A Dialog (between friends) on The Law of the Conservation of Computation
Russell [8:16 AM]
This is happening to programs and programming too. http://www.worksonbecoming.com/thoughts-prefaces/2015/10/1/this-is-contingency
Some Works
This is contingency
Remarks on the contingency of new forms and the phenemenon of replication.
Schoeller [8:16 AM]
Very NKS.
Schoeller [8:17 AM]
I’m somewhat less certain of this outcome than you — it relies heavily on everyone playing nice and working with each other.
Russell [8:18 AM]
That's just you.
Schoeller [8:18 AM]
Which is challenging — witness the web API boom/bust of 5 years ago.
Russell [8:18 AM]
The arc of assimilation is clear
Schoeller [8:18 AM]
It’s the pragmatism/skepticism in me.
Russell [8:19 AM]
Most humans almost 6.997 billion of them have no idea about computers
Schoeller [8:19 AM]
I get it. But the pace of progress can be furiously slow in the face of economics.
Schoeller [8:19 AM]
For instance — where’s my flying car?
Schoeller [8:20 AM]
We’re not going to have networked 3D printed robots manufacturing things for some time.
Russell [8:20 AM]
That's not progress
Russell [8:20 AM]
Flying cars aren't selected for
Russell [8:20 AM]
They lack survivability value
Russell [8:21 AM]
Amazons prime deliver moving to Amazon flex... As they push delivery times to zero one must manufacture close to the source
Russell [8:21 AM]
Of the transaction
Russell [8:21 AM]
It's happening
Russell [8:21 AM]
Who needs to fly except the drones
Schoeller [8:21 AM]
I understand the vision. I’m just not convinced it’ll happen...
Schoeller [8:22 AM]
Well me for one :simple_smile:
Schoeller [8:22 AM]
Drone delivery is another unlikely occurance in any large scale.
Schoeller [8:23 AM]
The economics/logistics just don’t make any sense. Packages are heavy.
Russell [8:23 AM]
Personal drivers. Personal shoppers. Personal virtual assistants. ... All are shaping the world to not need all this movement. Once were three degrees removed from these activities we won't care if it's a machine doing it all.
Russell [8:24 AM]
So make people want less heavy stuff
Russell [8:24 AM]
Sell them a kindle and ebooks
Russell [8:24 AM]
:)
Schoeller [8:24 AM]
Agree on that.
Russell [8:24 AM]
It's happening.
Schoeller [8:24 AM]
Although (sidebar) dead-tree’s not dead.
Schoeller [8:25 AM]
You can’t digitize the tactile feel of thumbing through the pages of a book.
Schoeller [8:25 AM]
I suspect it’ll become boutique. Soft-cover trade books are done. But hardcover, well-bound, limited edition will carry on and do quite well.
Russell [8:27 AM]
Nice try
Schoeller [8:27 AM]
Back on track — A lot of this future stuff is the same: the hyperloop is just the next space elevator which was the next flying car, etc.
Russell [8:27 AM]
You can destroy people's ability to touch
Russell [8:27 AM]
Negative sir
Schoeller [8:27 AM]
I like my fingers, thank you very much :wink:
Russell [8:27 AM]
I'm making a much bigger systematic argument
Russell [8:28 AM]
Don't care about the specific forms
Russell [8:28 AM]
Only that forms get selected and replicated
Schoeller [8:28 AM]
Well, it has to be grounded in something.
Russell [8:28 AM]
Replicability!
Russell [8:28 AM]
Is it computationally efficient!
Russell [8:29 AM]
Boom boyeeee
Schoeller [8:29 AM]
Much of the problem of flying cars, drone delivery, space elevators, 3d printed manufacturing, and hyperloops is the connection from physics -> economics.
Schoeller [8:29 AM]
We don’t have that with software. There, the challenge is the rate and format of the bits flying around.
Russell [8:30 AM]
Hence computationally efficient
Russell [8:30 AM]
Economic networks also replicate computational efficiency.
Russell [8:31 AM]
Commodities have stable ish values because the idea is computationally efficient. Utility etc is well established in the network. So they are exchanged etc.
Schoeller [8:32 AM]
You’re asserting, then, that competition == computational efficiency?
Russell [8:32 AM]
Correct
Russell [8:32 AM]
Efficiency must have survivability.
Russell [8:32 AM]
The trivial would not be efficient for economies
Schoeller [8:33 AM]
I can buy that. At least in the sense of efficiency from the perspective of the system as a whole. Not for any given agent participating in the system.
Russell [8:33 AM]
Yes.
Schoeller [8:33 AM]
The agents are horrifically inefficient.
Schoeller [8:33 AM]
(individually)
Russell [8:34 AM]
Hard to separate them from the system
Schoeller [8:34 AM]
True, unless you’re an agent.
Russell [8:34 AM]
I believe there is a law of the conservation of computation.
Schoeller [8:35 AM]
computation can neither be created nor destroyed, but can only change form?
Russell [8:35 AM]
Correct
Russell [8:36 AM]
And that results in all other conservation laws
Russell [8:36 AM]
And is why competition in all networks is computational efficient
Russell [8:36 AM]
And cannot be any other way
Schoeller [8:36 AM]
It’ll take a bit for me to wrap my head around that idea.
Russell [8:37 AM]
The singularity is pure probability. Computationally irreducible.
Russell [8:37 AM]
Once probability breaks down into four forces and matter and light etc. we have pattern
Russell [8:37 AM]
But by the law of the conservation of computation it can't go to all pattern.
Russell [8:37 AM]
Or that would reduce computation
Russell [8:38 AM]
So competition between networks must proceed.
Russell [8:40 AM]
And per my blog post the idea that replication normalizes nodes in the network as they become more fully normalized the network of replication starts to collide with other networks of replication where the normalizations selected started competing. Until a new form and new networks begin the process again.
Russell [8:40 AM]
Computation merely moves around these networks as the process of complexification and simplification double back over and over.
Russell [8:40 AM]
Even any american company is an example
Russell [8:41 AM]
We are simplifying and normalizing them all the time.
Russell [8:41 AM]
Employees replicate basic skills
Russell [8:41 AM]
And we recruit for these skills
Russell [8:41 AM]
revenue lines get simplified
Russell [8:41 AM]
marketing simplifies messages to the world
Russell [8:42 AM]
All for survivability.
Russell [8:42 AM]
But this is also exposes companies to competition
Russell [8:42 AM]
It gets easier to poach employees. And to see ideas and strategies on the outside.
Russell [8:42 AM]
Soon it tips and companies need New products. New marketing. New employees.
Russell [8:43 AM]
All the while computation is preserved in the wider network
Schoeller [8:43 AM]
Where I’m struggling is how this copes with the notion that the universe tends toward disorder.
Russell [8:44 AM]
Normalized forms become dispensable as individual nodes.
Russell [8:44 AM]
Disorder is pure noise.
Schoeller [8:44 AM]
Order in the universe is effectively random.
Russell [8:44 AM]
Total entropy.
Russell [8:45 AM]
Which if every network normalizes towards highly replicated forms they have less internal competition. They have heat death.
Russell [8:45 AM]
Which is total entropy.
Russell [8:45 AM]
Again. A singularity is pure probability.
Russell [8:46 AM]
No pattern.
Russell [8:46 AM]
Randomness.
Schoeller [8:46 AM]
I can buy that. Certainly there’s a low probability that any agent will succeed, thus the entropy tends to increase.
Russell [8:46 AM]
Fully replicated forms are those that maximize survivability.
Russell [8:46 AM]
So some super weird platonic object between order and chaos
Russell [8:46 AM]
Between infinities.
Russell [8:46 AM]
A circle for example is a weird object
Russell [8:47 AM]
Rule 110 is a weird object
Schoeller [8:47 AM]
Here’s a question — where does the computation come from to achieve fully replicated forms?
Schoeller [8:48 AM]
Presumably there’s some notion of “potential” computation?
Russell [8:48 AM]
Negative.
Russell [8:48 AM]
There's only computation
Russell [8:48 AM]
Potential is a relational concept
Schoeller [8:49 AM]
Hmm… then back to my question.
Russell [8:49 AM]
There is no potential time
Russell [8:49 AM]
There is no potential dimension
Russell [8:50 AM]
There is no potential temperature
Schoeller [8:50 AM]
Right, but time only moves forward — there’s no notion of conservation of time.
Russell [8:50 AM]
Ah!
Russell [8:50 AM]
But I'm suggesting there is
Russell [8:50 AM]
Time is computation
Schoeller [8:50 AM]
Actually, there is potential temperature. Temperature == energy.
Russell [8:51 AM]
Yes it gets rather semantic
Schoeller [8:51 AM]
The whole field is “thermodynamics"
Russell [8:51 AM]
Yes which is superseded by computation
Russell [8:51 AM]
Hence why info theory and thermodynamics are isomorphic
Russell [8:51 AM]
They are just substrate discussions
Russell [8:51 AM]
Which go away in the math
Schoeller [8:52 AM]
Well, strictly speaking that math doesn’t govern, but attempt to describe.
Russell [8:53 AM]
Look at how computer science handlse time
Russell [8:53 AM]
Steps or cycles
Russell [8:53 AM]
It defines time as compute steps
Russell [8:53 AM]
Hahahahaha
Schoeller [8:53 AM]
If info theory and thermo are isomorphic, then the principal of potential has to translate in some way. It’s important because that’s one of the foundations of conservation of energy.
Russell [8:54 AM]
Yes yes
Russell [8:54 AM]
I'll find a translation for you
Russell [8:54 AM]
It's got something to do with chaitins number
Schoeller [8:55 AM]
Computer science handles time as a long from a particular, arbitrary point. And calculates differences as a byproduct of the way it operates.
Schoeller [8:55 AM]
A “quantum” computer would handle time very differently.
Russell [8:56 AM]
Yes. Keep going.
Schoeller [8:56 AM]
“We” calculate time from celestial positions.
Schoeller [8:56 AM]
None of that relates to the more generalized notion of time.
Russell [8:57 AM]
I propose the translation of time fits within the law of conservation of computation
Russell [8:57 AM]
Quantum computers are closer to singularities. Computing with pure probabilities
Russell [8:57 AM]
Classical computers compute with approximated machine precision probabilities
Russell [8:58 AM]
Somewhere things get super weird with math (algebra and geometry meets probability theory)
Russell [8:58 AM]
Math itself suffers same challenge
Schoeller [8:59 AM]
Yes, well math likes to be very precise.
Russell [8:59 AM]
That which symbolically lacks pure probability humans and classical computers can handle
Russell [9:00 AM]
Once you deal with infinities and infinistimals you start getting to pure probabilities and math theory starts bleeding.
Schoeller [9:00 AM]
Okay, so I can accept a notion of a conservation of probability of time.
Russell [9:00 AM]
N-order logics require n+1 order and incompleteness and set paradoxes.
Russell [9:01 AM]
Math itself becomes computationally weird.
Schoeller [9:01 AM]
ie that the probably of an event occurring or not occurring within a system is 1. Of course, that’s tautological.
Schoeller [9:02 AM]
But also that it would hold for any number of events over any set of times.
Russell [9:02 AM]
Because once a math system becomes computationally inefficient it all of a sudden is incomplete. And we reduce to "somethings are true but we can't prove them in this system"
Russell [9:03 AM]
Yes pure probability is binary. Either everything happens or nothing happens.
Russell [9:03 AM]
If everything happens you must conserve computation as that everything happens
Russell [9:03 AM]
Can't be more than 1! Can't be less than 1!
Schoeller [9:04 AM]
Well, I think what I’m saying is that my need for “potential” computation is solved by probability.
Russell [9:04 AM]
And local events of everything take on less than all computation because of the halting problem.
Schoeller [9:04 AM]
Although I haven’t completely convinced myself.
Russell [9:04 AM]
If the halting problem weren't true every event / computation could self inspect and computation would tend to 0
Russell [9:05 AM]
Chaitins number is a measure of probability
Russell [9:05 AM]
Complexity is a measure of probability
Russell [9:05 AM]
Probability is a notion of unknown information
Russell [9:05 AM]
All data of everything would contain every program and all outputs
Russell [9:06 AM]
And has a probability of any and all events total of 1. All information is known
Russell [9:06 AM]
And the same time it is 0
Schoeller [9:06 AM]
Here wouldn’t the truth of the halting problem arise from the fact the system is influenced from elements outside the system?
Russell [9:06 AM]
Because all information is computationally irreducible of the maximal kind
Schoeller [9:06 AM]
(ie. similar to thermo)
Schoeller [9:06 AM]
Therefore a computation can never know its inputs.
Russell [9:06 AM]
Yes. Halting problem is exactly that
Russell [9:06 AM]
Unknowns
Schoeller [9:06 AM]
And thus, can never know its outputs.
Schoeller [9:07 AM]
Because the program can’t see beyond itself.
Russell [9:07 AM]
It's not a matter of inputs
Russell [9:07 AM]
It emerges from computation!
Russell [9:07 AM]
Elementary ca show this
Russell [9:07 AM]
Godel showed this
Russell [9:08 AM]
Mere DESCRIPTION! Description is computation
Russell [9:09 AM]
I think wolfram gave in too easily
Russell [9:09 AM]
He still believes in Euclidean time
Russell [9:09 AM]
Or whatever Greek time
Schoeller [9:10 AM]
Right. And if computation is probabilistic, the program couldn’t even know, necessarily, what it was actually computing at any given point (until that point occurrs).
Schoeller [9:11 AM]
Yeah, I think your theory only works if time is a probability not a discrete measure.
Russell [9:12 AM]
Time isn't discrete.
Russell [9:12 AM]
It's pure difference
Schoeller [9:12 AM]
Which is really to say that the outcome of a computation can’t be known until the state of the system is known.
Schoeller [9:12 AM]
Which itself can’t be known with any certainty until it occurs.
Schoeller [9:13 AM]
Or, it’s all wibbly, wobbly, timey, wimey stuff.
Schoeller [9:14 AM]
Or, possibly the Heisenberg uncertainty principal as applied to computation.
Russell [9:14 AM]
But 2+2 is 4
Schoeller [9:14 AM]
Only if the state of the system is consistent.
Schoeller [9:14 AM]
(which it happens to be)
Russell [9:15 AM]
And that math statement is a "localized" statement
Schoeller [9:15 AM]
So, the probably of 2+2=4 is very, very close to 1, but not exactly. Possibly so close that its limit approaches.
Schoeller [9:16 AM]
Right. So, part of why the state for 2+2=4 is consistent is because we’ve defined it that way.
Russell [9:16 AM]
It's what I call robust
Russell [9:16 AM]
In most universes 2+2 is 4
Russell [9:16 AM]
In the multiverse there are universes where that's not true
Schoeller [9:16 AM]
But, if you shift from say cartesian to spherical, it doesn’t necessarily hold unless you change what “2” and “4” mean.
Russell [9:17 AM]
But those are very small universes that reduce quickly
Russell [9:17 AM]
Yes.
Russell [9:17 AM]
Thank you!
Schoeller [9:17 AM]
i.e their definition is relative to the system you’re computing within.
Russell [9:17 AM]
Counting and the math emerges from the computational systems
Russell [9:17 AM]
Yes.
Russell [9:18 AM]
And in the entirety of the multiverse all maths exist. All description exists.
Schoeller [9:19 AM]
Sure. That’s as tautological as the probability that something either exists or does not is 1.
Schoeller [9:20 AM]
Since the probability of anything existing within an infinity, unbounded system would also be 1.
Russell [9:20 AM]
And your point?
Russell [9:21 AM]
Math loves tautologies
Russell [9:21 AM]
We have to state them all the time
Russell [9:21 AM]
Or reduce to them
Schoeller [9:22 AM]
Well, it’s consistent with probability theory. So, that’s nice.
Russell [9:22 AM]
Is that what symbolics and rule replacements are?
Russell [9:23 AM]
One giant computational tautology
Schoeller [9:23 AM]
If you’re going to have a theory that talks about local behvior within systems, you have to have consistency when you take that to its extreme limit — such as when the system contains everything possible.
Schoeller [9:24 AM]
Aren’t you just describing the state of the system with symbolics and rules?
Russell [9:25 AM]
Sure.
Russell [9:25 AM]
And the state of everything is what?
Schoeller [9:25 AM]
Here describe means “govern” (unlike my earlier math statement)
Russell [9:26 AM]
Isn't that the state of all sub states or local states?
Russell [9:26 AM]
Of which some local states are meta descriptions of sub sub states or neighboring states
Schoeller [9:26 AM]
I think the state of everything is that the probability of anything is 1.
Schoeller [9:26 AM]
It’s rather useless, but so is the notion of the state of everything.
Russell [9:27 AM]
Govern gets tricky because it's non sensible as a fundamental concept. Eg the spin of a quark doesn't govern. It's just a property.
Russell [9:27 AM]
Gravity and the other forces don't govern.
Russell [9:28 AM]
They are descriptions of relationships
Schoeller [9:28 AM]
Sure, but the definition of “2” on a Cartesian plane is.
Russell [9:28 AM]
If Gravity is merely space time curvature. A geometry that doesn't mean it governs.
Russell [9:28 AM]
What is the definition of 2 governing?
Schoeller [9:29 AM]
It’s governing the behavior of 2 within the cartesian system.
Russell [9:29 AM]
It's merely a description of relations between an X position and a y position on a description of a plane
Schoeller [9:29 AM]
i.e. that 2 can’t be 3 or an apple.
Russell [9:30 AM]
Ah. Yes. Definition bounds localized networks.
Russell [9:30 AM]
2 is a 3 in some systems
Russell [9:31 AM]
Say a simple system of primes and non primes without concern of actual quantity
Schoeller [9:31 AM]
I think this idea holds. The symbols and rules govern the system in a computational sense. But that does not mean that the system itself governs any physical phenomena. Only that it describes (to the extent that the rules reasonably describe the same.)
Schoeller [9:31 AM]
— moving back to describe and govern meaning different things --
Russell [9:31 AM]
Yes Im in agreement
Russell [9:31 AM]
Govern is a localized concept of bounding relations
Russell [9:32 AM]
Let's return to the main q in all this
Russell [9:32 AM]
WHAT DOES THE WORK OF COMPUTATION
Schoeller [9:32 AM]
Yes, bounding relations that define a specific system within the multiverse of possible systems.
Schoeller [9:35 AM]
Well, the computation would have to be done within the medium of the system, right?
Schoeller [9:36 AM]
It can’t be just one thing. Because we’ve already enumerated that there a quantum computers that are different than regular computers that are different than the human brain.
Russell [9:36 AM]
yeah, i haven't figured this out.
Russell [9:36 AM]
other than, it's everything i'm trying to figure out.
Schoeller [9:37 AM]
And to some degree, you pick the computational medium when you define the system. At least in the programming world. Mathematica vs Java vs Spark.
Russell [9:38 AM]
i think it's this.... or related.... to perceive/observe/describe/explain at all, whatever sub network of everything (whatever universe, computer, entity, person, rock...) IS. and the IS and IS NOT of breaking out of total relation to everything is COMPUTATION. and it's a super weird notion. but the mere simplification of total relation to partial relation IS the COMPUTATIONAL ACT.
Schoeller [9:39 AM]
And with a math problem, you’re defining the computational medium to be the human brain.
Russell [9:40 AM]
well, within the human / this universe frame of reference or partial relation to everything, yes.
Schoeller [9:41 AM]
Agree that it’s a weird notion that computational singularity doesn’t “seem” to underly everything. But the rules and computation have to be related and even dependent.
Russell [9:41 AM]
whether we can COMPUTE or "IS" with a different substrate... well, i think so.... i think "computers" and "virtual reality" are moving our COMPUTE/DESCRIPTION/RELATION to everything beyond/outside the Human Brain.
Schoeller [9:42 AM]
So, it’s easier if we constrain ourselves to the systems we make up.
Schoeller [9:43 AM]
As for what computes the physical world — maybe there’s a lesson in evolution theory, where “computation” is quite literally random mutations of the medium itself.
Schoeller [9:44 AM]
And where the “selection”/“survival”/“success” of the computation occurs outside the system (back to the halting problem discussion above)
Schoeller [9:46 AM]
I should clarify "But the rules and computation have to be related and even dependent.” … within a system. In the multiverse, anything goes. :simple_smile:
Russell [9:48 AM]
yes, on your evolutionary theory... or something similar to that. the resolution of probabilities IS computation. resolution being like the resolution of super positions in quantum stuff.
Russell [9:48 AM]
i believe that basically happens as you move from logic systems, computational systems, i.e. russell's theory of types etc.
Russell [9:49 AM]
related to all this numbo jumbo: http://plato.stanford.edu/entries/quine-nf/
Schoeller [9:50 AM]
It’s an example of a chaotic system where order appears to arise naturally, so it seems like it’d be a reasonable starting place to think about other physical systems.
Russell [9:50 AM]
yes, i say we conclude there for now
Schoeller [9:50 AM]
I think the key is the halting problem bit — that the computation can’t possibly know if its successful. That occurs outside the system where the computation is valid. It only blindly executes.
Russell [9:51 AM]
we've created something between chaos and order in this dialog
Russell [9:51 AM]
which will be non trivial to clear up.