RE: [OT] Interesting?
> From: Juergen Luethje [mailto:j.lue at gmx.de]
> Hi Matt, you wrote:
>
> > --- Juergen Luethje <j.lue at gmx.de> wrote:
> >
> >>> But there is no 'nature's' base.
> >>
> >> Yep. The whole concept of "numbers" was developed by humans, not by
> >> nature.
>
> I admit, that this sentence is somewhat nihilistic. 
> I belive I wrote it, because I've too often (not here on this
> list!) seen people using numbers for pseudo-religious purposes,
> and therefore I'm somewhat oversensitive in this respect.
Yes, numerology in all its guises seems silly to me. But, since certain
numbers continue to appear in nature, there must be *something* to them. To
me, it just means that the number represents a really efficient or elegant
(in the mathematical sense of the word) way of doing something.
> > Mmmmm. Metaphysics. What about e or phi (used to generate
> > the Fibonacci numbers)? These pop up in nature all the time
> > (exponential growth, flower petals, leaf patterns, etc).
>
> Ha!
> _After_ having sent my previous post, I was also thinking of 'e' as a
> 'natural number'. I really like it. Fibonacci numbers of
> course also are very natural (I only think of the reproduction of
> rabbits, which is often used to introduce Fibonacci numbers .
Here's a good link that talks about a lot of things that Fibonacci relates
to:
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
Of course, F. numbers are really just an approximation of the Golden Mean,
which the Greeks knew about (IIRC, (1+phi)/sqrt(5) )
> > We tend to think about things in additive terms,
> > but maybe it's more 'natural' to think in exponential /
> > logarithmic / multiplicative terms.
>
> Now _this_ is really interesting for me. And I think this hasn't got
> anything to do with the question, what base we choose to
> build a number system.
It doesn't have a direct relationship, except that if you were going to
start a numbering system from scratch, you'd want to have something that
related easily to the real world. If you mainly thought in multiplicative /
exponential / logarithmic terms, e would be an excellent base, since so many
things in nature can be calculated using e.
I think the original author's point about the potential for scientific
advancement potential after upgrading a number system is completely valid.
There was a lot of 'intellectual indigestion' even over the concept of zero,
including religious objections. But it's one of the most important things
to ever happen to science. Not to mention negative or complex numbers (the
former being mainly accepted by the general populace as true numbers, while
the latter are not, in part because of the 'imaginary number' notation hung
on 'i' the square root of -1).
A base-12 system really does make a lot of sense, though it would be
difficult to switch from today's base-10, except in some specialties (like
base-16 has taken over computer science). I suppose the number-theoretic
argument for base-12 vs base-10 has to focus on the factors (which the
author did).
> Maybe this can also be described as 'static' (additive terms:
> "How many apples/sheep/dollars do I have?") vs. 'dynamic' (exponential
> terms: "In which direction, and how fast will things develop?"
I think it's just a different point of view, not too disimilar from
scientific notation, which is an 'exponential' way of talking about things.
We're also very 'integer-centric', which isn't surprising, since most
numbers in our lives seem to be about counting physical objects. But a lot
of things can only be roughly approximated by integers, such as physical
dimensions.
Besides, multiplication and division are often described as ways to add and
subtract repeatedly, or more quickly. Why waste time with normal addition
and subtraction? :)
> I think both 'e' and 'phi' are very natural numbers. But if we ask:
> "What is the _most_ natural number?", we are again in a
> dilemma, that is artificially created by ourselves. It seems to be
> typically human (or does this only apply to cultures, that are based on
> a _mono_theistic religion??) -- but often not adequate to reality
> --, to try to put things down to "the one and only" base.
A good point, and I think I stumbled on to this above. Perhaps we need to
be more flexible, and try to find the proper base for the proper task.
After all, computer scientists move pretty easily between base-10 and
base-16, so why not with other disciplines? The world seems to do OK
converting between lots of different currencies (and since even Americans
can convert between metric and non-metric measurements, it can't be that
hard, right :).
Matt Lewis
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