Informational Bits in a PB Sandwich

How to measure the informational content or "quantitative measures you might use to describe CSI" is summarized as such in regards to biology:

If life spontaneously diversified at body plan level from microbes [500k - ~ 5 millions of DNA base pairs, each capable of storing 2 bits; and, BTW, that capacity is what Shannon info is about] to men, we need to credibly see how the required functionally specified, complex, organized fine-tuned information came to be.

ID supporters haven't specified the system. Darwinists have specified the system saying that organisms are made of cells containing four-bases-coded digital "firmware" (billions-bases-long genomes) and that random variation within this firmware, selected by natural selection, generated entire new organisms. Thus Darwinism itself has chosen the level of representation of the biological systems.

Of course, by doing so Darwinists have shot themselves in the foot because, given the genome of an ancestor species A and the genome of a derived species B, one can calculate the Hamming distance between the two, the probability that random mutations are able to "cover" this distance, and the functional information implied.

In a sense indeed the discovery of DNA was the conclusive nail in the coffin of Darwinism because reduced the problem of origin of species to the problem of comparing strings of symbols. Strings of symbols are what it is easier to deal with, both for information theory and for intelligent design theory.

Even Dawkins would agree with the methods used to calculate the informational bits:

In practice, you first have to find a way of measuring the prior uncertainty - that which is reduced by the information when it comes. For particular kinds of simple message, this is easily done in terms of probabilities. An expectant father watches the Caesarian birth of his child through a window into the operating theatre. He can't see any details, so a nurse has agreed to hold up a pink card if it is a girl, blue for a boy. How much information is conveyed when, say, the nurse flourishes the pink card to the delighted father? The answer is one bit - the prior uncertainty is halved. The father knows that a baby of some kind has been born, so his uncertainty amounts to just two possibilities - boy and girl - and they are (for purposes of this discussion) equal. The pink card halves the father's prior uncertainty from two possibilities to one (girl). If there'd been no pink card but a doctor had walked out of the operating theatre, shook the father's hand and said "Congratulations old chap, I'm delighted to be the first to tell you that you have a daughter", the information conveyed by the 17 word message would still be only one bit.

Now some Darwinists demanded that the informational bits in a peanut butter sandwich be calculated. The above example is not quite a sandwich but the above explanation still is relevant to how to calculate the informational bits used to represent any object.

Shannon’s definition of information is quite general. Its value is proportional to the base 2 logarithm of the ratio between the total number of elements of a certain set and the number of elements chosen from that set. These elements can be symbols or whatever else. Thus per se information theory says nothing about the level of representation
and gives us a lot of freedom. Simply the user himself specifies the set from which to choice. It seems to me that, as a consequence, in information theory there is no formalized rule regarding how to choose the level of representation (if any mathematician's have any more to say on this subject I would appreciate it).

Paradoxically, the best way to respond to the accusation of cherrypicking when choosing the level of representation is to give our debaters the right of choice of the model (and in turn the sets from which to choice). If we don’t specify the model, then no accusation. Given the model we try to apply the method of intelligent theory. Eventually, if the model is too simplified, we must show to our debaters the reasons why their model is not adequate to reality and suggest some improvements.

This will be done below after finishing the explanation for basic information theory:

Computer information is held in a sequence of noughts and ones. There are only two possibilities, so each 0 or 1 can hold one bit. The memory capacity of a computer, or the storage capacity of a disc or tape, is often measured in bits, and this is the total number of 0s or 1s that it can hold. For some purposes, more convenient units of measurement are the byte (8 bits), the kilobyte (1000 bytes or 8000 bits), the megabyte (a million bytes or 8 million bits) or the gigabyte (1000 million bytes or 8000 million bits). Notice that these figures refer to the total available capacity. This is the maximum quantity of information that the device is capable of storing. The actual amount of information stored is something else. The capacity of my hard disc happens to be 4.2 gigabytes. Of this, about 1.4 gigabytes are actually being used to store data at present. But even this is not the true information content of the disc in Shannon's sense. The true information content is smaller, because the information could be more economically stored. You can get some idea of the true information content by using one of those ingenious compression programs like "Stuffit". Stuffit looks for redundancy in the sequence of 0s and 1s, and removes a hefty proportion of it by recoding - stripping out internal predictability. Maximum information content would be achieved (probably never in practice) only if every 1 or 0 surprised us equally. Before data is transmitted in bulk around the Internet, it is routinely compressed to reduce redundancy.

DNA carries information in a very computer-like way, and we can measure the genome's capacity in bits too, if we wish. DNA doesn't use a binary code, but a quaternary one. Whereas the unit of information in the computer is a 1 or a 0, the unit in DNA can be T, A, C or G. If I tell you that a particular location in a DNA sequence is a T, how much information is conveyed from me to you? Begin by measuring the prior uncertainty. How many possibilities are open before the message "T" arrives? Four. How many possibilities remain after it has arrived? One. So you might think the information transferred is four bits, but actually it is two. Here's why (assuming that the four letters are equally probable, like the four suits in a pack of cards). Remember that Shannon's metric is concerned with the most economical way of conveying the message. Think of it as the number of yes/no questions that you'd have to ask in order to narrow down to certainty, from an initial uncertainty of four possibilities, assuming that you planned your questions in the most economical way. "Is the mystery letter before D in the alphabet?" No. That narrows it down to T or G, and now we need only one more question to clinch it. So, by this method of measuring, each "letter" of the DNA has an information capacity of 2 bits.

Why 4 nucleotides?

Back to Dawkins:

Whenever prior uncertainty of recipient can be expressed as a number of equiprobable alternatives N, the information content of a message which narrows those alternatives down to one is log2N (the power to which 2 must be raised in order to yield the number of alternatives N). If you pick a card, any card, from a normal pack, a statement of the identity of the card carries log252, or 5.7 bits of information. In other words, given a large number of guessing games, it would take 5.7 yes/no questions on average to guess the card, provided the questions are asked in the most economical way. The first two questions might establish the suit. (Is it red? Is it a diamond?) the remaining three or four questions would successively divide and conquer the suit (is it a 7 or higher? etc.), finally homing in on the chosen card.

I'm sure everyone remembers similar examples in Dembski's books?

Remember, too, that even the total capacity of genome that is actually used is still not the same thing as the true information content in Shannon's sense. The true information content is what's left when the redundancy has been compressed out of the message, by the theoretical equivalent of Stuffit. There are even some viruses which seem to use a kind of Stuffit-like compression. They make use of the fact that the RNA (not DNA in these viruses, as it happens, but the principle is the same) code is read in triplets. There is a "frame" which moves along the RNA sequence, reading off three letters at a time. Obviously, under normal conditions, if the frame starts reading in the wrong place (as in a so-called frame-shift mutation), it makes total nonsense: the "triplets" that it reads are out of step with the meaningful ones. But these splendid viruses actually exploit frame-shifted reading. They get two messages for the price of one, by having a completely different message embedded in the very same series of letters when read frame-shifted. In principle you could even get three messages for the price of one, but I don't know whether there are any examples.

I purposefully chose Dawkins to articulate the basics of information theory so no one could claim it was wrong because the source was an ID proponent. Dawkins is not wrong when it comes to the "how to calculate". The real question is whether Darwinian mechanisms are capable of producing this information, which is of course where we would disagree.

1. Do I include the 'information' in the genetic makeup of the ingredients of a pb sandwich?

No, like Dawkins illustrated (in the first paragraph I quoted) whether using a card or a verbal confirmation the message would still be only one bit. It's an abstraction. The information in DNA is likewise an abstraction, since the information content is not directly inherent to the chemical properties. The genetic makeup of the ingredients does not add to the specification of being a pb sandwich and as such is improper as a level of representation.

2. How does one measure a 'bit' of information? What is the difference in number of bits between, say, one slice of bread with peanut butter on both sides, or two slices of bread with peanut butter in the middle?

In your example you only gave 2 options so 1 bit is enough to represent that information.

3. I would like to see the math for the informational bits in a peanut butter sandwich. I think you need a measure that specifies the probability that THESE PARTICULAR atoms, out of all of the other atoms in the universe, are configured together in this region of space, as well as the informational bits in the biological materials in the sandwich, the informational bits in the particular configuration of those materials versus the possible configurations. The probability that all of the atoms in a peanut butter sandwich are in that particular configuration and cluster of space time is staggeringly high, certainly higher than the UPB of 500 informational bits.

Sorry, that's an unreasonable demand since that's not how information theory works. Now obviously this question is trying obfuscate the matter to the point where even the atomic pattern of an object/event would have to be considered, thus making the Explanatory Filter useless since it would always return a positive. It is a blatant attempt to attack ID by undercutting the foundation by which it builds upon.

In regards to calculations, unless there is information encoded into the atomic structure, which I doubt, it's irrelevant. The level of representational abstraction, or the pre-specification, is entirely dependent on whether the lower physical layer modifies the calculations. For example, ASCII characters only have a probability space of 256 (8 bits). So my name, Patrick, is 56 informational bits whether the storage medium is RAM or a hard drive. But if my name were written on the wall with paint in the middle of a splash pattern the probability space is much higher, and thus the informational bits would likely exceed 500. The information itself--my name--is not changed at all by the storage medium but the probability, and thus the informational bits required to represent my name, can be greatly influenced.

The reasons why the objection about atomic states is a real red herring can rigorously be shown to be so. The point is that the atoms really are totally irrelevant. Take the paint example. Suppose there are 10,000 drops of paint, each of area A (assume non-overlapping for convenience, though it would change nothing fundamental), on a wall of area 10,000,000A. To use informal Mathematica notation, there are roughly N = Binomial[10000000,10000] different possible configurations of paint on this wall (where Binomial is the binomial coefficient.) (This is assuming the paint is all the same color). Now a very tiny proportion of these, say M of them, will represent a pattern that would be considered "spelling your name" -- in ANY script, on any position of the wall. If I understand aright (this might be wrong in detail, but it's not crucial to my argument), this would represent an information content of I = -log(M/N), where log is base 2: I would be a reasonably large number.

But what if we consider atomic states instead of "paint states"? The crucial thing is, atomic states are completely orthogonal to paint states. What I mean is, each "paint state" has precisely as many atomic states representing it as any other paint state. So consider the (very improbable) paint state where a square of 100x100 "pixel" area in the top left corner of the wall is filled in, and the rest is blank. This is a macroscopic description, dealing with "paint" and "wall" etc. If you examine all the vastly different atomic states ("microstates") that would yield this macroscopic state ("macrostate"), it would be some phenomenally huge number, say L. But from the atoms' perspective, there is nothing special about this state! EVERY possible state -- all N of them -- correspond to about L different atomic configurations (the variance would be very, very tiny). So if you want to work on the atomic level, there are NL different configurations, and ML of them correspond to your name, so the information is I = -log(ML / NL) = -log(M / N). So this changes nothing.

The only time this WOULD change something is if, for some odd reason, the macrostates associated with spelling my name each had a higher average number of associated microstates (atomic configurations), in which case, such a configuration would indeed represent lower information than otherwise expected. However, this would be extremely odd, and would itself require a lot of explanation (why should the atoms prefer to spell my name than not?). In this example, of course, this would not happen, but even if it did, in my estimation it would merely push the question up a level to needing to examine why my name was a privileged macrostate.

So moving between levels of representation only changes the analysis if the lower level for some reason privileges certain messages/states. I hope this was at least vaguely clear, and somewhat accurate.

Now onto the pb sandwich. I'm not going to do any research for this, so the numbers won't be accurate, but I'll give a quick example for your sandwich.

The specification is that it is a peanut butter sandwich, an independent pattern based upon a purposeful 4-part arrangement and layering of 3 ingredients(bread, peanut butter, and jelly) which can vary in type. As in, it's not a pile of groceries.

I don't know how many types there are for each ingredient (nor will I bother looking that up) but I doubt there is more than 65536 types of bread, so that can be represented by 16 bits. Ditto for the other 2 ingredients. Note that I'm boosting these numbers. The sandwich has 4 parts, with 3 ingredients, which can be arranged 24 ways (4!=24). Now in that overall configuration space only 2 arrangements matter to us:

bread, pb, jelly, bread
bread, jelly, pb, bread

The other arrangements do not make a sandwich.

(16/bread)+(16/pb)+(16/jelly)+(16/bread)+(5/arrangement of parts)=69

So the pb sandwich contains 69 informational bits at most, which is not anywhere close to 500 bits so the Explanatory Filter would reject is as being designed in stage 2. Thus the informational content of a pb sandwich cannot be considered Complex Specified Information, since while the object IS specified the complexity is low. As I said, I boosted the numbers to highlight this point.

(Now, I eliminated question 2, "how the pb is spread", from the equation since it made the example more complicated since the number of parts and possible arrangements could then fluctuate.)

Yes, the pb sandwich is designed. Yes, that also means that the explanatory filter would produce a false negative for sandwiches, unless you happen to be making a Dagwood sandwich with around 20-30 parts (although, again, 16 bits per ingredient is likely overkill and 32! arrangements would require 128 bits by itself). Dembski has already explained why formalized design detection method are set up this way in order to prevent false positives.

Even though the Explanatory Filter is not a reliable criterion for eliminating design, it is, I argue, a reliable criterion for detecting design. The Explanatory Filter is a net. Things that are designed will occasionally slip past the net. We would prefer that the net catch more than it does, omitting nothing due to design. But given the ability of design to mimic unintelligent causes and the possibility of our own ignorance passing over things that are designed, this problem cannot be fixed. Nevertheless, we want to be very sure that whatever the net does catch includes only what we intend it to catch, to wit, things that are designed. –Dembski

4. Does something written in invisible ink carry the same amount of information as something written with black ink, or something written using animal tracks? Imagine having a deer hoof on the end of the stick, and writing your name in the sand with the deer hoof. the hoof prints are visible and tell us something. its hard to see how there is not information in that.

The information is abstracted from the storage medium. Dawkins used the example of whether you're using pink and blue cards or verbal words to say "it's a girl", which only conveys 1 informational bit no matter the storage medium. In the computer you're using it does not matter if the information is located in the RAM or hard drive, which store the information very differently. The atomic structure of the components in the computer don't change that information. It's still the same information.

And, yes, there is information in that the sand writings were done with deer hooves but it's a separate bit of information since, I repeat, the type of storage medium does not change the information itself. The probability calculations and thus the informational bits used to represent the information would of course be influenced, as already discussed with the paint splash on the wall example.

5. Take a loaf of bread, a jar of peanut butter and knife and put them in proximity. There is no certainty that a peanut butter sandwich will be made. Actually, without agency, there is a certainty that a peanut butter sandwich won't be made.

While that's fine enough for a weak design inference, we're trying to discuss formalized ID methods here. Stage 1 of the EF would be passed since a pb sandwich is not explained by a law. The informational bits is then calculated in stage 2, and its complexity is found wanting. So, a false negative.

Now one part of these objections makes sense to me. The major methods of ID are limited in usability for general purposes due to the propensity to produce false negatives. So why can't there be an extension to ID that is acknowledged as not being 100% accurate but is more practical? After all, our minds do it all the time: we detect design but it's not 100% accurate. A revised method that is optimized for realtime calculations would be useful for AI programs. I realize that the ID community has a focus of combating Darwinism now but producing such general purpose applications of ID would help ID become more acceptable.