The engineer's cake day coincidence

Marques Brownlee, Hayley Loren and Wren Weichman discuss the coincidental fact behind 1728, the birth year of Matthew Boulton.
LATERAL is a weekly podcast about interesting questions and even more interesting answers, hosted by Tom Scott. For business enquiries, contestant appearances or question submissions, visit www.lateralcast.com
GUESTS:
Marques Brownlee: ‪@mkbhd‬, / mkbhd
Hayley Loren: ‪@HayleyLoren‬, / thehayleyloren
Wren Weichman: ‪@Corridor‬, / sirwrender
HOST: Tom Scott.
QUESTION PRODUCER: David Bodycombe.
RECORDED AT & EDITED BY: The Podcast Studios, Dublin.
EDITOR: Julie Hassett.
GRAPHICS SYSTEM & DESIGN: Chris Hanel at Support Class.
GRAPHICS ASSISTANCE: Dillon Pentz.
MUSIC: Karl-Ola Kjellholm ('Private Detective'/'Agrumes', courtesy of epidemicsound.com).
ADDITIONAL QUESTIONS: Josh Halbur, Ben Justice, Lewis Tough, Arun Uttamchandani, Eglė Vaškevičiūtė.
FORMAT: Pad 26 Limited/Labyrinth Games Ltd.
EXECUTIVE PRODUCERS: David Bodycombe and Tom Scott.
© Pad 26 Limited (www.pad26.com) / Labyrinth Games Ltd. 2022.

[@TH-kc2no]

PLEASE BRING BACK FULL EPISODES ON KZbin

[@secretjameser]

No thank you.

[@benjaminanderson1014]

Yes please

[@ner2393]

+1

[@ToddTevlin]

I agree, put full episodes here please, thank you!

[@myhandlewastakenandIgaveup]

The amount of podcasts I don’t listen to bc I don’t have spotfity and don’t bother with the podcast app on my phone are longer than I would like.

The fact that 1728 is a perfect cube is also key for Ramanujan's number.

[@hairyairey]

Hardy-Ramanujan's number in fact.

[@expectationlost]

is that not 1729

[@hairyairey]

@@expectationlost it is, the smallest number obtainable by two cubes two different ways.

[@bbateson]

Yup, Hardy's story about Ramanujan is how I got this straight away.

[@damnecuadorian]

I immediately thought about Ramanujan's number, but it was off by one (1729). But it still put me in the right track, thinking about cubes.

[@JimC]

Me too. I thought the story was more well-known. I'm a bit surprised they didn't mention it, even on the full podcast. Maybe they did, and it was edited out.

[@hebl47]

Matthew Boulton was an engineer, not a time traveller.

[@annaczgli2983]

Haha! Same.

[@markchapman6800]

That it, a perfect cube, is off by one is the the whole point of Ramanujan's number, which is the smallest number expressible as the sum of two perfect cubes, 12^3+1^3 and 10^3+9^3.

[@rachelblaquiere9134]

Glad I'm not the only one 😂

[@OmegaDoesThings]

I somehow never expected a vid on YT containing both Tom Scott and Wren from Corridor Digital, but it was delightful!

[@melissatrible4214]

Doing things by 12 makes perfect sense *if* you're dealing with *fractions* rather than decimals all the time. For the majority of history (until about the 15th century, so saith Wikipedia), most Europeans were using Roman numerals or other numbering systems that don't necessarily handle decimals neatly, rather than Arabic numerals. If everything is in fractions, then you want numbers you can make into nice, neat fractions. The more things something is neatly divisible by, the more "neat" fractions you can make of it. 12 is divisible by 2, 3, 4, and 6. So, for example, if you have 12 inches to the foot, then you can neatly express 1/2, 1/3, 1/4, 1/6, and any multiples thereof as whole numbers of inches. It's honestly the same logic as the metric system having everything as 10ths and hundredths and so on, just applied to a different numbering system.

[@jolenethiessen357]

Thanks for pointing that out! Twelve is such a powerful number. Lots of things I still do by imperial exactly because of the fraction thing.

[@johndododoe1411]

Except Roman numerals don't facilitate 12, being too decimal in their nature. However lack of an easy way to write out decimals promotes the use of neat fractions instead, such as halves and thirds. Hence why ancient Egyptians and Babylonians created systems based on 12 and 60. Those systems perpetuated through history, leaving behind the US Imperial measurements and the common notations for time and angles: 360 degree circle, 12 hour day etc.

[@melissatrible4214]

@@johndododoe1411 That's... exactly the point I was making. It's not that 12 is especially easy to write with Roman numerals somehow, just that 12 has a lot of neat fractions.

[@nicholasmenzel201]

​@@melissatrible4214 12 would be quite a cool base for a numbering system, but it should be consistent across your whole numbering system, so 12 feet is 1 yard and 12 yards is 1 mile or something like that.

[@nacoran]

@@nicholasmenzel201 I seem to remember several societies used base 12 in their counting systems. You can count it easily on your hands, using your knuckles (excluding the thumb).

[@peterhawthorn-smith5005]

Tom writing down square root 1728 then saying there's no way he can work that out. He needs Matt Parker to teach him about prime factorisation - it will blow his mind.

[@KingstonCzajkowski]

oh yes

[@fghsgh]

There is an algorithm for calculating square roots that is remarkably similar to long division, actually! It especially works well in binary.

[@ElHeisa]

I thought this would be about the number e (2,718) so I was very confused what weird kind of date system writes years in that way.

[@redfrog9717]

To clarify for my fellow Americans, some countries separate the ones digit from the tenths (not tens) digit with a comma instead of a period.

[@johndododoe1411]

​@@redfrog9717Many countries in fact. And we also use the period to visually mark groups of 3 digits (4 in some Asian cultures) Thus giving us notations like 299.792.458,00 m/s . Which Americans would write 983,571,056.4 fps.

[@redfrog9717]

@@johndododoe1411 I know, I just only really felt like clarifying for the situation at hand

[@Wick9876]

Euler was 11 in 1728.

[@SioGG]

LOVE seeing Wren on here! Very sad we only get highlights though

[@hannahmecoe]

You didn't mention why the ratio of one cubic inch to one cubic foot would have been so significant to a steam engineer....

[@richardfarrer5616]

This is the first time that I've got one of these almost instantly. Being a nerdy mathematician myself, I know all the cubes up to 12, and also know about Hardy's taxi number, 1729. And being old enough to remember imperial measurements, it wasn't difficult to work out the most likely units being measured.

[@hairyairey]

Hardy-Ramanujan's number!

[@felixvarghese2307]

@@hairyairey Referenced many times in Futurama as well!!

[@AndreVandal]

Can we see the full episodes of these somewhere?

[@fullfungo]

Sadly, no. Full episodes are only available in audio format (through Spotify and such) on their website.

[@AndreVandal]

@@fullfungo too bad.

[@peterjf7723]

@@fullfungo Thanks, found it.

[@donaldasayers]

No

[@thameslinkrail4038]

Matthew Boulton featured on the old £50 note with James Watt (and the Queen) which was withdrawn at the end of September, didn't see many around though as they weren't widely accepted.

[@FozzyBBear]

Surprisingly 12x12x12 boxes are no good for storing 12" LPs. The vinyl platters are 12" in diameter, but the covers and sleeves are larger.

[@TarenNauxen]

Who let Wren out of the studio?!

[@morboed96]

I get that, I'm super excited that I'll probably be still be alive in the year 2048, and that won't even be my birth year.

[@yetanother9127]

The fact that it's to do with a measure of volume is actually significant; Boulton worked with the mentioned James Watt (the same Watt that gives us the unit of power by that name) to create the modern condensing steam engine, which was vastly more efficient than the atmospheric steam engines used previously. The Boulton-Watt Engine (as it's sometimes called) made steam power practical for general industrial use, and essentially sparked the First Industrial Revolution.

[@byeguyssry]

Me: finishes the prime factoring of 1728. Tom, immediately after: As if anyone would be able to calculate that

[@Maurice-Navel]

If you had only gone up just one, you could have the Hardy-Ramanujan number!

[@Cory_Springer]

As soon as I heard 1728 I was like "hmmm that sounds close to a taxi number!"

[@roadrunnercrazy]

Brilliant! Another bit of usless trivia to annoy my friends and family with.👍

[@bradaloop]

What episode is this from? There's only 1 on KZbin.

[@Damixisss]

podcast, ep4

[@bradaloop]

@@Damixisss Thanks, just saw the community post. Bit annoying that everything isn't all available here on KZbin, really don't get their reasoning behind it.

[@TheBioRules]

Well I felt foolish. I heard 1728 and thought "that's a taxicab number! He's a manufacturer, he must make taxicabs!". Then realized the taxicab number i was thinking of was in fact 1729.

[@TrickyNick79]

New favourite podcast

[@quintuscrinis8032]

2:04 1728 won't have an integer square root - it ends in 8 which isn't a square of the single digits at all. Square numbers end in 1,4,9,6,5,6,9,4,1,0. Which I've just realised is a neat little pattern.

[@NochSoEinKaddiFan]

WREN!!!

[@marcusmyge]

You just reminded me of a Citation Needed episode and the quote "Bring me another plate of wrens".

[@dave5194]

FULL EPISODES ON YT PLEASE 🙏

[@10thdoctor15]

Who buys boxes to move house? Just take the used ones from supermarkets. They're not 12x12x12 either.

[@hammerth1421]

So I was right about linking 1728 to James Watt! I just wasn't right enough...

[@jwvdvuurst]

The standard moving boxes in the Netherlands are (48*36*32 cm^3), where 48*36, so the floorspace of the box is 1728 cm^2. So not equal to the 12"*12"*12", but (12x12x12)*36 cm^3.

[@patrickclausen6922]

I think it's like this in most European countries..i was surprised to hear it's not in the UK. A perfect square box for moving. That's strange to me

[@peterhawthorn-smith5005]

As a Brit that's the standard boxes I know. I've not come across these cubic feet ones mentioned in the video.

[@dawnzac]

2:21 MKBHD : what is math ??🤣

[@omoliemi]

full episodes please 🥺

[@JimC]

In the whole podcast, there's one more error I know of that's in the novel _Lord of the Flies._ What is it? I didn't notice it on my own. I read it in a specific article which included the error mentioned in the podcast.

[@erictaylor5462]

a mile is 5280 feet, 1760 yards, 63360 inches and 1.61 kilometers.

[@geoffroi-le-Hook]

Four years later, George Washington was born in floor(1000 sqrt 3)

[@ArtturiSalmela]

It might not be obvious by the way he acts in videos, but I suspect Wren is trying to hide how smart he is.

[@X2Brute]

I was thinking yards in a mile, but that's 1760

[@shohamsen8986]

I kept shouting taxi cab number. Later I realized it's one more than this no

[@amitayudas1411]

This question is definitely leaked to the particitants

[@Atarian6502]

How is 12 by 12 by 12 more of "a perfect cube" than for example 10 x 10 x 10 or 13.456 x 13.456 x 13.456 ?? What am I missing here?

[@MatthewChowns]

It's just because there are 12 inches in a foot. So it's a 1ft x 1ft x 1ft cube.

[@copterinx0468]

A perfect cube is the cube of an integer. 10^3 is also a perfect cube, but 13.456^3 is not.

[@itiscujo]

Because the metric system wasn't relevant in england back then, all they had was feet, inches, etc.

[@highpath4776]

Also duodecimal system 12 is divisible by 1, 2, 3, 4 and 6 and nearly by 8 and 9 in easy fractions. The divisibles by 5 7 and 10 are really awkward and we dont talk about 11

[@ShankarSivarajan]

If he had been born in the year 1000, that would have been cool too.

[@LotsOfS]

I think you included the incorrect twitter link for Wren in the description

[@lateralcast]

Looks like this has changed since recording happened. Now fixed - thanks.

[@erictaylor5462]

I was born in 1969, and this is important as otherwise my mother would not have felt me kick insider her for the first time in the same moment Neil Armstrong stepped on the moon.

[@lforlight]

Took them a surprisingly large amount of time to get to cubed inches in a cubed foot from learning it's 12 cubed. "There are 12 inches in a foot" is so rudimentary, and I'm saying that as a metric person.

[@xanderporter8143]

How can I listen to the full thing with video?

[@dejafuture]

My answer (within a minute and a calculator) was: it's 12 x 12 x12. Now I'm gonna watch the rest of the video to see if I was right

[@dejafuture]

OK almost there. I didn't realise the whole inches and feet stuff. But I'm from the metric universe.

[@ericlewis3444]

Why the hell is Wren so smart? I know him as a special effects/cgi guy like me, but he WAY to smart for this field

[@lohphat]

The UK still uses miles. Thus it still uses feet and inches.

[@rustyknight1572]

And there I was, trying to figure out if MDCCXXVIII might be connected in some way.

[@cykkm]

1728=2^6×3^3. There's a lot of small factors in this number.

[@punklejunk]

This is the geekiest Lateral I have watched so far. And that is saying something.

[@spelcheak]

It does make sense to do things it multiples of 12 Tom

[@Programmdude]

Only if your number system is base 12 too, otherwise it's too frustrating to convert between them and you end up with weird numbers like 1728. And while metric uses the properties of base 10, imperial DOESN'T use the properties of base 12 for most things. If imperial was consistent (12 feet = yard, 12 yards = mile, 12 miles in a furlong, etc), it's highly likely metric never would have taken off at all.

[@keir92]

tom, 12 is actually better than 10 for multiplications. it has more divisors and it's easier to work out fractions from it.

[@witerabid]

I feel like Matt Parker would've sat out this question.. 😅

[@Fiznik3933]

Im like hey whats up hello

[@panda4247]

Something related to Ramanujan's taxicab numbers? That is 1729... so 1728 should be 12^3

[@martinpain7332]

I was disappointed there was no cake…… 🎂

[@DelfinaKS]

Very interesting. I was surprised, Tom, who is quite smart, initially went directly to the square root. I thought when you have no clue what is special about the number, it would make more sense to look at the factors rather than directly jump to checking square and cube roots. If we actually write out the factors, I think the answer here would become obvious sooner.

[@SteinGauslaaStrindhaug]

What? Your moving boxes are cubic? I'm pretty sure they're usually taller than they are wide and longer than they are tall here in Norway... yeah, just googled it and they come in a bunch of different sizes but they all have rectangular sides like I remembered.

[@erictaylor5462]

People born in the North American British colonies before 1776 are considered people born in the United States. A requirement to become the President of the US is, you have to be born as a US Citizen and you have to have lived in the United States not less than 20 years. The 7 Presidents that precede Martin Van Buren and William Henry Harrison (who followed Van Buren) were all born before 1776 and thus they were born before the United States existed. However, all 9 were born in what would become the United States.

[@denispol79]

I knew that Ramanujian taxi number was very close to that, but not quite the number. PS A cubic moving box doesn't sound like a comfortable thing to carry around.

[@secretjameser]

Hi wren!

[@harshilpatel684]

Thought it was to do with sequences 1728 39 4....

[@adammullarkey4996]

I feel like something like that could be true of practically any year, though. I mean, there are so many different numbers and measurements in the world around us, if you look hard enough, surely you'll find something about the year you were born that's relevant to your job.

[@TemporalZack]

Well if we try to break 1728 down into prime bumbers 1728 864x2 432x2x2 216x2x2x2 108x2x2x2x2 54x2x2x2x2x2 9x6x2x2x2x2x2 3x3x3x2x2x2x2x2x2 so you can see there are 3 3's and 6 2's, so it would be (3x2x2) cubed which mans the cubic root of 1728 is 3x2x2 which is 12. So realistically you can definitely just calculate the cubic root of 1728 on paper in like a minute or two. As for square root, that'd be one and a half 3's and 3 2's, 2x2x2x3x√3 = 24√3.

[@shaunhouse8469]

Hayley said something about partnerships but I don't think anyone got to Matthew Boulton being James Watt's business partner. Not that that is relevant to the question

[@nathandust]

I see Wren. I click.

[@zapfanzapfan]

You have small moving boxes...

[@severs1966]

Was Matthew Boulton more or less nerdy than James Watt?

[@phauntis]

WREN!!!

[@donaldasayers]

Richard Feynman's number: Is there no one that doesn't recognise 1728 as 12^3 and 1729 as Ramanujan's number 12^3+1^3=9^3+10^3?

[@SniperSpy10]

It is strange how strong wren's accent in this, despite it being quite weak in his vids

[@davidioanhedges]

In duodecimal it's 1000 .... it's a dozen gross

[@ethankoetsier]

Exactly. As a fan of the dozenal system, i recognized 1,728 immediately.

[@ZipplyZane]

I get why he's not doing full episodes on KZbin: he's trying to get people listening to the podcast. But it would be nice if he'd upload the videos to a paid tier or something. That way it won't interfere much with people who want to listen for free.

[@arm_613]

This was pretty obvious. Why, yes. I do have a degree in mathematics....What (Watt?) gave it away?

[@JennaGetsCreative]

The comment near the end about moving boxes being 12x12x12. Are we talking cardboard boxes? I don't think I've ever in my life seen a 1 foot cube cardboard box. For moving purposes, a 2 or 3 foot cube makes more sense. Now, if we're talking like a plastic milk crate, that makes more sense.

[@lightningblaze6449]

cube rootng 1728 isnt that hard actually for those that know the cube root trick for 1-100 You only need to learn cubes of 1-9 to do it split by first digit and everything after "1000" so 1 in the "thousands plus place", 1^3 = 1, 2^3=8... Its between 1 and 8, thus answer is 1X finally, ones place, its 8, every digit = exact same digit for this place, except swap 8 and 2, and swap 7 and 3, thus, 12 for 4096, its 16, 4 is between 1^3 and 2^3, thus 1X, and then last digit is 6, so its X6, so 16 You can do this all the way to 99, and then just know 100^3=1000000

[@SaszaDerRoyt]

Fun fact! Matthew Boulton's Soho Mint in Birmingham produced the famous Cartwheel pennies and tuppences from 1797-1799 (all were marked 1797), I think they were the first industrially milled coinage in Britain. He was also on the old 50 quid notes

[@Chris-im3ys]

Please don't upload full episodes to KZbin. No, wait. Do

[@sophiamarchildon3998]

Initial thoughts: the title is throwing me off, mentioning cake day. And the thumbnail is of a vertically tiered cake. 1728 might have been an important factor of his work~? Not a prime number, nor Fibonacci's. Was it said when about to die at 80 yo (1+7, 2+8)? Or died at 72-73, and got to see the new century? Sounds dubious for the time. The 1728th copy/model/reproduction/output of his design happened near or on a very important date (his deathbed/marriage/recognition/etc.). Could also be that his best design integrated 1728 as a deciding factor; like 1.728 L/HP engine, or 17:28 gear ratio. The gear ration is the most interesting, like in a transmission So, yeah, I don't have a real clue; just guesses.

[@sophiamarchildon3998]

Results: I was lost about them freedom units...

[@PianoKwanMan]

I like how Hayley is quiet. It definitely helps the format. So, it's less like citation needed. Need to let the contacts talk, go down the wrong path, and still arrive at the right answer

[@iComplainMyK]

alucarD .....his father dracula......spelled backwards. Gg

[@cannot-handle-handles]

Who's watching in 2197 or born in 2197? 😆

[@scidixreiznov8237]

I hope they delete tiktok and replace this

[@Milamber1982]

Oh, Tom! I'm disappointed that you didn't know that 12" was 1'. (It didn't help me get the answer mind you)

[@christopherbedford9897]

He was so nerdy he didn't think that maybe _a lot of people_ had to be born in that year, and that _more than a few of them_ would be engineers. That's not a coincidence, it's a "meh."

[@derschwartzadder]

They fact that Tom, knower of obscure things, native of Britain, the place that INVENTED AND STILL USES IMPERIAL UNITS doesn't understand them is more than a little disappointing.

[@bazahaza]

Where the full episodes ?I don't want these episodes.

[@kirelagin]

Those imperial measurements make the most simple things so unnecessarily complicated! Imagine some engineer being excited about being born in year 1000 because there are 1000 cubic mm in 1 cubic cm.

[@patrickclausen6922]

Can we please let the imperial system die now 😂