Subject: Re: [HM] A question around zero
From: Romulo Lins (romlins@rc.unesp.br)
Date: Mon Jan 24 1994 - 16:34:33 EST
In the city of Sao Paulo/Brasil, winters are particularly difficult
pollution-wise, and for many years there has been a winter rotation
system in place: on Mondays cars with plates ending with 0 and 1 cannot
be used; on Tuesdays car with plates ending with 2 and 3 are excluded,
and so on. Saturdays and Sundays are free. ( I may be mistaken and the
rule is 1-2 on Mondays, ..., 9-0 on Fridays; I do not live in Sao
Paulo!)
There are two points here. First, if there was an "odd/even" system--as
there is or was in Japan, I believe--, too many cars would be excluded
and the public transport system is quite poor in Sao Paulo (*very*
crowded at most times) and that would probably generate a huge outcry
from the middle-class, that is, politically untenable. Bad news:
self-interest and infra-structure problems having a strong limiting
effect on environmental initiatives. Would the people of Los Angeles
(US) agree on a permanent rotation system to help clean up the world's
atmosphere? The second point is that if the systems used in the
situations presented by Prof. Dr. Jochen Ziegenbalg and by Barry Cipra
were descriptive ones (plates ending with 0, 2, 4, 6, 8 on such and such
days, 1, 3, 5, 7, 9 on such and such days) the problem would have never
happened, *although most people would probably notice/describe the
situation as an odd/even one*.
In Brazil odd/eveness is *always* introduced as in Ralph A. Raimi's
posting, and only at high-school level pupils are *maybe* confronted
with something else. As a result most pupils completely fail when asked
to show that the sum of two odd numbers is an even number, never going
beyond specific examples, and the same situation happens if they are
asked to show that this and that is a multiple of 8, for instance. Many
of my tertiary level students have this difficulty.
All that apart, the doubt about zero seems an odd one to me (oops!). I
can think of a number of simple solutions to the problem. For instance,
I believe that most people would accept that even numbers go up and down
in jumps of two: if 2 is even, so should be--naturally--zero. Or: any
person with a reasonable level of mathematical education could have
acted as a consultant and told government officials that a number is
even whenever it is of the form 2n, where n is an integer. That this
apparently did not happen opens the possibility that maybe, only maybe,
zero is not believed by many to be *really* a number--that being the
problem, not the eveness--, something which would constitute a very
interesting situation, I guess.
With all the rational explaining offered, I have always had a huge
difficulty whenever I tried to emulate the ancient Greek and *really*
think as if 1 was not a number *but only* a 'unit'. If there are many
people today that do not really believe zero is a number some kind of
investigation on how and why this is the case could shed some "cognitive
light" on, for instance, 'no matter how much we see today a geometrical
algebra in Euclid it is truly possible that the separation between
numbers and geometry was not because of a failure to conceptualise
irrational numbers but because of a very strongly rooted belief.'
Is there anything published related to that?
all the best,
Romulo
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