huber> well, for example, you can look at a whole development of 'geometric algebra' starting with leibniz, up thru hamilton and grassman, then perfected by 
17:10 <Huber> clifford, further developments by dirac (spinors) finally you get up to conway and company, etc
17:10 <Huber> but, the point being, read the article in wikipedia
17:10 <Huber> about clifford algebra
17:10 <Utopiah> that's also why having a visualization of maths as interlinked field would help me (and hopefuly others), our visual cortex is dedicated material to find patterns (and thus extract structure to synthesize)
17:10 <Huber> and they mention the 'clifford functor'
17:11 <Huber> the 'clifford functor' summarizes the result at the highest level of generality
17:11 <Huber> essentially it discloses the sense in which clifford algebra is a 'universal'
17:11 <Huber> (unique universal algebra) for any geometry
17:11 <Huber> I mentioned this to the asperger's genius, and he said, 'yes, but the problem is
17:12 <Huber> you can put almost any branch of math into 'universal' form these days'
17:12 <Huber> and i said,.. 'right, but you miss the point, my late friends philosophy, that's exactly what that was: he discovered the 'Leon functor', so to speak, the universal form of any possible philosophy
17:12 <Huber> (in analogy to the clifford functor)
17:13 <Huber> this 'universal form' is the form taken when any field is stated in terms of category theory (which is where the term functor comes from)
17:13 <Huber> The point being, the fact that you can put almost any branch of math into that form
17:13 <Huber> is what gives you the possiblity of an 'overview' of every branch of math
17:13 <Huber> because it is also the simplest possible form to present any branch of math in
17:14 <Huber> I'm not saying that answers everything about math, it doesn't, but it does give the possibility of the overview
17:14 <Huber> etc.
17:14 <Huber> ok, enough on that for the moment, as your time is limited
17:14 <Utopiah> well
17:14 <Huber> If you work thru and understand what the 'clifford functor' is
17:14 <Huber> you will easily see what i mean
17:15 <Utopiah> then that generic abstraction should be leveraged to provide an overview (in visual or not form) then
17:15 <Huber> the point being, for example, grassmann developed the 'grassmann' product
17:16 <Huber> it is a total mess to write out explicitly
17:16 <Huber> clifford introduced the  clifford product (sort of a super cross product)
17:16 <Huber> which incorporates the grassmann product and more
17:16 <Huber> (vector cross product i mean)
17:16 <Huber> but all those people were working in components
17:17 <Huber> and it looks like one of those dissertations which would be impossible to read if you didn't have 10 years or a lifetime, and were a prof. mathematicians
17:17 <Huber> however, the 'clifford functor' proves there 'is' a product, that it 'is unique'
17:17 <Huber> and that it is specified by 3 or 4 simple statments, such as 'the produce is commutative'
17:17 <Huber> 'product is commutative' 'there is an identity'
17:18 <Huber> then, with that 'overview', you can spent months or more
17:18 <Huber> working out the exact explicit form of the product
17:18 <Utopiah> (naive question) could mathematical software libraries help there? I mean they are forced to organized themselves and are supposed to cover most fields
17:18 <Huber> but you don't have to, to have that overview of 'where the product is coming from and why it is unique'
17:18 <Huber> bourbaki takes that approach (which they didn't invent) to everything they touched
17:18 <Huber> for example, the determinant of a matrix
17:19 <Huber> it has a very simple universal specification as the only linear map from the matrices to the reals, etc.
17:19 <Huber> so, there you have the overview and understanding of what the determinant is, and you can prove thms about it from there
17:20 <Huber> without ever looking at how you would calculate it (which, however, follows from the that specification, just as the details of the clifford product follow from its universal specification)
17:20 <Huber> etc.
17:20 <Huber> <end of rant>
17:21 <Utopiah> :)
17:21 <Huber>  i want to write some stuff about how my late friend tried to apply the approach of bourbaki to philosophy
17:22 <Huber> so i've been reviewing these things, plus i have an independent interest in clifford algebras
17:22 <Utopiah> guess it related to epistemology too then since the goal is to organize knowledge
17:22 <Utopiah> I really have to go now though
17:23 <Huber> bye for now
17:23 <Huber> ciao
17:24 <Utopiah> have a nice afternoon
17:24 <Utopiah> (do you want me to make the logs available on my website?)
17:25 <Huber> let me think about that first, ok?
17:25 <Huber> but thanks for asking!
17:25 <Utopiah> sure
17:25 <Huber> i'll let you know later!
17:25 <Utopiah> ok, bybye!
17:26 <Huber> bye