From: Humanist Discussion Group (by way of Willard McCarty willard.mccarty_at_kcl.ac.uk>

Date: Sat, 25 Mar 2006 07:52:30 +0000

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

www.kcl.ac.uk/humanities/cch/humanist/

www.princeton.edu/humanist/

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

--[1]------------------------------------------------------------------

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

--[2]------------------------------------------------------------------

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.

Yours,

WM

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

*
This archive was generated by hypermail 2.2.0
: Sat Mar 25 2006 - 03:04:50 EST
*