Keep up the good work.

My basic quibble with base 10 is in doing time calculations. It would be so much more convenient to calculate in base 12! And if we're going to do time in base 12 why not do everything else that way? We already have a basis there especially in linear measurement.

My only quibble with Dozenal ideas is the symbology. I think using Arabic numbers with an X and E tacked on the end (or an A or B)leads to some mind-bending confusion especially in 'decimals'. Also if a dozenal system ever did become viable it would be nice to be able to instantly differentiate it from Arabic numbers. (Would using zodiacal symbols work for this? I think it would definitely be a stretch for people to learn to associate zodiac symbols (or some other twelve symbols) with numbers, but people who are interested in changing our whole number system aren't allergic to 'stretching.')

Also something that is rarely/never mentioned by advocates of a dozenal system is that every note of music we hear is formed from a base 12 division of tones (except perhaps for some primitive aboriginal music). Also, playing cards could be construed as a subliminal desire for a base 12 system depending on the game played. I am working on 'beta' version of a playing card game that emphasizes the base 12 connection.

Yes; it's not very satisfactory. I wish someone would produce some new suggestions for the symbols; I haven't any; lack of imagination and over-familiarity with the system, perhaps (or just Anno Domini...)

There have been many suggestions for symbols over the years - both "short" versions - just for ten and eleven and "long" versions - i.e. a complete set of new numerals. As several writers have pointed out, it shouldn't be beyond the wit of modern man to invent two new symbols at least, seeing as the Indians invented all ten of theirs - especially the zero - but in the sixty years since the DSA was founded (and the forty of the DSGB) no-one has produced any that have achieved unique status. Our reversed two and three were suggested by Sir Isaac Pitman (of shorthand fame); the DSA started with a cursive X and E, and then changed to a star and "octothorpe" (the "hash" or "number" sign in the US).


Maybe we should try a world competition to find a new set (or just the two)?

I have to say that my favourites are those htta I said before. Namely, the DSGB's symbols, or the other ones I suggested in the "other" thread.

the problem with time calculations is not a particular base,
but the lack of a single base


the current time system is a bewildering hybrid of 13 bases!!!


unit...................base

years..................10
months...............12
weeks.................52/53
days....................7/28/29/30/31/365/366
hours..................24
minutes...............60
seconds...............60
milliseconds.........10
microseconds......10
nanoseconds.......10


so it's not surprising that time calculations are complete science fiction

we only need 1 base

using a single base makes time calculations extremely simple
no matter which base you're using


the most practical time basis is the mean solar day (86400 s)
since this is the 1 time interval we cannot ignore

by measuring time only in units of days and fractions of days
time calculations are reduced from 7 step algorithms
to a single addition / subtraction that you can do in your head

the main consideration in terms of base is the resulting divisions of the day

here are a few examples of fractional day time units in various number bases...


BASE 2 (binary)

2^-20............0.082397 s
2^-19............0.164794 s
2^-18............0.329589 s
2^-17............0.659179 s
2^-16............1.318359 s
2^-15............2.636718 s
2^-14............5.273437 s
2^-13............10.546875 s
2^-12............21.09375 s
2^-11............42.1875 s
2^-10............84.375 s
2^-9............168.75 s
2^-8............337.5 s
2^-7............675 s
2^-6............1350 s
2^-5............2700 s
2^-4............5400 s
2^-3............10800 s
2^-2............21600 s
2^-1............43200 s
2^-0............86400 s

multiples of days

1 d
2 d
4 d
8 d
16 d
32 d
64 d
128 d
256 d
512 d
1024 d (2.8 y)

__________________________________________


BASE 3

3^-13............0.054192 s
3^-12............0.162576 s
3^-11............0.487730 s
3^-10............1.463191 s
3^-9............4.3895747 s
3^-8............13.168724 s
3^-7............39.506172 s
3^-6............118.51851 s
3^-5............355.55555 s
3^-4............1066.6666 s
3^-3............3200 s
3^-2............9600 s
3^-1............28800 s
3^-0............86400 s

multiples of days

1 d
3 d
9 d
27 d
81 d
243 d
729 d (2 y)

__________________________________________


BASE 4

4^-10..........0.0823974 s
4^-9............0.3295898 s
4^-8............1.3183593 s
4^-7............5.2734374 s
4^-6............21.09375 s
4^-5............84.375 s
4^-4............337.5 s
4^-3............1350 s
4^-2............5400 s
4^-1............21600 s
4^-0............86400 s

multiples of days

1 d
4 d
16 d
64 d
256 d
1024 d (2.8 y)

__________________________________________


BASE 5

5^-8............0.221184 s
5^-7............1.10592 s
5^-6............5.5296 s
5^-5............27.648 s
5^-4............138.24 s
5^-3............691.2 s
5^-2............3456 s
5^-1............17280 s
5^-0............86400 s

multiples of days

1 d
5 d
25 d
125 d
625 d (1.7 y)

__________________________________________


BASE 6 (heximal)

6^-8............0.05144032 s
6^-7............0.30864197 s
6^-6............1.85185185 s
6^-5............11.1111111 s
6^-4............66.6666666 s
6^-3............400 s
6^-2............2400 s
6^-1............14400 s
6^-0............86400 s

1 d
6 d
36 d
216 d
1296 d (3.54 y)

__________________________________________


BASE 7

7^-7............0.1049125 s
7^-6............0.7343878 s
7^-5............5.1407151 s
7^-4............35.9850062 s
7^-3............251.895043 s
7^-2............1763.26530 s
7^-1............12342,857 s
7^-0............86400 s

multiples of days

1 d
7 d
49 d
343 d

__________________________________________


BASE 8 (octal)

8^-6............0.329589 s
8^-5............2.636718 s
8^-4............21.09375 s
8^-3............168,75 s
8^-2............1350 s
8^-1............10800 s
8^-0............86400 s

multiples of days

1 d
8 d
64 d
512 d (1.4 y)

__________________________________________


BASE 9

9^-6............0.1625768 s
9^-5............1.4631915 s
9^-4............13.168724 s
9^-3............118.51851 s
9^-2............1066.6666 s
9^-1............9600 s
9^-0............86400 s

multiples of days

1 d
9 d
81 d
729 d (2 y)

__________________________________________


BASE 10 (decimal)

10^-6............0.0864 s
10^-5............0.864 s
10^-4............8.64 s
10^-3............86.4 s
10^-2............864 s
10^-1............8640 s
10^-0............86400 s

multiples of days

1 d
10 d
100 d
1000 d (2.73 y)

__________________________________________


BASE 11

11^-6............0.048770 s
11^-5............0.536476 s
11^-4............5.901236 s
11^-3............64.91359 s
11^-2............714.0495 s
11^-1............7854.545 s
11^-0............86400 s

multiples of days

1 d
11 d
121 d
1331 d (3.64 y)

__________________________________________


BASE 12 (dozenal)

12^-6............0.0289351833 s
12^-5............0.3472222 s
12^-4............4.1666666 s
12^-3............50 s
12^-2............600 s
12^-1............7200 s
12^-0............86400 s

multiples of days

1 d
12 d
144 d
1728 d (4.73 y)

__________________________________________


BASE 13

13^-5............0.2327003 s
13^-4............3.0251041 s
13^-3............39.326354 s
13^-2............511.24260 s
13^-1............6646.1538 s
13^-0............86400 s

multiples of days

1 d
13 d
169 d

__________________________________________


BASE 14

14^-5............0.1606473 s
14^-4............2.2490628 s
14^-3............31.486888 s
14^-2............440.81632 s
14^-1............6171.4285 s
14^-0............86400 s

multiples of days

1 d
14 d
196 d

__________________________________________


BASE 15

15^-5............0.11377 s
15^-4............1.70666 s
15^-3............25.6 s
15^-2............384 s
15^-1............5760 s
15^-0............86400 s

multiples of days

1 d
15 d
225 d

__________________________________________


BASE 16 (hexadecimal)

16^-5............0.082397 s
16^-4............1.318359 s
16^-3............21.09375 s
16^-2............337.5 s
16^-1............5400 s
16^-0............86400 s

multiples of days

1 d
16 d
256 d

__________________________________________


BASE 17

17^-5............0.060851 s
17^-4............1.034470 s
17^-3............17.58599 s
17^-2............298.9619 s
17^-1............5082.352 s
17^-0............86400 s

multiples of days

1 d
17 d
289 d

__________________________________________


BASE 18

18^-5............0.45724 s
18^-4............0.82304 s
18^-3............14.8148 s
18^-2............266.666 s
18^-1............4800 s
18^-0............86400 s

multiples of days

1 d
18 d
324 d

__________________________________________


BASE 19

19^-5............0.03489 s
19^-4............0.66297 s
19^-3............12.59658 s
19^-2............239.3351 s
19^-1............4547.368 s
19^-0............86400 s

multiples of days

1 d
19 d
361 d

__________________________________________


BASE 20 (vigesimal)

20^-5............0.027 s
20^-4............0.54 s
20^-3............10.8 s
20^-2............216 s
20^-1............4320 s
20^-0............86400 s

multiples of days

1 d
20 d
400 d (1.09 y)

__________________________________________


BASE 21

21^-5............0.021551 s
21^-4............0.444259 s
21^-3............9.329446 s
21^-2............195.9183 s
21^-1............4114.285 s
21^-0............86400 s

multiples of days

1 d
21 d
441 d (1.2 y)

__________________________________________


BASE 22

22^-4............0.368827 s
22^-3............8.1142 s
22^-2............178.5124 s
22^-1............3927.2728 s
22^-0............86400 s

multiples of days

1 d
22 d
484 d (1.32 y)

__________________________________________


BASE 23

23^-4............0.308746 s
23^-3............7.101175 s
23^-2............163.3270 s
23^-1............3756.521 s
23^-0............86400 s

multiples of days

1 d
23 d
529 d (1.44 y)

__________________________________________


BASE 24

24^-4............0.260416 s
24^-3............6.25 s
24^-2............150 s
24^-1............3600 s
24^-0............86400 s

1 d
24 d
576 d (1.57 y)

__________________________________________


BASE 25

25^-4............0.221184 s
25^-3............5.5296 s
25^-2............138.24 s
25^-1............3456 s
25^-0............86400 s

multiples of days

1 d
25 d
625 d (1.7 y)

__________________________________________


BASE 30 (trigesimal)

30^-4............0.106666 s
30^-3............3.2 s
30^-2............96 s
30^-1............2880 s
30^-0............86400 s

multiples of days

1 d
30 d
900 d (2.46 y)

__________________________________________


BASE 60 (sexagesimal)

60^-3............0.4 s
60^-2............24 s
60^-1............1440 s
60^-0............86400 s

multiples of days

1 d
60 d
3600 d (9.85 y)


this clearly shows that our time system is not sexagesimal (as it is so often called)

These are indeed unnecessarily complicated, but

The 365.2425 days per year is something we're stuck with. Even if we could change the revolution speed of Earth, the distances from the Sun which would allow a *100 day orbit (between Mercury and Venus) or a *1000 day orbit (in the asteroid belt) are uninhabitable.

Of course, the calendar could still be simplified somewhat. For example, by making the months a strict alternation of 30 and 31 days, with the 31st day of the last month omitted during non-leap years.

no need to change the earth's orbit

the earth orbits the sun perfectly well without anyone having to keep count
in fact if not for the weather changes, it wouldn't be that hard to ignore years completely
unless you're a farmer, a football hooligan, or a duck

days on the other hand are unavoidable

every 86400 seconds we start a new cycle of activity, biological functions, hygene,
nutrition, sleep, etc.. perfectly in sync with the sun

anyone who doubts this can try living 10 days out of sync with the sun
and they will end up looking and feeling like a putrified zombie on prozac
who sleeps on empty soup cans



Julian Day numbering is a good example of a complete time system that requires only days and fractional days

imagine life without having to wonder if it's a leap year or not,
being able to calculate the exact the number days between dates in your head

kids not having to learn how many days each month has,
because Roman emperors had a fetish for odd numbers
and naming months after themselves

or adding up the play time of 100s of mp3s without performing a 3 step algorithm
of calculating hours, minutes and seconds seperately

this is what life would be like with a single number base for time
in base fractions of a day

you know without looking at a calendar that day 53779 is followed by day 53780,
53781, etc.. one integer after the next without interruption

that 53781.500 is noon UT and 53782.000 is midnight UT

and that adding more decimal places increases the precision of the time
measurement without having to make up new units and new names for the new units


and the best feature of all is that this form of time keeping works with any number base
since 1 day always remains 1 day, divided by base ~ n

I would hate that system, it sums up everything that is wrong with the SI approach to measuring. People do not naturally think in decimals, they can think in fractions but are really only comfortable in whole numbers. That's exactly why the Imperial measurement system came about, it evolved to match how people think. Unfortunately it evolved differently in different places and we have a mish mash of values, that can be fixed without destroying the human aspect of the system. This imposition of the decimal representation of fractions in the name of logic is just plain wrong.

Besides the standard working day (8 hours) cannot be represented in your scheme, in Sweden you'd probably only have to work .3 of a day but in the US we'd have to work .4 :D

this really depends on who you ask

the english speaking world seems somewhat anti-metric and anti-decimal

where the rest of the world would never consider using non-decimal fractions
or uniquely named units

most of us in europa are decimalists, with centuries of decimal metrology behind us

so it's not only extremely easy, but completely natural for me and any non-english european to think in decimal fractions

the SI in fact is superior to every metrological system before it
exactly because of it's efficient use of prefixed base units with a single number base and decimal fractions

the metric system, and resulting SI was a major catalyst in the explosion in scientific progress during the past 200 years
since correlated metric units are the basis for most equations

the imperial system is extremely confusing in the eyes of most europeans

before the SI there was no clear definition of imperial units
which, (i should point out) have all been officially defined in SI units since 150 years ago

the pre SI yard was the distance from King Henry's nose to his thumb
(very high precision) a foot - the length of his foot, and the inch being the width of his thumb,
or x lengths of barley corn, or other rediculous basis
in other words, the most unscientific system imaginable

throughout the imperial measured world - imperial units had wildly variable values
in France alone there were 1000s of conflicting kaotic measures,
which is why the metric system was created in the first place


the metric structure of metrology is here to stay,
and we will never give it up for the english system, not even at gunpoint

but this doesn't mean it has to be base 10
the SI could just as well be dozenal and still be equally efficient

there is no real standard workday, the EU commission tried to force a standard 6.5 hour workday, but it wasn't very popular - a workday in sweden can be anywhere from 4 hours to 12 hours, and it's about the same in germany

a workday could be .333 d (which equals 8 hours)
or .350 d (8 hours, 24 minutes)

it doesn't have to be an even fraction - it's just a system of measurement
not holy dogma :blink:

also if the day is divided by base 12
then .06 d = 1 hour, .1 d = 2 hours, .2 d = 4 hours .3 d = 6 hours, .4 d = 8 hours, etc...
and noon would be at .600 (with 6 having the function of 5 in decimal)

Wow, you dismiss probably 100-150 years of scientific contributions by British (including empire and commonwealth) and US scientists so easily because they didn't use SI units? I spent 4 years working at Rothamsted Experimental Station in England and my boss there still used the occasional Imperial unit, mostly SI of course. I did learn that system at school (in England, I'm English), I still hate it and will never use it in my every day life, even at gunpoint. I'm still familiar with it as I have German and Japanese motorcycles and a Japanese truck.

The foot has been a metric unit since the late 1100s when it was inscribed on a column in St Paul's cathedral, it's still the same length. How it came to be that length is irrelevant.

no one is suggesting that countries using imperial measures have not contributed to science during the past 200 years,
only that the volume of scientific data has exploded worldwide directly due to these correlated metric units.

all scientists use the SI, including american and british scientists
Einstein could never have formulated his general and special theories without the SI
E=MC² is meaningless in Imperial units

actually nothing in metrology is irrelevant
metric standards are meaningless without precise definitions

standards based on artifacts are less reliable than those based on universal constants

the kg is the last remaining base unit in the SI defined by an artifact
it should properly be defined in terms of electron mass

inscribing notches on a column was more than adequate in the middle ages
but here and now in the age of nanoscience, we need higher precision than
ever dreamed about 200 years ago

Can you point me to some independent evidence of that? (A study of some kind perhaps)

I don't think the use of SI has had a significant effect on the explosion in science over the last 200 years. It has been far more to do with social and religous enlightenment and better communication.

here's a good reference..

E = mc²

energy (in Joule) = mass (in Kilogram) x c ~ the speed of light in a vacuum (in meter/second) - squared


c = 299 792 458 m/s
c² = 89 875 517 873 681 764

therefore the potential energy released by a 1 kg mass = 89 875 517 873 681 764 Joule

and the ratio of mass to energy = 89 875 517 873 681 764 : 1


in english measures there is no single base unit of anything
it's anyones guess which unit to take for an equation
this is not only confusing, it can be dangerous

but if we take 1 foot as a base length
1 pound as a base mass unit (the pound is actually a unit of weight and not mass btw. so it's not so useful here)
1 BTU as a unit of energy
and 1 second as a base time unit (unless you prefer using an hour) ;-)

let's see if i remember my Roman conversions

shall we take a troy or avoirdupois pound?
hmm.. i guess it depends on whether it's tuesday or not

1 BTU = 1055.87 Joule
1 foot = 0.3048 m
1 pound = 0.453592 kg (avoirdupois)

we'll start with c in Roman (sorry English) length units
which equals 983 571 056.4304461942257217847769 feet/second

c² would then = 967 412 023 047 703 971.79683248255385

and 1 pound of mass should equal 967 412 023 047 703 971.79683248255385 BTU

we know that 0.453592 kg = 40 766 815 903 359 058.696288 Joule by using SI units
so let's see if it works with King Henry's gammy foot


40 766 815 903 359 058.696288 / 1055.87 = 38 609 692 389 554.640908717929290538 BTU

ooooh!! it doesn't quite work does it

in fact it's off by a factor of 25056.196078615351447336149031089
i guess Einstein was wrong ;-)

i should explain why SI units are superior and how they work the way they do

1. correlation and consistency

2. 1 base unit for each domain of measure

3. base units defined by universal constants

4. derived units formed only from base units

therefore

1 Joule = 1 kg m²/s²




Imperial units have no consistency to them

the system has no base units, but a huge hodge-podge of bizarre uniquely named units with vulgar fraction relationships

there is no consistent number base
is it base 12? binary? base 36? octal? it's anyone's guess

the only precision in Imperial units is due to being defined in SI units


i can't blame 16th century English scientists for having to work without the SI

but since 1875 the world has been metric
so there is no excuse

no scientist today would use anything but SI units

and science would never have advanced this far in 200 years without metric standards

this is not to say that the SI is perfect
it is definitely not a perfect system,
but it's as close as any system of measurement has come to being perfect
in the history of metrology

the SI is still a work in progress

no significant improvements have been made to Imperial measures in 500 years
(again, other than defining them in SI units)

the fact that the whole world (except the USA and UK) has dropped imperial measures should be a major clue

since the 1970s the UK has (reportedly) been a metric country by law,
cable is sold by metre, petrol is sold by litre...
yet road signs still give distances in miles and yards

it's very strange

although it would be hard to imagine a british pub without pints B)

Read 1984.

Yes, Winston complained that he could no longer get a pint of beer, and that half a liter wasn't enough. Of course, this has an entirely different meaning for US readers!

On this exchange of views about SI and Imperial I find myself agreeing with Killer and against everything that Växan has said.

It is clear that Växan has been thoroughly brain-washed to into the SI religion!

The Imperial system is based mainly on the use of factors of the form (2^n)(3^m) which I call "basals" with higher prime factors occasionally coming in.

It seems that Växan has never learnt to think in terms of fractions, and has instead learnt only to process everything in inadequate decimal expressions.

It is misplaced decimal points that cause many disasters such as medical overdoses.

I don't specifically advocate the traditional Imperial units, though many of them are related to the human scale of things, just the use of units suitable to particular applications.

The units of day, month, year (in their various forms) naturally arise in the measurement of time and the organisation of the calendar. It is the approximation to their relative ratios by whole-number fractions that provide the organisation.

In the case of fundamental physics equations like E = m(c^2) it is natural to use atomic or Planck units, for instance to put c = 1, taking the velocity of light as a unit. (It is interesting to express other velocities in terms of fractions of the velocity of light.)

this is not a valid argument - one can just as easily misplace a vulgar fraction
11/60 rather than 1/160

nothing is more efficient and precise than decimal fractions
one has only to add more decimal places to increase precision

try doing that with vulgar fractions

in fact why don't you write Pi for me as a vulgar fraction - that should keep you busy
for several lifetimes

the SI is a metrological system - not a religion


from birth - i have never known anything other than the SI

however, by my own analytical nature - this alone is not enough to keep me from criticizing it (or any other system)

as an electronics engineer, i depend on the SI on a regular basis
Maxwell equations apply to SI units






there are no optional electrical Imperial units

i have many complaints with the SI - including the fact that the Ampere is not a base unit
but actually a derived unit, being defined as 1 Coulomb/second

therefore the base electrical unit should be the unit of charge - Coulomb
defined as 6 241 509 474 153 816 706 e (elementary charges)

where
e = 1.6021765314 x 10^-19 C



our high tech world could not function without the SI
unless there were something better to replace it

Imperial measure is not only inferior, it's not even an option
in my opinion it's not a system but a collection of medieaval relics

i have no special loyalty to base 10 - i accept that the human world is decimal
and therefore it's only practical to use base 10 numbering - since our number system is decimal

if the world were dozenal or octal then i would be using base 12 or base 8

it matters very little to me
keeping to 1 standard base is what matters to our civilization

the English cannot simply turn 2 blind eyes to the rest of the world
and think only of their own interests and tradition

we are all part of a global community
and we have to work as a unit

English speaking countries have resisted metric conversion for 200 years,
even though the USA signed the treaty of the metre in 1875, as did the rest of the world, and the american military and american science institutions have made SI the standard, the public still resists. it makes no sense

if the English think they are exempt from participating in world standards
because they are somehow a privileged class of human

they should think again

no nation state has special rights
we are 1 planet with 1 human species
and we need to work as 1

this is a metric planet
so get used to it

if you can come up with a better system
then present it to the international standards organisation
and the BIPM and let's talk about it

.

i think a degree of forum etiquette should be observed here

i've been in many forums where some members resorted to personal attacks
on the characters of other members - for lack of a valid argument

on the premise that...

* John agrees with my opinions - therefore John is right
* Bob disagrees with my opinions - therefore Bob is a Poo-Poo Head


(the characters: John and Bob are fictional, any resemblance to existing characters is purely coincidental)

I agree, I was about to say the same to you for that statement.

I realise that there is a language problem here but you are coming across, to me at least, as incredibly arrogant (and I should know, my nickname on another board is Arrogant Bastard :D )

if i come across as arrogant - i sincerely apologize

the subtleties of a language (especially english) can quickly make a simple statement seem intimidating or sarcastic

i try my best to convert a thought in my head into the equivalant in english
but i can't garantie the results - translation is a dangerous sport

i wonder how many wars have been ignited by translators? ;-P

Vaxan - I'll give you some examples where I don't think language is the issue, you're obviously an intelligent fellow and I don't want to put you off the discussions but...


"Imperial measure is not only inferior, it's not even an option
in my opinion it's not a system but a collection of medieaval relics"

"and the English are turning 2 blind eyes to the rest of the world
thinking only of their own interests and tradition, with a religious fanatasism"

"if the English think they are exempt from participating in world standards
because they are somehow a privileged class of human they should think again"

"you're not special we are 1 planet with 1 human species and we need to work as 1"

"this is a decimal metric planet so get used to it"

All of those are just blanket statements which leave no reasonable way of rebuttal, obviously since the other people in this thread are discussing the possibility of using Imperial units we don't agree with you, so to insult us on the basis of our beliefs or nationality is not going to be productive. I am open to persuasion but not force.

these are of course only generalizations

i admit i may have overstated my opinion of Imperial measures
i did not expect anyone here to take offence to such remarks

since the Imperial form of measurement was created millennia ago collectively by europeans and other cultures, and not just the english, the term "english measure" has taken hold i think mostly due to the english being the last to use this system

i think debate is a very good way of exposing problems, and finding solutions
as long as it's done responsibly, by clearly laying out the facts and reasons for or against.

i've done my best to give detailed facts and reasons why Imperial measure is detrimental to scientific and technological progress in the modern world, and why metric measure is ideally suited to science and technology.

these facts are undeniable by any responsible scientist or engineer, english or otherwise, however the majority of society have a tendency to over-romanticize old world traditions even to their own detriment.

which is why i find education and debate so important

everyone should understand where we've been, and where we are now
how we got to where we are, and where we are going from here


the whole world once used various forms of Imperial measure
the ancient world was built on cubits of various lengths

as soon as science became an issue in society
it became increasingly more aparent that these old measures did not measure up to the needs of science
so the newly created "scientific community" decided to do something about it
(with great resistance from the common public i might add)

the average villager couldn't have cared less about the precision of metrology
he just wanted things to stay the same until he died,
to know how much butter he could buy for his 2 coins.
and having to learn something new meant taking valuable time away from chopping wood.

today's industries depend on a level of precision beyond anything imagined possible by our ancestrors
VLSI processors with 1000s of millions of transistors etched into silicon at 90 nanometer scale!!!

no matter how one tries to romanticize Imperial measures
they are simply not suited to this level of precision

vulgar fractions are no longer useful in 21st century mathematics

this is the age of decimal high-precision measurement
whereby increasing the number of decimal places, the level of precision is increased
this method of computing is mathematically flawless, no matter which base is used


refusing to adopt a superior system on romantic or emotional grounds is irresponsible,
illogical, counterproductive and unscientific

science has nothing to do with beliefs or emotions
it serves only to increase our knowledge of physics and the precision of technology

there should be no other consideration

Växan is spelled with an ä ;)

but i guess you don't have that character on english keyboards

(poor english people, someone has stollen letters from your alfabet) :-(



in swedish these 2 dots can make a huge difference

for example the difference between :

Rova ~ a turnip
Röva ~ an arse

I also think that Imperial measure is not modern enough for scientific reason.

But there is one big advantage: it is based on human measures, such as foot length, hand width, and so on. The meter is too big for a base unit, I think. I never can estimate its length with my feet. It's a very big step, nearly a jump.

TGM is a step in the right direction, I think. It unites the virtues of the dozenal with the advantages of SI (base units, same number base for everything).

And decimal notation of numbers is not as good as you want to have it, växan. Ever tried dividing 12/7 or something like that? You get 1.7142857142857142... Or, in dozenals, 1.86 :A 35186 :A 35... Not very satisfying, because 12/7 says the same without needing so many figures.

And approximating Pi is no problem either: 22/7 is a good estimation, better than 3.14. I can give more exact fractions, if you like.

please explain, how is 22/7 better than 3.14?

also Pi is not simply 3.14

it's 3.14159265358979323846264338327950......

if you only count to the first 0

i assure you all these decimal places count when high precision is needed

(sorry i only have it memorized to 32 decimal places)



i have no problem computing large decimal fractions in my head
(at least to 6 decimal places)

i don't think this is an unusual ability

maybe our culture has become more accustom to decimal thinking
due to the longer period since using non-metric units

The approximation π ≈3.14 has an error of 0.00159, but π ≈22/7 has an error of only 0.00126 ;)

great! fantastic! but first you must divide the diameter by 7 and then multiply by 22
or divide the circumference by 22 and multiply by 7 (eitherway 2 operations)
and the result would still be in error by over 0.0012644892673496186802137595774971

since 22/7 = 3.1428571428571428571428571428571

where instead you could reduce the error to 1 x 10^-10000
and just calculate once by :

3.1415926535897932384626433832795028841971693993751058209749
445923078164062862089986280348253421170679821480865132823066
470938446095505822317253594081284811174502841027019385211055
596446229489549303819644288109756659334461284756482337867831
652712019091456485669234603486104543266482133936072602491412
737245870066063155881748815209209628292540917153643678925903
600113305305488204665213841469519415116094330572703657595919
530921861173819326117931051185480744623799627495673518857527
248912279381830119491298336733624406566430860213949463952247
371907021798609437027705392171762931767523846748184676694051
320005681271452635608277857713427577896091736371787214684409
012249534301465495853710507922796892589235420199561121290219
608640344181598136297747713099605187072113499999983729780499
510597317328160963185950244594553469083026425223082533446850
352619311881710100031378387528865875332083814206171776691473
035982534904287554687311595628638823537875937519577818577805
321712268066130019278766111959092164201989380952572010654858
632788659361533818279682303019520353018529689957736225994138
912497217752834791315155748572424541506959508295331168617278
558890750983817546374649393192550604009277016711390098488240
128583616035637076601047101819429555961989467678374494482553
797747268471040475346462080466842590694912933136770289891521
047521620569660240580381501935112533824300355876402474964732
639141992726042699227967823547816360093417216412199245863150
302861829745557067498385054945885869269956909272107975093029
553211653449872027559602364806654991198818347977535663698074
265425278625518184175746728909777727938000816470600161452491
921732172147723501414419735685481613611573525521334757418494
684385233239073941433345477624168625189835694855620992192221
842725502542568876717904946016534668049886272327917860857843
838279679766814541009538837863609506800642251252051173929848
960841284886269456042419652850222106611863067442786220391949
450471237137869609563643719172874677646575739624138908658326
459958133904780275900994657640789512694683983525957098258226
205224894077267194782684826014769909026401363944374553050682
034962524517493996514314298091906592509372216964615157098583
874105978859597729754989301617539284681382686838689427741559
918559252459539594310499725246808459872736446958486538367362
226260991246080512438843904512441365497627807977156914359977
001296160894416948685558484063534220722258284886481584560285
060168427394522674676788952521385225499546667278239864565961
163548862305774564980355936345681743241125150760694794510965
960940252288797108931456691368672287489405601015033086179286
809208747609178249385890097149096759852613655497818931297848
216829989487226588048575640142704775551323796414515237462343
645428584447952658678210511413547357395231134271661021359695
362314429524849371871101457654035902799344037420073105785390
621983874478084784896833214457138687519435064302184531910484
810053706146806749192781911979399520614196634287544406437451
237181921799983910159195618146751426912397489409071864942319
615679452080951465502252316038819301420937621378559566389377
870830390697920773467221825625996615014215030680384477345492
026054146659252014974428507325186660021324340881907104863317
346496514539057962685610055081066587969981635747363840525714
591028970641401109712062804390397595156771577004203378699360
072305587631763594218731251471205329281918261861258673215791
984148488291644706095752706957220917567116722910981690915280
173506712748583222871835209353965725121083579151369882091444
210067510334671103141267111369908658516398315019701651511685
171437657618351556508849099898599823873455283316355076479185
358932261854896321329330898570642046752590709154814165498594
616371802709819943099244889575712828905923233260972997120844
335732654893823911932597463667305836041428138830320382490375
898524374417029132765618093773444030707469211201913020330380
197621101100449293215160842444859637669838952286847831235526
582131449576857262433441893039686426243410773226978028073189
154411010446823252716201052652272111660396665573092547110557
853763466820653109896526918620564769312570586356620185581007
293606598764861179104533488503461136576867532494416680396265
797877185560845529654126654085306143444318586769751456614068
007002378776591344017127494704205622305389945613140711270004
078547332699390814546646458807972708266830634328587856983052
358089330657574067954571637752542021149557615814002501262285
941302164715509792592309907965473761255176567513575178296664
547791745011299614890304639947132962107340437518957359614589
019389713111790429782856475032031986915140287080859904801094
121472213179476477726224142548545403321571853061422881375850
430633217518297986622371721591607716692547487389866549494501
146540628433663937900397692656721463853067360965712091807638
327166416274888800786925602902284721040317211860820419000422
966171196377921337575114959501566049631862947265473642523081
770367515906735023507283540567040386743513622224771589150495
309844489333096340878076932599397805419341447377441842631298
608099888687413260472156951623965864573021631598193195167353
812974167729478672422924654366800980676928238280689964004824
354037014163149658979409243237896907069779422362508221688957
383798623001593776471651228935786015881617557829735233446042
815126272037343146531977774160319906655418763979293344195215
413418994854447345673831624993419131814809277771038638773431
772075456545322077709212019051660962804909263601975988281613
323166636528619326686336062735676303544776280350450777235547
105859548702790814356240145171806246436267945612753181340783
303362542327839449753824372058353114771199260638133467768796
959703098339130771098704085913374641442822772634659470474587
847787201927715280731767907707157213444730605700733492436931
138350493163128404251219256517980694113528013147013047816437
885185290928545201165839341965621349143415956258658655705526
904965209858033850722426482939728584783163057777560688876446
248246857926039535277348030480290058760758251047470916439613
626760449256274204208320856611906254543372131535958450687724
602901618766795240616342522577195429162991930645537799140373
404328752628889639958794757291746426357455254079091451357111
369410911939325191076020825202618798531887705842972591677813
149699009019211697173727847684726860849003377024242916513005
005168323364350389517029893922334517220138128069650117844087
451960121228599371623130171144484640903890644954440061986907
548516026327505298349187407866808818338510228334508504860825
039302133219715518430635455007668282949304137765527939751754
613953984683393638304746119966538581538420568533862186725233
402830871123282789212507712629463229563989898935821167456270
102183564622013496715188190973038119800497340723961036854066
431939509790190699639552453005450580685501956730229219139339
185680344903982059551002263535361920419947455385938102343955
449597783779023742161727111723643435439478221818528624085140
066604433258885698670543154706965747458550332323342107301545
940516553790686627333799585115625784322988273723198987571415
957811196358330059408730681216028764962867446047746491599505
497374256269010490377819868359381465741268049256487985561453
723478673303904688383436346553794986419270563872931748723320
837601123029911367938627089438799362016295154133714248928307
220126901475466847653576164773794675200490757155527819653621
323926406160136358155907422020203187277605277219005561484255
518792530343513984425322341576233610642506390497500865627109
535919465897514131034822769306247435363256916078154781811528
436679570611086153315044521274739245449454236828860613408414
863776700961207151249140430272538607648236341433462351897576
645216413767969031495019108575984423919862916421939949072362
346468441173940326591840443780513338945257423995082965912285
085558215725031071257012668302402929525220118726767562204154
205161841634847565169998116141010029960783869092916030288400
269104140792886215078424516709087000699282120660418371806535
567252532567532861291042487761825829765157959847035622262934
860034158722980534989650226291748788202734209222245339856264
766914905562842503912757710284027998066365825488926488025456
610172967026640765590429099456815065265305371829412703369313
785178609040708667114965583434347693385781711386455873678123
014587687126603489139095620099393610310291616152881384379099
042317473363948045759314931405297634757481193567091101377517
210080315590248530906692037671922033229094334676851422144773
793937517034436619910403375111735471918550464490263655128162
288244625759163330391072253837421821408835086573917715096828
874782656995995744906617583441375223970968340800535598491754
173818839994469748676265516582765848358845314277568790029095
170283529716344562129640435231176006651012412006597558512761
785838292041974844236080071930457618932349229279650198751872
127267507981255470958904556357921221033346697499235630254947
802490114195212382815309114079073860251522742995818072471625
916685451333123948049470791191532673430282441860414263639548
000448002670496248201792896476697583183271314251702969234889
627668440323260927524960357996469256504936818360900323809293
459588970695365349406034021665443755890045632882250545255640
564482465151875471196218443965825337543885690941130315095261
793780029741207665147939425902989695946995565761218656196733
786236256125216320862869222103274889218654364802296780705765
615144632046927906821207388377814233562823608963208068222468
012248261177185896381409183903673672220888321513755600372798
394004152970028783076670944474560134556417254370906979396122
571429894671543578468788614445812314593571984922528471605049
221242470141214780573455105008019086996033027634787081081754
501193071412233908663938339529425786905076431006383519834389
341596131854347546495569781038293097164651438407007073604112
373599843452251610507027056235266012764848308407611830130527
932054274628654036036745328651057065874882256981579367897669
742205750596834408697350201410206723585020072452256326513410
559240190274216248439140359989535394590944070469120914093870
012645600162374288021092764579310657922955249887275846101264
836999892256959688159205600101655256375678


now try to match that precision with vulgar a fraction :rolleyes:

Well, trivially, there's

157079632679489661923132169163975144209858469968755291048747229615390820
314310449931401741267105853399107404325664115332354692230477529111586267
970406424055872514205135096926055277982231147447746519098221440548783296
672306423782411689339158263560095457282428346173017430522716332410669680
363012457063686229350330315779408744076046048141462704585768218394629518
000566526527441023326069207347597075580471652863518287979597654609305869
096630589655255927403723118998137478367594287636244561396909150597456491
683668122032832154301069747319761236859535108993047185138526960858814658
837619233740923383470256600028406357263178041389288567137889480458681858
936073422045061247671507327479268552539613984462946177100997805606451098
043201720907990681488738565498025935360567499999918648902497552986586640
804815929751222972767345415132126115412667234251763096559408550500156891
937644329376660419071030858883457365179912674521437773436557978143194117
689379687597889092889026608561340330650096393830559795460821009946904762
860053274293163943296807669091398411515097601765092648449788681129970694
562486088764173956575778742862122707534797541476655843086392794453754919
087731873246965962753020046385083556950492441200642918080178185383005235
509097147779809947338391872472412768988736342355202376732310402334212953
474564665683851449457605237608102848301202901907509675562669121501779382
012374823663195709963630213496139839117739081800467086082060996229315751
514309148727785337491925274729429346349784546360539875465147766058267249
360137798011824033274955994091739887678318490371327126393127590920878733
644548888639690004082353000807262459608660860738617507072098678427408068
057867627606673787092473421926166195369707166727388120843125949178474278
104960961109213627512712844383589524730082673340249431361639589304289219
191398398834072705047694189318047534003211256260255869649244804206424431
347280212098264251110533059315337213931101959747252356185689348047818218
595864373388232878698120694543291632299790669523901379504973288203947563
473419917629785491291131026124470386335973913424130073849545132006819721
872765253410174812622587469982571571490459532962546861084823075785492919
370529894297988648774946508087696423406913434193447138707799592796262297
697971552498626234042299363682234792432691836811131304956230402562194219
522562206827488139039885784571799885006480804472084743427792420317671103
611291424432407922801425300842136972613373383944762606926127497733336391
199322829805817744311528872824901779681728408716205625753803473972554829
804701261443985544657283456843361437447028005075165430896434046043738045
891246929450485745483799263068277489094656489241084149947436132940242878
200713523877756618982072576187311718227142922239763293391052557067736786
976155671358305106798476811572147624246859355507288270179513996720187100
365528926953109919372390423924484166072285693437597175321510922659552424
050268530734033745963909559896997603070983171437722032187256185909608999
919550795978090733757134561987447045359324711598078397260404757327511261
580194096507104688106892797831946889354151953489603867336109128129983075
071075153401922386727460130270733296260074872142536625933300106621704409
535524316586732482572695289813428050275405332939849908178736819202628572
955144853207005548560314021951987975783857885021016893496800361527938158
817971093656257356026646409591309306293366078959920742441458223530478763
534786104587835583614554908454576400867533563742916114359176046769828625
605417895756849410457221050337551673355515706335556849543292581991575098
508257558425857188288091757782544245499492999119367276416581775382395926
794661309274481606646654492853210233762953545774070827492973081859013549
099715496224447878564144529616166304864985604221678663274469119559662987
318336529180207140694151601912451879492621872085145663828090468867220153
537346056009565101651900988105505502246466075804212224298188349194761434
239156177632910657247884286312167209465198432131217053866134890140365945
772055052234116263581005263261360558301983327865462735552789268817334103
265549482634593102823846562852931783100927905036468032993824305895522667
442517305682884337662472083401981328989385927804227648270633270426530717
221592933848757283070340035011893882956720085637473521028111526949728065
703556350020392736663496954072733232294039863541334153171642939284915261
790446653287870339772858188762710105747788079070012506311429706510823577
548962961549539827368806275882837567875891483322738958725056498074451523
199735664810536702187594786798072945096948565558952148914282375160159934
575701435404299524005470607361065897382388631120712742727016607859265307
114406879252153166087591489933111858607958038583462737436949332747472505
732703142168319689501988463283607319265336804828560459038191635832081374
444003934628014511423605201586059304102095002114830855981889606687875574
797507830248159314736327368212615408851837579533675117536417702835201933
717568111123857945752476549222446665481704390384662996989027096707236887
209213156493040499443437066302360784758119829322865108157990965975836769
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which matches that precision exactly.

The best non-decimal fraction I've found so far is 3126535/995207, with a error of about 1.14e-12.

Edit: 1068966896/340262731 is better. But still only 17 accurate decimal digits.

wow! i have to give you credit for effort at least


why would anyone want to work that hard just to use a non-decimal fraction?

Pi has been computed in decimal form to 1 241 100 000 000 decimal places

decimal fractions make life easy :D

Do you include France in the "imperial-measured world"?
When you talk about the Imperial measured world you seem to be talking about all non-metric units used in Europe. The Imperial foot is an Imperial System unit; the French foot, Danish fod, German Fuss (Bavarian, Austrian usw) are not.

(Units in France were a mess, but could have been standarised with the toise of Paris. And the French foot was divided into twelve inches and each inch into twelve lines...)
In Germany each principality or kingdom had its own systems - (as did each market place, according to Brockhaus).
The foot, pied, Fuss etc varied all over Europe; the only one that was used nationally was the British foot, standarised where many of the others weren't.

And I cannot understand why anyone should think we are insisting that you should give up your beloved metric system "even at gunpoint" for ours. Where on Earth do you get that idea from? We're the ones who don't want to give up our user-friendly system for the Metric!

What we are asking you to accept is a dozenal metric system that is superior not only to your decimal metric system but also to the Imperial system.

Get used to it? So suggestions to change are not acceptable? That's a bit heavy-handed!

And we have come up with a better system; which is why we are here and debating
the topic on this forum.

that's great!

please post this better system in the forums
so others (like myself) can read it


i sincerely hope you're not refering to TGM
as this proposal is severely flawed

American Standards are better,
cuz Miles, Yards, Inches, Gallons, Quarts, Pints, Pounds, Ounces and Hours are all duodecimal.

The Egyptians made the pyramids using the same American Standards,
and they've been around since the Bible days. (hundreds of years)

Have you really studied TGM? I got a copy from a Maths professor who thought it a brilliant well-constructed proposal, though he doubted the world would ever change to dozenal numeration; he classed us along with the Flat-earthers. He checked the calculations, pointed out a couple of typing errors, and wondered about unit-gravity.

And I then showed it to a Physics teacher, who said it was a well-thought out system and far closer to unifying the various units than the SI could ever get. He thought the unit-gravity idea might work and dismissed some other ideas I'd found on the web, like the pendulum and unity for Plack's constant (whatever that is - he knew what it was).

I disagree that TGM is counterfactual and imprecise; the only thing I dislike about it is the choice of words for the powers; they don't sound very pleasant.

Why "misguided", by the way?

yes, i actually took the time to read every word

i do not know your maths professor,
nor any of the physics teachers you refer to

but i can safely say that TGM is not a viable contender for replacing the SI

why?

first of all the base unit of time is improperly derived
being 1:20736 part of an hour - which is not a dozenal submultple of a day

the base unit of length is completely arbitrary
being improperly derived from the unit of time

and the units of volume and mass are MASSIVE!

25 litre and 25 Kg respectively

that's half the mass of a small person


now compare that to the dozenal units that i derived and posted here

where the mass unit is 1.7 kg and the volume unit 1.7 litre

Why do you insist on taking the day as a unit? Discussions with other dozenists led us to the conclusion that the half-day (and the half-circle) were more suitable.

One could also argue that the metre is improperly derived since it isn't a decimal submultiple of the Earht's ciecumference.

the day is the only natural unit of time that physiologically matters to us

our circadian cycles are tied to it



using half a day is an illogical attempt to keep hours


and of course the meter is not properly derived
who ever said it was?

i've mentioned here dozens of times that the SI is not perfect
because the protometric system of 1795 that it was based on was not perfect

again, it's just better than anything before it

Some of us think it important to keep hours.

I don't understand why you insist on using the emotive descriptions such as "shoddy" and "underhand", which suggest we are being less than honest. All our cards are on the table and there is no intention to mislead or deceive.

Using half a day keeps the hours we are used to and matches up with using the half-circle.

i think many people do

however not everyone is in love with hours


i have no romantic feelings for hours

i would be happier using 1 single base unit of time (decimal or otherwise)
which makes calculating time intervals easier

sorry, it's an old habit.. i have to stop doing that