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[Phys-L] Re: computation +- math skills



I have no idea what is causing the equal signs at the end of lines. =
=20

Please tell me if you know.

I'll repeat the broken links:

http://web.wt.net/~twayburn/computers.html=20

The tinyurl is http://tinyurl.com/dqvj8 . =20

and my home page is

http://web.wt.net/~twayburn/=20

By the way, we should all be aware of the http://tinyurl.com/ website=
. Just copy a long URL=20
like http://web.wt.net/~twayburn/Energy%20in%20a%20Natural%20Economy.=
html into the little window, click the button to get http://tinyurl.=
com/7sodz , copy it, and paste into your post. Probably, the googl=
e.com link below is wrong and could have been replaced by a tinyurl t=
hat would have worked. (I wonder if these long lines be broken by eq=
ual signs.)

Tom Wayburn, Houston, Texas


----- Original Message -----=20
=46rom: "Tom Wayburn" <twayburn@wt.net>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Friday, October 21, 2005 3:12 PM
Subject: Re: computation +- math skills


a) Mathematics has benefitted greatly from computation. The most
obvious examples are things like the four-color proof, which could
not have been done without a computer
=20
We always knew the Four Color Theorem was true (or strongly suspect=
ed=3D
). The beauty of the theorem is that the statement of the theorem =
ca=3D
n be explained to anyone; it is there before your eyes. But the pr=
oo=3D
f by computer is completely opaque and almost worthless. Even the=
v=3D
ery long proof of Fermat's Theorem is less than satisfying. What o=
ne=3D
wants is a short, elegant proof that stands before one's eyes as a =
s=3D
ingle object and can be taken in at a glance.
=20
Moreover, see the reference to the work by Clifford Truesdell in th=
e =3D
references to my paper Some Unintended Effects of Computers at http=
:/=3D
/tinyurl.com/dqvj8 , which contains some additional remarks on the =
ef=3D
fects of computers.
=20
Tom Wayburn, Houston, Texas, http://web.wt.net/~twayburn=3D20
=20
=20
http://www.google.com/search?q=3D3Dhaken+appel
but less-obvious effects are pervasive. Math (of the sort that
mathematcians do) is all about proofs ... and the standard of
proof involved in /proving/ the correctness of computer programs i=
s
dramatically higher than the old-style standards of the mathematic=
s
community.
=3D20
a') Conversely, computing has benefitted greatly from mathematics.
The algorithms you need for doing things on a computer are oftenti=
m=3D
es
different in detail from the algorithms you need for doing things =
w=3D
ith
pencil and paper ... but only in detail. The general thought-proc=
e=3D
sses
that go into designing a fiendishly clever algorithm are fundament=
a=3D
lly
the same.
=3D20
=3D3D=3D3D=3D3D=3D3D=3D3D=3D3D=3D3D=3D3D=3D3D=3D3D
=3D20
b) At the other end of the spectrum, as computers and technology i=
n
general become more sophisticated, the more they look like magic t=
o
the casual user.
=3D20
Belief in magic is extremely corrosive to rational thought. In a
democracy, this is a very very serious problem.
=3D20
On a smaller scale, but still a topic of concern, I don't like the
fact that a lot of mass-market software tells the user what to do,
not vice versa. The nightmare scenario of the sorcerer's apprenti=
c=3D
e
goes back ~2000 years ... not to mention Faust and probably 100
science-fiction dystopia stories per year for the last 100 years.
I want to be telling my machines what to do, not vice versa!
=3D20
This makes contact with Michael E's lament that students tend to a=
s=3D
sume
the powerpoint format must be the right report format, and the exc=
e=3D
l
"chart" format must be the right "chart" format. It is crucial to
teach the students that they are in charge ... and they have perso=
n=3D
al
responsibility for the final product.
=3D20
I see this in my student pilots. The ones that can afford fancy
electronics (GPS moving map etc.) would -- if I let them -- come t=
o
rely on that stuff too much. I counter this initally by asking lo=
t=3D
s
of hypothetical but pointed questions about what they would do if
this-or-that instrument failed. Later I make the lesson entirely
non-hypothetical by turning off all the fancy stuff when they leas=
t
expect it, giving them the "opportunity" to get us home using basi=
c
stick-and-rudder skills. Sometimes they are initially irate about
this, but a couple days later they call me up and say "let's go do
that again". It is easy for the flight instructor to motivate the
students, because these are clearly life-and-death issues. It is
harder to achieve the same level of motivation in intro physics cl=
a=3D
ss.

=20