Please Answer These Questions About "Dozenism"

Use this forum to discuss properties of number bases in general.

Please Answer These Questions About "Dozenism"

DominusVobiscum
DominusVobiscum

Dec 19 2006, 11:12 AM #1

Firstly, I would like to know how many people here believe it is actually possible for society to transition from the base-ten counting system to a base-twelve counting system. Do you believe it is really possible to create a movement influential enough to make such a transition possible? Or is this, really, more of a pipe-dream?

is it feasible? One must remember that Change is, in and of itself, a Negative, in the great work and expense it requires and in how it ruptures history and disconnects us from the Past. Thus, in order for any change to be acceptable, the benefits the end result is projected to bring must outweigh the destruction wrought by the change itself. Even then, it is a gamble. And even then, people might not go along with it. They might not be willing to "go over the hump" for whatever returns are on the other side. This is one reason why Esperanto and other such "universal language" attempts failed.

Lastly, and most importantly, is this project, as whole, beneficial. I strongly, strongly, strongly believe in the inherent superiority of that which evolves organically in society over that which is "pre-planned" based on some airy, intellectual theory. I strongly believe in the Natural, the Traditional, and the Organic over the deliberately engineered and implemented. This is the second big reason why Esperanto failed, in my opinion. For one this, engineering and implementing a change created destruction, chaos, and rupture--at least in the short term. Secondly, I also believe that engineered, micro-planned things are almost always inferior to that which evolves organically out of the natural flows of Human Society. Many, perhaps, think this hogwash, but I am strongly convinced of this concept.

Thus, a deliberate change in such an ancient and embedded aspect of our civilization as our counting system must have strong justification, to outweigh these negatives. I accept that it might be more mathematically convenient, due to factoring. But the question is this: Is it more natural to the human Psyche? If not, no argument based on "scientific efficiency" would justify it me, as science has gotten along just fine with base-ten. I would rather the scientists, capitalists and engineers (they are, after all, trained at this stuff) have to deal with the "inefficiency" of 3.333333 and so forth, than our civilization, as a whole, have to deal with a counting system that is not natural to the human mind.
And the evidence seems to show that the base-ten system is the most natural system for the human mind, as most culture (admittedly not all) have, often independently developed base-ten counting systems on their own. I understand that this is likely due to the fact that we have ten fingers on which we tend to count. Thus, it seems that the base-ten system is inherent in our very Anatomy! Admittedly, that is a physical trait, not a psychological one. But I feel such aspects of our Being tend to be intimately connected. Even speaking from the standpoint of evolutionary theory, after countless millennia of counting on our ten fingers, may we not have evolved brains more "in tune" with counting by tens than with counting by twelves. And, in any case, is it not useful to be able to count round numbers on ones fingers, which can't be done in a base-twelve system?

I suppose the 64,000 dollar question, for me, is: What is more natural to the Human Psyche, the Number Ten or the Number Twelve?
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DominusVobiscum
DominusVobiscum

Dec 19 2006, 11:37 AM #2

One more thing I forgot to add: what mechanisms would you propose to use to implement this change? I hope not through enforced government mandate. To me such enforcement and micromanaging would be unjust even if the overall superiority of the Twelve system could be proven. Rather you must convince the populace to voluntarily accept this change of their own free wills. To me that is very, very, very important.

Thank you and blessings,

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

Dec 19 2006, 02:31 PM #3

JJ,

I don't believe a society should be coerced to change a la government mandate. The systeme internationale (metric) didn't exactly go over very well in the USA, although some industries use converted customary measure in manufacturing.

We are familiar with human societies coping with less than optimal situations. There are cities at far northern latitudes, where the temperatures are extremely cold, something that isn't optimal for the human's initial natural (tropical) adaptation. People can live at high altitudes, and have acclimated. So it isn't necessarily true that just because mankind uses a less than optimal base that dozenal advocacy is unwarranted.

I believe dozenal is the optimal base for humanity. It is a natural "round number". The dozen is easily divisible by simple ratios, into fractions familar to the common man for millenia. The multiples of a dozen crop up most often in the commonest simple calculations. So dozenal's greater efficiency isn't just some engineer striving for a smoother glide. I think the efficiency and ease of use is an enabling mechanism. Fractions and computation become easier for those who use dozenal.

Dozenal differs from "Centrally planned" concepts like high-rise public housing, the esperanto or interlingua movements, communism, etc. in that it is not "planned". Dozenal is a method of numeration related to decimal in its position-based notation. The only difference is that the numeration system uses 2x2x3 rather than 2x5 for its base. Adjunct to this difference are systems of measure and quantification, and nature of symbols and nomenclature, that are or would be socially conceived. The most successful method of conceiving these adjunct properties would be that society develops them "organically".

I believe that one should use dozenal whenever practical, that the individual employs it "organically". Through practical everyday use, applications of dozenal should arise that, because these applications are advantageous in the marketplace, the dozenal process can be supported in society by its own merit. Let the marketplace decide what dozenal applications make sense. Forcing people by edict to use a technique, however superior, will not be popular or supported with any real gusto. It will only alienate people from the technique and the people who forced them into it.

There are plenty of de facto dozenal processes at work in society, mostly vestigial. These exist in the way we keep track of hours and in the arrangement and grouping of items to be bundled in manufacturing and shipping and sales, for instance. There is plenty of discussion about the merits on this site. I think the salesman and the manufacturer recognize the merits of groupings by the dozen or divisions into dozens. All the dozenal advocate is saying is that things could be easier and simpler if we only used a base that makes this grouping less difficult to envision and manipulate.

An example of a process in a different base that has found application in society comes through the use of hexadecimal. Computers use binary processes because of the nature of electronic switches. Hexadecimal is ideal for the compression of binary digits (bits) into more manageable notation. The computer mechanism itself, as conceived today, has no need for anything other than binary; hexadecimal aids human programmers. The reason people use hex is because it is a handy way to compress bits and envision their patterns. People can manipulate the bits in terms of bytes (two hex digits) easier (you'd have to talk to a programmer about this). The compression process via hex is so handy that even graphic designers, creative professionals that operate in a completely different mindset, have become familiar with hex. This is because the primary way of encoding 3 channel 24 bit color on the web is through RRGGBB or hex notation. I don't think graphic designers actually compute with hex; they only use hex to the extent it helps them with their job. Anyone forcing hexadecimal on the entire population would be met with opposition, confusion, and contempt from plenty of people. The market has identified a feasible application of hex in a niche and supports it.

At the large scale, I, and other dozenal enthusiasts, believe that perhaps "organically", society may evolve to become more dozenal. But a hard line putsch of decimal is simply not the right way to go. Enthusiasm for the dozenal system does not argue with adoption of the dozenal system "of one's own free will." The "mechanisms" used to implement the "change" should indeed be practical processes that prove themselves in the marketplace, and not Big Brother.
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Ruthe
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Dec 19 2006, 08:36 PM #4

DominusVobiscum,

I can't but agree with all of your sentiments.
Firstly, I would like to know how many people here believe it is actually possible for society to transition from the base-ten counting system to a base-twelve counting system. Do you believe it is really possible to create a movement influential enough to make such a transition possible? Or is this, really, more of a pipe-dream?

is it feasible? One must remember that Change is, in and of itself, a Negative, in the great work and expense it requires and in how it ruptures history and disconnects us from the Past. Thus, in order for any change to be acceptable, the benefits the end result is projected to bring must outweigh the destruction wrought by the change itself. Even then, it is a gamble. And even then, people might not go along with it. They might not be willing to "go over the hump" for whatever returns are on the other side. This is one reason why Esperanto and other such "universal language" attempts failed.
I believe I have posed the same question in another thread. Yes, I do believe such a system could be introduced, if and possibly only if, there can be shown a significant economic reason for its use.
Lastly, and most importantly, is this project, as whole, beneficial. I strongly, strongly, strongly believe in the inherent superiority of that which evolves organically in society over that which is "pre-planned" based on some airy, intellectual theory. I strongly believe in the Natural, the Traditional, and the Organic over the deliberately engineered and implemented. This is the second big reason why Esperanto failed, in my opinion. For one this, engineering and implementing a change created destruction, chaos, and rupture--at least in the short term. Secondly, I also believe that engineered, micro-planned things are almost always inferior to that which evolves organically out of the natural flows of Human Society. Many, perhaps, think this hogwash, but I am strongly convinced of this concept.
Quite right! The use of traditional measures, many of which had the dozen as their basis despite the introduction of a decimal based number system after these measures were already in place, vindicates your opinion. Traditional units are examples that of measures that "evolves organically in society" as opposed to something like the metric system which was "deliberately engineered and implemented".
Thus, a deliberate change in such an ancient and embedded aspect of our civilization as our counting system must have strong justification, to outweigh these negatives. I accept that it might be more mathematically convenient, due to factoring. But the question is this: Is it more natural to the human Psyche? If not, no argument based on "scientific efficiency" would justify it me, as science has gotten along just fine with base-ten. I would rather the scientists, capitalists and engineers (they are, after all, trained at this stuff) have to deal with the "inefficiency" of 3.333333 and so forth, than our civilization, as a whole, have to deal with a counting system that is not natural to the human mind.
And the evidence seems to show that the base-ten system is the most natural system for the human mind, as most culture (admittedly not all) have, often independently developed base-ten counting systems on their own. I understand that this is likely due to the fact that we have ten fingers on which we tend to count. Thus, it seems that the base-ten system is inherent in our very Anatomy!
Absolutely! Thats why despite a ten based number system the use of dozen based units remained in use for over two thousand years. Obviously the dozen based units were of no use to the people using them and so readily gave them up for decimal measures. Of course, the metric system was designed by scientists and engineers for their own purposes which were more important than the needs of the carpenter, baker, seamstress, builder, cooper, brewer and the myriad of other craftsmen and women.
Admittedly, that is a physical trait, not a psychological one. But I feel such aspects of our Being tend to be intimately connected. Even speaking from the standpoint of evolutionary theory, after countless millennia of counting on our ten fingers, may we not have evolved brains more "in tune" with counting by tens than with counting by twelves. And, in any case, is it not useful to be able to count round numbers on ones fingers, which can't be done in a base-twelve system?
Exactly. Of course they were no civilizations that counted on the separate sections or 'phalanges' of each finger to count in twelves (there are twelve phalanges on the four fingers of each hand). And of course the Romans were completely ridiculous to use a set of fractions based on twelfths as they were of greater use than fractions based on ten. Hmm, I wonder where we got 12 inches to the foot and 12 ounces in a Troy pound. So I suppose that there is no relevance to 12 men on a jury, 12 tribes of Isreal, that Jersusalem in Revelations is 12,000 by 12,000 by 12,000 stadia with twelve gates and twelve angels and the names of the twelve tribes, and with twelve foundations with the names of the twelve apostles on each foundation, and the walls were 144 cubits thick "by man's measurement", and-- oh forget it, there isn't any real significance to twelve anywhere.

PS The following quote is from your next post.
One more thing I forgot to add: what mechanisms would you propose to use to implement this change? I hope not through enforced government mandate. To me such enforcement and micromanaging would be unjust even if the overall superiority of the Twelve system could be proven. Rather you must convince the populace to voluntarily accept this change of their own free wills. To me that is very, very, very important.
Good for you, to force the adoption would be outrageous!!! . You obviously think that systems such as the metric system should not be foisted upon populations by mandate of the government which is the case in every single country that now is forced to use this system. Not one government has given their citizens the opportunity of a referendum for the adoption or rejection of the metric system.

We couldn't even contemplate doing the same as governments around the world have already done in mandating the use of the metric system without the consent of their citizens. As pointed out before, no government in the world has given its citizens a referendum on the acceptance of the metric system. We shouldn't do the same with a duodecimal based system. After all, this is very like an historical event where a government imposed taxation without representation upon its colonial citizens. It's enough to start a war of independence!!!!
Why a Roman pocket abacus? They used dozenal fractions as their main form of fractions, 12 inches per foot & originally 12 oz per pound (inch=ounce=uncia=1/12). Columns 1 & 2 of the abacus are for dozenal fractions, column two for twelfths and column one, dozenal fractions of a twelfth. Columns 3 through 8 provided a decimal place value system with values from 1s to millions where each lower bead counts as 1 & the upper beads count 5 of a column's base 10 power, Is, Vs, Xs, Ls, Cs ,Ds, Ms etc.
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Tony
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Joined: May 26 2006, 08:42 PM

Dec 22 2006, 11:44 PM #5

DominusVobiscum @ Dec 19 2006, 11:12 AM wrote: Firstly, I would like to know how many people here believe it is actually possible for society to transition from the base-ten counting system to a base-twelve counting system. Do you believe it is really possible to create a movement influential enough to make such a transition possible? Or is this, really, more of a pipe-dream?
Oh, I think decimal will remain our primary way of numeration, but I also think dozenal could be a very nice niche player, like binary.
Numbers in my posts can be taken as dozenal, with the exception of italicized numbers which are decimal (unless otherwise specified).

Effective: 1E-08-11EX (23-08-2014)
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Shredder05
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Shredder05
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May 4 2013, 11:02 PM #6

Some of your major points:
  • What's better, organically evolved or engineered?
  • Can society change radices; is it capable, ready, and willing?
  • Forcing base 12 upon society makes sense theoretically but could cause conflict.
These questions and the points you've brought up have got to be the most important ones of the entire forum. Even though base twelve is more convenient than base ten theoretically, base ten is more convenient because of it's usage.

We have changed base systems in the past before. Different civilizations have used different bases as we all know. And computers needed to be in binary and hexadecimal so programmers and hardware designers had no choice but to learn and use a new base. I've tried to use tau instead of pi in my university courses though and even such a simple switch as that ran into trouble. Eventually one of my profs got so pissed off at my usage of a non standard symbol he won the debate we'd been having over the term out of sheer dictation. He'd have none of it. I can't imagine what would happen if I used base 12 on my assignments.






Planning would be key. Say we were to make the switch tomorrow...

- Everyone would be reduced down to an elementary school level of arithmetic for a while. We'd have inefficiency for a long while, and a lot of frustration as people learned a new way of doing math

- There's already so much decimal ingrained into society. Some technology would be stuck in base ten, and programs and systems for money, cashiers, music... list goes on... and all sorts of other things are in decimal. You'd do a lot of converting back and forth... but you could use calculators to do the conversion for you at least. The biggest thing is the hardware on our technology... there's no key for 11 or 12. And there's next to no software for it either.

- Kids learning arithmetic would grasp it much faster. If they didn't even learn base ten then obviously they'd stick with base twelve. Slowly, as future generations came and went society as a whole would be more efficient.
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stevep
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Jun 4 2013, 02:49 PM #7

In reality I don't think it will ever happen and nor should it. The cost of conversion and upheaval would be too great, plus there would outright hostility from a large proportion of people.

My interest in Dozenalism comes from a fascination of how systems (numeric or otherwise) can be organized, and being able to determine the most logical, rational and efficient solution to a particular problem. I think that the more people are aware of alternative ways of doing things, the better. When it comes to designing a number system, I am sold on Dozenal as the optimal for human use. While it would be good if more people thought about place-value systems and number bases in general, any kind of change now would be in reality impossible.

There are lots of other things about the world that I also find annoying/illogical, and many of those could be more easily fixed before a change in number base.

The most likely way for dozenal to succeed would be if the entire population of the Earth was wiped out except for a handful of maths experts. This also assumes all records of previous civilization were destroyed. Only then would it be worthwhile starting again in Dozenal.
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dgoodmaniii
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Jun 4 2013, 07:00 PM #8

stevep @ Jun 4 2013, 02:49 PM wrote: The most likely way for dozenal to succeed would be if the entire population of the Earth was wiped out except for a handful of maths experts. This also assumes all records of previous civilization were destroyed. Only then would it be worthwhile starting again in Dozenal.
This put me in mind of something I recall from the old Dozenal Journal:

[quote=""Ariadne Tampion""]
What a challenge we of the Dozenal Society have set ourselves!  To review numeration and measurement and produce a revised version based on the more convenient dozen, . . . is no small task.
[/quote]

A general conversion of any significant section of society is not easy; indeed, it is so difficult that its possibility seems very remote. But it's not impossible; it's just extremely unlikely. Other historical unlikelihoods include:
  • * That a portion of a small island just northwest of continental Europe would wind up with the largest empire the world had ever seen.
    * That a bunch of backwoods rustics putting on airs of civilization would successfully break away from said Empire, and eventually take its place as the world's foremost military power.
    * That three human beings would sit in a crackerbox on top of a glorified intercontinental missile, launch themselves to the moon, walk around on its surface, and then come back, still alive---multiple times.
    * That one of the great civilized and literate powers of the world would abandon its alphabet of centuries and adopt one completely foreign to it within the space of only a few years.
    * That the various German states would unite themselves in adopting a decimal metric system invented and perfected in, of all places, their most ancient and threatening enemy, France.
    * That the entire world, over several centuries, would choose to lose approximately two weeks off their calendar, then adopting a new one with a more confusing rule for leap years, just to keep it synced with the seasons.
    * That the second-most-powerful financial system in the world would abandon its tripartite currency of centuries and thereby disrupt much of its trade in the process without any compelling economic reason to do so.</li>
And we can continue on, but I think the point is clear: don't discount the unlikely as impossible.

It's much too early in the process, even after seven unquades of active dozenalism, to posit dozenal as the exclusive system of society. But the transition from Roman to Indo-arabic numerals in Europe was a process of many centuries, as well. They went from outright forbidden; to grudgingly acknowledged but discouraged; to tacitly accepted; to majority use; to nearly exclusive use, and now their predecessors are a novelty, suitable only for ultra-formal clock faces, Super Bowl numbers, and copyright years in movies that nobody reads.

I see the same process for dozenals. It begins as a few fringe users, like us here and in the Dozenal Societies; at this stage dozenalists are cranks, or at least weirdos.

Next (and we're approaching this stage, I think) is the phase of grudging acknowledgement. At least the nerdier people now know about us; they have a vague idea of how dozenals work; they know that there are people who want to use dozenals in place of decimals. This will be a long period, likely longer than the last, and will continue until we can replace "the nerdier people" with "most people." Decimal will still be the dominant system; but dozenals will at least be known, even if mostly not used.

Then is the phase of tacit acceptance. People will start using dozenals in certain circumstances; e.g., when dealing with the ages of young children (generally cited in months), or when working with feet and inches (which show no signs of going away, at least in the States), or with telling time. We'll also see people (not just us) starting to use dozenal systems of measure. This is when we'll start to see some gathering momentum for phasing out decimals, especially in the monetary system. There will be crochety old decimalists who will tell their children to keep their stinking dozenals out of this house, and young, bright-eyed, idealistic twenty-somethings who make casual remarks about "dinosaurs" being too wedded to the ways of their youth.

Then will come majority use. The monetary system will be dozenalized; dozenal systems of measure will be established as legally acceptable. There will still be decimalists, but they'll be regarded as a bit odd, like the old man in 1984 grumbling about how his half-liter wasn't a pint.

And finally, decimals will be merely a memory, something people know only from old books and grandpa's genealogy studies.

The dozenal really is better than the decimal; substantially and usefully better. As long as we keep using it, expanding it, and teaching about it, it will triumph. But defeating any ingrained habit, even an ingrained bad habit like decimalism, is a long and difficult process.

As Ghandi said regarding his struggle for India's independence: "First, they ignore you; then, they laugh at you; then, they fight you; then, you win."

We should not be discouraged by the difficulty of the task before us; we should merely seek to adequately play our part. We're still pretty close to the earliest pioneers in the first major change in our arithmetic since the Renaiissance; we need to give these things some time. Ralph Beard, one of the DSA's elders and the first editor of the Bulletin, used to print frequently: "Each one teach one." That's what we need to be doing: using dozenals, and telling people why we use them when they ask.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use :A or X; for elv, I use :B or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!
Dozenal Adventures
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wendy.krieger
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Jun 6 2013, 07:42 AM #9

Base conversion has been known in the past, and it is quite possible for it to happen in the future. It's more likely to happen in a fallen society or in fallen times.

The north of europe (germanics) used base 120, and the west (celtics) used 20, these were adopted from substrate languages, since PIE used decimal. These still have reflexes right up to the modern era: calculations in twelfty are recorded as late as the xvi century (teentywise), and one of the number words we have from all languages including gothic, is a word for expressing 'hundreds teentywise', which supposes a different hundred.

The celtic 20 is seen in scores and the french and celtic number systems, even down to words like 'sixty-ten-seven' and 'four-twenty-ten-eight (quatre vingt dix-huit = 98).

So, conversion might happen for example, when money is fixed up (to a shilling of 12 pence), and then the weights and measures, and then the money. We managed to destroy our weights and measures over here within 20 years of the distruction of money.
Twelfty is 120 dec, as 12 decades. V is teen, the '10' digit, E is elef, the '11' digit. A place is occupied by two staves (digits).
Digits group into 2's and 4's, and . , are comma points, : is the radix.
Numbers writen with a single point, in twelfty, like 5.3, means 5 dozen and 3. It is common to push 63 into 5.3 and viki verka.
Exponents (in dec): E = 10^x, Dx=12^x, H=120^x, regardless of base the numbers are in.
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gingerbill
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Jun 6 2013, 12:20 PM #10

I believe the first move is to get dozneal into scientific work and/or engineering and architectural work. If a dozenal system was used in those fields, it may transfer slowly into the layman field (kind of like metric but not).

If the dozenal system was to be used, it must have a dozenal system of units. I am not going to say which one to use but the main ones on this forum are:
  • TGM
  • UUS
  • IDUS
  • Primels
All of these systems have there own advantages and disadvantages and the main one will be chosen by the industry that will use it.
X = Ten, E = Elv
or
ɤ = Ten, Ɛ = Elv
or
ᘔ= Ten, ᘍ = Elv
Dozenal number will always use radix point let it be a ; (semicolon) e.g. 103; 3;4
Decimal number may not use radix point but only when needed e.g 14 or 9.2

Preferred system of units: IDUS or UUS (or if needed SI)
Preferred prefixing system: SDN (excluding multipliers)
Preferred language: English, Français
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Ruthe
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Jun 6 2013, 08:36 PM #11

I have recently 'discovered' three separate supporting reasons for adopting an uncial number system.

1. Expanding telephone numbers available without increasing the number of digits for each unique number.

2. Increasing the available IP addresses in the same way as 1. above.

3. This is a commercial tweak that would allow manufacturers and service suppliers worldwide a one-off increase in prices, in much the same way decimalization in Britain increased prices. By adopting an uncial number system, all prices could be amended from x.99 to x.EE, a seemingly increase of 44% or ~53.44 per gross, but with the value of each penny reduced by 1/6 (10p becomes 12p i.e an uncial penny = 5/6 of a decimal penny), the actual increase in prices is 36.67% or 24.97 per gross.

What company director would turn that down?

PS An example of price increases due to UK decimalization is the following I encountered.

Pre-decimal, a Cadbury's Whole Nut chocolate bar was 6d and these were on sale with price printed on the wrapper. On the same display, the same bars were on sale at 5p. For those not familiar with the old and new monetary system, 6d was half a shilling of 12 pennies. The shilling was converted to 5p decimal. So the same bar was double the price in decimal currency than the sterling currency price during the changeover period. So for the non-optimal mathematically minded, 5p seemed less than 6d when in fact it was double. I knew, I bought all the old 6d bars!

PPS A much better solution to decimalization would have been to make the new £ sterling equal to the old 10 shilling note, so that the new penny was only 1.2 the value of the old pre-decimal penny, the 6d the new 5p, the 12d shilling the new 10p, the 2 shilling 20p, the 2/6 the new 25p, and the 5 shilling crown the new 50p. But I bet the heads of all companies that put forward a recommendation voted for the system we did get, the one with a penny 2.4 times the old penny. It made bigger price increases look smaller.
Why a Roman pocket abacus? They used dozenal fractions as their main form of fractions, 12 inches per foot & originally 12 oz per pound (inch=ounce=uncia=1/12). Columns 1 & 2 of the abacus are for dozenal fractions, column two for twelfths and column one, dozenal fractions of a twelfth. Columns 3 through 8 provided a decimal place value system with values from 1s to millions where each lower bead counts as 1 & the upper beads count 5 of a column's base 10 power, Is, Vs, Xs, Ls, Cs ,Ds, Ms etc.
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gingerbill
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Jun 6 2013, 09:05 PM #12

Ruthe @ Jun 6 2013, 08:36 PM wrote: I have recently 'discovered' three separate supporting reasons for adopting an uncial number system.

1. Expanding telephone numbers available without increasing the number of digits for each unique number.

2. Increasing the available IP addresses in the same way as 1. above.

3. This is a commercial tweak that would allow manufacturers and service suppliers worldwide a one-off increase in prices, in much the same way decimalization in Britain increased prices. By adopting an uncial number system, all prices could be amended from x.99 to x.EE, a seemingly increase of 44% or ~53.44 per gross, but with the value of each penny reduced by 1/6 (10p becomes 12p i.e an uncial penny = 5/6 of a decimal penny), the actual increase in prices is 36.67% or 24.97 per gross.

What company director would turn that down?

PS An example of price increases due to UK decimalization is the following I encountered.

Pre-decimal, a Cadbury's Whole Nut chocolate bar was 6d and these were on sale with price printed on the wrapper. On the same display, the same bars were on sale at 5p. For those not familiar with the old and new monetary system, 6d was half a shilling of 12 pennies. The shilling was converted to 5p decimal. So the same bar was double the price in decimal currency than the sterling currency price during the changeover period. So for the non-optimal mathematically minded, 5p seemed less than 6d when in fact it was double. I knew, I bought all the old 6d bars!

PPS A much better solution to decimalization would have been to make the new £ sterling equal to the old 10 shilling note, so that the new penny was only 1.2 the value of the old pre-decimal penny, the 6d the new 5p, the 12d shilling the new 10p, the 2 shilling 20p, the 2/6 the new 25p, and the 5 shilling crown the new 50p. But I bet the heads of all companies that put forward a recommendation voted for the system we did get, the one with a penny 2.4 times the old penny. It made bigger price increases look smaller.
1. This isn't a problem as in the UK at least where is 10 000 000 000 unique numbers
2. IP addresses are binary not decimal (IPv4 has approximately 2^32 addresses and IPv6 2^128).
3. Many countries have got rid of the penny/cent and have smallest unit as 5p/shilling. An unciaPound would be 8;4p and half of that is of course 4;2p.
X = Ten, E = Elv
or
ɤ = Ten, Ɛ = Elv
or
ᘔ= Ten, ᘍ = Elv
Dozenal number will always use radix point let it be a ; (semicolon) e.g. 103; 3;4
Decimal number may not use radix point but only when needed e.g 14 or 9.2

Preferred system of units: IDUS or UUS (or if needed SI)
Preferred prefixing system: SDN (excluding multipliers)
Preferred language: English, Français
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Dan
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Jun 7 2013, 03:47 AM #13

gingerbill @ Jun 6 2013, 04:05 PM wrote:1. This isn't a problem as in the UK at least where is 10 000 000 000 unique numbers
I don't know about the UK, but in the US, we've had a lot of area code splits in the past *20 years or so, and switching to dozenal would more than triple the number of 7-digit local numbers per area code.

The main problem is backwards-compatibility: How would people with old phones (ones with physical buttons, instead of a touchscreen that could be reprogrammed) be able to dial numbers that contain a ten or eleven? Perhaps we could reassign the * and # keys.
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gingerbill
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Jun 7 2013, 08:43 AM #14

Dan @ Jun 7 2013, 03:47 AM wrote:
gingerbill @ Jun 6 2013, 04:05 PM wrote:1. This isn't a problem as in the UK at least where is 10 000 000 000 unique numbers
I don't know about the UK, but in the US, we've had a lot of area code splits in the past *20 years or so, and switching to dozenal would more than triple the number of 7-digit local numbers per area code.

The main problem is backwards-compatibility: How would people with old phones (ones with physical buttons, instead of a touchscreen that could be reprogrammed) be able to dial numbers that contain a ten or eleven? Perhaps we could reassign the * and # keys.
In the UK, we have area codes too. The first number is always 0 and then the next 3 or 4 numbers in the area code or type of number. 07 numbers are usually exclusively mobile celluar numbers. So in a town, there will be 10^6 unique numbers and in a city 10^7. Leicester has the area code 0116 and then 7 more numbers after it. This is because back when all phone number were 7 digits long because that is the most people can usually remember.

Using dozenal would make there be more numbers so this is an advantage.
X = Ten, E = Elv
or
ɤ = Ten, Ɛ = Elv
or
ᘔ= Ten, ᘍ = Elv
Dozenal number will always use radix point let it be a ; (semicolon) e.g. 103; 3;4
Decimal number may not use radix point but only when needed e.g 14 or 9.2

Preferred system of units: IDUS or UUS (or if needed SI)
Preferred prefixing system: SDN (excluding multipliers)
Preferred language: English, Français
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dgoodmaniii
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Jun 7 2013, 12:45 PM #15

As gingerbill notes, this would not increase the number of IP addresses; a 28-bit number is a 28-bit number, no matter what base it's written in.

The others probably work, though.

Backwards compatibility would be an issue; you'd have to wait a while (say, a half-dozen years) for legacy phones to get phased out before starting to introduce the numbers with dozenal characters.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use :A or X; for elv, I use :B or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!
Dozenal Adventures
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icarus
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Jun 19 2013, 09:17 PM #16

My opinion has always been that any duodecimal adoption would indeed need to be "organic" and not foisted on the public by fiat. The thing to have happen (organically) is the development of a "killer app" or a system of applications for duodecimal. We sort of had this running in anglophone/Germanic countries, but it never got off the ground; this is why dozenalism to some seems like an old, musty idea from frostbitten lands.

We still have mighty, high tech applications for the dozen that decimal won't trump easily. Lots can be said about the entrenchment of decimal, but the 2 dozen hour day, the usefulness of gear ratios that are based on evenness and 3, the pica in design (in InDesign, the units are dozenal like feet and inches), these are all well-entrained duodecimal applications. The reason why they are "killer" is surely because the dozen marries even-evenness and threefoldness, the two simplest primes.

We'll also see 60 and will find that hard to iron out decimally.

I think a good candidate for utility is what I'd called a "twip" (but is actually a malappropriation of terminology, maybe like "malappropriation" itself). I mean a per-twelfty, 1 part in 120 to replace percents. Now granted, people think in percents, but the per-twelfty resolves thirds. Thus in my work I use 1 part in 120 often. My website will use this system and the user will have the option to use percent.

If we don't *use* dozenal, or any other tool, the tool won't see action on the worksite, and no one will know how awesome it is. The company that makes the tool will go out of business so to speak. So use the tools, even in business. I use them and that makes me pretty good money when the government isn't trying to destroy the economy by fiscal cliffs or sequesters, austerities.
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dgoodmaniii
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Jun 23 2013, 06:11 PM #17

We still have mighty, high tech applications for the dozen that decimal won't trump easily. Lots can be said about the entrenchment of decimal, but the 2 dozen hour day, the usefulness of gear ratios that are based on evenness and 3, the pica in design (in InDesign, the units are dozenal like feet and inches), these are all well-entrained duodecimal applications. The reason why they are "killer" is surely because the dozen marries even-evenness and threefoldness, the two simplest primes.
Indeed. Typesetting bein fundamentally dozenal has persisted even in metric countries, like dozenal time and Babylonian angles.
I think a good candidate for utility is what I'd called a "twip" (but is actually a malappropriation of terminology, maybe like "malappropriation" itself). I mean a per-twelfty, 1 part in 120 to replace percents. Now granted, people think in percents, but the per-twelfty resolves thirds. Thus in my work I use 1 part in 120 often. My website will use this system and the user will have the option to use percent.
I'm not a big fan of mixing bases, but I can't wait to see it on your website. Will you notate in decimal or dozenal (e.g., one part in 120, or one part in X0)?

Also, the word you're looking for is "malapropism," or possibly "misappropriation."
If we don't *use* dozenal, or any other tool, the tool won't see action on the worksite, and no one will know how awesome it is. The company that makes the tool will go out of business so to speak. So use the tools, even in business. I use them and that makes me pretty good money when the government isn't trying to destroy the economy by fiscal cliffs or sequesters, austerities.
Yep. If nothing else, keep your time and calendar in dozenal; these are fundamentally personal, so there's really no reason not to do it, and it provides a good conversation-starter when people notice it.

Unless you're doing it digitally; this is a problem, because calendar programs don't have dozenal options. I have a command-line calendar which is complete, and am busily designing a graphical frontend for it; this will run on Android and on desktops, and will hopefully go a good way to resolving this problem.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use :A or X; for elv, I use :B or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!
Dozenal Adventures
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stevep
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Jul 4 2013, 01:55 PM #18

Another possibility that could cause there to be a sudden and widespread interest in Dozenal.

Let's suppose the presence of alien life is detected. Like in the film "Contact". The signals are decoded and give us lots of information about the aliens, especially maths-related. Perhaps the aliens are using base 12. It would become relatively mainstream to think about a different base if it was known another civilization somewhere was using it.

Of course there's no guarantee aliens would be using base 12. Perhaps they also evolved a non-optimal number of their equivalent of fingers. Or perhaps some other (non-positional) system.

But at least this scenario is theoretically possible.
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Kodegadulo
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Jul 5 2013, 12:29 PM #19

stevep @ Jul 4 2013, 01:55 PM wrote: Another possibility that could cause there to be a sudden and widespread interest in Dozenal.

Let's suppose the presence of alien life is detected. Like in the film "Contact". The signals are decoded and give us lots of information about the aliens, especially maths-related. Perhaps the aliens are using base 12.  It would become relatively mainstream to think about a different base if it was known another civilization somewhere was using it.

Of course there's no guarantee aliens would be using base 12. Perhaps they also evolved a non-optimal number of their equivalent of fingers. Or perhaps some other (non-positional) system.

But at least this scenario is theoretically possible.
Theoretically possible, yes. Highly improbable though. But perhaps just a fictional account of such an encounter would be enough. Especially if it could be made into a multi-novel blockbuster book series, with a spin-off into a multi-movie blockbuster cinematic series. Consider the wild popularity of works such as the Harry Potter series, or the Hobbit/Lord of the Rings series. And of course Star Wars and Star Trek.

If someone could somehow make learning dozenal arithmetic as cool as learning Klingon, we could capture the imaginations of a whole generation.
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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Dan
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Jul 5 2013, 12:52 PM #20

The Na'vi from Avatar use octal.
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Kodegadulo
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Jul 5 2013, 01:03 PM #21

Kodegadulo @ Jul 5 2013, 12:29 PM wrote: If someone could somehow make learning dozenal arithmetic as cool as learning Klingon, we could capture the imaginations of a whole generation.
Hmm. Imagine a parallel-universe scenario, something like the TV series Sliders. Let's say there are two near-by universes parallel to our own, with two parallel Earths nearly indistinguishable from ours, both populated with human beings quite like us, except for the curious fact that evolution somehow resulted in different numbers of fingers and toes. There would be an "octal" universe in the "kata" direction, populated with four-fingered humans, and a "dozenal" universe in the "ana" direction, populated with six-fingered humans. Us "decimals" are sandwiched between them.

These days, CGI would make this pretty easy to do in movies: I mean, if they can get rid of Ray Fines' nose to turn him into Voldemort, they it should be child's play to add or remove fingers.

Suppose all three universes discover interdimensional travel at about the same time. There could be a lot of intrigue and even conflict at the sudden clash of cultures.

Let's say the "octals" are aggressive, warlike, and imperialistic, so they would be the "bad guys". The "dozenals" could be peaceful, rational, and egalitarian, so they would be the "good guys". Us "decimals" would be somewhat in-between, and there could be characters drawn one way or the other.

Maybe the octals are the way they are because they think a little too much like computers. Their psychology might even be borg-like. Everything is binary to them, black or white, yes or no. Their way or the highway.

Whereas the dozenals would be more flexible and inclusive, because they're used to seeing many more ways of dividing up the pie. They can easily see three ways of looking at issues, not just two.

There might be a natural affinity between decimal humans and dozenal humans because we both have more than one prime factor in our number 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)
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dgoodmaniii
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Jul 5 2013, 05:11 PM #22

Kodegadulo @ Jul 5 2013, 01:03 PM wrote:
Kodegadulo @ Jul 5 2013, 12:29 PM wrote: If someone could somehow make learning dozenal arithmetic as cool as learning Klingon, we could capture the imaginations of a whole generation.
Hmm. Imagine a parallel-universe scenario, something like the TV series Sliders.
Base-hatred could replace race-hatred!

Such a scenario would have to explain a lot of unlikely coincidences, though. For example, a planet where hominids developed with only four fingers on each hand, or six, would likely be very different from our own, as pentadactyly is almost universal among tetrapods and must have evolved a very long time ago. We could posit some bogus theory of parallel development stemming from some landmark of progress, like Star Trek did to explain its many societies identical to ones at various points in Earth history; but this is unsatisfying, a deus ex machina without even the romance of a deus to make it interesting.

I'm not a geneticist (though I'm pretty good friends with one, so I think I'll ask him), but some isolated population starting from very few members who happen to have a gene for polydactyly seems much more likely.

Say, during the early days of the Cold War, a secret government project in the Nevada desert spearheaded by a studly young beefcake of a rocket scientist (we'll call him "Biff," to maintain the stereotype) and his brilliant (and, naturally, impossibly attractive) young female assistant/wife (we'll call her "Eva," ditto), combine some of the insights of the Manhattan project and of Peenemunde to develop a "Save America" rocket, to stave off the destruction of The American Way&#153; in the event of a successful Russian nuclear first-strike. Packing the very latest in ca. 1164 (1948.) technology, and manned by Biff, Eva, and two or three other couples (selected in true mid-century fashion for their extremely high IQ scores and improbable good looks), they set their sights on some destination close enough to be reachable but far enough away that nobody on Earth is likely to have noticed them since then. Somewhere on Mars, probably. As the rocket left, the secret government filenotes that Eva is pregnant (not showing yet, as contemporary cinematography had a statutory minimum svelte content that would be contravened by such a revelation). No genetic abnormalities were noted in any of the passengers (that's one of the things they were selected for), but as a matter of fact several of them (at least one from each couple) had had notable cases of polydactyly in their lineage. Radio communication was lost almost immediately after launch, for reasons that ground control didn't understand; so the file was buttoned up, stamped "classified" several dozen times, and boxed up in a giant warehouse full of various covert projects that nobody will ever look at it again, a la Raider of the Lost Ark.

Time periods are important here. We are living in the third generation after the WWII generation that produced Biff and Eva. (My grandfather fought in Europe, and I'm in what most people would describe as the middle portion of my life.) We need at least two or three more than that, I think, though my geneticist friend can probably give me a better figure.

So cut to four or five unquades from the present (say, five or six generations after Biff and Eva and crew left Earth). This can be a net positive or negative future, whichever seems to serve the later storyline better. The first manned mission to Mars is getting ready to set out. (1201? Sure; I'll believe it when I see it. Which I won't.) At this point, Biff and Eva's great-great-grandchildren, in their young adulthoods, show up. They speak slightly different English (mid-century General American accents which developed in a different direction from ours), but are perfectly comprehensible. Their technology has developed in different ways (we can select our other ark-passengers based on their expertise, to ensure the outcome that will be most helpful to our storyline). And most curiously, each has a perfectly developed sixth finger on both hands.

We need the time periods to ensure that, by some happenstance, the sixth finger pops up in at least some of the offspring of each couple. While in our society the (extremely rare) case of functional polydactyly is quite unlikely to reproduce with another case of functional polydactyly, in this extremely small population it's quite likely, and in our story that's exactly what happens. In this first generation after Biff and Eva's there are enough polydactyls by perbiqua that they believe it normal; they might even brag about it to the pentadactyls. It could conceivably become a point of pride for them, leading them to accentuate the difference rather than, as in our society, minimize it. They start counting by it; they object to pentadactyl-centered arithmetic and metrics. For some reason th next generation is mostly polydactyls; by some chance several of the pentadactyls marry polydactyls, and a few other pentadactyls don't marry or die young or are exposed to a sterilizing radiation disaster or something, and the next generation there are very few pentadactyls remaining, probably only one or two given the size of our population. That's the generation contemporary with mine, made up almost entirely of polydactyls who think pentadactyls suffer from some kind of birth defect. A few more generations ot weed out the remaining pentadactyl genes, and we've got a reasonably-sized society (say, a few biqua people) who are all polydactyls, counting by twelves, who have just as much trouble imagining things being different as people here do now.

And take the storyline away from there.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use :A or X; for elv, I use :B or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!
Dozenal Adventures
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Kodegadulo
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Jul 6 2013, 12:40 PM #23

dgoodmaniii @ Jul 5 2013, 05:11 PM wrote:
Kodegadulo @ Jul 5 2013, 01:03 PM wrote:
Kodegadulo @ Jul 5 2013, 12:29 PM wrote: If someone could somehow make learning dozenal arithmetic as cool as learning Klingon, we could capture the imaginations of a whole generation.
Hmm. Imagine a parallel-universe scenario, something like the TV series Sliders.
Base-hatred could replace race-hatred!
Oh, indeed! Especially if the octal universe and the dozenal universe were so parallel to our own that they both included exactly the same ethnicities and races, but all with a dactyly different than ours. The characters in all three universes would have to come to grips with just how trivial their racist bigotries had been, when suddenly the number of fingers on one's hand becomes the criterion for solidarity or conflict, rather than superficial differences in skin color and facial features.

I can see some interesting possibilities for cloak-and-dagger intrigue: A spy from the dozenal or decimal universe, in order to go deep under cover and infiltrate the octal universe's society, might agree to undergo digital amputation surgery!
Such a scenario would have to explain a lot of unlikely coincidences, though.
But "coincidence" is problematic only if one assumes a single timeline, i.e., a single course of events. On the other hand, if the many-worlds hypothesis for quantum mechanics turns out to be true, then we are really talking about a potentially infinite number of parallel timelines. In fact, one form of the this hypothesis asserts that every course of events not precluded by the laws of physics actually does occur, somewhere out there in the infinite multiverse.

So it's perfectly reasonable to contemplate timelines containing sequences of events extremely similar to our own history, but with some detail just happening to be different. For instance, Harry Turtledove used this premise to very good effect in his novel A World of Difference. In it, he posits an Earth exactly identical to our own, with a history nearly identical to ours, all the way up to the launch of the first Viking interplanetary space probe in the 20th century, yet with a crucial but tiny difference tracing all the way back to formation of the solar system: When their ancient astronomers looked up into the night sky, instead of seeing a dull, reddish planet in the fourth orbit around the sun, they saw a larger, grey-white, more Earthlike planet, with a cloudy, oxygen-rich atmosphere, oceans of water, and massive polar ice caps. Instead of calling it "Mars" after their god of war, they named it "Minerva", after the grey-eyed goddess of wisdom. In that universe, H.G. Wells wrote a novel about invaders not from angry Mars, but from mysterious Minerva. And in that universe, Johnny Carson invited Carl Sagan on the Tonight Show, not to comment on images of a desolate rock-strewn Martian plain, but images of a tentacled Minervan native attacking and destroying the Viking lander with a primitive axe!
For example, a planet where hominids developed with only four fingers on each hand, or six, would likely be very different from our own, as pentadactyly is almost universal among tetrapods and must have evolved a very long time ago.
Actually, what I had in mind was two parallel timelines extremely similar to our own, including the rise of recognizably human beings with perhaps even the same ethnic and racial groupings, except that the common ancestor of all tetrapods just happened to be tetradactyl or hexadactyl instead of pentadactyl. Unless there is some unknown law of biology or physics that makes pentadactyly absolutely necessary rather than arbitrary, such timelines are not out of the question, given an infinite multiverse.
We could posit some bogus theory of parallel development stemming from some landmark of progress, like Star Trek did to explain its many societies identical to ones at various points in Earth history; but this is unsatisfying, a deus ex machina without even the romance of a deus to make it interesting.
I agree that the idea of convergent evolution and parallel history on a different planet in the same universe is immensely far-fetched. But the idea of parallel histories on the same planet in different universes within a multiverse is a fairly stock science-fiction trope.

Of course, the characters in my three universes would find it remarkable that the invention of hyperdimensional travel should connect them to these particular neighbor universes. Given the infinite possibilities, they would wonder how it was that they would be intersecting with histories with such similarities and yet with this one glaring detail so very different. Perhaps their scientists were aiming to find universes as close as possible to their own, but discovered that there was some quantum effect that required some minimal level of difference. Perhaps it takes exponentially more energy to create a "shorter" cross-temporal tunnel.
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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dgoodmaniii
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Jul 7 2013, 08:27 AM #24

I suppose that's true positing an infinite multiverse.

It is curious that pentadactyly is so universal on our planet among tetrapods. I've also found it odd that vertebrates all seem to have the same four basic appendages (land vertebrates, that is), while invertabrates run the whole gamut from no legs to six to eight to ten to twelve to...well, I know they say that centipedes and millipedes are true insects and really only have six legs, plus an immense number of pseudo-legs, but they sure look and act a lot like legs to my eyes. And yet very few have four!

I don't see any particular reason why pentadactyly is anything more than a coincidence. I was just thinking that a difference so long ago would surely have cascaded to immense differences today; and in most parallel universes that would doubtlessly be the case. But given an infinite number of such, there would have to be some nearly identical to our own, but with this small difference.

Now, why, with the infinite number of possibilites, they would have run into one so similar and yet so curiously different is, as you say, another question. I'm not sure I like the energy idea; wouldn't that mean that extremely different universes would require praqctically no energy to get to? You also run into that quantum stopping point; at some point, the energy required has decreased to a minimum, but with an infinite number of universes you then have an infinite number of universes which are, practically speaking, the same "distance" away.

You'd probably need a Sliders version of the time traveller's paradox, to explain why there aren't hordes of dimension-skipping tourists running all over the place (since there's an infinity of places for them to come from, and each can go to many), and chalk the rest up to a curious coincidence.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use :A or X; for elv, I use :B or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!
Dozenal Adventures
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