OT: Mathematical Conundrum II

[NY]

I think whoever said "Have even heard 10p referred to as two bob (but I think that may be a local thing)" meant specifically a 10p coin being referred to as a two-bob coin, in contrast to a pre-decimal two-shilling coin.

Apart from the immediate aftermath of decimalisation, I've never heard of post-decimalisation *coins* referred to by their pre-decimal names (eg a 5p coin referred to as a shiling, or a 10p coin referred to a two bob or a florin), even though some older people carried on referring to quantities of money or prices in pre-decimal terms for a fairly long while afterwards.

The decimalisation of currency and the (gradual) use of metric measurements rather than imperial ones are things about modern life that have definitely improved.

The main problem with the imperial system is that it used every base under the sun except the only one that it should have done - ten, since we count and are taught to calculate in base 10. And there isn't even a whole-number relationship between (for example) linear and volumetric measurement: there is not an integer number of cubic inches in a gallon. I had to estimate how heavy a copper hot-water cylinder would be when full of water, to decide whether the baulks of wood that I was planning to use would be strong enough. I only had an imperial tape measure. I measured the tank and worked out its volume in cubic inches from V=pi r^2 l. Now "all" I neede to do was to convert this to gallons to estimate the weight from knowing that a gallon of water weighs 10 lb. That's when I realised that I didn't know the conversion factor - looking it up on Google now I see that it's 277.419 cu in / gallon, but this was long before the internet. I wouldn't have had a clue even the magnitude of the factor, never mind its precise value.

So I had to convert the volume to cubic centimetres by multiplying by 2.5 (approximately) cubed, from which it was trivial to convert cc to litres and hence to kilogrammes.

[The Natural Philosopher]

And will we go back to the gold standard and 240d to the pound when we leave the EU?

[NY]

Duh yes. There's a remainder of 2, and what I was forgetting is that this is

2/3, since we're dividing by 3. For some reason I thought of it as 2/12 since there are 12 d in a shilling, though that is totally irrelevant to this bit of the calculation.

As a matter of interest, is there a quicker, more elegant or easier-to-calculate-in-the-head way of doing the division that the process that I described?

[ARW]

Such as miles, yards, feet and inches?

And yes I still weigh myself using stones and pounds.

[Adrian]

Well, a yard is to all intents and purposes the same as a metre, of course. Miles are in use all day, every day. Feet and inches? Not so much used. Whereas a groat or a farting or a crown hasn't been used for nearly half a century.

But, yes, this country has one VERY f***ed-up attitude to metrication. It's not big or clever. It really should be a national embarrassment.

And I don't weigh myself...

[Bod]

Who does then? ;-)

[Tim+]

Gotta love metrification. Just ordered some new hinges that are 102mm long. There's a nice round metric number. Such a shame I can't buy 4" ones any more. ;-)

Tim

[pamela]

You don't seem to have difficulty storing and recalling words or ideas from short term memory. I wonder why numbers are different.

I have difficulty recalling words, ideas and numbers but the difficulty is extreme and comes in bouts.

I wonder if you can recall what those numbers (or any digits making up those numbers) are when you attempt mental arithmetic.

[The Natural Philosopher]

what are you doing on a computer t5hen?

[The Natural Philosopher]

My father taught me: there are 960 farthings in a pound, convert it all to farthings, do it decimal and adjust a bit depending on what the answer is in fractions of a pound

[ARW]

I have a 1969 copy of New Penny Wise. 28 pages of stuff that I do not need to know.

[NY]

I always measure things in grammes/kilogrammes or in millimetres/centimetres. But I still estimate in imperial units and I know my weight and height better in those units. I'm a hybrid! But I've always used centigrade for temperature - in this case, both as a measurement unit and also as a folk unit.

[polygonum]

"Whereas a groat or a farting or a crown hasn't been used for nearly half a century."

Hmm, very odd interpretation of half a century!

Farthing (not farting) was withdrawn in 1961. So 54 years - which is close to half a century.

Groat issued between 1351 and 1662. So 457 years or more.

Crown has been revalued at five pounds and was issued as 60th anniversary of the Coronation in 2013. And is still a current coin.

The last 25 pence/5 shilling crown was 1981 marking Marriage of the Prince of Wales and Lady Diana Spencer. So 34 years but still current coin.

And my responses were meant very much tongue in cheek.

[polygonum]

It was indeed. And lasted as a 10p piece-equivalent for many years after metrication.

[NY]

Yes, it's weird, isn't it. I suppose it's because I need to see the carry digits or else I lose track of them. And I always calculate strictly on one column (eg units, tens) at a time: even on paper I would add up 7 and 5, carry the 1, then add up 2, 3 and the carried 1, rather than adding up 27 and 35 in a single step - apart from very easy combinations. And I can't visualise the digits to be added in my memory, unlike my wife who only has to look at a map or a page of a book and then, she says, she can "read" from her mental image of it. Mind you, in her case, this may be a coping strategy to overcome the fact that she can't read while in a car, train, plane or coach because of car-sickness, something that I'm grateful I've never suffered from, so she tends to look at a map before a journey or else for brief refresher glances while navigating as I'm driving, and then replays directions from her mental photograph. This replay-from-a-mental-image means that she finds exams easy whereas I find anything requiring replaying from memory a nightmare - and sadly in recent years I've even found working out something from what I *do* remember (ie not just regurgitation from memory) more difficult, but that's down to finding it harder to work well under pressure rather than when I've got limitless time.

What is more odd is that my long-term memory for facts (including numbers such as phone numbers or constants like pi) is very good; it's the short term "mental jottings" while working out that are crap, just like I can't navigate from a memory of a map - I need to keep looking a the map to see each turning that's coming up. On the other hand, if I travel a journey once or twice, I soon develop a good memory for the salient features (eg what certain buildings look like at junctions along the way) and navigate by those, which is something my wife can't do.

[NY]

I did say "unless there's a good reason for doing otherwise". Also, computers use a consistent base: *every* digit is twice the one to the right - there's none of the mixed-base problem of 12 inches in a foot, 3 feet in a yard, 1760 yards in a mile or 16 ounces in a pound, 14 pounds in a stone, 112 pounds in a hundredweight (*), 20 hundredweights in a ton. And where there are bases greater than 10, letters are used (eg in hex) so you always have the same number of digits.

[Albert Zweistein]

Using binary and hex when programming both of which I can do and still not enjoy.

[Fredxxx]

So having a shilling you can 1/2, 1/3, 1/4, 1/6 and 1/12 isn't a good reason?

[pamela]

Clinical psychologists say long term memory is deeply engrained but medium and short term memory is more fleeting. The difficulty holding on to intermediate numbers in a mental calculation is what I would call immediate memory. As you have described, immediate memory embraces visual as well as other forms of data (such as numberic).

When my visual organisation got bad, I noticed finding tools jumbled together in a drawer took far longer than it should do but I didn't realise the signifiance of this at the time. Following the plot in a crime film was hard for me because some of the visual clues would pass by too quickly for me to register them and when things got really bad, following a kid's cartoon became too hard.

My own experience is that immediate memory is affected by general health in a way that longer forms of memory are not. I lived most of my life without dietary supplements so I was pleasantly impressed by how much improvement in immediate memory I get from them. YMMV but I think it's worth experimenting because the results can be extremely valuable.

[polygonum]

What dietary supplements?

And on what basis? That is, was it a guess, a recommendation, a prescription? Any scientific justification?

Not calling you into question, but interested!