Comments by potato - Less Wrong

potato on Pascal's Muggle: Infinitesimal Priors and Strong Evidence

2013-05-09T11:52:27.467372+10:00

Here's a question, if we had the ability to input a sensory event with a likelyhoodratio of 3^^^^3:1 this whole problem would be solved?

potato on The Fabric of Real Things

2012-10-15T10:04:26.115194+11:00

Hmm, it depends on whether or not you can give finite complete descriptions of those algorithms, if so, I don't see the problem with just tagging them on. If you can give finite descriptions of the algorithm, then its komologorov complexity will be finite, and the prior: 2^-k(h) will still give nonzero probabilities to hyper environments.

If there are no such finite complete descriptions, then I gotta go back to the drawing board, cause the universe could totally allow hyper computations.

On a side note, where should I go to read more about hyper-computation?

potato on The Fabric of Real Things

2012-10-14T20:08:06.371948+11:00

At first thought. It seems that if it could be falsified, then it would fail the criteria of containing all and only those hypotheses which could in principle be falsified. Kind of like a meta-reference problem; if it does constrain experience, then there are hypotheses which are not interpretable as causal graphs that constrain experience (no matter how unlikely). This is so because the sentence says "all and only those hypothesis that can be interpreted as causal graphs are falsifiable", and for it to be falsified, means verifying that there is at least one hypothesis which cannot be interpreted as a causal graph which is falsifiable. Short answer, not if we got it right this time.

(term clarification) All and only hypotheses that constrain experience are falsifiable and verifiable, for there exists a portion of experience space which if observed falsifies them, and the rest verifies them (probabilistically).

potato on The Fabric of Real Things

2012-10-14T19:54:09.342459+11:00

I have to ask, how does this metaphysics (cause that's what it is) account for mathematical truths? What causal models do those represent?

My bad:

Someone already asked this more cleverly than I did.

potato on The Fabric of Real Things

2012-10-14T19:46:56.158194+11:00

I have a plausibly equivalent (or at least implies Ey's) candidate for the fabric of real things, i.e., the space of hypotheses which could in principle be true, i.e., the space of beliefs which have sense:

A Hypothesis has nonzero probability, iff it's computable or semi computable.

It's rather obviously inspired by Solomonoff abduction, and is a sound principle for any being attempting to approximate the universal prior.

potato on The Fabric of Real Things

2012-10-14T06:10:30.576476+11:00

It seems to me that this is the primary thing that we should be working on. If probability is subjective, and causality reduces to probability, then isn't causality subjective, i.e., a function of background knowledge?

potato on Causality: a chapter by chapter review

2012-10-11T22:02:43.609677+11:00

Looking it over, I could have been much clearer (sorry). Specifically I want to know. Given a Dag of the form:

A -> C <- B

Is it true that (in all prior joint distributions where A is independent of B, but A is evidence of C, and B is evidence of C) A is none-independent of B, given C is held constant?

I proved that when A & B is evidence against C, this is so, and also when A & B are independent of C, this is so, the only case I am missing is when A & B is evidence for C.

It's clear enough to me that when you have one none-colliding path between any two variables, they must not be independent; and that if we were to hold any of the variable along that path constant, that those variables would be independent. This can all be shown given standard probability theory and correlation alone. It can also be shown that if there are only colliding paths between two variables, those two variables are independent. If I have understood the theory of d-separation correctly, if we hold the collision variable (assuming there is only one) on one of these paths constant, the two variables should become none-independent (either evidence for or against one another). I have proven that this is so in two of the (at least) three cases that fit the given DAG using standard probability theory.

Those are the proofs I gave above.

potato on Causality: a chapter by chapter review

2012-10-02T14:43:50.688359+10:00

I have a question: is D-separation implied by the komologorov axioms?

I've proven that it is in some cases:

Premises:

1)A = A|B :. A|BC ≤ A|C
2)C < C|A
3)C < C|B
4) C|AB < C

proof starts:
1)B|C > B {via premise 3
2)A|BC = A * B * C|AB / (C * B|C) {via premise 1
3)A|BC * C = A * B * C|AB / B|C
4)A|BC * C / A = B * C|AB / B|C
5)B * C|AB / B|C < C|AB {via line 1
6)B * C|AB / B|C < C {via line 5 and premise 4
7)A|BC * C / A < C {via lines 6 and 4
8)A|C = A * C|A / C
9)A|C * C = A * C|A
10)A|C * C / A = C|A
11)C < A|C * C / A {via line 10 and premise 2
12)A|BC * C / A < A|C * C / A {via lines 11 and 7
13)A|BC < A|C
Q.E.D.

Premises:

1) A = A|B :. A|BC ≤ A|C
2) C < C|A
3) C < C|B
4) C|AB = C

proof starts:

1)A|C = A * C|A / C
2)A|BC = A * B * C / (B * C|B) {via premises 1 and 4
3)A|BC = A * C / C|B
4)A * C < A * C|A {via premise 2
5)A * C / C|B < A * C|A / C {via line 4 and premise 3
6)A|BC < A|C {via lines 1, 3, and 5
Q.E.D.

If it is implied by classical probability theory, could someone please refer me to a proof?

potato on Terminal Values and Instrumental Values

2012-09-16T17:50:30.774776+10:00

A real deadlock i have with using your algorithmic meta-ethics to think about object level ethics is that I don't know who's volition, or "should" label I should extrapolate from. It allows me to figure out what's right for me, and what's right for any group given certain shared extrapolated terminal values, but it doesn't tell me what to do when I am dealing with a population with none-converging extrapolations, or with someone that has different extrapolated values from me (hypothetically).

These individuals are rare, but they likely exist.

potato on Math is Subjunctively Objective

2012-09-16T17:27:11.184639+10:00

You've misunderstood me. It's really not at all conspicuous to allow a none-empty "set" into your ontology, but if you'd prefer we can talk about heaps; they serve for my purposes here (of course, by "heap", I mean any random pile of stuff). Every heap has parts: you're a heap of cells, decks are heaps of cards, masses are heaps of atoms, etc. Now if you apply a level filter to the parts of a heap, you can count them. For instance, I can count the organs in your body, count the organ cells in your body, and end up with two different values, though I counted the same object. The same object can constitute many heaps, as long as there are several ways of dividing the object into parts. So what we can do, is just talk about the laws of heap combination, rather than the laws of numbers. We don't require any further generality in our mathematics to do all our counting, and yet, the only objects I've had to adopt into my ontology are heaps (rather inconspicuous material fellows in IMHO).

I should mention that this is not my real suggestion for a foundation of mathematics, but when it comes to the challenge of interpreting the theory of natural numbers without adopting any ghostly quantities, heaps work just fine.

(edit): I should mention that while heaps, requiring only for you to accept a whole with parts, and a level test on any gven part, are much more ontologically inconspicuous than pure sets. Where exactly is the null set? Where is any pure set? I've never seen any of them. Of course, i see heaps all over the place.