More on "Meaningful" Information

In the ongoing debate about meaningful information at Uncommon Descent, one of the commentators asked:

"Does an of arrangement of nucleobases ‘adenine-cytosine-adenine’ in DNA mean anything?"

This is a surprisingly interesting and revealing question. To attempt to answer it, I would first like to put a limit on the question: let us consider the answer if the nucleotide sequence "adenine-cytosine-adenine" is in DNA (i.e. not RNA). If "meaningful" information is necessarily analogical, as I have suggested in the previous post on "Evolution, Information, and Teleology", then the answer to this question depends upon the circumstances in which the nucleotide sequence ACA is a part. If, for example, this sequence is part of a longer sequence of nucleotides in a longer DNA molecule, then there are several possible answers:

1) the DNA nucleotide sequence ACA could be located in a single strand of DNA that is suspended in a test tube (i.e. not in a living cell) and is therefore completely biologically inert (i.e. it is not binding to a complementary strand of DNA, nor being replicated, nor transcribed, nor translated);

2) the DNA nucleotide sequence ACA could be hydrogen bonded to the complementary sequence TGT (i.e. "thymine-guanine-thymine") in another strand of nucleotides that is anti-parallel with it and close enough to form hydrogen bonds between the nitrogenous bases;

3) the DNA nucleotide sequence ACA could be in a strand that is being replicated by DNA polymerase, which can synthesize the complementary sequence TGT in a newly synthesized strand of DNA;

4) the DNA sequence ACA could be in a strand of DNA that is being transcribed by RNA polymerase, which can synthesize the complementary sequence UGU in a newly synthesized strand of RNA;

5) the DNA sequence ACA could be in a strand of DNA that has already been transcribed by RNA polymerase into the complementary sequence UGU in a strand of mRNA that is bound to a ribosome and can be actively translated into an amino acid sequence in a polypeptide; or

6) the DNA sequence ACA could be in a strand of DNA that has already been transcribed by RNA polymerase into the complementary sequence UGU in a strand of mRNA that is bound to a ribosome and is being actively translated into an amino acid sequence in a polypeptide inside a living cell, within which the polypeptide has a biological function (i.e. participates in those biochemical reactions that maintain the cell alive/against the depredations of the second law of thermodynamics).

In case #1 the DNA nucleotide sequence ACA has no "meaning", in that it is not analogically related to anything. It also has no Shannon information nor Kolmogorov information nor Orgel information either, as it is not in the process of being transmitted or compressed, nor is it "specifying" anything.

In case #2 the DNA nucleotide sequence ACA has no "meaning" because its bonding with its complementary sequence is purely chemical, not analogical. Like the bonding together of water molecules in a snowflake (i.e. the regular crystalline solid form of water), the hydrogen bonding of the nitrogenous bases in complementary DNA sequences is wholly determined by "natural laws", and is therefore neither analogical nor meaningful.

Cases 3 and 4 appear to be the same as in case 2; the relationships between the nucleotide sequences and the bonding patterns therein are entirely the result of chemistry, with no analogical nor meaningful information involved.

However, in cases 5 and 6 we seem to come to a radical discontinuity. In both of these cases, there can be an analogical (and therefore "meaningful") relationship between the nucleotide sequence ACA in DNA and the corresponding amino acid sequence in a translated polypeptide, either in vitro or in a cell. What makes this difference possible (and what may make it necessary) is the analogical relationship between the nucleotide sequence and the corresponding amino acid sequence (if one exists). If the DNA sequence ACA is located in the template strand of an actively transcribed DNA sequence (i.e. a DNA sequence beginning with a promoter to which RNA polymerase can bind) and furthermore its complementary RNA analog is located in an mRNA molecule following the "start" codon AUG but not following a "stop" codon (either UAA, UAG, or UGA, assuming a three-base reading frame), then that the DNA sequence does indeed contain "meaningful" information: it is encoded in one medium, is translated into another medium, and has a function in the system of which it is a part.

It is not yet clear from current research whether or not the amino acid that is "translated" from the DNA sequence ACA (i.e. from the mRNA sequence UGU, assuming that the DNA sequence ACA is in a template strand) is necessarily related to that mRNA sequence. That is, we do not know with confidence whether the relationship between mRNA codons and the amino acids for which they code is purely arbitrary (i.e. the result of a "frozen accident") or if there is some as-yet-undetected necessary (i.e. "natural") relationship between them.

What we can say with reasonable assurance is that what distinguishes "meaningful" information from any other kind of information is not the material into which it is encoded, but rather the relationship between the information encoded in one physical medium and its decoded complement in a related physical medium. As Gregory Bateson pointed out many years ago, meaning is entirely in the relationship between material things; it is not the things themselves. Or, as Alfred Korzybski pointed out,

"The map is not the territory"

In the same way, meaningful information is not the medium in which it is encoded, transmitted, and decoded.

************************************************

As always, comments, criticisms, and suggestions are warmly welcomed!

--Allen

Evolution, Information, and Teleology in Biology

I am currently in the middle of a debate at Uncommon Descent, the leading "intelligent design" website. The debate focuses on the concept of "information": what it is, where it comes from, and what its properties are. In thinking about these questions, I have been struck by how central they are to biology in general and evolutionary biology in particular.

When one uses the term "information", one can be referring to at least four different phenomena: Shannon information, Kolmogorov information,complex specified ("Orgel") information[1], and meaningful information. To me, it appears that the first three types of information – Shannon, Kolmogorov, and complex specified information – are fundamentally different from meaningful information.

What do we "mean" when we say that something is "meaningful"? To me, "meaningful" information is encoded information in which the "bits" of information "encode" (or "stand for") other bits of information via analogy. A meaningful "bit" therefore "stands for" some other bit.

Furthermore, two bits of information that stand for each other necessarily not identical, even if they are written (i.e. symbolized) using exactly the same symbols. That is, two copies of the same symbol may "mean" the same thing, but they are not the "same" symbol, except via analogy. To be the "same" symbol, there could only be one symbol which "stands for itself". This is simply a reinterpretation of Aristotle's law of non-contradiction.

Moreover, it seems to me that not only is meaningful information necessarily analogical, it is also necessarily arbitrary, in the sense that the analogical relationship between the bits of a message and the concept with which those bits is associated is not "natural" (i.e. it is not the result of physical necessity), but rather "non-natural" (i.e. the result of arbitrary semantic association).

For example, consider the meaningful word "two". I can substitute the numeral "2" for the English word "two" without changing the meaning of the word. Indeed, the following words all "mean" the same thing: 2, ii, II, 10 (binary), dué, deux, duo, twa, zwei, etc. [see http://en.wikipedia.org/wiki/2_%28number%29 ] This list can be infinitely extended: 0 + 2, 1 + 1, 2 + 0, 3 - 1, 4 - 2, etc. (and, of course, zero plus two, one plus one, two plus zero, three minus one, four divided by two, ten divided by five, etc.). All of these words and phrases "mean" exactly the same thing: that which we refer to with the English word "two" (or, if you prefer, the Arabic numeral "2").

In the previous example, all of the words and phrases are encoded analogies of the concept of "twoness", none of them are more or less "twoish" than any other (You're twoish? That's funny, you don't look twoish), and indeed none of them are necessarily "twoish" at all. That is, the meaningful relationship between the various words and phrases and "twoishness" is arbitrary or, more precisely, non-natural. We may refer to such meaningful (and ultimately arbitrary) relationships between the "name" and "the thing named" as semantic associations, to distinguish them from non-arbitrary natural relationships.

It appears to me that arbitrary semantic associations such as those symbolized by the numeral "2" are fundamentally different from the natural relationship between the number of protons in an atomic nucleus and its chemical properties. Regardless of what one "calls" a nucleus with two protons ("helium" is the most common name for it, but there are others), and no matter which of the words or phrases one chooses to refer to the number of protons in the nucleus, the chemical and physical properties of the nucleus remains the same [see helium for more about the properties of this element]. Ergo, the "twoness" of the protons in the nucleus of helium is a non-arbitrary, "natural" property of such nuclei, and is therefore not a form of meaningful information.

By contrast, saying that the number of protons in the nucleus of an atom of helium has no more effect on the natural properties of such a nucleus than if one says that there are deux (or twa or zwei) protons in such a nucleus. No matter what you call it nor how you refer to the number of protons in its nucleus, helium is helium is helium (pacé Gertrude Stein).

Given the foregoing, it should be clear that the first three types of information I listed at the beginning of this comment are not necessarily meaningful. That this is the case for Shannon and Kolmogorov information is widely accepted. However, it is also the case for some (but not all) forms of complex specified ("Orgel") information. For example, if one constructs a string of random nucleotides (or any random string of bits), if that string does not subtend a promoter sequence, it will not "code" for the amino acid sequence of a polypeptide. Furthermore, unless such a string subtends a "binding region" (i.e. a sequence to which a protein or RNA molecule may bind via hydrogen bonding) it will also not have a regulatory function in a larger biochemical/cellular system. Under these circumstances, such a random string will not "encode" for any structure or function, but still possesses what Leslie Orgel [1] referred to as "complex specified information".

Ergo, "meaningful information" is analogical information; it "stands for" something else. Furthermore, the relationship between a bit of meaningful information and the thing it stands for is a functional relationship. That is, the meaningful bit specifies the function of the thing for which it stands (i.e. not "Richard Stans"). This means that meaningful information is necessarily teleological, as "functions" are semantically equivalent to "goals" which are semantically equivalent to "ends".

So, teleology must exist in any functional relationship, including those in biology. The question is not "is there teleology in biology"; no less an authority on evolutionary biology than the late Ernst Mayr (not to mention Franciso Ayala) emphatically stated "yes"! The real question (and the real focus of the dispute between EBers and IDers) is the answer to the question, "where does the teleology manifest in biology come from"? EBers such as Ernst Mayr assert that it is an
emergent property of natural selection, whereas IDers assert that it comes from an "intelligent designer". It has never been clear to me how one would distinguish between these two assertions, at least insofar as they can be empirically tested. Rather, the choice of one or the other seems to me to be a choice between incommensurate metaphysical world views, which are not empirically verifiable by definition.

This is not, however, to say that the distinction between evolutionary and non-evolutionary models of reality is purely and solely a matter of choice of metaphysics. On the contrary, the empirical evidence for evolution is overwhelming, as is the evidence for at least some of the characteristics of living organisms having arisen as the result of natural selection. What is still a matter of dispute is where meaningful information "comes from": does it arise as an emergent property of natural processes (such as natural selection), or must it be "read into nature" from some non-natural source?

That is the question...

REFERENCE CITED:

[1] Orgel, L. (1973) The origins of life, Chapman & Hall, London, UK, pg. 189:

"...living organisms are distinguished by their specified complexity. Crystals are usually taken as the prototypes of simple well-specified structures, because they consist of a very large number of identical molecules packed together in a uniform way. Lumps of granite or random mixtures of polymers are examples of structures that are complex but not specified. The crystals fail to qualify as living because they lack complexity; the mixtures of polymers fail to qualify because they lack specificity."

P.S. Shannon information, Kolomogorov information, and Orgel information need not be perceived to exist, but meaningful information does.

P.P.S. As for the second law of thermodynamics, it seems clear to me from what I know about biology (the only natural science that deals with meaningful information) that both encoding and decoding meaningful information requires the transformation of energy from a condition of lower to higher entropy. This is always the case when meaningful information is “transformed”, whether one is referring to the replication of DNA, the transcription of DNA into RNA, the translation of mRNA into polypeptides, the catalysis of biochemical reactions via enzymes, the transduction of changes in the physical environment into action potentials in the sensory nervous system, the transduction of action potentials in the motor nervous and musculoskeletal systems into behaviors, or the playing of a game of chess (regardless of whether one uses a board and pieces).

************************************************

As always, comments, criticisms, and suggestions are warmly welcomed!

--Allen