Oh, wow. It hadn’t occurred to me that GPUs could be useful in databases…

Thanks for the reply re SQL.

Having *huge* calculation speed could allow for brute force query evaluation techniques that are not practical on standard CPUs.

I just wanted to point you at a presentation on the GPGPU.org site about this very topic. http://www.gpgpu.org/s2005/slides/govindaraju.DatabaseOperations.ppt

Congrats on the book, looking forward to reading it.

Joe

For some reason your most recent comment disappeared into my WordPress spam filter. I just now noticed it there and fished it out…

Discussions about alternative foundations of mathematics always seems a bit pie-in-the-sky to me. Classical mathematics has worked well for a long time. In order to seriously consider something else, I’d need to see a simple example of where using an alternative mathematics was better than classical mathematics for some concrete problem.

Haha! Is being associated with you really so bad?!

> My e-mail address is r -~ -~ schwall -~ -~ verizon -~ -~ net (I wonder if the address-harvester bots have gotten smart enough to recognize that?).

My email is shane@vetta.org I don’t care about the bots, they’re no match for gmail.

> I’m NOT seeking paid employment. I only work for free these days.

Hopefully someday I too will be able to work for free. For the time being peanuts are accepted.

> So, in vague, imprecise English: is your new K-dot (sequence complexity) completely dependent on infinities? For example: the integers go on forever?

Math in general depends on infinities: it’s a mess without them. Consider addition and subtraction. If x = y + z then x – y = z right?
If you only have a finite number of integers then that no longer works in general as y + z might be larger than the largest integer permitted. When addition fails, so too does K-dot and most other things.

In many simple applications the fact that computers can only approximate mathematical numbers this isn’t a problem as the numbers don’t get too extreme. But in many numerical applications it’s a serious issue and all sorts of work has to go into making computations behave themselves.

> Suppose we admit that we’ll never need the integers out past 10^(10^6)?

What do you mean by “need”? Do you mean that we can implement an AI with normal double precision floating point numbers? Or do you mean that we should consider 10^(10^6) + 1 to not exist?

> Suppose we admit that any infinite set (such as the natural numbers) is a model, a construct in human language, that does not exist in physical reality? That has been a really convenient tool for a lot years, but maybe we’ve reached an area where something else will do better.

I think the problem is that you’re confusing the model with reality. In physical reality the number 3 doesn’t exist. Have you ever seen a 3? You may have seen 3 bananas. You may have seen a symbol “3″ that
represents the concept. But you’ve never actually seen a 3. It’s an abstraction, not a real thing. The same goes for infinity.

Many traditional cultures didn’t have the concept of negative numbers, fractions, zero, and in some cases they didn’t even have numbers beyond ten — after ten is was just “many”. This abstraction might work for counting your children, but it’s not much use for physics.

> Maybe the realm of limited-register computing is a new domain.

It doesn’t seem so new to me. Talk to anybody who works on numerical computation. Trying to get numerical simulations to work correctly despite the fact that floating point numbers have limited precision is a major problem they face. It’s a whole field of research.

> Natural Intelligence (AKA “politics as usual”) is NOT SAFE.

Yes, even if we avoid powerful AGI, long term I don’t think humans are sufficiently “Friendly” to avoid extinction. We’ll happily bring about the end of humanity and claim it to be god’s will, or some other nonsense reason.

> Give me a call. I’m REALLY committed to participating. I’ve been putting in 20 – 45 hours per week, but I may not be well-focussed on that which will make a difference. I need a research advisor.

I think I understand your general interests, but do you have a specific idea of what you want to achieve?

Congratulations on achieving the rank of Doctor of Philosophy! It’s good to know that the Philosophy of Machine Intelligence will get good health care.

Also, congratulations on earning the SIAI academic prize.

I am a contributor to and volunteer for an organization concerned about the future of mankind. I have agreed to their request to not say or imply that they are associated with me. I am between work assignments, and I would be willing to assist you in any way I can, from manual labor on up. I have a Ph.D. In chemistry. If you will send me an e-mail address, I’ll send you a resume. My e-mail address is r -~ -~ schwall -~ -~ verizon -~ -~ net (I wonder if the address-harvester bots have gotten smart enough to recognize that?). Even better, call me at 1 wait 805 pause 890 breathe 2514 whew! (USA, California).

I’m NOT seeking paid employment. I only work for free these days.

Just so this is not completely off topic, I do have an AI-complexity question. (You’re welcome to tell me this is a newbie question and send me off to read a textbook.)

My ‘understanding’ is that Gödel’s Incompleteness Theorems depend on the integers being an infinite set…

OK, I admit, I don’t understand this well enough to ask a question that is provably not stupid.

So, in vague, imprecise English: is your new K-dot (sequence complexity) completely dependent on infinities? For example: the integers go on forever?

Suppose we admit that we’ll never need the integers out past 10^(10^6)? Our Friendly AI’s low-level algorithms will return an error code if a million-digit register overflows. (And no, we won’t try to process your dissertation / book as a single string.) Does this cast new light on the fit of K-dot (and maybe even Gödel incompleteness) to physical reality?

Suppose we admit that our Friendly AI will be using floating point arithmetic (gasp!) a lot of the time?

Suppose we admit that any infinite set (such as the natural numbers) is a model, a construct in human language, that does not exist in physical reality? That has been a really convenient tool for a lot years, but maybe we’ve reached an area where something else will do better.

The past introduction of rational numbers, real numbers, imaginary numbers, etc. Reminds me that our constructs have a limited match with reality. Newton’s laws, which are still used in most engineering, are known to be inaccurate, but are “close enough” except in certain domains (the very fast, the very tiny, etc.). Maybe the realm of limited-register computing is a new domain.

I _am_ disappointed that we may not be able to mathematically prove that a given AI architecture and mission is safe and will stay safe. However, that doesn’t mean I’m going to just quit in despair. The AI crisis won’t go away just because we can’t map something onto a two valued, proof / disproof, world view. Get Bayesian.

We still need to learn all we can about making safER AI. We’ll need approximation methods. We’ll need to be able to compare architectures and components and choose the less dangerous ones.

Relinquishing all technologies that lead toward advanced AI just won’t happen. (Unless we crash our complexly-interwoven civilization.) If recursively self-improving AGI is possible, it is inevitable. HUMANS will make those decisions. (Go ahead, prove that humans are Friendly, safe or sane.)

Besides, we NEED the help of trans-human, hyper-moral, not-evolved AI. I can say with ‘certainty’ (well past 5 nines, or 15 bits) that Natural Intelligence (AKA “politics as usual”) is NOT SAFE. Especially not when armed with huge nuclear arsenals that can probably make us extinct. Just for starters.

And the upside potential of trans-human AI is unimaginable! (At least it is to my lowly level 126 intelligence.)

What? Hmm? Oh, yes, you’re right, that is a soap-box I’m standing on. Heh.

Give me a call. I’m REALLY committed to participating. I’ve been putting in 20 – 45 hours per week, but I may not be well-focussed on that which will make a difference. I need a research advisor.

Thanks for your time and your listening.

With respect and high regard,

Rick Schwall, Ph. D.

———————————–
When humanity has ENGINEERED (NOT evolved) the first super-human hyper-moral Artificial Generall Intelligence, it will be Humanity’s Triumph over Evolution.

After going to so much effort to write the thesis I figured I may as well give it a push with a flashy title! I’m curious to see if it attracts much attention. My guess is that it will largely be ignored… until 10 or 15 years from now.

Regarding reference machines. I take a different perspective. I think we should keep the reference UTM as simple and clean as possible. If we want to put prior knowledge into the inductive inference system, then we can just provide this as input prior to our training data. Any “prior knowledge” that goes into the design of the reference machine, should be only our most fundamental assumptions about the nature of the universe. Such as the Church-Turing thesis and Occam’s razor. Obviously we need to put enough in there to make induction possible, but we should not put in any more. From that point onwards we should “let the data speak for itself”, as the statisticians say.

I’d also like to say that I think that the problem of choosing the reference machine is overplayed by many people. Remember that the bound in prediction errors in Solomonoff’s result is ln(2)/2 K(\mu). Thus, if we switch from one simple reference machine to another the bound only moves by a few hundred bits, maybe a few hundred bytes, due to the compiler constant in the Kolmogorov complexity function. Unless you have a tiny data set, that’s still a very powerful bound.

Congratulations. I submitted a /. story on your prize but maybe I didn’t do a good enough job of explaining the value of your work to catch the attention of the reading public. “Machine Super Intelligence” is certainly catchy enough, one would think but we’ll see.

My question is: What do you make of Solomonoff’s statement:

“This subjectivity, the fact that they are based on choice of which Universal machine to use, is characteristic of all prediction systems based on a priori probability distributions. The choice of Universal machine and its instruction set is a necessary parameter in the system that enables us to insert a priori information into it. The dependence of the universal distribution on choice of machine is not a Bug in the System — it, too, is a Necessary Feature.”

Yes you can do it , you can write down a subset of all available strings ( and this the maxmum available ) .

>Ok, but let’s say that you just didn’t pick a big enough number. What if we considered the set of binary strings that are 10^1000 bits long, of which there are 2^10^1000 strings?

I think this is about the same . I think that a string long 10^1000 does not exist.

I explained something in my first post.
I think the world is not exponential so we can not think to resource functions like O(2^N) .
If I think to a system with limited power I can set a limit for example to the size of the strings .
If I place this limit M a starting consequence is that the space distribution is not 2^N but Min(2^N,M/N) .
From here we can change the universal distribution as I suggest for an interesting empirical test and others formula.
I show other consequences in the first post…
In a strictly practical point of view what can we do knowing this ? This is the most important question.
I think that this consideration emphasizes the role of existing data .
The existing real data let us to make such “jump” to “good” machine states impossible to reach with computations

>How can you write down any one of them ?

Of course I can write one of them down. It’s a string of 1′s and 0′s that is 10^6 = 1 million digits long. I just did a count and my thesis is just under half a million characters long. In ASCII binary that’s a string of 4 x 10^6 bits, and I typed it all in myself.

Ok, but let’s say that you just didn’t pick a big enough number. What if we considered the set of binary strings that are 10^1000 bits long, of which there are 2^10^1000 strings?

A string this long I can’t write down by hand, or with a machine. It’s too big. Ok, so why does this matter to somebody building an AI? For example, under a universal prior distribution the prior probability assigned to a randomly chosen string of this length is going to be on the order of 2^-(10^1000) which is extremely extremely close to zero. Technically they are not treated at impossible, but in any practical sense they are treated as though they are essentially “impossible”. In which case, how does your idea of considering these strings to be “impossible” make much difference?

This is my main claim , I think it is impossible to write down any one of them .
How can you write down any one of them ?
There is not a resource bounded program to do this.
There is not a resource bounded program able to write down any one of that strings.
Every existing (not every possible programs ) can cover only a part of that set of strings.
Ok this is an extreme deterministic (I am deterministic ) point of view but I think it is possible to have the same result in a probabilistic domain.

“Doing mathematics in a categorical framework is almost always radically different from doing it in a set-theoretical framework.” But also: “Still, it remains to be seen whether category theory should be “on the same plane,” so to speak, as set theory, whether it should be taken as a serious alternative to set theory as a foundation for mathematics, or whether it is foundational in a different sense altogether.”
http://plato.stanford.edu/entries/category-theory/

> certain categories called topoi (singular topos) can even serve as an alternative to axiomatic set theory as a foundation of mathematics.

Sure. People have built foundations for mathematics on all sorts of things. Many of these, if they are sufficiently rich, end up producing classical mathematics. If you choose to limit the power of the axioms, for example intuitionistic logic, then you can get some version of constructive mathematics.

Thus, I’m not at all surprised to hear that you can found mathematics on category theory, and I’m sure that if you make the axioms strong enough you’ll end up with classical mathematics — just like you get from some versions of set theory. (Actually I should say “some version of classical mathematics”, for example, do you or do you now include the axiom of choice (or equivalent statements in alternate axiomatic foundations)? Probably yes, but some argue otherwise.)

I still don’t understand what you’re talking about.

> In general there is no class/instance operator.

Sure there is. A set can represent a class and an instance is just an element of this set.

I also don’t see why a note is not a set. A note must have these for properties. Ok, just define the set of all notes to be the set of all things that have these four properties.

The whole of math can be founded on set theory. If you can express something mathematically, you can express it with sets.