> Kenneth Boyd,
>
> > Mathematics is Very Mystical.
>
> Mystical is usually used in conjuntion with ideas like "Soul" or
"God". Perhaps a better word
> would be "Mysterious"? Or were you refering exclusively to Cohesive Math?
I have no experience with Cohesive Math. I still have to make it over to
your Web page on it. [I have the website reference, still].
I'm running on several analogies [having had to work a general survey of
800+ math]:
1) The first fly-by-wire aircraft [Harrier jump jet?] had a design
team composed only of mathematicians. NO programmers, NO engineers. In
other words, mathematicians can learn the skills required to program or
engineer fairly easily, but the reverse does NOT hold: programmers are
usually not good at creating math, nor are engineers.
Please remember than in the typical program lifecycle, 75% of coding
time is DEBUGGING. This is because the typical programmer is a
mathematical incompetent. I generally spend about 20% to
25% of coding time debugging, often removing bugs that have not been
explicitly demonstrated by 'testing'. If one can prove that the source
is bug-free, the only source of bugs is the compiler. For those
oddities, looking at the assembly listing does wonders. Also, the risk
of introducing new bugs when fixing old ones is greatly reduced--typical
is 50%, while I can't measure it effectively--less than 5%. The
bug-introducing risks of optimization are also greatly reduced--I only
have to consider it seriously when totally rewriting a data type in C++,
and it usually doesn't happen. Also, provably debugged code requires
maintenance ONLY for optimization, and compiler upgrades. Most programmers
CANNOT write provably debugged code on large scales. This is why some
companies do not hire computer scientists to do their programming;
instead, they hire mathematicians and train them. The vastly improved
stability of the code is critical to these companies.
One way to look at proofs is that they are programs that CANNOT be
executed, and that a correct proof is analogous to a program that always
works, given correct input.
2) Mathematical analyses can be totally contrary to conventional
reasoning. For instance, [this actually happened to some California
farmers, back in the 1950's], it is possible to apply insecticide to a
field/grove [in this case, grove], which kills the pest devasting the
crops--and have the pest population INCREASE! ["A mystery to science..."]
[The pesticide also killed the unknown predator of the pest, with equal
efficiency.]
This is even before considering the spread of genes conferring
resistance to the insecticide, and has NOTHING to do with natural
selection.
Another example of this is the classical relativistic theory of
the electron. According to a 1950's book which one of my professors has
access to, the electron has to start accelerating in response to an
electromagnetic wave BEFORE the arrival of the electromagnetic wave!
[This is necessary to maintain sufficient smoothness in the path of the
electron.] This is truly bizarre, and it took me ten minutes to explain
this to a physics graduate student.
3) At least one author of the New Testament, when trying to
distinguish between 'spiritual' and 'worldly' reasoning, ended up using
the word for 'mathematical reasoning' to describe 'spiritual reasoning'.
One of my books on spiritual warfare [49 out of 50 right-wing radical
Christians would freak out--it's further out that way than THEY are]
recommends studying math for those that have just been delivered from
demonic oppression, since this is very close to spiritual thinking.
Something like a mind-building exercise.
4) Sufficiently accurate mathematical models can effectively coerce
physical events, in the hard sciences and some instances in the soft
sciences. This is analogous to the fictional spells in many
medievalistic-fantasy RPGs [and some others].
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/ Towards the conversion of data into information....
/
/ Kenneth Boyd
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