# The French should of switched to base12 instead of bringing Metric to base10

#62

Actually “Kilobucks” is a pretty common slang expression… although a “Grand” is the most common. --Mitch

#63

i don’t have a lot of time to reply to much of what you’ve said and i’ll get to it later but for the most part, i think the gist of what i’m saying isn’t coming through. (i used a lot of words to say two or three things so this is to be expected, i suppose )

but this: (which isn’t meant to clarify my points… just a sidebar)

actually, yes, it is.

it’s not called a millinch exactly… rather a mil (or a ‘thou’ is a common way to say it too)

for example:

those are 2.5 mil thick…

many trades in the U.S are working strictly in decimal inches… once you go smaller than 64ths, it’s no longer practical (or practiced) to use smaller increments in fractional terms… we use mils then.
(i mean, machinists for example aren’t working at 1/1024 inch tolerances, they’re using thous)…
when i’m using the CNC, i’m not expressing tolerances or dimensions in terms of fractions… it’s mil and/or decimal…
when you set tolerances in imperial Rhino, you set them at decimal values (while display tolerances can be set to either decimal or fractional)

likewise, when entering lengths in Rhino, i’m using decimals in a considerable amount of instances…
6.5" instead of 6-1/2… or 12.125… or 5.625… etc.

all the fractional values have a decimal value… and they are most certainly used interchangeably in many many scenarios.

but back to the thread, if a different base were used, the values would read 8.1 or 8.2" instead of 8.0625 or 8.125 to describe the same exact distance.
i think this is a part that i’m having the hardest time explaining.

#64

heh, yeah… same here… we use metric here too.
me personally, i use it every day.

i use metric tapes as well as metric tools (drill bits, wrenches, etc)…
often (or always, probably) on projects which are using imperial… and decimal inches too.

idk, i’m very familiar with metric and even more so familiar with decimal & base10… even if some of the stuff in this thread i’ve said may make it seem otherwise.

(Marc Gibeault) #65

Ok Jeff, you put a lot of time and effort to make your point. What’s your next step? Do you want to let all this die here? You can go forward two ways (in CAD-speach):

#66

more-or-less, yes… it dies here… with the incredibly slim possibility of serious consideration of making a new world standard, i just wanted to be sure to have in writing my opinion that the creators should not only make sure the numbering system is optimized (which is what all the talk elsewhere regarding this stuff is about… and not so much my worry)-- but to also make sure the root size is considered according to usability instead of something like “the distance light can travel through Louisiana swamp water after a cat4 hurricane”

other than that, it’s been super cold lately… so i’m just trapped inside doing my annual long winded blabbering online… last time i typed this much, i think it was regarding the validity of using booleans while modeling… this one, at least to me, is a lot more interesting though probably equally meaningless… or, i don’t care about this to the extent i imagine readers to be interpreting it as …i just find it interesting is all.

some of my thoughts on making a change to dozenal instead of decimal at this point:

1-- it’s too late… the costs are enormous… unimaginable even… (and not just monetary costs either… although in and of itself, these types of costs are astronomical)… the time to do it was before the industrial revolution…

(and, just btw, dozenal was on the table, on the cusp of the industrial revolution, when metric was being created… the commission responsible for designing the system consisted of five main players… one of whom was Pierre-Simon Laplace… basically, one of the greatest scientists to ever live and very likely the smartest person on the planet at that time… he pushed for a base12 counting system to be adopted and this is the how the original proposal to the [French legislature] was presented (as a system of units&measures in a base12 counting system)… however, the idea was rejected by the politicians as the prevailing view amongst them was that the system was bound to failure… the commission then came back to the assembly with what we mostly know of today as metric… this proposal was accepted)

anyway-- the costs…
since the onset of metric, we (humans) have built and/or created sooo much stuff with decimal system and/or metric/imperial units…
basically, every bit of data out there would need reconfigured to have two more characters… all of the machinery we have… all the infrastructure (from trains to pipes to wiring to younameit) revolve around standardized units… (this list could go on and on and on and touch on just about every imaginable topic/field… but you get the idea)…
all of that stuff would pretty much need replaced/updated… some of which has 100+ year lifespans.

most, by far, would be faced with “but why do we need to change this?? it works fine as is”… and the people saying that would be correct.

there are benefits to be had from incorporating a base12 system… vast benefits even…
but if trying to weigh those against the costs of making the switch at this point, i’m hard pressed to believe a case could be made to show it’s worth it, all things considered… unless, maybe, you could show the benefits for future generations over the next 300 or 600 or 1000+ years…
but…

2-- it’s likely my point-of-view is more along the lines of “base12 would have been good for the past 200 years… and it will be good for at least the remainder of my lifetime”… but if i try to consider humans in 2118, will the radix even matter?
i mean, say it takes 50 years for the world to switch to base12… in 50years from now, how much will it even matter? we’re digitizing rapidly… how long until our brains are supplemented with microprocessors for assistance with memory or tasks such as arithmetic? how long until the craftsman is no longer needed or, at least, the tools and scales currently in use are completely replaced by new paradigms of measuring/marking/communication of measurements.

i’m not convinced that by the time base12 would be the norm… that it would even really matter at that point… or, the further into the future we go, the less importance the counting system…

so, if someone can convince “no, the counting system will remain of high importance in 300 years from now” then i will change my view regarding this… but as of now, this is another reason i think the prime time to switch to base 12, as a species, has passed.

3-- resistance to change

the vast majority, i imagine, would resist/reject the change… humans as a whole do not like changes…
if a considerable majority were open to changing the counting and measuring system, it would go quick… there would be hurdles still, sure, but the hurdles would be overcome relatively easily if everyone were on board.

nothing i’ve seen in my lifetime shows me that switching to base12, even if it’s clearly proven to benefit society, will be faced with anything other than a giant wall.

e s p e c i a l l y__ if the idea of doing so is to be presented by an American or group of Americans…
using metric, at least in my eyes, carries with it some sort of superiority type complex over Americans… i have never once seen a discussion about measuring systems in which at least a portion of it didn’t have a tone or outright blatant “lulz usa… idiots using imperial…jajajaja… metric rulezz!!1” (or whatever)…
(but to be clear, it’s not so bad around here with you guys though it does still come up)

i’ve almost literally never seen anybody say anything negative about metric… it’s as if it has been taught to people that it’s perfect and people just believe it… regardless of some very simple and obvious flaws (such as it being based around an arbitrary counting system and an arbitrary unit size… it’s arguable that metric is based off nothing).

at the very least, one might expect to hear something like “metric has flaws… so does imperial… i prefer metric if given the choice”… but i really don’t think i’ve ever even heard that point of view…
just trying to explain where metric isn’t optimized or how a different system could be better is like pulling teeth… (though i have one more idea for an attempt at trying to show it… maybe tomorrow)
metric is flawless (and decimal is natural) in the majority of people’s minds which makes point#3, resistance, the largest hurdle in making the change.

4-- there’s more but i’ll stop
i just don’t see the change happening nor do i expect it to.

nah… neither of those are for me.
that said, if a Mcneel_er (as a personal preference) were able to make Rhino work reliably using the unit described in the top post… and i were able to find a manufacturer willing to make few custom tools using the unit (tape measures and a few other layout type tools) for a reasonable price (sub\$1000)…

i would most definitely do some projects using it… that, to me at least, sounds pretty fun.

#67

so you’re shipwrecked… basically like Tom Hanks except you managed to save your tools and the island has usable materials… the only thing that fell off the boat was your damn tape measure.

your tent is ok shelter for now but you’d like to build something more akin to a house… (please overlook that you would actually build a boat instead of a home )

the first thing you’re going to want is a scale… the way to create a scale from scratch is:

find something that you feel will be an ok length to work with… and there’s your scale… super easy.
i can now stack it end-to-end and measure stuff by counting how many of those units i use… i can measure logs to 4 units long and cut them to consistent lengths etc.

((( by the end of all of this, it should be clear(er) that we wouldn’t be cutting the logs to ‘4’ units… we haven’t actually created the character 4 yet… with this scale, we’d likely count something like the following in order to get to the value we know as 4:
|
| |
| | |
| | | |

just some tick marks as i’m pretty sure, we haven’t even made zero yet at this stage (clarify anyone?)

but please, don’t be a smarty pants on day one and draw a thumb across `| | | |` when you want to write the value we know as 5 simply because you realize it looks like your hand… as in, please don’t do this:

you’re the Adam on this island and i can assure you, if you start making that mark, you’ll likely ruin the counting system for all future inhabitants

(i don’t actually know if this is how the tally mark slash came to be… i mean it more as a joke but it seems legit… still, just a wild guess)

moving on…

you find the scale to be ok for measuring the distance to the tree… or ok to measure the outline of your house…
but you’re also finding the need for measuring smaller items or measuring a little more accurately… so you fold your scale in half to make 2 equal parts:

…and you’ve now doubled your precision:

if we need more precision, we can fold it in half again:

cool… quarters:

again:

(just by the way… that’s glue on my fingers and not some weird flakey skin thing. )

so now, eight equal parts:

you can stop this process when you no longer need the extended precision… also, at this point, you’re still free to use any of the previous steps… you could work in just 1/2 unit albeit the way you write the measurements will vary depending on when you agree to stop halving the scale…

earlier, upon doing the original fold, you created a middle tick mark which would be .1… in the latest iteration, the same mark is now .4
both of them are `1/2`… just like how in decimal, `1/2` is .5

the current version of the scale is base 8… there are 8 divisions in between 0 and 1… or, instead of counting it with the point ( `.1` `.2` `.3`) , you can slide the point over as we’re used to doing and see there are 8 divisions in between 0 and 10

when you do that, try to realize ‘10’ is not ‘ten’ nor the value we know as ten… it’s ‘eight’ and it’s the value we know as ‘8’… in base 8, there is no “ten”… we haven’t created enough marks yet in order to build up to the number ‘ten’… there is also no ‘nine’ or ‘9’…
likewise, we don’t have a character that looks like ‘8’ yet but we do have the word ‘eight’ now and it looks like ‘10’…

the important thing to realize here and why it might be best to understand the above is that yes, we are making a scale to build our house with… however, we are also making a scale in order to build all of the other numbers greater than eight with… we are building the counting system … we don’t want to have a unique character for all values imaginable… no, we want to make a base set of numbers which we can build everything else with… currently, in this exercise, we have made the integers:
`0, 1, 2, 3, 4, 5, 6, & 7` …we can build any value using only these numbers.

but back to building the house… let’s give it one more fold for good measure:

ok… sixteenths:

in today’s world, we write this scale in two ways so i’ll use the same characters as we see in hexadecimal :
(the black ones… those aren’t letters!! they’re numbers… at least i keep telling myself this … still, it tends to be visually confusing)

so yes, in hex/base16 using these characters, the number we know of as 13 is actually written D

the above scale uses the same proportions as we see in the inch… if we used a base 16 counting system, i wouldn’t have to write 15/16", i would just use .F instead…

i wouldn’t have to add
`15/16 + 15/16 = 1-14/16` (or 1-7/8)… instead, i could go:
`.F + .F = 1.E`

for the half, it would go:
`10 ÷ 2 = 8`

looks weird, huh?
i encourage you to work through the following familiar looking equations while looking at/using the scale (as opposed to using your memory):

``````.2 + .4 = .6
5 - 3 = 2
6 ÷ 2 = 3
2 x 4 = 8
``````

then try bringing in some of the new characters using the same basic math:

D - 3 = A
E ÷ 2 = 7

try to recognize everything you know about math stays the same when you use it on different bases… you don’t have to make any adjustments there…

it’s just the way the numbers look which requires the adjustment.

the other way we write this scale in today’s world, such as the inch, is via decimal therefore we have to describe this scale using only ten characters… (the red ones in the picture)

we end up using fractions for a lot of it but a different way to interpret it would be… instead of seeing 7/16" as seven-sixteenths inch, we might equally be saying “it’s seven units of a base 16 scale”
or
the sixth tick, the one that we’d write as .6 in hex, on the inch we call it `3/8"`
which can either be seen as a simplified form of the fraction `6/16`… or, it could be seen as meaning “the third unit on a base 8 scale”

anyway, the scale we just created is what the majority of imperial is done with… we have 16 ounces in a pound, 16 cups in a gallon, 16 divisions in an inch, etc…

it’s a sweet scale since it’s very easy to create and understand the workings of… probably THE easiest and most intuitive scale.

are we all on the same page so far?
ok… moving on

with your scale, you’ve realized you can easily divide the unit into a half… or quarters… then eights… then 16ths… then on-and-on through infinity… however, you keep encountering the problem of not being able to divide it into 3 parts… no matter how many times you make the halving move, making the divisions smaller and smaller each time, you can never seem to arrive at creating a tick mark which tells you where 1/3 unit is at exactly…
(ie- looking at this problem using decimal shows 16 ÷ 3 = 5.33333333forever

so, you set out to design a different scale with this problem in mind:

you realize you can fold the unit in 3:

which gives you this scale:

so that’s great… you now have a scale that shows you where thirds are… also, when you use this scale as your counting system, you recognize you can now do `10 ÷ 3 = .1` which means you have integers that land exactly on your third divisions.

you can use this scale alongside your original scale… switching between the two depending on wanting to target halves/quarters/eights or change to the new one for thirds.

however, when you need to increase precision and work in between the thirds on the new scale by doing the halving move (which will create 6ths… or base 6):

…you discover something else has happened… yes, you can now work in thirds… and you can now work in between the thirds via 6ths… but you’ve also just added a midpoint mark to this scale:

so now, you don’t have to switch between scales as often because you can use this one when needing thirds OR halves… you only switch to the other one when needing 1/4… but it doesn’t take long to realize, since you’ve created a half-way mark on this scale, you can make the move again in order to make quarter marks…

which will leave you with this:

base 12:

you have 12 equal divisions that you (might) name:
`0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, Ɛ`

this is how the imperial foot is divided…

for sake of familiarity, everybody here knows this scale… it’s on our clocks and it’s in our calendar.
to see an example of how trained we are to use memorized workarounds, we literally tell time using the wrong numbers and nobody even bats an eye…

we will say 2.5 hours to mean two-and-a-half-hours although the scale/clock quite clearly tells you to write 2.6 instead.

if i ask you to point to 1/4 hour on the clock, you’ll instantly point to the 3 except you’ll write it as .25
??
(or, maybe you decide to leave base12, switch to base60 for the individual hour divisions, find the .25 mark which actually says 3, describe the non-existent base60 character using decimal… and tell me “well, 15 is 1/4 hour… duh”

wacky? or no?
it is… imperial is full of this stuff because we use decimal counting to describe non-decimal scales… but i can assure you it’s not just idiot Americans using imperial who do this… it’s everybody… every last one of you…

anyway, i’ll hopefully be able to refer to our time scales later in the post as a means to make some points without needing to look at something as confusing as hexadecimal system…

…but for now, instead of talking more about base12 scale, let’s see how to create a base 10 scale… (and subsequently, how we create the decimal and metric systems)

ok, well, you don’t… there is no natural or intuitive geometric type logic that you will follow and arrive at a base 10 scale… instead, you go for a different approach… this new approach is done by looking at your hands…
(remember, while all of the previous scale design has been happening, there’s been another train of thought stemming from the very original tally mark system of counting that says 5 is an important or ‘strong’ number since it’s what we see on our hands)

under this approach, we throw away any sort of the preceding logic and replace it with ‘we need our scale to look like our hands’…

so we start with our unit:

we then fold it in half in order to create two hands:

so far, so good… by designing this move into the scale, we know we can divide by 2… this actually seems logical afterall…

e x c e p t…
now, we do this:

(we don’t actually do this to create our scale… the scale was never created/built… this is a workaround discovered after the fact…)

first, you need to introduce a Y axis to your linear scale in order to form a square (1/2 unit x 1/2 unit)… then, with a little assistance from this kid Crystal Flames’ youtube, you make this move:

[dramatic_interlude]

say what?!
that’s what makes the decimal system so great?
are you joking?
you’ve completely just ripped the heart and soul out of the scale and came up with this sterilized POS…

the scale started off great with the 1/2 mark… what you did next however just completely killed it.
the user is no longer in control of the system and instead, the system will now control them… there are no more moves you can do after that one that won’t carry with it the same unintuitive mess.
this scale is being forced upon you and you have to use it in very specific manners in order to use it effectively…

by designing this workaround into the system at a very early stage (2nd move), you’ve unwittingly just designed this workaround into every subsequent thing you build using this scale… or, more specifically, all future values/numbers you build with this scale will be infected with this thing we saw Crystal Flames fold…

you can not use it in the same way you use the previous scales as it’s lacking the important 1/3 and 1/4 division… instead, both of those have been replaced by 1/5
(and further, not only have you made the second most important fraction of 1/3 into a non integer, you haven’t even allowed it to be a rational number… thirds leaves you with irrational numbers in a base 10 scale… but hey, at least we have fifths now… just like our hands… )

many of these workarounds we don’t recognize as such since we’re generally taught basic numbers and math through rote memorization… we’re not (imo) properly taught what numbers are or how they come to be or, really, how to use them… instead, we’re taught numbers as if they are facts… and since they are facts, you should just memorize them… and if you encounter, early on, confusing math problems which don’t ever truly resolve then hey, that’s too bad… they’re facts and we just apply workarounds to dealing with them.

[/drama]

ok, so how do we weigh these scales against each other and arrive at a conclusion of which single scale would be best to use in the most amount of scenarios.
(i’m not actually sure the best or simplest way to do this but the following part of the post will be comparing different scales and/or trying to describe certain features of scales in general)

here’s a list of equations generated via dividing the base by all the integers designed into the base:

baseDivider.gh (6.7 KB)
(i used Grasshopper to generate the lists… you can try that .gh to see what happens with all the various bases regarding this comparison)

the basic way to interpret that is:
• a whole number in the result (such as `10÷2=5` in base10) means this number will appear on your scale…
• a rational number (such as `10÷4=2.5` in base10) means this number will not fall on the scale but we can still find it within the ticks of the scale.
• an irrational number (the long ones… they all repeat and never resolve and you’ll never find them on your scale)

basically, the results showing no decimal points are good, the ones with a point followed by a short number are OK, the long irrational numbers are bad…

using the above comparison, even if our only criteria for determining the best system is how many good numbers vs OK vs bad numbers… and we don’t even consider the concept that some numbers are more usable or used more often by us…
base12 clearly wins… as in:

base12 contains two additional factors which result in clean divisions vs base10…
50% of the numbers in base12 are good… 25% are OK… 25% are bad.

for base10,
40% of the numbers are good… 20% are OK… 40% are bad.

why are just 2 more good numbers in base 12 to be considered a landslide win? or, why are you (jeff) placing so much emphasis on dividing within the scale itself?

remember, we created this scale to build our house… except, we also see how the same scale is used to build every additional number…

any trait you designed into the original base scale will be carried throughout all additional numbers you create…

for example, we designed the ability to divide by 3 into the foot… one-foot ÷ 3 = 4 inches…
what that means is any amount of feet over 1 will also be dividable by 3…
i can divide 2’ by 3 and have a mark on my scale… 8 inches… or:

22' ÷ 3 = 7'4 (or 7.4)
23' ÷ 3 = 7.8
24' ÷ 3 = 8
25' ÷ 3 = 8.4
26' ÷ 3 = 8.8
27' ÷ 3 = 9
(you see the pattern, right?)

but point being, since the base is divisible by 3, all multiples of the base will also divide by 3… i can literally divide any amount of feet into thirds and arrive at a clean number… either a whole number or a single digit rational number( as in-- an inch mark… in this case of thirds, only the 4" mark or 8" or an exact foot value)

doing that with decimal:
22 ÷ 3 = 7.333333
23 ÷ 3 = 7.666666
24 ÷ 3 = 8
25 ÷ 3 = 8.333333
26 ÷ 3 = 7.666666
27 ÷ 3 = 9

again, the traits that are built into the base will carry forward to all other numbers built on top… so it’s not just 2 additional ‘good’ numbers in base12, it’s millions upon millions infinity…

only every third number in a sequence of decimal will land on a whole number… all the other ones will be irrational… nothing even judged as ‘ok’ in there.

fourths work good in base 12 and they’re OK in decimal (27÷4=6.75)
the only time there’s much good coming out of decimal is when you divide by 5 or 2
22 ÷ 5 = 4.4
23 ÷ 5 = 4.6
24 ÷ 5 = 4.8
25 ÷ 5 = 5
26 ÷ 5 = 5.2
27 ÷ 5 = 5.4
(with every fifth attempt landing on an integer)

it’s important to realize that there aren’t more irrational numbers in base10 than there are in base12… if there are a million irrational numbers in decimal then there are a million in dozenal… (there are infinite amounts in both, in all reality)…

the point is that base10 tends to expose the irrational numbers to us everyday users much more often… the ticks on the scale are placed in such a way that when we want to do a simple calculation, it happens to expose one of these bad numbers in a large percentage of uses… where as the way the base12 scale is layed out, it tends to land on a good number or an ok number much more often…

complex equations aren’t going to be any easier or any more solvable in base12 vs base10… in these cases, you’re likely exposing or dealing with bad numbers much more often to the point of them being equal… you’re doing math for the sake of math and the numbers themselves don’t really matter at that point.

but for our every day uses in society, base12 will keep much more of these complex numbers out of our sight (and because of this, potentially make math itself seem more inviting to a larger percentage of people)

the preceding comparison shows what happens when we pretend as if all numbers are equally usable… in that type of comparison, we see base12 trumps base10.

however, in my experience at least (i really can’t think of a good way to quantify this part… for now, it’s anecdotal i suppose even though i know it’s more than that)… so in my experience, some numbers are more important than others… we use certain numbers more often.

the fraction you’ll most likely see used by any given person is 1/2… everybody knows and can use 1/2 and has plenty of scenarios where they’ll need to apply 1/2 (whether they realize it or not)…

to me, 1/2 is what i’ll call the most important fraction…
from there, i believe thirds and fourths are next… etc.

i am probably hundreds of times more likely to use a third or fourth division than a fifth… except 1/3 sucks in decimal… 1/4 is ok but not optimal… fifths are good… sixths suck… etc…

both 3 and 4 work great in dozenal… it’s the first and smallest number that allows this to happen…

in this regard, i argue the use of base12 is exponentially greater than using base10… far far more usable than the head-to-head type comparison done in the previous example…

base12 not only has a considerable amount more good factors than base10, these additional factors also happen to be the ones we are most likely to use… by a long shot.

… and hey, there goes my Saturday up there
i’m going to stop now though i do have more to add… still, i’m not doing my Saturday night like this too.

i wish i was more of a poet and was able to present a more compelling argument using less words but i do feel i’ve provided enough suggestions for people to begin exploring some of this on their own.

i truly (TRULY!) believe this however:
nobody here… not one single person will be able to say base10 is the system we should be using once they understand the differences… i will go so far as to say it would be impossible for someone to know what they’re talking about and still attempt to argue base10 as a superior system for humans… impossible… there’s not a single reason which says base10 is better…
(unless, of course, you actually feel like our counting system base should match the amount of fingers we have… and that this is the most important thing to consider… that’s literally the only valid argument in my eyes in favor of base10… but even then, i’m using the word ‘valid’ very loosely in that statement )

there’s not a trade-off that happens if switching to base12… you lose nothing and gain a lot…

however, if you were to switch from base12 (or, arguably base16) to base10, you lose a lot and gain nothing…
maybe next time you try to take a stab at an imperial system user, consider this… are you sure certain Americans when being presented the metric system a few hundred years ago were just dumb so they continued building the country using an outdated system?
or do you think maybe, luckily even, there were a few observant people around who refused to adopt this moronic metric system (hey, their words, not mine ) since it totally destroys how we know a measuring scale should work and replaces it with something far less useful?
(that said, my point is actually nothing to do with imperial or metric or imperial VS metric… read back through the thread… i’ve said multiple times they are both flawed… imperial should die a sudden death… etc… and i still mean it…
my point is that metric is equally flawed… or in my reality, it’s even more flawed…
just for different reasons.

there’s a much better, easier, cleaner, more logical, more universal, and above all-- more user friendly system out there for all of us…
it’s just a matter of us building it and adopting it.

#68

We already do it with clock faces!

(Graham) #69

The French still partly count in scores (20) as in quatre-vingt for 80, soixante dix (sixty-ten) for 70, etc. The Swiss, Belgians and French Canadians have corrected this to give variants on septante, huitante and nonnante for 70,80,90…
I presume the scores relate to the aforementioned base 60 which is so beautifully pluridivisible.

(David Rutten) #70

The English did too once upon a time. “Four-and-twenty” still being in use today in some places.

(Tom) #71

After 12 month of reading time… we can finally continue arguing

Sorry I did not finish reading yet, I‘ll need 6 month more to give constructive replies

(Tom) #72

Four and Twenty is literally german. Meaning Vierundzwanzig or 4 and/und 20. Thats how we say 24.

#73

you’re absorbing it though subconsciously at least

like your statement above is using 12 as a base and 6 as a half… and it makes total sense to you.

just write the same exact thought/values using the characters 10 and .6 and we’ll really be getting somewhere (instead of 12 and .5)

#74

(Tom) #75

but we also counting like this for all numbers until 100 ->99 is 9 and 90 , 33 is 3 and 30. then we switch 101 is 100 and 1

(Graham) #76

In the UK we have the baker’s dozen -ie buy 12 scones get one free. Lucky we didn’t all switch to that as 13 is prime.
Hmmm… scones

#77

ha… i literally ate lunch there today:

https://goo.gl/maps/BoXmpWMzMpJ2

(but yes, a baker’s dozen is a familiar concept in the u.s. as well)

(and yes— base13 sounds nightmarish )

#78

When I was a boatbuilder, we used this sort of tape measure.

(Tom) #79

Since my grandfather was architect, I grew up with them (I own dozens of them in different scales…):

I don’t know if there is a metric and imperial mix of them already out. But different scales, different advantages:

(Graham) #80

I got this one from a supplier.

Handy if you forget to change the page size on the printer

(David Rutten) #81

As a Dutchman living in Tyrol I’m aware that that is the case. Just saying that in times past English used the same ordering but had the good sense to simplify it. Fünf-und-dreizig-tausend-sechs-hundert-acht-und-neunzig is a disgustingly cryptic way to pronounce a number…