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Max Maxfield

Heteromorphic Hobby Projects

Max Maxfield
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EdV
EdV
8/21/2012 3:59:12 PM
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Re: Any photos?
I was hoping to find a group theoretic solution to the SOMA puzzle as part of aa cahllenge presented to Leonardo's Basement in 2006 by the Minnesota State Fair Commitee.  The challenge "Prove That Math Is Fun"

SOMA in general:

http://www.fam-bundgaard.dk/SOMA/SOMA.HTM

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

Leonardo's Basement "Proof"

http://www.leonardosbasement.org/2slideshow2.php

 

I want to make a bigger one!

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rfindley
rfindley
8/21/2012 2:26:33 PM
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Re: Any photos?
@EdV,

That brings back memories!  I was a math nerd in high school, and as part of a state math competition, I competed in the "Oral Presentation" section.  The topic that year was "Group Theory".  So I had to learn the subject such that I could teach it to others, answer questions, etc.

Unfortunately, the only thing I really remember is that Group Theory lets you manipulate whole sets (groups) of numbers or symbols at a time, instead of individual values.  And a main advantage is that you can then work at a more abstract level.

The Rubik's cube is a great sample application:  No matter the state of the cube, there are only 12 possible operations (twists of the cube) that can be performed, and each of those operations will result in a different state.  If you group all equivalent/symmetric 'states' of the cube into Groups, you can then solve all possible states of the cube with a relatively small set of 'operation sequences'.  You can also graph the states and operations (i.e. create a state machine) to prove that all states are reachable within 20 operations.

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EdV
EdV
8/21/2012 11:11:56 AM
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Re: Any photos?
I also I am trying to get my head around a branch of mathematics called Group Theory which is often described as the mathematics of symmetry.  When ever I use the word "group" it kind of gets me pondering about what is the context of "group" here.

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Max Maxfield
Max Maxfield
8/21/2012 10:03:41 AM
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Re: Any photos?
@EdV: On re-reading your comment I saw "teaching piano to groups (people generally)"

... as opposed to what? Parrots ... dogs ... cats ... ?

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Max Maxfield
Max Maxfield
8/21/2012 10:02:22 AM
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Re: Any photos?
@EdV: I just received the pics -- they are FANTASTIC -- I can't wait to create a slide show so everyone can see them -- but first we need some more submissions from the others... (hint hint)

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EdV
EdV
8/21/2012 9:03:05 AM
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Re: Any photos?
Oddly enough one of my current "hobbies" (ongoing since 1998) is teaching piano to groups (people generally).  One approach I am working on involves pairing "Starry Night by van Gogh" with the opening bars of "Moonlight Sonata" by Beethoven.  Participants do a "note spelling exercise" on a piece of sheet music with specific crayon colors assigne to specific notes; red = C, orange = D, for instance. Next to the music sheet is a panel of a painting.  The colors they use on the music sheet are the only colors used on their assciated pice of the painting.  The result is a color coded mosaic of sorts that one can play music from.  Provided they know the code.

The latest work involves pairing Tchaikovsky's Nutcracker with painting by Paul Klee for an elementary schooll classical music program in Minneapolis.

 

I will send you some pics.  

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rfindley
rfindley
8/20/2012 4:55:46 PM
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Re: Heavy hobby
Yes, I saw that coming!  FPGAs are definitely part of the plan, but my workflow is more suited to software-only for now.  The design will eventually partially serialize the massively-parallel neurofunction network through a less-massively-parallel FPGA network, much as a modern graphics card serializes billions of vertices through a few hundred parallel processing units.

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Max Maxfield
Max Maxfield
8/20/2012 3:59:48 PM
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Re: Heavy hobby
@rfindley: You know what my next question is going to be, don't you (grin)?

Are you using FPGA(s) to model your "neurons"?

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rfindley
rfindley
8/20/2012 3:44:21 PM
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Re: Heavy hobby
@Max, I'm not currently using Fuzzy Logic, though I have used it in the past for a few small AI projects.  For artificial general intelligence (AGI), I have my own model of neurofunctional networking, which takes cues from neurophysiology to implement intelligence using building blocks at a level a bit above the neuron.

For comparison: If you wanted to emulate an ARM processor on an x86, you wouldn't emulate the ARM's transistors.  You would emulate at the instruction-set level.  Likewise with the brain, where a neuron roughly equates to a transistor.

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Max Maxfield
Max Maxfield
8/20/2012 2:52:06 PM
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Any photos?
@All: I'd really like to see photos of past or on-going projects so I can build a slide show to share with everyone...

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