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

[twayburn at WT.NET (Tom Wayburn)]

> 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

We always knew the Four Color Theorem was true (or strongly suspected=
).  The beauty of the theorem is that the statement of the theorem ca=
n be explained to anyone; it is there before your eyes.  But the proo=
f by computer is completely opaque and almost worthless.   Even the v=
ery long proof of Fermat's Theorem is less than satisfying.  What one=
 wants is a short, elegant proof that stands before one's eyes as a s=
ingle object and can be taken in at a glance.

Moreover, see the reference to the work by Clifford Truesdell in the =
references to my paper Some Unintended Effects of Computers at http:/=
/tinyurl.com/dqvj8 , which contains some additional remarks on the ef=
fects of computers.

Tom Wayburn, Houston, Texas, http://web.wt.net/~twayburn=20


>   http://www.google.com/search?q=3Dhaken+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 is
> dramatically higher than the old-style standards of the mathematics
> community.
> =20
> a') Conversely, computing has benefitted greatly from mathematics.
> The algorithms you need for doing things on a computer are oftentim=
es
> different in detail from the algorithms you need for doing things w=
ith
> pencil and paper ... but only in detail.  The general thought-proce=
sses
> that go into designing a fiendishly clever algorithm are fundamenta=
lly
> the same.
> =20
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
> =20
> b) At the other end of the spectrum, as computers and technology in
> general become more sophisticated, the more they look like magic to
> the casual user.
> =20
> Belief in magic is extremely corrosive to rational thought.  In a
> democracy, this is a very very serious problem.
> =20
> 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 apprentic=
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!
> =20
> This makes contact with Michael E's lament that students tend to as=
sume
> the powerpoint format must be the right report format, and the exce=
l
> "chart" format must be the right "chart" format.  It is crucial to
> teach the students that they are in charge ... and they have person=
al
> responsibility for the final product.
> =20
> I see this in my student pilots.  The ones that can afford fancy
> electronics (GPS moving map etc.) would -- if I let them -- come to
> rely on that stuff too much.  I counter this initally by asking lot=
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 least
> expect it, giving them the "opportunity" to get us home using basic
> 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 cla=
ss.
>