Eric Holloway has returned to The Skeptical Zone, following a long absence. He expects to get responses to his potshot at phylogenetic inference, though he has never answered three questions of mine about his own work on algorithmic specified complexity. Here I abbreviate and clarify the recap I previously posted, and introduce remarks on the questions.

If there is a fundamental flaw in the second half, as you claim, then I’ll retract it if it is unfixable.
— Eric Holloway, January 2, 2020

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In Section 4 of their article, Nemati and Holloway claim to have identified an error in a post of mine. They do not cite the post, but instead name me, and link to the homepage of The Skeptical Zone. Thus there can be no question as to whether the authors regard technical material that I post here as worthy of a response in Bio-Complexity. (A year earlier, George Montañez modified a Bio-Complexity article, adding information that I supplied in precisely the post that Nemati and Holloway address.) Interacting with me at TSZ, a month ago, Eric Holloway acknowledged error in an equation that I had told him was wrong, expressed interest in seeing the next part of my review, and said, “If there is a fundamental flaw in the second half, as you claim, then I’ll retract it if it is unfixable.” I subsequently put a great deal of work into “The Old Switcheroo,” trying to anticipate all of the ways in which Holloway might wiggle out of acknowledging his errors. Evidently I left him no avenue of escape, given that he now refuses to engage at all, and insists that I submit my criticisms to Bio-Complexity.
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… in regard to his article “Expected Algorithmic Specified Complexity”

Question 1. Is your definition of algorithmic specified complexity precisely equivalent to the definition given by Ewert, Dembski, and Marks in “Algorithmic Specified Complexity,”

(A)  

even though you write in place of ?
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Eric Holloway has littered cyberspace with claims, arrived at by faulty reasoning, that the “laws of information conservation (nongrowth)” in data processing hold for algorithmic specified complexity as for algorithmic mutual information. It is essential to understand that there are infinitely many measures of algorithmic specified complexity. Nemati and Holloway would have us believe that each of them is a quantification of the meaningful information in binary strings, i.e., finite sequences of 0s and 1s. If Holloway’s claims were correct, then there would be a limit on the increase in algorithmic specified complexity resulting from execution of a computer program (itself a string). Whichever one of the measures were applied, the difference in algorithmic specified complexity of the string output by the process and the string input to the process would be at most the program length plus a constant. It would follow, more generally, that an approximate upper bound on the difference in algorithmic specified complexity of strings and is the length of the shortest program that outputs on input of Of course, the measure must be the same for both strings. Otherwise it would be absurd to speak of (non-)​conservation of a quantity of algorithmic specified complexity.
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… proved without reference to infinity and the empty string.

Some readers have objected to my simple proof that computable transformation of a binary string can result in an infinite increase of algorithmic specified complexity (ASC). Here I give a less-simple proof that there is no upper bound on the difference in ASC of and To put it more correctly, I show that the difference can be any positive real number.

Updated 12/8/2019: The assumptions of my theorem were unnecessarily restrictive. I have relaxed the assumptions, without changing the proof.
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In “Evo-Info 4: Non-Conservation of Algorithmic Specified Complexity,” I neglected to explain that algorithmic mutual information is essentially a special case of algorithmic specified complexity. This leads immediately to two important points:

1. Marks et al. claim that algorithmic specified complexity is a measure of meaning. If this is so, then algorithmic mutual information is also a measure of meaning. Yet no one working in the field of information theory has ever regarded it as such. Thus Marks et al. bear the burden of explaining how they have gotten the interpretation of algorithmic mutual information right, and how everyone else has gotten it wrong.
2. It should not come as a shock that the “law of information conservation (nongrowth)” for algorithmic mutual information, a special case of algorithmic specified complexity, does not hold for algorithmic specified complexity in general.

My formal demonstration of unbounded growth of algorithmic specified complexity (ASC) in data processing also serves to counter the notion that ASC is a measure of meaning. I did not explain this in Evo-Info 4, and will do so here, suppressing as much mathematical detail as I can. You need to know that a binary string is a finite sequence of 0s and 1s, and that the empty (length-zero) string is denoted The particular data processing that I considered was erasure: on input of any binary string the output is the empty string. I chose erasure because it rather obviously does not make data more meaningful. However, part of the definition of ASC is an assignment of probabilities to all binary strings. The ASC of a binary string is infinite if and only if its probability is zero. If the empty string is assigned probability zero, and all other binary strings are assigned probabilities greater than zero, then the erasure of a nonempty binary string results in an infinite increase in ASC. In simplified notation, the growth in ASC is

for all nonempty binary strings Thus Marks et al. are telling us that erasure of data can produce an infinite increase in meaning.

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1. ‘Information’, ‘data’ and ‘media’ are distinct concepts. Media is the mechanical support for data and can be any material including DNA and RNA in biology. Data is the symbols that carry information and are stored and transmitted on the media. ACGT nucleotides forming strands of DNA are biologic data. Information is an entity that answers a question and is represented by data encoded on a particular media. Information is always created by an intelligent agent and used by the same or another intelligent agent. Interpreting the data to extract information requires a deciphering key such as a language. For example, proteins are made of amino acids selected based on a translation table (the deciphering key) from nucleotides.

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I did a talk recently on a new way of understanding Irreducible Complexity using computability theory. I’m curious to see what you all think about it.

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