[HN Gopher] My Love Affair with Dozens (1972) [pdf]
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My Love Affair with Dozens (1972) [pdf]
Author : dalke
Score : 48 points
Date : 2021-04-19 06:37 UTC (1 days ago)
(HTM) web link (www.dozenal.org)
(TXT) w3m dump (www.dozenal.org)
| canjobear wrote:
| For the Tolkien nerds, Elvish numerals use base 12.
|
| https://www.languagesandnumbers.com/how-to-count-in-quenya/e...
| n4r9 wrote:
| That system is base 10, although like a lot of Western
| languagea it has remnants of when it was in a different base.
| jacknews wrote:
| i much prefer seximal/heximal.
| prestonbriggs wrote:
| One of my favorite moments in literature: "... and nothing more
| was said - may God forgive me - of duodecimal functions."
| BasicQuestion wrote:
| Are there any algorithms anyone knows that are more efficient/
| can only be achieved in a given base?
| zokier wrote:
| I wonder if the original Atlantic article is available somewhere
| for reading, it would be interesting from historical curiosity
| point of view.
| Andrew_nenakhov wrote:
| Base 8 is ideal. Easy to count: multiplication table is almost
| half that of decimal, numbers have just a bit more digits than
| devimal, very easy to convert to binary.
|
| And we can count using fingers! Just discard thumbs! They are not
| standard anyway.
| chriswarbo wrote:
| Base 8 is pretty naff IMHO.
|
| 8's prime factors are 2x2x2, so the only nice patterns it can
| represent involve twos, fours and eights; but we can already do
| that using binary, so it's rather a waste of factors. Base 8 is
| useful as a 'compact notation' for binary (hence why it's easy
| to convert); along with base 16, base 24, base 32, base 64,
| etc. Even then, I prefer hexadecimal over octal.
|
| If we change one of octal's factors to a 3 we get base 2x2x3 =
| 12, which can represent patterns involving twos, threes, fours,
| sixes, eights and twelves. That's a lot more 'bang for the
| buck' than octal.
|
| Dozenal is still 'wasteful' by having two factors of 2. If we
| get rid of one we get seximal, which can represent patterns
| involving twos, threes, fours and sixes. In that sense, dozenal
| _almost_ a 'compact notation' for seximal, but not as easy to
| convert as octal<->binary; we get easy conversion for base 36,
| base 216, etc. but they seem unwieldy.
|
| The next meaningful jump up from seximal/dozenal is base 2x3x5
| = 30, which also seems unwieldy. Dropping the factor of 3 gives
| us decimal that we all know and hate ;)
|
| > And we can count using fingers! Just discard thumbs! They are
| not standard anyway.
|
| We can count dozenal _on one hand_ , using the finger joints.
| Our non-standard thumbs can be useful for pointing at the
| joints.
| Andrew_nenakhov wrote:
| > so it's rather a waste of factors
|
| Not really. Multiplication by two is by far the most common
| thing that happens in life (when cells divide, they divide by
| 2, not by 3). So easy multiplication by 2 AND 4 is far more
| important than the occasional by 3, which is no better,
| really, than in the decimal system.
| travisjungroth wrote:
| I enjoy dozenal. I also enjoy weightlifting. An interesting
| property of dozenal is how compatible it is with American barbell
| weights. I haven't heard anyone mention this before (who knows
| why. the intersection of mathematicians and powerlifters?)
|
| American weights are normally a 45lb barbell, 45lb plates, and
| then additional smaller plates. The large plates are just called
| "plates" and counted on one side. 1 plate -> 135 (45*2+45bar), 2
| plates -> 225, 3 plates -> 315, 4 plates -> 405. These seemingly
| weird numbers become "round" when you've been lifting them a
| while.
|
| What about jumps smaller than that? It gets a little weird. 45
| doesn't exactly break up nicely. You might have 35s, definitely
| 25s, maybe 15s (especially olympic lifters) then 10s, 5s, and
| 2.5s (called "twos"). "A plate, a twenty-five and a two" is 190.
| Then you get into "washers". Maybe a 1.25. Or if you have a few
| pairs of 0.75s and 0.5s you can make any integer.
|
| This is not ideal. You need to have more different types of
| plates than is most necessary. The math is summing up lots of odd
| numbers.
|
| Enter dozenal plates. I'll put a d at the front for dozenal
| measurements. A dozenal plate would be d40, or 48lbs. Pretty darn
| close to the 45s. The bar is also d40. So a bar with a plate on
| each side is... d100. Well that's nice. 2 plates -> d180, 3
| plates -> d240, 4 plates -> d300. And the smaller plates: d20,
| d10, d6, d3. If those jumps of 6 total pounds are too big, you
| could add d1.6, and d0.9 washers. All perfectly split.
| mellavora wrote:
| Not much of a powerlifter, but my working squat was > 2x
| bodyweight for a while.
|
| I find it easier to lift weights in metric. It helps that I'm
| EU based, so my plates are in KG.
|
| One plate is 20kg, and the bar is also 20kg Jumps smaller than
| that, 10kg, 5kg, 2.5kg, 1.25 kg. I've never needed to get down
| to washers, 1.25 kg jump is small enough to make even with
| 'small muscle' exercises (wrist curls)
|
| Powers of two all the way down, sums are easy.
|
| The trick is to do sets of 12. Sets of 10 are too easy. So the
| dozenal still comes in :)
| n4r9 wrote:
| That's a neat trick. Of course some of the number weirdness
| comes from that fact that standard kg plates are translated
| approximately into lbs in the US. So your 45lb plate is
| actually a 20kg plate and your 25lb plate is based on a 10kg
| plate. Although 10kg is actually around 22lb. I'm not sure
| whether the same colour plates genuinely weigh slightly
| differently in the US vs the rest of the world.
| bcbrown wrote:
| I don't understand the benefit - either system can accurately
| represent any integer number of pounds, right? And as you said,
| after a while the "weird" numbers become normalized after a
| little while. And it seems like you need the same number of
| different smaller-weight plates either way (45/25/10/5/2.5) vs
| d(40/20/10/6/3). If you want the plates to be integer multiples
| of each other, why not go with the already-widely-adopted
| kilogram weights?
|
| Also, with d(6/3/1.6/0.9), you're still summing up odd numbers.
| phamilton wrote:
| I feel strongly that base 6 or base 11 would make more sense than
| base 5 or base 10. yes, I have 10 fingers, but I can also
| represent 0 with no fingers, giving me 11 states.
|
| 11 is awkward, but using one hand for the ones place and one hand
| for the sixes place works quite well.
| loloquwowndueo wrote:
| That's because you're doing it wrong. Go full binary and you
| can count to 31 with one hand, 1023 with both.
| mellavora wrote:
| and this is surprisingly easy to learn.
|
| Start with the pinky, and 4 becomes an interesting number
| Nevermark wrote:
| 4 works fine with thumb = 1 too!
|
| But clearly you are right, the pinky is by nature the
| smallest digit. :)
|
| <Hand raised with 9> Rock on!
| ThrustVectoring wrote:
| Binary finger counting does not line up well with the manual
| dexterity of the human hand. What _does_ line up well is
| base-12 counting by touching each of 12 phalanges in your
| hand with the thumb in order.
| mellavora wrote:
| 16 hours since this post was made, and not one Spinal Tap
| reference. I'm getting old.
| zokier wrote:
| How often do you count with your fingers?
| jerf wrote:
| 11 is terrible for a numeric base, because it's prime. It
| doesn't evenly divide into anything until 121. 12 is nice
| because it's a highly composite number. 6 is as well, but kinda
| on the small side, and the extra 2 in 12 relative to 6 would be
| nice.
| kemiller wrote:
| Not mentioned is that you can count to 12 on one hand using your
| thumb to point to finger joints/segments and still have a zero
| state. So you can actually pretty compactly represent up to 144
| on your hands!
| phaedryx wrote:
| I worked with a member of the Dozenal Society of America. He
| taught me that pandas have 6 digits on each paw, which is why the
| panda is their mascot and why almost all panda merchandise is
| wrong.
| FredPret wrote:
| For a moment there, I held my breath, thinking the dozen is
| somehow built into the structure of Pandas, the Python library
| phamilton wrote:
| I once saw a carpenters square that was a foot long on each side,
| but one side was divided into quarter inches and the other
| divided into thirds of an inch.
|
| I was told it was used to make 3/4/5 right triangles, which was
| kinda fascinating.
| hervature wrote:
| Why would 3/4/5 right triangles be useful for carpenters?
| 30-60-90 are definitely useful though.
| pdbwimsey wrote:
| To make sure your 90 is really a 90. Easy and quick to check.
| hervature wrote:
| You can do that with the square itself.
| thechao wrote:
| You can check the _corner_ is square with a square.
| Checking the walls and the room can be done with a
| string.
| Grakel wrote:
| In layout, to determine a right angle longer than your
| framing square. We measure multiples of 3/4/5 on
| perpendicular walls to check their square, and then measure
| diagonally corner to corner to check again.
| Jedd wrote:
| Not parent, but I was also confused by the tool -- if the
| square (which is by definition 90 degrees where the two
| sides joined) is x and y long on the two sides -- then
| what's the purpose of being able to make a square from the
| 3/4/5 rule that's _limited_ to the x and y lengths?
|
| I'm having trouble explaining more succinctly why this
| seems like a totally pointless feature of a _woodworking
| square_ - so it 's possible I've misunderstood how it could
| be used to extend beyond the length of its arms.
| Grakel wrote:
| I just meant for a larger project we lay aside the
| square, and measure out 3/4/5 on the ground or whatever.
| So you're gonna dig the foundations of a house, use a
| string line and measure out 30 feet and 40 feet. If
| they're 50 feet apart, you're good.
| Grakel wrote:
| Oh I understand your question now, yes I agree.
| dadzilla wrote:
| a^2 (9) + b^2 (16) = c^2 (25)
| romwell wrote:
| Without addressing the benefits of using base-12, the supposedly
| simplifying arithmetic example is atrociously awful:
|
| >The clerks then described a typical problem, getting the cubic
| content of a package measuring 2'6" x 3'6" x 4'2"
|
| Duodecimals (or any positional system) are a bad representation
| of these numbers. The author proceeds with a very tedious
| computation of 2,6 x 3,6 in base 12.
|
| Instead, you can do it all in your head:
|
| 2'6" x 3'6" x 4'2" = (5/2)" x (7/2) " x (4 1/6)" = 35 x (1 1/24)
| ft^3 = 35 + 35/24 ft^3 = 36 11/24 ft^3
|
| There is more to say for the "duodecimal" musical notation, where
| each note lives on its own line (abolishing the sharps and
| flats).
|
| This notation is called _the piano roll_ , as it was already in
| use in mechanical player pianos. It's not great for writing with
| a pencil, but excellent for screens and editing - which is why
| most producers would go straight to the piano roll.
|
| It's not, however, connected to base-12 in any way.
| cjhveal wrote:
| One of my favorite language Youtubers, jan Misali, has an
| interesting video on Dozenal and "Seximal" (base 6) number
| systems.
|
| https://www.youtube.com/watch?v=qID2B4MK7Y0
| jacknews wrote:
| Very good, but I think all these alternate base systems need
| entirely different digits. People are too used to thinking of
| '10' as ten.
| a1369209993 wrote:
| Also has a followup at
| https://www.youtube.com/watch?v=wXeX_XKSNlc including a
| comparison of various bases in representing reciprocals (eg 1/3
| = 0b.010101 = 0s0.2 = 0d0.333333 = 0z0.4 = 0x0.555555).
| mkaic wrote:
| jan Misali makes excellent content! Most of what I know about
| linguistics I learned from him!
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