Re: [OT] Interesting?
Hi Matt, you wrote:
<snip>
> 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.
I agree.
<snip>
> 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
Thanks, I'll add this link to my Math Bookmarks. 
It's especially interesting for me, because I learned something about
'e' at school, but *nothing* about 'phi' or Fibonacci numbers (IIRC).
> 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.
Yep.
However, imagine using this system in daily routine. Say, you have
4 children ("four", in the normal decimal number system). Using base
'e', you would have about 10.3102021 children.
Another consideration, which I regard as interesting: IMHO it's not
necessary, that in a number, each place (proper expression?) has the
same base. Just for illustration, a short repetition of what we all
know, of course. In the number system with base x, for instance "273"
means:
2*x^2 + 7*x^1 + 3*x^0
How about a number system with a "progressive base", for instance so
that "273" means:
2*(x+2)^2 + 7*(x+1)^1 + 3*(x+0)^0
I *vaguely* recall, having read about this idea in one of Martin
Gardner's books many years ago. I don't know, whether such a system
would be of any practical use, though.
BTW: When I read Gardner's book 'The Ambidextrous Universe' IIRC
I believed, that '2' would be "nature's base".
> 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).
I agree, however the original author (and anyone else) is free to use a
base-12 system if and when he needs it.
>> 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.
Yep.
> 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.
That's exactly what I mean. From this list, I recently learned the
English saying: "Horses for courses."
> After all, computer scientists move pretty easily between base-10 and
> base-16, so why not with other disciplines?
That's an interesting question. Maybe just because it's not so
important/useful in other disciplines? I don't know.
> 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 :).
Hmm, some time ago, the NASA had to learn a pretty expensive lesson. 
But I can talk! Many Germans, including me, are not yet familiar with
the Euro (which was introduced as cash on 1.1.2002). In order to know,
what something "really" costs, I have to calculate the price in DM.
Best regards,
Juergen
--
The difference between men and boys
is the price of their toys.
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