X-Google-Language: ENGLISH,ASCII-7-bit
X-Google-Thread: 107c0a,299d0bc3500e024c
X-Google-Attributes: gid107c0a,public
X-Google-Thread: f4886,dbda22a9ac78d3f2
X-Google-Attributes: gidf4886,public
X-Google-Thread: 10ffde,299d0bc3500e024c
X-Google-Attributes: gid10ffde,public
X-Google-Thread: 109d8a,535e80416e502a8c
X-Google-Attributes: gid109d8a,public
X-Google-Thread: f996b,535e80416e502a8c
X-Google-Attributes: gidf996b,public
X-Google-ArrivalTime: 1994-07-31 23:39:45 PST
Path: 
 bga.com!news.sprintlink.net!hookup!yeshua.marcam.com!usc!howland.reston.ans.net!news.cac.psu.edu!news.pop.psu.edu!psuvax1!psuvax1!flee
From: flee@cse.psu.edu (Felix Lee)
Newsgroups: sci.bio,alt.sci.physics.plutonium,sci.chem,alt.ascii-art,sci.math
Subject: Art, math, realism, ascii (Re: PARASITES INSIDE OF VIRUSES?)
Followup-To: alt.ascii-art
Date: 01 Aug 1994 06:39:17 GMT
Organization: Penn State Comp Sci & Eng
Lines: 55
Message-ID: <FLEE.94Aug1023918@colossus.cse.psu.edu>
References: <317b4o$4pp@dartvax.dartmouth.edu>
 <317jrc$ale@dartvax.dartmouth.edu>
	<318qce$fna@jac.zko.dec.com> <31bdjr$ppn@dartvax.dartmouth.edu>
	<31bp9n$a1h@riscsm.scripps.edu> <31e91i$5fk@dartvax.dartmouth.edu>
	<FLEE.94Jul30161307@dictionopolis.cse.psu.edu>
	<31hsf7$e1o@dartvax.dartmouth.edu>
NNTP-Posting-Host: colossus.cse.psu.edu
Xref: bga.com sci.bio:4881 sci.chem:7394 alt.ascii-art:10760 sci.math:17282

Ludwig Plutonium:
>  Some math theorem which states that given a math object, given a
>finite number of bits, then there is a maximal art rendering of that
>object and all others are inferior.

This is *rendering*, which is perhaps the least interesting aspect of
art.  You may be able to develop some maximization function that
describes how faithful a particular rendering is to a particular
abstract conception, but so what?

Consider a straight line.  Since a mathematical line has no thickness,
a perfect rendering would use no ink, no bits.  This is useless for
most purposes.

Let's restate the problem as: find the best rendering of a particular
thin, rectangular area.  (Note that this choice is arbitrary.  Why not
a thin, sinusoidal area?)

If you want to render it in grayscale pixels, then the anti-aliasing
algorithm is arguably the best method.  (Though this is hardly
a trivial argument.)

But in ascii, the choice of an optimization function is far from
straightforward.  Let's simplify even further: ignore the problem of
the different shapes and proportions of different fonts.  Limit the
problem to just one particular font ("courr12" from X11) that's
represented by 1-bit pixmaps.

An obvious optimization function is to count the number of "on" bits
within the thin rectangle and subtract the number of "on" bits outside
the thin rectangle.

For one particular thin rectangle, it turns out the "optimal"
rendering looks like this:
	,,,,,,,,,,,

but I would argue that this:
	___________

is a better rendering for most purposes, despite the fact that all of
its "on" bits are outside the thin rectangle being rendered.

At every step in this quest for a mathematical definition of maximal
art rendering, I had to make gross simplifications and "aesthetic
judgments", and the result is still lacking.

If you really want to develop a rigorous, mathematical definition of
perfect art, I wish you luck, but I doubt such a thing is particularly
useful.

(On a different point, art != realism.  But this is another long,
boring argument that I don't want to get into.)

(Followups narrowed to alt.ascii-art again.)
--