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Re: Arbitrariness of pi
Posted:
Mar 3, 2013 2:34 PM
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On Sun, 03 Mar 2013 15:36:29 +0100, Ralf Bader wrote:
>pepstein5@gmail.com wrote:
>
>
>> I think that 2 * pi comes up quite a bit more in modern maths than pi, but
>> that wasn't necessarily true at the time the pi notation originated. From
>> the standpoint of the contemporary mathematician, it would make more sense
>> to call pi = 6.28...
>>
>> Is this connected with transcendence? Not really, e is also
>> transcendental. It's very important in mathematics to define notation and
>> concepts to be as simple and transparent as possible. Defining pi as the
>> number that we now call 2 * pi would be an improvement. But the
>> improvement is not significant enough to overcome inertia -- there is
>> value in sticking to historical precedents, too.
>>
>> Having to restate all pi-based formulate would be irritating too.
>
>It can't be restated in books that are already printed. And probably pi
>appears in (the source code of) a lot of computer programs used e.g. to
>control devices. I think the world is in enough trouble already without
>having to deal with the mess most probably following such a redefinition of
>pi.
Agreed.
In hindsight, the definition of pi as 3.14... instead of 6.28... does
not seem to be the better choice.
I don't agree with the tauist claim that as a result of "fixing" it
now "the world would become numerate." Instead, there would be two
equations for the circumference of a circle, depending on the constant
used. How would this encourage mathophobes to delve deeper into what
they already perceive to be arcane?
There have been other "wrong" choices that persist, for example:
http://en.wikipedia.org/wiki/Electric_charge
the direction of the conventional current is opposite to the drift
velocity of the actual charge carriers, i.e., the electrons. This is a
source of confusion for beginners.
How many automotive electrical systems would be damaged by the
"improvement" of re-labeling the positive and negative terminals on
batteries to "fix" the inconsistency mentioned in Wikipedia?
Smaller "fixes" have been done:
http://en.wikipedia.org/wiki/Atomic_mass_unit#History
the reference standard for both physics and chemistry was changed to
carbon-12 in 1961.
http://answers.yahoo.com/question/index?qid=20080412023027AAPnaOn
My teachers at school were originally taught that Avogadro's Constant
was 6.023*10^23, but upon checking this i find that most people agree
it is around 6.02214*10^23.
But the conversion from pi to tau changes the 'circle constant' by a
factor of two. Simple errors in algebra would spawn publication of
countless formulas that are wrong by a factor of four.
Would that 'circle constant' had been defined as 6.28... by the first
users. But it wasn't.
Which is more difficult now:
1. Suffer the consequences of errors in "fixing" the circle constant?
2. Write and compute with an 'extra' factor of 2 where needed with pi?
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