As usual (often) I am humbled... in complement to your (EricS's) "if I
were smart and I had time" I counter "if I were smart and I had
focus"... this stuff just seems too hard (intellectually) for me to stay
focused on long enough to carefully puzzle it out, but/so I really
appreciate your and Marcus (and any latent laggards to the party)
engaging with the question.
I have imaginated that the value of reversibility in energy consumption
is that to "clear a computation" (dispose o the slag) the obvious answer
is to simply "uncompute" the computation... thereby (only?) *doubling*
the computational time? Of course the "readout" of the state of the
"halted" computation is it's own bit-burning exercise... But if in
fact, the answer really is 42 as predicted, then a mere 6 bits
suffices? What was the question again?
I'm guessing I've got something really fundamentally wrong here though.
My ideation is squarely in the "free lunch" regime I fear whilst the
current methods *seem* to produce more waste heat than might be
absolutely necessary if more "skillful means" were applied?
Your reference to "slag" was excellent and very apropos of the other
tangent I referenced of Gosper's Hashlife where every computation is
hashed for potential re-reference. 2D nearest neighbor CA is "easy" to
quadtree down and memoise in such a way as to avoid recomputing any
repeating patterns... so much of the GofL game is in various states of
translation and reflection that most evolutions might degenerate to
translations/reflections of existing patterns with any *new and novel*
computation having to, by definition, happen at a larger and larger
scale? Another as-yet-unfulfilled exercise was to re-implement
hashlife with a less efficient but more thorough kernel (N-1xN-1
recursive decomposition instead of N/2xN/2) andinstrumented so as to
identify where "novel" computation was going on... where it *wasn't*
degenerating to simply hash collisions and look ups at scale.
Regarding slag: all slag is re-used or recognized for being unique (and
therefore acutely interesting?).
Thanks to all for enduring my half-gassed speculations here.
- Steve
On 1/11/25 2:56 PM, Santafe wrote:
It seems like there are two separate questions here.
Steve talked about reversible gates, and suggested them as solutions
to heat wastage. But I think that doesn’t go through. I too thought
of Marcus’s point about unitary quatum gates as the obvious case of
reversibility (needed for them to function at all for what they are).
But quantum or Toffoli or Fredken, the point of the Landauer relation
et al. is that you can move around where the dissipation happens (out
of the gate and into somewhere else), but reversibility itself isn’t
obviating dissipation. (f it is to be obviated, that is a different
question; I’ll come back in a moment to say this more carefully.)
The different matter of superconducting or other less-wasteful gates
seems to be about _excess_ dissipation that can be prevented without
changing the inherent constraints from the definition of what the
computational program is.
So back to explaining the first para more carefully: As I understand
it (so offering the place to tell me I have it wrong), the point is
that we use a model in which the state space is a kind of
product-space of two ensembles. One we call the data ensemble, and
its real estate we have to build and then populate with one or another
set of data values. The other is the thermal ensemble which gets
populated with states that we don’t individually control with boundary
conditions, but control only in distribution by the energy made
available to them.
Then what is the premise of computation? It is that every statement
of a well-formed question already contains its answer; the problem is
just that the answer is hard to see because it is distributed among
the bits of the question statement, along with other things that
aren’t the answer. If we maximally compress all this, what a
computation is doing is shuffling the bits in a one-to-one mapping, so
that the bits constituting the answer are in a known set of registers,
and all the slag that wasn’t the answer is in the remaining registers.
In a reversible architecture, that can be done in isolation from the
thermal bath, so no entropy “production” takes place at all.
But the slag is now still consuming real estate that you have to
re-use to do the next computation, and even the answer has to get
moved somewhere off-computer to re-use that part of the real estate.
If the slag is really slag, and you just want to get rid of it, then
you are still going to offload entropy to somewhere in doing so. Not
in the gates that did the computation, maybe, but in the washer that
returns clean sheets for the next day. If we stay within the
representational abstraction that we have only the two ensembles (data
and thermal), then every version of that dissipates to heat.
The reason I said that whether dissipation is unavoidable or not is “a
different question”, rather than “already known”, is that it is not
obvious to me that one _must_ “dispose” of the slag that wasn't the
“answer-part” of your first question. Maybe it isn’t true slag, but
part of articulation of other questions that request other answers.
One might imagine (to employ the metaphor of the moment),
“sustainable” computation, whereby all slag gets reversibly recycled
to the Source of Questions, to be re-used by some green questioner
another day.
That’s a fun new problem articulation, but I think the imagination
that it solves anything just displaces the naivete to another place.
One might make computation “more sustainable” by realizing that there
will be new questions later, and saving input bits in case those
become useful. But there is no “totally sustainable computation”
unless we are sure to ask all possible questions, so that every bit
from the Source is the answer to something that eventually gets used.
No Free Lunch kind of assertion. This is Dan Dennett World where
volition is modeled by deterministic automata. But Dennett world is
not our world: everything we do works because we are tiny and care
about only a few things, with which we interact stochastically, and
the world tolerates us in doing so. In that world, returning the slag
to the Source of Questions should create a kind of chemical potential
for interesting questions, in which, like ores that become more and
more rarified, finding the interesting questions among the slag that
one won’t dispose of gets harder and harder. So there should be
Carnot-type limits that tell asymptotically what the minimal total
waste could be to extract all the questions we will ever care about
from the Source of Questions, retuning as much slag as possible over
the whole course, and dissipating only that part that defines the
boundaries of our interest. That Carnot limit could be considerably
less wasteful than our non-look-ahead Landauer bound, but it isn’t
zero. And the Maxwell Deamon cost of the look-ahead needed to recycle
the slag in an optimal manner presumably also diverges, by a
block-coding kind of scaling argument.
Could be a delightful academic exercise, to work out any tiny model to
illustrate this concept. If I were smart and had time, I would want
to do it. But then those with social urgency would chop my head off
too, in the next French Revolution, for having wasted time doing
academic things when I should have been providing a more useful
service. (Sorry, between meetings and the incoming emails over the
past few days, I have been spending lots of time with those who think
that the reason there are still problems in the world is that we let
go of the Struggle Sessions too early. I can’t argue that they are
wrong, so I am keeping my head down in public.)
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