Eric Holloway: Wrap up Experiment on Mutual Information

[swamidass (S. Joshua Swamidass)]

@EricMH

If you are done trying to convince me, perhaps our time has come to a close. At least for now.

Ok, so you admit you cannot prove ID is empirically intractable. Fine, why have I wasted my time here?

As I see it,

1. You are a leading light in ID Information Theory, trained by the best of the movement.

2. You made several theoretical claims that you believed transferred over to practical measurement.

3. Two times now, you produced simulations meant to demonstrate a claim.

4. In both cases, your simulations did not demonstrate your claims true. Perhaps they were uninterpretable, but they certainly did not demonstrate your claims true.

5. Several other claims have been made that are all demonstrably false. In fairness, I will list one below, but there are many more like it.

6. There is no reason any one should trust the claims we have not tested, because not one of the claims you have tested has been demonstrated true.

As an example of a false claim:

@EricMH

My algorithm will give MI(Y;Y) > 0 on long enough sequences, but not on every sequence due to LZ taking awhile to get warmed up.

@swamidass

I increased the length to 10000, and got this result:

Prediction I_LZ(Y:Y)>0
Experiment 5: iid Y
Average success: 0.0

Increasing the string size does not fix this problem. Your instinct is false. Why didn’t you do the simulaiton yourself instead of putting out an obviously false claim like this? Why would you make these claims without testing them? This is really bad form.

There are so many claims like this through out your work. It takes too much effort for me to demonstrate them all false, but in this case I did.

This gets to the heart and soul of information theory, as I explained to you long ago:

@swamidass

You did not really answer my questions. What you did was far more surprising. Your simulation actually falsified your own equation. This at least makes clear what you were thinking. It also shows your equation is wrong in that you have not articulated or understood its limits. If you had, you would never have written the simulation this way.

@swamidass

Why Uncomputability Matters

Remember our exchange on this?

This clarifies are your using emperical compression as an aproximation of Komologrov complexity (which is uncomputable).

The reason why uncomputability is so important is because it means it is impossible to accurately measure information from data alone. That means we cannot accurately measure the information content of DNA. This is a fundamental finding of information theory.

Why does that matter? We cannot accurately measure anything in this world. So what?

Now you are seeing why it matters. If you can’t keep this straight you will end up totally misunderstanding what your proofs mean. This one of the most important results in information theory, and must be thoroughly grasped to apply it correctly. This is why your control failed worse than your main experiment.

I have demonstrated that your theoretical constructs have not even one time transferred over to an empirical simulation. Maybe someone else can succeed where you failed, and I’d welcome this. For example, maybe someone can solve this Open Challenge to ID Advocates.