# Genuinely useful applications of Dozenal

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Bakers_Dozenal
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I've recently begun investigating Dozenal and I can see many of the mathematcal benefits.
One problem I have is in trying to convince other people who are non-mathematicians.
You might get so far with saying 12 has more factors than 10, which means there are more options for dividing things up evenly. This is a nice argument, but needs to be illustrated with a concrete real world example.
One was suggested to me was as follows:
"If I was dividing a pizza up before I knew how many people were coming to share the pizza, 12 would be a good number of slices to divide into.
I totally get this example, but it has some major weaknesses:
1. When did anyone ever divide up a pizza before they knew how many people were going to eat it?
2. The number of people coming changes the number of pizzas you should buy. No-one just buys one pizza hopes all of the 11 people they have invited will be happy with 1/12 of a pizza if they all turn up.
As I say the example is a fine illustration, but not realistic, so I ask:
"Does anyone have any genuinely real world examples which are understandable to the layman, where Dozenal really is advantageous?"
I think there might be something good in splitting the bill or dividing prize money, between teams (which maybe of size 1,2,3, or 4).
Any ideas gratefully recieved.

Dozens Demigod
Double sharp
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Joined: Sep 19 2015, 11:02 AM
Well, nothing is preventing you from using 12 as a number to divide things up easily even if your main base is decimal, as it is for all of us. The point is instead that 12 having more factors than 10 means that base 12 has more easy patterns in the multiplication table (think decimal 2 and 5; in dozenal 2, 3, 4, and 6 are all that easy). The fact that 3 is also among those factors means that thirds can now be handled directly as dozenal fractions instead of resorting to dealing with vulgar fractions or repeating decimals, although this is probably handier when adding fractions rather than dividing into fractions (because if the smallest unit is small enough, the error that truncating or rounding repeating decimals leads to can be considered negligible).

In general, I think the main difference between a dozenal world and a decimal world is in the basic arithmetic, which is unsurprising since the difference between using different bases is essentially about how arithmetic looks like. That, however, is not really a concrete difference by itself; it can only lead to them. So while a dozenal world may well improve children's acquisition of arithmetic (though this is hard to test), and may well result in increased numeracy in the general population, I think that real world examples would have to simply be examples of people dealing directly with basic arithmetic.

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Bakers_Dozenal
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Thanks for your comment Double Sharp. I appreciate your ideas. People doing basic arithmetic is good I can work with that, but I am still struggling to think of a case where I can actually apply this.

Dozens Demigod
icarus
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Joined: Apr 11 2006, 12:29 PM
I've written a lot about the subject of dozenal and I too am more interested in real world examples. I'm in construction, for chrissakes. My longwinded essay explains the whole thing in a more "grown up" way that could put the average person to sleep in less than a minute, perhaps. It's good for knowing the abstract nuts n bolts. Let's leave that behind and look at it this way.

Here in St. Louis, the local pizza is cut in bands that cross such that you get rhomboid "squarish" (ha if lucky) pieces, and you get "a ton" of them in various sizes, including the "sampler" tapa size corners. I think the commonest way to cut a pizza is to swivel the round pan and run the roller, whatever you get you get. Six, eight, even ten. Some studious pizza cutter people get to 8 before a dozen. I've not seen sixteen pieces or not notably often.

Focusing on the pizza question:

a. makes you jones for it.
b. overemphasizes what might've been a once-handy handle on what an author deemed a way of illustrating a wider point, e.g., a flexible means of reaching a more equitable partition of a greater whole.

The question that seems most basic is how to divide a unitary whole? I have this one big thing and I would like to divide it as flexibly as possible to cover as many instances as possible. A crate or box of eggs, a box of doughnuts (my I am getting hungry...), or pizza slices on 8th avenue and 16th street manhattan are things that come to mind, but a big thing that should also come to mind, and is far more basic, is the day.

There is a reason, despite people losing heads left and right in Jacobin France in the wake of revolution, why the decimal clock didn't tick. The notion was, systeme internationale was going to decimalize everything to make it easy. (some believed it ought to have been dozenal, cf. PDF page 173, which is 185/231) So divide the day into tenths. Read how it went (here). Ten is clumsy. You want a third of a day for shifts. I don't know why three. Why couldn't people be happy working just what amounts to six hours or slog on to a half day? Don't ask me. I work ten hours a day, when I work. Which is oddly nondecimal. Surely one might use .375 of a day, but ask Generation Millennial falcon what 3/8ths ackshully, like, is, and you'll, like, literally, get a blank stare. "three eighths? Is that even, like, possible?" (to be sure, my generation invented "like", like, way back in the day and y'all caught it and for that I am totally sorry, dude. The advantage of tossing in a couple likes in a sentence is it gives us time for the rocks to stop rattling around in our head when we have to think. Which is like too much trouble.) You'll more likely get "why don't we like just make it 3 tenths of a day?" but that doesn't come out in the end. There's one tenth of a day where people are standing around scratching heads. Even if the world were brighter, we would get .333333333333333333333 of a day and that is mighty inconvenient. So we find it easy to go on using twenty-fourths of a day, which were originally just twelfths, something the Romans did. The romans had tens above and twelfths below, and thereby we had ounces and inches. Why? Because didn't they use roman numerals? Well that would prove troublesome. XII inches? Why not just X? Because twelve is convenient, man. That's why until jackbooted global "leaders" foist the "revolutionary" systeme internationale upon us all to make us One, we used inches and ounces and shillings etc. in profusion. It is more convenient to break a master unit into dozenths or multiples thereof, because we then get division into 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 64, 72, 81 (under 100) rather than 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, (okay, 100) under same arbitrary limit. And breaking something into threes is more commonly needed than breaking things into fives.

When we frame a house, we divide a panel into thirds. (here in the US it's 48 inches broken into 16 inch stud spacings). Sometimes halves. This panel, 1:2 in aspect ratio, is divided into fours or sixes the other way. Look at all the construction in your town today. It's been done like this for a long time. If I am striking a bridge over the river Kwai I want one, maybe two piers, much less I want three. By the time I get to four piers, well is there a river Kwai? Or a dam over the river Kwai? Three is the "magic Number". Look up why. We tend to get to three more commonly than 5, and threefoldness appears in life more often than fivefoldness. Mr. Benford and his law would agree.

Now you say, "You Americans" and I would say, "who, us? Disunited us?" and you would resume, "you cling to that silly inch and foot thing" and I would say, "thank the Good Lord Above". So let's push aside US Customary and leave inches behind. We find in metric countries the curious module "1200 mm". const.png
Why? The same as why we have 4'-8-1/2" railway track because Roman chariot? (fact check if you believe in the whole concept of ensuring you're on point with the narrative du jour, eastasia, eurasia, who can keep track, pun intended).

Okay let's say the canucks are too close for comfort to their imperial overlords to the south, or maybe simply that they did use the "Imperial" system too long and too recently and all their equipment manufactures what had been 48 inch paneling and studs 16 inches on center, etc. Let's go to La France. Right from the horses mouth: Example: "Hauteur Meuble Salle De Bain Norme étonnant Logiciel"

const2.pngThis is the layout of cabinetry. (Edit: note the 1 mm tolerance there for the micro-onde / microwave! 761 mm! That's really funny! That ain't gonna happen: they'll prolly get 750 mm to line up with edge of sink. Unless it is existing)

Cabinetry is a great example of needing to divide into flexible modules such that we can get whatever we need. We might want a washer and a sink and a couple drawers and big drawers for those fancy cooking utensils Mom likes to use on Easter, and a narrow little sideways pull out drawer for the trash, etc. we get a variety of widths, but have to divide a master unit (the length of the kitchen). I am an architect and keenly know the module in the US of A is three inches. Our notation is in inches. We would write "4230" for a 42" high, 30 inch wide cabinet.

En France they seem to use that old 1200 mm again. Quel domage! What about le metre sancte? Why not take the meter and divide it into, say, 75 mm increments, or just use 100 mm increments? Why did we get forced to three places in the first place? I mean why 1000 mm? Is it, could it be divisibility? Yes. We have simple, flexible inches and can divide away. But with metric decimal wobblyness, we are forced to le mille so that we avoid fractional mess wherever the heck we're trying to use number in a very practical way, like the jobsite. We want as much as possible to avoid the decimal point, because it gets lost in translation on the grubby muddy worksite. So we use millimeters, and make it so we can ably cut it in half, thirds, quarters, (we get fifths), sixths. That's why we use 1200 of them and not 1000.

Twelve hundred hunts. Ten hundred puts you through paces and jacks everything up.

I can cut twelve in more ways than I can cut ten, and I get to choose the ways as necessary. Ten makes me jump to government-approved folly. (here meaning some pointy-headed bow-tie wearin apparatchik "expert's" opinion of what hunts, for those of you who likes them some gubmint and to be told what to think from your betters.) Even without my survival bunker libertarian schtick, you know you got more and smaller, more convenient choices with the dozen than you have with ten. Truth is truth. (Quid est veritas?)

So the entire "pizza" argument is a sort of quick, handy way to say, "flexible divisions that give you the common man the freedom to design things your way, not LE METRIQUE COMMISSION D'EUROPE ET TOUT LE MONDE's" jackbooted way. Not even Le Roi's (or bad bad leroy brown baddest man in the whole damn town's) way. Your way, as you see fit. And you'll need thirds, because threefoldness appears more often than fivefoldness. Make your gubmint grabby taxes out in triplicate; good, bad, and ugly; gimme three steps; easy as abc 123; once, twice, three times a lady; two's company three's a crowd. It's just the way the universe works, and 10 is not as suited as 12 at dealing.

Ha it's funny, the construction approach is not as "shine on your brother everyone's equal" soviet way of approaching pizza distribution. (soviet pizza? I think that's a great oxymoronic name for a place! You'd have to wait in line and then it would taste horrible once you got your ration and you'd be sorry you got it but thankful for not starving, then you might be sent to gulag for any complaining to the People's Cook. But you'd be equal, just as Rush once sang, "the maples formed a union / and demanded equal rights / "the oaks are just too greedy / we will make them give us light!" / now there's no more oak oppression / for they passed a noble law / and the trees are all kept equal / by hatchet, axe, and saw) It's have your cabinetry your way. The way you need, not us.
Flexibility = Freedom.
This is just a start. Want more I gots more. Even in different shticks. We could try the potpourri scented shtick next, because the dozen, being the product of 2² and 3 yields 6 divisors, 4 of them the smallest possible integers, and 10 doesn't offer as much. Independent of shtick, creed, color, political persuasion, the whole ammonia-vs-water as "best drink" controversy we hear throughout the universe (water is so speciesist). But it's okay. We could've ended up with base 8...after all, thumbs technically aren't fingers...

The flexibility of the dozen is so strong I even covered the counterargument, but it's kind of mussed on this site now the way it is. This is how we know something is true. Try to knock your pet belief down. I did leave my church (and came back). I did visit "The Enemy" when it was still soviet. Kick those tires*. If they deflate, well. They weren't Lightyear brand Lightning McQueen tires*, were they. (*English: tyres).

; )
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Obsessive poster
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In terms of flexibility, here's a tidbit: Consider how many different ways there are to arrange a dozen objects, be they eggs, donuts, whatever.  Let's go with donuts.  You could pack them in a single layer in two rows of 6, or in three rows of four. Or you can have two layers with two rows of three each.  Now, how many arrangements of ten items can you make?  Two rows of five each. That's it.

All sorts of stuff used to be sold by the dozen, and much still is sold that way. When you've negotiated to to buy a dozen things from someone at a certain price, and then at delivery time they try to force you to accept only ten items for that price, they're trying to "dicker you down". "Dicker" comes from Classical deca/decem.  A dozen used to symbolize fair value, ten symbolized getting cheated.
As of 1202/03/01[z]=2018/03/01[d] I use:
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Silvano2
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Icarus,
Please don't use French if you don't know it.

The reason why the decimal day didn't catch up was there was ONE system of time measurement, and this system couldn't be changed if you didn't rebuild all the clocks all over the country, while weight, length and capacity measurement was a mess.

Obsessive poster
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Silvano2 wrote:The reason why the decimal day didn't catch up was ...
I think the idiom you were looking for was "catch on", which means "to become popular". To "catch up" means to "come up to or overtake" someone or something, for example in a race.  But, being charitable, I think we all know what you meant.

Silvano2 wrote:Icarus, Please don't use French if you don't know it.
If we were not being charitable here, Icarus could easily retort that you shouldn't use English if you don't know it.

Silvano2 wrote:... there was ONE system of time measurement, and this system couldn't be changed if you didn't rebuild all the clocks all over the country, while weight, length and capacity measurement was a mess.
This is an interesting observation, one that I honestly never considered before.  I can see how that may have been a factor.  But at the time of the French Revolution, could we even say that this one system of time was actually very well established? By that I mean, the whole system?  Certainly hours of the day might have been in the consciousness of the general population, perhaps half-hours and quarter-hours too, especially if the clergy in the nearest church tower were punctual about ringing the bells. But how many people really were thinking in terms of minutes and seconds?  France, and Europe in general, was still largely an agrarian society. Industry existed in the form of various skilled trade guilds in the major cities. But this was still the very pre-dawn of the industrial revolution and not even the Age of Steam.  No railroads yet, with their down-to-the-minute timetables.  Perhaps the scientific elite might have been familiar with minutes and seconds, but would the average sans culotte ever be in possession of an expensive pocket-watch?

I still think the main reason decimal didn't take off or take hold () was that people who were used to "a quarter past" and "a quarter til" happening when the big hand reaches the nice-and-simple 3 and  9, respectively, could not stomach the notion that those would now occur at the 2.5 and the 7.5, with those fiddly decimals. I'm sure that must have been a case of practical people disdaining the pedantry of the eggheads.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
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Dozens Demigod
icarus
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Joined: Apr 11 2006, 12:29 PM
Ok, silvano2 (what happened to the original??) Okay I won't use french. Let's use swiss.

.beat was cool for about a beat. It decimalized the day into thousandths. Know anyone using it? (I wish I had one of those watches.) Curiously it does say one can still get into .beat. The converge-o-pedia article does suggest that .beats are an extension of French Revolutionary Time so we still can't shake le français. Savvy? (Sorry, even more French. I can't help it, our city hall is a replica of le Hôtel de Ville - not a hotel - as this city is daughter of Paris, named after a saintly king. None of our leaders are saintly now, when we most need it).

I am not sure anyone can completely wash extant systems from memory. We'll have to wait till there are colonists on Mars (you know my thought on this - we're too involved in our navels and crippled by our own sentiments to do this anymore) who might use whatever system they please there on another planet. Any reason not to decimalize? They will use sols, 668.69 to a martian year. Surely they have to coordinate with Mission Control so even then that might infect them. The other scenario is the one I think we are more certainly in for, and not long from now, maybe within our lifetime. When society falls and we are disconnected from one another in a way that hasn't happened for a thousand years, it will be once again possible to have communities adopt various systems of time. Short of a "system reset" and the renewed need to track time, we won't be rid of extant systems.

This leads us to ponder why the extant system was the system to "win out" and remain in place for more than a millennium. if you are a Darwinist then you would suggest "survival of the fittest". This exercise in thought leads us to consider other things that have "survived" and are ubiquitous...

No one wants to use an awkward system.

Decimal time _is_ in use in certain punch-clocks. The reason why it works there is that they are simply logging tenths of hours. If you worked 2:15 hours, say from 8 pm to 10:15 pm, you'd punch and see 2.3. This was in a day when it was a pain to add another digit or resort to sexagesimal logging of hours. The equivalent of .1 hour is 6 minutes, so it frames quite well with extant systems. Another decimal place would issue problems in conversion, but might also be used. The boss would speak of "working two point three hours Wednesday night" but beyond that she would say "ten fifteen" or a quarter past ten is when to quit.

But I digress.

If you are french look into an old book called «Douze, notre dix futur». You might prefer his writing over mine.

Something that is curious is that decimalization does take, provided we have enough places such that the error doesn't matter. Commonly we use percents and parts in a thousand to do what we might with dozens. 1/3 then would be 333, as if on a gas (petrol) pump. If we get a bit more or a bit less no one cares. So in .beat time, maybe it's okay that, having arrived at work at 333, I can leave at 667. It still looks inelegant.

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What I want to know is why the French Metricists, supposedly so scientific and logical, seemed incapable of actually applying their own systematic procedures to time? Why did they describe a tenth of a day as a "decimal hour", a thousandth of a day as a "decimal minute", and a hundred-thousandth of a day as a "decimal second"; when they could easily have called these the "deciday", "milliday", and "centimilliday"  respectively? (Although I suppose in French those would have been décijour, millijour, céntimillijour.)  Of course, then they might not have given short shrift to the intermediate powers like the "centiday" (14.4d minutes), and the "decimilliday" (8.64d seconds). Eventuslly, once they enhanced the prefix system, they could have referred to the "microday" (0.0864d seconds) and so forth. It's really ridiculous to me how so many people, over so many eras, have been completely brainwashed into thinking that the only way to measure time is with units that slavishly emulate the old Babylonian system of "hours", "minutes", and "seconds". Metric was supposed to be decimal base, not centessimal-wannabe-sexagesimal base.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Dozens Disciple
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Bakers_Dozenal wrote: I've recently begun investigating Dozenal and I can see many of the mathematcal benefits.
One problem I have is in trying to convince other people who are non-mathematicians.
:
"Does anyone have any genuinely real world examples which are understandable to the layman, where Dozenal really is advantageous?"

Any ideas gratefully recieved.
I think we have wandered slightly from this original request.
What examples do we have that will persuade (if not actually convince) the layman that dozenal is better than decimal?

Dozens Demigod
Double sharp
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Kodegadulo wrote:Certainly hours of the day might have been in the consciousness of the general population, perhaps half-hours and quarter-hours too, especially if the clergy in the nearest church tower were punctual about ringing the bells. But how many people really were thinking in terms of minutes and seconds?  France, and Europe in general, was still largely an agrarian society. Industry existed in the form of various skilled trade guilds in the major cities. But this was still the very pre-dawn of the industrial revolution and not even the Age of Steam.  No railroads yet, with their down-to-the-minute timetables.  Perhaps the scientific elite might have been familiar with minutes and seconds, but would the average sans culotte ever be in possession of an expensive pocket-watch?
A clock with a minute dial was first mentioned in a 1475 manuscript (see the Wikipedia article History of timekeeping devices; it's cited), and minute hands on portable timepieces first became the norm in the 1650s according to this article. Both of these are quite a while before the late 18th century, perhaps giving the innovation some time to trickle down into the general consciousness. The average sans culotte indeed probably didn't have a pocket watch of his or her own, but by the time of the French Revolution some public clocks did have minute hands. Indeed the Wikipedia article notes (again, cited) that one factor that doomed the adoption of the decimal clock was the cost needed to replace all the nation's clocks.

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Bakers_Dozenal
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Just as a reminder of the question I originally asked.
Does anyone have a convincing practical example of where dozenal would be superior to decimal, that would be suitable for a layman to understand.
It seems that many of the people on this forum are alreeady so convinced of Doudecimal's superiority that they have forgottent the reason they were so convinced in the first place.

Obsessive poster
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Well, getting back to the practical superiority of dozenal: One thing that a few of us here have experienced in our dabbling with metrologies, is that the great richness of regular numbers in dozenal compared to decimal makes it rather easy to find auxiliary units that can enhance an otherwise sterile "dozenal-metric" system, without actually degrading its "metricness".

For instance, consider Primel's 'biqua•lengthel, or 'ell•length. That's a pure dozenal-metric power of Primel's base unit, the 'lengthel or 'morsel•length. In pure "metric" fashion, it can be divided into a dozen 'unqua•lengthels or 'hand•lengths, and each 'hand•length in turn can be divided into a dozen 'morsel•lengths. We can of course extend this "metricization" in both directions by continuing to multiply or divide these units by dozens.

But we're not limited to that scheme. We can easily divide the 'ell•length into four 'foot•lengths, each a close approximation of the TGM Grafut, and each exactly three 'hand•lengths. We can "metricize" the 'foot•length by dividing it into a dozen 'thumb•lengths, each an approximation of an inch, but each exactly a quarter 'hand•length or exactly three 'morsel•lengths. We can extend this "metricization" of the 'foot•length in both directions and effectively get a close approximation of the entire TGM system as a free bonus, all embedded right within Primel, without ever straying from "pure" Primel powers by anything more than simple one-digit subitizing factors of 3 or 4.

Imagine how the building trades for instance would benefit from this in a Primel world. You could get boards or sheets of materials in standard 1 'ell•length "modules" and then easily cut them in quarters into 1 'foot•length "submodules". Or you could just as easily divide them in thirds into 14z•'thumb•length = 4•'hand•length sections, like the usual stud separation.

And this kind of dove-tailing carries through to all scales. A 'dromal•length is a galore (1000z) of 'ell•lengths (a 'triqua•ell•length or 'pentqua•lengthel). That's almost exactly 2 kilometers, kind of a big brother to a mile, and what I expect a Primel world would use to measure road distances (hence "dromal").

But a galore of 'foot•lengths (a 'triqua•foot•length) is also a useful quantity. It's almost exactly half a kilometer, and hence quite a good approximation of a Chinese li, which is traditionally considered the length of a Chinese farming village (Latin rus), hence the colloquial name 'rustical•length.

Well, a 'rustical•length is simply a quarter of a 'dromal•length, or exactly three 'stadial•lengths (which are dozenths of a 'dromal•length). Thus we see exactly the same interplay between two interleaved "dozenal-metric" scales, with simple subitizing factors of 3 and 4, that we saw at the 'ell-'foot-'hand-'thumb-'morsel level.

The "Primel Zoom" presentation I put together a couple years ago demonstrates that the exact same dove-tailing works at all scales, from the microscopic to the cosmic. The key point is if we stray from a "pure" dozenal-metric power by a factor of 3, a subsequent factor of 4 snaps us back onto the next power -- and vice versa.

------
Now let's compare the situation in decimal metric. Practical cases of needing to divide by 3 or 4 are going to arise, but decimal metric will make this a challenge. Dividing a meter of construction material in four is not a simple matter of measuring decimeters; you have to get down to the centimeter to express 25%d. Dividing by 3 is even more problematical; you have to avail yourself of any and all digits available in order, for instance, to express 33.3% -- but even then it's only an approximation. Hence we are forced to use millimeter accuracy or better for tasks that wouldn't have required that in dozenal.

We could try to alleviate this by sneaking in a factor of 12d, and use 1200d mm as a modular unit. Think of it as a kind of "metric•ell". Well, in one direction it can be divided into four "metric•feet" of 300d mm each, or a dozen "metric•hands" of 1 decimeter each. A "metric•foot" can be divided into a dozen "metric•inches" of 25d mm each, or a quarter of a decimeter ("metric•hand") each.

But then what? There is no neat whole number of "metric•ells" that will snap nicely into the decameter, the next pure power up. Nor is there any neat multiple that will evenly fill a hectometer -- or a kilometer -- or any decimal power of the meter. In the other direction to snap from a "metric•inch" to the next viable pure power down, we either need an awkward factor of 2.5d to yield a centimeter, or 25d to yield a millimeter. Forget about trying to divide this by 3 to get a "metric•morsel" of 8.3333...d millimeters, or by 12d to get a "metric•line" of 2.08333...d millimeters (whereas in Primel a 'linial•length of 0.3z 'morsel•length is perfectly doable).

This trick of sneaking in a dozenal factor can only go so far. The more you try to play that card, the more you might as well go completely dozenal. But in most cases, the intrinsic powers of ten are all you've got to work with. So the tendency is to express quantities using lots of fiddly digits of precision -- oftentimes excessive precision.  Gives you the illusion of scientific accuracy, but in reality it just grants the con-artists more opportunity to mesmerize you with numbers to the point where they can easily swindle you.
Last edited by Kodegadulo on May 9 2018, 02:41 PM, edited 1 time in total.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

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Silvano2
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icarus wrote: Ok, silvano2 (what happened to the original??)

Dozens Demigod
icarus
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Joined: Apr 11 2006, 12:29 PM

Divisibility. I have not forgotten the reason.

[EDIT]

Flexibility. Most of the flexibility of the number twelve derives from its divisibility.

Where ten is
 1 2 4 8 16 ... 5 10 20 40 80 25 50 100 200 400 125 250 500 1000 2000 625 1250 2500 5000 10000 ...
we have in twelve (dozenal):
 1 2 4 8 14 ... 3 6 10 20 40 9 16 30 60 100 23 46 90 160 300 69 116 230 460 900 ...
This grid is denser and contains smaller numbers, numbers that crop up more often in life because of this fact. From this divisibility and flexibility all the benefits we can describe about base twelve derive.

 Posts 615
Dozens Disciple
Paul Rapoport
Dozens Disciple
Joined: Dec 26 2012, 01:59 AM
I just had a look at the Swatch .beats, thanks to icarus. I don't know how well a sort of UTC based in Biel has worked out. If it has merit, then surely using real UTC in dozenal, based in Greenwich, not the commercially promoted Biel, should work even better. (That a few of us want to base UTC in Munich is a separate issue.)

Some know that I've produced UTC clocks in many configurations, in both the traditional sexagesimal and the preferred dozenal, including time bands (not zones) and ways to know where the sun is locally (not "local time"). Also, if you want a decimal clock, with ten divisions of the day in both analog and digital formats, go here.

All that by way of saying the obvious: telling time dozenally is much better than the traditional sexagesimally. Even straight dozenal time (no UTC, no roving numerals) is simpler. So there's one answer to the original question: take the traditional clock and extend its dozenal properties thoroughly. As others know, using dozenal time in the TGM way (also available here) preserves hours and just divides them by powers of a dozen. That too is better than the traditional way.

Kodegadulo's Uncial Clock Deluxe is also an elaborate demonstration of the same point.

harold.potts.46
harold.potts.46
icarus wrote:

En France they seem to use that old 1200 mm again. Quel domage! What about le metre sancte? Why not take the meter and divide it into, say, 75 mm increments, or just use 100 mm increments? Why did we get forced to three places in the first place? I mean why 1000 mm? Is it, could it be divisibility? Yes. We have simple, flexible inches and can divide away. But with metric decimal wobblyness, we are forced to le mille so that we avoid fractional mess wherever the heck we're trying to use number in a very practical way, like the jobsite. We want as much as possible to avoid the decimal point, because it gets lost in translation on the grubby muddy worksite. So we use millimeters, and make it so we can ably cut it in half, thirds, quarters, (we get fifths), sixths. That's why we use 1200 of them and not 1000.

Twelve hundred hunts. Ten hundred puts you through paces and jacks everything up.
OK.  Your comment is actually coming from someone on the outside looking in and is totally clueless.  Can you show me in any of the BIPM or CGPM documentation that insists or requires the use of 10 for everything?  Fact is, you won't as there is no requirement.  This type of comment comes from those people upset that they are in a minority when it comes to units of choice and are looking for excuses to convince the majority that SI units aren't useful.

The only place that the number ten is important is the ratio of the prefixes.  Each prefix is scaled based on a power of 10.  Nowhere else is 10 encountered.  The units are all on a 1:1 basis with each other.

SI does not dictate to users their number choices, that is up to the professions and the professions have chosen the millimetre.  In construction, the 100 mm module is the standard and any value that is an increment of 100 mm is acceptable.  Thus one will encounter 300, 400, 600, 1200, 180, 2400, 4800 mm, etc modular components.

In fact the 100 mm module is an ISO standard:

https://www.iso.org/standard/5470.html

So, rather than look and sound ridiculous by lack of knowledge, you need to research the reality and make conclusions from that.

harold.potts.46
harold.potts.46
Silvano2 wrote: Icarus,
Please don't use French if you don't know it.

The reason why the decimal day didn't catch up was there was ONE system of time measurement, and this system couldn't be changed if you didn't rebuild all the clocks all over the country, while weight, length and capacity measurement was a mess.
I agree.  Also, the SI already has a fixed and accurate time unit if you want to use it, it is the second (s).  But, we still need clock reform in such as a way as to eliminate once and for all the 12 h notation and go completely 24 h.  No more confusion with what am and pm means.  Also, dates and times need to be universally stated in the ISO 8601 date & time format.

That would be reform enough.

harold.potts.46
harold.potts.46
icarus wrote: Ok, silvano2 (what happened to the original??) Okay I won't use french. Let's use swiss.

.beat was cool for about a beat. It decimalized the day into thousandths. Know anyone using it? (I wish I had one of those watches.) Curiously it does say one can still get into .beat. The converge-o-pedia article does suggest that .beats are an extension of French Revolutionary Time so we still can't shake le français. Savvy? (Sorry, even more French. I can't help it, our city hall is a replica of le Hôtel de Ville - not a hotel - as this city is daughter of Paris, named after a saintly king. None of our leaders are saintly now, when we most need it).

Something that is curious is that decimalization does take, provided we have enough places such that the error doesn't matter. Commonly we use percents and parts in a thousand to do what we might with dozens. 1/3 then would be 333, as if on a gas (petrol) pump. If we get a bit more or a bit less no one cares. So in .beat time, maybe it's okay that, having arrived at work at 333, I can leave at 667. It still looks inelegant.
Beat has never taken off because beat is not harmonised with the second.  The second is the true SI unit defined from the Cesium Atom.

Current definition: The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
Proposed definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.
There is no need for a unit called beat and since the second is defined by the BIPM and if the BIPM doesn't sanction any other unit (they never will) don't expect it to take off.

There is this hang up with opposers to SI with division by 3.  Since SI doesn't demand what the numbers used with the units are, there is no demand to use 1, 2 & 5 as factors and in many engineering and commercial systems, numbers are picked that are easily workable.   Thus factors of 100 mm or 300 mm are quite common.  1200 mm and 2400 mm divide nicely into 3 if three is that important to you.  It's just amazing the this fixation with division by three is only mentioned by people on the outside looking in and never by real workers and manufacturers.

You may keep repeating your fantasy but only you will be convinced by it and since you are of no importance no one else will listen to your arguments.

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
Well harumph harry ain't you a happy knowitall? How's bout a how are ya before you totally get psycho vicious?

if the BIPM doesn't sanction any other unit (they never will) don't expect it to take off
So a fan of top down and not a fan of grassroots are ya? Ok. Whatever gubmint and a gang of closed-door technicrats say goes.

people on the outside looking in and never by real workers and manufacturers

Long live the Real Worker and Manufacturer!
(In this brief instructional clip, icarus is played by Ellie Goulding "on the outside", this argument (and the Real Workers and Manufacturers, may they ever live, like Real Wisconsin Cheese) is represented by the brunette "on the inside", and Measurement Itself is Calvin Harris.
since you are of no importance
Ad hominem. Grounds for censure. Watch it. Unless you can prove I am actually of zero importance, you can find another way to make your point, or rant somewhere else. Mt 10:26-33, right from the Boss. Sorry. Try again.

Right now, given the energy with which you're attacking me specifically, ex nihilo, you have degraded your otherwise reasonable argument, like a tadpole flailing around in a teacup. You can discuss these things without all this negative emotion. This will frip your bonnet: I don't give a damn.

 Posts 29
Casual Member
hotdog8
Casual Member
Joined: Feb 21 2018, 01:52 PM
I must point out to you Harold that just because scientists CHOSE the Caesium-133 atom, obviously because it has such a fine tiny period of radiation such that they could calculate a whole number that co-incidentally happens to equate with the second, doesn't mean that somehow this proves that decimal is superior. The decimal number of periods per second of 9192631770 can be expressed dozenally as well i.e. 1946716076

harold.potts.46
harold.potts.46
icarus wrote: Well harumph harry ain't you a happy knowitall? How's bout a how are ya before you totally get psycho vicious?
I love how you deliberately connected into by my conclusive comments but failed to answer the questions or comment on the points.  Care to?  Tell me where it is written that only factors of 10 can be used.  Tell me about how often you needed to divide a measurement into thirds and resulted in a repeating decimal value.  What's that?  Never.  Just as I thought.

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Yep, pretty much a troll. Not interested in a civil conversation, just one-upmanship.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
harold.potts.46 wrote: But, we still need clock reform in such as a way as to eliminate once and for all the 12 h notation and go completely 24 h.  No more confusion with what am and pm means.  Also, dates and times need to be universally stated in the ISO 8601 date & time format.

That would be reform enough.
This is really rich. Harold my boy, I work in the software industry, so I'm the insider on this one: ISO 8601 is a format for data interchange of dates-and-times between computing systems. And it's already the norm in my industry. So your pontificating to us about it is the equivalent of some busybody scolding everyone to buckle their seatbelts and wash their hands and brush their teeth and don't smoke indoors. That battle is already over ... didn't you get the memo?

ISO 8601 is perfectly logical: put the parts of the date and time in order of significance: year, month, day, hour, minute, second, etc... I've been doing it that way myself for years, long before 8601 was even a thing. I even do it in dozenal Primel ⚀trice-time. For instance right now my local date/time (including timezone) is 1202-06-12.856−200z (in decimal that would be 2018-06-14T16:55−04:00d). (You can see I express the time down to the ⚀trice as just a dozenal fraction of the day after the radix point.)

That said, 8601 is not a dictate from Big Brother about how everyone must talk dates and times in all walks of life. Just a contract for how computers will talk dates and times to each other reliably. It's a practical thing, not a governmental/bureaucratic thing.

So I'd appreciate it if you cut it out with this "have-you-stopped-beating-your-wife" shtick of yours, Harold.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)