19.678 mathematics

From: Humanist Discussion Group (by way of Willard McCarty willard.mccarty_at_kcl.ac.uk>
Date: Sat, 25 Mar 2006 07:52:30 +0000

               Humanist Discussion Group, Vol. 19, No. 678.
       Centre for Computing in the Humanities, King's College London
                     Submit to: humanist_at_princeton.edu

   [1] From: Ryan Deschamps <Ryan.Deschamps_at_Dal.Ca> (25)
         Subject: Re: 19.676 the advantages of studying mathematics

   [2] From: Willard McCarty <willard.mccarty_at_kcl.ac.uk> (126)
         Subject: mathematics and us

         Date: Sat, 25 Mar 2006 07:39:04 +0000
         From: Ryan Deschamps <Ryan.Deschamps_at_Dal.Ca>
         Subject: Re: 19.676 the advantages of studying mathematics

OK -- This quote shows a lack of business math skills.

"Choose math because you will make more money.

Winners of American Idol and other "celebrities" may make money, but
only a tiny
number of people have enough celebrity to make money, and most of them get
stale after a few years. Then it is back to school, or to less rewarding
careers ("Would you like fries with that?"). If you skip auditions and the
sports channels and instead do your homework -- especially math -- you can go
on to get an education that will get you a well-paid job. Much more than what
pop singers and sports stars make -- perhaps not right away, but certainly if
you look at averages and calculate it over a lifetime."

I've heard this argument used by supporters of the NHL (ice) hockey players to
justify their high wages. The argument goes, "since they have such a short
period of time to make money, they have to get a whole wack of money as early
as possible."

Well, if you do the math and follow future value formulas, having 10 million
right away, is much, much, MUCH better than having 10 million over 20 years.

Thus, even if the American Idol winner bombs out after 5 years, he/she will
still be doing better than your average Mathematician who has to work his/her
life away until retirement.

This is a nit-pick of course, considering a) most of us are not
talented/attractive/self-loathing enough to be American Idol winners and b)
music talent is helped immensely by a knowledge of mathematics.

Ryan (practising his vocal chords). . .

Ryan Deschamps

         Date: Sat, 25 Mar 2006 07:44:38 +0000
         From: Willard McCarty <willard.mccarty_at_kcl.ac.uk>
         Subject: mathematics and us

Frustration might be defined as not being able to have or to do what
you desire to have or do. I've found mathematics frustrating because
I fell in love with it at an early age, worked hard enough at it to
be encouraged in some quite substantial ways, but on meeting a real
mathematician, first when I was 16 (he was 15, and the focus of much
attention from nearby professors), then another some years later as
an undergraduate (he was the same age, able to do at the speed of
writing what took me all week), I realized that my road would never
go there, no matter how hard I tried. But now, in a wrestling match
with computing, I've found that having some appreciation of
mathematics is really unavoidable -- but also that there are
mathematicians out there who spend no little effort in writing about
their passion for the likes of me. One of these, as perhaps I've said
before, is Solomon Feferman (Stanford), whose papers can be
downloaded. (May all of us specialists be like him in this regard at
least.) C. W. Kilmister's little book, Language, Logic and
Mathematics (English Universities Press, 1967), is very helpful,
though its road does get steep after a bit. A much more recent
attempt in a worthy OUP series, Very Short Introductions, is Timothy
Gowers' Mathematics: A Very Short Introduction. It entices me from a
nearby bookshelf, but I have yet to read it.

And then there's Richard Hamming, more of an engineer, I suppose, but
with a profound understanding of maths. His paper, "The Unreasonable
Effectiveness of Mathematics", American Mathematical Monthly 87.2
(Feb 1980): 81-90, available via JSTOR -- what does one say? Should
be required reading? Yes, it should, but that doesn't express the joy
and exhiliration from reading it. I was led to Hamming by Mike
Mahoney, historian of technology and of computing at Princeton, who
is at home with mathematics and whose papers help build a bridge for
us between humanities computing and mathematics. A remark by Northrop
Frye many years ago, that mathematics is the imaginative language of
the natural sciences as poetry is of the humanities, eventually got
me to go looking for a comprehensible expression of the mathematical
imagination, hence to David Hilbert and S. Cohn-Vossen, Geometry and
the Imagination (Anschauliche Geometrie). You may be familiar with
how mathematicians use the word "beautiful". This is a beautiful book.

Below I reproduce a brief parable told by Edsger Dijkstra, one of the
greats in computer science, which in his typical style helps to make
the distinction between how programmers think and how mathematicians
think. And this helps in turn make the point that although computing
and mathematics are closely related, computing has grown from its
roots in a rather different direction.


A Parable

Edsger W.Dijkstra, sometime in 1973
from http://www.cs.utexas.edu/users/EWD/ewd05xx/EWD594.PDF

Years ago a railway company was erected and one of its directors --
probably the commercial bloke -- discovered that the initial
investments could be reduced significantly if only fifty percent of
the cars would be equipped with a toilet, and, therefore, so was decided.

Shortly after the company had started its operations, however,
complaints about the toilets came pouring in. An investigation was
carried out and revealed that the obvious thing had happened: despite
its youth the company was already suffering from internal
communication problems, for the director's decision on the toilets
had not been transmitted to the shunting yard, where all cars were
treated as equivalent, and, as a result, sometimes trains were
composed with hardly any toilets at all.

In order to solve the problem, a bit of information was associated
with each car, telling whether it was a car with or without a toilet,
and the shunting yard was instructed to compose trains with the
numbers of cars of both types as equal as possible. It was a
complication for the shunting yard, but, once it had been solved, the
people responsible for the shunting procedures were quite proud that
they could manage it.

When the new shunting procedures had been made effective, however,
complaints about the toilets continued. A new investigation was
carried out and then it transpired that, although in each train about
half the cars had indeed toilets, sometimes trains were composed with
nearly all toilets in one half of the train. In order to remedy the
situation, new instructions were issued, prescribing that cars with
and cars without toilets should alternate. This was a move severe
complication for the shunting people, but after some initial
grumbling, eventually they managed.

Complaints, however, continued and the reason turned out to be that,
as the cars with toilets had their toilet at one of their ends, the
distance between two successive toilets in the train could still be
nearly three car lengths, and for mothers with children in urgent
need -- and perhaps even luggage piled up in the corridors -- this
still could lead to disasters. As a result, the cars with toilets got
another bit of information attached to them, making them into
directed objects, and the new instructions were, that in each train
the cars with toilets should have the same orientation. This time,
the new instructions for the shunting yard were received with less
than enthusiasm, for the number of turntables was hardly sufficient;
to be quite fair to the shunting people we must even admit that
according to all reasonable standards, the number of turntables was
insufficient, and it was only by virtue of the most cunning
ingenuity, that they could just manage.

With all toilets equally spaced along the train the company felt
confident that now everything was alright, but passengers continued
to complain: although no passenger was more than a car length away
from the nearest toilet, passengers (in urgent need) did not know in
which direction to start their stumbling itinerary along the
corridor! To solve this problem, arrows saying "TOILET" were fixed in
all corridors, thereby also making the other half of the cars into
directed objects that should be properly oriented by the shunting procedure.

When the new instruction reached the shunting yard, they created an
atmosphere ranging from despair to revolt: it just couldn't be done!
At that critical moment a man whose name has been forgotten and shall
never be traced, made the following observation. When each car with a
toilet was coupled, from now until eternity, at its toileted end with
a car without a toilet, from then onwards the shunting yard, instead
of dealing with N directed cars of two types, could deal with N/2
identical units that, to all intents and purposes, could be regarded
as symmetrical. And this observation solved all shunting problems at
the modest price of, firstly sticking to trains with an even number
of cars only -- the few additional cars needed for that could be paid
out of the initial savings effected by the commercial bloke! -- and,
secondly, slightly cheating with regard to the equal spacing of the
toilets. But, after all, who cares about the last three feet?

Although at the time that this story took place, mankind was not
blessed yet with automatic computers, our anonymous man who found
this solution deserves to be called the world's first competent programmer.

I have told the above story to different audiences. Programmers, as a
rule, are delighted by it, and managers, invariably, get more and
more annoyed as the story progresses; true mathematicians, however,
fail to see the point.

Platasnstreat 5 prof.dr.Edsger W. Dijkstra
NL-4565 NUENEN Burroughs Research Fellow
The Netherlands

Dr Willard McCarty | Reader in Humanities Computing | Centre for
Computing in the Humanities | King's College London | Kay House, 7
Arundel Street | London WC2R 3DX | U.K. | +44 (0)20 7848-2784 fax:
-2980 || willard.mccarty_at_kcl.ac.uk www.kcl.ac.uk/humanities/cch/wlm/
Received on Sat Mar 25 2006 - 03:04:50 EST

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