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RE: covariation and declarative randomness RE: Re (2): Turing completeness and syntactic elegance;

From: David Dailey <ddailey@zoominternet.net>
Date: Tue, 4 Dec 2012 20:58:29 -0500
To: <steve@fenestra.com>
Cc: <www-svg@w3.org>, "'Eric Elder'" <ericjelder@gmail.com>
Message-ID: <002301cdd28c$05c51970$114f4c50$@net>
I wish my thoughts were more in the midst of it at the moment, so perhaps it
was a bad time to raise the issue. In the HTML-WG, an ill-formulated idea
was prone to evoke derision, slanderous IRC's and intensely juvenile
behavior for which no known antidote short of senility is known. The SVG
community tends to be a bit more forgiving, thankfully.

I will try to resurrect some of the conceptual threads that underlay my
admittedly unsubstantiated conclusion, but all that I can recall for now is
that when one plays within the rich constructional framework provided by
declarative randomness together with <replicate> one wants a way to a)
remember values that have been generated during one pass so that they might
be reused in a next iteration and b) many aspects of scene generation are
correlated in ways that invite declarative syntax, but which to date have
eluded our simple conceptualization of what that syntax might be. I think,
alas, one sort of has to play with replicate and random to get a sense of
what I'm talking about, and for many people this would be tantamount to some
sort of ideological blasphemy -- sort of like when Dada came to Zurich.

I'll try to be more concrete in later post, and I will try to complete said
post within a finite number of months.

I'm not being sarcastic, really, just realistic.

Regards
D

-----Original Message-----
From: Steve Schafer [mailto:steve@fenestra.com] 
Sent: Tuesday, December 04, 2012 1:27 PM
To: David Dailey
Cc: www-svg@w3.org; 'Eric Elder'
Subject: Re: covariation and declarative randomness RE: Re (2): Turing
completeness and syntactic elegance;

On Tue, 4 Dec 2012 07:29:10 -0500, you wrote:

>What we'd like to be able to add in, and welcome suggestions for how to 
>do it, is to be able to control the amount of covariation between two 
>random variables --- for example as the y position of trees varies we 
>might also want their brightness to increase (but with a fixed 
>coefficient of correlation). It is the co-dependency of random 
>variables for which we are trying to craft a declarative solution.

Can you give some concrete examples? I'm not sure I understand what kinds of
covariance you're looking for. There is quite a bit of literature covering
joint probability distributions of random variables, with all manner of
combinations of correlation and independence.

I'm reasonably confident that any useful joint probability distribution can
be specified in terms of functions of a finite number of independent,
uniformly-distributed random variables. That is, given a set A, B, C, etc.
of variables of interest (that may be involved in various degrees of
correlation and dependence), and a set a, b, c, etc.
of independent random variables, you should be able to write:

 A = f1(a, b, c, ...)
 B = f2(a, b, c, ...)
 C = f3(a, b, c, ...)
 ... 

If you do it right, then some of the parameters in the functions f1, f2,
etc. could serve as the "knobs" that a non-technical user would be able to
tweak to vary the effect. How you would go about that is left as an exercise
for the reader. ;-)

-Steve Schafer
Received on Wednesday, 5 December 2012 01:59:00 GMT

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