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 2020-08-12, 17:50 #78 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 100010001010112 Posts 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.
2020-08-12, 22:44   #79
chalsall
If I May

"Chris Halsall"
Sep 2002

928610 Posts

Quote:
 Originally Posted by Uncwilly 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...

2020-08-13, 05:51   #80
tuckerkao

Jan 2020

23×3×5 Posts

Quote:
 Originally Posted by Uncwilly 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.
Attached Thumbnails

Last fiddled with by tuckerkao on 2020-08-13 at 06:03

 2020-08-13, 06:05 #81 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 132708 Posts 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?
2020-08-13, 06:23   #82
tuckerkao

Jan 2020

23×3×5 Posts

Quote:
 Originally Posted by retina 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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Last fiddled with by tuckerkao on 2020-08-13 at 06:40

 2020-08-13, 10:33 #83 tuckerkao   Jan 2020 23×3×5 Posts 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. Attached Thumbnails     Last fiddled with by tuckerkao on 2020-08-13 at 10:38
 2020-08-13, 12:28 #84 Dr Sardonicus     Feb 2017 Nowhere 22·5·179 Posts 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
2020-08-13, 12:37   #85
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

23×727 Posts

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 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.

2020-08-13, 13:35   #86
S485122

Sep 2006
Brussels, Belgium

2·7·113 Posts

Quote:
 Originally Posted by retina ... 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

2020-08-13, 13:40   #87
tuckerkao

Jan 2020

23·3·5 Posts

Quote:
 Originally Posted by Dr Sardonicus 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 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 (22²). 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 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.

Last fiddled with by tuckerkao on 2020-08-13 at 13:49

2020-08-13, 13:48   #88
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

8,747 Posts

Quote:
 Originally Posted by tuckerkao 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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