Isn't It A Weird Coincidence…

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

Isn't It A Weird Coincidence…

Troodon
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Troodon
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Nov 6 2016, 02:00 PM #1

I have noticed that the oldest humans manage to exceed decimal 100 years in lifespan, which, coincidentally, also happens to be the number base system that the vast majority of humans worldwide have selected to use. This is not the first time I have thought about this; I remember I had these same thoughts about three years ago, when I realized that, in dozenal, no human would be able to say that their life spans three grossuries, while there are, indeed, some humans who can say that their life spans three centuries for decimal.
Imagine a world in which no humans would be able to break that coveted three-digit barrier in lifespan. Some might view it as a disappointment, and while I concur that I find myself in some agreement, I also find it a really weird, serendipitous coincidence that humans chose a number base that would allow the oldest members among them to pass the three-digit mark.

(It is notable to point out, though, that decimal is not the largest base in which this is possible; rather, undecimal is. In undecimal, only one human in history, Jeanne Calment, would have passed the three-digit mark, living to the ripe old age of undecimal 101/decimal 122/dozenal A2).
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Shaun
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Shaun
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Nov 6 2016, 05:17 PM #2

I shall be most disappointed if I cannot reach *100 ...
But then, if I did reach *100, would I know I had?

Creak creak, rattle rattle ...
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Treisaran
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Treisaran
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Nov 6 2016, 06:39 PM #3

Adam and Methushelah got quite close to the third decimal power, but they only just passed half of the same for dozenal, with 656z and 689z years respectively. Leave dozenal lifespans to Tolkien. ;)
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heynonnymouse
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Nov 7 2016, 12:35 PM #4

Treisaran @ Nov 6 2016, 07:39 PM wrote: Leave dozenal lifespans to Tolkien. ;)
Tolkien's elves obviously benefitted from their national Elf Service ... living for groceries of years.
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DavidKennedy
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Nov 7 2016, 03:38 PM #5

Do you think Tolkien had that in mind when he wrote, in The Hobbit, chapter An Unexpected Party:
He looks more like a grocer than a burglar!
-- David Kennedy
Double negative is a plus
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Double sharp
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Dec 9 2016, 03:22 PM #6

Tolkien's views on the base his Elves used changed during his lifetime. Originally they were indeed originally duodecimal (though the form for eleven appeared to have originated decimally as 10+1), but in the latest writings their languages are all decimal, with the possibility of at most a "Plain English" kind of duodecimal system with names for the multiples of 12, 144, and probably also 1728. Their lifespans would indeed go into the thousands and tens of thousands, though I think that passing the dozenal myriad of 20736 might be only for Círdan among the named ones (he is one of the original 144 who first awoke, and is still alive after the events of LOTR).

In octal, reaching one "century" would be unremarkable today (a few centuries ago it would have been a lot more dicey), but no one would yet have reached two (Calment only got to octal "172", six years away from "200"). I wonder when the first person will manage that, hitting the next power of two...
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schildkroete
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May 13 2017, 09:54 PM #7

That is interesting, but likely just a coincidence.

With the pending baby boomer seniority, we will "soon" see if anyone can break the record and how many do. And by soon, I mean 2068! Whats scary is how close and how far that is to now. Ill be in my 70s. Yikes, no rush
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icarus
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icarus
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May 14 2017, 03:54 AM #8

I will be *82 in 2068 and am not even half that now. Not worried about it.
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Dan
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Dan
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May 14 2017, 11:02 PM #9

Double sharp @ Dec 9 2016, 10:22 AM wrote: In octal, reaching one "century" would be unremarkable today (a few centuries ago it would have been a lot more dicey), but no one would yet have reached two (Calment only got to octal "172", six years away from "200").
And in base-9, "100" is roughly the average life expectancy in First World countries.
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Double sharp
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May 15 2017, 06:19 AM #10

One could probably come up with nice coincidences like this for most bases. Already in decimal, the "snapping points" of round numbers are close enough that one can fit most things to them without too much violence being done. Maybe in an obnoxious large prime base like 641 it would be different, but as long as there are some reasonably small prime factors, there will be so many round numbers that not a lot of rounding will be needed.

If you let yourself vary the base too, you're essentially making every number round, because everything is round in the lens of one base or another. 80 is round in decimal and hexadecimal; 81 is round in nonary; 82 is round in base-41; 83 is round in base-83; and 84 is round in dozenal and tetradecimal. Sure, we might exclude the large primes, but while most numbers are not products of small primes, a surprisingly large number of small numbers are.
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Ruthe
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May 20 2017, 12:37 PM #11

Troodon @ Nov 6 2016, 02:00 PM wrote:I also find it a really weird, serendipitous coincidence that humans chose a number base that would allow the oldest members among them to pass the three-digit mark.
I think that the use of base 10 for our number system had nothing to do with the ability to reach the 3 digit mark of 100. First, the decimal system was probably just a result of humans having 10 digits on two hands. Secondly, the choice of decimal with respect to that 'magical' number 100 would probably been totally absurd as a reason since the decimal system was adopted long before human lifespans came anywhere near to that target.
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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icarus
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icarus
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May 20 2017, 02:03 PM #12

Adding on Ruthe's comment, though we may have counted and grouped in tens, the grouping of tens of tens may have taken a while to innovate. Some grouped in 6s of tens, or perhaps 2x 10 (more likely 4x 5), etc. The frequency of needing to manipulate numbers in the hundreds and beyond seems to have required civilization to make all nested groups based on the same number.
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Double sharp
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May 22 2017, 05:08 AM #13

To be fair, Troodon did not claim it to be anything more than a coincidence.

Given that 5 is pretty much a subitising number and 10 is not, I would not be surprised if 10 and 20 were instead constructed as 2*5 and 4*5, the latter perhaps 2*(2*5). The cases of 2*5 might more easily weather down to an unanalysable range of ten forms because 5 is really rather small as a base. Thus it seems that while our current algorithms may allow for bases within the range {5-16} to be reasonable, the forces that historically caused the development of bases may well lead to a higher range like {8, 10, 12, 14, 16, 18, 20} being favoured.

The grouping of 100 may develop as 5*2*10 well as 10*10, judging from the number of hybrid decimal-vigesimal languages. Such a case would imply a sort of 'crowning' of 20 among multiples of 10, while simultaneously not disturbing 10's position as the king of the numbers (though it is kind of a usurper, grafted onto mathematics by the needs of human cognition; 12 would be such a usurper too, with 2 perhaps having the best claim to the throne despite being unsupportable for humans).

Icarus makes a very reasonable conjecture in the immediately preceding post. To be fair, just about everything we are saying here is highly conjectural.
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dgoodmaniii
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Jul 6 2017, 02:58 PM #14

Double sharp @ May 22 2017, 05:08 AM wrote: To be fair, Troodon did not claim it to be anything more than a coincidence.
Yep! But coincidences are fun, especially when we use them to assign deep meaning to arbitrary things! (Not that I"m saying anyone here is doing that; I'm genuinely amused by doing such things.)

Hey, folks! Long time no see!

Anyway, to join the speculation, the age span of one hundred years doesn't even seem particularly coincidental to me. After all, the average lifespan is between six and seven dozen years in first-world countries. It's also important to remember that average lifespans in premodern times were greatly reduced by the high infant mortality rates; if you made it to, say, a dozen and a half, you were probably good for four or five dozen years, but a much higher percentage of people died in youth than do now. When was the last time you met someone who had lost a child to measles, or smallpox? Used happen a lot.

I think we could draw conclusions supporting most any base based on lifespans if we wanted. Average lifespan is six dozen years! The longest lifespans are about ten dozen! (Conclude something about decimal or dozenal in this?) Adulthood happens at approximately a dozen and a half (or two dozen, more appropriately, at least in our days)!
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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alysdexia
alysdexia

Aug 8 2017, 08:53 AM #15

Ugh IPB is trash. I had to multiquote by hand and enter the attributes by copypaste.
Troodon @ Nov 6 2016, 07:00 AM wrote:I have noticed that the oldest
old:new::eld:young.
humans manage to exceed decimal 100 years in lifespan, which, coincidentally, also happens to be the number base system that the vast majority of humans worldwide have selected to use.
They use base-10, not base-100.
This is not the first time I have thought about this; I remember I had these same thoughts about three years ago, when I realized that, in dozenal, no human would
would -> could, should
be able to say that their life
their -> whose
spans three grossuries, while there are, indeed, some humans who can say that their life spans three centuries for decimal.
No:https://en.wikipedia.org/wiki/Longevity_myths.
(It is notable to point out, though, that decimal is not the largest base
large:rare::great:small::big:lite::mickel:littel.

Double sharp @ Dec 9 2016, 08:22 AM wrote:but no one would yet have reached two
would -> should
(Calment only got to octal "172", six years away from "200").
From means after.
I wonder when the first person will manage that, hitting the next power of two...
Plenty already will. But shall they?
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Double sharp
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Aug 8 2017, 09:22 AM #16

That's not how English works.

By the way, "spanning three centuries" does not mean 300 years. It would mean something like the case of someone who was born in 1899 and died in 2001. His life would include parts of the 19th, 20th, and 21st centuries.
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Double sharp
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Aug 8 2017, 09:26 AM #17

Incidentally, from "alysdexia"'s username and made-up revisionist forms of English, I have to wonder if this is just yet another incarnation of long-term Wikipedia troll Lysdexia. It would hardly be the first time she has been doing this off-Wikipedia.
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alysdexia
alysdexia

Aug 8 2017, 03:28 PM #18

What's not how English works? (English, which has been dead for 1000 years sith the Norman Conquest. Everyone talks in "Einglish" now.) I did not make up the meaning of auxiliary verbs.

This is Lysdexia from Wikimedia but I'm too honest to be a troll. Halfwits in power tend to be dishonest, ignorant, censorial, and defamatory.
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Kodegadulo
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Aug 8 2017, 08:27 PM #19

English is alive and well, and doing quite nicely, thank you very much. Far from spelling its death, the Norman Conquest was the singular greatest contributing factor to its current richness.

What _did_ die at the hands of William the Conqueror, however, was English's predecessor language, Ænglisc. That tongue has passed on. It is no more. It has ceased to be. It's expired and gone to meet its maker. It's a stiff. Bereft of life, it rests in peace. If professors hadn't nailed it into dusty textbooks, it'd be pushing up the daisies. Its semantic processes are now history. It's off the twig. It's kicked the bucket, shuffled off its mortal coil, run down the curtain, and joined the bloomin' choir invisibile.

In short, Ænglisc is an ex-language.

;)
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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Shaun
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Shaun
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Joined: Aug 2 2005, 04:09 PM

Aug 8 2017, 09:24 PM #20

alysdexia -

be able to say that their life
their -> whose
And your point is? We don't go in for criticising our posters' linguistic abilities.

Though the language of the Forum is English we recognise that it is not the first language of many posters on the Internet. Sniping at other members of the Forum is not encouraged and if you are here merely to pick holes and sneer at others for their ideas or use of language then you might be happier on some other forum.

Our fundamental topic here is the use of base twelve, not spelling and grammar.
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.
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Double sharp
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Double sharp
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Aug 9 2017, 04:02 AM #21

alysdexia @ Aug 8 2017, 03:28 PM wrote: What's not how English works?  (English, which has been dead for 1000 years sith the Norman Conquest.  Everyone talks in "Einglish" now.)  I did not make up the meaning of auxiliary verbs.

This is Lysdexia from Wikimedia but I'm too honest to be a troll.  Halfwits in power tend to be dishonest, ignorant, censorial, and defamatory.
Brilliant, exactly the same sort of sciolism from Wikipedia, combined with a refusal to be corrected and a scorn for those in power.

Can we please stop letting her make the same nuisance of herself at yet another website, as she has frequently done?
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Shaun
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Shaun
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Aug 9 2017, 06:44 AM #22

Double sharp @ Aug 9 2017, 05:02 AM wrote:
Can we please stop letting her make the same nuisance of herself at yet another website, as she has frequently done?
Have banned alysdexia.
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.
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Double sharp
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Double sharp
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Aug 9 2017, 07:03 AM #23

Thank you! Ordinarily I would not have rushed for this quick an application of the banhammer, but given her pattern of similar behaviour across many sites and general intransigence for over a decade I think this is a worthy exception.
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Ruthe
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Aug 19 2017, 06:26 PM #24

Shaun @ Aug 9 2017, 06:44 AM wrote:
Double sharp @ Aug 9 2017, 05:02 AM wrote:
Can we please stop letting her make the same nuisance of herself at yet another website, as she has frequently done?
Have banned alysdexia.
Olé
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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