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Re: Landau letter, Re: Mathematica as a New Approach...
*To*: mathgroup at smc.vnet.net
*Subject*: [mg128003] Re: Landau letter, Re: Mathematica as a New Approach...
*From*: János Löbb <janos at lobb.com>
*Date*: Sat, 8 Sep 2012 03:08:48 -0400 (EDT)
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*References*: <k1n71e$e5m$1@smc.vnet.net> <20120831075725.55C076873@smc.vnet.net> <20120907085529.D1FB867FE@smc.vnet.net>
The bit as the measuring unit of information is a human creation, just
as the meter is for distance. It is a human abstraction, to describe a
physical attribute. It is a "secondary" abstraction, made by humans,
who themselves are built from "primary" abstractions called elementary
particles. Does not matter how hard do I look an elementary particle,
or even a mountainy, I do not see just from the "outside" the
intelligence that is capable to make this secondary abstraction. Now a
machine is a "tertiary" abstraction, and being so it is much more
convoluted and complicated and slower than a primary one, for example a
simple molecule. A computer, a machine does not have a connection to
Information Ocean, like a human has, because it is not built from
humans, but by humans. So a machine is stuck at the secondary or
tertiary abstraction level and till humans are not building that special
parts - like a human brain -, for the machine to communicate to
Information Ocean, the machine will never able to do more, just to build
things starting with "n", - like numeric :-) Telling otherwise the
information in Information Ocean is not really that bit that we humans
use to measure information content, just as distance is not really the
same as the meter to measure it. Probably we would run into similar
difficulties with human perceivable information as we go down the scale
as we had with distance as we approached the atomic scale.
On Sep 7, 2012, at 4:55 AM, John Doty wrote:
> On Thursday, September 6, 2012 2:19:40 AM UTC-6, Vince Virgilio wrote:
>> To borrow a pithy from Wheeler: It-from-Bit?
>
> That's a great example of how psychology drives the preferences of
scientists and mathematicians. Dualism is a powerful psychological drive
in human beings, but it gets little support from reality. Is it true
that Pluto is a planet? That's a big deal to some people, but it matters
little. "Planet" is the name of a simple (and rather shifty) story we
tell about celestial objects. "Pluto" is the name of another story, but
that's much more complex. The concrete reality behind the story is
easier to find, and we can relate it to other stories (e.g. "methane").
Dualism is actually a barrier to real understanding here.
>
> The powerful instinct to dualism misleads in other ways. Many people
have a superstitious faith in its elaboration, (two-valued) logic. But
while logic is useful in elucidating the relationships between
hypotheses, it cannot determine truth. Logic steps from falsehood to
falsehood as easily as it steps from truth to truth.
>
> Then note that Boole believed his algebra (a further elaboration of
dualism) to represent the "Laws of Thought". But we've constructed
machines that can evaluate Boolean expressions trillions of times faster
and more accurately than we humans can. Actual thought based on Boolean
mechanism remains elusive. I thus think Boole's belief has been
comprehensibly falsified.
>
> One might note that bits are decent raw material for some kinds of
mathematical modeling. Still, they have unfortunate limitations. A newly
synthesized simple molecule can find its "ground" configuration in
picoseconds, while a highly complex binary supercomputer takes hours or
days to compute the same thing. It thus seems unreasonable to think that
bits are fundamental to anything physical.
>
> The gnurdiest fortune cookie fortune I ever saw read "Digital devices
are composed of analog components." A fine piece of wisdom.
>
> Wheeler was an example of the kind of theoretical "physicist" who
forgets that physics is fundamentally, well, physical. The mathematical
stories we tell are not fundamental: in the end, they are only stories.
The physical phenomena themselves are fundamental.
>
> But clearly, dualism is an expression of a very important cognitive
mechanism for the practice of mathematics. So, while we might wish to
dismiss it as a bad metal habit, that would surely be a mistake. Indeed,
this message is full of dualism: while dualism isn't very true to how
the world works, it seems essential to human communication. Can we, in
mathematics and science education, learn to better exploit this
mechanism while also teaching awareness of its profound difficulties?
>
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