On Thu, 13 Aug 1998 21:46:06 +0100, Vernon Jenkins wrote:
VJ>The final paragraph of my posting of Tuesday last, 'The Music Lesson'
>suggested that evolutionists might have a problem explaining the
>significance of music in people's lives. For though tastes differ, the
>inherent principles are identical.
>
>However did the twelfth root of two (or its early approximations) become
>part of man's psyche? (I speak of the ratio of frequencies represented
>by the semitone interval - the indivisible step in music ranging from
>Bach to boogie, and beyond). Is it possible that an anthropoid
>possessing such a faculty had some survival advantage over a brother who
>hadn't? If so, what might that advantage have been?
>
>I think the matter deserves an 'evolutionary' explanation - otherwise
>Darwinists could be justly accused of not thinking through the
>implications of their faith.
Thanks for this. It is related to the peculiar fact that according to
Darwinism a series of historical accidents in the shape of random mutations
in species of apes, which were selected for survival in Africa 5-10 mya,
have produced a species (namely Homo sapiens) that has a mathematical
facility to understand the underlying mathematical laws upon which the
universe is constructed:
Denton notes that there is a "unique correspondence" between "the logic of
our mind and the logic of the cosmos" that enables us "to comprehend the
world" and that "it is hard to avoid the impression that a miracle is at work
here":
"Our success as a biological species has depended on many factors: on our
being smart, on our being terrestrial, on our possessing a body of a
dimension and design appropriate to handle fire and explore the
environment, on the fitness of the earth's atmosphere to support fire and
technological advance. However, there is another intriguing aspect to our
success-the mutual fitness of the human mind and particularly its propensity
for and love of mathematics and abstract thought and the deep structure of
reality, which can be so beautifully represented in mathematical forms. In
other words, the logic of our mind and the logic of the cosmos would
appear to correspond in a profound way. And it is only because of this
unique correspondence that it is possible for us to comprehend the world.
If the laws of nature could not be formulated in simple mathematica terms,
it is unlikely that science would have advanced so quickly. It might in fact,
never have advanced at all. The physicist Eugene Wigner, who was much
struck by the correspondence between mathematics and the physical world,
spoke for many mathematicians and scientists when he remarked:
`It is hard to avoid the impression that a miracle is at work here.... The
miracle of the appropriateness of the language of mathematics for the
formulation of the laws of physics is a wonderful gift which we neither
understand nor deserve.' (Wigner E. P:, "The Unreasonable Effectiveness
of Mathematics in the Natural Sciences," Communications on Pure and
Applied Mathematics, Vol. 13, 1960, pp1-14)
(Denton M.J., "Nature's Destiny: How the Laws of Biology Reveal
Purpose in the Universe," The Free Press: New York NY, 1998, p259)
Paul Davies similarly says that "it is both incredibly fortunate and incredibly
mysterious that we are able to fathom the workings of nature by use of the
scientific method", especially since "human intellectual powers are
presumably determined by biological evolution, and have absolutely no
connection with doing science":
"The success of the scientific enterprise can often blind us to the
astonishing fact that science works. Although most people take it for
granted, it is both incredibly fortunate and incredibly mysterious that we
are able to fathom the workings of nature by use of the scientific method.
As I have already explained, the essence of science is to uncover patterns
and regularities in nature by finding algorithmic compressions of
observations. But the raw data of observation rarely exhibit explicit
regularities. Instead we find that nature's order is hidden from us, it is
written in code. To make progress in science we need to crack the cosmic
code, to dig beneath the raw data and uncover the hidden order. I often
liken fundamental science to doing a crossword puzzle. Experiment and
observation provide us with clues, but the clues are cryptic, and require
some considerable ingenuity to solve. With each new solution, we glimpse
a bit more of the overall pattern of nature. As with a crossword, so with
the physical universe, we find that the solutions to independent clues link
together in a consistent and supportive way to form a coherent unity, so
that, the more clues we solve, the easier we find it to fill in the missing
features.
What is remarkable is that human beings are actually able to carry out this
code-breaking operation, that the human mind has the necessary intellectual
equipment for us to "unlock the secrets of nature' and make a passable
attempt at completing nature's "cryptic cross word." It would be easy to
imagine a world in which the regularities or nature were transparent and
obvious to all at a glance. We can also imagine another world in which
either there were no regularities, or the regularities were so well hidden, so
subtle, that the cosmic code would require vastly more brainpower than
humans possess. But instead we find a situation in which the difficulty of
the cosmic code seems almost to be attuned to human capabilities. To be
sure, we have a pretty tough struggle decoding nature, but so far we have
had a good deal of success. The challenge is just hard enough to attract
some of the best brains available, but not so hard as to defeat their
combined efforts and deflect them onto easier tasks.
The mystery in all this is that human intellectual powers are presumably
determined by biological evolution, and have absolutely no connection with
doing science. Our brains have evolved in response to environmental
pressures, such as the ability to hunt, avoid predators, dodge falling
objects, etc. What has this got to do with discovering the laws of
electromagnetism or the structure of the atom? John Barrow is also
mystified: "Why should our cognitive processes have tuned themselves to
such an extravagant quest as the understanding of the entire Universe?" he
asks "Why should it be us? None of the sophisticated ideas involved appear
to offer any selective advantage to be exploited during the pre-conscious
period of our evolution.... How fortuitous that our minds (or at least the
minds of some) should be poised to fathom the depths of Nature's secrets."
(Barrow J., "Theories of Everything: The Quest for Ultimate Explanation,"
Oxford University Press: Oxford, 1991, p172)
(Davies P.C.W., "The Mind of God: Science and the Search for
Ultimate Meaning," [1992] Penguin: London, 1993, pp148-159)
Davies adds that "it is very hard to see how abstract mathematics" and
"musical ability" "has any survival value":
"It has also been argued that the structure of our brains has evolved to
reflect the properties of the physical world, including its mathematical
content, so that it is no surprise that we discover mathematics in nature. As
already remarked, it is certainly a surprise, and a deep mystery, that the
human brain has evolved its extraordinary mathematical ability. It is very
hard to see how abstract mathematics has any survival value. Similar
comments apply to musical ability." (Davies P.C.W., 1993, p152).
Davies accepts that "Darwinian evolution has equipped us to know the
world by direct perception" but this does not explain our "dual capability
for knowing the world" through "mathematics...abstract reasoning, and
other rational procedures" which "is of no apparent biological significance
at all":
"It seems to me that Darwinian evolution has equipped us to know the
world by direct perception. There are clear evolutionary advantages in this,
but there is no obvious connection at all between this sort of sensorial
knowledge and intellectual knowledge. Students often struggle with certain
branches of physics, like quantum mechanics and relativity, because they
try to understand these topics by mental visualization. They attempt to
"see" curved space or the activity of an atomic electron in the mind's eye,
and fail completely. This is not due to inexperience-I don't believe any
human being can really form an accurate visual image of these things. Nor
is this a surprise quantum and relativity physics are not especially relevant
to daily life, and there is no selective advantage in our having brains able to
incorporate quantum and relativistic systems in our mental model of the
world. In spite of this, however, physicists are able to reach an
understanding of the worlds of quantum physics and relativity by the use of
mathematics, selected experimentation, abstract reasoning, and other
rational procedures. The mystery is, why do we have this dual capability
for knowing the world? There is no reason to believe that the second
method springs from a refinement of the first. They are entirely
independent ways of coming to know about things. The first serves an
obvious biological need, the latter is of no apparent biological significance
at all." (Davies P.C.W., ", 1993, p153)
Davies notes that "the mystery becomes even deeper when we take account
of the existence of mathematical and musical geniuses":
"The mystery becomes even deeper when we take account of the existence
of mathematical and musical geniuses, whose prowess in these fields is
orders of magnitude better than that of the rest of the population. The
astonishing insight of mathematicians such as Gauss and Riemann is
attested not only by their remarkable mathematical feats (Gauss was a child
prodigy and also had a photographic memory), but also by their ability to
write down theorems without proof, leaving later generations of
mathematicians to struggle over the demonstrations. How these
mathematicians were able to come up with their results "ready-made,"
when the proofs often turned out to involve volumes of complex
mathematical reasoning, is a major puzzle...We are, of course, used to the
fact that all human abilities, physical and mental, show wide variations.
Some people can jump six feet off the ground, whereas most of us can
manage barely three. But imagine someone coming along and jumping sixty
feet, or six hundred feet! Yet the intellectual leap represented by
mathematical genius is far in excess of these physical differences..."(Davies
P.C.W., 1993, pp153-154)
Davies points out that "surviving...doesn't require knowledge of the laws of
nature" and he "sees no evidence for the claim that these two apparently
very different sets of properties are actually the same, or that one follows
as a (possibly accidental) byproduct of the other":
"After all, surviving "in the jungle" doesn't require knowledge of the laws
of nature, only of their manifestations. We have seen how the laws
themselves are in code, and not connected in a simple way at all to the
actual physical phenomena subject to those laws. Survival depends on an
appreciation of how the world is, not of any hidden underlying order.
Certainly it cannot depend on the hidden order within atomic nuclei, or in
black holes, or in subatomic particles that are produced on Earth only
inside particle-accelerator machines. It might be supposed that when we
duck to avoid a missile, or judge how fast to run to jump a stream, we are
making use of a knowledge of the laws of mechanics, but this is quite
wrong. What we use are previous experiences with similar situations. Our
brains respond automatically when presented with such challenges; they
don't integrate the Newtonian equations of motion in the way the physicist
does when analyzing these situations scientifically. To make judgments
about motion in three-dimensional space, the brain needs certain special
properties. To do mathematics (such as the calculus needed to describe this
motion) also requires special properties. I see no evidence for the claim
that these two apparently very different sets of properties are actually the
same, or that one follows as a (possibly accidental) byproduct of the
other." (Davies P.C.W., 1993, pp155-156)
To put it in a nutshell, Davies observes that "mathematics...is...unique to
humans" and yet "there is, in fact, no direct connection between the laws of
physics and the structure of the [human] brain" the "wiring pattern" of
which "cannot be explained by the laws of physics alone" but "depends on
many other factors, including a host of chance events that must have
occurred during evolutionary history":
"Awareness of the regularities of nature, such as those manifested in
mechanics, has good survival value, and is wired into animal and human
brains at a very primitive level. By contrast, mathematics as such is a higher
mental function, apparently unique to humans (as far as terrestrial life is
concerned). It is a product of the most complex system known in nature.
And yet the mathematics it produces finds its most spectacularly successful
applications in the most basic processes in nature, processes that occur at
the subatomic level. Why should the most complex system be linked in this
way to the most primitive processes of nature? It might be argued that, as
the brain is a product of physical processes it should reflect the nature of
those processes, including their mathematical character. But there is, in
fact, no direct connection between the laws of physics and the structure of
the brain. The thing which distinguishes the brain from a kilogram of
ordinary matter is its complex organized form, in particular the elaborate
interconnections between neurons. This wiring pattern cannot be explained
by the laws of physics alone. It depends on many other factors, including a
host of chance events that must have occurred during evolutionary history.
Whatever laws may have helped shape the structure of the human brain
(such as Mendels laws of genetics), they bear no simple relationship to the
laws of physics." (Davies P.C.W., "1993, p156)
Note here that while Darwinian natural selection cannot explain the
capabilities of the human brain to know the underlying mathematical laws
of physics, an Intelligent Designer *could* arrange these so-called "chance
events" to progressively build the "wiring pattern" of the human brain in
such a way that it could in the future be called upon to comprehend and
master the laws of physics!
Steve
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Stephen E (Steve) Jones ,--_|\ sejones@ibm.net
3 Hawker Avenue / Oz \ senojes@hotmail.com
Warwick 6024 ->*_,--\_/ Phone +61 8 9448 7439
Perth, West Australia v "Test everything." (1Thess 5:21)
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