Complexity

Discussion in 'Health and medical' started by Chupacabra, Apr 14, 2004.

  1. Irr

    Irr Guest

    "Tim Tyler" <[email protected]> wrote in message
    news:[email protected]...
    > irr <[email protected]> wrote or quoted:
    > > "Tim Tyler" <[email protected]> wrote in message
    > > > IRR <[email protected]> wrote or quoted:
    >
    > > > The best-established way of measuring complexity is to
    > > > use Kolmogorov complexity.
    > > >
    > > > This:
    > > >
    > > > * Confines discussion to digital phenomena;
    > > > * Is difficult to measure;
    > > > * Has a subjective element - since it depends on a
    > > > choice of descriptive language.
    > > >
    > > > The first is no problem, if we are content to confine
    > > > ourselves to the complexity of genomes.
    > > >
    > > > The second is a problem in theory:
    > > >
    > > > * Except in a few trivial cases, you can only put
    > > > bounds on the
    metric -
    > > > rather than measure it exactly (and even then the
    > > > lower bound is
    rarely
    > > > much use). I would suggest ignoring this problem -
    > > > and measuring the value using a conventional high-
    > > > quality compressor of a type that is capable of
    > > > dealing well with repeated sequences.
    > > >
    > > > ...and in practice...
    > > >
    > > > * You need to sequence the genome in question before
    > > > you can measure its complexity;
    > > >
    > > > The third makes the metric less asethetically
    > > > attractive. My approach would probably be to say
    > > > something along the lines of:
    > > >
    > > > "Always use FORTRAN-77 as your language".
    > > ....]
    > >
    > > IMO this third problem -- choosing a language with which
    > > to quantify complexity -- is still *the* showstopper
    > > when it comes to biology.
    >
    > I like the answer I gave.
    >
    > I almost always give this answer.
    >
    > So far - IMO - I have had no serious complaints ;-)

    Better check your audience ;-).

    >
    > There may be a few even more "unbiased" languages out
    > there - but FORTRAN-77 is convenient enough.
    >
    > > While we might all agree that the primate brain is an
    > > incredibly complex organ, it's not at all agreed upon
    > > what it is we mean by this. For example, a Kolmogorov
    > > measure fails miserably in classifying the brain as
    > > complex, after all you're really only talking about two
    > > dozen or so different recognized cell types stamped out
    > > in enormous repetition with iterated connections between
    > > them -- in other words, a digital representation of the
    > > brain is incredibly compressible.
    >
    > IMO - this makes no sense at all :-|
    >
    > An acceptable digital version of the brain would handle
    > the same I/O - and produce similar inputs from similar
    > outputs. This sounds like a job for a huge computer with
    > an *extremely* lengthy description to me - and of course a
    > correspondingly enormous Kolmogorov complexity.
    > --
    > __________
    > |im |yler http://timtyler.org/ [email protected] Remove
    > lock to reply.
    >

    Certainly a huge computer, but really an extremely lengthy
    description? Check out the top 500 list (top500.org) -- the
    fastest computers in the world are and will continue to be
    iterations of the single processor system you're likely
    reading this reply on right now. While such massively
    parallel systems -- including the human brain -- are
    increadibly impressive to look at, they are remarkably
    regular. Kolmogorov essentially a measure of regularity; low
    in highly parallel architectures and high in random ones.
     


  2. Irr

    Irr Guest

    "John Wilkins" <[email protected]> wrote in message
    news:[email protected]...
    > irr <[email protected]> wrote:
    >
    > > "Tim Tyler" <[email protected]> wrote in message
    > > news:[email protected]...
    > > > IRR <[email protected]> wrote or quoted:
    > > >
    > > > > So for example (and in loose reference to one of
    > > > > your other posts),
    > > there
    > > > > are many, many groups of bacteria that cooperate,
    > > > > differentiate into
    a
    > > > > multitude of morphologically distinct cell types,
    > > > > and build
    elaborate,
    > > > > macroscopic (differentiated though monoclonal)
    > > > > structures. [See,
    for
    > > > > examples, hyphae-producing Streptomyces, akinete
    > > > > and/or heterocyst
    > > forming
    > > > > cyanobacteria, iron-scavenging Shewanella
    > > > > macrocolonies, or the
    wondrous
    > > > > assortment of organisms that comprise e.g.
    > > > > thermophilic, alkaline
    > > microbial
    > > > > mats]. Yet the Kolmogorov complexity of the genomes
    > > > > from these
    > > organisms
    > > > > are indistinguishable, they all have roughly the
    > > > > same number of
    genes,
    > > the
    > > > > degree of their metabolic and protein interaction
    > > > > networks are all
    scale
    > > > > free (power-law distributed) with nearly identical
    > > > > scaling
    exponents,
    > > etc.
    > > > > etc. ad nauseum. Find me some underlying, unifying
    > > > > Standard Model
    of
    > > > > Complexity that has evaded notice in all studies to
    > > > > date, and I'll
    pay
    > > all
    > > > > the publication charges on your paper.
    > > >
    > > > The best-established way of measuring complexity is to
    > > > use Kolmogorov complexity.
    > > >
    > > > This:
    > > >
    > > > * Confines discussion to digital phenomena;
    > > > * Is difficult to measure;
    > > > * Has a subjective element - since it depends on a
    > > > choice of descriptive language.
    > > >
    > > > The first is no problem, if we are content to confine
    > > > ourselves to the complexity of genomes.
    > > >
    > > > The second is a problem in theory:
    > > >
    > > > * Except in a few trivial cases, you can only put
    > > > bounds on the
    metric -
    > > > rather than measure it exactly (and even then the
    > > > lower bound is
    rarely
    > > > much use). I would suggest ignoring this problem -
    > > > and measuring the value using a conventional high-
    > > > quality compressor of a type that is capable of
    > > > dealing well with repeated sequences.
    > > >
    > > > ...and in practice...
    > > >
    > > > * You need to sequence the genome in question before
    > > > you can measure its complexity;
    > > >
    > > > The third makes the metric less asethetically
    > > > attractive. My approach would probably be to say
    > > > something along the lines of:
    > > >
    > > > "Always use FORTRAN-77 as your language".
    > > ....]
    > >
    > > IMO this third problem -- choosing a language with which
    > > to quantify complexity -- is still *the* showstopper
    > > when it comes to biology.
    While we
    > > might all agree that the primate brain is an incredibly
    > > complex organ,
    it's
    > > not at all agreed upon what it is we mean by this. For
    > > example, a Kolmogorov measure fails miserably in
    > > classifying the brain as complex, after all you're
    > > really only talking about two dozen or so different
    > > recognized cell types stamped out in enormous repetition
    > > with iterated connections between them -- in other
    > > words, a digital representation of
    the
    > > brain is incredibly compressible. I can think of
    > > examples with a
    fraction
    > > of the genes present in a human brain cell that can give
    > > rise to at
    least
    > > that many different recognizeable cell types, and I can
    > > just as easily
    think
    > > of organisms with a vastly larger proteome that show
    > > none of the interactions or differentiation of neural
    > > progenitor cells.
    > >
    > > In my mind the obstacle here is that we have not yet
    > > rightly /defined/
    the
    > > problem. Our inherent notion of what is complex is
    > > prominently if not exclusively based on (as evident in
    > > my examples) visual cues, but
    prominent
    > > biological observables such as cell morphology have been
    > > -- at least
    thus
    > > far -- incredibly poor indicators of complexity.
    >
    > Chaitin suggests that you pick a suitably comprehensive
    > and capable language - he uses LISP - and stick with it.
    > So long as you can express or model what you are trying to
    > comparatively measure, then the results are notionally
    > commensurate. But the problem here is that this makes
    > "complexity" a measure of what we can *say* about
    > something. And this seems right to me - complexity is the
    > surprisal value, as it were, of our descriptions of
    > things. The relative scales will change as we are able to
    > describe more and more, unless we artificially restrict
    > ourselves to some aspect of the things, like the DNA
    > (introns or exons? Expressed or regulatory? Methylation or
    > not?) sequences of organisms, in which case complexity is
    > a measure of some theoretical quantity and is *still* an
    > abstract notion. I don't see a way to avoid measuring only
    > what we know about things in this regard.
    > --
    > John Wilkins [email protected]
    > http://www.wilkins.id.au "Men mark it when they hit, but
    > do not mark it when they miss"
    > - Francis
    > Bacon

    I very much agree with this, which is why I advocate
    'calling a spade a spade', against Tim Tyler's notion of a
    generalized complexity (or complexity metric) applicable
    throughout biology and transcending evolution. It's not hard
    to find statements saying that human beings are more complex
    than bacteria, and while this statement seems palatable
    enough, my basic argument is that we need to be absolutely
    clear about what it is that we're calling complex.

    To the best of our knowledge, the most complex life was much
    simpler 3.8 billion years ago than it is today, and so we
    have this general idea that complexity increases over time.
    But as you point out above, without establishing a rigorous
    context within which we can define and measure complexity,
    we're doomed to follow the same ill-fated path that lead to
    the idea that big brains and opposable thumbs represent some
    sort of evolutionary pinnacle towards which all living
    things will eventually migrate.

    And much like our big brains, complexity to me seems to be
    more of a specialized -- as opposed to universal -- solution
    that some organisms have arrived at (which I've tried to
    outline examples of in the above thread). Clearing this
    hurdle in the discussion opens the door to, IMO, a much more
    interesting set of questions such as *why* complexity is
    only found in a limited number of organisms (for example,
    one wonders immediately of the increased necessity for high
    fidelity replication -- that is, more parts to copy -- among
    more complex organisms).
     
  3. "chupacabra" <[email protected]> wrote in message
    news:[email protected]...
    > "Frank Reichenbacher" <[email protected]> wrote
    > in message
    news:<c5m9ck$30f8
    > >
    > > How large do you think the niche space is, or how many
    > > niche spaces do
    you
    > > think there are, for sentient beings on this planet?
    > > Will the next
    sentient
    > > being have to develop some new structure or function
    > > (say telepathy) in order to out compete us, or find a
    > > new niche space?
    > >
    > Presently, as you know, the most successfull and,
    > probably, smartest people usually have few offsprings,
    > and, at least in the developed countries, the birth rate
    > is much higher in undereducated people with lower
    > intellectual status So, in modern humans we, in fact, have
    > a "devolution" where every next generation is, on average,
    > less "smart" than a previous one. It may be objected by
    > the Dawkins idea that for the progress of the human
    > civilization what really matters is not a selection of the
    > genes but the selection of memes or ideas. But, as humans
    > will biologically grow more and more stupid, it may once
    > appear that they simply have not got sufficient brainpower
    > to command the collected memes.
    >

    What does this have to do with your question, "why does
    evolution progress from the simple to the complex?"

    Frank
     
  4. Guy Hoelzer

    Guy Hoelzer Guest

    Hi Tim,

    in article [email protected], Tim Tyler at
    [email protected] wrote on 4/17/04 2:21 PM:

    > Complexity - as everyone agrees - is a scalar property,
    > not a binary one.

    I don't think that "everyone" agrees with this point of
    view. Proposed and often used "measures" of complexity are
    indeed scalars, but that issue is about estimation rather
    than physical reality. I would describe an alternative,
    binary view of complexity as the one promoted by Prigogine.
    I think that he would have agreed with something like the
    following: complexity emerges along with function and
    structure from the merely complicated. Emergence is a
    process, so there would certainly be a period of ambiguity
    as to whether complexity has been achieved, but the concept
    would still be essentially binary and not fairly represented
    by a scalar parameter.

    Guy
     
  5. Tim Tyler

    Tim Tyler Guest

    chupacabra <[email protected]> wrote or quoted:

    > Presently, as you know, the most successfull and,
    > probably, smartest people usually have few offsprings,
    > and, at least in the developed countries, the birth rate
    > is much higher in undereducated people with lower
    > intellectual status. So, in modern humans we, in fact,
    > have a "devolution" where every next generation is, on
    > average, less "smart" than a previous one. It may be
    > objected by the Dawkins idea that for the progress of the
    > human civilization what really matters is not a selection
    > of the genes but the selection of memes or ideas. But, as
    > humans will biologically grow more and more stupid, it may
    > once appear that they simply have not got sufficient
    > brainpower to command the collected memes.

    The reverse has been happening over the last 5 billion years
    - as fairly convincingly demonstrated by skull fossils.

    I don't see any good reason to think things have changed in
    that department.

    Fitness is not about counting offspring - it's about leaving
    descendants.

    Having many offspring might be an insurance strategy against
    hostile local conditions - and should not necessarily be
    interpreted as a sign of fitness.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  6. Tim Tyler

    Tim Tyler Guest

    Guy Hoelzer <[email protected]> wrote or quoted:
    > in article [email protected], Tim Tyler at
    > [email protected]

    > > Complexity - as everyone agrees - is a scalar property,
    > > not a binary one.
    >
    > I don't think that "everyone" agrees with this point of
    > view. Proposed and often used "measures" of complexity are
    > indeed scalars, but that issue is about estimation rather
    > than physical reality. I would describe an alternative,
    > binary view of complexity as the one promoted by
    > Prigogine. I think that he would have agreed with
    > something like the following: complexity emerges along
    > with function and structure from the merely complicated.
    > Emergence is a process, so there would certainly be a
    > period of ambiguity as to whether complexity has been
    > achieved, but the concept would still be essentially
    > binary and not fairly represented by a scalar parameter.

    I don't know what you mean.

    For instance, what's this distinction between complexity and
    complicated all about:

    ``complexity emerges along with function and structure from
    the merely complicated''

    ...?

    *Maybe* there are some folk somewhere who think complexity
    is a binary quantity.

    I'd be inclined to show them Kolmogorov complexity - and ask
    them the equivalent of "how many hairs make a beard" - i.e.
    how they would defend their preferred "complexity
    threshold".
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  7. Tim Tyler

    Tim Tyler Guest

    irr <[email protected]> wrote or quoted:
    > "Tim Tyler" <[email protected]> wrote in message
    > > IRR <[email protected]> wrote or quoted:

    > > > > The bacteria are disadvantaged - since they can't
    > > > > easily cooperate with one another, and build large
    > > > > structures - and such cooperation seems to pay off.
    > > > >
    > > > > They have been (literally) overshadowed - and
    > > > > relegated to the nooks and crannies of the world.
    > > > > These days much of the work gets done by macroscopic
    > > > > organisms - such as trees.
    > > > >
    > > > > Once bacteria ruled the world - but now they in the
    > > > > middle of a period of decline. Their decline seems
    > > > > likely to continue - as much of the world's chemical
    > > > > processing gets taken over by machines - who will
    > > > > have stolen the bacteria's enzymatic secrets from
    > > > > their genomes.
    > > >
    > > > This anthropocentric misinformation that you've
    > > > slipped in at multiple points in this thread has no
    > > > factual basis and no support in real science. There
    > > > have been at least half a dozen articles in just the
    > > > past few years in Science and Nature alone that point
    > > > towards an inverse scale free relationship between
    > > > organism size and organism density. That is, the very
    > > > smallest organisms outnumber slightly larger organisms
    > > > by orders of magnitude, and outnumber even larger
    > > > organisms by many more orders of magnitude.
    > >
    > > Well, yes - becuase they are so tiny. I am outnumbered
    > > millions-to-one by my own gut bacteria - but that
    > > doesn't mean that they are more important than I am.
    >
    > Certainly not what I meant to imply -- I'm not even sure
    > if Kolmogorov had a metric by which we could start to
    > categorize importance :). But I would maintain that the
    > enormous numbers of microorganisms that are out there
    > argue they aren't in any sort of period of decline. In
    > fact in the middle of this 6th mass extinction we've
    > apparently instigated, I'd say they are in better shape
    > than anyone.

    Once they were the only form of life - but now they are
    excluded from many large and significant niches by
    competition from plants.

    The rise of complex organisms seems destined to continue -
    and if life remains confined on Earth, as complex organisms
    rise, bacteria practically must fall back - and give up
    their carbon atoms to make more room.

    > > > In fact the largest organisms on Earth (ourselves
    > > > among them) make up only a minute fraction of the
    > > > global biomass.
    > >
    > > A *lot* of the global biomass is in the form of trees
    > > - e.g.:
    > >
    > > ``The ongoing enrichment of the atmosphere with CO2
    > > raises the question of whether growth of forest trees,
    > > which represent close to 90% of the global biomass
    > > carbon, is still carbon limited at current
    > > concentrations of close to 370 p.p.m.''
    > >
    > > ...most of which are much bigger than us.
    >
    > Unfortunately these very dated statistics are only valid
    > if you're on Bush's Science Advisory Board. See for
    > example Whitman et. al's "Prokaryotes: The unseen
    > majority" (Proc. of the National Academy of Sciences, 95:
    > 6578-83. 1998) for a starter read and follow the trail of
    > references therein.

    It seems that agrees that plants have equal or greater
    biomass than procaryotes. Does it really support the idea
    that complex organisms make up only a minute fraction of the
    global biomass?

    > Notice that this article is already 6 years old and so
    > predates recent major discoveries into the "deep
    > subsurface" biosphere (e.g. Lidy hot springs and similar
    > studies) that we've only scratched the surface of, and
    > that may represent an unseen microbial contingency larger
    > than all combined terrestrial life.

    *Maybe* there's an "unseen microbial contingency larger than
    all combined terrestrial life". Maybe not.

    Even if true, that wouldn't make the biomess of organisms
    larger than us "a minute fraction of the global biomass".
    Trees really are pretty significant carbon sinks - and I
    think they do not deserve dismissal.

    > And of course I'd argue that the counting is already
    > biased -- every cell from every macroscopic organism has
    > anywhere from one to a few dozen mitochondria (and quite a
    > good number have chloroplasts) that were unjustly abducted
    > from the microbial domain and now count towards the
    > eukaryotic total!

    These are systemtically surrounded by their clones - with
    whom they cooperate in order to perpetuate themselves.

    ISTM that they should be counted among the cooperators -
    rather than as among the "free livers".

    True, they once worked for the other side - but allegiances
    can change...
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  8. Tim Tyler

    Tim Tyler Guest

    John Wilkins <[email protected]> wrote or quoted:
    > irr <[email protected]> wrote:
    > > "Tim Tyler" <[email protected]> wrote in message

    > > > The best-established way of measuring complexity is to
    > > > use Kolmogorov complexity.
    > > >
    > > > This:
    > > >
    > > > * Confines discussion to digital phenomena;
    > > > * Is difficult to measure;
    > > > * Has a subjective element - since it depends on a
    > > > choice of descriptive language.
    > > >
    > > > The first is no problem, if we are content to confine
    > > > ourselves to the complexity of genomes.
    > > >
    > > > The second [...]
    > > >
    > > > The third makes the metric less asethetically
    > > > attractive. My approach would probably be to say
    > > > something along the lines of:
    > > >
    > > > "Always use FORTRAN-77 as your language". [...]
    > >
    > > IMO this third problem -- choosing a language with which
    > > to quantify complexity -- is still *the* showstopper
    > > when it comes to biology. [...]
    >
    > Chaitin suggests that you pick a suitably comprehensive
    > and capable language - he uses LISP - and stick with
    > it. [...]

    My suggestion exactly [OK - except for the bit about
    "LISP" ;-)].

    Complexity metrics are dependent on the language used
    to specify them with ... but not all languages are
    created equal.

    You can build a FORTH interpreter in a smaller physical
    space than you can build a Java interpreter. Picking small,
    simple languages with efficient hardware implementations
    makes the choice of language *much* less arbitrary.

    Instead of "length of description", you could use "size of a
    computer made entirely of NAND gates" - and this would get
    you pretty close to the goal of getting a fundamental
    complexity metric.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  9. Tim Tyler

    Tim Tyler Guest

    irr <[email protected]> wrote or quoted:
    > "Tim Tyler" <[email protected]> wrote in message
    > > irr <[email protected]> wrote or quoted:
    > > > "Tim Tyler" <[email protected]> wrote in message
    > > > > IRR <[email protected]> wrote or quoted:

    > > > > * You need to sequence the genome in question before
    > > > > you can measure its complexity;
    > > > >
    > > > > The third makes the metric less asethetically
    > > > > attractive. My approach would probably be to say
    > > > > something along the lines of:
    > > > >
    > > > > "Always use FORTRAN-77 as your language". [...]
    > > >
    > > > IMO this third problem -- choosing a language with
    > > > which to quantify complexity -- is still *the*
    > > > showstopper when it comes to biology.
    > >
    > > I like the answer I gave.
    > >
    > > I almost always give this answer.
    > >
    > > So far - IMO - I have had no serious complaints ;-)
    >
    > Better check your audience ;-).

    Do you have an objection? If so, what is it?

    > > > While we might all agree that the primate brain is an
    > > > incredibly complex organ, it's not at all agreed upon
    > > > what it is we mean by this. For example, a Kolmogorov
    > > > measure fails miserably in classifying the brain as
    > > > complex, after all you're really only talking about
    > > > two dozen or so different recognized cell types
    > > > stamped out in enormous repetition with iterated
    > > > connections between them -- in other words, a digital
    > > > representation of the brain is incredibly
    > > > compressible.
    > >
    > > IMO - this makes no sense at all :-|
    > >
    > > An acceptable digital version of the brain would handle
    > > the same I/O - and produce similar inputs from similar
    > > outputs. This sounds like a job for a huge computer with
    > > an *extremely* lengthy description to me - and of course
    > > a correspondingly enormous Kolmogorov complexity.
    >
    > Certainly a huge computer, but really an extremely lengthy
    > description? Check out the top 500 list (top500.org) --
    > the fastest computers in the world are and will continue
    > to be iterations of the single processor system you're
    > likely reading this reply on right now. While such
    > massively parallel systems -- including the human brain --
    > are increadibly impressive to look at, they are remarkably
    > regular. [...]

    The human brain is not "remarkably regular" - and as such
    requires a lengthy description.

    Some computer systems are very regular - at least when they
    are turned on - but they are not very much like brains.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  10. Chupacabra

    Chupacabra Guest

    Tim Tyler <[email protected]> wrote in message news:<[email protected]>...
    > chupacabra <[email protected]> wrote or quoted:
    >
    > > Presently, as you know, the most successfull and,
    > > probably, smartest people usually have few offsprings,
    > > and, at least in the developed countries, the birth rate
    > > is much higher in undereducated people with lower
    > > intellectual status. So, in modern humans we, in fact,
    > > have a "devolution" where every next generation is, on
    > > average, less "smart" than a previous one. It may be
    > > objected by the Dawkins idea that for the progress of
    > > the human civilization what really matters is not a
    > > selection of the genes but the selection of memes or
    > > ideas. But, as humans will biologically grow more and
    > > more stupid, it may once appear that they simply have
    > > not got sufficient brainpower to command the collected
    > > memes.
    >
    > The reverse has been happening over the last 5 billion
    > years - as fairly convincingly demonstrated by skull
    > fossils.
    >
    > I don't see any good reason to think things have changed
    > in that department.

    In our society success of people is usually measured by
    their status, money, education etc. You just look up some
    relevant demographic statistics tables: more successive,
    educated, rich people definitely have less offspring. This
    means that human evolution has either reversed or is guided
    precently by other factors less known to scientists.

    > Fitness is not about counting offspring - it's about
    > leaving descendants.
    >
    > Having many offspring might be an insurance strategy
    > against hostile local conditions - and should not
    > necessarily be interpreted as a sign of fitness.

    You are right, what matters is the offring that managed to
    survive to the reproductive age. Yes, in underdeveloped
    countries and among less successive social groups child
    mortality is usually higher. Yet, as this is often not too
    high in modern society almost everywhere, anyway less
    successive groups will leave more reproductive offspring and
    progress through generations.
     
  11. R Norman

    R Norman Guest

    On Wed, 21 Apr 2004 03:34:27 +0000 (UTC), Tim Tyler <[email protected]>
    wrote:

    >irr <[email protected]> wrote or quoted:
    >> "Tim Tyler" <[email protected]> wrote in message
    >> > IRR <[email protected]> wrote or quoted:
    >
    >> > > > The bacteria are disadvantaged - since they can't
    >> > > > easily cooperate with one another, and build large
    >> > > > structures - and such cooperation seems to pay off.
    >> > > >
    >> > > > They have been (literally) overshadowed - and
    >> > > > relegated to the nooks and crannies of the world.
    >> > > > These days much of the work gets done by
    >> > > > macroscopic organisms - such as trees.
    >> > > >
    >> > > > Once bacteria ruled the world - but now they in the
    >> > > > middle of a period of decline. Their decline seems
    >> > > > likely to continue - as much of the world's
    >> > > > chemical processing gets taken over by machines -
    >> > > > who will have stolen the bacteria's enzymatic
    >> > > > secrets from their genomes.
    >> > >
    >> > > This anthropocentric misinformation that you've
    >> > > slipped in at multiple points in this thread has no
    >> > > factual basis and no support in real science. There
    >> > > have been at least half a dozen articles in just the
    >> > > past few years in Science and Nature alone that point
    >> > > towards an inverse scale free relationship between
    >> > > organism size and organism density. That is, the very
    >> > > smallest organisms outnumber slightly larger
    >> > > organisms by orders of magnitude, and outnumber even
    >> > > larger organisms by many more orders of magnitude.
    >> >
    >> > Well, yes - becuase they are so tiny. I am outnumbered
    >> > millions-to-one by my own gut bacteria - but that
    >> > doesn't mean that they are more important than I am.
    >>
    >> Certainly not what I meant to imply -- I'm not even sure
    >> if Kolmogorov had a metric by which we could start to
    >> categorize importance :). But I would maintain that the
    >> enormous numbers of microorganisms that are out there
    >> argue they aren't in any sort of period of decline. In
    >> fact in the middle of this 6th mass extinction we've
    >> apparently instigated, I'd say they are in better shape
    >> than anyone.
    >
    >Once they were the only form of life - but now they are
    >excluded from many large and significant niches by
    >competition from plants.
    >
    >The rise of complex organisms seems destined to continue -
    >and if life remains confined on Earth, as complex organisms
    >rise, bacteria practically must fall back - and give up
    >their carbon atoms to make more room.
    >
    >> > > In fact the largest organisms on Earth (ourselves
    >> > > among them) make up only a minute fraction of the
    >> > > global biomass.
    >> >
    >> > A *lot* of the global biomass is in the form of trees -
    >> > e.g.:
    >> >
    >> > ``The ongoing enrichment of the atmosphere with CO2
    >> > raises the question of whether growth of forest trees,
    >> > which represent close to 90% of the global biomass
    >> > carbon, is still carbon limited at current
    >> > concentrations of close to 370 p.p.m.''
    >> >
    >> > ...most of which are much bigger than us.
    >>
    >> Unfortunately these very dated statistics are only valid
    >> if you're on Bush's Science Advisory Board. See for
    >> example Whitman et. al's "Prokaryotes: The unseen
    >> majority" (Proc. of the National Academy of Sciences, 95:
    >> 6578-83. 1998) for a starter read and follow the trail of
    >> references therein.
    >
    >It seems that agrees that plants have equal or greater
    >biomass than procaryotes. Does it really support the idea
    >that complex organisms make up only a minute fraction of
    >the global biomass?
    >
    >> Notice that this article is already 6 years old and so
    >> predates recent major discoveries into the "deep
    >> subsurface" biosphere (e.g. Lidy hot springs and similar
    >> studies) that we've only scratched the surface of, and
    >> that may represent an unseen microbial contingency larger
    >> than all combined terrestrial life.
    >
    >*Maybe* there's an "unseen microbial contingency larger
    >than all combined terrestrial life". Maybe not.
    >
    >Even if true, that wouldn't make the biomess of organisms
    >larger than us "a minute fraction of the global biomass".
    >Trees really are pretty significant carbon sinks - and I
    >think they do not deserve dismissal.
    >
    >> And of course I'd argue that the counting is already
    >> biased -- every cell from every macroscopic organism has
    >> anywhere from one to a few dozen mitochondria (and quite
    >> a good number have chloroplasts) that were unjustly
    >> abducted from the microbial domain and now count towards
    >> the eukaryotic total!
    >
    >These are systemtically surrounded by their clones - with
    >whom they cooperate in order to perpetuate themselves.
    >
    >ISTM that they should be counted among the cooperators -
    >rather than as among the "free livers".
    >
    >True, they once worked for the other side - but allegiances
    >can change...

    Tim, I am afraid the facts indicate that prokaryotes really
    do outweigh everything else. The PNAS paper by Whitman,
    Coleman, and Wiebe which was cited above
    (http://www.pnas.org/cgi/content/full/95/12/6578 does
    indicate that the total carbon fixed in prokaryotes was of
    the same order of magnitude, but somewhat less, than the
    carbon fixed in plants. That is as you say. But carbon and
    total biomass is a poor measure of biological abundance.
    Virtually all the carbon content of plants is inert
    cellulose in the cell wall. If you look at functional
    material, the proteins as measured by the nitrogen content
    or nucleic acids (plus many other active metabolites) as
    measured by phosphorous content, then prokaryotes overwhelm
    the plants. Yes, trees are nice, but the oceanic bigger and
    richer and the soil even more so. And all this doesn't even
    begin to count the enormous mass of archaea that were
    discovered since that paper. You don't mention that the
    title of that paper is "Prokaryotes: the unseen majority".

    You say that prokaryotes are "but now they are excluded from
    many large and significant niches by competition from
    plants". Perhaps you don't realize that the only reason
    plants can grow in these "large and significant niches" is
    that they are supported (both physically and metabolically)
    by the soil which is totally dependent on the microbes
    living there. Yes, the terrestrial world we live in is
    dominated by eukaryotes. But we live in only a small
    fraction of the earth. Several people have repeatedly
    pointed out to you that aquatic and soil/substrate ecology
    is dominated by microbes and that these form by far the
    largest component of the biosphere.

    I'll accept your argument that counting mitochondria and
    plastids as part of the "prokaryotic" side is a bit of a
    stretch. But given that these organelles are a small
    fraction of the biomass in eukaryotes (although they
    outnumber the eukaryotic cells) and that the eukaryotic
    biomass is a small fraction of the total prokaryotic
    biomass, it really doesn't make that much of a difference.
     
  12. Irr

    Irr Guest

    "Tim Tyler" <[email protected]> wrote in message
    news:[email protected]...
    > irr <[email protected]> wrote or quoted:
    > > "Tim Tyler" <[email protected]> wrote in message
    > > > irr <[email protected]> wrote or quoted:
    > > > > "Tim Tyler" <[email protected]> wrote in message
    > > > > > IRR <[email protected]> wrote or
    > > > > > quoted:
    >
    > > > > > * You need to sequence the genome in question
    > > > > > before you can
    measure
    > > > > > its complexity;
    > > > > >
    > > > > > The third makes the metric less asethetically
    > > > > > attractive. My
    approach
    > > > > > would probably be to say something along the lines
    > > > > > of:
    > > > > >
    > > > > > "Always use FORTRAN-77 as your language". [...]
    > > > >
    > > > > IMO this third problem -- choosing a language with
    > > > > which to quantify complexity -- is still *the*
    > > > > showstopper when it comes to biology.
    > > >
    > > > I like the answer I gave.
    > > >
    > > > I almost always give this answer.
    > > >
    > > > So far - IMO - I have had no serious complaints ;-)
    > >
    > > Better check your audience ;-).
    >
    > Do you have an objection? If so, what is it?
    >
    > > > > While we might all agree that the primate brain is
    > > > > an incredibly complex organ, it's not at all agreed
    > > > > upon what it is we mean by
    this.
    > > > > For example, a Kolmogorov measure fails miserably in
    > > > > classifying the brain as complex, after all you're
    > > > > really only talking about two
    dozen
    > > > > or so different recognized cell types stamped out in
    > > > > enormous repetition with iterated connections
    > > > > between them -- in other words,
    a
    > > > > digital representation of the brain is incredibly
    > > > > compressible.
    > > >
    > > > IMO - this makes no sense at all :-|
    > > >
    > > > An acceptable digital version of the brain would
    > > > handle the same I/O -
    and
    > > > produce similar inputs from similar outputs. This
    > > > sounds like a job
    for
    > > > a huge computer with an *extremely* lengthy
    > > > description to me - and of course a correspondingly
    > > > enormous Kolmogorov complexity.
    > >
    > > Certainly a huge computer, but really an extremely
    > > lengthy description? Check out the top 500 list
    > > (top500.org) -- the fastest computers in the world are
    > > and will continue to be iterations of the single
    > > processor
    system
    > > you're likely reading this reply on right now. While
    > > such massively parallel systems -- including the human
    > > brain -- are increadibly
    impressive
    > > to look at, they are remarkably regular. [...]
    >
    > The human brain is not "remarkably regular" - and as such
    > requires a lengthy description.
    >
    > Some computer systems are very regular - at least
    > when they are turned on - but they are not very much
    > like brains.
    > --
    > __________
    > |im |yler http://timtyler.org/ [email protected] Remove
    > lock to reply.
    >

    >From Erdi's "The Complexity of the Brain: Structural,
    >Functional and Dynamic
    Modules": "Experimental facts from anatomy, physiology,
    embriology, and psychophysics give evidence of highly
    ordered structure composed of 'building blocks' of
    repetitive structures in the vertebrate nervous system. The
    building block according to the modular architectonic
    principle is rather common in the nervous system. Modular
    architecture is a basic feature of the spinal cord, the
    brain stem reticular formation, the hypothalamus, the
    subcortical relay nuclei, the cerebellar and especially
    cerebral cortex." and on and on....

    Going back to my original message, the neurohistology and
    neuroanatomy (that is, the number of differentiated cell
    types and their organization) is incredibly well laid out
    with astonishing regularity and organization. This is not
    remarkable. What is remarkable is that such a regular
    structure can exhibit amazingly complex features (look at,
    e.g. any of Christof Koch or Francis Crick's recent work,
    among a wide field of other 'computational
    neuroscientists').

    These complex features that arise from a regular structure
    are very real and active points of interest these days. This
    is popularly referred to as emergence, and one major
    question is if this emergence corresponds to the appearance
    of language, consciousness, etc. Now going back to my
    'original original' message, none of these complex features
    are apparent when looking at the characteristic
    neuroanatomical structure, and so here again is another
    example where a swath of different complexity metrics will
    fail to meet our standards.

    On the other hand, we could look instead at other features,
    such as the interconnectiveness of various parts of the
    nervous system (scale free? I'm not sure) and perhaps get a
    better measure of complexity for a given metric. I wouldn't
    argue against this, and Koch and many others argue
    convincingly for this. But the bottom line is, as I've been
    trying to convince you of, the solution depends entirely on
    how you define your space and choose to measure the
    complexity of that space.

    Though it might apply great in theory or in determining
    regularity of strings of numbers, your argument of "though
    the definitions may differ in detail... it tends not to
    matter which one you use" just flat out fails when it comes
    to applications in biology.
     
  13. Tim Tyler

    Tim Tyler Guest

    IRR <[email protected]> wrote or quoted:
    > "Tim Tyler" <[email protected]> wrote in message
    > > irr <[email protected]> wrote or quoted:
    > > > "Tim Tyler" <[email protected]> wrote in message
    > > > > irr <[email protected]> wrote or quoted:
    > > > > > "Tim Tyler" <[email protected]> wrote in message
    > > > > > > IRR <[email protected]> wrote or
    > > > > > > quoted:

    > > > Certainly a huge computer, but really an extremely
    > > > lengthy description? Check out the top 500 list
    > > > (top500.org) -- the fastest computers in the world are
    > > > and will continue to be iterations of the single
    > > > processor system you're likely reading this reply on
    > > > right now. While such massively parallel systems --
    > > > including the human brain -- are increadibly
    > > > impressive to look at, they are remarkably regular.
    > > > [...]
    > >
    > > The human brain is not "remarkably regular" - and as
    > > such requires a lengthy description.
    > >
    > > Some computer systems are very regular - at least when
    > > they are turned on - but they are not very much like
    > > brains.
    >
    > >From Erdi's "The Complexity of the Brain: Structural,
    > >Functional and Dynamic
    > Modules": "Experimental facts from anatomy, physiology,
    > embriology, and psychophysics give evidence of highly
    > ordered structure composed of 'building blocks' of
    > repetitive structures in the vertebrate nervous system.
    > The building block according to the modular architectonic
    > principle is rather common in the nervous system. Modular
    > architecture is a basic feature of the spinal cord, the
    > brain stem reticular formation, the hypothalamus, the
    > subcortical relay nuclei, the cerebellar and especially
    > cerebral cortex." and on and on....

    Repetition does not signifiy simplicity. The Encyclopaedia
    Brittanica has many copies of the letter "e" in it - but has
    no short description nontheless.

    You need repetition *without* much variation for there to
    exist a short description.

    The adult brain is *very* complex. The argument that there's
    a short description of it - and so its Kolmogorov complexity
    is very low - and so such metrics give a counter-intuitive
    low value for the complexity of the brain falls down -
    because no such short description exists.

    What there /might/ be a short description of is the
    infant brain.

    Instructions to build this are contained in the genetic
    program - which fits on a CD or so.

    *If* you are arguing about the brain of a child, then
    perhaps we can agree that its Kolmogorov complexity doesn't
    exceed a few hundred megabytes or so - at least early on.

    However, after birth the complexity of the brain explodes -
    as it accumulates information from its environment - and
    encodes this information in irregular patterns of neural
    weights - rapidly producing stupendous levels of complexity.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  14. Tim Tyler

    Tim Tyler Guest

    chupacabra <[email protected]> wrote or quoted:
    > Tim Tyler <[email protected]> wrote in message
    > news:<[email protected]>...
    > > chupacabra <[email protected]> wrote or quoted:

    > > > Presently, as you know, the most successfull and,
    > > > probably, smartest people usually have few offsprings,
    > > > and, at least in the developed countries, the birth
    > > > rate is much higher in undereducated people with lower
    > > > intellectual status. So, in modern humans we, in fact,
    > > > have a "devolution" where every next generation is, on
    > > > average, less "smart" than a previous one. It may be
    > > > objected by the Dawkins idea that for the progress of
    > > > the human civilization what really matters is not a
    > > > selection of the genes but the selection of memes or
    > > > ideas. But, as humans will biologically grow more and
    > > > more stupid, it may once appear that they simply have
    > > > not got sufficient brainpower to command the collected
    > > > memes.
    > >
    > > The reverse has been happening over the last 5 billion
    > > years - as fairly convincingly demonstrated by skull
    > > fossils.
    > >
    > > I don't see any good reason to think things have changed
    > > in that department.
    >
    > In our society success of people is usually measured by
    > their status, money, education etc.

    Well - that's not nature's metric. Nature rewards
    reproductive success - not financial independence.

    > You just look up some relevant demographic statistics
    > tables: more successive, educated, rich people definitely
    > have less offspring. This means that human evolution has
    > either reversed or is guided precently by other factors
    > less known to scientists.

    That goes to prove material wealth is not the only factor -
    not that evolution has reversed course.

    > > Fitness is not about counting offspring - it's about
    > > leaving descendants.
    > >
    > > Having many offspring might be an insurance strategy
    > > against hostile local conditions - and should not
    > > necessarily be interpreted as a sign of fitness.
    >
    > You are right, what matters is the offring that managed to
    > survive to the reproductive age. Yes, in underdeveloped
    > countries and among less successive social groups child
    > mortality is usually higher. Yet, as this is often not too
    > high in modern society almost everywhere, anyway less
    > successive groups will leave more reproductive offspring
    > and progress through generations.

    You meant to say "less successful"?

    If they leave more offspring, they are probably not "less
    successful".

    Regarding intelligence - maybe the most intellectual are
    reproductively handicapped (I agree there is evidence to
    support this).

    ...but the least intellectual are *also* reproductively
    handicapped.

    To argue that mankind is getting stupider is to argue
    that the first effect is more significant than the second
    one - but I don't know of any evidence to suggest that
    that is true.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  15. Jim Menegay

    Jim Menegay Guest

    Tim Tyler <[email protected]> wrote in message news:<[email protected]>...
    > Guy Hoelzer <[email protected]> wrote or quoted:
    > > in article [email protected], Tim Tyler
    > > at [email protected]
    >
    > > > Complexity - as everyone agrees - is a scalar
    > > > property, not a binary one.
    > >
    > > I don't think that "everyone" agrees with this point of
    > > view. Proposed and often used "measures" of complexity
    > > are indeed scalars, but that issue is about estimation
    > > rather than physical reality. I would describe an
    > > alternative, binary view of complexity as the one
    > > promoted by Prigogine. I think that he would have agreed
    > > with something like the following: complexity emerges
    > > along with function and structure from the merely
    > > complicated. Emergence is a process, so there would
    > > certainly be a period of ambiguity as to whether
    > > complexity has been achieved, but the concept would
    > > still be essentially binary and not fairly represented
    > > by a scalar parameter.
    >
    > I don't know what you mean.

    Tim,

    I'm surprised at you. I just did a Google search of the WEB
    for "complex", "more complex", "less complex", etc. It
    appears that most people use "complex" without modifiers. It
    is binary. The people have spoken. Get with it. ;-)

    Guy may have a tough sell, though, convincing the
    Kolmogoroff fans on this thread, especially since most of
    them probably learned of the existence of Kolmogoroff
    through the writings of the Brussels school. One can
    speculate that Guy prefers the term "complex" for the state
    that the Belgians refer to as "chaotic".

    He will have an even tougher sell convincing Edser that
    "dependent level of fitness" and "independent level of
    fitness" are NOT binary - since Guy is doing this on a
    thread where Edser has just complained that no one besides
    himself uses these terms. It will be fun to watch these two
    threads play out.

    Still, one must admire the man's independent thought. Or,
    should I say complex? Or perhaps chaotic?

    Jim
     
  16. Guy Hoelzer

    Guy Hoelzer Guest

    in article [email protected], Tim Tyler at [email protected]
    wrote on 4/20/04 8:34 PM:

    > Guy Hoelzer <[email protected]> wrote or quoted:
    >> in article [email protected], Tim Tyler
    >> at [email protected]
    >
    >>> Complexity - as everyone agrees - is a scalar property,
    >>> not a binary one.
    >>
    >> I don't think that "everyone" agrees with this point of
    >> view. Proposed and often used "measures" of complexity
    >> are indeed scalars, but that issue is about estimation
    >> rather than physical reality. I would describe an
    >> alternative, binary view of complexity as the one
    >> promoted by Prigogine. I think that he would have agreed
    >> with something like the following: complexity emerges
    >> along with function and structure from the merely
    >> complicated. Emergence is a process, so there would
    >> certainly be a period of ambiguity as to whether
    >> complexity has been achieved, but the concept would still
    >> be essentially binary and not fairly represented by a
    >> scalar parameter.
    >
    > I don't know what you mean.
    >
    > For instance, what's this distinction between complexity
    > and complicated all about:
    >
    > ``complexity emerges along with function and structure
    > from the merely complicated''

    The term "complexity" is appropriately used to describe a
    complex. In this context I would define a complex as a
    coherently structured network parts that primarily interact
    with each other and are less well connected to the external
    environment. Webster's simply defines it as a "unified
    grouping." In effect, when complex and systemic dynamics
    emerge, things become LESS complicated. Complexity breeds
    simplicity. I think that some things appear to be far more
    complicated than they really are, because we haven't yet
    recognized the wholeness of the system or the wholenesses of
    subsystems. The existence of macroscopic wholes
    significantly reduces apparent complicatedness. There would
    be no value, for example, in drilling down
    reductionistically to the level of quarks to gain a better
    understanding of animal behavior.

    > *Maybe* there are some folk somewhere who think complexity
    > is a binary quantity.
    >
    > I'd be inclined to show them Kolmogorov complexity - and
    > ask them the equivalent of "how many hairs make a beard" -
    > i.e. how they would defend their preferred "complexity
    > threshold".

    I would distinguish between a measure like this and its
    underlying concept.

    Guy
     
  17. Tim Tyler <[email protected]> wrote in
    news:[email protected]:

    > irr <[email protected]> wrote or quoted:

    >> While we might all agree that the primate brain is an
    >> incredibly complex organ, it's not at all agreed upon
    >> what it is we mean by this. For example, a Kolmogorov
    >> measure fails miserably in classifying the brain as
    >> complex, after all you're really only talking about two
    >> dozen or so different recognized cell types stamped out
    >> in enormous repetition with iterated connections between
    >> them -- in other words, a digital representation of the
    >> brain is incredibly compressible.

    > IMO - this makes no sense at all :-|

    > An acceptable digital version of the brain would handle
    > the same I/O - and produce similar inputs from similar
    > outputs. This sounds like a job for a huge computer with
    > an *extremely* lengthy description to me
    > - and of course a correspondingly enormous Kolmogorov
    > complexity.

    I agree with Tim that a digital computer that mimics the
    brain would be huge by today's standards. I however also
    agree that this capability is achieved using a relatively
    small amount of genetic code. Part of the secret is that
    brain development relies on input from the environment - in
    other words much of the data needed to code for a brain
    resides outside of the genes. Trying to capture this
    complexity entirely in a computer program would in fact
    require specifying a lot of data that the actual developing
    brain doesn't include as different cell types but gathers as
    input to the neural net.

    Yours,

    Bill Morse
     
  18. Tim Tyler

    Tim Tyler Guest

    Jim Menegay <[email protected]> wrote or quoted:
    > Tim Tyler <[email protected]> wrote in message
    > news:<[email protected]>...
    > > Guy Hoelzer <[email protected]> wrote or quoted:
    > > > in article [email protected], Tim
    > > > Tyler at [email protected]

    > > > > Complexity - as everyone agrees - is a scalar
    > > > > property, not a binary one.
    > > >
    > > > I don't think that "everyone" agrees with this point
    > > > of view. Proposed and often used "measures" of
    > > > complexity are indeed scalars, but that issue is about
    > > > estimation rather than physical reality. I would
    > > > describe an alternative, binary view of complexity as
    > > > the one promoted by Prigogine. I think that he would
    > > > have agreed with something like the following:
    > > > complexity emerges along with function and structure
    > > > from the merely complicated. Emergence is a process,
    > > > so there would certainly be a period of ambiguity as
    > > > to whether complexity has been achieved, but the
    > > > concept would still be essentially binary and not
    > > > fairly represented by a scalar parameter.
    > >
    > > I don't know what you mean.
    >
    > I'm surprised at you. I just did a Google search of the
    > WEB for "complex", "more complex", "less complex", etc. It
    > appears that most people use "complex" without modifiers.
    > It is binary. The people have spoken. Get with it. ;-)

    Touche.
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
  19. Chupacabra

    Chupacabra Guest

    Tim Tyler <[email protected]> wrote in message news:<c69ku1$8kp$1
    >
    > Regarding intelligence - maybe the most intellectual are
    > reproductively handicapped (I agree there is evidence to
    > support this).
    >
    > ...but the least intellectual are *also* reproductively
    > handicapped.
    >
    > To argue that mankind is getting stupider is to argue
    > that the first effect is more significant than the second
    > one - but I don't know of any evidence to suggest that
    > that is true.

    Do you mean that humanity is progressing towards ordinarity
    and mediocrity?

    By the way, how would you explain significant changes in
    human phenotype during the last century, I mean people have
    become much taller, weigh more, are less susceptible to some
    diseases etc. These changes were apparently too fast to be
    explained by the natural selection.
     
  20. Tim Tyler

    Tim Tyler Guest

    William Morse <[email protected]> wrote or quoted:
    > Tim Tyler <[email protected]> wrote in

    > > An acceptable digital version of the brain would handle
    > > the same I/O - and produce similar inputs from similar
    > > outputs. This sounds like a job for a huge computer with
    > > an *extremely* lengthy description to me
    > > - and of course a correspondingly enormous Kolmogorov
    > > complexity.
    >
    > I agree with Tim that a digital computer that mimics the
    > brain would be huge by today's standards. I however also
    > agree that this capability is achieved using a relatively
    > small amount of genetic code. Part of the secret is that
    > brain development relies on input from the environment -
    > in other words much of the data needed to code for a brain
    > resides outside of the genes. Trying to capture this
    > complexity entirely in a computer program would in fact
    > require specifying a lot of data that the actual
    > developing brain doesn't include as different cell types
    > but gathers as input to the neural net.

    See:

    ``Epigenesis:

    The ontogenetic program is limited in the amount of
    information that can be stored, thereby rendering the
    complete specification of the organism impossible. A well-
    known example is that of the human brain with some 10^10
    neurons and 10^14 connections, far too large a number to
    be completely specified in the four-character genome of
    length approximately 3 x 10^9. Therefore, upon reaching a
    certain level of complexity, there must emerge a different
    process that permits the individual to integrate the vast
    quantity of interactions with the outside world. This
    process is known as epigenesis, and primarily includes the
    nervous system, the immune system, and the endocrine
    system. These systems are characterized by the possession
    of a basic structure that is entirely defined by the
    genome (the innate part), which is then subjected to
    modification through lifetime interactions of the
    individual with the environment (the acquired part). The
    epigenetic processes can be loosely grouped under the
    heading of learning systems.''

    - http://www.cs.bgu.ac.il/~sipper/poe.html
    --
    __________
    |im |yler http://timtyler.org/ [email protected] Remove
    lock to reply.
     
Loading...