I want to talk about slide rules, this is a slide rule, but to explain what it is
So what we have is a classic old school Faber-Castell slide rule. Anyone who is over 50 or
maybe over 60 would have had to learn to use one of these at school and actually the
use of mathematics for the previous three hundred odd years required the use of
this and you could say that every single scientific invention oh you know through
the age of enlightenment through the nineteenth century and the 20th century
would have relied at some level
on ease of calculation through use of the slide rule
and these are only a few out of the wide
variety of problems that can be worked with the standard slide rule
this is what scientists had
so it was shorthand for being a scientist and it's so wonderfully nerdy and I think that
the nerds were like yeah this is this is our this is our sword you know it's a light saber
its actually rather lovely
the way this moves in and out it's so beautifully done this instrument is actually really
pleasurable just going like this here with a slide rule it's not like a calculator
it's not digital you don't get the exact answer you get an approximate answer but
normally within two to three significant figures which
should usually be enough for the job that you're trying to do
we have one of these scales on the top line here "A" which is the top line
we have another identical scale underneath it on "B" so
there are lots of different types of scales here but I'm just going to be using "A" and "B"
"A" is this one here "B" is underneath it
let's say we want to multiply three times four
we look at "A" and we go to where three is
and we put the bottom one at one where three is
then we go up four and then we read where four is on the original one and you can see four is at twelve
because it's ten eleven twelve
just say we do something else as let's say this is something more complicated
seven is a complication number let's multiply seven by seven
seven squared
so we put the number one at seven here
and we go up to seven at the bottom one
and it exactly comes up to forty-nine so that's cool
so what logarithms do and what this is a physical interpretation of
is that they change multiplication into addition
so we're multiplying two things but actually we're just adding two lengths
the reason why this is useful obviously seven times seven we know that in our heads
just say we wanted to multiply 2345 times 6457
ok what we do
we turn that into 2.345 times 6.457 and let's do the sums
so we go to 2.345
2.345
it's probably about there
and we got here at 6.457
6.457
and that is
that's almost exactly 15
ok so get rid of our things
that would tell me within a few seconds that 2345 times 6457 is 15 million
and why don't we just check that
...457 equals wow
the real answer 15,141,665
this gives us a handy idea of what the answer's going to be
multiplication is addition so division is subtraction
so let's say we want to divide 20 by 3
we go to 20 and we basically just need to take away 3
so we put 3 where the 20 is there
and go down to 1
and where is 1 we use our hairline here
oh look it's 6
between 6.6 and 6.7
this is something which is quite cool and fun and a bit of a historical relic
but it's not a particularly beautiful thing
unlike my other slide rule my prized possession
and this is the Halden Calculex
ok I'm going to open it is from 1906 and it comes almost like you know
like I'm proposing marriage to you
that I'm getting down on my bended knee and giving you a Halden Calculex
will you be my mathematical bride
so what this is is it is a circular slide rule
here we have the logarithmic scale along a line
in a circular slide rule it's in a circle
now let's put that down for a second
this comes with this fantastic sort of set of instructions
the thing is not that many people collect mathematical instruments and so you get probably get loads of
you know this might have been found by someone just clearing out their attic didn't know what it was
like it can't have been more than a few dozen dollars
so revised rules tables and formulae for the Halden Calculex
which is a circular slide rule
this is just wonderful absolutely wonderful
price one over six that's a penny isn't it I don't know I'm too young even though I'm old to understand old English
I'm going to read you a story
although the ordinary slide rule is usually acknowledged to be a most useful and reliable instrument
it has one or two great disadvantages
for instance it is a most inconvenient article to carry about in one's pocket
also in the hands of the average user it is rendered almost useless for any unusual calculation
so in other words you couldn't put this in a pocket and it's not very elegant
on the other hand the Halden Calculex is beautiful it's like a pocket watch
and it's something that if you ever needed to do fast approximate analogue calculations on the fly
and it was 1906 you could whisk this out
here there are two moving parts there is
you're moving this logarithmic scale against the top one so two sides
and you've got the hairline
here you can move the middle one
and you've got the hairline
so again there are lots of different scales for doing lots of different things
I'm just going to concentrate on multiplication and division
so just say again we wanted to say
do 4 times 5
and we can see if you can see close up
we know it's 20 and it's on 20
this is lovely this thing what do you do with this
what do you do you do calculations
but what do you do with it
I sort of take it out and stroke it and polish it and put it up there and talk to it
quite a lot of times things are just made for being functional
and this is something which is not only functional it is a rather beautiful object
and it's you could say it's a kind of iPhone of the early English 20th century
because this is the height of technology packaged with beauty
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