The Problem With Infinite Summations On YouTube

[@PrimerBlobs]

"Now THAT's the right amount of math!" I might steal that.

[@Cato_Minor]

It's Primer!

[@3Ppaatt]

Seriously the best line of the vid!

[@gabor6259]

If you take that line, will you share it?

[@scottybob]

Crikey! Now that's what I call the right amount of maths!

[@andy-kg5fb]

Yeah do it.

[@Jabrils]

I love what you're doing with the channel Matt, let me get that Casio Calculator tho 👀

[@mimkyodar]

Nah, the Gaxio is where it's at

[@ShadowsinChina]

You are going to need it to calculate the infinite logarithmic taxes that come with it, seems like.

[@akshaychandrashekaran3777]

He's gonna give you the Casio Calculator tax formula instead.

[@anthonyhart7878]

Jabrils, when are we gonna see your fanbase have a pokemon AI tournament with a bag of gummies as the main prize?

[@reidflemingworldstoughestm1394]

HP is the Ferrari of calculators. Just sayin'.

[@Zeuskabob1]

Danny: "That's too much math" Matt: And I took that personally.

[@JCintheBCC]

Matt: "That's just information in your mind! Government can't tax that!" Government: And I took that personally.

[@Felipemelazzi]

@@JCintheBCC I thought the same thing 😂

[@MrCmon113]

It's literally Calculus I math.

[@MinecraftMasterNo1]

@@MrCmon113 Infinite series are Calc 2 content.

[@HaydenSchiff]

I appreciate that after Danny made two uppercase Ks and one lowercase K for no reason, Matt did the exact same on his whiteboard.

[@Qsie]

I only just noticed this a moment ago! Glad I'm not alone lol

[@JohnSmith-rf1tx]

Danny's method seems like a perfect example of how an engineer solves this problem as opposed to how a mathematician solves it.

[@imhotep2223]

Definitely. I'm an engineer and I would have just tried a few numbers until there was enough left over after tax to cover the car

[@ChrisLuigiTails]

@@imhotep2223 Of course you're an engineer. Engineers always find an apportunity to tell everyone they're engineers. I know that because I'm an engineer.

[@VinayPai]

How bad engineers solve it. Good engineers understand and use basic math.

[@fashnek]

No.

[@KirkWon]

Pretty much. Danny’s not looking for a systematic formula, just an instance of that calculation. At some point after N iterations the numbers decay lower than what is significant. Something easy enough for a spreadsheet.

[@dr_cheez811]

I actually think Danny's computer science education may have led him to think of the problem more like a recursion than an algebra word problem.

[@travcollier]

Doing it as a recursion problem is trivial too. It won't take many cycles (for a computer) to get it down so the extra tax is fractions of a cent. It's a 4 or 5 line program. Of course, Matt's method is much more efficient.

[@samuelthecamel]

Why do the math when you can have a computer just run a recursive program to eventually find the answer.

[@vigilantcosmicpenguin8721]

@@samuelthecamel The n-th rule of programming is, "don't spend ten minutes on a problem when you could spend an hour on a way to automate it."

[@cinemarat1834]

doesn't matter. he should still be familiar with infinite sums if he's a compsci student

[@JohnFX3]

I have a compsci degree and my first thought was that it’s just algebra. But then again that’s because a lot of people working in tech get stock bonuses, so we deal with “how much does the stock need to sell at for me to have $X left over after taxes to buy Thing” all the time.

[@jishcatg]

This is analogous to fueling a rocket too. A set amount of fuel will take a rocket of a certain weight to a certain speed/height. If you want to go higher, then add more fuel, but now you have to carry the weight of that too.

[@thomasreese2816]

Unfortunately, that one is >1

[@rschroev]

The tyranny of the gift equation

[@gmalivuk]

@@thomasreese2816 The number analogous to r can be greater than 1 for a rocket, but fortunately since you get rid of propellant as you accelerate, it gets multiplied by smaller and smaller numbers as the exponent increases, so it still approaches a finite limit.

[@JonWilsonPhysics]

Good old Tsiolkovsky

[@MrKyltpzyxm]

This was my first thought. The tax on the tax on the tax... The fuel for the fuel for the fuel...

[@fcw2bom]

"He has a degree in computer science so I don't mind dunking on him" Oh god, they never told us that getting a CS degree would make us fair game as far as mathematicians are concerned.

[@sharpfang]

You're still allowed to approximate the result using a recursive program that stops 1mln recursions in. BTW, IT majors are allowed to use plain loops to iterate. You theoretical CS graduates - recursion only!

[@ccreutzig]

Should have been on the brochure, right next to “everyone will think you can fix their computers and be a wiz at Excel, but we don't teach any of that.”

[@Kalmakka]

@@sharpfang But having your recursion stop 1 step in is stretching it a bit too far.

[@adfaklsdjf]

It's open season on CS majors

[@sharpfang]

@@Kalmakka For a CS major - definitely! Luckily I'm an engineer, so doing 1 iteration then eyeballing the safety margin on top of that is ok in MY case.

[@rdear]

I love that you linked to Drew’s channel!!!! So subtle, and so funny. A masterfully crafted joke. Chef’s kiss, Matt.

[@jagobot1487]

I wasn’t expecting a Danny mention in his videos, let alone learning he’s in on the jokes too

[@Stratelier]

Another, unrelated, example of an infinite series is in standard musical notation: When you add a dot to a given note, this instructs the note is to be played +50% as long (as if you tied a note of the next smaller interval to it). Two dots mean to add the next smaller interval again. Theoretically you could add an infinite number of dots to the note, at which point its effective length converges to twice its original value, because each dot is +(0.5)^x .

[@GibusWearingMann]

I really hope some cheeky composer has done this at some point.

[@johnchestnut5340]

Can't be done. Not enough paper for the notation. But theoretically sound.

[@RandyHawkeye]

@@johnchestnut5340 Not true! Simply draw the first few dots and then follow them with an ellipsis. Problem solved!

[@Qermaq]

@@RandyHawkeye How do you know when the dots have started and the ellipsis begins? It always ends up looking like you forgot them. Maybe a bar over them like in a reptend, like 1/3 = 0.3 with a bar over the 3.

[@fattestallenalive7148]

​​@@johnchestnut5340 you will have enough paper if you draw the next dot half as small as the previous dot then the question becomes whether the composer has enough dedication and calligraphy skills to complete the notation

[@rainworldenthusiast]

As a fan of both Danny Gonzalez and Matt Parker, I can confidently say that this is the most unexpected crossover ever.

[@antoinebugnicourt808]

I was looking for a way to say that, turns out I just had to scroll down to your comment

[@GodlessPhilosopher]

1,000%

[@patricial.3929]

I actually was so confused and half expected an entirely different person to pop up, that just so happened to have the same exact name as Danny lol

[@chaotickreg7024]

It feels like Danny edited this video

[@ikefortytwo]

Danny fans be sure to watch the end (21:06) where he plugs Danny's channel.

[@ericdesrosiers6286]

I was watching this video and thought to myself: "I don't need to be watching this" until Matt said "That's not too much math; that's the right amount of math.". Honestly, the right amount of math is all I can take, so I watched the whole thing until the end. Well done sir!

[@mulgerbill]

I do believe that this could have been solved much more quickly if brown paper was used as the medium of calculation

[@sebastianjost]

That would have been much easier to read than the green marker.

[@lily_littleangel]

@@sebastianjost Yeah, the marker should have been black, with a red one for highlighting. And there should also be a small blue paper too.

[@tonyhakston536]

@Tyler brown paper is actually comparatively untreated.

[@JorgetePanete]

with Brady recording 📝

[@angelxenmai4413]

@Tyler we do math* here

[@sadabetas]

An important note about danny's method seems to be that when he does the initial calculation, he is basically using the first term in his infinite series and throwing out the rest, then rounding up because he is making the assumption that a low tax rate (idk

[@temporarychannelname8620]

Yeah that was the first thing I thought of two. MAYBE leave in the second term if it you wanna be sure but we do that all the time in engr. "Oh this has a smaller magnitude. Meh that's not important than." 🤣

[@eekee6034]

Further evidence that computer science is actually engineering. ;) (mostly)

[@mikeychrisanthus9948]

Dude, Boston is pretty great

[@emilyrln]

Yup. Sufficient rigor for the problem.

[@xxportalxx.]

@@eekee6034 I'd say compsci has an engineering component, and a theoretical mathematic component, depending on where you fall in the design tree.

[@secondengineer9814]

Matt skillfully avoiding talking about Negative Income Taxes sounds like me at a work party

Thanks for the reminder, I wanted to Google what that was

[@TheBoshy]

@ It's welfare for anyone who reads this and wonders.

[@freshrockpapa-e7799]

Negative income tax is equivalent to universal basic income, or the government just giving away free money to everyone.

[@richardmyers6372]

@@TheBoshy Welfare doesn't reward you for working, negative income tax does. They are not the same at all.

[@sheeplessknight8732]

​@@richardmyers6372 It still is a welfare program, it is helping people who are poorer earn more

[@RJA10001]

"it's just information in your mind. ... Government can't tax that" KILLED ME. I ABSOLUTELY LOST IT 😂😂😂😂

[@luizchagasjardim]

Not yet.

[@novastar6112]

@@luizchagasjardim Oh no.

[@szilveszterszalai230]

@@luizchagasjardim Sooner or later they gonna tax taxing itself. Which creates a loop and basically all your money is gonna get taxed.

[@kenj0418]

@@szilveszterszalai230 Line 1: How much did you make last year?, Line 2: Send it in.

[@robertkesselring]

@@szilveszterszalai230 They already do... We pay income tax on gross earnings, then they deduct Social Security tax. I.E. the money you pay into Social Security has already been taxed. Then when you receive Social Security benefits, you'll pay income taxes on that money again.

[@__dane__]

The Drew Gooden joke and parodying Danny’s outro really caught me off guard. Good job Matt On rewatch: I didn’t notice he also copied their editing style with the zoom-ins, skewed crops, fried audio, and EVEN a photo of himself on the wall

[@vigilantcosmicpenguin8721]

The Drew Gooden joke really was the icing on the cake. Such a great detail.

[@idontwantahandlethough]

He said "Hey maths" instead of "hey greg" at the start too

[@vicmit25]

So many Easter eggs, I love it

[@magicman4326]

@@vigilantcosmicpenguin8721 Where was the Drew joke, I completely missed it!

[@handitover.]

@@magicman4326 21:10

[@killermonkey1392]

Here I sit, feeling like an idiot for using something as overkill as a geometric series after seeing Matt's much simpler derivation, only for him to do the geometric series right afterwards

[@slice6298]

I had exact same feeling

[@malteplath]

It works the other way round, too. In his working out, I thought: Hold on, now you are hand-waving a bit too much! But Matt did point out the "disclaimer" that the series has to converge, in the end.

[@adarshmohapatra5058]

Matt's simpler derivation involved something called "keep rate" which itself is derived using a geometric series. Using a geometric series isn't overkill, it's just the right amount of maths!

[@MrCmon113]

The argument is the same as the geometric series imo. Works exactly for r in between 0 and 1.

[@jameshowlett1546]

"You will only pay tax on the income in each bracket of course" ugh, the amount of people I have had to explain that too...

[@icp7201]

Yeah, it's amazing how many people I've talked to that have told me that sometimes getting a pay raise is bad, because it may take you up a bracket in income tax and result in you getting less money... That's not how that works =P

[@Scapestoat]

@@icp7201 I have experienced this, unfortunately. But it was ages ago, in the Netherlands. Could it be that you talked to people for whom it was true, due to where they lived?

[@Jothamvvw]

@@Scapestoat It's not true. What is true is that having a certain income will disqualify you from certain benefits, and thus the money you can spend on things could be less.

[@icp7201]

@@Scapestoat Nope. I'm from Brazil and we implement the same exact tax bracket system here =] But are there any countries where that would be true? It seems like it would be a huge oversight that would quickly be corrected

[@Scapestoat]

@@icp7201 I honestly could not tell you. It was in the Long Long Ago, and I remember getting a small raise, and it ended up being -30 monies netto due to some sort of tax reason.

[@lordpokesmoke]

I’m a fan of yours and of Danny’s; these are 2 channels I never imagined would collide and it’s great!

[@tweer64]

I tried to connect them via 6 degrees in my head, and came up with: Tom Scott has featured in a video on Matt’s channel, Tom Scott and Jacksfilms collabed on the Jingle Bells video, and Jacksfilms and Danny Gonzalez both were in the Trial episode of the Gus and Eddy podcast.

[@ImMacke3000]

@@tweer64 Tom Scott is usually a BIG connector when it comes to connect people by as few degrees as possible. Also Hot ones and H3H3

[@tweer64]

@@pozatat Yeah, you could.

[@justinwarthen]

Agreed

[@RMC123ify]

"And then that would explode, and that's not covered by the warranty" cracked me up 😂

[@Buggaton]

Me too. I love his silly humour.

[@pvic6959]

he was extra funny and silly this video!

[@mrgabgob4675]

@@Buggaton Yeah same

[@ewrh78]

perfect easter egg ^^

[@Lord_Volkner]

At least now we know why we can't divide by 0. We can't very well have these things exploding all over the place.

[@unpythonic]

"It could go on forever" would only apply if we pay in infinitesimals, luckily, we're limited to pennies, and luckier yet that the IRS rounds to the dollar, so eventually it will end.

[@somerandomweeb4836]

When we are in math world we aren't bothered by the trivial annoyances of the real world

[@PhilBagels]

@@somerandomweeb4836 Same with politics.

[@platospotatoes6205]

I was surprised he didn't bring this up: money, and taxes especially, cannot divided infinitely and do the very unmathematical thing and ROUNDS. This changes your considerations when you're attempting to be so precise...

[@nielskorpel8860]

It depends from which direction you argue to the proper result i think. Matt showed that you could find the answer by asking 'what gift money do i need to give so that giftmoney*keeprate=giftprice'. No need for infinite series. The govt won't care anyway. They'll see the total amount given and go, "i want x% of that". And then that would be rounded. Idk, saying you need to pay less tax because of rounding in an infinite series feels like arriving at your destination by travelling half the remaining distance at a time, only to complain about the practicalities of it all. Why the hassle?

[@platospotatoes6205]

@@dsdsspp7130 in some instances the government does deal with this incrementally (e.g. 2017 tax law and reimbursement for moving expenses... When you work for the government). Sadly they don't use an infinite series and simply stick the difference to the employee. The difference is likely a matter a single digit pennies, but mostly philosophical.

[@axelnilsson6478]

My goodness the obnoxious editing is exquisite. I love you (In a purely platonic way of course)

[@johnmulhall5625]

I erotically love Matt Parker

[@machineman8920]

@@johnmulhall5625 same

[@calebthompson8230]

The editing on this one is so much more chaotic than usual. Love it

[@riley-pepper]

its a nod to the style reaction youtubers like Danny Gonzales use to edit their videos. Really funny by matt!

[@pjaj43]

This reminds me of the time I worked for a year in California for IBM. They were very generous (at the time, sadly no more). Not only did they pay me my UK salary, they added a $2000 per month living allowance (I had my family with me). This, of course had US tax implications, but fortunately we had Price Waterhouse on our side to sort them out. IBM paid the tax on all our US derived income. Since this payment fell into the next tax year, tax was due on that the following (3rd) year. IBM settled that as well, but by this time our US derived income (the tax on the tax) had fallen below some threshold (or IBM / PW had some agreement with the IRS that forbade infinite geometric series) and there were no further tax implications in the 4th and subsequent years.

[@oz_jones]

That's nice. :)

[@hettvaya]

lucky

[@monkey314159]

A couple of things. Gifts are not taxable income. The gift-giver pays the gift tax which is technically a lifetime credit. The Tesla in this case is not a gift, but a prize giveaway which is taxable. It is designed this way to keep people from getting cute with the tax law and saying, "oh no, this isn't income, it's a gift, so I don't have to pay income taxes on it".

[@Theexplorographer]

^^^This.

[@Theexplorographer]

Also worth noting that in the US you can give a gift up to 15K WITHOUT paying taxes on it. 16K in 2022. So, sorry Matt, this video is just wrong. Which I completely understand seeing that it deals with the US Tax laws.

[@bruhjonson1131]

@@Theexplorographer well the wrong video would be danny's, wich it's strange since he mentioned consulting an accountant/lawyer

[@TheBaldr]

The gifter has to claim gifts they give over annual gift tax $15,000, with the IRS. This doesn't mean they have to pay taxes. Once you reach the lifetime limit of $12.06 million, then you have to pay taxes. These numbers are for 2021 and can change each year. So gifting away a Tesla is usually the income tax of filling out paperwork. On the other hand if it is a contest, then a lawyer really has to be involved with prizes over $10,000 on top of the taxes. (It would be really stupid move not to involve a sweepstakes lawyer)

[@CaptainGreenHawk]

Per IRS "The donor is generally responsible for paying the gift tax. Under special arrangements the donee may agree to pay the tax instead. Please visit with your tax professional if you are considering this type of arrangement." Generally, those game shows made just that special arrangement because they had gotten the car for free in return for promoting it on the show.

[@derekhasabrain]

I never would have thought I'd see a maths channel and Danny Gonzalez crossover. And then editing the maths video in Danny's style? That's uncanny valley right there

[@ps.2]

Not unlike the time Matt produced a tutorial for US talk show hosts trying to figure out How To KZbin, and he did it in a pretty convincing Seth Meyers style. kzbin.info/www/bejne/qnamaaRvnpeZhdk

[@2Cerealbox]

This sort of problem actually shows up in accounting a few times. Lets say you have an IT department and an adminstrative department. You assign all of your expenses to either IT or Admin. Except, the problem is, all the people in IT are also on the payroll, so a portion of Admin is actually because of the size of the IT department and if you wanted to know how much money you would save by eliminating or downsizing IT, you have to take that into account. But then Admin also uses IT services sometimes. In accounting classes, they will actually make you assign some portion of money to dept. B from dept. A, then a portion of that from dept. B back to A again until the value settles into something less than a penny. Tax, though, there's just a simple formula.

[@BladeMoonFlare]

This seems like a nightmarish way to do cost accounting, aka spending 100$ to trace down a 1$ variance. This sounds a lot more like what the FDD / fp&a people would do, rather than external reporting. Usually for simplicity, in real life, companies generally allocate this cost by headcount. There are 60 people in admin team and 40 people in IT team, and this year 100$ of cost was incurred? Boom, 1$ for each person. And this treatment would be in conformity with GAAP.

[@2Cerealbox]

@@BladeMoonFlare Well, its actually just one step in a spreadsheet. But you learn it by doing it by hand.

[@2Cerealbox]

@@Simoxs7 it's basically the same problem as those "a train leave a station going x miles an hour while another leaves going y mph ... when do they meet?" problems. But in the US we're never taught about it from an accounting perspective - that would obviously be too practical and down to Earth.

[@tmrogers87]

The attention to detail is truly outstanding. Rewatch value 10/10

[@47f0]

That brought back memories of writing finance and insurance software for car dealerships. If you go with a total finance option, the financed amount includes the insurance for the loan. As soon as you add the insurance to the loan amount, the loan amount goes up, and the insurance needs to go up to cover the increased loan amount, which... Some banks helpfully offered us the massive tables they used on their mainframe computers - which wasn't really practical on a Commodore CBM 8032. And if you haven't tried to accomplish recursion in CBM BASIC, your life is unfulfilled (and relatively unscarred).

[@amarissimus29]

Known to posterity as the least interesting problem in the history of usury.

[@ruberhernandez-ruberyuka]

I really love all the references to how Danny does his videos, the "hello maths", the editing, the sounds effects, the set disign, the drew gooden joke.

[@alveolate]

only problem is... matt wobbling the whiteboard on his lap so much that his camera got an aneurysm xD

[@bread8465]

Where's the drew gooden joke? I think I missed it

[@ruberhernandez-ruberyuka]

@@bread8465 at the end of the video 21:10 whe he saids that if you want to wacth more videos of Danny go to his youtube chanel but he saids the drew chanel instead.

[@bread8465]

@@ruberhernandez-ruberyuka thanks!

Searched the comments for this. I was wondering why he sent us to DG. I know that channel, but not Danny's. Does Danny usually make that joke?

[@amyshaw893]

I was almost shocked at Matt for giving away a free Casio calculator. I cant imaging he would dare to give away such a terrible knockoff when Gaxio calculators exist

[@szilveszterszalai230]

Those are the best. Doing taxes with one always results in lower numbers. It’s genius.

[@vigilantcosmicpenguin8721]

I think Matt included that as a joke that we'd get if we'd seen the video where he did the fake "review" of a Casio calculator. Everyone knows Gaxio is the actual brand he loves.

[@LostLargeCats]

@ Matthew Shaw Your comment was hijacked by a "verified" bot and is now top comment.

[@asheep7797]

@@LostLargeCats i hate bribe

[@Asterism_Desmos]

This feels like a fever dream crossover episode and I love it. The amount of little references, from the picture of him in the background with an inhaler, to the giant letters spelling out MATH, this is the best and strangest episode I have seen.

[@vigilantcosmicpenguin8721]

In a parallel universe, this is a completely normal video for Matt Parker. He always refers to the fanbase as Math, which he claims is "the fanbase with the highest growth rate, but don't check those calculations." He makes a lot of commentary videos where he reads terrible examples of math. He has a popular video about how he and James Grime are not the same person.

[@DuxihrXV]

The fact that Matt spent time on set design for this video makes it just that much better

[@Red-Door]

Totally used this today! I was working on a slider-crank mechanism where there is friction on the slider. This friction demands more crankshaft torque, adding more sideways force on the slider, creating more friction, demanding more torque. Exactly this problem but mixed with trigonometry. Love it! Thanks for the video!

[@sheldoncooper5522]

Being a Greg, I don’t think there’s anyway better this video could’ve ended.

[@breakfast-burrito]

Hey Greg!! Greg here This is a phenomenal mash up that I was not expecting. I gd love it

[@trickytreyperfected1482]

But did you notice the picture of Matt with an inhaler in the background?

[@sheldoncooper5522]

@@trickytreyperfected1482 Not to mention ‘MATH’ in the background, Drewgooden1, the way he presents himself and the outro

[@mjohnson2807]

I worked for a tv network and was in charge of distributing prizes. It's sad but almost half the people turn down the prizes because they can't afford to pay such a high tax. They could sell it instantly but since most people entering the show really need money and the prize can take months to arrive, they can't afford it and leave without collecting new cars/vacations. And the gameshows know this which is why a lot say no cash equivalent prizes provided.

[@vez3834]

So the higher the prize, the more likely it is that someone can't afford it. That sucks :/

[@nickfifteen]

I thought legally the gift giver is responsible for the tax, as it's to prevent people from just giving all their money away and NO ONE has to pay taxes on it. Unless it's some stupid contract from the gift giver that the gift receiver is supposed to sign that says "you will have to pay my (the gift giver) taxes on the gift I'm giving you, otherwise no gift"?

[@NetAndyCz]

I have won 2 US game-related competitions and even though I have received the prizes both times (it was nothing big, a brand new GPU, book, T-shirt, stuff like that), getting the paperwork to get them through customs in Europe and paying the taxes was nightmare and I can totally understand people who refuse to get the prize, maybe especially if it is something bigger. Especially stuff like holiday stays can be extremely expensive on taxes and hard to resell if you actually need the cash.

[@mikumikuareka]

Income taxes are legit robbery

[@octopussua]

It's only taxed when the goods are in exchange for services. If it was truly a gift the giver would pay a gift tax. You worked for a company that exploited guests by claiming it as a service payment instead of a gift.

[@Hat_shaped]

This is edited like a Danny Gonzalez video and I love it 0:40

[@FeeblePenguin]

The series would converge for -1 < r < 1 wouldn't it? We're missing half our solutions

[@AkademiaFlirtu]

Matt: "It's in your head, government can't tax that!" Government: "Try me."

[@alveolate]

vaccine patent holders: the govt is in our pocket

[@SuperLol]

Elon Musk to the Government: do u need help?

[@khaoscero]

Sounds like crypto private keys.

[@grunda]

The part we didn't see is that he said "........yet" after the camera cut.

[@robumf]

New Law.. can't call bankruptcy on school loans

[@adjoint_functor]

As a Danny fan/calculus nerd, I never thought I’d get the joy of hearing “the greatest value of dArmy/dt”

[@lynnwalsh7517]

I never in a million years would have guessed that this exact crossover in KZbinrs that I watch would occur. When Danny first popped up, I had to stop the video in shock! (That's what I get for excitedly clicking on videos before reading the whole thumbnail...)

[@johnchessant3012]

There are two other uses of the geometric series in economics I can think of: calculating the total value of a government investment (where the common ratio is the marginal propensity to consume), and calculating the total value of an annuity (where the common ratio is the inflation rate). One of my favorite facts is that, at 3% yearly inflation, $1 billion is roughly what it costs to give away $1 every second, forever.

[@sovdee]

that is a really neat fact!

[@JungleLibrary]

Do you mean yearly interest? I agree, it's an interesting idea.

[@minikretz1]

Loved the editing style to mimic Danny, especially the picture on the wall, wish I could buy one

[@2teKnoA]

"Mathematicians don't fear things going on forever. They love it!!" hahaha You're great!!!

[@viewera]

As a fan of danny, i'm so happy to see you a video about him

[@wektion]

In the US, gifts are taxed separately than income and are subject to up to a $16,000 (yearly per person) exclusion which would be deducted from the value of all gifts given from one person to another per year before tax. Also Gift Tax is paid by the Gift-er rather than the Gift-ee 90% of the time, so the giveaway contract would have to be specifically setup to put the burden on the recipient in this scenario.

[@arthurdoktor]

If this is true it should absolutely have been in the video

[@ModernEphemera]

And I didn’t catch if this was mentioned by Danny or Matt or both, but the US federal income tax is progressive not flat-24% is the rate on the portion of an individuals income between 86k-165k, as applicable. So even if it was considered income, the effective rate would be less than 24% for most Americans.

[@lufax]

@@ModernEphemera, yes he mentioned in the video. The calculation was done on the "worst case scenario" where the full amount is taxed at the 24% bracket

[@FlamingBehar]

Absolutely loved the video 😁 The Drew Gooden bit and outro song cover were particularly entertaining 😂

[@nujuat]

That's actually a good intuitive way to see where the geometric series comes from. I feel like when it showed up in my functional analysis course as a way of dividing linear operators like I'd seen it a lot and knew what it was, but I kinda lost intuition for why it worked.

[@chair547]

I mean all you have to do to make it a formal proof is proof that the geometric series converges

[@jadegrace1312]

13:30 I also experienced the infinite recursion as the more intuitive way to think about it, even if it is easier to derive the formula the other way.

[@rufusdrumknottvgc]

Not a crossover I ever expected, but a very welcome one!! Love that Matt had so much fun with references to Drew's channel, I know someone who's truly Greg when I see one

[@chris_dietz]

I have first hand experience in this, won a contest that included a trip to New York City and ended up costing me more in taxes than the awarding company actually spent on the plane tickets and hotel.

[@jerryseinfeld4211]

That would imply the tax rate is more than 50%

[@RonParker]

@@jerryseinfeld4211 Or that the awarding company got the prizes at a steep discount in exchange for some promotion.

[@ThisIsStapes7]

Been both a Greg and a big fan of Matt for a while now. Always thought of them occupying very different spaces on KZbin. Really great to see this 🙌 P.S. Especially appreciate the detail that Matt has put into recreating the classic Danny background/style.

[@monhi64]

This kind of reminds me of how rockets work, where you calculate the fuel needed to lift the load but then you have a new load to lift, so you need more infinitely. Fortunately they both approach a max

[@sander_bouwhuis]

This is exactly the example I teach/explain to non-maths people. It's very useful to make it intuitive that an infinite series can indeed converge. Another topic where you can encounter infinite series converging is with combinatorics.

[@scottwhitman9868]

but in that case it has more to do with the fact that you don't have to carry all the fuel all the way up

[@dragonoax]

The editing in this is killing me Matt, I love it 🤣

[@LeoStaley]

I see that sub count just hover above 900k for so long, and I just wish there were something Matt could do to help subscriber count get to 1M, like maybe a calculator giveaway.

[@ctownskier]

I feel the need to mention that in the US a true gift, ie parents giving you $10k for a house downpayment or whatever, is not considered income so no taxes are paid. Technically if the gift is over the annual exclusion it counts against the givers lifetime gifting limit (~$10 million) and only when that is exhausted does the giver (not the recipient) pay a gift tax.

[@AliceYobby]

Gifts aren’t the same as giveaways

[@woobilicious.]

The parents have already paid income tax on it, the problem comes in when it's company gifting items, since they can use it as a loophole to avoid income taxes. This seems like an odd way to avoid the loophole.

[@mralistair737]

@@AliceYobby but what if greg met someone in the street, befrended them then gave it? isn't that a gift?

[@AliceYobby]

@@mralistair737 like he could do that but he couldn’t do the giveaway. He would just have to meet someone and give it to them, no raffle or competition involved. He wouldn’t even be able to film it I don’t think. The closest I could imagine getting would be to have an event where his fans showed up and then randomly telling one of them in private “I got you a Tesla” but even that would probably be looked into if discovered, although it could maybe go either way.

[@zarblitz]

@@AliceYobby This. You can try all the loopholes you want, but at the end of the day you probably don't want to try your luck with IRS. Unless you're fabulously wealthy, then tax laws are made with custom loopholes just for you.

[@JohnBarrett]

2:37 *INCOME*

[@TheRunningLAG]

Honestly... you, or more precisely Dany, are answering a question ive been asking myself for quite some time, but was always to lazy to calculate myself... Awesome...

[@allandnothing5338]

As a finance guy, more often that not, there are some advanced mathematics on this channel where I'm completly out of my depth. This is the first video, where after the first minutes, I was like: "How can this even be a considered problem? You just need to divide by (1 - t)" (we usually use "t" as the tax rate notation) 🙂

[@tombaker5926]

This video changes the way I want to teach the geometric series- not sure quite how yet, but dividing by (1-r) always felt like algebraic magic, but now I have a concrete example of why!

[@kristenmork4316]

"it's just information in your mind. ... Government can't tax that" In some cases, they very much can and do. If you get free education, the value of the tuition can be considered income. Especially if the individual is not pursuing a degree-such as watching educational materials posted to KZbin. You are giving the knowledge away, but that could be viewed as a gift to your viewers, which would be taxed. So, to be safe, you need to acknowledge that the information you have provided is worthless. 😁

[@JavierSalcedoC]

Matt's picture in the back drinking water is the attention to detail that we all love

[@ImDemonAlchemist]

I haven't seen much of Danny Gonzales's stuff, but my roommate has and did confirm this. Matt did a whole bunch of things mimicking Danny's style, jokes and delivery and I respect the effort.

[@Lion-xl8gy]

love that crunchy INCOME at 2:37

[@deefdragon]

Given its tax season in the US, I would actually be all for discussion of different methods of tax brackets, negative taxes etc. I think it would be an interesting mathematical discussion.

[@joepgeuskens527]

Next video on this channel: imaginary tax rates!

[@mralistair737]

god help us, it's not like the internet isnt endlessly filled with people talking about tax, and ads for all things taxy and IRSy at this time of year. being a non USA resident it's like "we get it, you have a terrible system for collecting taxes, sort it out or shut up about it" quite why anyone with a single income and job needs to do a tax return seems about as backwards as using a chequebook... oh yeah you still have them as well.

[@adfaklsdjf]

nope

[@oz_jones]

@@mralistair737 Waah

[@FlankingLinex]

If the giveaway was for a framed picture of Matt using an inhaler, I'd participate.

[@kylebowles9820]

Dude your humor has been on point since the beginning but the editing is really taking it to the next level!

[@fiveoneecho]

The second you wrote the general “tesla giveaway equation” I like like, “Oh yup. Geometric series… Of course”

[@danielshepherdaccounting8979]

18:22 Yes, there sometimes are 'effective' tax rates greater than 100%, especially where two rates are added at the same time, such as income tax plus a reduction in benefits impacted by the same income/gift.

[@hannahwatermelon]

I am actually learning about geometric series in my calculus course, and just as I was about to get frustrated at the math, I saw this video, and I decided to watch it to remind myself about how cool math is, and i'm so glad I have this channel to do that with (among others) because i love videos like this.

[@pawelkorzeniewski4897]

Living in a high tax "socialist" country of Sweden, just imagine the enormous tax I'd have to pay for such a gift... oh wait, gifts are not taxed here.

[@cityuser]

But we have 25% sales tax vs their 7.5% :p

[@tonyhakston536]

@@cityuser yeah but it’s listed, which means businesses can’t abuse human psychology and thus have to lower the prices to make any sales.

[@octopussua]

They aren't in the US either - Matt was wrong

[@AlenobaLP]

@@tonyhakston536 Actually, I don't think that companies lower their prices in countries with high tax rates. The products just get more expensive and people are used to paying more money for stuff. If a company wants to make 100$ on a sale then it's gonna be listed as 100$ in America (although customers pay 107$) and as 125$ in Sweden. I live in Germany and regularly notice that American products like iPhones are ~12% more expensive in Germany than they would be in America.

[@MrKhaz101]

@@octopussua yes they are, as are things like somebody paying for the down payment on your house or even forgiveness of debt. Additionally, US citizens can be taxed FOR giving gifts if the value of gifts given over their lifetime exceeds ~$12M.

[@katelynt1555]

Holy moly! I took calculus c last semester and the moment you mentioned it was a geometric series I recognized the equation you had already made followed Sn=A/1-r. This was so great to watch! It’s great to be able to apply stuff you learn!

[@katelynt1555]

And then the convergence too! This was literally all I learned about just recently!!

[@singerofsongss]

this is hilarious, especially because i already watched Danny’s video and praised it for its educational qualities

[@lukasschwager5876]

Matt 6:39: "I mean, you only pay tax on the income in that bracket. Of course" Every german: _cries out in pain_

[@Ruslan-S]

That works the same in Germany, the UK, the US, Australia, etc. You pay tax on the income in each respective bracket that your income falls into. In this case Matt was only concerned with the Tesla money income tax, and then referenced that Danny must have assumed the "worst case" when the whole amount of the Tesla money falls into this 24% tax bracket, as opposed to a better case where it would only partially fall into it, therefore some part of it would be taxed at a lower rate. Matt meant that you don't pay tax at 24% for all your income, instead only for income that falls into that bracket. But you still pay taxes for income that falls into lower brackets, if any. 100% of our income is taxed, progressively, with some small amount taxed at 0% and then increasingly more from there.

[@TheNewYear75]

Love this well-thought-out response to Danny’s vid that expands upon his ideas. Feels like old KZbin !

[@Shacklefty]

"Actually if R was 1, then you can see we're gonna have problems because we're dividing by zero, and that would explode, and that's not covered by the warranty." I laughed too much at this. No, that's incorrect. I laughed the right amount.

[@kwdavids1]

Well the biggest mistake is that gifts are taxable not to the recipient in the US. If they BUY a lottery ticket they pay tax on the winnings, but if someone just give some something out of the blue that they didn't have to earn, it's not taxable to the recipient. On some HUGE amounts of money (over $11.7 million over a lifetime) there is a gift tax BUT the donor pays that tax. The IRS says: "The donor is generally responsible for paying the gift tax."

[@AliceYobby]

Gifts =/= prizes

[@arrgghh1555]

I hope lottery tickets are tax deductible.

[@kwdavids1]

@@AliceYobby The video text describes a gift, "Just gives someone a Tesla." If it's prizes, awards, sweepstakes, raffles or lotteries, then it's ordinary income.

[@kwdavids1]

@@arrgghh1555 Yes, the price of lottery tickets are deductible up to the amount of winnings. If you don't win, then that max is zero.

[@AliceYobby]

@@kwdavids1 I think that’s a problem with his terminology when in fact what they are describing are giveaway raffles

[@jacobdegeling]

This is my new favourite Mathematics video in the world ever. Matt you're brilliant 👍🏼

[@Slikx666]

I'm so glad I'm subbed to this channel, I didn't do well at school and have learnt more after than I did in school. Thanks Matt for the mattmathics.

[@emrazum]

I love Drew Gooden's channel, glad to see him featured here.

[@ChrisLindsley]

Shoulda bought the Tesla in New Hampshire, Delaware, Montana, Oregon, or Alaska (no sales tax on cars) and given it away in Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington, and Wyoming (no income tax). Basically KZbinrs should all be in Alaska.

[@RonParker]

"Live in Washington, shop in Oregon" seems like a great idea for that reason, but then you realize that you'll be living in Vancouver.

[@ChrisLindsley]

@@RonParker Long Beach is nice. I hear good things about Walla Walla...

[@n00dle_king]

The problem with infinite series on KZbin is that PBS canceled it 😢

[@RyanAtOptimism]

100%!!!

[@LeoStaley]

Oh good I'm not the only one who misses it.

[@ShadowsinChina]

So true & so sad 😢

[@curiodyssey3867]

True dude :(

[@renerpho]

I totally clicked on this video expecting something related to the PBS show.

[@aaronrosenberg1769]

For whatever reason, the way you said "They love it" around 14:44 reminded me of Monty Python's SPAM skit. "Shush dear, don't have a fuss. I'll have your maths. I love it. I'm having maths, maths, maths, maths, maths, maths, maths, baked beans, maths, maths, maths, and maths!"

[@thepencil448]

When I was thinking about the problem it felt like trying to find the cost of the car then add the income tax then add the income tax off that ad infinitum was almost the hardest way to solve the issue. Why not work backwards and calculate an amount of money that, when taxed, leaves enough money to buy a Tesla? Glad to know that I was on the right page.

[@KraylusGames]

Matt: "This is just information in your mind. The government can't tax that!" Government: "Hold my beer"

[@JakeWitmer]

Makes you wonder if he's read "1984"...

[@newtonvitas5633]

The crossover episode I didn't know I wanted.

[@MumboJ]

"The government can't tax information in your head." Don't give them any ideas!

[@Idkevenwhatisnttaken]

Damn this works on so many levels

[@DrLennieSmall]

Cape Verde has over 100% import tarrifs for certain cars, when I was there the driver told me that his car cost less than the tax to bring it into the country.

[@chrissdehaan]

I feel like -1 < r < 1 is a better range for that series converging. I know you talked about a bigger range in passing, but you wrote down 0 ≤ r < 1 which felt too restricted for me.

[@sdlovell718]

LOL “I give away knowledge on this channel.” True. True.

[@AlteranKing]

I'm glad someone else worked out this equation. I often day dream of winning money or things while I shower. And I often try to keep things as real as possible so I work out the math of how much money I'd need to win to be able to buy things or pay off other people's debts.

[@KuK137]

That is called a subsidy. And that's exactly what ultra-rich in the USA claim each year thanks to bribed right wing scum "legislators". You're 1% oil baron with insanely high profits or huge industrial farm company? Have an extra handout on top of that, as long as you share a few bribes with the "business" party...

[@SiMeGamer]

@@KuK137 not sure if you know, but right wing (in modern day) are against this stuff in fundamental terms. Not completely but mostly. Small government with minimal involvement in the economy is precisely designed to not protect and not help big businesses. But a big government that is involved in the economy, or more specifically here, in the markets of said big companies, they are kind of ruining the business of said companies and thus are almost forced to either regulate (which ALWAYS benefits the big players; so left wingers who want to go against the rich are fking idiots when they propose regulations), subsidize (education and agriculture mostly) or even bail (mostly seen in the financial sector). Even if it is true that right wing politicians currently are the ones making the deals, it is also true that right wing ideology goes completely against that. Meaning that if more right wing legislation goes through, those right wing politicians will have way less power over the economy in terms of lobbying. I highly encourage researching right wing policy and how to would affect government corruption when it comes to tycoons. It's not very complicated kinda sheds a bad light on big government ideology (modern left). Also important to remember that just because people in politics say something, doesn't mean they actually believe it. It's often for populist reasoning rather than honest thoughts. So if you are in right wing party, it doesn't mean you actually believe in right wing ideology (Donald Trump famously hopped from party to party at least 3 or 4 times and touted whatever the party's ideology was at the time).

[@GabrielJones]

Matt: Information in your brain can't be taxed. Government: Challenge accepted.

[@marscience7819]

Actually, in the U.S. there is no tax on gifts that has a yearly upper limit ($17,000 in 2023), and a lifetime upper limit (in the millions), so as long as you do not go over the lifetime upper limit, no federal income tax will be due, although you do have to claim it.

[@cheeseninja1115]

the fact that at 5:27 the 3.6K is also lower case is just golden

[@rainerheller2429]

1:20 love it!😂 That's what I wanted to hear :)

[@wakafeek]

It took me 42 seconds into the video to notice the background. That's hilarious!

[@redpandamaniacal]

I feel like Danny did that calculation to demonstrate how more money needs to be paid in a funny way without needing to work out the actual math in the video. It feels like there's a decent amount of the population that has difficulty with algebra and fractions and it likely wasn't their goal to explain exactly how you would calculate it. That said, this is something I love to see from Stand-up Maths!

[@MathVisualProofs]

At the title I thought you were gonna roast videos like my animations of classic visual series decompositions. Nice work here!

[@MultiSteveB]

I think it would fall under the "gift tax", and not "income tax". While income tax is in brackets, I cannot say if the same is true of the gift tax. If so, then infinite summation will not happen, as once the "loop" reduced to a small enough size where one iteration doesn't take you into the next higher bracket, the loop ends. But I am not a Tax Attorney, so YMMV.

[@elizabethh8579]

I was thinking something similar- how do tax brackets change the rate? Does the recipient’s normal income factor in?

[@MultiSteveB]

@@elizabethh8579 For Income tax, the 1040 publications include tables to determine the tax owed. The tables can't list every single dollar amount, so they list ranges. I.e., if say, you earned between 30,000 and 31,000, you owe X, a single amount.

[@charleslivingston2256]

The recipient doesn't pay gift tax. Corporations can't give "gifts."