View Full Version : English units and decimals

Jens

2008-Jun-12, 04:43 AM

This is something that came up in my office, and I'm a bit stumped.

Why is it that in the English measurement systems, we never use decimals? We always end up using fractions, like one inch and 3/4 instead of 1.75 inches. Is there some reason for using fractions? What occurred to me is that it could be related to the lack of a zero. Or is it just a consequence of not using base 10?

Graybeard6

2008-Jun-12, 05:55 AM

Ah, but we do. Or did, rather, before we went metric. Somewhere in amongst my old tools is a ruler maked in inches and tenths. I have used a rule marked in feet and tenths/ft. I also have my father's first micrometer caliper, which measures up to one inch in thousands of an inch.

captain swoop

2008-Jun-12, 08:52 AM

I have an Imperial and a Metric Combo Micrometer it's marked in Thou on the Imperial scale.

Remember the Imperial system uses a whole bunch of different Bases.

20 Shillings in a Pound.

12 Pennies in a Shilling.

20 Fluid Ounces in a Pint

8 pints to the gallon.

Different to US pints - beware!

36 Gallons or 4 Firkins in a Beer Barrel (still in use)

3 feet in a Yard

22 Yards in a Chain

10 Chains to the Furlong

8 furlongs to the Mile

here is a long list with lots of obscure Imperial measures

http://home.clara.net/brianp/quickref.html

14 Pounds in a Stone

20 Stones in a n Hundredweight

20 hundredweight to a ton

(Different to American Tons known here as a 'Short' Ton)

mahesh

2008-Jun-12, 09:41 AM

quote from captain swoop's link:

Clove

Obscure unit of weight, equal to 7 pounds (av.)

i have always wondered, all these years......why the sauce tasted funny!

Aha, she used a clove of garlic! Oh, how frightfully English!

and i ate it and she said that she was glad i liked it and that it was the first time she had used garlic! i thought it was quaint, that it was the first time! oh, she used a whole clove! a really charming hostess! she was! bless her!

hhEb09'1

2008-Jun-12, 11:31 AM

Oh, how frightfully English!Points up another difference in the dialects: where we in the states say "A pint's a pound the world around", they say "a pint of pure water is a pound and a quarter". What we got in common is, we like to nearly rhyme.

Maksutov

2008-Jun-12, 11:38 AM

Heck, the differences between the English and metric systems aren't that great. They would probably take up no more space than a bushel, hogshead, and peck combined.

dhd40

2008-Jun-12, 01:08 PM

Heck, the differences between the English and metric systems aren't that great. They would probably take up no more space than a bushel, hogshead, and peck combined.

I´ll convince my wife to buy our weekly wine-needs exclusively in hogshead-unit-bottles (2 or 3 may be good enough)

Jens

2008-Jun-12, 02:18 PM

Sorry, my question was really about why they are in fractions rather than decimals. You can say 6 feet 2 inches, but if you want to go more precise than that, you have to say something like 6 feet, 2 inches, and 1 fourth of an inch.

Trebuchet

2008-Jun-12, 02:28 PM

What's always interested me is that the commonly used fractions -- 1/2, 1/4, 1/8, 1/16, and so on -- are inherently binary. Much more up-to-date than the decimal system, in which we are just counting on our fingers!

Edited to add: Wouldn't it have been easier to learn programming if we had only eight digits?

Swift

2008-Jun-12, 02:39 PM

This is something that came up in my office, and I'm a bit stumped.

Why is it that in the English measurement systems, we never use decimals? We always end up using fractions, like one inch and 3/4 instead of 1.75 inches. Is there some reason for using fractions? What occurred to me is that it could be related to the lack of a zero. Or is it just a consequence of not using base 10?

As Graybeard6 said, we do. I have done a little machining myself, and certainly have worked a lot with machinists. I've seen lots of blueprints that had something like 1.375 inches for a dimension. It depends on the precision to which one is making an object. There is nothing in the metric system that makes it inherently more precise. Its just easier dividing by 10s.

That might explain the fractions for less precise work - it is easier for most people to go know that half of 1/2 is 1/4, than 0.250.

SeanF

2008-Jun-12, 02:41 PM

I've seen lots of blueprints that had something like 1.375 inches for a dimension.

That's 1 3/8, you know. :)

Swift

2008-Jun-12, 02:53 PM

That's 1 3/8, you know. :)

Of course. But when you are machining a precise part, 1.375 +/- 0.005, means something different than just saying 1-3/8.

weatherc

2008-Jun-12, 03:33 PM

I usually use inches in the page layout programs I work with, but it's easier to input decimals into measurement fields in the applications, so I have a bunch of the metric to english conversions memorized. It's second nature for me to type .0625 when I want a sixteenth of an inch, or .3125 when I want three sixteenths of an inch. With the work I do in packaging design, we often get dielines created by the engineers with the english units written as fractions (1.25, .6875, etc.).

Of course, most graphic designers are used to juggling all kinds of units, including points, picas, inches, millimeters, and pixels. It's just something you get used to.

captain swoop

2008-Jun-12, 04:08 PM

I´ll convince my wife to buy our weekly wine-needs exclusively in hogshead-unit-bottles (2 or 3 may be good enough)

Sorry a Wine Barrel was 31 and a half gallons not the 36 of a Beer Barrel. You can't buy Wine by the Hogshead.

Tobin Dax

2008-Jun-12, 05:34 PM

It's second nature for me to type .0625 when I want a sixteenth of an inch, or .3125 when I want three sixteenths of an inch.

I hope not with regards to the second measurement. Six times three isn't close to thirty. ;)

weatherc

2008-Jun-12, 06:04 PM

I hope not with regards to the second measurement. Six times three isn't close to thirty. ;):lol: Oops. I meant five sixteenths.

danscope

2008-Jun-12, 07:54 PM

This is something that came up in my office, and I'm a bit stumped.

Why is it that in the English measurement systems, we never use decimals? We always end up using fractions, like one inch and 3/4 instead of 1.75 inches. Is there some reason for using fractions? What occurred to me is that it could be related to the lack of a zero. Or is it just a consequence of not using base 10?

Hi, I have a background in more than a few trades, tool making and carpentry amoung them.

We use decimal inches all the time. 3/8 = .375 . 1/4 = .250,

an inch and a 1/4 is 1.250 Simple, usefull and widely used ....everywhere.

Your initial premise is misunderstood by yourself, in as much as

our educators seldom give children a view of real industry, just the picture of the smoke stack.

There is nothing wrong with fractions or decimals.

If I need the center of 184, I can do it in my head....accurately....

every time. 92 And fractions are WONDERFUL !!!! Awesome in the minds of professionals who use them.

People fear systems they don't understand. But it is as simple as learning to cook and double or halve a recipie.

Don't give me metric. I am very comfortable with the english system.

My lathe is in inches. My threads are in inches. My mind has been formed around this superb system with simplicity in mind. It has been the foundation of working people for centuries. I shall not abandon it. THIS WORKS. :)

May it serve you well.

Best regards, Dan

Oops...need a one there. Always check your work.....hmmm.

Tobin Dax

2008-Jun-12, 09:25 PM

:lol: Oops. I meant five sixteenths.

It happens. I just had to point it out, since you claim to do this so well. I'd make a similar mistake, and danscope just did as well. :)

HenrikOlsen

2008-Jun-12, 11:11 PM

Of course, most graphic designers are used to juggling all kinds of units, including points, picas, inches, millimeters, and pixels. It's just something you get used to.

Which points though?

The 72 points to the inch or the 72.27 points to the inch?

Jeff Root

2008-Jun-13, 12:53 AM

Henrik,

I wasn't aware of (or possibly have forgotten about) the 72.27 points to

the inch. Where did that come from?

I have a steel pocket ruler (which I keep in the desk drawer under the

keyboard I'm typing on (along with larger rulers and a measuring tape),

rather than in a pocket, in part because the shirt I'm wearing doesn't

have a pocket), which has inches (subdivided in 16ths) and millimeters

on one side, and decimal equivalents of fractions (8ths, 16ths, 32nds,

and 64ths) on the other side.

-- Jeff, in Minneapolis

weatherc

2008-Jun-13, 01:10 AM

Which points though?

The 72 points to the inch or the 72.27 points to the inch?That would be the "PostScript Points," or 72 points per inch.

I'd have a little more trouble working with the traditional 72.27 points per inch in my head.

weatherc

2008-Jun-13, 01:14 AM

I wasn't aware of (or possibly have forgotten about) the 72.27 points to the inch. Where did that come from?Before publishing went digital, the points were actually measured at 72.27 points per inch. My guess is that to make the math easier when Adobe created their PostScript language (which is used to translate graphics created on the screen into information that can be output by printing devices), they just rounded down that .27 points. Since then, it's just carried over to the rest of the industry. I don't know anyone that actually uses the extra .27 when they measure in points.

HenrikOlsen

2008-Jun-13, 01:18 AM

I don't know anyone that actually uses the extra .27 when they measure in points.

Anyone using TeX to typeset does, which means a lot of the scientific community, though they may not be aware of it.

It does have the 1/72" point as a supplemental unit called a big point, with bp as symbol.

All units known in TeX:

Dimensions

pt: Point

pc: pica (12 pt)

in: inch (72.27 pt)

bp: Big point (72 bp = 1 in)

cm: Centimeter

mm: Millimeter

dd: Didot point

cc: cicero (12 dd)

sp: Scaled point (65,536 sp = 1 pt)

ex: Nomimal x-height

em: Nominal m-width

Jens

2008-Jun-13, 01:24 AM

Your initial premise is misunderstood by yourself, in as much as

our educators seldom give children a view of real industry, just the picture of the smoke stack.

There is nothing wrong with fractions or decimals.

I wasn't trying to say there's anything wrong with one or the other. I was just trying to understand why we use one or the other. Maybe I have to be clearer about the situation. For some work I have to do, we have to convert sizes of paintings in imperial units into metric units. So they're listed like, 6 3/8 by 7 1/4 inches. And people around (who grew up in a metric environment) asked me why we use fractions instead of decimals. And I don't know, so I was trying to think about why.

The answer so far that seems closest to what I was asking about is Swift's:

That might explain the fractions for less precise work - it is easier for most people to go know that half of 1/2 is 1/4, than 0.250.

Makes sense.

danscope

2008-Jun-13, 04:53 AM

Hi, Yes, you run into this with painting sizes. The ratio for standard frame sizes

is easily expanded with fractions.

As a carpenter, we work with standard lumber dimensions and especially sheet

goods (panels ). Laying out for any job with a 4 by 8 sheet becomes a very convenient chore employing inches and fractions .

A day in the trades is revealing. A good scratch of your brain . :)

Best regards,

Dan

captain swoop

2008-Jun-13, 08:09 AM

Publishing has a variable units as well based on the width of some characters, the 'm' space is an example.

mahesh

2008-Jun-13, 12:45 PM

..........You can't buy Wine by the Hogshead.

Yes, but you may buy pretty decent wine in Hog's Head, second to the right of Hog In The Pound

Ivan Viehoff

2008-Jun-13, 01:40 PM

I wasn't aware of (or possibly have forgotten about) the 72.27 points to the inch. Where did that come from?

It comes from printers deciding to use an inch (or foot) which was variously 0.375% or 0.4% shorter than an English inch (or foot), and differences and changes in the definition of the inch across time and between countries. 0.375% is precisely 27/7200. See http://en.wikipedia.org/wiki/Point_%28typography%29

mike alexander

2008-Jun-13, 04:05 PM

I remember reading an essay many years ago by Philip Morrison where he noted that the binary nature of English measurement could arise naturally from the process of equal division. Once an arbitrary unit is agreed upon, halves and doubles are easy to do, then those can be halved or doubled, and so on.

captain swoop

2008-Jun-13, 08:59 PM

So why 12 pennies in a shilling and twenty shillings in a pound? if it was halving and doubling wouldn't it be 2 4 8 16 all the way?

mike alexander

2008-Jun-13, 10:09 PM

If people were logical instead of historical, I suppose so. Since monetary divisions were originally based on weights of precious metals I assume the answer could be found there, but I don't know. (The 12 suggests troy weights, other than that I don't know). There were ha'pennies and farthings (fourthings?) though.

For measurements of length and mass, doubles/halves and their multiples worked well in a low-tech environment, I guess.

Maksutov

2008-Jun-13, 10:18 PM

For engineering/machining drawings, decimals and fractions play a role in determining what the tolerance is when not directly specified for a dimension. Usually there's a tolerance block on the drawing that states something like

_____

UOS

All dimensions are in inches.

3 place decimal ± 0.001

2 place decimal ± 0.005

1 place decimal ± 0.01

Fraction ± 1/64

Angular = ± 0o30'

_____

Of course, tolerance blocks are a cop out since they're applied in blanket fashion to many different features, each of which very probably needs a looser or tighter tolerance. But that might involve actual design engineering work.

Acolyte

2008-Jun-14, 12:40 AM

I've been puzzled by the avoirdupois system for a long time. I've wondered if maybe whoever invented it had 6 fingers & toes.

Think of it this way. You're in the process of becoming 'sophisticated' & need a way to count more than 'one or many.' Surely you'd come up with a system based on 10's? Or 5's perhaps? There you are with 5 fingers & toes - what would be more natural than to start counting in groups of 5's?

And in fact, that is what happened - our number system is base 10 & that works out well.

So why on Earth would measurements be based in 6's & 12's? It's awkward to say the least to try to use such a system while simultaneously running with a base 10 number system.

360º in a circle, 60', 60" - why? Why not something that makes sense in 10's?

If you try tracing it back, it goes a long way. There's guesses that we use 360º because it matches the days in the year - no it doesn't! And to do it that way, the ancients would need to know the Earth travels in a circle.

So it's another of those 'this doesn't fit' puzzles.

Van Rijn

2008-Jun-14, 01:04 AM

And in fact, that is what happened - our number system is base 10 & that works out well.

I like base 16.

So it's another of those 'this doesn't fit' puzzles.

Like the QWERTY keyboard? :)

danscope

2008-Jun-14, 04:22 AM

I've been puzzled by the avoirdupois system for a long time. I've wondered if maybe whoever invented it had 6 fingers & toes.

Think of it this way. You're in the process of becoming 'sophisticated' & need a way to count more than 'one or many.' Surely you'd come up with a system based on 10's? Or 5's perhaps? There you are with 5 fingers & toes - what would be more natural than to start counting in groups of 5's?

And in fact, that is what happened - our number system is base 10 & that works out well.

So why on Earth would measurements be based in 6's & 12's? It's awkward to say the least to try to use such a system while simultaneously running with a base 10 number system.

360º in a circle, 60', 60" - why? Why not something that makes sense in 10's?

If you try tracing it back, it goes a long way. There's guesses that we use 360º because it matches the days in the year - no it doesn't! And to do it that way, the ancients would need to know the Earth travels in a circle.

So it's another of those 'this doesn't fit' puzzles.

The division of a circle by degrees has worked out just fine for the convenience of carpenters, architechts and engineers as well as artists

for quite some thousands of years The simple functions of a circle as it is described , could not be simpler or better. Field geometry reveals much.

And the twelve comes from the twelve points of the compass. A nod to

astronomy.

The more you try to out-smart the ancients, the more you come to respect their elegant simplicity.

Best regards, Dan

Delvo

2008-Jun-14, 04:31 AM

If you accept devision by 2 as the source of the 2s, 4s, 8s, and such, then the source of the 6s and 12s and 60s is pretty simple: division by 3 is also a pretty basic kind of division to want to do.

Whirlpool

2008-Jun-14, 05:02 AM

If you accept devision by 2 as the source of the 2s, 4s, 8s, and such, then the source of the 6s and 12s and 60s is pretty simple: division by 3 is also a pretty basic kind of division to want to do.

But if you do divisions with higher numbers , using a calculator is the easiest thing to do .

:p

Jens

2008-Jun-14, 05:44 AM

If you try tracing it back, it goes a long way. There's guesses that we use 360º because it matches the days in the year - no it doesn't! And to do it that way, the ancients would need to know the Earth travels in a circle.

Other than the minor nitpick that the Earth doesn't travel in a circle, I don't think you would have to know anything about orbits. You would merely have to observe that the seasons repeat themselves in a roughly 360 day cycle. Or that the day becomes long and then short again on the same cycle.

360 is also divisible by every number 1-10 with the exception of 7, making it easy to divide a circle up into some number of zones without resorting to partial degrees.

HenrikOlsen

2008-Jun-14, 12:55 PM

I would expect it to be be remnant from the babylonean base 60 floating point numbers.

Acolyte

2008-Jun-14, 01:21 PM

Like the QWERTY keyboard? :)Nah... there's basic engineering behind that. QWERTY was designed to slow typists down so the typewriters didn't get jammed up.

Long before electronic keyboards, before even electric typewriters, the old mechanical actions relies on a lever action to get the letter or number to strike a ribbon, behind which is the paper. Typing too fast would cause the levers to jam together.

The division of a circle by degrees has worked out just fine for the convenience of carpenters, architechts and engineers as well as artists for quite some thousands of years The simple functions of a circle as it is described , could not be simpler or better. Field geometry reveals much.

And the twelve comes from the twelve points of the compass. A nod to

astronomy.

The more you try to out-smart the ancients, the more you come to respect their elegant simplicity.While I agree about respect for the ancients, the fact that since we began the 360º trip we have learned to use it doesn't lessen the puzzle of how we came up with it.

And points of a compass are 4, 8 or 16, not 12. So that doesn't explain things either.

Acolyte

2008-Jun-14, 01:29 PM

Other than the minor nitpick that the Earth doesn't travel in a circle, I don't think you would have to know anything about orbits. You would merely have to observe that the seasons repeat themselves in a roughly 360 day cycle. Or that the day becomes long and then short again on the same cycle.Except it's a very poor approximation. Using 360 means you have continuous adjustments to make, year in year out. If they were smart enough to note the cycle, they'd be smart enough to note that it's 365, even if they didn't at first notice the fraction by which the year exceeds 365 days.

Ascribing inventions to the ancients doesn't work unless you also admit they are as intelligent as we are. They wouldn't mandate a measure that simply doesn't work. if the discrepancy was across many years, maybe, but this is one they'd notice in the first couple of years.

And there is evidence they knew more than just the basics of Earth's movements.

For the others who tried to address this question, it does no good to look at us now & say that this is how things are because it works well. It works well because we have adapted to it over thousands of years.

But I grew up in an avoirdupois world that converted to metric when i was in my teens - metric makes so much more sense it is a little amazing anything else could have been used. Metrics measures things on base 10, the same system as we use for numbers. No awkward conversions required.

The question remains - we have counted in base 10 for as long as we have records, but for some reason we have only recently begun to measure in 10's. Why?

hhEb09'1

2008-Jun-14, 01:40 PM

360 is also divisible by every number 1-10 with the exception of 7, making it easy to divide a circle up into some number of zones without resorting to partial degrees.Don't forget 12. 360 is divisible by every number 1-12 with the exception of 7 and 11. 12 is divisible by the first four numbers (1, 2, 3, 4) and 6. But 60, the Babylonian base, is divisible by the first six numbers--that divisibility by low integers cannot be ignored in the success of those two numbers.

Acolyte

2008-Jun-14, 01:53 PM

360 is also divisible by every number 1-10 with the exception of 7, making it easy to divide a circle up into some number of zones without resorting to partial degrees.Very true, but the problem is... first you have to have the knowledge that such a property is needed.

Try to picture it - early on, at a time lost in history (because all the records seem to indicate that the 360º system as well as the other odd measurements were in place from the beginning) someone came up with a non-metric system that used all kinds of odd numbers to make up measurements rather than making them from the natural base 10 system.

Why would they do that? Wouldn't it seem to be more natural, in such an early environment, presumably before a need for complex codes & engineering techniques, to come up with something which would be easily divisible by 10's & 5's? 500º divided into 100' would give higher accuracy than 360º & 60' & given the level of technology, it's feasible at least they would have had no way to measure more accurately than 100º & 100'

Instead we have the weirdness of 6's & 12's, as well as a few other oddnesses. It is strange.

Delvo

2008-Jun-14, 01:53 PM

Nah... there's basic engineering behind that. QWERTY was designed to slow typists down so the typewriters didn't get jammed up.

Long before electronic keyboards, before even electric typewriters, the old mechanical actions relies on a lever action to get the letter or number to strike a ribbon, behind which is the paper. Typing too fast would cause the levers to jam together.This is a modern myth. The speed it takes to get the hammers to bind is much lower than a normal typing speed, so you'd need to hold yourself back no matter what keyboard layout you were using. QWERTY just simply doesn't and can't do the job people say it's supposed to do. Not only that, but before the keyboard was standardized, there were public typing speed competitions put on by the makers of competing keyboards and typewriters, and QWERTY didn't produce particularly slow results. Also, you can see some of how the keyboard's form was determined by looking at it. It's just too much of a coincidence for D, F, G, H, J, K, and L to be right in a row with E and I right above D and J so it's practically the alphabetical order for 9 letters in a row, especially with M and N in order going away from L right blow that and O and P mirroring them right above. If it had been designed for some unrelated goal such as maximizing or minimizing speed, then it wouldn't have so much influence from alphabetical order.

Acolyte

2008-Jun-14, 01:59 PM

This is a modern myth. The speed it takes to get the hammers to bind is much lower than a normal typing speed, so you'd need to hold yourself back no matter what keyboard layout you were using. QWERTY just simply doesn't and can't do the job people say it's supposed to do. Not only that, but before the keyboard was standardized, there were public typing speed competitions put on by the makers of competing keyboards and typewriters, and QWERTY didn't produce particularly slow results.Not a myth. I've used an old typewriter, one made in the very early 1900's & it had none of the smoothness of later manual models. The keystroke was very long, pressure required was quite high, & if I ignored actual accuracy & just pressed keys as fast as I could, it jammed regularly - I got in trouble for doing it.

Later models could also jam if one mis-keyed slightly & had 2 keys move together. Use of a recent (post 1960) manual typewriter doesn't convey what it was really like trying to use an original technology one. The sticking keys was a reality in the early models.

Delvo

2008-Jun-14, 02:14 PM

we have counted in base 10 for as long as we have records, but for some reason we have only recently begun to measure in 10's. Why?We haven't counted in base 10 for as long as we have records. Some cultures have used base 12. (I don't know of any other used bases but can't eliminate them.) Our own did at one time, which is why 11 and 12 have unique names instead of "oneteen" and "twoteen".

And measurements have simply been based on "natural" amounts. A cubit was the distance from fingertip to elbow on an average adult, a hand was the width of an average adult's hand, a mile (short for mile passus) was a thousand paces (2 steps per pace, 5 feet per pace, 5000 feet total, originally), a cup was just the amount you could put in a normal cup, a pound was the weight of a normal brick or tile or such, and so on. Ratios between one natural measurement like that and another don't lend themselves to a decimal system any more than the number of days in a year or a lunar orbit, or the number of lunar orbits in a year, does.

Delvo

2008-Jun-14, 02:53 PM

I've used an old typewriter, one made in the very early 1900's & it had none of the smoothness of later manual models. The keystroke was very long, pressure required was quite high, & if I ignored actual accuracy & just pressed keys as fast as I could, it jammed regularly... The sticking keys was a reality in the early models.I didn't say it wasn't an actual problem. I'm talking about a matter of what the limiting factors are in which situations, and the ones you've just described only make the keyboard layout even more irrelevant for the mechanical problem. People can learn to press keys very rapidly in any layout, so any difference in how rapidly between different layouts can only show up in the high speed range. That can only be the limiting factor when typewriter mechanics are not. You're talking about things that would force people to stick to lower speeds than that no matter what kind of arrangement the buttons were in, which would make THOSE issues, not button arrangement, the limiting factor at those lower speeds.

Just think about how fast you or someone else you've seen can type on a modern electronic keyboard without the issue you described. They're doing that with a QWERTY keyboard. If the mechanical issues force a typist to go slower than that, then QWERTY arrangement was not slowing them down enough for the old mechanical devices; the machinery, not the button arrangement, was the limiting factor. The button arrangement could have, and today does, allow for faster speeds than the old machines did, so the button arrangement simply does not slow people down enough to be a solution for the mechanical issues.

hhEb09'1

2008-Jun-14, 03:09 PM

Why would they do that? Wouldn't it seem to be more natural, in such an early environment, presumably before a need for complex codes & engineering techniques, to come up with something which would be easily divisible by 10's & 5's? 500º divided into 100' would give higher accuracy than 360º & 60' & given the level of technology, it's feasible at least they would have had no way to measure more accurately than 100º & 100'An equilateral triangle would have 83 1/3 degrees instead of 60. An isoceles right triangle would have 62 1/2 degrees instead of 45. Nasty stuff. Those were basic implements.

We haven't counted in base 10 for as long as we have records. Some cultures have used base 12. (I don't know of any other used bases but can't eliminate them.) Base 60, still the most widely used base today, was mentioned earlier.

Delvo

2008-Jun-14, 03:34 PM

Base 60, still the most widely used base today, was mentioned earlier.A system with sixty unique digits, where sixty is the lowest number requiring two digits, is the most widely used? Who uses it?

hhEb09'1

2008-Jun-14, 03:45 PM

A system with sixty unique digits, where sixty is the lowest number requiring two digits, is the most widely used? Who uses it?No, of course not. We are like the Babylonians, probably the originals, where we use a modified sexagesimal system, and the sexagesimal digits are written in base 10.

danscope

2008-Jun-14, 04:55 PM

Hi hheb......Good stuff there. Once you start using geometry, you soon see the wisdom

of 360° .

( Just a side note; to get that little ° , just hold down alt and press 2-4-8 ).

Best regards, Dan

HenrikOlsen

2008-Jun-15, 02:41 AM

A system with sixty unique digits, where sixty is the lowest number requiring two digits, is the most widely used? Who uses it?

Actually, due to the way the Babylonians wrote numbers, 61 was the lowest integer requiring two digits.

Lots of other lower (noninteger) numbers required more digits, such as the square root of 2 (1;24,51,10) (http://it.stlawu.edu/~dmelvill/mesomath/tablets/YBC7289.html)

hhEb09'1

2008-Jun-15, 03:39 AM

Here's a page (http://it.stlawu.edu/~dmelvill/mesomath/obsummary.html)describing the old base ten digits, and it also touches on what HenrikOlsen meant about 60 being represented by a single digit.

HenrikOlsen

2008-Jun-15, 04:15 AM

Perhaps I should have spelled it out, babylonian numbers was written with an implicit decimal point, not an explicit one as we use, and with no symbol for 0, so (30) could also mean 1/2, and 60 was written (1).

Maksutov

2008-Jun-15, 05:10 AM

No, of course not. We are like the Babylonians, probably the originals, where we use a modified sexagesimal system, and the sexagesimal digits are written in base 10.Hey, watch it! This is a family board.

Van Rijn

2008-Jun-15, 05:59 AM

Nah... there's basic engineering behind that. QWERTY was designed to slow typists down so the typewriters didn't get jammed up.

There were many possibilities for a keyboard layout. There was some logic behind it, but there was a certain amount of arbitrary choice as well. Then, even after the jamming issue was solved back in the typewriter days, it remained the standard because people were used to it.

Similar things happened with measurement systems that you find puzzling. There was some logic behind the choices made based on common use at the time, but some arbitrary choices as well. They continued to be used because people were used to them.

Jens

2008-Jun-15, 06:38 AM

Ascribing inventions to the ancients doesn't work unless you also admit they are as intelligent as we are. They wouldn't mandate a measure that simply doesn't work. if the discrepancy was across many years, maybe, but this is one they'd notice in the first couple of years.

I guess the logical alternative is that the 360 degrees in a circle is not related to the length of the year. And anyway, I don't think I'd be able to argue that the ancients were not as intelligent as us. AFAIK it's an evolutionary trait mainly, and 5,000 or 6,000 years seems not enough to make any change in the basic makeup of our brains.

Jens

2008-Jun-15, 07:53 AM

Hi hheb......Good stuff there. Once you start using geometry, you soon see the wisdom

of 360° .

( Just a side note; to get that little ° , just hold down alt and press 2-4-8 ).

As long as you have an "alt" key on your keyboard. Otherwise, it's a combination of "option" and something.

But it is interesting about the geometry and 360. Obviously the people who set the number did so for good reasons.

Jens

2008-Jun-15, 07:58 AM

And measurements have simply been based on "natural" amounts.

That sounds like a good working hypothesis to me. The answer to my original question may be: (1) that the decimal system was not always used for measurements because measurements were often based on natural amounts, and (2) fractions were used instead of decimals because it is simpler for people to use. Saying 1/4 is easier than saying 0.25, and knowing that a half of 1/4 is 1/8 is obviously easier than finding 0.125. Probably people didn't generally need things in real precision, so fractions served the purpose well.

Acolyte

2008-Jun-15, 10:50 AM

I didn't say it wasn't an actual problem. I'm talking about a matter of what the limiting factors are in which situations, and the ones you've just described only make the keyboard layout even more irrelevant for the mechanical problem. People can learn to press keys very rapidly in any layout, so any difference in how rapidly between different layouts can only show up in the high speed range. That can only be the limiting factor when typewriter mechanics are not. You're talking about things that would force people to stick to lower speeds than that no matter what kind of arrangement the buttons were in, which would make THOSE issues, not button arrangement, the limiting factor at those lower speeds.

Just think about how fast you or someone else you've seen can type on a modern electronic keyboard without the issue you described. They're doing that with a QWERTY keyboard. If the mechanical issues force a typist to go slower than that, then QWERTY arrangement was not slowing them down enough for the old mechanical devices; the machinery, not the button arrangement, was the limiting factor. The button arrangement could have, and today does, allow for faster speeds than the old machines did, so the button arrangement simply does not slow people down enough to be a solution for the mechanical issues.People only type fast on QWERTY because they've grown up with it. Once upon a time, they tried to bring in typewriters & found that if they based the keyboard logically (based on common letters under the easiest fingers) then people could easily outpace the ability of the mechanical action to produce the type. You have to realise, on the original typewriters, the limiting faactor wasn't in how fast the keys could be made to hit the ribbon, it was how fast the mechanism could get the lever away from the ribbon. ie. before the next one came in.

Again, unless you've used one, you wouldn't know what the limitations were. And even the later manual typewriters would have sticky key problems with high speed stenographers. Once upon a time there were typewriter mechanics who kept critical resources in mint condition to ensure the highly paid typist could get her work done without problems.

Acolyte

2008-Jun-15, 11:00 AM

An equilateral triangle would have 83 1/3 degrees instead of 60. An isoceles right triangle would have 62 1/2 degrees instead of 45. Nasty stuff. Those were basic implements.Base 60, still the most widely used base today, was mentioned earlier.Once we detach the #º from the year then it's free form. Why not 300º? Internal angles in a triangle then sum to 150º which divides nicely for an equilaterals & is also natural for a race with 5 fingers per hand.

There's another problem with this reasoning - it's the idea that they need to know the intricacies of geometry before they come up with the units to measure it.

Cubits hands & palms are all natural but even there, there were 'sacred' measures based on 6 eg. the Hebrew tabernacle had them. eg. Stonehenge & Avebury seem to have been built on a 'sacred' rod that is 6/5ths of the neolithic rod. The units that come out in whole numbers for the Giza plateau also seem to be 6/5ths of the standard units.

Acolyte

2008-Jun-15, 11:08 AM

I guess the logical alternative is that the 360 degrees in a circle is not related to the length of the year. And anyway, I don't think I'd be able to argue that the ancients were not as intelligent as us. AFAIK it's an evolutionary trait mainly, and 5,000 or 6,000 years seems not enough to make any change in the basic makeup of our brains.That's my point - if it isn't related to the year, then from where do we get it? 6's & 12's are everywhere - just look at the ** we go through to work out our calendar so we can have 12 months to match the 12 'houses' of the constellation. 13 months of 28 days would work VERY nicely thanks you - add in a New Year holiday & you have a year that needs adjusting something like every century rather than every four years, unless the year can be divided by 100, unless it can be divided by... etc. All to make 12 months work out.

It takes some effort of imagination, but before just saying 'it works' or 'it's natural' try to think through what a primitive people may have known BEFORE they required these measurements. Suggesting they came up with 360º because they needed to work out geometry is getting it the wrong way around. They were measuring Sun & Moon long before they needed the formula for internal angles of a triangle - they had to be - knowing the year cycle, understanding the seasons meant they got to eat better. Being able to measure where the sun came over the horizon is part of that. But measuring where the sun rises doesn't lead 'naturally' to 360º in a circle.

weatherc

2008-Jun-15, 12:12 PM

As long as you have an "alt" key on your keyboard. Otherwise, it's a combination of "option" and something.

But it is interesting about the geometry and 360. Obviously the people who set the number did so for good reasons.Option + shift + 8 will give you the ° symbol if you're using a Mac.

hhEb09'1

2008-Jun-15, 01:25 PM

Once we detach the #º from the year then it's free form. Why not 300º? Internal angles in a triangle then sum to 150º which divides nicely for an equilaterals & is also natural for a race with 5 fingers per hand.I also mentioned the isosceles right triangle. In that scheme, it would have 37 1/2 degrees

There's another problem with this reasoning - it's the idea that they need to know the intricacies of geometry before they come up with the units to measure it.Well, they weren't stupid. :)

As I point out, they did use a base ten sort of grouping, which might have been part of the early evolution. When they needed more involved and sophisticated measurements, they went with base 60. Why? we don't know for sure obviously, but it seems reasonable to me.

When the French introduced the metric system, they also introduced metric forms for time and degree measurement, the two places where sexigesimal is/was most firmly entrenched. The attempt was mostly abandoned.

Tobin Dax

2008-Jun-15, 05:25 PM

Once we detach the #º from the year then it's free form. Why not 300º? Internal angles in a triangle then sum to 150º which divides nicely for an equilaterals & is also natural for a race with 5 fingers per hand.

Just how many hands do you have? The factor of 3 doesn't seem to fit with your reasoning.

We have 5 fingers on two hands. Why not 10º or 5º in a circle?

I can count from 1-12 using my two hands that have five fingers each. Can't you?

Of course, the natural thing to do for an race with any number of fingers is to use 3.14159º or 6.28319º in a circle.

Acolyte, you're arguing semantics based on different cultural thought processes. There is no right answer, no matter how much you want there to be one. This is how hheB keeps pointing out flaws in your new scheme.

Finally, sexagesimal math is something that practically everybody uses. I have this circular object on my wall that counts in base 60. It also counts in base 12, but that's done much more slowly. Shouldn't we use something other than 60 minutes per hour?

Delvo

2008-Jun-15, 08:00 PM

I also mentioned the isosceles right triangle. In that scheme, it would have 37 1/2 degreesTo be short and simple about it, there are more simple, easy ways to divide up 360 than to divide up the other suggested numbers, since the latter tend to have fewer distinct factors.

I don't know whether any still do or not, but engineers at one time (when my father was training to be one at Rolla in the early 1960s) had an angle-measurement system using "grads" instead of degrees or radians. (The word was probably made by smashing the other two words together and sweeping away the loose debris from the impact.) It can still be found on some calculators but not others. A right angle was 100 grads, so a circle was 400. This meant that division by three would get you a repeating decimal instead of an integer, but, as my father told it to me, this system was invented by engineers for engineers, and engineers LIKE their repeating decimals. :D

When the French introduced the metric system, they also introduced metric forms for time and degree measurement, the two places where sexigesimal is/was most firmly entrenched. The attempt was mostly abandoned.Probably because they couldn't even stop arguing among themselves over whether a metric year should have 100 days or 1000. :D

mugaliens

2008-Jun-15, 11:33 PM

One major reason is that stock materials used in machining are still measured in fractions, such as a 3/4" drill bit, and 1/8" rolled steel.

Same goes for bolts, such as the 6-32 machine screw, in which the first number can be translated into a diameter using a formula, and the second number is the number of threads per inch (thus, each thread is 1/32" from the next). The formula for the diameter is:

d=(#*0.013")+0.060", where # is the first number of the machine screw.

Personally, I'd prefer the metric system, as you know exactly what you're getting. But what really complicates things is that there are more than a dozen drive heads out there, each size screw probably comes in most of them, if not all of them, and to really complicate matters there are thousands of various materials used and manufacturing methods, each of which yields vastly different results in terms of tensile strength, shear resistance, etc.

All of this is why engineers specialize and why most carpentry fasting techniques are mandated by code that's signed off by both engineers and architects.

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