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 ай бұрын

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

@loreleihillard5078

6 ай бұрын

His motto is "give it a go"

@mikaderhacker2869

6 ай бұрын

Parkerputer

@idontwantahandlethough

6 ай бұрын

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

@bowfuz

6 ай бұрын

@@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

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 ай бұрын

😂

@ironnwizzard

6 ай бұрын

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

@EcceJack

6 ай бұрын

Thanks, that gave me a very good laugh 😂😂

@EliasMheart

6 ай бұрын

Wow. Amazing, thank you xD

@ain92ru

6 ай бұрын

@@ironnwizzard r/BrandNewSentence is free ;-)

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 ай бұрын

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

@petevenuti7355

6 ай бұрын

In binary, snakes and eggs. Not base 1010

@anon_y_mousse

6 ай бұрын

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

@rithvikmuthyalapati9754

6 ай бұрын

Aah the double meaning!

@linkinparker896

4 ай бұрын

sorry can anyone explain

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 ай бұрын

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 ай бұрын

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

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 ай бұрын

You're a hero for doing that. 😊

@CiaraOSullivan1990

6 ай бұрын

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

@estherstreet4582

6 ай бұрын

Did you check it with a tree though

@ChucklesTheBeard

6 ай бұрын

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

@boo0o0o00o

6 ай бұрын

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

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

@antivanti

6 ай бұрын

I came here to exclaim this! 😅

@pihungliu35

6 ай бұрын

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

@HellbladesFFXI

6 ай бұрын

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 ай бұрын

Merry Multiplication-Mas (✖️-Mas) 😜

@iabervon

6 ай бұрын

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

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

@maf654321

6 ай бұрын

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 ай бұрын

​​​​​@@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 ай бұрын

@@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 ай бұрын

what is the meaning of this? mommy?

@jamessylviasyracuse-little865

6 ай бұрын

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

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

@jasoncookuk

6 ай бұрын

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

@aceman0000099

6 ай бұрын

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

@nanamacapagal8342

6 ай бұрын

HERE WE GO

@mattgies

6 ай бұрын

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

@nowymail

6 ай бұрын

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

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

@theadamabrams

6 ай бұрын

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 ай бұрын

Parkerversary

@servvo

5 ай бұрын

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

Alan Turing has been really quiet since the parker machine dropped

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 ай бұрын

One might say it's comically small

@thedoublek4816

Ай бұрын

Comically large dials vs comically small display

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

@CaraesNaur

6 ай бұрын

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

@Zraknul

5 ай бұрын

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

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

@neilbarnes3557

6 ай бұрын

The one with square roots, obviously.

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

@yonaoisme

6 ай бұрын

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 ай бұрын

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

making a log table using a tree is pure genius

@CaraesNaur

6 ай бұрын

Ahem, log tree.

@andrewsutherland7913

6 ай бұрын

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

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.

Finally, we have it. PC2

@lvn5609

6 ай бұрын

And PC stands for Parker Computer

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 ай бұрын

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

@dojelnotmyrealname4018

6 ай бұрын

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

@Pystro

5 ай бұрын

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

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 ай бұрын

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

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

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 ай бұрын

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).

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).

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.

This video deserves reCOGnition...

@_Ari_B

6 ай бұрын

reCOGNITION!

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.

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

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

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

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.

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

@standupmaths

6 ай бұрын

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 ай бұрын

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

@zygoloid

6 ай бұрын

It's a Parker Quatercentenary.

@jpaugh64

6 ай бұрын

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

@AlexSh789

6 ай бұрын

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

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 ай бұрын

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

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!

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

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 ай бұрын

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

@savoytruffles

6 ай бұрын

but that's no fun!

@3snoW_

6 ай бұрын

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 ай бұрын

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

@cephelos1098

6 ай бұрын

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

Move aside Parker Square, here comes the Parker Cog!

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!

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.

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.

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!

Well, that was unexpected. Love these videos!

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

This is great content. Well done.

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.

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.

The christmas tree idea was sooooo good!!

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

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

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 ай бұрын

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 ай бұрын

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 ай бұрын

@@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.

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

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

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!

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

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

Stand Up Maths is such a useful channel

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

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 ай бұрын

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

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

I love how proud Matt is of his cogputer

The amazing amount of work 😮

That computing tree is amazing! Loved this video

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

6 ай бұрын

Yes! That was my thought too!

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.

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.

The Christmas tree is worth it for the log table joke

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 :)

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

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)

I like your more math-ey videos like this

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

you sir, are mathematics. an universal treasure. never change. also, looking forwards to pi day!

That display though!

What a lovely Calculate-mas Look Up Tree-ble

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.

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.

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.

Every day, Matt is closer to becoming an Adeptus Mechanicus tech-priest... look, he's using cogitators now!

The Christmas tree made me crack up like a Christmas cracker

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)

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

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 ай бұрын

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 ай бұрын

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

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!

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 ай бұрын

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

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

This had me chuckling

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

The multiplicating christmas tree is amazing

I need to buy two of those cards

This would go nicely with a rotary phone style dial!

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.

that tree really sold it, amazing

You make maths so fun mate!

@TradieTrev

6 ай бұрын

How's this mad dog, I was like I want an xmas card like that for the family; He's released all the source code so let's get the dog hahahaha!

Tbis looks more like something that Matt uses to remind everyone how many days are left to get him something for Christmas 🎄

Mechanical computer complete with 2 and 4 bit bugs. Love it!

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

WELL DONE PERCY!!!

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.

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

Long division? OH BOY, my FAVORITE!

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.

Brings a new meaning to 'Christmas log'.