Logistic Map

Hey Everyone,

I just put this together, it's a quick flash thingy that lets you play with the logistic map, without having to do math, HOORAY!

Just move the left slider thing to change the beginning population from 0 (all the way down) to 1 (all the way up) and the bottom slider thing to change the R value from 0 (all the way left) to 4 (all the way right).

It's a little sloppy, I'll probably fix it up a bit in the near future. In the mean time, enjoy your chaos.

-Nick

Ant Comic

Hey team, I found this comic on the Internet, it pretty much sums up last week's conversation. Enjoy.

Newsletter 9/15

Hey Team,

This week we discussed emergence, holism, reductionism and, of course, post modernism. One can only guess at the ism we'll address next week.

• Suggested reading for next week is GEB: English French German Suite (pg 366) and the following chapter (pg 369)
• As of now, we'll be meeting in our usual place (Learning Center Conference Room) at our usual time (5:00 PM).
• Thanks to Joe for bringing coffee to the meeting.
• Don't forget, everyone's welcome to post stuff on Centophilia. Get to it.

I'll see everyone next week,

-Nick

Newsletter 9/8

Hey Team,

Here's this week's really late newsletter.

• Next week (9/15 at 5:00 PM) we're back in the Learning Center's Conference room. If anything changes, I'll do my best to let everyone know.
• Suggested reading for this week is ...Ant Fugue and Ch. 11: Brains and Thoughts (GEB: 311-365).
• There was some discussion about reading parts of ...Ant Fugue out loud.
• There should be a few new members attending next week.

Once again, if anyone wishes to be taken off this mailing list, please let me know.

I'll see you Tuesday,

-Nick

Newsletter 9/1

Hey Team,

As we begin to move into the fall, things are being mixed up quite a bit. If you are on my newsletter list and don't wish to be, please let me know, I'll fix that.

This Week's notes:

• Suggested reading for next wee (9/8) is Prelude... (GEB pg 275) and Chapter X (pg 285-310).
• As we begin Part II of GEB, we're losing a few members of our group, but remember that this is also a great time to bring new members in.
• If you (or someone you know) would like to join us next week via webcam, let me know a few days a head of time, and I'll come prepared.
• Our meeting time is now 5 PM, the day and place haven't changed.

See you next week,

-Nick

Resources

http://www.bahai.org/

http://www.bahai-education.org/ocean/ (A cool repository of religious writings. Muslim, Christian (several branches, Jewish, Hindu and Baha'i)

Newsletter 8/4

Hey Team,

Very valuable presentation by Micah today, very interesting, informal and enlightening. Also: Mormons.

Next week we'll be discussing Part 1 of GEB (pg. 1-272)

Soon Micah will be posting his presentation on Centophilia, be sure to check it out.

Happy Birthday to Micah's sister.

-Nick

Newsletter 7/28

Hey Team,

This week we discussed MU, TNT, different based arithmetic, Zen, Godel Numbering and Pirates.

• Next week is Micah's Presentation
• 8/11-- General Discussion of Part 1 (1-272)
• We played a Pirate Game I found on Wikipedia today. Click the link if you want to know more.

Have a good week,

-Nick

AI Comic

http://www.macboy.com/cartoons/sfr/archive.php?comicID=6

Just stumbled upon this, and thought I'd share.

Induction

Induction, hooray!

So this is one of the easiest proofs by induction to understand. And it's cool.

Suppose we wanted to add all the natural numbers from 1 to 100, what would we get? (1+2+3+...+99+100 = ??)

Don't reach for a calculator (or Excel spreadsheet) yet, that'd just be obnoxious, instead lets look at a simpler problem. What is the sum of the natural numbers from 1 to 5? 1+2+3+4+5 = 15. What about from 1 to 6? 21. Let's create a table of these sums:

1	1
2	3
3	6
4	10
5	15
6	21
7	28

On the left we have number, and on the right we have the sum of all the numbers from one to that number. Before going any further, see if you can detect a pattern in the right column.

One pattern is very obvious, to get the next number on the right column, all you have to do is add the number to its left to the number above it (7+21=28). So the next number down will be 28+8=36. In general we can write the formula:

F(n+1) = (n+1) + F(n)

This is a recursive formula, written in terms of the previous value. This is helpful, because if we know value, we can easily figure out what comes next, but it doesn't really help trying figure out what the 100th value is (unless we want to first figure out 99 others).

So while our recursive formula is nice, it's not nice enough. Some more observations might lead to:

F(n) = n(n+1)/2

(Side note: I gave this assignment to a group of nine sixth graders and they found this result on their own in under 45 minutes). Now to find all the numbers from 1 to n, all you have to do is multiply n by n+1 and divide that by 2. But is does that formula really work? Well now we finally get around to induction (I know it's taken a while).

To prove something by induction, we have to show it's true for the initial case, then show that if it's true for the nth case, it'll always be true for the (n+1)th case. The first step is easy:

F(1) = 1(1+1)/2 = 2/2 = 1

So our formula certainly holds true for the first case. Now assume that it's true for the nth case:

F(n) = n(n+1)/2

and if we add n to both sides of this equation we get:

F(n)+(n+1) = n(n+1)/2 +(n+1)

From our recursive function we get:

F(n+1) = n(n+1)/2 +(n+1)

Some algebra magic gives:

F(n+1) = n(n+1)/2 +2(n+1)/2 = (n²+n+2n+2)/2 = (n²+3n+2)/2 = (n+1)((n+1)+1)/2

Which is exactly what we would get if we plugged (n+1) in for every n.

So, the 100th number (our original goal) is:

F(100) = 100(101)/2 = 5050

Some final thoughts:

Can you figure out why these are called "triangular numbers?" (Googling = cheating)

I used heavy use of function notation here, if anyone has a problem with that, let me know.

Newsletter 7/21

Nick sent this in an email to us, but I wanted to upload it to keep our documentation up. The response from Joseph is posted as well.

Hey Team,

As usual, an excellent meeting. A lot of notes this week:

• Our schedual as of right now:
• 7/28 -- Mu Discussion (231-272)
  
• 8/4 -- Micah's Presentation
• 8/11-- General Discussion of Part 1 (1-272)
• 8/18 -- There was some discussion of doing a Chess day this day.
• There was a lot of Chess discussion in general today, anyone who wants to play email chess with me, let me know (by responding to this email).
• We played a game I found in This Book in which the rules were to "pick the smallest number that is not chosen by anyone else." The results are included below as well as in the Excel attachment.
• In reference to the TNT, we discussed mathematical induction. on Centophila, I'll be posting a short paper on the subject.

Game Results:

Joe	5	4	4	3	2	2
Eric	7	2	5	6	4	5
John	5	2	1	2	2	2
Veronica	7	3	1	6	1	1
Derek	3	3	3	3	3	3
Nick	27	4	8	4	4	4
Kera	9	1	2	3	1	4

 
See you next week,

-Nick

FYI, for those not present today, the results of 6 iterations of the game below
can be interpreted as follows:  

1. "game" results are the columns
2. the "winner" is the smallest positive integer not chosen by anyone else
(so, for example, the winner of game 1 is Derek, game 3 winner is Kera, etc.)
3. "learning" (of some sort) occurs because the results of each game's choices
are publicly known and the cumulative choices are part of the group's "memory"
as well.  

Obviously, the game is NOT interesting if there are just 2 players, since the 
right choice is 1 in each case (if you choose 1, you can't lose) and there should 
never be a winner.  With as little as 3 players, it gets interesting.  With too many 
(say, 25 or more) players, it also is probably not very interesting.  In between 2 and 
"too many" is where the interest lies. 

/Joe

Reading suggestion

Hey there. I thought I'd try to contribute something of substance while away, so I've picked out a few books that I think might jive well with the themes we've been discussing.

The First Law trilogy by Joe Abercrombie is a good answer to the fantasy tradition of grand narratives. It concerns itself largely with random chance and pointlessness. (It's also fantastic).

The Prince of Nothing by R. Scott Bakker is a great example of philosophical, theological and very gritty fantasy. It's a bit like Dune, and a bit like the Second Crusade.

Enjoy, and I'll see you all on the 28th.

Newsletter 7/14

Hey Team,

Here's a new and improved (proposed) game plan for the next few weeks:

7/21 -- TNT Discussion (199-230)
7/28 -- Mu Discussion (231-272)
8/4 -- Micah's Presentation
8/11-- General Discussion of Part 1 (1-272)

We did not discuss GEB again this week, instead we had a great discussion about Santa, and his relationship to both the platonic realm and Eric's mom, and a little bit of logic. Next week we should pick up from where we left off a while ago.

Note that before reading Chapter 9: Mumon and Godel (246-272), you should first read Chapter 1: The MU puzzle (33-42).

I'll see everyone next week,

-Nick

Prime Time: Reductio Ad Absurdum

Last week (7/7) we discussed the intuitionist philosophy, and it came up that the rejected Reductio Ad Absurdum. The example John used was the proof that there are infinitely many prime numbers (personally I think the irrationality of the square root of two is a little cooler).

Anyways, we didin't actually go over the proof, so here it is.

A quick refresher: A prime number is a number that can only be divided by one and itself. So 3 is prime (only 1 and 3 divide 3) and so is 7, but 9 us not (can be divided by 3) nor is 24 (2, 3, 4, 6, 8 and 12 all divide 24). The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19...

As you get higher and higher up on the number line, there are less and less prime numbers, so the natural question to ask is, do the prime numbers ever run out?

Well let's assume they do. Let's assume we eventually run out prime numbers. That must mean that there's a biggest prime number, right? Let's call our biggest prime number P. Now let's make another number, we'll call it Q. Where going to make Q but multiplying all of the prime numbers together, then adding one. Symbolically:

Q = (2*3*5*7*11*13*...*P) +1

So we do we know about Q? For starters, we know that Q can not be divided by any number between 1 and P. How do we know that? Well, Q is divided by any number between 1 and P, then the remainder will always be 1.

For the sake of comprehension, lets assume 7 is the biggest prime number (P). then:

Q = (2*3*5*7) +1 = 211

Q can't be divided evenly by 2, 3, 5 or 7 (try it, remainder 1 every time, right?). That means that there's either a number bigger than 7 (our "biggest prime") or 211 is prime (it's prime, trust me).

In general, every time we pick a P, we can always find a Q that's either prime, or has a prime factor larger than P. Therefore there's no largest prime number, and our original assumption (that P is the largest prime) is shown to be absurd. This is called Reductio Ad Absurdum (Reduction to the absurd, we say it in Latin because it reminds us that we are better than other people).

I'm not sure this is really a great outline, but I imagine most of you reading this have already seen this a few times before. If I'm wrong, and if it needs to be cleared up a little (or if you notice a mistake I've made) please leave a comment.

Newsletter 7/7

Hey Team,

Here's a (proposed) game plan for the next few weeks:

7/14 -- TNT Discussion (199-230)
7/21 -- Mu Discussion (231-272)
7/28 -- General Discussion of Part 1 (1-272)
8/4 -- Micah's Presentation

We did not discuss GEB this week because we were running on depleted numbers, next week we should pick up from where we left off a while ago.

Note that before reading Chapter 9: Mumon and Godel (246-272), you should first read Chapter 1: The MU puzzle (33-42).

I'll see everyone next week,

-Nick

I have ennui.

He has ennui!

Dilbert

Found by Joe, posted by Nick, Loved by all.

Newsletter 6/30

Hey Team,

So I a few days late this week, sorry.

Some points:

• For next week (7/7) read Crab Canon (pg 199) and Chap. 8 (pg 204).
  
• Big thanks to Kera for an enlightening presentation.
• At the end of this month (7/28) Micah will be doing a presentation.

-Nick

Hi everyone,

Thanks for being so receptive to my presentation. Here's a copy of it for those who missed parts of it.

It was great to get all your feedback, thanks again!

Please do send me any notes you all have on what you see as the future of art and what you believe would be the most important aspects of our manifesto.

Kera's Philosophy Presentation

New Book List

I added a new book list with the additions you all suggested that we can work from after we finish Gödel, Escher, Bach which will allow us to zoom in further on some of the main ideas we've been exploring.

I think it will work well if we pick one book from each section that we all read together (like one of the math or science books). The books from other disciplines we can choose whether or not to read individually and those who do read them can present on them. This is a good way of exploring the full constellation of these theories and ideas by each bringing our own areas of interest and expertise to the group.

You can get to it by clicking on the Book List link on the left. Let me know if you have others you want to add.

Great Article

You all may have already seen this, it was published in April, but just in case:

http://www.wired.com/wiredscience/2009/04/newtonai/

I especially enjoyed the comment thread that follows.

I miss you guys!

Kelsey

Message Table

Ruth Typed up the table of messages after Tuesday's meeting. I thought composing this table was the most fun and the most educational part of the night. Here it is:

	Frame	Outer	Inner
Record	Disc	Sound	Music/Emotion
*DNA	Aperiodic crystal	Genotype (Genes)	Alleles (Traits)
Message in a bottle	Paper in glass container, floating in water but dry	Letters in message, signifier, "h" "e" "l" "p"	Signified HELP!
Painting	Frame	Colors and Lines	Feelings/Idea depending on the period
Bird Flying South	Meat, Feathers, Sky, Light	Science	Season, Air exists! Laws of Aerodynamics
π	numerals	"3." "1" “4” “1” “5” “9” etc.	A circle's circumference divided by its diameter
Virus	Protein stuff	RNA	Copy Me!
Billboard	Wood, paper, Position	Images, Logos, Alphabet	Buy Me!
White dove	Meat & feathers	(Western) Cultural reference	Love (Peace)
Page 176 of GEB	Paper with ink	“CCGTCAGG…”	DNA*

Thanks so very much Ruth for typing this up. Does anyone want to add anything more? (leave a comment!).

This Week's Newsletter

Hey Team,

Thanks again to everyone for challenging me this week. Big thanks to Hope for giving us a place to meet.

Some announcements:

• We're reading Chromatic Fantasy, And Feud (pg 177) and Crab Canon (pg 199).
• Chapter VII (pg 181) is Propositional Calculus. This is probably going to be one of the hardest things for most of us. Write down your questions.
• I'm really going to try to bring food this time. Seriously.
• Two weeks from now, Kera will be presenting (6/30).
  
• While you're here on Centophilia, leave some comments.

-Nick

publishing pdf files into a blog

Nick ran into issues with getting math symbols into his post, and used separate pictures for each. If anyone prefers to upload a pdf when using images, graphics, etc., here is a link which explains how to do it. 

http://www.bloggertipsandtricks.com/2007/09/embed-pdf-file-into-post.html

Largrangian Interpolation

Today I mentioned something about interpolation but breezed over some of the algebra intensive parts because I know that for the most part you're not all enthusiastic about Euclid (that alliteration is intentional, I also considered "giddy about Gauss" and "pleased with Pythagoras") I feel I've done the world a disservice, so here's a post pretty much no one will read.

This is called Lagrangian Interpolation, named after some guy Lagrange. Given any number of points, you can create (find?) a polynomial that describes it. For the sake of simplicity, I'll use just three points, but it'll be really obvious how you can expand to any n+1 number of points.

Consider three points, for the sake of avoiding subscript we'll call them (a,A),(b,B) and (c,C). This is just like your high school algebra class, the first number (the lowercase letter) tells you how far over in the x (horizontal) direction and the second (capital) tells you how far up in the y (vertical). It's like Battleship. So if (a,A) = (3,4) you'd go over three and up four (grab some graph paper and play along).

Now here's the formula you've all been waiting for:

(I’m going through formatting hell right now, so please bear with me).

With this equation, if x = a, both the second and third terms reduce to zero, and the first term reduces to A:

So the curve passes through the point (a,A) (and (b,B) and (c,C)). I feel like it might be a little confusing at this point, but it’s difficult to explain without a white board, so deal with it.

Stop! Example time. (like Hammer time, but without baggy pants). Consider the points (1,1), (2,3) and (5,8). Ultimately our goal is to find the equation for a curve that passes though all of these points. We can use Lagrange interpolation to find the equation:

And if we really wanted to (and we really do) we could reduce it even further:

Which actually isn’t too intimidating. Hooray for algebra.

This connects directly to the complexity stuff we were talking about quite nicely. You can see how lengthy the equation is for just three points, and it just gets obnoxiously bigger as you add more and more points.

For 7 points: (1,1),(2,8),(3,2),(4,7),(5,0),(6,6),(7,0) we get this crazy graph.

This can be described by the offensive equation:

-0.2681x⁶ + 6.4208x⁵ - 60.743x⁴ + 287.9x³ - 712.49x² + 858.18x – 378

The more and more “random” points we add, the worse and worse our descriptive formula gets. At this point, it’s obvious (I hope) that the descriptive equation for random points is just as complex as the bunch of points themselves.

If you’ve gotten this far, leave a comment or something so I can get a feel for whether or not there’s a call for something like this.

-Nick

Complexity, criticality and meta-modernity

-What brings novelty and persistence together in the same condition? Modernity is characterized by the new, and postmodernity by recyclage of the old. Meta-modernity will have to synthesize both. One of the conceptual themes we've been studying all along achieves such a synthesis: complexity. Complex systems are on the edge of chaos. Their intricate internal structure allows them to maintain their organization in the face of changing conditions, while also allowing them to adapt and change. The complex brings together novelty and persistence because it is that state which allows enough chaos for change and enough order for recurrence at the same time.

-Push order to its limit and it becomes chaotic. Push chaos to its limit and order emerges. In between order and chaos is a critical region of complexity. Criticality, too, will be a central motif of meta-modernity. What is criticality like? Critical states are scale-invariant: they possess structures of all sizes on all scales. In the critical phase-transition of a magnet, there are clusters of north-pointing atoms and clusters of south-pointing atoms of all sizes, from one atom to system-spanning percolating clusters. The geometry of these mixed clusters is fractal. Critical states are also coherent: what happens in one part of the system quickly affects the rest of the system. And critical states are optimally free. A critical system has all its possible states equally present; it can transform into any of its states in a minimum number of steps.

-At this critical moment in history, the synthesis of modern and postmodern can be seen as between them rather than as beyond them. Meta-modernity is a critical phase transition in culture, a fractal boundary between different cultural states. Categorical distinctions are neither erased nor ossified in this critical state. Instead, every entity can become anything at any time, in one step. Entities turn into information-bearing monads that can flip states spontaneously. A monad can choose to be living or non-living, art or non-art, conscious or unconscious, human or inhuman.

This week's Newletter

Hey Team,

Everyone already got this as an email, this is mostly for me to make sure I get what I'm doing.

Just some reminders:

• Next Tuesday we'll be back in the Learning Center's Conference Room.
• We'll be reading Little Harmonic Labyrinth (p 103) and Canon by Intervallic Augmentation (pg 153).
• I'm planning on resuming my duties as food bringer (not really a reminder... but what the hell).
• Three weeks from now, Kera will be presenting (6/30)
  

Also, we briefly discussed our mutual love for Arrested Development. For those of you out of the loop, WATCH IT HERE. Seriously, one of the best shows ever.

Used copies of Godel, Escher, Bach are really cheap on Amazon. (under $10 including shipping!)

Thanks everyone for this phenomenal opportunity to push my mind to the limit, and a cosmic sized thanks to Joe for dinner.

Modernism vs. Postmodernism

Some of the characteristics of modernism and postmodernism that we talked about at the last meeting. (From Ihab Hassan's The Dismemberment of Orpheus, full list here)

Modernism.....................................Postmodernism

Form (conjunctive, closed)...............Antiform (disjunctive, open)

Design.............................................Chance

Art Object/Finished Work................Process/Performance/Happening

Creation/Totalization......................Decreation/Deconstruction [Derrida]

Centering........................................Dispersal

Genre/Boundary..............................Text/Intertext [Julia Kristeva]

Selection.........................................Combination

Narrative/Grande Histoire...............Anti-narrative/Petit Histoire [Lyotard]

Determinacy...................................Indeterminacy

We also talked quite a bit about:

Universality.....................................Relativity

others to explore further

Modernism...................................Postmodernism

Romanticism/Symbolism...............Pataphysics/Dadaism

Hierarchy.......................................Anarchy

Mastery/Logos..............................Exhaustion/Silence

Synthesis......................................Antithesis

Presence.......................................Absence

Paradigm......................................Syntagm

Root/Depth...................................Rhizome/Surface [Deleuze & Guattari]

Interpretation/Reading..................Against Interpretation/Misreading

Signified........................................Signifier

Lisible (Readerly)...........................Scriptable (Writerly) [Roland Barthes]

Type..............................................Mutant

Paranoia........................................Schizophrenia [Deleuze & Guattari]

God the Father..............................The Holy Ghost

Metaphysics..................................Irony