Daniel Carrera wrote:
I don't know about hexadecimal but some cultures have used a base eight
counting system. You count using the spaces between your fingers rather
than the fingers themselves.
We could start a culture that has a base 1024 counting system. I can
show you how to count to 1024 using your fingers (does you guys all
remember your binary algebra?).
Umm ... there are only 10 kinds of people in world, those that
understand binary and those that don't?
Daniel.
Pat McBride wrote:
Didn't the ancients in the Middle East base their number system on
hexadecimal, or something like that. In the Bible, it says that Noah
built the ark using cubits as a length. And as Bill Cosby once said
"What's a cubit?"
Pat
-----Original Message-----
From: Ian Lynch [mailto:[EMAIL PROTECTED]
Sent: 2008/05/21 01:45
To: [email protected]
Subject: Re: [social] I am not receiving anything from this list
On Tue, 2008-05-20 at 23:23 -0400, Gregory J. Neumann wrote:
Robert Derman wrote:
Rod Engelsman wrote:
Hey Greg!
Well, that's what democracy is about.
There is an argument that politicians lead the people and represent them
so that the people don't have to have a referendum on every issue and
that although accountable to them there is more stability and better
informed government if occasionally politicians do unpopular things on
particular issues. Depends on the view of democracy. If it was simply
about immediate voting majorities, minorities would always be suppressed
and democracies tend not to do that either.
One can convincingly argue that even w/o the immediate voting
majorities, minorities are very poorly represented.
Again that depends on your circumstances. If it cost you money to change
you will probably take that view. If you are a student working towards
an exam dealing with several incompatible systems of units you probably
wouldn't.
I think this touches on my point. Oddly enough, in every day life, they
rarely interact in such a way as to highlight those incompatibilities.
If that were the case, they never would have lasted. Inch, yard, food,
mile, etc. in Imperial are surprisingly close to the Roman versions from
1000 years or more before the "thumb to nose standard".
The meter
Metre. A meter is what I have on the wall to measure my electricity
usage :-)
It's meter south of the 54th parallel. Can't help it if you Canadians
don't know how to spell. ;-)
Because it gives an international standard that is transparent open and
is interoperable (heard this before somewhere? :-) )
We have a decimal counting system because we have 10 fingers. If we
actually had a number system based on base 12 - and the basis for
counting in 12s is to use your thumb to count the finger joints in your
hand - then a duodecimal system with 01,2,3,4,5,6,7,8,9,A,B would then
make feet and inches work well but everyone would have to learn to think
with two new number symbols and the arithmetic that goes with them.
There is a mathematical argument that 12 is better because it divides by
2,3,4,6 whereas 10 only divides by just 2 and 5. Since the number
systems are built on 10 and 10 symbols, it is just as strong an argument
to base units on multiples of 10. So your US currency is a decimal
currency system. In the UK we changed from 12 pennies in a shilling and
240 pennies in a pound to decimal currency because for most people its
simpler to have the symbolic number system compatible with the system of
arithmetic. Try dividing £3 12s and 6d between 4 people compared to
£3.63.
Unless I'm very mistaken, and it's been years, the very first extensive
mathematics users, the Sumerians, used base 12, hence the 360 degree
circle, and 24 hour day. It wouldn't at all surprise me if the commoners
used base 10 for everyday counting, fingers and all.
Why I should discard a system of measure that divides into fractional
parts far more evenly than SI for my everyday usage is still not very
clear to me.
Dividing it fractional parts is only one part of the equation. It would
be cut and dried if the number system was duodecimal but it isn't so
there is as much argument that its easier to use decimals to represent
fractional parts as it is fractions. Its just a matter of when I say 1/4
you visualise what that looks like easier than if I say 25% or 0.25.
1/4 is easier to visualize than 0.25 & 25%. Very few people actually
think in percentages. Though my data is purely anecdotal based on the
group I observe. It may be very different in a different culture.
I do think SI's integration of linear, volume, weight/mass and
temperature is a great idea, but I don't see why a decimal system
based on a weird estimate should have to be part of that.
The actual basis of the metre is not really important. Let's face it a
yard was based on the distance from the king's nose to the tip of his
fingers. Hardly any more scientific. The thing is to define a basic unit
that becomes familiar. How that is then subdivided etc has two
considerations, the number system to be used and how appropriate the
number system is for arithmetic operations. Either change the number
system to fit neat integer operation or change derived units to fit the
number system. Decimal systems do the latter.
Exactly my point. The SI system is just as unscientifically and
arbitrarily based as the Imperial. The disadvantage SI has is that it
was designed by a group that was quite biased against any existing
system. It was a top down arbitrarily imposed standard forced on people
who were given no choice. Gee, that sounds familiar, too! ;-) The lack
of logical intermediate subdivisions like inches, and ounces, makes SI
cumbersome.
One of the reason yards, feed, etc. nearly match the ancient Roman
equivalents is because it's a very convenient system. That should have
been taken into account. I can visualize 1/3 of meter/re, but actually
measuring it? Well, I guess we'd just have to agree on "nearest
millimeter/re"? Decimal is only used because we learned it. If we
started teaching Duodecimal tomorrow, the kids would adapt perfectly.
I had far less trouble learning "inch, feet, yards" than I did trying to
make the metric system work outside of the lab. It's hard to imagine a
better system for manipulating measurement data than SI, but that
doesn't make it a good system for measuring things.
Computers use hexadecimal because it relates well to the natural binary
number system used in digital electronics but getting the public to
think in binary or hexadecimal is rather more tricky than changing to a
system of units that naturally works with decimal.
It's rather more tricky to get the public to change from a very
convenient, workable system to a more difficult one. Especially when one
is not any more accurate than the other. Since the advent of the
"International Inch", the very reason for the SI in the first place,
replacing all the regional measuring systems in France, is removed.
Oddly, it seems that you may be moving toward my position that the SI is
not better than Imperial, just different. It's just as open and
accessible. Needs reform in places, but that's a lot simpler than
chucking one system for another that's completely incompatible, and
designed to be that way.
It's all moot, of course. This is some 50 years too late. But this is
very fascinating. And I'm learning lots. Thanks for your patience.
-Greg
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