The extra footage is now available at kzread.info/dash/bejne/qK6Kl5Kgn7rFh7A.html

@johnlbales2773

7 жыл бұрын

Numberphile Quite the gem! Thanks.

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!

@jeetkumar3134

3 жыл бұрын

Replies

@mahadevganujlkhad9799

3 жыл бұрын

Mahadev

@bayustress9321

2 жыл бұрын

1256

@bayustress9321

2 жыл бұрын

1256

@mahailansari1694

2 жыл бұрын

@@mahadevganujlkhad9799 Ok

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

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.

@theshuman100

7 ай бұрын

the antilog table

@EebstertheGreat

7 ай бұрын

@@theshuman100 Yeah, that's what it's called.

@lollol-tt3fx

6 ай бұрын

@@EebstertheGreatis this sarcasm

@EebstertheGreat

6 ай бұрын

@@lollol-tt3fx No. This is how people used to multiply. (Well, it's one way some people used to multiply. They also used long multiplication, slide rules, and in many parts of the world, abacuses. And starting around the turn of the century, adding machines became available, so it was possible to multiply mechanically by repeated addition. Rare methods included lattice multiplication, multiplication tables, Napier's bones, and the stepped reckoner.)

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

I cover that sometimes at sixtysymbols (my physics channel)

Keep up the great work numberphile! (P.S this guy is awesome!)

A-Mazing. loved it. Logs are both a fascination and an issue to me. Thanks numberphile and plz keep bringing them on. I look forward to comments on logs to other bases!

@babajibaba6539

2 жыл бұрын

⁸⁹⁵⁰⁵¹⁹⁶⁵⁶..,,ok....ok

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

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

@ynmol7830

3 жыл бұрын

I think the editor did some work to get that , seems very deliberate

@inx1819

3 жыл бұрын

@@ynmol7830 haha replying to a comment older than most fortnite players

@benoitb.3679

2 жыл бұрын

This comment also has exactly 42 likes. NOBODY MOVE.

@kasturylbs5905

2 жыл бұрын

Buat hk kong malam ini lur 4d kirim. Kemarin. Keluar., 0478,coba mistik sekarang

@nidhalsyaqief2627

2 жыл бұрын

Vv

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

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.

@stevecummins324

2 ай бұрын

Engineering slide rules, sometimes lookup results for functions of more than two inputs ;-) You may also be surprised to hear that 20 years ago undergraduate mechanical engineers were still being taught to use a set of tables referred to as the steam tables. Tabular results of thermodynamic properties for things like water or refrigerants. You may have been taught things like Boyles law in physics . It's a fair aproximation that is often very useful, but real gases.... they don't follow that to accuracy that can be needed. There are polynormal formulae that have been curve fitted to fit real world thermodynamic properties... but those formulaes themselves need like 20 terms to be accurate. So tables were still much easier. No calculator I've seen has ever had such a button! Spreadsheets can have functions to do such added in.

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

@xwiliamaligatorx2214

7 жыл бұрын

With complex numbers it is easier to use "ln", which is logarithm with base of eulers number. It is much harder to multiply two brackets like (25456+321*i)(52516+123*i), when you convert it to an exponencial form: Pol(25456;321)*Pol(52516;123) = [25458.02382*eˇ(0.7224611278*i)][52516.4404*eˇ(0.1341946834)]; then u just multiply eulers number multipliers and add up exponents of eulers number: (25458.02382*52516.4404)*eˇ(0.7224611278*i + 0.1341946834*i) = 1336964791*eˇ(0.8566558112); which we convert back to an algebraic form by Rec(1336964791;0.8566558112) = (1336815356*19988890*i). Show me easier way to do it.

@lancome4600

6 жыл бұрын

A few years back, my country's 12th graders taking exams at a similar level to a gceo cant use calculator to work out calculus. That book helps tremendously.

@qwerty687687

6 жыл бұрын

but in these situations you have your log tables with you?

@jasoncola6071

6 жыл бұрын

Alex Baraban, take it on math test and use it.

And what lovely video, I always wondered what the use of logarithms really was!

This was exactly what I was looking for, thanks again O wise sage!

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.

@hypenheimer

6 жыл бұрын

10:1

@remixener22

6 жыл бұрын

make it a meme lol

@dozenazer1811

5 жыл бұрын

I do this all the time in German when I hear 2-digit numbers.

@Szczawik324

5 жыл бұрын

It's "Whoops to the power of two" xD

@redrock9319

5 жыл бұрын

Not me.

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.

Can't wait for the next part. I want to know how the tables were worked out.

@stevecummins324

2 ай бұрын

Was there ever a follow up? For functions that can be described/aproximated as polynomials, an algorithm called the method of finite differences can be applied to generate tables row by row

I just missed the log table era, by the time I started O Level Maths in 1980 we were using calculators. Learned how to do all these tricks with logs, but not using tables.

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.

Logs are used in calculating PH and PoH in chemistry, that why I'm here at least.

@harjitsingh7308

5 жыл бұрын

That's so cool! In computer science logarithms are one of the many techniques used in complexity analysis to calculate the efficiency of an algorithm

In india during junior college board exams log tables are still being used which are provided by the examiners and calculators are not allowed in exams.

Great to see prof Bowley again!

Finally, Someone explains Logs to where its understandable and usefull. Thanks!

Just keep in mind log isn't always base 10, somtimes they use e or some other value as the base.

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

@AvinashtheIyerHaHaLOL

6 жыл бұрын

*a natural log cabin

@xCorvus7x

6 жыл бұрын

squ34ky2 He threw it into the sea.

@alexwang982

6 жыл бұрын

what about the C

@TnseWlms

6 жыл бұрын

The integral of 1/cabin is actually log cabin + C, or houseboat (a log cabin by the sea.)

@tamircohen1512

6 жыл бұрын

Actually you would get a natural log of the absolute value of cabin / d/dx(cabin) + C so your joke kinda falls apart there :)

One of my absolutel favourite subjects in mathematics is Benford's Law, and I can feel myself getting excited because Numberphile is getting pretty close to touching upon the subject!

@babajibaba6539

2 жыл бұрын

⁸⁹⁵⁰⁵¹⁹⁶⁵⁶..,,ok.....ok

Can't wait for the story telling!!! :)

In practice, how big do the numbers have to be that doing this extra logarithm work, and flipping through pages beats the time it would take to do it long hand?

@AssortedIdiocy

7 жыл бұрын

At least for me, using logarithms became faster than doing a pair of three digit numbers by hand, especially for division.

@ImranKhan-kj4fm

6 жыл бұрын

doa

@ImranKhan-kj4fm

6 жыл бұрын

Abhi Abhi so kar Uthe khana Banane ja rahe hain

@lordihlendam3619

4 жыл бұрын

It depends. I find that with two 3 digit numbers, it's already faster to use a table of logs, but that's just me. YMMV

@RudaMader

2 жыл бұрын

Hi

Pause at 0:00 - Prof. will be like: :O

@slolilols

4 жыл бұрын

Lol 😂

Its good to see Prof Bowley back!

I'm looking forward to the "more logarithms" video. This topic is quite interesting.

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

@user-xv7sm6mf2s

6 жыл бұрын

^This

@hungryfareasternslav1823

6 жыл бұрын

Yeah

@hva25

3 жыл бұрын

WTF GRANDAYY ???? What you doin here lol

@Desam1000

3 жыл бұрын

Iff and only iff

@sonurelwani7719

3 жыл бұрын

\Q&A

I'm still waiting for the next part of this...

@rogerbowley3994

10 жыл бұрын

So am I --Brady filmed it twice, and then forgot about it. Napier imagined a number (1 -0.1)^(10) and then took powers of it. So the power of 0.2 is ((1 -0.1)^(10))^0.2=(1-0.1)^2=0.81. For 0.3 it is 0.9*0.81=0.729 and so on To get more accuracy he started with (1-0.001)^1000, and then did the same trick. It took 20 years to work ot the table using 10^7 instead of 1000 or 10. In the limit of 10 going to infinity the result is1/e where e is Euler's constant.

@BagaJr

10 жыл бұрын

Roger Bowley I'm obsessed with making everything as intuitive as possible so would you mind explaining why he was imagining lim n -> inf of (1-1/n)^n and how that relates to creating the log table because I don't see where that came from? I've always wondered this since I first saw this definition of e, but nobody ever explained it; they just stated it.

@numberphile

10 жыл бұрын

kzread.info/dash/bejne/qK6Kl5Kgn7rFh7A.html

@coopergates9680

8 жыл бұрын

+Baga Jr It wasn't about approaching e, it was to make the arithmetic easy; I think it would have been easier to use the additive form. The limit of (1-1/n)^n as n rises to infinity is 1/e, so you might as well use (1+1/n)^n. For instance, 1.001^1000 is one that can be used. The point is that there is already an exponent (1000) that can be divided by a power of ten to get fractional powers of the base. 1.001^1000 = b b^0.001 = 1.001 b^0.002 = 1.002001 (Pascal's triangle :) ) .... b^0.006 = 1.006015020015006001 and so on.

I remember doing these in my high school homeschooling. The instructions were minimal and I had no idea what it was used for. So thanks guys.

@mdhhh6066

2 жыл бұрын

Hi camera so much I wish you know but I didn't

I got one from my uncle about 15 years back. Thought it was the coolest thing ever. Can still use it a bit. You can keep your pocket calculators.

THERE WERE NO CALCULATORS! (or are you trolling!?)

@thiyaradesilva26

4 жыл бұрын

Y'all get to use calculators? 😂

@RoderickEtheria

3 жыл бұрын

Surely, there were calculators, but surely they weren't mechanical.

@pinklady7184

3 жыл бұрын

I remember using log tables in Irish high schools in 1980s. Personal calculators in that decade were considerably expensive and they were banned in schools.

@basuk7500

3 жыл бұрын

Doog

@user-kn9cu9pg5b

3 жыл бұрын

दिसावर में गेम भेजिए सर

I think a modern computer has simpler algorithms for doing multiplication. These were used for really big multiplications more complicated than the example shown.

That is a pretty good question. Obviously they are going to cover that in a future video. Using the definition of a Log see how many iterations of a "by hand" binary search it would take to duplicate the accuracy of the table. I'm pretty sure that would be the quickest way to do it if you were stuck on a deserted island.

Talking about logarithms and things used before calculator, it would be really great if you made an episode about slide rulers. My dad used to do calculations for his diploma thesis with one of them. Awesome tool.

Logarithms can also be used to calculate square roots by using the formula b^(log_b(n)/2), where base b is real and > 1 and n is a positive number.

This is actually quite brilliant. I must get my hands on one of these.

@Rebecca Beirne You just learn the tables by heart. Like you do with the multiplication table. Quite a few people have been known to learn them. You can also learn the natural log tables while you’re at it.

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).

Thankyou! I recently learnt logarithms and I understood them I just didn't see the point of them. But what is the use of logarithmic graphs? Why not just use an exponential graph?

Yes, obviously, but there's a relation between the binary representation and the 2log of a number (for the length of the representation n, floor(2log x) = n-1). My question was if higher precision is possible, which might provide interesting insights into the computation of logarithms in computers using exactly the same principle you mentioned.

@reginamarialemesdospassos3699

2 жыл бұрын

Kero ganhar

@jithenlet908

2 жыл бұрын

Go ki

Professor Bowley is back!

As late as 1995 I was using log, trig, and other assorted tables from not a single tome, but from a voluminous set of books, each page going out to umpteen decimal places.

Unless you have a log table at hand, how is it easier to do logarithms than multiplying and dividing

Good old days, remember doing this in secondary school.

@sattakingsattaking7906

3 жыл бұрын

9899615673 WhatsApp,

it's been ~ 4 months and I'm still waiting for the next part.

Try it, and you will discover why Napier's Bones, Log Tables and Slide Rules ruled the world until the digital calculator came along. They were all faster than long multiplication (and you made less mistakes). and it was a perfect match for physics because you could easily handle mantissa and exponent separately - and easily check your multiplications.

They should continue teaching log tables and cursive

I thought the same thing. The only time in school I can recall ever having trouble with math was in 4th grade when we had to do long multiplication and division. It took forever before I finally understood how to do it.

@abimonei8825

2 жыл бұрын

me in

why doesnt this have that many views? This is a good video!

Brady I'd love to see a video about Euler's identity! It'd be completely fascinating

Could you expand on Natural Logs too?

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.

that's 62700, 5 seconds (my process : 1x75+4x32=203 +4x100=603 attach 32x75=32/4x100x3=2400 attach to 603x100and there you are 6 27 00

Roger is amazing, but then again, all of the professors are

I have just got a book of these, and cos and sin and natural log, etc etc... Sooooo cool cool cool

@sattakingsattaking7906

3 жыл бұрын

9899615673 WhatsApp,

Great explanation of log tables. Now do a video on slide rules. (I still have the ones my parents used.)

@babajibaba6539

2 жыл бұрын

⁸⁹⁵⁰⁵¹⁹⁶⁵⁶..,,ok.....ok

Might have been a good spot to mention the slide rule...

@sidharthcs2110

6 жыл бұрын

Chris Gonzales Slide rules brought me here

@marklammas2465

3 жыл бұрын

Slide rules brought me here too. I usually use one (I have several), but I found my old book of log tables, and thought I would refresh my memory. This explanation is beautifully succinct. My log table book is very old; its first user was in the flyleaf in 1917, and its final user wrote into the page in 1926. Several users; all schoolkids at the same school, presumably.

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

I used to think that the secret to life was applying some function to each component, adding them together, and then taking the inverse function of the sum. Works with multiplying with logarithms, the Pythagorean theorem, resistors in parallel, parallel processing, etc. But I could never find the right function to apply.

This is the underlying principle on which slide rules are based.

@sattakingsattaking7906

3 жыл бұрын

9899615673 WhatsApp,

@pardisantun7173

2 жыл бұрын

Minta buat haka ea

i just learnt from this vid about what logarithms really meant.

@sattakingsattaking7906

3 жыл бұрын

9899615673 WhatsApp,

So instead of just doing multiplication, you just need to print out a Log table on a scroll, find the corresponding log, add those numbers together and then look at your scroll to find the answer. How convenient

@AlchemyAtLarge

7 жыл бұрын

Max Yakovlev it was convinient before calculators were invented

Thumbs up for selecting 42 as the first number not a multiple of 10!!!!!

@ankitaaarya

4 жыл бұрын

Yep

@TimothyReeves

3 жыл бұрын

But he did 100 and 1000 before 42.

@davew2098

3 жыл бұрын

@@TimothyReeves .

@tribektiagustinus157

2 жыл бұрын

Berearti harus jago rumus fisika&kimia.baru memang lotry.ok?.

@tribektiagustinus157

2 жыл бұрын

Brearti harus jago rumus matematika,aritmatika,&algoritma.

How do they make these tables? I do not understand how you can calculate a number a ^ b.c. For example 10^3.8756. I know how to calculate it if b.c is a whole number..

@coopergates9680

8 жыл бұрын

+Quran Channel Using Napier's base, a would eventually be raised to all sorts of fractional powers, so you end up with log (base a) (something) = something else How to get the common log? Easy. log (something) = log (base a) (something) / (log (base a) 10).

@rrc5982

6 жыл бұрын

Cooper Gates how would you find the log using base10 or 2 of 57 without a calculator or table? Any videos for that floating around?

@MartinezRBA

6 жыл бұрын

Ryan Rubidoux-Cosman exactly! How they come up with those tables!? I cant find videos of that

@lordihlendam3619

4 жыл бұрын

Oh, there are lots of ways you can work out the logs of numbers. The simplest method I can think of is to taylor expand log(1+x). This will give you the logs of numbers between 0 and 2 (not including 0 and 2). You can then construct every other log using log(x)+log(y)=log(xy). AFAIK, using taylor series along with precomputed tables is how modern calculators/computers calculate logs.

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.

Engineers used this trick on slide rules before calculators came along

@devbhaisattakingdevbhaisat9024

3 жыл бұрын

Whatsapp karo....

@devbhaisattakingdevbhaisat9024

3 жыл бұрын

9394359940...

A 5 minute video just explained logs better then an entire semester of College Algebra.

No mention of slide rules? I'm surprised

@sattakingsattaking7906

3 жыл бұрын

9899615673 WhatsApp,

@alkaka6616

2 жыл бұрын

@@sattakingsattaking7906 i

my slide rule just got way more awesome.

We still use logs in exams...

agreed, my parents generation used to learn this at school and it was much faster and precise than multiplying manually. Back in the day when this was commonly used, those who used it a lot (eg. that motgage payment mentioned above) could do it really quickly

Logarithms are really useful for exponentiation as well; a^b = 10^(b*log a)!

"The Slide Rule" is a mystical object I've always heard about but never seen. Does Prof. Bowley have one he could show us?

if you're going to use a table, you might as well just use a multiplication table and look it up, idk i don't see the benefit.

@EdwinFairchild

7 жыл бұрын

when you find a multiplication table that has the number 23456 * 98754.67 let me know

@expirydate2000

7 жыл бұрын

You're right. There isn't a multiplication table for those numbers. But while you faff about with your log tables, I'll have the answer by long-hand multiplication. Right off the bat I can see it is going to be around 2.31 billion.

@lordihlendam3619

4 жыл бұрын

@@expirydate2000 Alrite, now divide those numbers. I'll have the answer in 20 seconds with a log table.

Or you could...have a multiplication table?

@aizenadante78

6 жыл бұрын

So easy for him

@josephcote6120

5 жыл бұрын

Not so convenient to find 385 x 12922

but isn't 1.6232 to 5 significant figures, not four?

@drinkingthatkool-aid3193

8 жыл бұрын

I think he meant 4 digits after decimal

@NotCallum

8 жыл бұрын

Moaiz Shahzad so like four decimal places? fair enough thanks for clearing that up for me, I was questioning if i was doing sig fig right this whole time xD

@George70220

8 жыл бұрын

+NotCallum No he was talking about significant figures, not just decimal places. The 1 is a placeholder and is not calculated into the number of significant figures. This is just how logarithms work.

This mathematics professor complaining about doing multiplications because he might make a mistake. Seriously?

@wierdalien1

7 жыл бұрын

expirydate2000 physicist

You people waste lot of paper. Hope you are planting trees

इंग्लिश समझ नहीं आती इंग्लिश समझ नहीं आती

we've done it!

I grew up using the log tables brings back memories thank you next step was slide rule and that made sense because you will be adding logs on a scale. still love my slide rule. still remember interpulating but the was a special scale for that if I remember

@Ray-qb7tk

4 ай бұрын

1/C

I never thought about it this way but it totally makes sense! :)

where can we get a copy of the log and the anit log table?

I remember log tables when I took math analysis aka the math class between Algebra II and Pre-cal. This video does take me back to Senior math class, which I totally forgot about log, sin, and cos.

I absolutely enjoyed this video! At 0:51 I think he meant decimal places

Awesome explanation.

Would it be possible to do a vid on slide rulers?

'This is all we 'ad down t'mine!' Brilliant

@robertvesetas8751

4 жыл бұрын

Deserves 1/0 likes

I lost my old log-log when I was a senior in college (about the time I got my first scientific calculator). And just a few years ago in a fit of nostaliga I went on EBay and purchased a replacement (over 30 years after my first one).

could u explain how the slide rule works?

this stuff is prehistoric, yet so awesome.

Slide rules do use a visual representation of logarithms. Only instead of adding numbers you're adding distances.

There are University U tube channels that post entire lecture series of calculus and other math and science courses. Try something like Stanford University. Maybe MIT. I believe they also direct you to print resources. The lectures are usually free under Creative Commons licencing. Good luck!

He added the log for 37 and the log for 59 together. He had a table showing him what these logs were for each whole number from 1 to 100 i think.