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.
Will not discuss that in this thread as off topic — we’re going to have a hard enough time staying on topic as it is. You’ll hear more about that from me in other threads soon.
Physicist Paul Davies, the Mind of God, which won the Templeton Prize for religion, argues the mathematical (algorithmically compressible form) of the laws of physics are another kind of “fine tuning” (I use the phrase loosely) and constitute evidence of purpose in the universe. It is a qualitative argument for God, though Davies is an agnostic.
Only a narrow range of Planck’s constant allow for this property of detectable compressibility. Otherwise, we would be able to see or comprehend or live, much less do science to explore the universe. We tend to take for granted we can know anything about the universe. Such fine tuned, decipherable universes are far from ordinary expectation from random processes.
Similar ideas are in Wigner’s essays, and Dembski’s essay, “The Last Magic.” Randomness does not make highly algorithmically compressible data that is also easily recognizable as compressible. Somethings are compressible, but one needs specialized knowledge to see that it is.
The OP seems like a more formal description of the issue Davies, Wigner, and Dembski raise.
So not connected to Demsbki’s argument that CSI cannot be put into the genome by natural selection (or other natural evolutionary processes). If natural evolutionary processes do the job, but it’s because the universe is Special that they do, then the take-home message for this thread is that they do do their job in our universe. When biologists say what evolutionary processes do, they are not saying “in other universes”, they are talking about what happens in this universe. Which is what this thread is discussing.
That’s mostly good to hear. I have to repeat that Dembski radically changed the meaning of CSI in 2005, so “CSI” is ambiguous. The “CSI” of No Free Lunch (2002), in which Dembski sketched an ostensible proof of the Law of Conservation of Information, is very different from the “CSI” / “specified complexity” of “Specification: The Pattern that Signifies Intelligence” (2005), in which Dembski said nothing about a conservation law. The 2005 paper has received a lot of attention in the Zone. See, for instance, Elizabeth Liddle’s “The eleP(T|H)ant in the room.”
Algorithmic specified complexity clearly derives from the 2005 formulation of specified complexity, not Dembski’s earlier work.
I should tell you that I had an OP almost ready to go when you arrived. When you see it, please don’t take it as a response to what you’ve written here. I’m going to try to ignore this thread until I complete the OP.
Tom English,
Yes, I saw the title, and I am looking forward to your argument. I have written a proof of the opposite, which will someday get published in Bio-C, hopefully within my lifetime.
Sooo…does anyone have an opinion regarding the OP? I saw it left Felsenstein flabbergasted in another thread. It seems to prove the universe is intelligently designed, and I haven’t been able to think of a good counter argument, yet.
Hi Eric:
Levin calls his result ‘conservation of independence’ and you sometimes refer to ‘independent specification’. So I’d like to make sure I understand how the word ‘independent’ is to be interpreted.
The theorem says that for Kolmogorov MI, the mutual information I(X:Y) ≥ I(f(X):Y) where f is any function involving deterministic and stochastic elements. So I understand “independent” as referring to the nature of the function f in this theorem.
My concern is that in ‘independent specification’, there seems to be an implication that the definition of the function f cannot involve Y. Whereas in Levin usage, the word seems to refer to the degree of relationship between X and Y as formalized by I(X:Y). Now perhaps both of these are the same as f only being able to have deterministic and random components (and of course computable in the usual Church-Turing sense).
For the subsequent discussion, I think it is important to pin down what is being assumed. Is the following English gloss OK: the definition of f must be such that it does not involve Y and it is Turing-Church computable
Is that the complete implication in your use of ‘independent specification’.
(ETA: typos and phrasing)
Hi Eric:
I have some questions on the Empirical Application section, which I think you are referring to in the above post. But first I want to make sure I understand how you are using ‘independent’ as detailed in my previous post.
I have philosophical reply in addition the technical questions to be asked after I understand ‘independent’. My philosophical reply is this:
Your post assumes there is something new and substantive about Wigner’s unreasonable effectiveness. But really it is just another instance of the fine tuning argument.
Here is what I mean.
Mathematics is something we invent. Part of the reason we invented it is that we noticed regularities in our perceptions of and interactions with the world. So there is nothing to be explained in its success in science since we either build it or select it to best capture that existing regularity.
Now of course you can ask why the universe is regular. That’s the fine tuning regress.
Or you can claim that the success is unreasonable in some sense. And indeed, that is an open philosophical issue (link to related discussion in SEP). But that discussion is at a philosophical stalemate, so one can reasonably take the position that Wigner’s problem is simply a restatement of the fine tuning concern.
I agree with this. Just wanted to add that this is the reason I thoroughly reject the premise that “mathematics exists independently from the universe”.
Uhh no it seems to prove that mathematics is intelligently designed to describe the universe. Which it is. By us.
There’s an infinite number of ways to WRONGLY describe the universe with mathematics, and occasionally we happen to come up with ways that seem pretty well fitting. Often through trial and error by going through lots of ways that are wrong.
Oh, for fuck’s sake:
I’m not Joe, but the OP left me flabbergasted because of its astounding conceptual incompetence.
Well, either you cannot read, or your conceptual and philosophical frameworks are deeply problematic.
It seems to claim that the intelligent designer was a halting oracle. Since halting oracles cannot exist, that would prove that there is no intelligent designer.
Don’t get hung up on the words, you have to just look at the math.
😉
Neil Rickert,
Why not?
All in good t (=time). But Eric’s “Empirical Applications” in his linked post has a bit of math, more English, and I think insufficient mapping from the English to the math.
I am still totally unable to think clearly about that assertion. So I am not going to get involved in discussing it. Especially since whether or not the universe is “designed’ seems irrelevant to whether natural selection is responsible for adaptation.
I will concentrate here on whether we can assess Dembski’s assertions about CSI in biological organisms, in light of Eric’s arguments about mutual information, and by examining what happens in evolutionary algorithms.
If we spend this thread on the mathematics / universe argument, I hope that Eric will agree to participate in another that examines the Dembski / CSI / evolutionary-algorithm arguments.
Given that many people here seem to think that evolutionary algorithms are actually examples of evolution in action, and even of natural selection in action, that might be a good idea.
I think the problem with this discussion is that the term ‘information’ has a variety of meanings depending on the context. The one being examined may be a purely abstract concept that has no relevance to biology. We can bypass this problem by considering that however we define information in the end we know what its doing: its generating the complexity of living things. So the question should be: can the complexity of a system increase by following only natural laws? I think the answer to that question is an obvious ‘yes’
My math professors in college had a term for that. They called it “hand waving”.
RodW,
What is the model that gives you confidence here?
Ok, well consider the earth when it first formed. It was essentially a single molten mineral. Natural processes immediately started to work and after a few billions years there are thousands of different minerals as part of a very complex geology. This is the case even if we dont consider the minerals produced as a result of life. Or you can go back further and consider a few cubic parsecs of space filled with hydrogen atoms. After a round or 2 of star formation there will be complex star systems with rocky and gas-giant planets each with it own complex geology and weather. In each case there is a clear increase in complexity in an essentially closed system.
RodW, Your comment reminds me of Mike Elzinga.
Thanks everyone for your comments. It looks like there are three main objections:
1. Halting oracles “cannot exist.” Unsure whether a logical impossibility, or physical impossibility is meant. More detail is welcome.
2. Math is generated by the physical universe (e.g. the physical brain), so it is not independent. In other words, 1+1=3 in an alternate universe, if I understand the objection correctly. This objection seems pretty clear.
3. The law of non-growth is false, and mutual information can increase without bound. More detail here is welcome as well.
I do not see any criticism of the argument’s logical validity or the mathematics, although objection #3 hints in that direction. Perhaps everyone is fine with those aspects.
@Felsenstein, I am considering a specific application to evolutionary algorithms, but like most of my side projects it will be awhile until it is completed. For the time being, you might be interested in a related paper Dr. Marks and I wrote showing open ended evolution is not algorithmically detectable, titled “Observation of Unbounded Novelty in Evolutionary Algorithms is Unknowable.” It is a conference paper that was a poster presentation at ICAISC 2018 and the proceedings are published by Springer. I do not know of a public pdf, so here is a link to the paper on my box.com account:
https://app.box.com/s/bs52nllkqaxpkqhj9c23gq5t1g0lstau
@BruceS, your gloss is a workable paraphrase. However, it is not quite accurate, because the law considers all possible fs that are an input to a universal Turing machine, and some of these fs have mutual information with Y (some are or contain Y, too). However, it turns out when we take the average over all f, using a computable probability distribution, then there is no expected information gain.
So, independent in this case means that Y does not change as we change f while taking the average. Another project I have is to improve the link between the math and the English.
Thank you everyone for your time, and I hope you all have a great Thanksgiving.
It seems to me you don’t, then.
In other words, 1+1=5 in an alternate universe, if I understand the objection correctly?
You’re a funny guy Mung, that’s why I’m going to kill you last.
Thanks for that description of f and independence. I am not sure I fully appreciate how it could apply to using Levin to formalize Wigner’s argument. So I’ll just go ahead and post all my concerns and you can let me know if the description of f that I presume is inappropriate.
I’ll grant for the sake of argument the claim that Wigner’s unreasonableness raises a new issue; that is, it is not enough to reply that we choose the math to make our physics work.
To start, it is important we have an agreed definition of Wigner’s argument. In this post, I’ll provide a detailed description of the argument as I understand it from his paper and this Wiki article on the paper. In the next two posts, I’ll use that description to raise questions with your ideas.
Wigner’s argument is more than noting mathematics works in science and in particular fundamental physics, for that alone is easily explained as described in my earlier post. I think instead the argument involves these four requirements:
1. Science is about explaining, predicting, and controlling the empirical world. In physics, explanations use mathematics.
2. Independently of science (and hence the universe as humans perceive it), mathematicians create many abstract structures.
3. When physicists discover unexplained phenomena, they review existing mathematics and sometimes find that previously unused mathematical structures can be used as part of explaining these phenomena. On its own, that is not unreasonable because physicists work with idealizations, meaning they decide how much much of the phenomena the mathematics has to describe. Further, there is much mathematics to choose from and only some is useful. Scientists have a lot to choose from and are bound to find something useful, especially given the idealizations. So far, there is nothing unreasonably surprising.
4. What is surprising is that physicists find in some cases that the new mathematics generates unexpected, novel, confirmed predictions. These predictions cover phenomena beyond those phenomena that led to the new math being incorporated into physics.
I believe your attempt to formalize and explain Wigner’s argument using Levin’s result has to capture the following things to fully reflect Wigner’s point:
1. The universe itself.
2. The mathematics created by human beings.
3. The mathematics used by scientists after the scientific process of examining various theories.
4. The process of science itself, including selection and testing of various candidate theories expressed mathematically. That selection includes experimentation where the universe gets its say.
I’ve omitted any attempt to fully capture the notion of unreasonableness, since I cannot see how to do that formally. But the above will be enough for me to list some concerns with your derivation over my next two posts.
(post 2 of 3)
In your derivation, you work with I(U:M) and you say U is the universe and M is Mathematics, with U and M being bit strings. But later you say M is the laws of physics as encoded as a set of computer programs.
ISSUE 1: What does “U is a bitstring” mean.
It cannot be a (human) description, since that idea is already used in M as the laws of physics. Perhaps you mean U is the description of the Universe as captured by the descriptions produced by some future, perfected physics? But that too would not capture Wigner’s argument, since it’s definition of U presupposes human science and does not only to the universe itself.
You also compare U to a video game and say U is a recording of the game. So perhaps you mean U, the universe, is information and information only. That is how I understand Wolfram, Lloyd, and possibly Tegmark. So it’s defendable and might work for the rest of your argument. But few scientists accept this idea, so that would be a concern. Another concern with this approach would be how humans access that information. So even if we go with that approach as U as information, I think we need to build into the Levin formalization a means for humans to capture and describe excerpts of that information via experiements.
Do you have anything else for the meaning of “U is a bitstring”?
ISSUE 2: Two different meanings for M.
On the one hand, you define M as mathematics. On the other, you define it as the laws of physics, encoded as computer programs. But those are two different things, since physics is science, and the output of physics is a subset of extant mathematics (or algorithms) along with a mapping of the math (or variables in the algorithms) to the observable outcomes of experiments.
Now I believe we do need to separate math from physics, as capture by requirements 2-4. More on that in the next post.
(post 3 of 3)
ISSUE 3: Defining math without reference to physics.
Perhaps you can define math as a platonic universe, separate from the spatio-temporal universe U. The problem with that approach is that it does not capture Wigner’s argument, since he assumes physicists search human mathematics only.
So you could define M as all human created mathematics, encoded as a bit string. That seems a reasonable approach, at least for use in your argument.
ISSUE 4: Making the argument using three strings: U, M, P (physics).
To capture Wigner’s argument, I think you need to consider the universe, math, and physics separately. Provisionally, take U as saying the universe is information, take M as human math captured as a bit string, and take P as current best physics, encoded in math plus an English description mapping variables to the observable world. How can then we use then Levin to capture Wigner?
If you work with I(U:M) then it is unclear if there is MI between M and U. Although among M might be mathematical statements also used in physics, M alone lacks the descriptions of how to map variables to the observable world. Further, what would the function f be? It is true changes to human math don’t care about capturing the world. So math in that sense might be independent of U in your formalism. But again, Wigner’s argument is about science, not math on its own.
So what about working with I(U:P)? That would say that P and U have mutual information. We could say that the predictions made by P capture or predict a subset of U, hence there is MI. But the problem is that P predicts human observations of U, not U as pure information. So we need some way to incorporate that concern.
Suppose we find one. Now what is the function f? I think it has to be a function that applies to P, not U. Then f refers to an update of P and the claim is it cannot increase the MI between U and P, that is that improved physics does not yield better predictions. That seems wrong which immediately raises doubts about the application of Levin you use. But perhaps more details on the issue will help explain it better.
Now f is defined to capture steps 3, 4 of my requirements: the search of existing math and the application of scientific process to test and review theories. But any test is going to involve U and in particular observations of U. Further, f will vary with the results of observations of U, which is the only human way to understand U. So it seems to me that any function f cannot meet the independence requirement.
Nope. those are not the main objections, those are the ones you choose because you don’t know what to do about the rest of your nonsense, so you’d rather ignore those problems. The main problem with your OP is that it’s a conceptual, unsalvageable, mess. It cannot be fixed.
You’re refuting your own claim here.
Math is conceptual. It was invented by people. It is based on our observations of “the universe.” Therefore it cannot be an “independent target.”
Precisely because it’s not an independent target 1+1=3 doesn’t make sense. IOW, 1+1=3 doesn’t make sense given the referents we’ve used to produce math. You’re refuting your own fucking assertion. If math was an independent target, then we’d have no referents to verify if 1+1 should be 3, 5, or anything else. As I said, you are immersed in some profound conceptual mess. (No wonder Joe prefers to leave your OP alone.)
Not only that, since math is human, your bullshit, if it wasn’t the conceptual mess that it is, would prove that there’s humans, not that there’s magical beings in the sky.
You obviously don’t understand the objections, which is not surprising, since you don’t understand your own assertion that math is an independent target.
I didn’t say that. I didn’t see anybody else saying that. What I said is that if there’s such a thing, and if that’s supposed to be a natural law, then intelligence should not be able to break it. So, if intelligence can break it, then it’s not a natural law and other natural phenomena can break it too. So, whether the “law” is true or false, doesn’t matter, it’s a lose-lose deal for your bullshit.
Your assertions, which you pretend to pass for premises, are worse than wrong. They’re conceptually messy. They’re nonsense. Thus, checking the form of the argument, or the math, is unnecessary. Garbage-in-garbage-out.
Entropy,
I hope whatever objections I missed comes up again if they are important. For now I’ll be focusing on those 3, along with BruceS’ comments.
Regarding #2, it sounds like you are saying that in some universes 1+1=2 does not make sense, and there is no universe where 1+1=3. Is this correct? If not, perhaps you can clarify.
I’ve now posted a proof that there is no upper bound on the increase of algorithmic specified complexity due to data processing.
As for what you’re claiming here about your OP, you’ve received highly pertinent comments about the underlying assumption. You have not replied to those comments, and I’d say now that it’s not good form for you to suggest that we’re ignoring your main claim.
As far as I know, no one except for you, Jon Bartlett, and fifthmonarchyman believes that non-Turing computation implies intervention of a nonnatural intelligence in nature.
🙂
Well, I wish I could just say that you’re playing the fool. But the rules here state that I should give you the benefit of the doubt about that, that I have to assume that you’re commenting in good faith. Thus, I can only conclude that you’re too mentally incompetent to understand how deep your problems are. Thus I’m wasting my time even trying.
If you can be incompetent enough to be this wrong about what I meant, then you’re too incompetent to understand your own claims in the OP. This means that I cannot expect any further explanations to help you out. So I won’t bother.
I would suggest we not debate whether EAs are or are not actually themselves examples of evolution in action, or natural selection in action. I can see a useless wrangle over that.
They are models of natural selection, mutation, recombination, and (some of them) genetic drift. Models of simple cases. And these simple cases can, some of them, have their outcomes predicted mathematically. Thus we can see whether they predict that natural selection will result in adaptation.
And then, hopefully, we can check this against William Dembski’s predictions, or Eric Holloway’s.
The one thing not to waste our time on is whether we get to call the selection in those models “natural” or whether we get to say that these models actually are themselves “examples” of evolution. They are models of it, that’s what, and very useful ones for discussions like the one we should have here.
The value of a model lies not in its perfection, but in whether it suggests productive lines of research.
To add my 10 cents, I don’t see why one would object to a model because it’s not the real thing. Of course, if it misses a vital aspect of the real thing, causing unjustifiable conclusions (it happens), that would be a different matter, but this has to be a specific, not a generalised, issue.
Does anyone disagree that modelling is a useful process? I’m just suggesting that testing a model that emulates/simulates an aspect of a postulated evolutionary process is better than testing one that doesn’t. Further, concluding that a model which is not a reasonable emulation/simulation cannot produce results predicted by a postulated evolutionary process reflects on the model and not evolution.
Joe Felsenstein,
The root of all evil in neo-Paleyism is conflation of science and engineering.
Experience tells me that it’s an awful error to play along with an engineer who immediately seeks to put engineered artifacts [ETA: tools for solving problems] in place of biological models. You know the pitfalls (but perhaps don’t appreciate them as I do, given that I know better than you how technologists think). Why do you believe that things will go differently this time than they have before?
The fact that you and I can see a model of a purposeless process in an evolutionary algorithm doesn’t imply that we will ever encounter an ID advocate who is capable of doing the same. An ID proponent will always see a fitness function in an EA as guiding the computer to an ultimate objective called the target. An ID proponent will always see the computational process itself as inherently purposeful, “cuz the computer only does what you tell it to do,” etc., etc.
To put it a different way, it’s an error to start by specifying the simulator instead of the simuland. I guarantee you, Eric Holloway doesn’t know jack about biological modeling, and thinks that understanding an algorithm for simulation of an evolutionary process is the same as understanding the biological model that the computational process implements. I know for a fact that what we instruct the computer to do, in order to simulate a biological process, bears little relation to what occurs in the biological process that is modeled.
I suggest requiring that Eric Holloway start by describing the evolutionary [ETA: biological] process to be modeled. The second step is to discuss how to model the process. Only then is it appropriate to discuss how to implement the model. Again, the implementation of the model, e.g., what a computer is instructed to do, usually is very different from what is supposed to occur in the evolutionary process itself. IDists always mistake components of the simulator for the simuland. So the question is how to get them to look at things more appropriately. I don’t claim to have found the answer, but I’m pretty sure that I’ve got the right question.
Excellent idea.
The sex-life of the scale insect for instance. Here adult females attach parasitically to plants and lose all power of movement. Loss of function, no? Females (depending on species) go though 3 or 4 metamorphoses before producing offspring, which may be male or female. The first instars are motile (referred to as crawlers) and also feed parasitically on plant sap while developing via five metamorphoses (males) into winged non-feeding (function loss?) adults that seek out females (following pheromone trails), mate and die. In some species, females are able to retain and “grow” sperm, resulting the ability to reproduce without mating (loss of function?). Scale insects are also parasitised – often by particular wasp species.
Don’t know why I came up with this example. Would be hard to model, though? What’s driving the sexual dimorphism towards parthenogenesis?
And neo-Platonism mistaking models and concepts for their referents.
RodW,
Example this comment in Joe’s OP at Panda’s Thumb: (Hope Mike Elzinga doesn’t mind me quoting)
…there is a direct explanation from physics for why all this CSI and “computer science” stuff doesn’t apply to physical systems that interact with the rest of the universe. It comes directly from statistical mechanics and the Helmholtz free energy.
The Helmholtz free energy is given by the equation F = U – TS, where U is the internal energy of a thermodynamic system, T is the absolute temperature, and S is the entropy transferred to the environment at that temperature. The connection to the microscopic state of a system turns out to be
where N is the number of particles, k is Boltzmann’s constant, and Z is the partition function which is the sum over all
, in which E(i) is the energy of the ith quantum state.
Notice that energy is involved in these exchanges with the external environment. If one wants to convert this to “information,” just divide by
(EDIT: Oops, didn’t notice the missing T. Divide by 
); but notice that “information” is not conserved in the system exchanging energy with the environment. All physical systems in biology exchange energy and matter with the environment. All biological systems have emergent properties that determine the details of how those energy and matter exchanges take place.
I agree that we need to start with the requirements. I wonder if we can set some ground rules by providing a minimally acceptable set of requirements. As you say and as I believe Eric admits, Eric does not know the biology. So it may be helpful to have requirements in advance.
Perhaps some simplifications would be acceptable, for example: fixed population size, fixed environment, focus on some representation of the population aggregate genome over one or more generations and ignore other factors, incorporate a way to assess natural selection by incorporating some representation of the effects of the environment in the formalism.
ETA: Any use of probability must reflect biological constraints, and not just simply be by counting combinatorial possibilities.
The criticism of the ID models I have seen seems to be after the fact; it explains why the proposed formalism does not capture biological evolution. The idea here is to set a standard in advance: unless your formalism does this, it is not worth considering further.
ETA: Old programmers joke: “I can make it as fast as you like, as long as it does not need to meet the requirements”.
Possibly ID variation: “I can make biological evolution as low probability as you like, …”
The Friston article that I linked in Sandbox centers on free energy as a unifying explanatory concept for many aspects of life, eg perception, action, cognition, mental illness, culture.
The free energy concept, or at least its equation, is used in AI learning as well as thermodynamics, and Friston claims to be able to unify the two.
BruceS,
I’ll have a look. Thanks, Bruce.
Heehee, that is super complicated. You could probably keep 3 PhDs busy full-time modelling all aspects of sexual conflict, sex determination, male dispersal and sex- and stage-specific differences in selection pressures.
I guess you don’t really like Eric. 😀
Let the poor guy first model an instance of directional selection on a single polygenic quantitative trait.
Overstatement, of course.
The fallacy I often see may be driven by neo-Platonistic impulses, but is not itself neo-Platonism. From Wikipedia:
LOL.