Re: Memes are Interactors - Long

Aaron Lynch (
Wed, 15 Apr 1998 02:44:19 -0500

Message-Id: <>
Date: Wed, 15 Apr 1998 02:44:19 -0500
From: Aaron Lynch <>
Subject: Re: Memes are Interactors - Long
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Aaron Lynch responding to John Wilkins.


>| >So, you agree with me that (as I first said, correcting for a typo) "the
>| >physical systems in which information is stored degrade as a function of
>| >thermodynamic entropy", that is, the systems degrade due to a
>| >thermodynamic effect. This is not a different point but a restating of
>| >the same point. Note that I do not specify what sort of entropic change.
>| If you are going to use the quantity entropy (S), and refer to "a
>| of entropy," then you should define that function, which you cannot do
>| without specifying the system under study. (You should also specify how
>| entropy is added or removed from a system.) The comments you make do not
>| even characterize whether error rates or "degradations" increase or
>| decrease with entropy at the entropy level of 100 Joules/Kelvin for some
>| particular system. Bear in mind that separating all the elements in your
>| microprocessor into pure crystals of elements at nearly absolute zero
>| temperature is a vast reduction in entropy in the processor's matter, but
>| most people would consider this to be a functional "degradation." If you
>| cannot use the quantity S properly, I suggest dropping the term "entropy"
>| from your discussion instead of using it in a vague, almost meaningless
>| manner. (I already disregarded the typo.) If we start accepting vague
>| misuses of the term "entropy," then we are unwittingly supporting similar
>| fallacies by the "scientific creationists," and others.
>OK, I'll restate my view once more without the term. Changes in information
>content of messages - memetic or otherwise - are an inevitable result of
>physical processes, including thermodynamic agitation [which is a function
>of entropic change, according to Brillouin]. This is distinct from intropy.
>Noise introduced into the information channel creates novel variation on
>which selection can act.

That's better. Thank you... This entropy talk was making my brain overheat ;-)

>| You are clearly one who prefers a rewriting the definition of "meme"
>| >in a
>| >| way directly contradictory to Dawkins and others. To my thinking, the
>| >way
>| >| you have done this is akin to rewriting the definition of "gene" to
>| >refer
>| >| to information stored and transcribed in all sorts of physical systems
>| >| other than nucleic acid, (or, more generally, whatever an organism's
>| >| "genetic material" may be.) This being the case, it is worth noting
>| >that a
>| >| great enough reduction in the thermodynamic entropy of your computer
>| >will
>| >| also wipe out all of the information that makes the device useful to
>| >you.
>| >Is this a rewriting of Dawkins? In his "Replicators and Vehicles" (1982)
>| >he states, in response to Gould's criticism of the selfish gene
>| >metaphor, that
>| >
>| > A replicator may be defined as any entity of which copies are made. ...
>| > the basis of their selection. [1984 version: 163, 164]
>| >
>| >Now here we have all the elements of my own definition implicitly or
>| >explicitly stated back in 1982. Dawkins says that replicator size is
>| >arbitrary, replicators are information not nucleotides, the Williams
>| >definition is the basis for memes, behaviour/artifact (note: not just
>| >brain structures store memes, a point made by Brillouin 25 years
>| >earlier) is the phenotype.
>| Dawkins treats genes as information whose instantiation locus is (on this
>| planet) nucleic acids. They are information, not nucleotides, but they
>| defined not as just any information, but information whose physical
>| substrate (instantiation locus) is nucleic acids. Thus, a videocassette
>| "Titanic" does not contain "genes." Dawkins (1982) is also explicit that
>| the instantiation locus of the information called "memes" is the brain.
>| uses the term "replicator" as a more general term than either "genes" or
>| "memes."
>Yes it obviously is, and that is how I used it, I believe. You introduced
>the claim that I make genes non-nucleotidal, but all I was doing was
>showing that Dawkins makes replicators a superset of nucleotides (have you
>read Jablonka and Lamb's attempt to reintroduce non-nuclear inheritance,
>BTW? If it is faux biology it is very well presented faux biology.). Of
>course memes are not genes, nor are genes anything but nucleotide polymers
>of some kind.
>But it was Williams who makes *evolutionary* genes cybernetic abstractions,
>and in this Dawkins is explicitly following him, and so am I. For instance,
>this is why Ghiselin's recent attack on Dawkins is wrong, I think, when he
>complains that Dawkins is faced with a reductio over deletions being genes
>(Ghiselin 1997: 144-147). If the selective context is the background of the
>functionality of genes in a population, then a deletion is information
>relative to that context, not a loss of information (although it can be
>that as well). A nonbiological example: I remove the rule that one can
>castle in chess. That has all sorts of ramifications for defensive
>strategies, and will favour those players who do not rely on it, at least
>in the 'burbs. The *loss* of a permitted move is information about the

I suggest reading section 15 of my paper, too.

>| >Apart from my insistence in a forthcoming Biology and Philosophy paper
>| >that some memes at any rate are particulately inherited, Dawkins and I
>| >are saying exactly the same thing. That is not revisionism but
>| >explication.
>| Disagreed, with respect to the instantiation locus (by definition) of
>| memes. See The Extended Phenotype, p. 109.
>The Dawkins quote I gave explicitly introduces artifacts. Dawkins
>prevaricated a bit early on over replicator substrates. Hull, Plotkin,
>Cziko, RJ Richards, and a number of others (but not Dennett, in a talk I
>attended) have accepted that selection occurs not on naked memes but on
>their effects and so did Dawkins. Whether they are instantiated wholly in a
>given central nervous system (CNS) or not is irrelevant. Why can a meme not
>be distributed over a number of CNSs? And if it can be stored there, why
>not in the relations between CNSs? And if there, why not in intermediate
>physical objects (such as books, recordings or a particularly fine example
>of Ming dynasty porcelain)? If, and I have given reasons why I do not think
>he does, but if Dawkins restricts memes to brain states (as Delius 1991
>did), then he is wrong, in my view. Information can be stored in a number
>of systems and not all of them are hydrocarbon-based dissipative structures

Dawkins also discusses artifacts in The Extended Phenotype. But he
explicitly excludes them from the definition of "meme."

My paper is very explicit that information can be stored and replicated in
other media and distributed networks of brains. That is why I introduce the
term "cultural repliconics" as the superset of memetics. Declaring
instantiation locus "irrelevant" is vague and unsupported.

When I re-invented memetics in 1978, unaware of Dawkins's 1976 chapter, I
(necessarily) used my own tentative neologism instead of "meme." I was
quickly told about Dawkins, but refused to use his previously vague word
"meme" until he clarified its meaning in The Extended Phenotype. Now that
the term has been in long use to refer to a specific subclass of cultural
information, you better have VERY good reasons before proposing to take the
word away from those who have used it this way without even offering a good
replacement term. If you don't, then you have no grounds for complaint when
yet another newcomer arrives with still another definition totally contrary
to yours. There are many reasons to keep such a (relatively) specific term
(allowing for writing a more formal definition for clarity), and these are
discussed in sections 10 and 11 of my paper.

>| >| The main pseudoscientists and charlatans I allude to, of course, are
>| >the
>| >| ones who attempt to invoke the second law of thermodynamics as an
>| >argument
>| >| against biological evolution. Naturally, I would rather not see
>| >erroneous
>| >| "second law" arguments emerging in memetics.
>| >
>| >I entirely agree with this. I'm a denizen, and can testify
>| >to the ubiquity of thermodynamic mumbo-jumbo by anti-evolutionists.
>| >However, that's entirely different from stating the truism that
>| >thermodynamics introduces noise. I never made any claim about novelty
>| >being the result of either an increase or decrease in entropy. Novelty
>| >is the result of changes in entropy relative to the prior state.
>| Unless you define a quantity "novelty" for some system and explain its
>| relationship to the to the entropy of that system, I recommend leaving
>| term out of your discussion. The term "entropy" may sound sophisticated,
>| and may even cause "physics envy" in social scientists, but I do not yet
>| see any scientific advantage to the above usage. We need to set the best
>| possible examples for the crowd.
>Do I need to do this a priori, or can I have some time to formulate it? As
>it happens, I do have a conception of novelty as the degrees of freedom
>permitted to a system that it has not yet attained. The relevant reference
>is M Boden's 1991 book on creativity (I do not have the full ref to hand
>right now). Anyway, the last thing I want to do is excite physics envy.
>It's enough that social scientists have rarely attempted to assuage their
>biology envy, or even acquire it in the first place.
>| >| Section 12 of my paper does mention that full ordering systems are
>| >easily
>| >| constructed for texts and nucleic acids. But in [order] to ever
>| >consider
>| >| brain-stored information (memory items) as memes, you would need a
>| >full
>| >| ordering system for them before incorporating a "least units" phrase
>| >in the
>| >| definition.
>| >Why "for them", that is, for brain states?
>| The full ordering system is, of course, needed for any medium for which
>| wish to identify "least units" of sociocultural information. My above
>| sentence is intended to call attention specifically to brain-stored
>| information.
>| > ...How information is stored is
>| >not relevant - how information is expressed and transmitted is. That's
>| >what makes a replicator. There is a category error in identifying brain
>| >states with concepts that is well known in the philosophy of mind. Apart
>| >from anything else, how a brain state is located in a context determines
>| >its meaning.
>| I was discussing brain-stored information rather than offering an
>| identification of brain states with concepts. Nevertheless, how
>| is stored is relevant to many things. For those interested in
>| thermodynamics (for instance), it is worth noting that the thermodynamics
>| of storage in an "active" system such as vacuum tube or CMOS flip flops,
>| a system of neurons, is quite different from the thermodynamics of
>| in a "passive" system like a diskette. You yourself use differing
>| terminology for information stored in nucleic acids versus socioculture.
>| Within categories, there are also consequential differences between media
>| of storage. Storage of information in a cell's RNA has different
>| consequences from storage in the cell's DNA. Just when a difference of
>| medium warrants a difference in nouns is perhaps partly a matter of
>| but Dawkins coined "meme" to refer to information in a specific kind of
>| medium--namely, brains. Scientists do have a right to name subclasses of
>| phenomena, including subclasses of cultural information.
>And they - or at least charlatan pseudoscientist philosophy writers - have
>a right to revise or extend them, or should "gene" still be restricted to
>Mendelian factors, or better, should "allelomorph" ("allele") still refer
>to _acquired_ hereditary information?

There are fundamental discoveries which are the basis for modifying the
terms "gene" and "allele." These constitute the VERY good reasons for
radically changing the definition of a scientific word long in use. They
also provide guidance as to HOW to change the word's definition, rather
than just changing it to change the subject, for instance. You have offered
nothing like this level of compelling, fundamental new science. You haven't
even worked out the serious problems in the subordinate "least units"
clause of your revisionist definition.

>Information that cannot be expressed and implemented is not information but
>mere structure or organisation. By the same token, if cultural information
>can be stored in a number of heterogenous physical systems from CNSs to
>networked computer systems, we cannot either identify that information with
>any given physical instantiation, or expect to find some common way to
>compare that diversely stored and expressed information at any level *other
>than* the level it gets expressed at.
>What counts as a meme is what gets differentially transmitted in some
>common language or conventional protocol. "Meme" is a supervenient property
>(or entity, I'm vascilating), not a reductive property. So all (!) we must
>do, to track memes, is find some way to represent that information that
>allows us to measure the selection coefficient (and of course drift). I do
>not attempt to specify that ordering system because I expect that there
>will not be just one.
>| The inter-medium transfer of information (e.g., brain to paper, paper to
>| brain) is of course important in replication. This does not, however,
>| that there needs to be a complete instantiation of a replicator in
>| media. Even using a medium-neutral definition for a computer virus, for
>| instance, does not mean that a cable connecting two computers can ever
>| an entire copy of the virus, (unless the cable is very long and/or the
>| rate very high). Likewise, a telephone wire generally will not contain an
>| entire instantation of a spoken word, even taking a medium-neutral sense
>| the term "word" into account.
>If I understand you, you are saying that memes need not be stored in a
>single brain. Which was to be demonstrated...
>| >| As for finding competitors, contrary beliefs are often good examples
>| >of
>| >| memes that compete in a population. Beliefs that "abortion is murder"
>| >and
>| >| "abortion is a right," for instance, propagate as contrary
>| >competitors.
>| >
>| >It is circular to argue that we can identify alleles in order to find
>| >alleles.
>| Fortunately, I do not do this. Unlike the medium of nucleic acids, the
>| medium of brain storage allows for certain pieces of information to be
>| "contrary" to other pieces. Definitions of "meme," for instance. The
>| is not isomorphic to the gene-locus scheme of chromosomes, nor to
>| for that matter.
>No, and I do not expect that they will be, but I do think that there is a
>heterogenous class of phenomena - replicators - that get replicated in ways
>that are dynamically similar. Some are nucleotides, and some of those are
>nonnuclear, while others are messages transmitted between and among CNSs.
>[Before a reader asks, a heterogenous class is like a polythetic set in
>taxonomy or a cluster concept in philosophy of language... (qv "family
>| That these things propagate in competition is something you can
>| >only find out if you can first individuate them, and you cannot assume
>| >that this is unproblematic, as your definition seems to do. This is
>| >analogous to the same problem in systematics between phenetics and
>| >cladistics. The choice of phenotypic traits ("phenes") was quite
>| >subjective in phenetics if it wasn't based on theroretical
>| >considerations, and that's what sank it in the end, although many of the
>| >techniques survive.
>| There are various empirical ways to observe that the belief that
>| is a right" propagates in competition to the belief that "abortion is
>| murder." A very low frequency of simultaneous instantiation (mainly in
>| those who view murder--not just killing--as a right), coupled with data
>| showing inversely related fluctuations in adherent populations would
>| constitute significant evidence.
>And you are observing what? Behavioural regularities or semantic
>equivalences. If the former, you are in the behaviourist dilemma unless you
>can specify what behaviour signifies something relevant, and if the latter
>you are in Quine's "gavagai" dilemma for the same reason. Radical
>underdetermination of the significance of behaviour and language means that
>you have *already* assumed some common way to identify the "propositions"
>that count as memes if you are doing this. To say that there are
>"empirical" ways is just to say that you have made your (subjective, or at
>best relative and still question-begging) decision as to how to represent
>those memes.

These opinion memes are functionally defined when surveys are designed, for
instance. The correlations in question can, for instance, be computed from
a poll on the subject. That I don't identify a universal system for
identifying the "propositions" that count is a point I emphatically make in
my paper. This is where I leave the term "meme" maximally flexible, to
accommodate different ways of conceptualizing the mental information of a
whole population of individuals. This does not, however, mean that all such
conceptualizations are equally useful. Again, see the paper.

>Think about a simple case: the observance of a solstice like Easter
>(apropos the season, and the reason why I can wax so prolix - from today
>it's back to short snippets). When is the observance of the spring solstice
>the "same" memeplex? When there is some influence shared by two cultures
>(identity of descent) I would suggest. If the pre-Columbian Incas observed
>it, that counts as convergence not homology. But what "empirical" features
>of either festival show this? Not the season, nor even the crop rituals
>(which tend to be similar the world over), but the cultural content, which
>you must already be able to individuate.

The observance itself is not a meme complex. People can have a meme but not
express it, or even behave as though expressing a meme they do not have.
Avoiding the confusion of behavior with its mental concomitants is one of
the advantages of not trying to load too many meanings upon the one word
"meme." The brain-stored portion of the information that causes the
observance is the meme complex. A belief in celebrating the resurrection of
Jesus may play a key role in causing a springtime ritual in one culture,
while a belief in appeasing a rain god might play a key role in causing a
spring ritual in another culture. You don't always find out people's
beliefs just by observing their gross behavior. You may actually have to
learn their language and interview them.

>| >| I do not see you offering any method to distinguish a "size"
>| >difference
>| >| between (for example) the the idea that people represent with the
>| >phrase
>| >| "abortion is murder" and the idea that people represent with the
>| >phrase
>| >| "abortion is mortal sin" even within a single brain, let alone between
>| >| brains. Nothing you say below solves this problem either. You need to
>| >| develop the ordering system not just for textual information, but also
>| >for
>| >| brain information before treating information unit sizes as knowable
>| >within
>| >| a definition of "meme." It would also help if you could choose a
>| >| non-arbitrary ordering system, which for text would include such
>| >| possibilities as letter counting or binary magnitudes of concatenated
>| >| byte values. Other reasons for not going with "size" restrictions
>| >appear in
>| >| my paper.
>| >I must read it in detail. I read the draft you had on the web but
>| >haven't had time to get to the full version. However, you appear to be
>| >hung up on the word "size". I mean "least" in the sense of
>| >"nonredundant", which was the point of the S and P example left in
>| >below.
>| The discussion of S and P looks seriously confused, so I did not comment
>| it before--but added just a few comments now. It seems as though you
>| be attempting to mix the notations of set theory, propositional calculus,
>| and metric spaces, but I am not sure. I have degrees in mathematics and
>| philosophy, (as well as physics), and have taken courses specifically on
>| set theory, metric spaces, and symbolic logic. But I do not see a
>| well-formed argument in the passage about S and P. Reasonable books on
>| these subjects are "Set Theory and Metric Spaces" by Irving Kaplanski,
>| University of Chicago Press, 1972; and "Symbolic Logic" by Irving M.
>| Macmillan, 1973. (Section 12 of my paper does not require all of this as
>| background.)
>I've read Copi, and I'll get a copy of Kaplanski some time. However, I have
>no degrees in mathematics - it's one of my deepest regrets. If the argument
>is not well formed, then I must rework it, sometime when I get the chance.

I don't see any way of salvaging the S and P discussion. But if you try, it
would help if you start the argument by stating clearly what your premises
are (1, 2, 3, etc.). Then state what it is you are attempting to prove.
Then give the argument, and a Q.E.D. to signal its end.

>| If you wish to discuss non-redundancy, you would probably to make
>| more clear by not attempting to identify it with "least units." There are
>| already others who write about least or greatest units in a sense not
>| on redundancy. The S and P discussion does not seem to explain the
>| redundancies you have in mind, however.
>| Something is redundant if it is expressed in numerous different
>| >ways.
>| I'm not sure how you plan to identify the most non-redundant units of
>| sociocultural information in general (including in the brain).
>It depends on the coding scheme, and would be an iterative refinement
>process. I guess - and it is nothing more than a guess - that it would
>start with an instance matrix of presence or absence of features (like a
>cladistic instance matrix), and the coding would be varied to take into
>account features encountered for the first time. In medical social research
>this is called grounded theory method.

If you do not yet have the procedure for identifying the most non-redundant
units of sociocultural information, then the existence of such a procedure
should not be presumed by a meme definition.

Coding schemes vary across information substrates. Another reason for
keeping a word that was designed to refer to information coded in an
individual brain. (You were probably referring to a social science data
coding scheme, but the substrate point still warrants making.)

>| Nonarbitrary is nice, but in the end all metrics are arbitrary in
>| >the sense that an infinite number of alternate metrics are possible,
>| >parsimony considerations notwithstanding. What does matter is that
>| >whatever more or less arbitrary metric we do use, the comparisons are
>| >objective. [Arbitrary is not a synonym for subjective.]
>| In section 12 of my paper, the full ordering system for the meme set
>| S' = {A, A*B, A*B*C, A*B*C*D} is not arbitrary, given the definitions of
>| B, C, and D. There are not an ifinite number of orderings in this special
>| subset of memes, either--just 24 possibilities. The most sensible full
>| ordering for S' (given the definitions of A, B, C, and D) is A*B*C*D >
>| A*B*C > A*B > A. Most sets of memes are, as I said in section 12, only
>| partially ordered, however.
>And as a trivial result of logic, one can make an infinite number of
>orderings by adding an indefinite number of new elements. Sure, that
>special subset is artificially restricted, but add a few more elements and
>see what happens. This is equivalent to the problem of the number of trees
>in cladistic analysis. With 3 branches and no internodal taxa there are 4
>polytomous trees and 3 dichotomous trees. According to Felsenstein (1978),
>with 10 branches there are 282,137,824 polytomous trees and 34,459,425
>dichotmous trees. Add internodal taxa (ancestors) and it increases
>accordingly. In any *real world* case you have too many items or data
>points to use a simple ordering system.

If you cannot make even a partial ordering system (a special case of which
is a full ordering system), then you of course cannot have metric spaces
and coordinate systems. I will assume that Felsenstein's combinatorics are
correct, as this is a tangent.

>| >What does behaviour X and behaviour Y have in common when they are
>| >expressions of the same meme? In my paper I wrote:
>| >
><snip quote...>
>| >This was rather aphoristic, but the inference is that we must begin in
>| >the middle (in media res), as it were, and seek to identify parts and
>| >wholes. We can do this, and indeed we do it every time we evaluate an
>| >expression in a natural language. We find kinds, types, classes and so
>| >forth. What they have in common is some structure, which when encoded in
>| >transmission becomes information, and that *can* be measured in Shannon
>| >Weaver bits.
>| Information exists in the brain, not just in the transmissions on their
>| from, to, or bypassing brains. Brain-stored information is important,
>| if you have not found a full ordering system for it.
>Of course. Did I give you the impression that I thought otherwise? In fact,
>I think that being the sort of reflective cognisers we are, most cultural
>information exists in this form. But not all.

My remark comes in response to the clause "which when encoded in
transmission becomes information." I would say "remains" instead of
"becomes" to avoid giving the wrong impression.

>| >| >A set theoretic approach requires a full understanding of
>| >| >classification. One must be able to determine the set membership
>| >| >criteria.
>| The arguments below do not identify sets. S looks like a disjunctive
>| proposition.
>It is, and I made that clear by saying that it is "entirely distinct" from
>set membership. But as I also said when I introduced the example, if it
>gets transmitted entire - that is, as a unit - then the entire unit
>includes semantic content that is exclusive of P, in the sense that if you
>transmit P then you do not transmit S, since a part of P is in direct
>contradiction to S. I could do a modal formulation but I'd rather not -
>suffice it to say that if S leaves A open as a possibility and P does not,
>then they are exclusive memes. Does that clarify what I am saying?

If you want to talk about the probability that P is true in terms of
probabilities that each of A, B, C, are true if S is true, then go ahead.
Other than that, I would rather not talk about "a sense" of logical

>| >| >But that is entirely distinct from determining whether one
>| >| >message is commensurate with another. Moreover, there is a sense of
>| >| >logical exclusion of statements in which if message A is exclusive of
>| >P,
>| >| >then S = (A or B or C) is exclusive of P.
>| The propostion (A or B or C)*(A --> not P) does not imply not P.
>What is the asterisk operator here? Is this from your paper? I do not have
>internet access enough to read it as yet. However, as I argue above, <>S ->
>~<>P in modal terms.

The asterisk here is logical AND. (Different logic notations exist.)

The propostion (A or B or C)AND(A => not P) does not imply not P. ("=>"
means "implies")

>| If we always transmit (A or B or C)
>| >| >as a unity then S is commensurate with P, even if P is just a
>| >| >simple atomic proposition like A, B and C.
>| This statement is unsupported, as is the alternative statement that A is
>| commensurate with B. "Atomic" is not defined.
>I thought that was clear as well - atomic relative to the protocol or
>encoding scheme used to measure the data. This happens in ordinary science
>- why is it so hard to understand in the memetic context? You choose your
>way of measuring phenomena and stick to it, unless you have to refine it to
>take in new cases. And "commensurate" in philsci just means that you can
>compare and contrast statements or views, which Kuhn and Feyerabend was not
>formally possible between competing paradigms, or, in Feyerabend's more
>radical view, between theories or even disciplines. If A, B, C, P and S all
>represent some coordinates in a semantic space, ie, values of parameters,
>then they may be compared and contrasted, nicht wahr?

"Atomic" is still undefined, because no protocol is undefined.
"Commensurate" as you use it has vastly less meaning than its meaning than
in mathematics. If they are "commensurate" on some coordinate axis, then
(depending on how you define the term) they must have the same "size" or
coordinates. Given that you were attempting to show the existence of a
definite method of determining meme sizes or levels of non-redundancy, I
had every reason to assume that you were discussing a quantitative meaning
of "commensurate."

>| Size doesn't matter as
>| >such,
>| >| >rumours to the contrary notwithstanding. What does matter is that S
>| >and
>| >| >P share a metric and are exclusive coordinates in that metric.
>| You have not defined a partial ordering, let alone a metric space, let
>| alone a coordinate system.
>| The
>| >| >*metric* is what selection defines, in terms of what is an allele in
>| >| >that population.
>| The meaning of this eludes me.
>It is my growing opinion that we are talking right past each other, perhaps
>on entirely distinct channels. However, I regret to tell you that you
>haven't convinced me that anything I said was wrong, and no doubt you can
>return that favour.

We may be talking past each other on different channels, but I do not
consider all modes of talking to be "equally valid." Indeed, some ways of
talking produce gobbledygook on a impressive graduate reading level, which
survives because no one has the time to go over it line by line. In sum,
however, I do not see your arguments as having established the requisite
full ordering system for meme sizes or levels of non-redundancy.

>As of today (Wed, Aust time) I am unable to continue this discussion in
>much detail, and will have to return to argumentum ad aphorism. Sorry to
>anyone still listening and interested, and to the rest, well, sorry it took
>so long to get here.
>Refs [snip]

--Aaron Lynch

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