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Old 2020-08-12, 17:50   #78
Uncwilly
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I get to use feet and inches at work as well as decimal feet.
Some people tend to have problems dealing with decimal feet and want inches. It is easy to get a quick approximation of feet and inches from decimal feet.
1 foot = 100 (hundredths of a foot, 0.01 foot)
1 foot = 12 inches = 96 (1/8ths of an inch)

0.01 foot ≈ 1/8th of an inch
And it is easy to correct for the difference.
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Old 2020-08-12, 22:44   #79
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Quote:
Originally Posted by Uncwilly View Post
I get to use feet and inches at work as well as decimal feet.
I used to be a firm believer that Metric was always the best space (even though it was invented by the French...).

And I still do believe Metric Makes Sense (TM) for most measurement spaces.

But, for the smaller spaces interacted with by human trades-persons, being devisable by 2 (and 3, etc) makes a lot of sense.

For someone who's worked in this space for a long time, being able to add 1/64 to 1/4 (then divide by two, then multiply by four) is trivial.

I call it "folding". Map the numbers into different dividers as required, and then unfold as the last step.

Now, why a Mile contains 5280 Feet completely escapes me...
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Old 2020-08-13, 05:51   #80
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Quote:
Originally Posted by Uncwilly View Post
You appear to be in conflict with yourself. You advocate a base 12 system. Then you advocate a base 10 system to measure. And you point out the one base 12 unit of measure as supposedly inferior.
The dozenal metric system can be integrated as the following which is shown on the screenshot below. [Dozenal] 10 = [Decimal] 12. So the highest unit(kilowolf) is slightly longer than 1 mile and the lowest unit(milliwolf) is slightly shorter than 1 millimeter. Apply the same patterns to grams and liters.

Foot and Inch are way different than the dozenal metric system as 1 yard ≠ 1 dozen feet.
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Old 2020-08-13, 06:05   #81
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log2/log10 ~= 0.3 means that a simple approximation for 210 ~= 103. Useful for estimating binary computer values.

But log2/log12 ~= 0.2789429.... gives us no usefully close conversion ratios.

There fore base-12 is inferior to base-10. Right?
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Old 2020-08-13, 06:23   #82
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Quote:
Originally Posted by retina View Post
log2/log10 ~= 0.3 means that a simple approximation for 210 ~= 103. Useful for estimating binary computer values.
There fore base-12 is inferior to base-10. Right?
The powers of 2 are way easier to be memorized in dozenal than decimal if people are familiar with both bases.

Petabyte and Quadrillion are already not so close. Hexadecimal is the best for any computer-related math, but not divisions of 3 or 6.
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Old 2020-08-13, 10:33   #83
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Unless 2^5 * 2^5 = exact [decimal] 1,000, it's not that superior as you think, otherwise we would already have a zettahertz CPU.

Multiply the first 4 composite numbers together -> 4 * 6 * 8 * 9 = [decimal]1,728

Time to pack up lots of toilet paper rolls for the Coronavirus pandemic, dozenal is way more efficient than decimal for this job.
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Old 2020-08-13, 12:28   #84
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What notation one uses for numerals has nothing to do with the physical problem of packing . Just as it has nothing to do with composing or playing music. Musical notation (clefs, notes, rests, etc) is not primarily numerical. The only numerals in music scores that spring immediately to mind are "time signatures," which specify the numbber of "counts" or "beats" to the measure, and which note gets one "count". Thus, in 3/4 or "waltz time," there are three beats to the measure, and the quarter note gets one beat. There are time signatures in which at least one of the numbers is large enough that its base ten and base twelve notations would differ, but I have never seen them expressed in any other than decimal notation.

Musical notation has a binary feature. A "whole note" is an oval with a void. Adding a stem makes it a "half note." Filling in the void makes it a "quarter note." Adding a "flag" to the stem on a note divides the length of the note by 2. One flag, an eighth note. Two flags, a sixteenth note. Three flags, a thirty-second note. Four flags, a sixty-fouth note, AKA a hemidemisemiquaver.

Another "binary" feature to music is the fact that two notes differing by one octave have frequencies that differ by a factor of two.

I also note that there is a standard notation for base-sixteen, or hexadecimal numbers. It uses the decimal digits with their customary values, and A = ten, B = eleven, C = twelve, D = thirteen, E = fourteen, and F = fifteen. It therefore seems entirely appropriate to use A = ten and B = eleven for base twelve notation.

Last fiddled with by Dr Sardonicus on 2020-08-13 at 12:29 Reason: Rephrasing
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Old 2020-08-13, 12:37   #85
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I use hex numbers far more than any other base (except for base ten) in my normal daily activities.

I rarely care about exactly dividing anything into 3 parts, or even 5 parts, so a base that has many "interesting" divisors makes no difference to me.
Quote:
Originally Posted by CRGreathouse View Post
I'm not opposed to changing our conventions, but base-16 would seem to bring more advantages. (You still get easy divisibility by 2, 3, and 5, plus all the advantages of binary, computing and otherwise.)
I would not object to changing to base-16 (2). It has many more advantages than base 12 IMO.
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Old 2020-08-13, 13:35   #86
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Quote:
Originally Posted by retina View Post
...
I rarely care about exactly dividing anything into 3 parts, or even 5 parts,
...
I often have to divide "things" in 3 or 5 (equal) parts ... when cutting up a cake for instance. But for those tasks the base to express the result of the division plays no role.

Jacob
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Old 2020-08-13, 13:40   #87
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Quote:
Originally Posted by Dr Sardonicus View Post
It therefore seems entirely appropriate to use A = ten and B = eleven for base twelve notation.
Then I'll say I want A-ty(hex) item 1 and eighty(hex) item 2, how would you pronounce them?

Quote:
Originally Posted by retina View Post
I use hex numbers far more than any other base (except for base ten) in my normal daily activities.

I rarely care about exactly dividing anything into 3 parts, or even 5 parts, so a base that has many "interesting" divisors makes no difference to me.I would not object to changing to base-16 (2). It has many more advantages than base 12 IMO.
Except the multiplication tables will be too much for the elementary school students to memorize. Hex multiplication tables are not as easy as the Dozenal versions.

Quote:
Originally Posted by Dr Sardonicus View Post
Musical notation has a binary feature. A "whole note" is an oval with a void. Adding a stem makes it a "half note." Filling in the void makes it a "quarter note." Adding a "flag" to the stem on a note divides the length of the note by 2. One flag, an eighth note. Two flags, a sixteenth note. Three flags, a thirty-second note. Four flags, a sixty-fouth note, AKA a hemidemisemiquaver.
I play triplets on 1 hand and 8th notes on the other hand all the time. There are also triplets vs 16th notes in several Chopin compositions.

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Old 2020-08-13, 13:48   #88
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Quote:
Originally Posted by tuckerkao View Post
Then I'll say I want A-ty(hex) item 1 and eighty(hex) item 2, how would you pronounce them?
"A Zero" and "Eight Zero" You say the characters.
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