Sunday, September 22, 2019

Robert Marks - Five Years Later, Still No Answers!

Five years ago, the illustrious Baylor professor Robert Marks II made the following claim: "we all agree that a picture of Mount Rushmore with the busts of four US Presidents contains more information than a picture of Mount Fuji".

I didn't agree, so I asked the illustrious Marks for a calculation or other rationale supporting this claim.

After three months, no reply. So I asked again.

After six months, no reply. So I asked again.

After one year, no reply. So I asked again.

After two years, no reply. So I asked again.

After three years, no reply. So I asked again.

After four years, no reply. So I asked again.

Now it's been five years. I asked again. Still no reply.

This is typical behavior for advocates of intelligent design. They do not feel any scholarly obligation to produce evidence for their claims. That's one way you know that intelligent design is pseudoscience.

I wish some brave Baylor student would have the courage to ask Marks in one of his classes for why he refuses to answer.


JimV said...

It is a puzzling remark even from the ID point of view, in which information is defined as something like "that which denotes the involvement of an intelligent designer"; since they would claim the whole universe was intelligently created, including Mount Fuji.

I suspect they are not fans of abstract art.

Tom English said...


To divulge a punchline I intended to deliver years ago, the nonsense image "Sunset in the Garden of Id" (here) is the bitwise XOR of comparably sized images of Fuji and Rushmore (the larger of the two is cropped to match the smaller in dimensions). According to Ewert, Dembski, and Marks (2015), "Measuring Meaningful Information in Images: Algorithmic Specified Complexity," the meaningful information of the nonsense image, measured in the context of the Wikimedia Commons, is ginormous.

You can see the image of Mount Fuji in this post, where I use it to illustrate that algorithmic specified complexity is not conserved. I generate a "noise" image by taking the cumulative 8-bit sum of RGB values in the image of Fuji. According to Ewert, Dembski, and Marks, there's much more meaningful information in the noise than in the image of Fuji.

By the way, I worked with high-resolution images because the amount of "meaningful information" depends on scale. That is, if you convert a high-resolution image to a lower-resolution image, then there is, according to Ewert, Dembski, and Marks, a great reduction in the amount of meaningful information.

As best I can tell, these crypto-creationists do not subject their own claims to the most basic and obvious of sanity checks.

Unknown said...

Responding to Tom English’s comment:

It’s not that complicated. The shape of Mt. Fuji was not directly designed or altered by an intelligent human creator to represent something else. That is to say “no meaningful information”on Mt. Fuji. The sculptures on Mt. Rushmore were designed by intelligent human creators to represent 4 leaders of the USA. If one knows something about US history, one would then think, “oh, I know what those sculptures are supposed to represent!”That is what is called “meaningful information”.

The point of contention with you seems to be the idea that intelligent design of rock formations, letters on a page, the positions of various plants in a garden, or DNA is an indicator that an intelligent designer exists, even if we don’t see them standing over their creation saying “I made that!”. If you do the statistical analysis, and people are starting to do it, you will come to realize that even the most basic DNA strand could not have happened randomly, but must have come about through the agency of an intelligent designer. You are smart enough to understand the religious implications, but rather than accept where the science (in this case statistical analysis) is taking you, you shut down your otherwise intelligent thinking and deny the whole train of thought, including the idea that sculptures have more information than a random mountain. That’s just not rational.

Jeffrey Shallit said...

What units do we use to measure "meaningful information", and exactly how is it calculated? Please give an example and show your work.

JimV said...

Reply to Tom English: I followed the link and read some of your series on creationist "information theory". Thanks for undertaking that investigation and analysis. But ... I have a minor complaint. Your post on "Evolution is not Search" did not convince me, as in my own opinion, biological evolution, human design work, and probably human intelligence itself, all apply variations of an evolutionary algorithm, which is basically trial-and-error search with selection criteria and memory. (E.g., we have all seen cars and phones and other designed mechanisms evolve in our lifetimes.) (Which is to say that there is no magic to it: keep looking for improvements and if they exist they will be found. No magic, so no reason to extrapolate human design to a magic designer, and in fact human design work supplies more evidence for biological evolution. Paley's pocket watch evolved, just like the trees of the forest.)

Your counterexample was that a evolution model which selected on fitness always produced a population with a semi-gaussian distribution of fitness, even when starting from a population which had maximum fitness in every member. It seems to me we could say that that evolution model selects not just for fitness but for fitness with diversity; that is, although diversity is not a specified selection criterion, the mechanics of the search are such that diversity is produced (as in actual biological evolution), and diversity can be a desirable quality (since environmental conditions may change and what used to be maximum fitness may no longer be). So I feel somewhat justified to say that biological evolution is a sort of search, but one which maintains some diversity in its search for fitness and reproducibility.

Another way of looking at it is that biological evolution is a search which never ends, rather than one which terminates at some fixed target; and since it never ends it must sometimes step away from the best results it has found. Similarly, human design often produces an Edsel or a Pentium bug or a Boeing 737 Max. (There is diversity in human designs too.)

Anyway, sorry for the long-winded dissertation, but I feel it is more correct to argue that human design and intelligence are not magic, just as biological evolution is not, than to argue that biological evolution and human design are not following similar algorithms. (Which I have seen some non-creationists do.)

dean said...

"If you do the statistical analysis, and people are starting to do it, you will come to realize that even the most basic DNA strand could not have happened randomly"

I notice you have no statement of or link(s) to anything that support your assertion. Why?

Jeffrey Shallit said...

Because he's a poseur.

Unknown said...

What units do you use to measure the value of this blog?

dean said...

"poseur" is an enjoyable word to use -- especially when it's use is as appropriate as this.

Tom English said...


I appreciate the feedback on Evo-Info 3: Evolution Is Not Search." (I'm distressed to hear that you thought I was using an animation as a counterexample, and not merely as an illustration. But it's good to know your impression.) There's a limit to how much I should say in response, here in the comments section of Jeff's blog.

It seems that you, like me, are better acquainted with evolutionary computation than with evolutionary biology. So I'll point out that the term evolutionary search, as used in the field of evolutionary computation, is somewhat misleading. An evolutionary search can be decomposed into two components, one of which samples the space of possible solutions to a given problem, and the other of which uses the sample to generate an output (hopefully a good solution, or a collection of good solutions, to the problem). There is no analog of the latter component in biological evolution. The role of simulated evolution in an evolutionary search is only to generate the sample. I'll point you to "Evo-Info sidebar: Conservation of performance in search," where I say quite a bit more about this (and evidently do not communicate very well, given the confusion in the comments section).

My remarks are underwritten by some math: see "Sampling Bias Is Not Information" on my blog. I'd long thought that what we call "search" in the context of the "no free lunch" (NFL) theorems had to have been addressed elsewhere, and after writing that post, I finally came up with the right keyword, adaptive sampling, to plug into Google Scholar. There is no formal difference in search, as defined in NFL theorems, and adaptive sampling, which had been investigated for some years before NFL came along. A great deal of confusion about NFL, including some on my part, would have been avoided if we had referred to adaptive sampling instead of search.

You evidently do not intend to attribute purpose to biological evolution. But that is what you are doing, when you say that evolution is searching for something. I'm not going to hash this out with you here. I'll merely suggest that you try replacing the term search with the term adaptive sampling, and see if it costs you anything. If you want further discussion of the matter, then I propose turning your comment and this comment of mine into an opening post at The Skeptical Zone.

MSEE said...

It's a simple thing to answer why Marks has not taken up on this. It's because the challenge did not provide a human context which includes intention for what kind of example Shallit has in mind. It's also because the amount of information on the carvings is dependent on what the end use of the information is, since information does not exist outside the context of mind. In other words, the problem context was not provided to Dr. Marks.

Example 1: to yours truly, the mountain as is provides no information if I were to be transported there, because I already know what persons' visages are carved, hence no surprisal value, plus I have no interest in detailed measurements of the carving. If the raw data acquired in example 3 below were handed to me, it would represent null self-information because I am not in possession of the decoding and formatting schemes necessary to make any sense of it. Sense as can only be considered as in reference to intelligence.

Example 2: A person from say Kenya has studied American history, but does not know what persons are carved into the mountain nor is familiar with the faces from history. Such a person could be provided with a montage of a set of 100 most famous Americans and assign a probability to each one as to the likelihood they would be carved based on a fame score. Then the total self-information on the mountain would be the sum of the log2 of the inverse probability of each face appearing, with care to recalculate the individual probabilities of each in the set remaining after a face has been identified, knowing from logic of common sense that the same person would not be carved twice. Notice the dependency here on individual opinion as to fame score. But this is maybe the best as can be expected since information measure requires the context of mind in these less rigorous more philosophical discussions of information theory.


MSEE said...

Example 3: Now we introduce a sculptor who wants to create a scale model of the Rushmore work based on actual measurements from a laser profile scan of the mountain. If the measurement tool were transported in time back to 1930, and the scan parameters set up, there would be a scan result having zero informational value to the sculptor, supporting the thesis of Professor Marks. But to return to the present day, the sculptor or a skilled helper would need to PROVIDE information in order to specify the information content of what is received, kind of like Dembski's specified information. So this sculptor would need to provide a 2D grid of points to be projected onto the mountain, with either a position tolerance or position probability distribution supplied by the sculptor's helper. Let's pick the pdf approach. The error s.d. of each x,y grid point plus its coordinates would determine the information contained in that point specification and the x and y coordinates of each with equivalent x and y pdf's with s_x, s_y as s.d. of each point coordinate the total information SUPPLIED by the sculptor would be with N grid points. Say each grid point is at X,Y, with randomness. Then the information supplied by sculptor would specify an individual grid point self information of:

I_XY = log2(X/(2^1/2(s_x)) + log2(Y/(2^1/2(s_y))

Next the measurement is made of the Rushmore work. Each grid point now comes with a depth measurement with error statistics similarly taken into account. Say the measurement device distance to the work mean plane is D, which can be used to specify z information of each measurement, with s_z the s.d. The distance D is very large compared to the depth variation across the extents of the Rushmore work. So we then have for each point, a z dimension self-information of:

I_Z = log2(D/(2^1/2(s_z))

Next, formatting information I_format must be supplied to the sculptor.

Then the total information supplied to the sculptor for the scan would be the SUM of all the grid points' information plus formatting information:

I_Rushmore = Sum_over_N[I_XY_N + I_Z_N] + I_format

This then is the information of Mt Rushmore as needed by the sculptor for the scale model, based on the intentions and needs of same.

MSEE said...

So the conclusion is that the problems of information theory applied to areas within AND outside of engineering and science have to be set up as to the intended context, since intention is central to any problem concerning mind. Dr. Shallit did not set the problem up by specifying the intentions of the users of any information mined from an example supplied by Dr Marks, the latter could not even begin to supply a specific answer and probably does not have the time or motivation to spend as yours truly is now doing.

Additionally, if Dr. Shallit may not clearly agree that the application of information theory outside of the realm of high rigor supplied by Shannon requires discussing intelligence itself, then Dr. Marks probably sees the futile nature of spending such effort to discuss. Shannon himself skirted the issue with explicit disclaimers as to the application of VALUE or determination to his original conceptions of information in engineering applications. But that does not forbid others to try to extrapolate into more philosophically interesting areas the concepts of the theory, even applying some of the math in only example form as I just did. Since Marks and Dembski think about these philosophical applications every day, the application of the ad-hominem "poseur" is extremely unfortunate. Especially given that the person making the judgement seems opposed at the ground level of inquiry to consideration of the dependencies between information theory and intelligence. There is no a priori reason to exclude links between philosophical applications of science, and in actuality science depends upon philosophy, irregardless of claims to the otherwise of a recently deceased cosmologist.

So as a concluding observation, the philosophical commitments of the two principals to this discussion should be considered, and as for one party, the implications of the postulated unbreakable link between intelligence and information has bearing on the discussion of the genetic code, and for the other party these implications are anathema to the corresponding philosophical commitment.

The first two above equations are made by applying a principle revealed in the following unpublished text eq(12):

Jeffrey Shallit said...

The claim "information does not exist outside the context of mind" is completely wrong, showing that you do not understand information theory.

The Kolmogorov theory of information does not make any reference to "mind" at all. Neither does Shannon's theory.

dean said...

"Since Marks and Dembski think about these philosophical applications every day..."

Marks and Dembski try to do one thing; use the language of a rigorous discipline in ways that don't meet the details of the discipline: in short, they are trying to put a rigorous veneer on assertions that have no support.

Perhaps poseur isn't the correct term. "Liar" would be more accurate.

Unknown said...

Hey Jeff:

Does the picture of a fugitive on a wanted poster add information to the poster?

Mike E.

Jeffrey Shallit said...

Hi, Mike: First tell me precisely what your definition of "information" is, and how to measure it. In the definition used by mathematicians (Kolmogorov complexity), it might or might not; it depends on many things.

JimV said...

Reply to Tom English:

Thanks very much for taking the time to reply.

It seems the main issue is one of semantics: the distinction between "search" and "adaptive sampling", with the intent to remove any suggestion of purpose, with the implication that purpose implies a directing intelligence of some kind.

Humans can and do use adaptive sampling to search for engineering solutions, and in common English purpose has synonyms such as reason-for, cause, and impetus, but there is not much point in arguing semantics, especially when it may involve technical terms which I am not familiar with. So I won't, except to repeat that I dislike approaches which seem to privilege human actions/intelligence/purpose above the rest of nature, as it hints of dualism. (E.g., the purpose of humans is to survive and reproduce, just like the rest of biology, and all our actions, including searches, are ultimately linked to that.)

MNb said...

The IDiots from Seattle have replied to your post.

Three highligts:

"How can we quantify this kind of information?” ... is an interesting question beyond the scope of this post."

"Shallit is still rankled by Dr. Marks’s assertion that carving faces on rock adds information to the rock."

"We all agree that a page of Dr. Shallit’s textbook contains more information than a blank page - Mr. Shallitt doesn't agree."

Dean is right - poseur is not the correct term.

dean said...

"We all agree that a page of Dr. Shallit’s textbook contains more information than a blank page - Mr. Shallitt doesn't agree."

That is (to me) the key comment there. It has two sources:
a) The ID folks have worked long and hard to convince their supporters that they are doing hard work (science and math) to validate ID. Part of that means they borrow the language from the relevant disciplines but use them in non-technical ways, like

"... contains more information than a blank page..."

A non-technical audience will, generally, believe this is technically correct.

b) The belittling of real academics has been a strong tool of the right for several years, with the goal of pre-emptively weakening the critiques of the stuff ID folks put out. Sadly, it works more often than not.

bloggarious said...

Jeffrey Shallit said...
In response to "What units do we use to measure "meaningful information", and exactly how is it calculated? Please give an example and show your work."

I respectfully submit my work in which the unit of "meaninglessness" is defined and used in an example that shows how "meaningful information" can be identified, described, analysed and therefore measured.

MEANINGLESSNESS - SI symbol MSSSS, is defined as "way nor furnished sir procuring therefore but. Warmth far manner myself active are cannot called. Set her half end girl rich met. Me allowance departure an curiosity ye. In no talking address excited it conduct. Husbands debating replying overcame blessing he it me to domestic.

Among going manor who did. Do ye is celebrated it sympathize considered. May ecstatic did surprise elegance the ignorant age. Own her miss cold last. It so numerous if he outlived disposal. How but sons mrs lady when. Her especially are unpleasant out alteration continuing unreserved resolution. Hence hopes noisy may china fully and. Am it regard stairs branch thirty length afford."1.

In conclusion "touchrs I as ctriganed arkeye ad agad catiour, ious, I a Baidur. Mowiluredorkepior thevisknonol scagr s o fe ark ar ay. Martouro, r mo we sos, I fo ad Sowon ce agesctr t Filatepofir rlilcedeskeses Man Maillontidede fo, Ther Mowasks allyeprers ot'sche, S arouss ag Sort teepr Ruskepige ai"wivigns pluskelieit I ft fo sctive Thaiskseplims ag ce I avimaiga wiso Thatre mo y.

I as. Sor on Bate ntiow be I obrkear a Thinous ngaio I ar im: t careft y a o blagagear St May. marire Magr Fis fthar ara the w" 2,3.

1. (it may differ when checked)
2. Generated using settings: Chars=500 and Order=2 on input text taken from:

Jeffrey Shallit said...

You don't seem to realize that a random text string generated by coin flipping has, w.h.p., the maximum possible amount of information.

Prōtos Ēgapēsen said...

I wonder what you make of Paul Vitanyi's work on 'Meaningful Information.' While it is only one example of a long list of similar proposals, much of this kind of work seems directed at characterizing what is commonly understood as information from either an epistemic or goal-directed point of view, such as the way engineers or knowledge workers would speak of 'information.' Similarly authors developing notions such as computational depth (e.g. Fortnow) refer to such quantities as 'useful information.' I think most of these sort of concepts are defined using supporting concepts of Kolmogorov complexity and some also make use of concepts introduced by Shannon. Gell-Mann, Bennett, Adriaans, etc. all seem to think that on its own, Kolmogorov complexity is not a good fit for talking about the sorts of structured complexity that correspond to more familiar notions of information and knowledge.

Jeffrey Shallit said...

I think the Vitanyi's ideas are good. I myself am a fan of the approach of Oded Goldreich, Brendan Juba, Madhu Sudan, in their paper, "A theory of goal-oriented communication". I should note that none of these ideas have anything to do with "intelligent design", nor do any of the ID advocates seem to be up on this literature.

Prōtos Ēgapēsen said...

Thank you for that. I appreciate the reference. (Seems like it is related to game theory.) While goal-oriented communication sounds like an interesting idea, I'm not sure their work relates directly to the recent attempts to quantify structured/useful information. Several of these attempts to find a productive definition of quantified information that captures a quality for which Kolmogorov complexity is not particularly well suited relate directly to one or another sort of randomness deficiency. What if any significance do you see in this? Do you see these as fitting into general categories of the informational for which the concepts of Kolmogorov complexity and Shannon information do not account? If so, how might you characterize these senses of what is informational?

Betzalel said...

Theorem: Mount Fuji has less information than Mount Rushmore.

Proof: We will use Chaitin's definition of information in his Algorithmic Information Complexity theory:

Suppose we have a program F which outputs an image of Mount Fuji that can be recognized by anyone to be an image of Mount Fuji.

And suppose we have a program R which outputs an image of Mount Rushmore that can be recognized by anyone to be an image of Mount Rushmore.

Let K(F) the minimum number of possible bits in program F and let K(R) be the minimum number of possible bits in program R.

Clearly K(R)>K(F), since program R must output an image that looks like the faces on Mount Rushmore as well as an image of a mountain, while program F only has to output an image of a mountain with no man-made structures. QED

Jeffrey Shallit said...

There is no actual argument presented here, only an assertion. You are assuming, for example, that every mountain looks the same as every other mountain. What if Fuji has special Fuji-characteristics that, in order to be recognizable as Fuji, cause it to have more info? And what if Mt. Rushmore would be recognized just by 4 line-drawings of faces, with no mountain at all?

Jeffrey Shallit said...

For example, this: is easily recognized as Mt. Rushmore, with no obvious mountain there.

And in any event, the definition of information in the Kolmogorov theory demands lossless compression, so the answer to the question largely depends on exactly which photographs one is talking about.

Betzalel said...

Jeffrey, just look at a generic picture of Fuji. And look at a generic picture of Rushmore. It is obvious that the picture of Rushmore is more difficult to reproduce than Fuji. Therefore Rushmore has more information.

Not sure how you cannot see this.

Jeffrey Shallit said...

"It is obvious" is a clear dodge when you cannot actually produce an argument.

Betzalel said...

Not everything requires an argument to be convinced that it is true. For instance, I don't need an argument to be convinced that grass is green. Similarly, I do not need an argument to be convinced that an image of Mt. Rushmore take more lines of code to produce than an image of Mt. Fuji. Or that an image of the Mona Lisa requires more code than an image of a stick figure.

Jeffrey Shallit said...

That's nice for you, but it doesn't convince me at all.

For example, consider the following problem. Take a string of n zeroes. Compute its information. Now add some extra zeroes on the end. Does the result have more or less information than the original string? Using your "logic", it seems clear that the new string must have more, but this is in fact not always true.

Betzalel said...

The algorithmic information complexity of a string of zeroes depends on the algorithmic information complexity of the length of the string. This is not a monotonic function.

Here is another question: What has more information (the algorithmic information complexity definition)?

A shack or the White House?

A grain of sand or an animal?

A lightbulb or a Pentium computer?

A Model T car or a self driving car?

If you don't know, then it is clear to me that the reason is because you are wearing intellectual blinders.

bloggarious said...

Same collection of letters in 2 strings:
you are wrong
raeuw oro yng

Only one gives an information about your thinking.
Luciano Floridi attempts to explain whether information theory can explain meaning. It doesn't.

Jeffrey Shallit said...

Betzalel: you seem really confused. In the Kolmogorov theory, complexity is only defined up to an additive + O(1) term, so not only is not computable for large enough individual instances, but you can't compare two specific examples unless you specify the computing model.

Betzalel said...


Let the computing model be BASIC computer language for both Mt Fuji and Mt Rushmore and we are done. The fact that the Kolmogorov complexity is not computable for large enough individual instances does not mean one cannot estimate it. Furthermore, one could also use some model of computation that is restricted in some way (for instance, only primitive recursive functions) instead of BASIC. And that would solve the problem of not being computable.

This the type of reasoning is used everyday with respect to choosing whether to create computer programs. People estimate how much time it will take to create various computer programs and make decisions based on these estimations as to whether to create them or not. The fact that they are estimations and not exact does not mean they are worthless.

Jeffrey Shallit said...

You seem very confused. BASIC is a universal computing model, equivalent to a TM.

As for your other remarks, I'm fine with it if you actually do the computation. But so far you haven't. You've just made an assertion. Let's see an actual computation. I will be happy to provide you with the photographs of Fuji and Mt. Rushmore I have in mind.

Betzalel said...

Jeffrey, you are looking at the trees. I am looking at the forest. Actual computing would be a waste of time.

Here is another way to do it without any computation. Go to your favorite artist and ask him or her how long it would take to produce a painting that could be recognized as Mt. Fuji and how long it would take to produce a painting that could be recognized as Mt. Rushmore. The longer length of time for Mt. Rushmore could be explained by the fact that there is more information in Rushmore than Fuji.

Jeffrey Shallit said...

Translation: "I have no evidence, only assertions."

As for your painter example, now you are confusing computational complexity (a measure of the amount of time to solve a problem) with Kolmogorov complexity (where time is not even considered).

You are very, very confused.

Betzalel said...

As I said before, you are seeing trees while I am seeing the forest. Whether we are talking about Kolmogorov complexity or computational complexity is irrelevant to my point.

Furthermore, I do have evidence, or at least an experiment that would produce the evidence that you require to be convinced:

Do the following experiment on 100 artists: Ask them to produce a picture of Mt. Fuji and Mt. Rushmore, in their fastest time possible such that their pictures could be recognized as Mt. Fuji and Mt. Rushmore. Time them for both of their drawings.

All of the artists should take a much longer time to paint Mt. Rushmore than Mt. Fuji. This would prove that Mt. Rushmore has more information than Mt. Fuji. QED

Jeffrey Shallit said...

You continue to make the same silly error. Time to produce something has little to with its Kolmogorov complexity.

You also have the burden of proof reversed: it's not up to me to conduct any experiment. You are the one making the claim, you do the work.

Betzalel said...

Suppose the above experiment were conducted by a reputable objective scientist and the results came out as I predicted above. Would you then admit that Mt. Rushmore contains more information than Mt. Fuji?

Jeffrey Shallit said...

I've already explained twice that the time to create a painting has nothing to do with it. You seem immune to understanding this.

Also, the original claim was not about the information in Mt. Rushmore, but rather a picture of Mt. Rushmore.

Betzalel said...

If you give me two particular pictures as computer files, one of Mt. Fuji, the other of Mt. Rushmore, I would agree that they probably contain the same amount of information, by any reasonable definition of information.

However, I doubt that was Robert Marks was talking about. He was probably talking about something like what I was suggesting, how fast it takes to draw each mountain.

Jeffrey Shallit said...

In your world does "probably" mean "something I pulled out of my butt for which there is no actual evidence"?