Why You Can't Bring Checkerboards to Math Exams

[@WrathofMath]

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[@qsquared8833]

That looks to be a portion of A Go Board, not a checker board

[@phylactic]

So when my calculator runs out of battery during an exam I can't rely on my backup chessboard?

[@bubblyphysics]

Unfortunately, no.

[@LunarMoonPhase]

But maybe you can use your back up Rubix Cube I heard that can also be a calculator also haha.

[@WrathofMath]

It would be a lark!

[@ZDTF]

​@@WrathofMathWhat does lark mean

[@thesmasher.]

@@ZDTF 0:58

[@davidmurphy563]

You describe lark as an obsolete word but where I live it's in everyday use. "We did it for a lark", "the kids were just larking about". Hopefully it'll catch on on your side of the pond! Solid word!

[@WrathofMath]

Absolutely! I'd like to bring back hootenanny, hullabaloo, swanky, lark, and cattywampus

[@summerishere5146]

What’s real fun is that you can just draw this “board” on any piece of paper and immediately produce a calculator. Add more rows and columns for bigger numbers

[@WrathofMath]

Any calculating power you desire can be yours

[@bjorntorlarsson]

The division procedure made it obvious why this invention of the a bit too brilliant Napier did not catch on very much.

[@WrathofMath]

yes 😂

[@whtiequillBj]

if you break math down like in lambda calculus you find that all operations can be unary, not just square roots and some other operations.

[@wernerviehhauser94]

I'd allow checkerboards in my math exams. Good luck trying to do formal algebra on it :-)

[@Salsmachev]

That... actually sounds kind of interesting to try.

[@R.F.9847]

Charles Babbage and Ada Lovelace have entered the chat...

[@richardcheney6964]

you could make a ternary calculator this way with a Go board. Empty for 0, white and black for 1 and 2

[@WrathofMath]

We're gonna push this calculator to the limit

[@Salsmachev]

Teacher: "You can bring a 3x5 reference card for the exam" Me: **frantically tracing graph paper grids onto a 3x5 card and snapping off bits of pencil lead to use as counters**

[@WrathofMath]

😂😂

[@torydavis10]

When you got to root 2 I was really hoping you'd pull out a second chessboard and move into the 4th quadrant.

[@WrathofMath]

my camera is usually very zoomed in, so that would have been a good time for a dramatic cut to zoom out

[@Axacqk]

Prophecy: a board like this, except with one of the axes labelled with powers of 3, will one day be used to settle the Collatz conjecture.

[@Rack979]

5:09 But you do have a bigger chessboard! Ol' Johnny Napes labeled all 15 diagonals, so he had labels on the left and top as well, so 256 all the way up to 2^(15-1).

[@vampire_catgirl]

Finally, a use for all 6 of my chess boards

[@WrathofMath]

This is their true purpose!

[@ZDTF]

Oh my god girls are real

[@ZDTF]

Hello holy beauty

[@ZDTF]

Are you a vampire? Cuz I want u to suck me dry😉 WAIT Are you a cat? Cuz I want to bite you Woof Dog rizz No But Like I've always had desires to bite humans eh Oh wait A paradox I hate her now because I'm a dog I hate cats Oh but she's a vampire Idea Oh No 😖 She's hypnotizing me with her vampire powers I don't hate her at all oh no I want to hate her so badly Are you a girl? Because I want to marry you Bro:Bro I swear I have rizz Also Bro:Whatever that trash line was

[@virdrae]

Step 1: have some sort of flat candies Step 2: have a piexe of squared paper Step 3: calculate all square roots >:j

[@WrathofMath]

Computers are sweating; we're coming for them!

[@user-dq9nx7ut3c]

I'm just gonna draw a calculator in class

[@WrathofMath]

Just seeing it may be enough to inspire your mind's calculations. I know how inspired I feel when I see a TI-108

[@JonathanMandrake]

Honestly i think that introducing this to schools might be quite good, this is both useful as a tool to make some calculations easier as well as being a good showcase for some mathematical principles, which should also make it easier to do these steps in your head. Additionally, unlike with real calculators, there is a high likelihood that over time, the students will do more and more steps, only including the more difficult parts, since that takes less effort. The only real problem is that it can't be used for the more difficult calculations involving fractions and irrationals.

[@NoisqueVoaProduction]

Very nice video! Nice to see another Napier device for facilitating calculations (I was only familiar with the Napier's bones and this other little thing called logarithms) Great that you looked on the original source, and there is a lot on number theory embbeded there. Great job!!

[@luisfonseca2299]

I think this is my favourite video from you so far

[@WrathofMath]

Thanks so much! I love talking about these weird calculating methods!

[@avriten]

to be fair, I think you could convince a fairly large amount of professors to substitute your calculator for this for fun (except when there's not enough space)

[@WrathofMath]

Yeah I don't know how a professor would feel, but I think a high school teacher would say no way - you're not gonna use some dumb useless old calculating method and tank your grade, get a TI-84 out the bin.

[@avriten]

@@WrathofMath Very true

[@FaerieDragonZook]

Next, why not take the step up and discuss the Slide Rule?

[@WrathofMath]

I need to get one. I have an addometer, an old mechanical calculator, but no slide rule! I have a lot of old vintage electronic calculators as well

[@roboxenogaming2047]

They start trembling when i do 100 moves in one hour

[@WrathofMath]

😂

[@rodrigoqteixeira]

You can make this use signed bytes instead of unsigned bytes (2's complement) by replacing 128 by -128.

[@danielyuan9862]

The division method makes me feel iffy. I was expecting you to complete the rectangle by columns, but sometimes you randomly decide to move a penny up to the top row before moving the next penny to finish the column. Which is weird because once you set a penny to a square, one in its column _must_ have a penny unless you backtrack. But you prioritize filling in the rows first.

[@thomasschodt7691]

"a lark" is very much still in common use in british english.

[@logannuculaj487]

I get why the multiplication works but not the division part. This was way more OP than I thought.

[@WrathofMath]

square root of 22? no problem, let me just bust out my 12 by 12 checkerboard

[@thatonefrenchguy937]

4:58 "and if we had a bigger chess board" It doesnt work like that... A bigger chess board would still be 8x8

[@ClarkCox]

Nope: en.wikipedia.org/wiki/Chess_on_a_really_big_board

[@darinpringle5611]

Chess on a "bigger board" not on a bigger CHESS board.

[@thatonefrenchguy937]

​@@ClarkCox Well... yea he didn't specify if it was a "standard" chess board or not but who uses 16x16 chess boards anyways?

[@thatonefrenchguy937]

​@@darinpringle5611listen again to what he said. I understand I can be the "🤓" type of guy but he clearly said "bigger chess board". I still understood that he wanted to have more squares don't worry.

[@WrathofMath]

I get to say something technically wrong because everyone will know what I mean and it is a short way to say it, and you get to tell a funny joke, it's a win win

[@Moongrum158]

Gotta say, I don't hear "oldfangled" nearly enough

[@WrathofMath]

One day we'll all be oldfangled, might as well embrace it!

[@welafobie]

i've never really thought of bringing a checkerboard to a math exam but thanks for the extra info

[@WrathofMath]

np

[@mumujibirb]

you can also use a set of checkers

[@SwankiestPants]

I feel like remembering the rules of operating this calculator is harder than remembering the formulas needed to solve the problems by hand (the exception maybe being square roots as those are a pain"

[@nayutaito9421]

It is AS HARD AS the formulas you want to remember, because the only difference is the base

[@FrankAnzalone]

You could have two different color markers 7 * 7 is a lot of markers but you could do the math for 9 with a different color for the one telling you to subtract 1 from the 8

[@WrathofMath]

A great idea!

[@koppadasao]

You know what... I've been using that method on math exams multiple times. Never used a chessboard, though, just a strip of paper where I write the binary sequence of whatever number I'm calculating

[@QSBraWQ]

Is it faster than normal?

[@WrathofMath]

Come to think of it, you're usually permitted all the scrap paper you want, you could easily rip some up, use it as counters and use more paper to make the board. Check mate.

[@koppadasao]

@@QSBraWQ I don't know

[@koppadasao]

@@QSBraWQ I've never actually been that good at math. I've always been faking it.. counting on fingers; using scrap paper to write binary calculations...

[@jasonnelson9141]

​@@koppadasaoWait, you're not supposed to do that!?

[@greenstonegecko]

can division also be done by sliding down the perpendicular diagonal? 16/8. Place coin on intersection, slide down perpendicular diagonal until you hit the edge. If you go off the edge, just divide by 2 for each square you went off the grid? Edit: nvm you'd have to do some reaally wonky stuff

[@vikm580]

This cool and all, but how do i divide by 0?🧐

[@wompastompa3692]

It's okay, Texas Instruments already knows about this. Their chips are miniaturized chess boards.

[@stzss1027]

Bishops:Ha Ha my value will never change

[@robertethanbowman]

When Mr Logarithm has a lark, it is still fairly intense for ordinary mortals.

[@WrathofMath]

True 😂

[@ZDTF]

Wait so If I can imagine chess positions in mu head I have a calculator in my head? I can expand it like 3* more than a normal chess board Does that mean stronger calculator?????

[@Mekelaina]

This makes me wonder if you could transfer this to a circuit. Like there are already ways to do multiplication and division through essentially emulating the hand process. But could this be an easier way?

[@Kubamorlo]

Such circuits have long been in use to increase the speed of multiplication at the cost of more transistors used. Typical implementation is a grid of AND gates with some complicated addition circuitry. Addition also tends not to use the traditional ripple carry method due to it being too slow.

[@DanielRossellSolanes]

cool trick but it's a bit limited. by the way, you explained multiplication, division and square roots but... can we do addition, substraction and exponentiation?

[@emireri2387]

addition subtraction is kinda simple

[@WrathofMath]

It reduces every problem to addition, so it can't do addition itself. Same thing with subtraction. Exponentiation sure, you just need to keep doing multiplication.

[@ศกรโสมาภา]

Why do I feel like it’d be faster doing it in my head.

[@WrathofMath]

you're probably suffering from hubris!

[@willlagergaming8089]

Sir that is a graphing calculator

[@WrathofMath]

I should have included a joke about that, regarding the board as an xy plane

[@timmy18135]

Like slide rules meets Taoist math

[@isobarkley]

swanky indeed1!

[@WrathofMath]

Facts!

[@lyrimetacurl0]

16 × 16? 😂 (256 isn't on the board) (edit: oh you could put 2 coins on an 8 to get 2 lots of 128)

[@Ion-g3i]

I swear I saw this video before

[@markjackson5806]

Are you sure that's not just the Mancala Effect?

[@Anonname-vb1ns]

Luigi Mangione

[@Jiglias]

luigis mansion

[@biometrix_]

Nobody cares.

[@denorangebanan]

why are mentioning him on a math video?

[@vampire_catgirl]

Who

[@enio3698]

​@@vampire_catgirl the guy who killed the healthcare ceo

[@byeguyssry]

I love how useless this is

[@CutleryChips]

Man I was stuck on qn one so difficult