Shades of Paul Nelson!

Wow, this is so familiar. Jeff Shallit, who studies information theory, asked a simple question of those intelligent design creationists who love to pretend information theory is on their side.

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.

Can you guess what their answer was, can you, huh? No prizes if you guess correctly though, because this is way too easy.


  1. StonedRanger says

    Im going to guess that their answer was: No reply, did not reply, were you talking to me? or some other such nonsense. Did I win?

  2. PaulBC says

    They do seem to get the concept of information consistently backwards. A digital representation of an irregular jagged surface is inherently less compressible than a smooth surface like George Washington’s nose. It is likely that a lossy compression of Mount Fuji would be indistinguishable to most human beings who don’t really know the irregularities, but that is a difficult argument to make. It would also be useless as a topographic map. So yes, it would be very “interesting” to find out what they are trying to say here. It seems like it requires more memory to store the information about Mountain Fuji.

  3. mnb0 says

    @3 PaulBC: you’re too optimistic. They don’t have anything on information at all that could be called a concept. That would require clear, unambiguous definitions, which would make their claims even more vulnerable. This again explains why they’ll hardly ever even try to show their work.
    Sometimes an IDiot “justifies” this by appealing to intuition.

  4. a_ray_in_dilbert_space says

    I think that there is an inherent disconnect in the creationists brain that inhibits any attempt to explain to them what “information” actually is. They simply equate information=meaning. The former is objective. The latter inherently subjective.

  5. raven says

    Is there even any way to answer this question?

    One would need a definition of information.
    Then, one would need a way to calculate the information content of a photo.

    Important quantities of information are entropy, a measure of information in a single random variable, and mutual information, a measure of information in common between two random variables. … The choice of logarithmic base in the following formulae determines the unit of information entropy that is used.
    Information theory – Wikipedia › wiki › Information_theory

    There are a few complicated looking equations on the wikipedia article on information content.
    I couldn’t copy the equations properly which is OK because they don’t mean anything to me anyway.

  6. raven says

    “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”.

    This is a meaningless question anyway.

    Why Mt. Rushmore and Mt. Fuji?
    I’d guess a wildflower meadow with many types and colors of flowers would contain more information than a photo of Mt. Rushmore.
    But this is just a guess.
    Without any way to measure the information content of photos, there is no way to prove this.

    AFAICT, more creationist fallacies and lies.
    They frequently claim that evolution cannot create new information.
    This is a lie because evolution does create new information and we can see it in Real Time.

  7. Akira MacKenzie says

    Why do I suspect when the Creationists are talking about “information” they mean “features that indicate manufacture or usefulness.” i.e. Mt. Rushmore has “information” because it was specifically made and each sculpture represents a person with a unique history, while a extinct volcano in Japan doesn’t look it was made and therefore doesn’t tell anyone much of anything.

  8. says

    My favorite example to defeat this sort of thinking:

    Which has more information in it — (choose a nonrepeating irrational number; pi, e, 2^0.5) or a Fibonacci sequence? It’s fascinating to watch the internal gyrations as they try to justify whatever their answer is. (The “answer” is “neither,” and if you really want some fun do it in a base other than ten.)

  9. mathman85 says

    @Jaws #10

    Is that in terms of Kolmogorov complexity, Shannon entropy, or some other measure of “information”?

  10. says

    Saying “goddidit” is one bit of information. Darwin’s theory is a whole bunch more. Their explanation lacks the kind of complexity I would expect from a theory explaining the origin of life.

  11. Ed Seedhouse says

    I mean, it’s not as if information theorists have provided a clear and consistent definition of what “information” is or anything, right?

  12. whheydt says

    Re: Akira MacKenzie @ #9…
    Fuji is not, so far as I know, extinct.
    (According to Wikipedia, it is active, having last erupted in 1707-1708.)

  13. says



    Pick one and show the work… BUT if choosing either Shannon or Kolmogorov, also account for Szilard’s calculations of chaos and entropy, which are not in fact the same thing, introduced by the comparison itself, and determine how that affects both reference-frame and “objective” information quantity. (This is probably necessary for other frameworks, too, but until specified I’m not going to ideologically say “must also account.”) AND it’s an automatic fail if the definition of “information” changes at any point in the chain or there is a divide-by-zero (or other corresponding) error that is just “cancelled out” by another operation.

  14. unclefrogy says

    taking what I would guess is the creationist criteria for information mostly cultural significance and history to supply meaning as a standard i would have to go with Mt Fuji as containing more “information” then the limited representations in the Mt Rushmore busts .
    I would be shocked if anyone would ever get a straight answer out any of the religious fanatics at any time.
    uncle frogy

  15. answersingenitals says

    How long did it take the Borglum’s (father and son) to carve the faces on Mount Rushmore? How long would it take them (if they were still alive) to carve a full scale precise duplicate of Mt. Fuji? Isn’t this a good measure of information for this question? The carving process can be said to communicate a steady stream of information from the sculpture’s mind to the stone, and photos of the sculptures, if they are truly accurate, are just proxies for the real thing.

  16. mathman85 says

    @Jaws, #16:

    Let’s see how badly an algebraist can screw up information theory…

    For the sake of this calculation, I’m choosing e as my irrational constant. Assuming that e is normal, a fortiori the probability of each base-10 digit appearing at an arbitrarily chosen decimal place in the expansion of e is 0.1, whence the Shannon entropy (using the base-10 logarithm) has the form

    Η = –[(10)(0.1)(–1)] = –(–1) = 1.

    If e is not normal, then I will need some other means of assessing the probabilities associated to a given digit appearing in an arbitrary decimal place. And, obviously, a different choice of logarithm base would give a different numerical answer.

    As for a Fibonacci sequence, I’ll choose the standard 1, 1, 2, 3, 5, …, so that the decimal expansion looks like 1.123581321345589144233377… At this point, I find myself somewhat at a loss as to determining the probability of any particular digit appearing in a given decimal place. I suppose I could look into having a computer analyze a long sequence of this decimal expansion so as to get empirical probabilities for the digits, but I don’t off the top of my head know if that can be directly translated asymptotically to the classical probabilities that I’d need. I’ll need to give that some thought.

  17. lochaber says

    If a photo of Mt. Fuji contained less “information” then a photo of Mt. Rushmore, wouldn’t the file size be smaller?

  18. birgerjohansson says

    I recall an early 1980s pop song beginning with the line “information let me down, but I don’t care”.
    That could be their theme song.

  19. Rob Grigjanis says

    lochaber @20: Isn’t the file size simply determined by the number of pixels and bit depth? What does that have to do with information, however you define it?

  20. PaulBC says

    Rob Grigjanis@23

    Nearly all image files are now compressed. If you make an image that’s all one color and save it as a JPEG, for instance, it will be pretty small no matter how large the bitmap. In terms of measuring information content, it is reasonable to ask about compressibility. However, that gives the opposite answer to what creationists want. If you fill a bitmap with the results of uniform random coin flips, that is highly incompressible (essentially, no matter what your compression algorithm, the probability of generating a compressible image with coin flips is vanishingly small). So I have no idea what kind of “information” they are trying to measure here. I doubt very much that they know either.

  21. colinday says


    Two thirds of the ones digits of Fibonacci numbers are odd. The ones digit repeats in a cycle of 60. There are four of each even digit and eight of each odd digit..

  22. lochaber says

    Rob Grigjanis @ 23
    I wasn’t accounting for compression, but just as far as the computer is concerned, both photos have the same number of pixels, just the individual color of each pixel is different. It may not be information that’s useful or relevant to us, but it’s still information from the perspective of the computer.

  23. DanDare says

    Mt Fuji is a very precise representation of the arachnid cone god, while Rushmore is just a bunch of knobs. Fuji must therefore have more information.

  24. Pierre Le Fou says

    I’ve not read all the comments here yet, but my guess is they said something like:

    “We’ll give you the equations/answers in one year.”

    I’ve been reading Pharyngula long enough to recognize the Paul Nelson reference in the title.

  25. garysturgess says

    Hang on, hang on – creationists said this?

    Isn’t the whole point of creationism that Big Sky Daddy carved out Mt Fuji in a not dissimilar fashion to the sculptors of Mt Rushmore? Shouldn’t the information content of Mt Fuji be higher even by their standards then (I assume they do not wish to claim that BSD isn’t as skilled a sculptor as the Mt Rushmore dudes)?

    I honestly don’t see how you can have it both ways – do they think that humans were created but mountains evolved?

  26. Pierre Le Fou says

    Right, so I read the original post on the other blog, and it’s been five years…. eh eh eh. Just like Nelson.

  27. says

    colinday @ 26:

    Like I said, try this in a nondecimal numeric base. Not just the famous New Math/Tom Lehrer illustration (base 8), but something prime, like base 11). And that’s my point: Much of the information “in” the Fibonacci sequence is that imposed by the way its representation is communicated from observer A to observer B using convention C. The same goes for something from any irrational number, or indeed any properly and truly randomized sequence.

    mathman85 @ 19:

    Which rather makes my point about Shannon (that it’s a methodology applicable only at equilibrium in a closed system, and then only if one can somehow evade Szilard’s refutation of Maxwell’s Daemon). Given that by definition “life” is not at equilibrium (if it was, there would be no death or any cellular process)… which I’m reasonably sure you understand, but creationists do not…

  28. llyris says

    @ birgerjohansson
    I think the song was “communication let me down, but I dont care”, which is also accurate.

  29. llyris says

    @birgerjohansson (part 2)
    On further scrutiny, the words were “communication let me down, but I’m left here”.
    However, I suggest that arguing about song lyrics is at least as useful as arguing about the relative merits of Mt Fuji and My Rushmore. At least the song lyrics have a verifiable correct answer. The arrogance involved in the mountain picture argument are astounding. The images don’t impart so much information, but idiots pre-fill information and opinions they already know or believe. And then have the arrogance to assume one set of beliefs is superior to another.