# Breaking the law of information non growth

Part of my broader point that Dembski’s argument is support by standard information theory.

The article is pretty technical, though not as technical as the paper by Leonid Levin I got the ideas from.  If you skim it, you can get the basic idea.

https://am-nat.org/site/law-of-information-non-growth/

First, I prove that randomness and computation cannot create mutual information with an independent target, essentially a dumbed down version of Levin’s proof.  Dembski’s CSI is a form of mutual information, and this proof is a more limited version of Dembski’s conservation of information.

Next, I prove that a halting oracle (intelligent agent) can violate the conservation of information and create information.

Finally, I show that there is a great deal of mutual information between the universe and mathematics.  Since mathematics is an independent target, then by the conservation of information there should be zero mutual information.  Therefore, the universe must have been created by something like a halting oracle.

I cannot promise a response to everyone’s comments, but the more technical and focussed, the more likely I will respond.

## 117 thoughts on “Breaking the law of information non growth”

1. If I accept, for the sake of argument, that “randomness and computation cannot create mutual information”, how does this impede evolution from creating arbitrarily large quantities of new information in genomes?
The claim that the correlation with ancestral genomes does not increase does not appear to me to be a barrier.

2. First, I prove that randomness and computation cannot create mutual information with an independent target, essentially a dumbed down version of Levin’s proof.

Are you assuming that a biological organism is a computer plus a random number generator? Because that seems weird. And if you are not assuming that, then I don’t see how what you prove is relevant to biology and evolution.

Next, I prove that a halting oracle (intelligent agent) can violate the conservation of information and create information.

There are no halting oracles. Does that mean that there are no intelligent agents?

3. Can someone give me an example of a DNA sequence known in a living organism that could not have been produced by an accumulation of mutations(possibly subject to natural selection)?

If no one can give such an example, of what worth are these information-gobbledygook “proofs”?

4. Thanks Alan, I’m seeing if TSZ’s overt aggression provides better technical feedback than the passive aggressiveness over at PS.

An underlying assumption is all natural processes, including evolutionary processes, are reducible to Turing computation. If not, then my argument does not apply.

Not being a biologist, and still looking into FI, I cannot really comment on the applicability to specific biological mechanisms. The general point is if there is a target independent of possible evolutionary mechanisms that describes what we see in biological organisms, then the organisms cannot have been generated through evolutionary mechanisms. What such a target might be I cannot say.

So, instead of biology, I refer to Wigner’s thesis that the universe is highly describable with mathematics. If we grant that mathematics is the same regardless of how the universe is formed, i.e. mathematics is an independent target, then Wigner’s thesis indicates the universe is intelligently designed.

5. Can someone give me an example of a DNA sequence known in a living organism that could not have been produced by an accumulation of mutations(possibly subject to natural selection)?

Are you ok re stating your question replacing “could not have” with ” is unlikely to have”?

6. So would it be correct to say that you agree that it has not yet been shown that your argument here is relevant to biological evolution?

7. Hi Eric,

“…Finally, I show that there is a great deal of mutual information between the universe and mathematics. Since mathematics is an independent target, then by the conservation of information there should be zero mutual information. Therefore, the universe must have been created by something like a halting oracle…”

You don’t know me but I think that QM has a much better way of explaining and experimentally testing the information theory, not only in evolutionary theory but also in the cell differentiation process, based on the law of conservation of information that applies to both classical and quantum information…

Do you perhaps have a background or interest in QM?

8. colewd: Are you ok re stating your question replacing “could not have” with ” is unlikely to have”?

Yeah I would be fine with that.

9. @rumraket, yes I have not shown whether my argument is relevant to biology. On the other hand, if someone could show biological processes are not Turing reducible, that would be pretty interesting.

@J-Mac, I do not know much about QM.

10. Hi Eric, welcome to TSZ.

It appears the link to the Leonid Levin paper is broken. The other link works fine.

11. EricMH: Not being a biologist, and still looking into FI, I cannot really comment on the applicability to specific biological mechanisms.

Not being a mathematician, I find mathematical arguments hard to follow. But, maybe you can explain one thing that has puzzled me about Bill Dembski’s “complex specified information”.and related concepts. That’s what raw data you start with? I’ve been reading Uncommon Descent and one contributor there, gpuccio, seems to start with similarities between gene sequences in various species. The argument seems to be, a sufficient variance means you can’t get from A to B by a series of evolutionary steps. But Demski’s method seems simpler, any change to which you can attribute a number larger than can’t have evolved. I just don’t quite see what is being counted. Is it just nucleotides?

12. A to B by a series of evolutionary steps. But Demski’s method seems simpler, any change to which you can attribute a number larger than 10^150 can’t have evolved. I just don’t quite see what is being counted. Is it just nucleotides?

Gpuccio is measuring AA sequences and estimating information based on preservation over deep time. If that measurement is 500 bits or more, then he infers design. The 500 bits is approximately Demski’s 1^150 number. Alan, I am surprised you did not know this already.

13. Gpuccio is measuring AA sequences…

I think it would be more correct to say gpuccio is taking counts from publicly available gene sequence databases.

…and estimating information based on preservation over deep time.

Would it not be more correct to say he’s producing a figure or count of differences between two database sequences?

If that measurement is 500 bits or more, then he infers design.

That’s the bit I don’t understand. Why the arbitrary threshold? Evolutionary processes are incremental, not all-at-once.

The 500 bits is approximately Demski’s 1^150 number.

Indeed. So what is different? Demsbki never talked about gene sequence differences across sequencesspecies.

Alan, I am surprised you did not know this already.

What I don’t understand is how the mathematical figure derived from raw sequence counts becomes a problem for evolutionary processes.

ETA correction to typo (better Corneel? 🙂 )

14. What I don’t understand is how the mathematical figure derived from raw sequence counts becomes a problem for evolutionary processes.

Because you think that the needles almost = the haystack. 🙂 I don’t think you can support the claim that all biology works this way. It is likely that a lot of it is subject to Erics information argument. We observe a combination of layered complexity and long sequences that code for that layered complexity.

15. Does everyone here think evolutionary algorithms are good models of evolution? If so, I can apply the information argument to evolutionary algorithms, at least for illustrative purposes.

16. colewd: Because you think that the needles almost = the haystack.

Do I, I did not know that. Wouldn’t it be more correct to say that we don’t yet know how rare potentially functional proteins are in sequence space, nor do we need to search the complete space, just look till we find something that works well enough for the moment.

I don’t think you can support the claim that all biology works this way.

Which way? I think evolution works by iterations of random variation then being sifted by selection.

It is likely that a lot of it is subject to Erics information argument.

But Eric quite candidly stated upthread he is not familiar enough with biology to make a biological argument.

We observe a combination of layered complexity and long sequences that code for that layered complexity.

We observe long (a bit vague as a description) DNA sequences in genomes, sure. “Layered complexity”? What’s that?

17. EricMH:
Does everyone here think evolutionary algorithms are good models of evolution?If so, I can apply the information argument to evolutionary algorithms, at least for illustrative purposes.

Any algorithm that includes a niche, reproduction with variation, competition for limited resources in the niche, would be a good model.

18. Which way? I think evolution works by iterations of random variation then being sifted by selection.

I know you believe this but you can’t model this so it’s not a testable claim.

We observe long (a bit vague as a description) DNA sequences in genomes, sure. “Layered complexity”? What’s that?

Start here: https://youtu.be/oweNT288BXo

19. colewd: Start here: https://youtu.be/oweNT288BXo

Human designers strive for simplicity and modularity. Understandability. Ask any good programmer you may know.

Why do you conclude design when observing mechanisms unlike those that human designers are known to design?

20. Why do you conclude design when observing mechanisms unlike those that human designers are known to design?

I already derailed the last discussion 🙂 Eric has already stated that he does not know yet how to converge his hypothesis with Biology.

21. colewd: Start here

colewd: I know you believe this but you can’t model this so it’s not a testable claim.

What? Two ways to produce data:
1. From observation and measurement.
2. From experiment and measurement.

22. colewd: I already derailed the last discussion Eric has already stated that he does not know yet how to converge his hypothesis with Biology.

23. EricMH: An underlying assumption is all natural processes, including evolutionary processes, are reducible to Turing computation.

I do not make that assumption. I cannot see any basis for it.

If not, then my argument does not apply.

I guess that’s why I am unpersuaded.

The observation of functional information and systems that appear designed for a purpose. To me DNA/Proteins and all they do is the smoking gun behind design being behind our universe.

As you remember I agree with J-Mac that we will see the similar evidence once we have a better understanding of atoms and their properties like quantum mechanics.

25. EricMH: An underlying assumption is all natural processes, including evolutionary processes, are reducible to Turing computation. If not, then my argument does not apply.

You get points for expressing the assumption outright. You’d get considerably more if you were to provide a cogent account of why you made the assumption in the first place. (I do not regard Jonathan’s paper as cogent. I’d be interested in hearing how you, yourself, came by the notion that there was value in making the assumption.)

Naturalism does not entail describability of nature, let alone describability in terms of Turing computation. Nor does it entail a computational theory of mind.

If you embraced naturalism, then you might take a particular stance compatible with naturalism. But as someone who rejects naturalism, you do not get to reduce naturalism to some particular stance, and then equate refutation of the particular stance with refutation of naturalism. Having listened to your talk on imagination sampling several times, I know that’s in fact what you have done.

ETA: Jonathan Bartlett, “Using Turing Oracles in Cognitive Models of Problem-Solving

26. EricMH: Does everyone here think evolutionary algorithms are good models of evolution?

I see them as half-baked.

They are reasonably good algorithms for what is happening in the population of biological organisms. But they do not adequately model the dynamic changing of the environment.

27. 1. If there is such a thing as a natural law of information non-growth, then, intelligence would not be able to “break” it.
2. If intelligence could break it, then it would not be a natural law, and therefore anything could break it.
3. In case you didn’t know, intelligence is but one more natural phenomenon.
4. Therefore whether I took a look or not doesn’t matter. No matter how “technical” that link must lead to mere bullshit.

As an aside, Mathematics started its development based on “The Universe.” It’s not an independent target. Not only that, it’s the product of humans, not of magical beings in the sky. Therefore, if everything above worked (yeah, right), Math would only prove that we exist, not that magical beings in the sky exist.

ETA: Crap, this OP is worse than wrong. Mutual information refers to the correlation between two variables. IOW, mutual information is relative. Therefore, the mutual information between two things can increase without increasing/decreasing the “information” of the whole system/universe/whatever. The OP seems to be/point-to a conceptual mess.

28. FYI, evolutionary algorithm is an engineering term. Of course, theoretical biologists sometimes model evolutionary processes as algorithms. But, conventionally, people are talking about problem-solving, not biological modeling, when they talk about evolutionary algorithms.

29. Entropy: Mutual information refers to the correlation between two variables.

Algorithmic mutual information is deeply related to, but not the same as, mutual information in classical discrete information theory.

30. EricMH in OP: Dembski’s CSI is a form of mutual information, and this proof is a more limited version of Dembski’s conservation of information.

You can’t just toss off remarks like that. Not even algorithmic specified complexity, which is formally quite similar to algorithmic mutual information, is a form of algorithmic mutual information.

Are you referring to algorithmic specified complexity as “Dembski’s CSI”? Dembski radically changed his formulation of specified complexity in 2005, and algorithmic specified complexity does derive from that formulation. I haven’t a clue as to why anyone would refer to the “specified complexity” in No Free Lunch (2002) as a form of algorithmic mutual information.

You asked for formality in the OP. But you’re playing it terribly fast and loose with your remarks. When you neglect to make the formally necessary connections, you come off as a crackpot. Perhaps you can make the connections. In all sincerity, I’d rather be shown that you’re competent, and just prone to be in a bit too much of a hurry, than be left with negative conclusions about you. So go ahead and show me.

Advice on using : If you edit a comment, then you have to put double backslashes everywhere you put backslashes in the original comment. You might want to compose math-laden comments in a environment, and then copy-and-paste the source into the comment box here.

31. Tom English:
Algorithmic mutual information is deeply related to, but not the same as, mutual information in classical discrete information theory.

Yep, which is why I didn’t write “… is the same as …”

32. colewd: The observation of functional information and systems that appear designed for a purpose.

But what “purpose” is that? It sounds like you are confusing “function” and “purpose”.

colewd: To me DNA/Proteins and all they do is the smoking gun behind design being behind our universe.

What do proteins “do”? What is their purpose? It seems to me the mere fact that something does something is what you are basing “design” on.

The inert gases “do” almost nothing. And yet they are designed. Other elements are far more promiscuous in their reactions. And yet they are designed as well. Heads colewd sees design, and the purpose of a coin is to be flipped and that’s also design. Tales? Design.

I suspect a variant of pareidolia. Mistaking function for design. Hemoglobin transports oxygen around the body. Therefore it was intelligently designed to do that! That is it’s purpose.

I cannot convince someone they are not seeing a face in the clouds. Likewise there is no escape for colewd. Not any real insight or progress to be had from him.

colewd: As you remember I agree with J-Mac that we will see the similar evidence once we have a better understanding of atoms and their properties like quantum mechanics.

joke, rite?

33. colewd: Because you think that the needles almost = the haystack.

No, nobody has to actually think this, that is just plain false.

34. colewd: We observe a combination of layered complexity and long sequences that code for that layered complexity.

Yadda yadda. That sure sounds fancy. But what follows? We aren’t shown.

35. colewd: Alan Fox,

Which way? I think evolution works by iterations of random variation then being sifted by selection.

Colewd: I know you believe this but you can’t model this so it’s not a testable claim.

What? Are you claiming an evolutionary process that works by random variation subject to selection can’t be modeled? That’s so obviously false it boggles the mind. That statement can’t be entertained by a thinking person.

Here’s one such model: http://boxcar2d.com/

36. colewd: The observation of functional information and systems that appear designed for a purpose.

The idea that you observe “systems that appear designed for a purpose” is just question-begging subjective interpretation aka an assumption you make. We look at the same thing, and I don’t see that at all. And in any case we’ve been over the whole FI nonsense in several previous threads, and it all came down to the same issue, that you basically just assume that if you can find some way to calculate the FI for some sequence to be 500 bits or more, then it couldn’t have evolved. But you actually don’t even know, you just declare it.

37. EricMH:
Does everyone here think evolutionary algorithms are good models of evolution?If so, I can apply the information argument to evolutionary algorithms, at least for illustrative purposes.

I am traveling but quickly: yes. At least if you can show that a conservation law prevents increase of fitness in an EA, that would cause me concern. More after I get where I’m going.

38. Joe Felsenstein: At least if you can show that a conservation law prevents increase of fitness in an EA, that would cause me concern.

This would be at odds with reality.

39. I do not have anything formally written down showing CSI is mutual information. Up till now it has been an intuitive connection. I’ll work on formalizing the connection, but it’ll be awhile.

40. I am traveling but quickly: yes. At least if you can show that a conservation law prevents increase of fitness in an EA, that would cause me concern. More after I get where I’m going.

It appears where the ID guys are going including Sanford and Behe is a slow longterm loss of fitness with a few positive adaptions along the way. Do these claims concern you?

41. (Finally in hotel room — for a few minutes)

Welcome, Eric. You will find the comments of varying quality here and taking all sorts of contradictory positions. Also a lot of opportunities for going off-topic. I applaud your willingness to grapple with the arguments.

Let me make a few points:

1. Yes, let’s look at evolutionary algorithms, perhaps best initiall to look at ones with infinite population sizes as then change in deterministic and easier to do the math.

2, Ignore all the people take the position that evolutionary algorithms are not good enough to evaluate your arguments. They don’t work in theoretical population genetics, I have done so for decades. And realism isn’t needed — indeed you want to test your arguments in simple cases where we can do the math easily. If our arguments are going to fail, they will fail there. Yours too.

3. I think the important specification is fitness.

Go to break off for an hour or two now.

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