Re: Tetrits and "stickiness"
> Date: Thu, 15 Apr 2010 08:36:12 -0500
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: Nate Hayes <nh@xxxxxxxxxxxxxxxxx>, stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Tetrits and "stickiness"
Baker, et al,
>
> Dan et al,
>
> The implications of this will require some additional thought. In
> particular, how the tetrits will actually
> be used in computations should be reviewed carefully. My guess is that,
> if an argument is not totally in
> the domain of part of the expression, we need to say the argument is not
> wholly within the domain of
> the entire expression. This would be important to know in the case of
> computational fixed point
> theorems. To remind people, an example is
>
> g(x) = \sqrt{x}+1, and take \x = [-2,4]
>
> Then, g([-2,4] = {[1,3],{domainIn,domainOut}}, but the Brouwer fixed
> point theorem
> would say there is an x in [1,3]\subset [-2,4] with g(x)=x, except for
> the DomainOut tetrit.
I am familiar with this theorem only by a different name.
Associated with contraction maps in topology as I recall.
And I don't recall any issues of domain being associated
with it. They tend not to crop up in topology.
> From this point of view, the sticky part is most important. (Note that
> I have not distinguished
> sticky and non-sticky here.)
Entirely agreed. The sticky part needs to be preserved.
We need to decide just what information is going to be
useful to preserve but it DOES need to be kept around.
>
> The main potential use of the non-sticky part would be to find out where
> in the expression
> (through a user check of the tetrit, say) the domain condition is violated.
For this reason (& some circuits reasons) I would like
to keep them separate.
The circuits reason is this: if the non-sticky part is
a function of the input intervals & the operation only
then it can be computed in hardware not unlike the
interval part is computed & with the same interlocks.
Then if the sticky part is a function of the input
decorations only (both non-sticky & sticky parts), it
is ALSO easy to compute without delays in the pipe.
In this way it becomes easier for the hardware guys to
justify doing the whole job for us & leaving nothing to
some sort of slow software support.
And the interpretation for the user is also easy: The
non-sticky part is information about the last operation.
And the sticky part is historical information about all
previous operations that led up to this result.
Simple.
>
> Do we need both the sticky part and the non-sticky part? If we don't,
> can we simplify
> this even more? I'd be interested in Arnold's and John's opinions,
> among others. Otherwise, I don't
> see adding an additional bit a problem, but what do hardware people
> think? Perhaps we even have
> an extra bit of "Lagniappe" (as we say here in South Louisiana), since
> perhaps we could even carry a fourth
> bit free of charge to make it an even half-byte :-)
>
> Baker
>
I was hoping to eventually make a very simple motion
concerning the interpretation of tetrits alone. That is,
I wanted to lock down the meaning of the non-sticky part
alone & leave issues such as encodings & propagation
rules for another day.
We could still do that.
But Nate has raised a possible method of making sticky
just those states we might want to have hanging around.
If the famous New Orleans largess extends its lagniappe
to permitting an extra bit or two then tetrits & sticky
information is something that can be truly separated.
Shall we approach it that way then?
Shall I make a motion about tetrits only that specifically
excludes encodings, propagation rules, & decoration names
in a way that allows us to choose Nate's propagation method
or some other in a follow on motion?
I certainly think it would simplify our decision.
I will be guided by the opinions expressed here.
Thanks, folks...
Dan