I designed a silly but semi-functional computer.

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Get your calculating christmas card! Support me on patreon: / standupmaths
All Patreon supporters will be emailed a personalised card (deadline end of December, but sign up sooner for an earlier email) and "statistically significant" or higher get posted a physical signed card (deadline end of December but sign up by end of November to get it before christmas).
Check out Mark Dominus's great blog. Link to follow-on post at end of this one.
blog.plover.com/math/irish-lo...
Here is the sign-up to volunteer for Pi By Hand 2024. forms.gle/CVocrwomCe1Q4iuX6
Paper on other method to get Ludgates's values: treasures.scss.tcd.ie/miscell...
All of the numbers I found are below. So many numbers. Presented three different ways, which is really unhelpful.
Huge thanks to my Patreon supporters. They put the teeth on my cogs. / standupmaths
CORRECTIONS
- Yes, the invention of logs in 1614 is 410 years ago, not 400, as I said around 06:10. On the fly my brain confused it with the 1624 publishing of Arithmetica Logarithmica, the first great log table book. First noted by AlexSh789.
- In the completed table around 11:54 I accidentally put in some products where are not the result of two one-digit numbers (60, 80 and 90), and thus are not needed. First pointed out by Frederico via email.
- Let me know if you spot anything else!
Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Produced by Nicole Jacobus
Cogputer build by Lisa Mather and Katie Steckles
Tree build by Nina, Carrie and assisted by Laura.
Extra material by Adam Atkinson
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...
0-9 COGPUTER
0 cog: 1 teeth
1 cog: 42 teeth
2 cog: 41 teeth
3 cog: 27 teeth
4 cog: 40 teeth
5 cog: 8 teeth
6 cog: 26 teeth
7 cog: 18 teeth
8 cog: 39 teeth
9 cog: 12 teeth
LABELS ON MIDDLE COG:
CE, --, 00, --, --, --, --, --, --, 00, --, --, --, 00, --, --, 25, --, --, 00, 45, --, --, --, 81, --, 35, 00, 00, --, 63, --, --, --, 30, 15, 49, --, 54, 27, 00, 00, 00, 00, 42, 21, --, 40, 20, 10, 05, 72, 36, 18, 09, --, --, 56, 28, 14, 07, --, --, --, --, 48, 24, 12, 06, 03, --, --, --, --, --, --, --, --, 64, 32, 16, 08, 04, 02, 01
1-9 CHRISTMAS TREE
Present 1 is 7 units tall
Present 2 is 5 units tall
Present 3 is 18 units tall
Present 4 is 3 units tall
Present 5 is 21 units tall
Present 6 is 16 units tall
Present 7 is 28 units tall
Present 8 is 1 units tall
Present 9 is 29 units tall
Bauble 1 is 14 units high
Bauble 2 is 12 units high
Bauble 3 is 25 units high
Bauble 4 is 10 units high
Bauble 5 is 28 units high
Bauble 6 is 23 units high
Bauble 7 is 35 units high
Bauble 8 is 8 units high
Bauble 9 is 36 units high
Bauble 10 is 26 units high
Bauble 12 is 21 units high
Bauble 14 is 33 units high
Bauble 15 is 39 units high
Bauble 16 is 6 units high
Bauble 18 is 34 units high
Bauble 20 is 24 units high
Bauble 21 is 46 units high
Bauble 24 is 19 units high
Bauble 25 is 42 units high
Bauble 27 is 47 units high
Bauble 28 is 31 units high
Bauble 30 is 37 units high
Bauble 32 is 4 units high
Bauble 35 is 49 units high
Bauble 36 is 32 units high
Bauble 40 is 22 units high
Bauble 42 is 44 units high
Bauble 45 is 50 units high
Bauble 48 is 17 units high
Bauble 49 is 56 units high
Bauble 54 is 45 units high
Bauble 56 is 29 units high
Bauble 63 is 57 units high
Bauble 64 is 2 units high
Bauble 72 is 30 units high
Bauble 81 is 58 units high
2-9 CHRISTMAS TREE CARD
2: 3
3: 12
4: 2
5: 17
6: 11
7: 24
8: 1
9: 20
height: bauble number
2: 64
3: 32
4: 16
5: 8
6: 4
12: 48
13: 24
14: 12
15: 6
18: 40
19: 20
20: 10
21: 72
22: 36
23: 18
24: 9
25: 56
26: 28
27: 14
28: 30
29: 15
31: 54
32: 27
34: 25
35: 42
36: 21
37: 45
40: 81
41: 35
44: 63
48: 49
THE END
PS forms.gle/UqZQRwYe26SLJjMn8

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26 ноя 2023

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Комментарии : 772

@unvergebeneid 6 месяцев назад

For someone who doesn't like being associated with something almost working, Matt Parker produces a lot of almost-working things and shows them to the world.

@bowfuz 6 месяцев назад

Sharing stuff that worked only once during development is my Forte lmao

@loreleihillard5078 6 месяцев назад

His motto is "give it a go"

@mikaderhacker2869 6 месяцев назад

Parkerputer

@idontwantahandlethough 6 месяцев назад

@@bowfuz wait, do you type Will Forte's name enough that your phone automatically capitalizes it...?

@bowfuz 6 месяцев назад

@@idontwantahandlethough no my phone just, legit has the dumbest autocorrect, it regularly turns "is" to "I'd" and also capitalizes even conjunctions among other things

@johnchessant3012 6 месяцев назад

Noah sent his animals to "go forth and multiply", but a pair of snakes told him "we can't multiply, we're adders" - so he builds them a log table.

@TheComputerCrasher42 6 месяцев назад

I wish I could do more than like this comment lol, this is great

@petevenuti7355 6 месяцев назад

In binary, snakes and eggs. Not base 1010

@anon_y_mousse 6 месяцев назад

It's really great that log has that double meaning too.

@rithvikmuthyalapati9754 5 месяцев назад

Aah the double meaning!

@linkinparker896 4 месяца назад

sorry can anyone explain

@FrankGevaerts 6 месяцев назад

I didn't expect my belief in the commutativity of multiplication to be threatened by the thought of having to balance a box on a flamingo

@becauseimafan 6 месяцев назад

😂

@ironnwizzard 6 месяцев назад

I'll take "Sentences First Said Today" for $500, Trebeck.

@EcceJack 6 месяцев назад

Thanks, that gave me a very good laugh 😂😂

@EliasMheart 6 месяцев назад

Wow. Amazing, thank you xD

@ain92ru 6 месяцев назад

@@ironnwizzard r/BrandNewSentence is free ;-)

@mattb5816 6 месяцев назад

We're all worried about intelligent machines taking over, but here's Matt teaching trees how to do multiplication when they already outnumber us by trillions.

@weare2iq376 6 месяцев назад

Hi, I'm from the year 2024, and unfortunately machines already outnumber all humans, and trees, except TREE(3)+... I'm sure this joke will have aged well by the end of next month. I thank you.

@vigilantcosmicpenguin8721 6 месяцев назад

The Ents wouldn't have died off so soon if only they had arithmetic.

@nightchicken3517 6 месяцев назад

Don't worry. I double-checked the first calculation, and 9 * 5 is 45. (Fixed typo) and that one guy really did a proof on this \/

@hancocki 6 месяцев назад

You're a hero for doing that. 😊

@CiaraOSullivan1990 6 месяцев назад

I don't believe either you or Matt and I request that you provide a detailed proof of your hypothesis.

@estherstreet4582 6 месяцев назад

Did you check it with a tree though

@ChucklesTheBeard 6 месяцев назад

@@CiaraOSullivan1990 I have discovered a truly remarkable proof which this youtube comment is too small to contain.

@boo0o0o00o 6 месяцев назад

the first calculation was 9*5 though, can you check that too please?

@wtspman 6 месяцев назад

I’m surprised you missed the obvious branding for the tree: it’s a Yule Log™️

@antivanti 6 месяцев назад

I came here to exclaim this! 😅

@pihungliu35 6 месяцев назад

Well, he did say it is a "log table" at 21:27

@HellbladesFFXI 6 месяцев назад

I was so about to say, "Not just a log table, a Yule log table!" XD So glad I'm not the only one lol

@RichardBronosky 6 месяцев назад

Merry Multiplication-Mas (✖️-Mas) 😜

@iabervon 5 месяцев назад

He has another computer in the fireplace, but we couldn't tell because it's a discreet log.

@kodirovsshik 6 месяцев назад

Alan Turing has been really quiet since the parker machine dropped

@maf654321 6 месяцев назад

Now we gotta have a Python-running Christmas tree that can generate multiplication algorithms automatically with any given set of presents

@maf654321 6 месяцев назад

Which makes me wonder, what are the constraints on size of the presents given the size of the tree? I imagine you’d want a variety of sized presents to distribute the baubles evenly…

@aceman0000099 6 месяцев назад

@@maf654321the presents have to be a very specific size based on the size of your "unit" height. (In this case I think 8 is the shortest present so that one represents one unit). The unit height is constrained by the tree height (and bauble droopiness), such that the tree is a minimum of 58 units tall PLUS the droop of the top bauble (so the top bauble sits at 58 units but is attached a bit higher). So if your tree is 5 ft exactly (60"), and the droop is 2 inches, then your max unit height is 58 inches ÷ 58units = 1 inch. So your presents will be multiples of an inch up to 29 inches

@DFPercush 6 месяцев назад

@@maf654321 The height just has to match the numbers in the input table (whatever 2-9 corresponds to) times some arbitrary unit of length. If you can come up with another table that works, you can use those measurements.

@ivanborsuk1110 6 месяцев назад

what is the meaning of this? mommy?

@jamessylviasyracuse-little865 6 месяцев назад

Could that tree multiply 3 variables by using rotation in the plane as wall as height???

@o0superflu0o 6 месяцев назад

For some reason, the reveal of the display of the cogputer had me nearly falling off my chair with laughter. It's so ridiculously tiny, absolutely perfect!

@crumble2000 6 месяцев назад

One might say it's comically small

@thedoublek4816 Месяц назад

Comically large dials vs comically small display

@dumntuftv8853 6 месяцев назад

“This could be improved dramatically.” A quote for the ages. 18:34

@jasoncookuk 6 месяцев назад

it's a shame we won't have the sequel, "Somebody improved my cogputer by 40,832,277,770%"

@aceman0000099 6 месяцев назад

He's begging for fans to send him better ones there

@nanamacapagal8342 6 месяцев назад

HERE WE GO

@mattgies 6 месяцев назад

Likewise 21:49, "Do not eat my face!"

@nowymail 6 месяцев назад

The first mechanical calculator was built in 1642 by Wilhelm Schickard.

@mscha 6 месяцев назад

What I'm worried about, is Matt's increasingly parallelogram-shaped bookcase.

@CaraesNaur 6 месяцев назад

He must be disappointed that it isn't becoming a rhombus.

@Zraknul 5 месяцев назад

If it's Ikea, it's a design choice to change shape slowly.

@GTwinn 6 месяцев назад

Matt: needs a computer to work out 9*5 Also Matt: 2024 is the 400th anniversary of 1614 Yes, this tracks

@theadamabrams 6 месяцев назад

Wonderfully on-brand, yes :) According to his comment in other thread, Matt was thinking of the fact that _Arithmetica Logarithmica,_ the first great table for log₁₀, was published in 1624.

@bunnyrape 6 месяцев назад

Parkerversary

@servvo 4 месяца назад

it's the fact that he didn't realise this in the writing, recording, or editing stages 😂

@DasGanon 6 месяцев назад

Adding new meaning to "What tree has the best logs?"

@neilbarnes3557 6 месяцев назад

The one with square roots, obviously.

@lightninbolt986 6 месяцев назад

Mom can we have a computer? No, we have a computer at home Computer at home:

@yonaoisme 6 месяцев назад

most original joke you've ever written. and holy moly, how specific this joke is, like there is no way to write this exact same joke about literally anything

@papeleradereciclaje4375 6 месяцев назад

Frankly, I would have loved to get something like this as a child

@zaffyr 6 месяцев назад

making a log table using a tree is pure genius

@CaraesNaur 6 месяцев назад

Ahem, log tree.

@andrewsutherland7913 6 месяцев назад

@@CaraesNaur It is puns like that which make me wish I could subscribe to Patreon to NOT support Matt

@annie4424 6 месяцев назад

As an elementary STEM teacher, I think I need to make one of these for my students to use. The fact that the answer window is so tiny is actually awesome for multiple students to use it for the same problem.

@paddythomas7416 6 месяцев назад

I hate to be that guy but…. Babbage built part of his difference engine and it was used to calculate log tables and tide times, but never completed it, but it would be described as a mechanical calculator. His analytical engine was something he designed but never built and it was the first design of a programmable computer, inspired by Jaquard and his looms. The analytical engine would be more akin to what we call a computer today, whereas his difference engine (and your nifty machine) would be a calculator not a computer, and I personally prefer the term “cogulator” as opposed to “cogputer”

@EebstertheGreat 6 месяцев назад

He completed two difference engines. Only one of them (the one the government actually wanted) was incomplete. Also, a "computer" is not necessarily a general-purpose computer. In fact, no such mechanical computer has _ever_ been built. Rather, the term "mechanical computer" refers to calculating devices like this (mostly adding machines).

@DavidBeaumont 6 месяцев назад

You could embed a small magnet in each input cog and on the background to hold it in its neutral position while other cogs are turned.

@becauseimafan 6 месяцев назад

Oooh, use magnets, I like this idea a lot!! 😁

@dojelnotmyrealname4018 6 месяцев назад

Alternatively, use a weak coil spring. Same idea just a lot cheaper and works on non-ferro materials (like plastic).

@Pystro 5 месяцев назад

All it would really take is for the dials to be asymmetric, so that gravity keeps them in the disengaged position.

@AlRoderick 6 месяцев назад

The way that 20th century mechanical computers did multiplication was really simple and clever. They used the formula for a line Y=MX. Inside the machine is a flat grid, you have a sliding input along the bottom for x that has a perpendicular track going straight up riding along and a rotating track that's centered around the origin, it has its slope set by a vertical sliding input at x = 1. Those two tracks constrain a pin that would always be at the intersection point of the two input tracks, and there'd be a third horizontal track that would be pushed up or down to read out the y value, and that's your answer. You had to know in advance what range of values you had to work with, but you could multiply any of the inputs or outputs by a constant using a gear ratio to force it into the right range.

@rerere284 6 месяцев назад

ooh that sounds like the mechanical equivalent of a nomogram! neat

@zacharyoleksy1804 6 месяцев назад

Finally, we have it. PC2

@lvn5609 6 месяцев назад

And PC stands for Parker Computer

@Apoque 6 месяцев назад

The derivation of the math function he used seems very similar to a notion I've heard about in computer science called "Perfect Hashing" because really, what I'm seeing is that what he wants is very similar. Both are given a set (all pairs of base-10 digits) to find a function that spreads them into distinct buckets with no collisions.

@PJRye 6 месяцев назад

The alternate table is what I was taught as the "times table" in primary school. What is relevant is that the first computer I ever used, the IBM1620 (early 1960's computer, used in 1968) employed decimal, not binary arithmetic, and did its multiplication using a times table - in 100 2-digit decimal memory locations 200 to 399, I recall.

@rewindoflow 6 месяцев назад

Mechanical computing is such a fascinating area! I have a small collection of mechanical calculators, including a fully automatic four function one that I'm restoring. The amount of engineering effort and ingenuity that wen't into those things is amazing, but so it the sheer variety of methods of operation. For example, some machines do subtraction via a reverse of the addition mechanism, but some do it via 9's-complement which means they can add and subtract with the same mechanism! There's also a relevant example to this video which is the MADAS Millionaire, which uses a special kind of lookup table to do "single-operation" multiplication. That's not the mention the hook-and-crook slide adders, the ingenious ways of doing various operations on the comptometer (once the biggest educator in the UK), and even "Consul, the Educated Monkey"! And all that is just 'digital' calculators, not to mention all the analogue calculating mechanisms around (which made their way into all sorts of places, like WW2 bombing computers, and automatic gearboxes).

@82melmar 6 месяцев назад

You need to make a Hitchhiker's Guide edition of the xmas card where if you multiply 6 by 9 it reads 42.

@otteydw 6 месяцев назад

That Christmas tree card seems like something that could be used in an Exit "escape room in a box" puzzle!

@rosuav 6 месяцев назад

8:17 It makes good sense for the multiplicative identity 1 to translate into the additive identity 0. Saves them duplicating entries.

@AlexSh789 6 месяцев назад

6:13 - If logs came around in 1614, then wouldn't 2024 be the 410th anniversary, not the 400th?

@standupmaths 6 месяцев назад

Good point! My brain confused it with the 1624 publishing of Arithmetica Logarithmica, the first great log table book. I’ll add it to the corrections.

@ilogik999 6 месяцев назад

@@standupmathsi just assumed you thought it was 2014. 2024 doesn't sound real :)

@zygoloid 6 месяцев назад

It's a Parker Quatercentenary.

@jpaugh64 6 месяцев назад

Wait, what about calendar corrections which happened in Europe right around that time.

@AlexSh789 6 месяцев назад

@@jpaugh64 - The adoption of the Gregorian calendar yielded an adjustment of about 10~11 days in the 17th Century, not 10 years.

@medic2310 6 месяцев назад

This video deserves reCOGnition...

@_Ari_B 6 месяцев назад

reCOGNITION!

@kentslocum 5 месяцев назад

The reveal of the cog-puter's microscopic display had me in stitches. 😂

@asicdathens 6 месяцев назад

I did multiplication with logic gates (2 8bit numbers) when I learned how full / half binary adders worked. I designed my own calculator (terribly inneficient) to do the 4 basic calculation

@_Mute_ 6 месяцев назад

My first thought is the lookup table could be folded up into a n-dimensional array where n is the number of primes you include. A dimension for 2, 3, 5, 7, 11, etc.

@filipsperl 6 месяцев назад

That's pretty much it, but it's then compressed to 1D as compact as possible

@amarissimus29 6 месяцев назад

Oh man... this is why I love this channel. You've got a megaminx, a mirror cube and a fluctuation cube on your shelf. Just as I do, right behind me, among a billion others. Makes me feel a little less stupid as I try to keep up with your explanations. Thanks for all your work. Cripes my megaminx is dusty... can't have that.

@AnselmWiercioch 6 месяцев назад

Is it just me or is Percy's method more work than just having a multiplication table with the answers on it and directly looking them up?

@DavidBeaumont 6 месяцев назад

It is for a human, but not for a machine made of cogs and rods etc.

@savoytruffles 6 месяцев назад

but that's no fun!

@3snoW_ 6 месяцев назад

I assume Percy would want to have several 1 digit multipliers and combine them to have a multiple digit multiplier. Which would also be why the entries for 0 would be important to include.

@aikumaDK 6 месяцев назад

Maybe he wanted a working proof of concept before scaling it to the point where multiplication tables were unwieldy.

@cephelos1098 6 месяцев назад

This is your brain when you learn math without learning anything about computation

@dino2808 6 месяцев назад

yes! ive been looking for this everywhere for a year since i heard that "Z_(p-1) with addition is isomorphic to Z_p - {0} with multiplication" in my group theory class for some values of p. that made me think that there had to be a method to multiply integers through addition that could be efficient for computers? and i found (almost) exactly this and built some "paperputers" like yours. thank you for the video!

@Kazutoification 6 месяцев назад

Move aside Parker Square, here comes the Parker Cog!

@champnessjack1154 6 месяцев назад

This method should be taught in schools everywhere, with the two tables provided on pieces of cloth that must be flattened out, repeatedly, to read, but with the option given that it's acceptable to memorize the results, should you find that, umm, a little bit faster.

@RedHair651 6 месяцев назад

"Now THAT's a log table" needs to be a t-shirt

@HerbertLandei 6 месяцев назад

Why not using integer logarithms? As the biggest result is 9*9 = 81, we can work modulo the next prime, which is 83. 83 has 2 as a primitive root, so you just need to tabulate all values of 2^x mod 83. So, for 5*9 you find that 2^27 = 5, and 2^62 = 9, you add 27+62 = 7 (mod 83) and 2^7 = 45 -> your solution.

@jan_kulawa 6 месяцев назад

the idea is that Percy's method (and its adaptation by Matt) is supposed to compute products with a very rudimentary mechanical computer, so it has to exploit number theorerical properties of integers which can easily be encoded and manipulated by such a machine. modular exponentiation surely doesn't fit the bill, though indeed it is more simple and elegant in a purely mathematically setting

@justforplaylists 6 месяцев назад

Would it work to use 79 instead of 83, and replace 9x with 78x mod 79? I think you could get the largest gear a bit smaller that way.

@sbares 6 месяцев назад

@@jan_kulawa The computer would still only be doing addition and table lookups, just like with Percy's method. You only need exponentiation to create the table.

@coastalsandwich 5 месяцев назад

Merry Christmas Matt, thanks hugely for your part in getting me back into Maths this year after shunning it in my youth! Ive had such fun messing about with my own silly equations and tricks, long may your channel continue!

@buzz.b 23 дня назад

Matt's voice going ever more high pitched with excitement as the presents align with the correct results is fantastic.

@jonidcrushfire 6 месяцев назад

My goodness, the lengths you go to do math in the most entertaining and abnormal method possible is an inspiration to us all. Love the tree! Love the cogputer!

@mduvigneaud 6 месяцев назад

Fascinating! Matt, that is awesome! A while back I started writing a Reed-Solomon coding RAID driver... sadly I never finished it though: I got distracted with real work. In it addition and subtraction are just XOR but multiplication and division are 2 log table lookups, addition or subtraction of those respectively, then an inverse log table lookup.

@itssandman2u 6 месяцев назад

No way! I love Mark's blog! I've been following him for a year or so now. Wild to see him featured in a video.

@JohnDlugosz 6 месяцев назад

18:00 The way the cog has 15 teeth that engage reminds me of production mechanical calculators where entering a digit with a button would have a similar effect -- either as you enter it (like yours), as with the famous Curta, or setting up the mechanism so that when the crack it turned it issues a linear gear with the right number of teeth. The printer or readout often uses a similar mechanism, too.

@Houshalter 6 месяцев назад

Before logarithms people did a similar trick to simplify multiplication to addition by using a lookup table for squaring numbers. Used since the Babylonians. a*b = ((a +b)^2 - a^2 - b^2)/2

@zygoloid 6 месяцев назад

When multiplying similar numbers (especially when they differ by an even number) I like to use ab = ((a+b)/2)² - ((a-b)/2)². Eg, 77 x 81 = 79² - 2² = (80² - 80 - 79) - 4 = 6237.

@flatfingertuning727 6 месяцев назад

@@zygoloid Yeah, I found the cosine-squared approach a bit odd, when a table of (a/2)² works more simply..

@name_o_person 6 месяцев назад

I love this channel! Not only is the content informative, it's delivered with comedy, and the comments are always gold. P.S. i first came here to mention laughing hard enough over the Self on the shelf, that my coworkers checked in on me.

@Mikumikku 6 месяцев назад

not sure if anyone had the same thought, but at 12:00, the second grid perfectly overlaps the left grid if you rotate it 180 degrees. instead of only fitting the first row of the second grid into empty spaces, you could do it with all the rows

@briannussbaum9513 5 месяцев назад

Yes! That was my thought too!

@supertron6039 6 месяцев назад

Stuff like this makes me even more interested in computation algorithms.

@yobgodababua1862 6 месяцев назад

One "easy" improvement to help with the alignment problem would be to have a second large cog uncoupled from the output cog with every subsidiary cog fully toothed to that gear so that they are always in sync.

@PhilR0gers 6 месяцев назад

I did multiplication at school using log tables, so it's all relatively familiar stuff. Matt's Christmas Tree is a variant of the slide rule, but with fixed cursors (baubles)

@Reddles37 6 месяцев назад

For the tree you should have just made 1 a card with ~0 thickness, so you can multiply by 1 by adding the card to the stack without changing the height.

@schwingedeshaehers 6 месяцев назад

That doesn't work, as the hight isn't the number itself. (in his version)

@macronencer 6 месяцев назад

When you mentioned the Christmas card on the podcast, I assumed it was the standard type of logarithm. Pleasantly surprised and entertained to discover there was a little more to it!

@W.M.- 4 месяца назад

This is brilliant, I love how much effort goes into his gags

@andrewmullen4003 6 месяцев назад

this went straight over my head, think I'll have to watch it again.

@SoulOfNemiss 6 месяцев назад

17:47 I think you said toward the end that the 9 cog has 15 dents but it's 12 as stated in the description :D Great stuff nonetheless had a lot of fun trying to recreate your table to put back the triangle of number together (01 02 04 up to 81) ( 05 10 20 up to 45) (07 14 up to 63) (even the 00 works) and seee those flying 25 35 and 49 (and three 00) and I wonder if you could try to minimise the space of those geometric shapes (while fitting the flying unit around) to find other minimal triangles

@timblack7828 6 месяцев назад

Matt, you were so close to getting each number to appear at its own index (like you discuss at 15:10)! You could replace each value x in your first lookup table with 42 - x. That way 1 would map to 0. You would also replace each index z in the second lookup table with 84 - z. This works because x + y = z if and only if (42 - x) + (42 - y) = 84 - z. As a bonus, your second lookup table would only have to go up to 82 instead of 84. And, your outer wheels would only need a total of 166 instead of your current 254 (though Percy still wins in this regard; their design would only need 141 total teeth on the outer wheels). With this change: 0-9 COGPUTER 0 cog: 41 teeth 1 cog: 0 teeth 2 cog: 1 teeth 3 cog: 15 teeth 4 cog: 2 teeth 5 cog: 34 teeth 6 cog: 16 teeth 7 cog: 24 teeth 8 cog: 3 teeth 9 cog: 30 teeth LABELS ON MIDDLE COG: CE=01, 02, 04, 08, 16, 32, 64, --, --, --, --, --, --, --, --, 03, 06, 12, 24, 48, --, --, --, --, 07, 14, 28, 56, --, --, 09, 18, 36, 72, 05, 10, 20, 40, --, 21, 42, 00, 00, 00, 00, 27, 54, --, 49, 15, 30, --, --, --, 63, --, 00, 00, 35, --, 81, --, --, --, 45, 00, --, --, 25, --, --, 00, --, --, --, 00, --, --, --, --, --, --, 00 (This scheme has CE and 1 in the same place, which you may have understandably chosen to avoid, but it also seems appropriate to have the multiplicative identity also be the "clear" value)

@zecuse 6 месяцев назад

An extremely elaborate way to show that addition is commutative and infer that multiplication is too.

@Cats-TM 6 месяцев назад

The difference engine! I have actually seen the actual build of it in real life at the Science Museum in London. It is decently large but it probably works quite well.

@AndyLundell 6 месяцев назад

Although when we say Babbage designed a "Turing complete" computer, we mean his "Analytical engine", which was never built.

@GilesBathgate 6 месяцев назад

I was studying the attention mechanisim in machine learning and was struggling to find the equivalence between Additive Attention, and Dot Product attention. Your simple formula which reminds us that: A*B = f(g(A) + g(B)) finally led to the aha! moment, Thanks.

@KelniusTV 6 месяцев назад

I found a sudoku puzzle book in an op shop for cheap and I bought it, but something about it intrigued me, and surely it has some interesting mathematics. See, the book is organized into "easy", "medium" and "difficult" puzzles and they do tend to be harder as you go along. Newspapers also often have both an easy and hard sudoku puzzle, if they provide it. And I was wondering how the hell they do that. I thought it was just "the easy ones have more numbers", and whilst that is often the case with the easiest puzzles, it isn't always with the harder ones (in my book, anyway). Some of the "medium" puzzles have as few as 27 clue numbers, and the "difficult" puzzles have as many as 32. So, how the hell do they make them "harder"? I'm sure the maths of sudoku must be well understood, if we can make them so easily, but I couldn't find it online.

@AdminBenni 6 месяцев назад

I'm tempted to call this the Parker 'Puter but I think I'll have to settle for the Parker Cogputer, since with his now advanced levels "terrible python code", Matt's bound to create his own computer one of these days, operating system and all!

@MegaTeXHaPb 6 месяцев назад

Great video! Thank you! I have an idea how to improve your cogputer, stabilize cogs and prevent them from sudden rotations. You can add some metal pieces close to lover point of cogs, so they will become unbalanced and will try to turn this side down. It will become like a toy named Weeble (don't know correct English name for Russian "Неваляшка", but this seems to be closest). Or you can even use small thin magnets to stick cogs in their positions.

@Poutrel 6 месяцев назад

I applaud the dedication and amount of effort just for the pun at 21:30

@UnrivaledLimit0500 6 месяцев назад

This is great content. Well done.

@drdieding 5 месяцев назад

Well, that was unexpected. Love these videos!

@mr_rede_de_stone916 6 месяцев назад

The christmas tree idea was sooooo good!!

@RandalLSchwartz 4 месяца назад

I know and have worked with Mark! Smart dude! Wrote a brilliant book on functional programming with Perl, that I still reread occasionally for interesting tricks.

@gnramires 6 месяцев назад

You might improve this by adding a "click" in place in the correct alignment of the output (can be achieved with a spring-loaded rounded rod resting on the main cog, for example). Wonderful, merry Christmas :)

@CyanPhoenix_ 6 месяцев назад

to fix the issue of the erroneous cog engaging, you could set it up so that the segment of each cog with teeth is pointed directly away from the center cog when the number on the front is at the 12 o'clock position - that way you can easily just keep all the numbers right way up and just do one full rotation every time you use a number.

@mileskidson1970 6 месяцев назад

All that for the most incredible log pun. God i love this channel

@jan_kulawa 6 месяцев назад

tricking a tree into doing multiplication defines a whole new paradigm of computing. we should have Parker machines instead of Turing machines in our theoretical computer science curriculum

@kentslocum 5 месяцев назад

Who needs calculators, when we have Christmas trees?

@johnr2724 6 месяцев назад

This is yet another an incredible video from Matt, but I can not unsee the shelves being tilted to the right in the background, I think it might be an optical illusion but still

@ErikScott128 6 месяцев назад

I'm a sucker for mechanical computer designs. Some cranks, detents, and spring-ball plungers would make that cogputer actually quite usable. Basically, instead of everything being free-spinning, a detent would hold each input wheel in an unengaged position, and detents (one detent for each tooth/position) would hold the center wheel in position. When turning an input wheel, you could click the center wheel through the requisite number of positions and you wouldn't have to worry about the subtalties of engagement and disengagement. Adding cranks to the input and reset wheels will help you track when you do a full turn and simply make it more usable.

@manudude02 6 месяцев назад

So many lookup tables just to avoid a couple of additions! I prefer the name Cogulator to describe the device.

@valdemar91 6 месяцев назад

Mat: "... this tree can do multiplication. Now THAT is a Log table!" Me screaming out loud (completely alone!): "ITS A YULE LOG!"

@AliceYobby 6 месяцев назад

It would be incredible if you could make a video on the statistical claims of past chess grandmaster Kramnik accusing current chess grandmaster and second best player in the world Hikaru Nakamura of cheating, like you did in the Dream probability stuff. Many people have made blog posts about Kramnik’s poor methods but there’s a lot of confusion everywhere and a nice, simple explanation of the statistics involved would be incredible!!!

@GlennBrockett 6 месяцев назад

A Yule Log table to be more appropriate.

@Ilandris505 6 месяцев назад

To improve the cogputer: You could lift the cogs up to disengage them (with a system that clicks them into off and on positions). So that you can reset and use the cogputer eseaier. Perhaps there could be markings on all the interactor wheels (including the main cog) to show where the neutral positions are. A mechanical magnifier so the output can be bigger (The main cog will be further back from the first improvement giving some space for this) Otherwise, I absolutely love the Cogputer I fully expect these never to be implemented but I had to get my ideas out there

@-_Nuke_- 6 месяцев назад

That display though!

@kekke2000 6 месяцев назад

Are you going to cover the Kramnik vs Hikaru Chess cheating accusations? It has a lot of stats and probabilities with elo involved.

@eekee6034 6 месяцев назад

As the table was filled out, my mind was blown!

@widgity 6 месяцев назад

This would go nicely with a rotary phone style dial!

@dylanbreglio 6 месяцев назад

I love how proud Matt is of his cogputer

@petevenuti7355 6 месяцев назад

The professions of comedian and mathematician are inherently mutually exclusive, with one notable exception, Matt Parker.

@mattymerr701 5 месяцев назад

You could add detents to the cogs to make them need purpose to start turning and to have them lock in to position where they wont interfere.

@philipmurphy2 6 месяцев назад

Stand Up Maths is such a useful channel

@JDB2552 6 месяцев назад

Matt, if you title your next book Terrible Python Code, you’ve probably already written it.

@robo3007 5 месяцев назад

By far my favourite multiplication shortcut is the "finger method". 1. Give each finger on both hands a number from 6 to 10, starting from the thumb and counting outwards. 2. With your hands face down, place the finger with the number being multiplied on your left hand on top of the finger with the number you wish to multiply it with on your right hand. This separates your fingers into those "in the loop" ( the two overlapping fingers and everything in between ) and those "out of the loop" ( the rest ). 3. Multiply the number of "in the loop" fingers by 10 to get the tens digit. 4. Multiply the number of "out of the loop" fingers on your left hand with the number of "out of the loop" fingers on your right hand. Add this to the result from step 3 to get the units digit. 5. That's your answer. The only drawback to this method is that it requires you to memorise your first five times tables, but everyone should already have those memorised from school! Also please let me know if anyone knows exactly why this works.

@mattgies 6 месяцев назад

I await your collaboration with Chris at Clickspring for a brass, high-precision, perhaps guilloche version of the cogputer!

@DFPercush 6 месяцев назад

This would make a great child's toy. A great mod for it would be a spring loaded roller and an eccentric cam on the underside of the number gears, to keep them from drifting too far. Also if you show the answer on the side instead of the top I think you could make the window bigger. Cool idea though. The Christmas tree is hilarious. :P

@agargamer6759 6 месяцев назад

The Christmas tree is worth it for the log table joke

@notmyname327 6 месяцев назад

That computing tree is amazing! Loved this video

@LyuboRyuk 6 месяцев назад

The amazing amount of work 😮

@oyahfftlisawsome 6 месяцев назад

"This could be improved dramatically" the title of everything Matt attempts (but he attempts while most would not)

@hadz8671 6 месяцев назад

I have an old book of maths tables. At the back is a table of "quarter-squares" which allows multiplication through the identity ab = [(a+b)^2]/4 - [(a-b)^2]/4

@GoranNewsum 6 месяцев назад

I spent the entire video terrified those shelves were going to fall down!

@JonFawkes 5 месяцев назад

I feel like the cog-puter would be great in a steampunk/gearpunk setting Aslo, that christmas card is so wonderfully nerdy

@uIteriormotives 6 месяцев назад

YAAAAY NEW MATT VIDEO!! i need this after the shitty day i had

@PopeLando 6 месяцев назад

I'm just watching this and with the first problem I was literally saying "36" and looking to see if the 3 wheel or the 6 wheel were turning. Then he shows "45" and I 🤦‍♂️