Woshi understands you. But this is the easy part. Woshi can calculate a plan for your studio/farm/workshop/operation/unit… according to your wishes and demands, nobody else can.
And yes, Woshi is in fact an army of algorithms stationed in our server.
How many bytes of computer memory, at minimum, would it take to store every possible chess position of which there are 10^47 according to the latest calculations? If done right, less than 1 kB!
How come?
Because all those positions are equivalent to the following algorithm:
step 1: take the opening position and append it to an empty list
step 2: calculate all legal moves from the given position (if it’s the last move of a game, go to the next element of the list)
step 3: for each legal move found, write down the corresponding position and append it to the aforementioned list
step 4: proceed to the first unprocessed element in the list of positions and go to step 2, else stop
This algorithm would run for a long, long, long time before completing the task of generating them all.
But the time doesn’t count, only bits do, just like in zipping or unzipping files.
All and every chess position is there, compressed inside the algorithm described above.
The pressing question however, is how to minimize the product of the number of steps required and the bit-length of the algorithm.
It must be done fast and not use up all the resources (free enthalpy) of the observable Universe in the process. What’s the smallest possible effort required to generate all legal chess positions explicitly?
An estimation can be made. To write down all the positions, an Earth mass size object made of C12 and C13 atoms would suffice as storage.
Several self replicating nano-bots could be the seed of the mega structure. As they go, they follow the following procedure:
– multiply
– calculate legal positions, storing them inside yourself, informing your peers about the positions you are calculating, until there is no storage left
– dock and assimilate into the main structure
With the advances in nano technology it would be doable in a century or less, if we really wanted to.
2^6 years after Shannon, we need a century instead of a billion times the current age of the Universe, to do the job he envisioned back then.
Perhaps we will be able to do it in a minute, later in the 21st century, if we are still interested in chess at all.
I am not holding any world record of any kind.
But a computer program I’ve kind of invented and even helped to program, has 35 new world records. Published yesterday, here:
The program is called Pack’n’tile, to help you navigate.
I know, what some people will say: Yes, you know, I also played with genetic algorithms. But that’s not the real thing!
And I know what I have to reply to this: Excuse me, your toys haven’t achieved anything. And I prefer to call mine simply:
The Evolutionary Algorithm!
Him: We have all grown up. Nobody expects a Singularity anytime soon any more, as we used to, 10 years ago.
Me: I haven’t grown up.
Him: I know. But be realistic, we have no idea how brains work, nor do we have any idea of what algorithms might bypass the brain.
Another guy: The Moor’s law alone isn’t enough, we have no idea what to put into these machines or how to program them.
Me: You are both wrong, we have the (Universal!) Levin search, for example.
Him: What is that, another Solomonoff induction or something?
Me: Yes, you could say that.
Him: It’s useless. With it, you’d need exponential resources to solve even a minor problem. Sure it’s possible with an infinite amount of computation, in which case it would be a super-intelligence, but you don’t have unlimited processing power required — so you don’t have anything useful with this Levine search.
Me: It just so happens, that we have the Hutter paper which considers the Levin search.
Him: Who’s Hutter? What’s this paper about?
Me: The paper demonstrates, that if the best possible algorithm to sort a certain list requires N steps, then the Levin search can find this optimal sorting algorithm in 5*N steps. At the most. The same is true for any other algorithm, if the optimal algorithm can do something in a second, you can invent this same algorithm in 5 seconds, at most!
Him: Really? I can’t believe that’s true. That would indeed be a superintelligence. But I don’t think that’s possible. There must be some big constant involved here.
Me: The constant is 5 now, it was much greater before Hutter’s paper. Google it, I’ll not help you there. Even funnier theorems have been proven before, funnier, but none of the same importance, I admit.
Him: If that’s really true, I will change sides. Has anybody implemented at least a portion of the Levin search method, using Hutter’s theorem yet?
Me: Maybe they haven’t, maybe they have, Google it yourself! But you’ll find nothing in either case because if someone is using it they probably won’t speak openly about it. For the pure theory, however, Google will bring you enough.
Him: Do you realize what kind of danger the existence of such a possibility could pose?
Me: I don’t share your concerns at all, but you already know that.
We all know what black holes are. The places where matter goes, but from whence it can hardly return. To the extent that it does come back, it does so due to Hawking radiation. Very, very, very slowly.
Because of this, black holes are actually grey holes – a very dark shade of grey.
What about some other examples of grey holes in different contexts? There are plenty of them, in various contexts. Western Germany was once a grey hole for Eastern Germans. Once across the border, they hardly ever came back to the East, not vice versa. Until the whole country was swallowed, in a span of 45 years from 1945 to 1989, this was a clear case of a figurative grey hole, swallowing not only the Eastern Germans, but also the Turks and the people from the Balkans, as well as many others.
The USA is another, even bigger example of a demographic grey hole. For centuries it has attracted and kept many of those who travelled there. Some Americans escape to Sweden or to the UK, but not that many, by far.
A bathroom sink-hole is a grey hole for your hair. They tend to go there, but they hardly ever come back. There are lots of gruesome grey holes everywhere we live. We must exhort special effort to make those clean again.
Whenever the probability of an object O, travelling from A to B is greater than the probability of the same object travelling from B back to A — B is a grey hole for O kind of objects.
Then, we have a build-up of such a grey hole, until the directional probabilities change. The water molecule in the kitchen air has a small chance of colliding with the ice already built up in your freezer. There is a much lower chance of it ever coming back spontaneously. Therefore ice is growing in all older models of deep freezers. There is no energy for those molecules to come back once they land on ice.
Antarctica is the same kind of a grey hole. When a water molecule from the Pacific lands there, it simply lacks the energy to return to the sea – at least when the temperature is, on average, 40 degrees bellow zero. Which it is now, and has been thus for a long time already.
Understanding this rather trivial fact, prevents you from being baffled, like certain scientists allegedly are as to why the Antarctic ice is growing.
A lake in the European Alps, is a grey hole for water molecules from the glacier above. The probability of them travelling to the lake and then to the sea is greater than vice versa. At least until it becomes much colder than it has been for centuries now.
There is no science more powerful than simple maths. If the simple maths/physics doesn’t agree, then no fancy science is even feasible.
protokol2020 