Inclines - how to measure

[deibid]

A % number is not decimal nor imperial.... is a proportion, by definition it does not mean any "unit"... 5% means anything you want it to mean, five inch each 100 inches or 5 cm each 100 cm... the choice of units is yours.

Regarding railway signals... modern HS lines in Spain express gradients in %

[Malc]

I remember reading a post script in one of Terry Pratchett's disc world books where he explains old British Imperial currency for young or American readers.
He starts off by saying 2 half pennies make one penny, three pennies make a threepenny bit, two threepenny bits make six pence.... He ends up with one pound and one shilling make a guinea. The general public were afraid of decimalisation.

[daveg]

I remember reading a post script in one of Terry Pratchett's disc world books where he explains old British Imperial currency for young or American readers.
He starts off by saying 2 half pennies make one penny, three pennies make a threepenny bit, two threepenny bits make six pence.... He ends up with one pound and one shilling make a guinea. The general public were afraid of decimalisation.

Loved the quirky old LSD! I was the 'decimilisation officer' for my employers when the Big Change happened and converted thousands of prices in a 300 page catalogue to the new system.

I still find it fun converting back to pounds shillings and pence every now and then but finding it's taking a bit longer than it used to! 

Dave G

[Dorsetmike]

Last time I went driving, gradients were on the signs as a percentage. So surely road sign gradients are more familiar

Probably an age thing, at 81 I knew where I was with  1:x and used it for many more years than %

Not sure I see a connection here. Decimalisation of numerical quantities has been going on for centuries,

We in UK had been using feet and inches and £sd and Fahrenheit for centuries, many other countries also used non decimal units, the EU more or less forced us to abandon our units, if we had adopted the Euro then we would have lost £sd, but as we did not go Euro why change to decimal, businesses made a lot of money out of that,  customers were used to ten pence being less than 1/-  so happily paid it not realising it was equal to 2/-, it took some time for us to wake up to reality by which time it was too late.

explain why a non-decimal system be better than a metric system?

I didn't say one was better than the other, just that we had managed for centuries with our system, if it ain't broke don't fix it!

[railsquid]

I must admit, as a comparative youngster (hey, at least I remember when King George VI shillings were still in circulation), and despite having spent most of my adult life in fully decimal countries, the "old" notation still feels more intuitive.

[NeMo]

explain why a non-decimal system be better than a metric system?

I didn't say one was better than the other, just that we had managed for centuries with our system, if it ain't broke don't fix it!

Non-decimal systems actually work better for mental arithmetic, especially dividing, for example into thirds. You can divide one shilling into three lots of 4 pennies, but trying the same thing with one pound and you always get something left over. "Old money" had lots of fractions built in: farthings (1/4 penny) and ha'pennies (1/2 penny) within a penny; thruppence and sixpence were quarters and halves of a shilling; a crown (5 shillings) was a quarter of a pound, and various others. Such a system was very flexible with lots of options for dividing up a sum of money in a neat way that didn't leave odd bits leftover. So yes, non-decimal systems actually can be better for money systems before calculators and computers.

In fact fractions are generally better than decimals when it comes to precision. If I say 1/3rd of something, that's precise and you know exactly what I mean. But if I do that in decimals, at best you'll get an approximation, 0.333 or something like that. Not the exact, precise number because you can't write down a third in decimals without using an infinite number of digits!

But oddly enough decimals are much better at informing you about how precise a measurement is. If you measure things in fractions, usually you end up approximating to some degree, depending on what you judge a sensible about of precision for the situation. So I might measure a bit of wood and say it measures 6 and three-sixteenths of an inch. But how precise were you in actual fact? Did you read off to the nearest line on your ruler? Was the wood actually somewhere between two lines on the ruler? With decimals I can say 6.2, or 6.19, or 6.188, or 6.1875 or whatever... and it's clear what my level of precision was (even better if I say 1 dp, 2 dp, 3 dp or 4 dp in this case). So in science and engineering, decimals are better.

I find all of this fascinating, especially when you reflect on how routinely we mix base-10 (decimal currency) with base-12 (such as feet/inches) and base-60 (time, angles and coordinates on the globe). Nobody fusses about the base-60 because it's actually a lot better than trying to do base-10 for that sort of thing. 60 is divisible in lots of ways (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) so you hardly ever need to use fractions in most day to day situations. But mention the idea of base-60 without reminding them about time, angles or coordinates and people freak out!

Cheers, NeMo

[MattJ]

I think better in metric these days.  Especially as 1km = 10 minutes walk.

[MalcolmInN]

[smg id=24347 type=preview align=center width=400]

Brilliant !
(pun intended )
Nice one !

[MalcolmInN]

A % number is not decimal nor imperial.... is a proportion, by definition it does not mean any "unit"... 5% means anything you want it to mean, five inch each 100 inches or 5 cm each 100 cm... the choice of units is yours.

Regarding railway signals... modern HS lines in Spain express gradients in %

It is a proportion and dimensionless but it can still have (dimensionless) units, so not always units of your choice.

[MalcolmInN]

Gosh !
Just a minute folks, ( pun also intended), if we are to deviate without a pause but perhaps some repetition into monetary metrics then try also :
Metric tensors and Reimann manifolds,
oh no, perhaps not else we will be back to motor cars/bikes !!
I suppose it is all relative Albert.

Wot, no opinions on stall currents ?

[MalcolmInN]

and base-60 (time, angles and coordinates on the globe). Nobody fusses about the base-60 because it's actually a lot better than trying to do base-10 for that sort of thing. 60 is divisible in lots of ways (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) so you hardly ever need to use fractions in most day to day situations. But mention the idea of base-60 without reminding them about time,

60 - Oh gosh, any minute (duh)  now we'll be debating if it was a good idea to get rid of Babylonian hours ( and Italian for that matter), which we were all used to in days of yore, from of off sundials 

Edit:
PS It is said, or supposed, or our only evidence (in cuniform clay), is that the Babylonians first ( were the first ?) used  base-60 for trade / business because of (as NeMo says) its convenient divisibility from quantity.

[Jon898]

One of the challeges of this computerised, GPS world is that the base-60 concept is gradually being perverted.  GPS systems can read out (IIRC) in degrees-minutes-seconds (and decimal seconds!), degrees-minutes-decimal minutes, and even degrees-decimal degrees.  Usually it's a user choice, but sometimes that choice is so buried in the depths of the user configuration menus one can be unaware of the meaning of the results being reported on the little screen.  When you superimpose that onto people who don't understand that a minute of longitude is not the same length as a minute of latitude, all chaos can break loose.

I grew up in the UK learning long division and multiplication in bases 112, 14 and 16 (hundredweight, stones, pounds, ounces) and 20 and 12 (currency).  Then the science classes changed to metric (actually SI) and the engineering degree was done in SI as well.  Out of college I joined a firm working in the oil industry and suddenly everything was in traditional (american) units (aargh, what's a kip? ).  Before I retired, I headed up engineering for a major multi-national company and was continually challenged with (otherwise excellent) American engineers who had no clue how to work in "metric" units and were too proud to call their european colleagues to find out what units were normally in use (at best they'd call the UK or Ireland and end up being led astray when it came to mainland european usage) .  Getting anyone to understand the significance between an "m" prefix and an "M" prefix was a lost cause.

[MalcolmInN]

American engineers who had no clue how to work in "metric" units

It is said ( but I have not read the originals ) that some of them did try, but lost a Mars mission as a consequence.

[Jon898]

You're spot on: http://www.cnn.com/TECH/space/9909/30/mars.metric.02/

[Tom U]

On a recent train journey in Sri Lanka (I posted a few pictures earlier) I was talking to the driver, and he referred to distances along the track in "chains".  I vaguely remember mention of chains in my school days, so refreshed my memory with wiki...
Quote: A chain is a unit of length. It measures 66 feet, or 22 yards, or 100 links,[1] or 4 rods (20.1168 m). There are 10 chains in a furlong, and 80 chains in one statute mile. An acre is the area of 10 square chains (that is, an area of one chain by one furlong). The chain has been used for several centuries in Britain and in some other countries influenced by British practice. Unquote.

So then I recalled "perch" as a measure of area - wiki again:
Quote: As a unit of area, a square perch (the perch being standardized to equal 161⁄2 feet, or 51⁄2 yards) is equal to a square rod, 30 1⁄4 square yards (25.29 square metres) or 0.00625 acres, or 1/160 acre. There are 40 square perches to a rood (A rectangular area with edges of one furlong (10 chains i.e. 40 rods) and one rod respectively), and 160 square perches to an acre (an area one furlong by one chain (i.e. 4 rods)). This unit is usually referred to as a perch or pole even though square perch and square pole were the more precise terms. Confusingly, rod was used as a unit of area but it meant a rood. Unquote.

Now I remember why I liked it when metric came along.  Oh! and pocket calculators saved my life from slide rules and log tables.

Tom.