MDMD(2): Notes and Questions

[andrew at cee.hw.ac.uk]

David Casseres writes:
> Andrew sez
> >*One* of the oppositions, certainly. But what about e.g. the
> >opposition between an aristocratic society and a meritocratic one?

> That too, certainly.  Actually I think today's tension between "pure 
> science" and technology still contains a great deal of that opposition, 
> which is now expressed in terms of "academic" and "industrial" endeavors 
> but is really about funding.  Yet Mason & Dixon, were by no means 
> aristocratic, nor were the early Astronomers Royal as I recall.  The AR's 
> were gentry, of course, and ranked well above Harrison and the other 
> watchmakers.

> >... And also perhaps the opposition between Faith and
> >Reason. Reason should suggest that Harrison's chronometer was an
> >adequate solution, but faith in Divine Purpose suggested that there
> >was an `exact' solution to be found in the stars, should we only be
> >able to unravel it...

> That hadn't occurred to me but it certainly fits into the picture.  Such 
> an exact solution would have been seen by many as a vindication of the 
> astrological tradition, as well.  I would love to know just how long the 
> overlap lasted, in educated circles, between the continued acceptance of 
> astrology and the emerging rationalism of astronomy.

Sorry to requote so extensively but . . . the thing is these two
points are not unrelated. The pure/applied science distinction is
rooted in the notion of an `exact' solution vs an `accurate' one,
which in itself gives the game away about the nature of the endeavour
undertaken by the pure/applied scientist and is best exemplified by
contrasting those die-hard purists the mathematicians with, die-hard
technologists like, say, mechanical engineers. I recall my maths
teacher explaining to me that (1 + sqrt(5))/2 was a much better
solution to the equation x^2 - x -1 = 0 than 1.618 (or rather the same
but to a few more digits) since it was `exact' whereas the number was
only an approximation and therefore `incorrect', to be strictly proper
about these things.

Whereas, in fact, both are `correct solutions' -- or rather the latter
may be correct given a purpose which requires no more than 4 (or
whatever) figure accuracy. The mathematician's `solution' is useful
for doing more maths e.g. subsequent algebraic manipulation may make
the sqrt(5) term disappear giving a whole number answer. The
engineer's `solution' is useful if, say, it is required to know how
long, wide or thick to make a given beam in a structure. Trading in a
symbol for a number earlier or later makes no difference to the final
result of computation (assuming you take care with the number of
significant figures, naturally).

What is interesting is that my teacher's comment is not untypical of
mathematicians. Why? Well, nominally, because they are playing a game
with symbols and cashing in the symbols for numbers usually stops the
game progressing. And they are of course right to insist that other
mathematicians follow suit, since mathematical utility is what
mathematicians ought to strive for in their construction of new
mathematics. But the idea that the engineer's solution is `incorrect'
is pervasive and perhaps reflects that old aristocratic prejudice when
maths was an end in itself, pursued more as an aesthetic or religious
discipline than a practical one. Personally, I blame Plato.


Andrew Dinn
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We drank the blood of our enemies.
The blood of our friends, we cherished.