Anton Aylward

Do Algorithms Discriminate?

http://cio.ittoolbox.com/groups/general/tech-news/do-algorithms-discriminate-5766423

Personally I think this is unfair.
It fails to differentiate between what I might term loaded or even pre-loaded algorithms and pure algorithms

Consider, if you will a Fibonacci sequence generator.
Such a sequence is defined by the formula

F(n) = F(n−1) + F(n−2)

Normally the seed values are 1 and 1, so the sequence becomes

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

That’s what I was taught at school.
What’s being taught these days is with seed values of 0 and 1 giving rise to

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

So what we have is a really a SET of sequences with different starting conditions. Was what I was taught 50 years ago wrong? No, it just had a different set of prejudices starting conditions.

The ALGORITHM is not prejudicial, it is how it is loaded with a starting condition that makes the difference.

Back in 1984 I applied for a job with a mathematical form and part of the interview test was to write a MINIMAL Fibonacci generator.

So I wrote on the board

while true do
      print "0, "
 done

Only one guy on the interview team was actually a REAL mathematician and he laughed his head off. he said to me “set theory?“; I said “Russell“; he replied “Cantor“. He insisted I get the job.

And that is the point. There are a whole set of such sequences depending on the initial starting conditions. The core algorithm that moves F-sub-zero and F-sub-one along is a pure algorithm. It doesn’t care what the parameters are.

In pure mathematics this is called “Closed Form”.
The closed form of Fibonacci is sometimes generalized as Binet’s Formula. This is relevant to astronomy a it is one of the few analytic way of solving orbital equations, sort-cutting second order nonlinear ordinary differential equations. More to the point, Binet’s work allows for off-axis non-circular motion, that is when the center of force and the focus of the orbit do not coincide. That, in case you weren’t watching, is something like the 3-body problem.

Let face it, would you prefer to iterate the successive integrations of ordinary differential equations to solve that?

The mathematics – read algorithms – of orbital equations carry a lot of assumptions about heliocentricity, gravitation, inverse square law, and if you want to be picky Mach’s principle for the distant stars. Its also not difficult to drift into Relativity. All this does, of course, discriminate against those who believe in the inerrant Word of The Bible – probably also believing, despite other evidence – that it was the literal word of God dictated to Moses and the Prophets and Scribes by an angel. The fact that such is an Islamic tradition and not a Christian or Jewish one is beside the point to such people. Science discriminates against them!

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