
The Dozenal Society of America - adius
http://www.dozenal.org/
======
nwatson
An uncle who designed jet engines at General Electric said one advantage GE
had over European counterparts was the greater diversity in sheet metal
gauges/thicknesses used to build the engines; they could maintain required
strength throughout an engine while paring down engine weight. He attributed
the better mix to the English system encouraging divisibility by 2/3/4/6
rather than 2/2.5/5/10 at various scales.

~~~
jacobolus
Ideally this kind of thing should be roughly on a log scale, along the lines
of
[https://en.wikipedia.org/wiki/Preferred_number](https://en.wikipedia.org/wiki/Preferred_number),
e.g.
[https://en.wikipedia.org/wiki/Renard_series](https://en.wikipedia.org/wiki/Renard_series)
[https://en.wikipedia.org/wiki/E-series_of_preferred_numbers](https://en.wikipedia.org/wiki/E-series_of_preferred_numbers)

You can pick a coarser or finer scale depending on the particular need.

For a base twelve world, I would recommend using binary logarithms written in
base twelve (“dublogs”) whenever possible; 0.1 on such a scale matches one
semitone in a 12-note-per-octave equal-tempered musical scale.

~~~
eadmund
I'm honestly not sure what you're saying, but it _sounds_ compelling!

~~~
jacobolus
I'm saying that if redesigned today for our current society (either metric or
imperial) sheet metal gauges should probably use something like preferred
numbers for widths.

In a hypothetical base twelve world, they could instead use a log scale (think
decibels) explicitly, and one nice option is to use binary logarithms, since
then twelfths correspond approximately to nice duodecimal fractions. This is
the basis of the Western musical scale.

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nonbel
The most interesting argument I've heard from the dozenal society is that the
decimal system is inherently selfish. There is a reason that cases of beer
come in packs of 6, 12, 18, 24, 30 instead of 5, 10, 15, etc. It is much more
likely you will be able to divide them equally amongst a group of arbitrary
size.

~~~
vole
Isn't that their entire argument?

~~~
Avshalom
Well it isn't usually couched in terms of morality.

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suddensleep
Only marginally related, but I spent one of my summers at PROMYS[1] doing
research into which complex numbers could be successfully used as bases. As
different as the various common integer bases "feel" in terms of hand-
computation, there's nothing like cranking out conversions of fractions to
base 1+i to make you realize that there's a whole wacky universe of number
representations out there. I thought it was a really cool field of study, and
I remember wishing there were more readily apparent applications. Anyone?

[1] [https://www.promys.org/](https://www.promys.org/)

~~~
espeed
Similarly, see Pavel Grinfeld's argument [2] advocating the vector basis L =
{1, x, x²-1/3} w.r.t. Legendre polynomials.

[1]
[https://en.wikipedia.org/wiki/Pavel_Grinfeld](https://en.wikipedia.org/wiki/Pavel_Grinfeld)

[2] MathTheBeautiful: _Why {1,x,x²} Is a Terrible Basis_ [video]
[https://www.youtube.com/watch?v=pYoGYQOXqTk&index=14&list=PL...](https://www.youtube.com/watch?v=pYoGYQOXqTk&index=14&list=PL..).

[3]
[https://en.wikipedia.org/wiki/Legendre_polynomials](https://en.wikipedia.org/wiki/Legendre_polynomials)

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ceautery
I stumbled onto these guys a few years back when I was going nuts about base
18 (which you can do on a standard 5x2 abacus!). I think they have their own
symbols for digits > 9 instead of using 'a' and 'b' in the hexadecimal
fashion.

Non-standard radixes are pretty fun, and it makes you think about nebulous
questions like "what does ten mean", and if you happen to carry that train of
thought way past the station, "what does it mean to be a number?"

~~~
kw71
I learned base 12 arithmetic in gradeschool and the textbook used T and E for
10, 11.

I'm pretty sure this was before people started using hex notation for
computing and logic.

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kabdib
For a fictional treatment of converting a society to base 12, Leo Frankowski's
_High Tech Knight_ series is a lighthearted and fun read (starts with _The
Crosstime Engineer_ ).

[I didn't like the books past the original 4, YMMV]

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nixpulvis
I wonder how they feel about base e?

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pc2g4d
I can't tell if this was meant as a joke or not

