History Of The Fano Plane

ok - fano is about knowing an answer: the transavanian lottery

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

network effect - the internet as finite geometry.

why it's helpful

http://math.ucr.edu/home/baez/octonions/node4.html

wiki ref:

history:

http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Fano.html

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

wiki: Gino Fano: http://en.wikipedia.org/wiki/Gino_Fano

Classic quote:

As a basis for our study we assume an arbitrary collection of entities of an arbitrary nature, entities which, for brevity, we shall call points, but this is quite independent of their nature.

plane was documented in 1892

http://www.freewebs.com/desargues/combinatorics.htm

Chris Niemann, All Roads Lead to the Golden Ratio
The celebrated Fano Plane (Gino Fano, 1875 - 1950) will form the basis for this discussion. If each of the seven lines of the Fano Plane is given a certain direction, these vectors can be made to correspond to the seven imaginary units of the octonions. By introducing coordinates onto the two dimensional (2-D) Fano Plane, one can easily move into 3-D and 4-D by appending one or two coordinates, respectively. Deleting one or two coordinates leads one back to the 1-D Fano Line and the 0-D Fano Point, respectively. The Fibonacci Formula combined with the standard quotient sequence induces the Golden Ratio, regardless of the number system used.

http://www.math.fsu.edu/~smith/maabbr2005/

from fano to shannon

c e channon teams up with robert fano for information theory
robert: http://en.wikipedia.org/wiki/Robert_Fano

"I didn’t like the term Information Theory. Claude didn’t
like it either. You see, the term ‘information theory’
suggests that it is a theory about information – but it’s not.
It’s the transmission of information, not information. Lots
of people just didn’t understand this… I coined the term
‘mutual information’ to avoid such nonsense: making the
point that information is always about something. It is
information provided by something, about something.
[Interview with Fano, R. 2001]"
http://cc.oulu.fi/~llh/IT2006/luentomateriaalia/Fano.pdf
encryption

http://www.maths.sussex.ac.uk/Staff/JWPH/PROF/lecture.pdf

shannon picked up fano system for encryption/decryption - > DRM

Shannon: http://en.wikipedia.org/wiki/Claude_Shannon

"The fundamental problem of communication is that of reproducingt one point either exactly or approximately a message elected at another point."

huffman

student of R fano
Note that no code word is a prefix of any of the other code words, hence, this code can be decoded unambiguously. Huffman discovered his famous approach to data compression as an "exercise" in a class assigned by Robert Fano (son of Gino Fano, for whom the finite projective plane with 7 points is named) of MIT.

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

Huffman codes used:

"Huffman Codes" are used in nearly every application that involves the compression and transmission of digital data, such as fax machines, modems, computer networks, and high-definition television (HDTV), to name a few.

he never patented - so it's widely used

wiki: hoffman: http://en.wikipedia.org/wiki/David_A._Huffman

leads us to 'information theory'

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

(how to get a signal through to someone via noise) - nice on for the marketeers!

applet that shows Huffman coding really well

http://www.cs.sfu.ca/cs/CC/365/li/squeeze/

step by step example

http://www.cs.pitt.edu/~kirk/cs1501/animations/Huffman.html

non geek version of hoffman's work

http://www.huffmancoding.com/david/scientific.html

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