01-27-2017, 02:19 PM

Is anyone familiar with the Dozenal Society? (Link: http://www.dozenal.org/) The organization is advocating that we switch over from Base 10 to Base 12 in every day life.

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01-27-2017, 02:19 PM

Is anyone familiar with the Dozenal Society? (Link: http://www.dozenal.org/) The organization is advocating that we switch over from Base 10 to Base 12 in every day life.

01-27-2017, 02:52 PM

Hi Eddie. Hmm, I don't think that will ever happen. We are too entrenched in base 10. I once re-purposed (with Katie's help) the 12c+ calculator as a base 12 machine; I forget which two keys I used as A and B. It was fun to play with, but had no practical value.

01-27-2017, 03:43 PM

Great idea & a very nice link.

My own hobby-horse is base 6, having the great advantage of simplicity & economy of type face, not requiring any additional symbols for additional digits.

Counting would look like this:

Decimal style 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12.....

Sixers style 1, 2, 3, 4, 5, 6, 21, 22, 23, 24, 25, 26, 31.....

I prefer using the symbol 1 for zero in an attempt to demystify zero, many people not being sure zero is a number (sadly I don't know how to do the same trick with negatives & imaginaries), & reducing the values of the following single digits by one.

The reading of "1" would be "one" to ease people into the new system, similarly "2" would be read as "two" etc, however the values of the digits would all be one less than traditionally, again to reduce the learning curve.

I have suggested this outline to some friends but have met with a general negative response.

My own hobby-horse is base 6, having the great advantage of simplicity & economy of type face, not requiring any additional symbols for additional digits.

Counting would look like this:

Decimal style 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12.....

Sixers style 1, 2, 3, 4, 5, 6, 21, 22, 23, 24, 25, 26, 31.....

I prefer using the symbol 1 for zero in an attempt to demystify zero, many people not being sure zero is a number (sadly I don't know how to do the same trick with negatives & imaginaries), & reducing the values of the following single digits by one.

The reading of "1" would be "one" to ease people into the new system, similarly "2" would be read as "two" etc, however the values of the digits would all be one less than traditionally, again to reduce the learning curve.

I have suggested this outline to some friends but have met with a general negative response.

01-28-2017, 03:50 AM

(01-27-2017 03:43 PM)Gerald H Wrote: [ -> ]My own hobby-horse is base 6 ... I have suggested this outline to some friends but have met with a general negative response.

You are in good company. Isaac Asimov proposed universal adoption of base 6 (I forget which of his books that essay appeared in). He too received underwhelming support.

01-28-2017, 05:18 AM

President Ford's effort to convert the U.S. to metric was a lot easier, but he failed anyway.

01-29-2017, 11:39 PM

(01-27-2017 03:43 PM)Gerald H Wrote: [ -> ]Great idea & a very nice link.

My own hobby-horse is base 6, having the great advantage of simplicity & economy of type face, not requiring any additional symbols for additional digits.

Counting would look like this:

Decimal style 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12.....

Sixers style 1, 2, 3, 4, 5, 6, 21, 22, 23, 24, 25, 26, 31.....

I prefer using the symbol 1 for zero in an attempt to demystify zero, many people not being sure zero is a number (sadly I don't know how to do the same trick with negatives & imaginaries), & reducing the values of the following single digits by one.

The reading of "1" would be "one" to ease people into the new system, similarly "2" would be read as "two" etc, however the values of the digits would all be one less than traditionally, again to reduce the learning curve.

I have suggested this outline to some friends but have met with a general negative response.

If 1 is used for 0 in sixers style, am I correct in assuming 2 is used for 1, 3 is used for 2, etc?

01-29-2017, 11:41 PM

(01-27-2017 02:52 PM)Don Shepherd Wrote: [ -> ]Hi Eddie. Hmm, I don't think that will ever happen. We are too entrenched in base 10. I once re-purposed (with Katie's help) the 12c+ calculator as a base 12 machine; I forget which two keys I used as A and B. It was fun to play with, but had no practical value.

That is wild. I would love to see the program if you find it. I agree, we are far too invested in base 10, which is fine. Base 10 comes in handy for dividing, halving, and working with factors of 5 and 9.

Eddie

01-29-2017, 11:42 PM

My blog entry on base 12: http://edspi31415.blogspot.com/2017/01/b...ciety.html

01-30-2017, 06:15 AM

(01-29-2017 11:39 PM)Eddie W. Shore Wrote: [ -> ](01-27-2017 03:43 PM)Gerald H Wrote: [ -> ]Great idea & a very nice link.

My own hobby-horse is base 6, having the great advantage of simplicity & economy of type face, not requiring any additional symbols for additional digits.

Counting would look like this:

Decimal style 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12.....

Sixers style 1, 2, 3, 4, 5, 6, 21, 22, 23, 24, 25, 26, 31.....

I prefer using the symbol 1 for zero in an attempt to demystify zero, many people not being sure zero is a number (sadly I don't know how to do the same trick with negatives & imaginaries), & reducing the values of the following single digits by one.

The reading of "1" would be "one" to ease people into the new system, similarly "2" would be read as "two" etc, however the values of the digits would all be one less than traditionally, again to reduce the learning curve.

I have suggested this outline to some friends but have met with a general negative response.

If 1 is used for 0 in sixers style, am I correct in assuming 2 is used for 1, 3 is used for 2, etc?

Yes, Eddie, you are correct.

01-30-2017, 06:16 AM

And to think that until disabused of the notion, I misheard the famous library cataloguing system as "The Duodecimal System" -- and thought it was tied to the operation of base 12 numbers.

My goodness, what a nerd....

My goodness, what a nerd....

01-31-2017, 06:42 PM

(01-27-2017 02:19 PM)Eddie W. Shore Wrote: [ -> ]Is anyone familiar with the Dozenal Society? (Link: http://www.dozenal.org/) The organization is advocating that we switch over from Base 10 to Base 12 in every day life.

One question: Why?

Tom "Tenfingers" Lake

01-31-2017, 07:33 PM

(01-31-2017 06:42 PM)toml_12953 Wrote: [ -> ](01-27-2017 02:19 PM)Eddie W. Shore Wrote: [ -> ]Is anyone familiar with the Dozenal Society? (Link: http://www.dozenal.org/) The organization is advocating that we switch over from Base 10 to Base 12 in every day life.

One question: Why?

Tom "Tenfingers" Lake

There's really only one good reason to have a larger base: to be able to represent more fractions exactly.

12 = 3*2*2, so it can represent 1/2 and 1/3 fractions exactly (and all their powers and combinations).

10 = 2 * 5, 1/2 and 1/5 are exact, still 2 prime numbers so there's no clear advantage in using 12 vs 10. Since we have 10 fingers, 10 seems more logical, although 1/3 fractions are perhaps more common than 1/5 (can't prove that, though).

Why 12? I don't think 12 is good enough, if the goal is to have more fractions, we should use 30.

30 = 2*3*5, so 1/2, 1/3 and 1/5 (and all their powers and combinations) can be represented exactly. Quite difficult to remember 30 different symbols, though.

On the other hand, hardware uses only one base (2), so it would make more sense to move to a binary system (or a power of 2, octal, hex, etc) than a dozen.

02-01-2017, 12:26 AM

(01-31-2017 07:33 PM)Claudio L. Wrote: [ -> ]There's really only one good reason to have a larger base: to be able to represent more fractions exactly.

If we all adopted the HP 32SII/33S/35S "double dot notation", then we could represent ALL fractions exactly, using decimal notation. Example: 1+2/3 is entered directly into the 32SII/33S/35S as "1.2.3". Although the RESULT in those machines is not exact, the NOTATION is. Thus instead of writing \[4\frac{5}{6}-1\frac{2}{3}=3\frac{1}{6}\]you could write simply \[4.5.6-1.2.3=3.1.6\]

This would be the best of both worlds; the familiarity of base 10, and the concise precision of fractions in other bases. Bonus feature: HP invented it.

02-03-2017, 02:21 PM

(01-31-2017 07:33 PM)Claudio L. Wrote: [ -> ](01-31-2017 06:42 PM)toml_12953 Wrote: [ -> ]One question: Why?

Tom "Tenfingers" Lake

On the other hand, hardware uses only one base (2), so it would make more sense to move to a binary system (or a power of 2, octal, hex, etc) than a dozen.

On the other hand, I only have five fingers as well!

Tom L

02-03-2017, 08:26 PM

(02-03-2017 02:21 PM)toml_12953 Wrote: [ -> ]On the other hand, I only have five fingers as well!

Bad pun. I assume intentional, but if not, even better!

02-06-2017, 06:16 PM

ps:

the Jethro Bodine school of ciphering has open matriculation for the digitally challenged. Shoes are optional for undergraduate study and unnecessary for graduate study.

BEST!

SlideRule

the Jethro Bodine school of ciphering has open matriculation for the digitally challenged. Shoes are optional for undergraduate study and unnecessary for graduate study.

BEST!

SlideRule

02-07-2017, 02:21 AM

Meanwhile, on the gripping hand (you gents have set this one up too well to resist), the fingers are not supple enough to use for counting. Thus, base 12, using the 6 fingers each of the two right arms, is the natural choice.

02-07-2017, 07:53 AM

(01-27-2017 02:19 PM)Eddie W. Shore Wrote: [ -> ]Is anyone familiar with the Dozenal Society? (Link: http://www.dozenal.org/) The organization is advocating that we switch over from Base 10 to Base 12 in every day life.

I use base 16 everyday in my work (and my HP 16C / DM 16L are put to good use), but never had to use base 12 even once, ever. Since I still have 10 fingers, though, I'm not going to advocate switching over to a not decimal system for everyday life. Are those Dozenal people from the GATTACA movie, with 6 finger on each of their hands ?

02-07-2017, 02:11 PM

The idea to use base 12 is by no means new. If I remember correctly, Pascal wrote a paper on computing in base 12 in the first half of the 17th century, and some decades later another famous mathematician (Leibniz?) advocated seriously for a change from the decimal system to base 12.

Historically, we owe a lot to the sexagesimal system of the Babylonians: The 360°, the 12 hours, the 60 minutes, and 60 seconds. Thus, a base with factor 12 is still omnipresent.

During the French revolution they tried to use base 10 everywhere. The day should have 10 hours with 100 minutes each, the week should have 10 days. There exist even revolution clocks of famous clockmakers like Berthoud that stick to this system. Exept for what we now know as "gon" (which I personally do not like very much because you frequently use 1/3rd of a right angle but almost never 1/5th) nothing survived.

Thomas

Historically, we owe a lot to the sexagesimal system of the Babylonians: The 360°, the 12 hours, the 60 minutes, and 60 seconds. Thus, a base with factor 12 is still omnipresent.

During the French revolution they tried to use base 10 everywhere. The day should have 10 hours with 100 minutes each, the week should have 10 days. There exist even revolution clocks of famous clockmakers like Berthoud that stick to this system. Exept for what we now know as "gon" (which I personally do not like very much because you frequently use 1/3rd of a right angle but almost never 1/5th) nothing survived.

Thomas

02-08-2017, 02:20 AM

(02-07-2017 07:53 AM)vido Wrote: [ -> ]... but never had to use base 12 even once, ever.

What? You've never ordered a dozen donuts?

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