Log Tables - Numberphile

Logarithms and log tables - what Professor Bowley used before calculators!
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Professor Roger Bowley is an emeritus professor at the University of Nottingham.

NUMBERPHILE

Videos by Brady Haran

[numberphile]

Loving your comments....

But these tables are not a proposal or new idea or some crazy method used by weirdos...

It is a HISTORICAL FACT that people - like engineers and scientists - used these almost universally for many years because it made life easier....

And not every calculation was as simple as 37 x 59... We just used a simple example to show the table in use!

[EebstertheGreat]

It certainly is a shortcut. If you want to multiply large numbers, it can take quite a while. For instance, multiplying two five-digit numbers by "long multiplication" requires 25 single-digit multiplications and 20 to 24 single-digit additions. And at each step you can make an error. And for division, the situation is even worse. But using a log table, you just have to look up two numbers in the table, add (or subtract) them, and look up the result in the antilog table.

[KingJKlass]

Blame the schools for not showing us this i hated math up until i found this channel.

[refl]

I see what you did there! It always makes me smile when 42 is used as an example .

[Fleshcut]

A big thanks to Prof. Bowley for explaining it. It's quite embarassing but I missed in school when we first had logs and never understood it therefore. Now I'm nearly done with my chemistry degree and for the first time ever I have an idea what this is all about XD So thank you Mister <3

[jonsenk]

We really do have it much easier these days with all our electronic tools.
It would have been really cool to see how my great grand father worked as an engineer back before WWII, using log tables and slide rules.
And to think of how the field of engineering were changed while my grand father was working. With the transition from these old techniques, to using computers and pocket calculators.

[ChosenOne]

I love that "whoops" at 0:11. I always do that when writing numbers. I get ahead of myself and write the last digit first. Happens to us all I guess.

[chrisisteas]

I've heard my parents talk about this who both studied maths and I finally understand what they meant. Thank you for this video. Doing maths the old fashioned way instead of using calculators intrigues me.

[Rasmhck]

Love the fact that the professor said "42" at 0:42 exactly

[numberphile]

THERE WERE NO CALCULATORS!

(or are you trolling!?)

[numberphile]

I cover that sometimes at sixtysymbols (my physics channel)

[alexbar]

pretty sure if you are already have a calculator and are finding log of numbers, might as well just type in 37x59

[evildude]

They can be estimated the same way one might estimate pi. Pi was found to a few dozen digits thousands of years ago by segmenting the circle into n-sided polygons. A similar process can be done with logs, testing each possible answer until you get one more digit of accuracy, and repeating until you got tired of it or the rounding error was insignificant.

[resonance]

Logs stump me. I once worked out the integral of 1/cabin and got a log cabin.

[rageagainstthebath]

No judgement intended, just a common comment. It's great that you actually satisfy my expectations without even asking. I am really thankful for that.

[papa]

I did use these in high school and for the first few weeks of college. Then I acquired my very first mechanical log table ... Looked a bit like a 'RULER' except it was calibrated in a logarithmic scale and had this neat little 'SLIDE' bit so you could multiply and divide numbers just by lining up the bit that would slide then move this neat little 'INDEX' window and read off the answer. It even had 'TRIG' tables built in ... The name of the device was a Log-Log-Deci-Trig-Slide-Rule.

[Deimoclese]

It's nice to see Prof Bowley again! Haven't seen him much since he retired. I hope he and his wife are well!

[grande]

If you're using big numbers and calculators don't exist, then yes it's easier to use the log tables.

[HansTheBoss]

To get your head around rational exponents, consider square roots. You might find it intuitive that a number multiplied by itself "half a time" is its square roots, e.g. 9^(1/2)=root(9)=3.
If you accept this, it's just a matter of writing, say 10^(1.56), as (10^(156))^/(1/100), i.e. the 100th root of 10^(156).

[Lttlemoi]

I remember seeing this kind of tables for the trigonometric functions and the normal distribution as well. Two years ago, my silly teacher at high school made us learn how to use them "for the case you don't have a calculator at hand". XD