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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