http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html

Pretty neat.  I love the hubris that just oozes from everything Wolfram 
says, even tho what he says is pretty cool.  "See? If you just listened 
to me, you'd realize all your engineering is wrong."

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Darren New wrote:
> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html
> 
> Pretty neat.  I love the hubris that just oozes from everything Wolfram 
> says, even tho what he says is pretty cool.  "See? If you just listened 
> to me, you'd realize all your engineering is wrong."

OOC, what is "hubris"? (And how the heck do you pronounce that?)

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It's funny how close the words "provably" and "probably" are. Prone to
cause confusion... :P

-- 
                                                          - Warp

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On Wed, 24 Oct 2007 20:02:26 +0100, Orchid XP v7 wrote:

> Darren New wrote:
>> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html
>> 
>> Pretty neat.  I love the hubris that just oozes from everything Wolfram
>> says, even tho what he says is pretty cool.  "See? If you just listened
>> to me, you'd realize all your engineering is wrong."
> 
> OOC, what is "hubris"? (And how the heck do you pronounce that?)

http://www.google.com/search?q=define%
3Ahubris&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-
US:official&client=firefox-a

(or http://tinyurl.com/26hb4y )

For pronunciation:

http://dictionary.reference.com/search?q=hubris&x=0&y=0

Has a pretty good reference.

Jim

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On Wed, 24 Oct 2007 11:52:46 -0700, Darren New wrote:
> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html
> Pretty neat.

Have to note that I have no idea how that machine
that is represented as a pile of gold supposedly works.

-- 
Joel Yliluoma - http://bisqwit.iki.fi/
: comprehension = 1 / (2 ^ precision)

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Joel Yliluoma wrote:
> On Wed, 24 Oct 2007 11:52:46 -0700, Darren New wrote:
>> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html
>> Pretty neat.
> 
> Have to note that I have no idea how that machine
> that is represented as a pile of gold supposedly works.

I believe the six states are these:

cur	read	new	write
State	color	state	color	move

up	orange	up	yellow	left
up	yellow	up	orange	left
up	white	dn	yellow	right

dn	orange	up	white	right
dn	yellow	down	orange	right
dn	white	up	orange	left

(Of course, if you don't know what a Turing machine is and how it's 
"built", that table there will be equally babelicious.)

The "pile of gold" is a trace of execution starting with a line (or 
tape) of all white except one pixel of maybe orange(?) under the head, 
and in an unknown up/down position. (Unknown as in I can't tell from the 
picture, not unknown as in the author of the picture didn't know.)

Follow the link to the 110 rule to see more examples of how to read the 
things.

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Joel Yliluoma wrote:

> Have to note that I have no idea how that machine
> that is represented as a pile of gold supposedly works.

The "pile of gold" represents the activity of the machine (for a 
specific initial configuration). The little boxes and dials represent 
the design of the machine itself.

Essentially, you have a "tape" that extends to infinity in both 
directions. That tape is divided up into squares, each of which can be 
white, yellow or orange (in this particular example). The machine itself 
can be in one of two different modes or "states". The machine has a 
read/write head that it can shuffle over the tape.

At each point in time, depending on which state the machine is in and 
what colour square is under the read/write head, the machine changes to 
a new state (possibly the one it was already in), writes a new colour to 
the square on the tape (possible the same colour that was already 
there), and moves the tape head 1 square left or right.

Then we repeat the operation all over again. And that's how the machine 
runs, basically.

Each row in the graph represents the contents of the tape at a 
particular point in time. What you're looking at is actually the 
*compressed* graph; generally Turing machines spend ages winding the 
head back and forward across the tape without actually changing 
anything. The compressed graph only shows the tape when something 
actually *changes*. This makes the graph much smaller, while still 
showing you the essential features.

If any of that made any sense...



(Turing machines are interesting because you can design one such that if 
you encode two numbers into patterns of coloured squares and put them on 
a tape, and then run the machine over the tape, eventually it produces 
the sequence of coloured squares representing the sum of the original 
two numbers. In other words, you can design a Turing machine that 
performs mathematical addition. And many other operations besides.

Now, the *universal* Turing machine is just a Turing machine that can 
simulate any possible Turing machine. Since you can build a Turing 
machine for any possible algorithm, it follows that a universal Turing 
machine can perform any possible algorithm...)

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Orchid XP v7 wrote:
> Since you can build a Turing machine for any possible algorithm, 

Or, more precisely, the word "algorithm" is defined (at least in these 
realms) as "those calculations for which a Turing machine can be 
designed to perform."

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Darren New wrote:
> Orchid XP v7 wrote:
>> Since you can build a Turing machine for any possible algorithm, 
> 
> Or, more precisely, the word "algorithm" is defined (at least in these 
> realms) as "those calculations for which a Turing machine can be 
> designed to perform."

Point being that many people know what an algorithm is, but few have 
heard of a Turing machine (and fewer know what one is). ;-)

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Darren New <dne### [at] sanrrcom> wrote:
> Orchid XP v7 wrote:
> > Since you can build a Turing machine for any possible algorithm, 

> Or, more precisely, the word "algorithm" is defined (at least in these 
> realms) as "those calculations for which a Turing machine can be 
> designed to perform."

  That sounds a bit like a circular definition. "A turing machine is
something which can perform any algorithm." "An algorithm is something
which a turing machine can perform."

-- 
                                                          - Warp

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