1. Re: [OT] Interesting?
- Posted by Juergen Luethje <j.lue at gmx.de> Aug 01, 2003
- 383 views
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.