The iPhone of Slide Rules - Numberphile

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 thanks to audible.com for supporting this video Audible has more than a hundred and eighty thousand downloadable titles across all types of literature including fiction non-fiction and periodicals I'm an Audible user and particularly enjoy listening to books when I'm walking the dogs are driving the car or slugging along on the treadmill they really make the time pass so much more quickly now among audibles huge collection is a book by Alex Bellos the person you just watched talking about slide rules here is Alex's Adventures in Numberland super easy to find and download onto your Audible app why not check that one out to find out more about how to do it go to audible.com/numberphile there you can sign on for a 30 day free trial including your first book and see what you think that's 30 days free trial it's great service easy to use and a thanks to audible for supporting the channel

Channel: Numberphile

Views: 621,032

Keywords: numberphile, slide rule, calculex

Id: xRpR1rmPbJE

Length: 8min 39sec (519 seconds)

Published: Wed Jan 06 2016