Eric Holloway: Algorithmic Specified Complexity

[EricMH (Eric Michael Holloway)]

First, I echo your appreciation. I have found the discussion to be helpful for my own thinking on the matter, and it has been constructive. I also apologize for any strong wording on my part, or unfairness in portraying your argument. If I have been unfair, point it out and I will correct.

Unfortunately, I find your closing arguments to not be so great. On the other hand, letting me post the closing comment is very fair minded of you, and this increases my level of trust, which is great.

First, I previously proved that we do not need an exact P to avoid over estimating ASC,

@EricMH

Therefore, by your criteria, the estimated P is only valid if and only if it exactly equals the true P.

If we are just looking at a subset of the possible X, then the estimated P does not need to equal the true P to be valid. In any practical scenario we are looking at a subset of physical phenomena, anyways.

and then you seem to completely ignore this point:

@swamidass

ASC (i.e. OASC) is guaranteed to be less than CSI, provided the implementation uses the correct P. If the wrong P is used, then ASC might be higher than CSI.

I should emphasize that this standard is not achievable in practice. Not a single ID computation of information in biology uses a valid P by this standard. Remember:

1. We do not know all natural causes, and we expect to find new causes.
2. Even for those we do know, we do not know how they interact to produce a P.
3. For those we do know, most need more information than is within a DNA sequence to accurately compute P.

Notice that all these factors collaborate to increase ASC:

1. An unaccounted natural cause that orders the data will make P invalid.
2. Inability to accurately model how different causes interact will make P invalid.
3. Ignoring critical information for computing P will make P invalid too.

For those three reasons, we can be certain that observed ASC may be wildly higher than CSI. Essentially our ignorance or inability to implement P is the most likely reason for high ASC, not CSI. None of this appears to dampen Marks enthusiasm that ASC is an empirical way of detecting CSI.

The way I propose, of only considering a subset, is also not the only way. As an addition, after just a little thought, there are at least two other criteria I know of that can avoid overestimation:

1. If we sample according to any P_{est.} , then the expected value of the self information (first) term is \sum_{x\in X} P_{est.}(x)\log_2 \frac{P_{est.}(x)}{P_{true}(x)}, which is the Kullback-Liebler distance, and is always non-negative, mathematically proving we are always expected to underestimate P_{true} with any choice of P_{est.}.
2. If overestimation is unavoidable, we can correct with an extra term subtracting the possible overestimation.

And even if the probability somehow remains that we overestimate, unless the probability will most likely be greater than 50% and the amount of overestimation is very large, then a very large ASC value is still going to give us true positives.

So, the bottom line is your primary proof, that we must exactly know P_{true} in order to avoid overestimating ASC, does not work. There are at least three reasons it does not work as you initially state, so we need further development of that proof for it to strongly refute the practicality of ASC.

Second, you claim there is a fundamental theoretical issue with ASC,

@swamidass

The real problem is the theoretical errors, which I can demonstrate wrong with simulation more effectively than arguing with symbols.

but then cannot provide a proof in “symbols” and claim that you can only demonstrate it empirically. If there is a theoretical problem with ASC, you need to give some kind of concrete idea what this problem is, even if you cannot symbolically prove it. Hand waving and reference to non-existent simulation is not a counter argument.

Third, you claim the mutual information issue was settled in our last exchange,

@swamidass

Recall, we demonstrated that #1 was false in our last exchange, for exactly the same reason. There is gap between theory and practice.

which I most certainly do not agree with. Perhaps you misunderstood my apology in that thread as a concession. I should have been clearer. Your argument above is the same kind of fallacy you make regarding ASC that somehow the mathematics is disproven by empirical experiment. I have no idea why you say this sort of thing. It is a category error to claim a mathematical proof can be disproven by empirical experiment. One could, perhaps, disprove a mathematical conjecture with empirical evidence, but the core property of ASC and of mutual information non growth is proven, not a conjecture.

I stand by my entire argument in the mutual information exchange. I’ll only grant the experiment I performed can be specified to greater mathematical rigor, but that is not a crucial point that somehow disproves my whole thesis, so it is disingenuous to act as if it were.

Finally, it isn’t “evolution” that reduces humans to matter,

@swamidass

Nothing in evolution implies this. I just don’t understand what you are getting at here. Same goes for following paragraphs. This is not sensible. Nothing in science demonstrates that humans are reducible to matter. What exactly are you arguing against?

it is materialism that does so, which claims that everything in existence operates according to the laws of physics. I agree with you that nothing in science demonstrates that humans are reducible to the laws of physics, but it is also true that materialism is the status quo of the scientific establishment, and the status quo of many leaders in our day and age who make life and death decisions. However, it is a highly unfounded philosophical position with no scientific evidence, as you rightly point out, and ID is a great scientific counter to that position.