From stuart at gathman.org  Thu Mar  2 00:08:40 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Thu, 2 Mar 2006 00:08:40 -0500 (EST)
Subject: [Verba] Meeting summary
Message-ID: <Pine.LNX.4.44.0603012042410.17704-200000@fairfax.gathman.org>

Rebecca and Jillian worked some more on the robots game in python.  
(Attached.) You can now move around a black dot on the screen with the
keyboard!  While considering edge mappings, we very briefly discussed
"topology" - the properties of shape that are invariant under stretching.  
The wrap around edge mapping we chose is topologically a torus (donut
shape).  We will have to investigate that more, because it is closely
related to - you guessed it - group theory.

Speaking of which, I mentioned using group theory to chose a spouse. :-)
(Disclaimer - the assumptions in this model are vastly over simplified and
are for instructional purposed only.  In particular, I would question the
assumption that candidates can be rank ordered.  And, of course, the goal
of the "courtship" movement is by careful preparation to have only one
proposal which you accept.)

It works like this (taken from "The Equation that Couldn't be Solved"):  
Assume you will get 4 marriage proposals, and that if you could consider
all the proposals at once, you could rank them from worst to best.  
However, you get only one proposal at a time in random order.  And you
must accept or reject each in turn.  Your strategy is to reject k - 1
proposals, then accept the first proposal that is better than any previous
proposal.  What is the optimal value of k?

There are 24 permutations of the rank order in which your proposals may 
come:

1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431,
3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321

For k == 1, you accept the first proposal.  6 of the 24 permutations have
the best proposal come first.  So your chances are 6/24 or 1 in 4 of getting
the best match.

For k == 2, you get the best match for cases 1423, 1432, 2143, 2413, 2431,
3124, 3142, 3214, 3241, 3412, 3421.  That makes your chances of getting the 
best 11/24.

For k == 3, your chances are 10/24.  For k == 4, you are back down to 6/24.

So, for 4 expected proposals, the optimum strategy is to turn down the first,
then accept the first that is better than any previous proposal.

For 5 to 8 expected proposals, the k == 3 is optimum (turn down the first 2,
the accept the first that is better than any previous).

For a large number, 'n', of proposals, k == 1 / e is optimum.

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.
-------------- next part --------------
from livewires import *

def place_player():
  global player_x,player_y
  player_x = random_between(0,63)
  player_y = random_between(0,47)
  return circle(player_x*10+5, 10*player_y+5, 5, filled=True)

def move_by(x,y):
  global player_x,player_y
  player_x += x
  if player_x < 0: player_x = 63
  if player_x > 63: player_x = 0
  player_y += y
  if player_y < 0: player_y = 47
  if player_y > 47: player_y = 0
  move_to (player, player_x * 10 + 5, player_y * 10 + 5)
  
def move_player(k):
  if k == "1":
    move_by(-1,-1)
  if k == '2':
    move_by(0,-1)
  if k == '3':
    move_by(1,-1)
  if k == '4':
    move_by(-1,0)
  if k == '5':
    move_by(0,0)
  if k == '6':
    move_by(1,0)
  if k == '7':
    move_by(-1,1)
  if k == '8':
    move_by(0,1)
  if k == '9':

    move_by(1,1)
  if k == 'q':
    finished = True
  #teleport()

begin_graphics()
allow_moveables()
player = place_player()
finished = False
while not finished:
  for k in keys_pressed():
    move_player(k)
  sleep(0.25)
end_graphics()


From stuart at gathman.org  Fri Mar 17 18:17:34 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Fri, 17 Mar 2006 18:17:34 -0500 (EST)
Subject: [Verba] Meeting Summary
Message-ID: <Pine.LNX.4.44.0603171800420.7550-100000@fairfax.gathman.org>

Last week (I'm behind on summaries), we cut up paper to model the many
ways of gluing together the edges of a screen (choices for what to do when
reaching the edge of the screen in a 2D game).  Most of the resulting 2D
surfaces can be modeled with paper, but 2, the Klein bottle and projective 
plane require 4 dimensions.  We then added a place_robot function.

This week, I went to the Chenettes, and Jilian joined via AIM.  Rebecca
and I made the place_robot function actually work, while Jilian figured
out how to CD her Windows Command prompt to the proper directory and run a
python script.  Then I played some hymns in Jazz style for Rebecca, who
very sweetly professed to like them.

Let me remind everyone that our excursions into group theory are not 
directly related to programming, but were needed to understand a problem 
domain of interest (solving Rubik's cube).  But, understanding it will 
help you excel at Math - especially abstract algebra and modern physics.

To build programming skills, you need to keep doing it - just like 
learning an instrument or sport.  Try to come up with problems to solve 
using your skills, and solve them.

Here is a simple problem related to group theory.  Remember that any group 
(including Rubik's cube) is isomorphic to a permutation group.   A basic 
operation needed for dealing with permutation groups is to list their 
members.  We introduced Python "generators" for the deal_position 
function.  This assignment asks you to create a generator that lists all 
the permutations of a sequence.  It should be written as a generator.
For instance, 

  def permute(s):
    ... blah
    blah ...
    ... yield something
    ... blah
  
print permute([1,2,3])

should output:

[1,2,3]
[1,3,2]
[2,1,3]
[2,3,1]
[3,1,2]
[3,2,1]

or the same permutations in any order.  Do not assume that the members of 
the permutation group are numbers.  They can be any Python object.

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.



From stuart at gathman.org  Mon Mar 20 18:09:02 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Mon, 20 Mar 2006 18:09:02 -0500 (EST)
Subject: [Verba] Rubik's cube robot
Message-ID: <Pine.LNX.4.44.0603201805130.10771-100000@fairfax.gathman.org>

Taylor wanted some C source code to look at for solving the cube (skipping
the whole group theory thing).  Instead of just mailing the code, I 
thought I'd show y'all a Lego Mindstorms robot that solves cubes.

http://jpbrown.i8.com/cubesolver.html

The link to the C code is at the bottom under part 6.  It would sure be
cool for the computer club to have a robotics kit (Lego or other).

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.



From stuart at gathman.org  Wed Mar 22 19:10:56 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Wed, 22 Mar 2006 19:10:56 -0500 (EST)
Subject: [Verba] Last Meeting Summary :-(
Message-ID: <Pine.LNX.4.44.0603221831150.31681-200000@fairfax.gathman.org>

	Copyright Law

Somehow we started out with a discussion of Copyright law and fair use.
No, it is not OK to give copies of CDs to your friends without 
permission.  Yes, it is OK to make copies for your own use, including 
copying to different formats for Car, Ipod, etc.  Internet friendly 
publishers often due give permission for limited copies.  I showed

http://magnatune.com 

as an example.  MP3s from that site be copied according to a
Creative Commons (http://creativecommons.org) license:

http://magnatune.com/info/openmusic

Mrs. Brown - I happened to have a copy of Magdalena with me:

http://magnatune.com/artists/albums/joglaresa-magdalena/

These are Medieval hymns in Latin (a few in old French).  Good
practice for Latin students.  You (and students) can play and download the MP3s
free of charge, but the "non-commercial" clause on the CC license I think
means you need to buy a license for the school to play the songs
for the students as part of school:

https://magnatune.com/artists/license/?artist=Joglaresa&album=Magdalena&genre=World

We then discussed the DMCA and the case of "DVD Jon":

http://en.wikipedia.org/wiki/Jon_Johansen

who didn't actually spend time in Jail as I alleged (although someone
else did for similar charges).

	Permutations

No one else had come up with a permutations program, so we reviewed
mine.  (Attached).

	Intelligent Design

Somehow, permutations led to a discussion of the difference between
complexity and "specified" complexity, and then to the philosophical 
basis of materialism.

	Summer School

   Reading

I loaned "Adventures in Group Theory" to Jillian, and Rebecca
currently has "The Equation that Couldn't be Solved".  My new copy
of "G?del, Escher, Bach" arrived a few minutes after I left for Ad Fontes :-(
I am reserving it for Computer Club members.  My old copy I already
loaned out it turns out.

GEB is directly related to computing - and should take precendence
over the group theory books for learning programming.  Group theory
is a "problem domain" (as well as being interesting and several
Club members being Rubik's Cube fanactics).

   Hands On

A big road block for the club was learning to handle shell prompts / command
prompts and basic system administration like creating directories / folders
(and finding them again).  My (probably ambition) recommendation is for
students to spend their entire summer going dumpster diving for junk PCs,
refurbishing them, and installing free/open software on them (e.g. Linux).
They will become confidently familiar with BIOS settings, hardware diagnosis
and repair, boot sectors, partitions, file systems, firewalls, etc.  :-)

I'll probably have to settle for something less ambitious, if anything - like
maybe an old system lying around the house, or installing an extra disk
drive for dual booting between Windows and Linux.

On that note, Taylor has obtained an external 10G firewire disk drive
for his Mac Mini.  His project is to install PPC Linux on it.  Way
to go Taylor!  (Here's hoping you don't accidentally wipe your OSX disk.)

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.
-------------- next part --------------
def permute(s):
  if not s:
    yield s
    return
  if type(s) is str:
    for i,first in enumerate(s):
      for cc in permute(s[:i]+s[i+1:]):
	yield first + cc
  else:
    for i,first in enumerate(s):
      first = [first]
      for cc in permute(s[:i]+s[i+1:]):
	yield first + cc

for x in permute('abc'):
  print x
for x in permute([1,2,3]):
  print x

From stuart at gathman.org  Sat Mar 25 14:12:56 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Sat, 25 Mar 2006 14:12:56 -0500 (EST)
Subject: [Verba] The Interconnectedness of all Things
Message-ID: <Pine.LNX.4.44.0603251332190.28414-100000@fairfax.gathman.org>

"And HE, [Christ], IS before all things and in and through Him the universe is
a harmonious whole." Collossians 1:17 WEY

	Question 1

In our last meeting, we talked about how Materialism denies the
reality of "meaning".  We talked about the game of Boggle?, and the
difference between complexity and specified complexity.  Specified
complexity means certain combinations are intelligently chosen beforehand.
The word "intelligence" literally means "to choose between".  I claimed
that symbols have meaning when they are chosen by an intelligent
person.

In "G?del, Escher, Bach" on page 50, Hofstadter gives his definition
of "meaning" - meaning is an isomorphism between symbols and some
portion of "reality".

Are these definitions of "meaning" the same, different, related?

	This guy just doesn't know when to quit ...

    Exercise 1

At the bottom of page 39, Hofstadter describes a genie with all the
time in the world creating theorems in the MU system.  Write a python
program to output MU theorems using the method described.  Besides
time, what limits the number of theorems the program can output?

    Exercise 2

In the newpaper, there is a "Jumble" puzzle.  Write a program that
takes jumbled letters as input, and lists all permutations that
are english words.  "English word" is defined as any word occuring
in the "Official Scrabble Players Dictionary" version 3.  You can
download this at:

    http://gathman.org/python/OSPD3.gz

You will need some things we didn't mention in class.  Use the Library
Reference and Module Index at http://www.python.org/doc/

Hints:  

a) you will need the gzip module to unpack OSPD3.gz

b) you will need to use File objects:

    http://docs.python.org/lib/bltin-file-objects.html

Here is the output from my version:

$ python2.4 jumble.py
~ terp
PERT
~ alksf
FLASK
~ an
AN
NA
~ 

I will share my solutions when you are ready.

You can learn a lot from looking are python code from people all over
the world:

    http://www.python.org/community/

	Future Directions (Next year?  Summer?)

Python is a very high level imperative language.

a) We can go low level and tackle assembler code and Knuth.  A Linux or Mac
   system is required.  Windows is too dangerous to play around with assembler
   (and you will learn basic precautions such as not testing your cool
   brand-new assembler program as root or even with your normal login).

b) We can go non-imperative and tackle Prolog or Functional programming.

c) We can go mid level and look at Forth or C.

d) We can go really low level and look at logic gates and memory cells
   in various technologies from TinkerToys? to CMOS.

e) We can go really hands on and buy a robotics kit to play with.

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.



From stuart at gathman.org  Sat Mar 25 17:31:37 2006
From: stuart at gathman.org (Stuart D. Gathman)
Date: Sat, 25 Mar 2006 17:31:37 -0500 (EST)
Subject: [Verba] Musical Offering
Message-ID: <Pine.LNX.4.44.0603251729480.29850-100000@fairfax.gathman.org>

It adds a lot to a reading of GEB to be able to hear the music:

http://www.amazon.com/gp/product/B000050GK0/

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.