A Problem Squared - 136 = How to Discuss The Number e and When to Disclose the "Real Me"

Episode Date: June 8, 2026

#️⃣ What’s the best way to explain the number e to an 8-year-old?💗 How early in a relationship should you reveal that you’re a bit weird?🤧 And there’s some any other blow-your-nose-nessHead to our socials to see The Beautiful Old Calculator and The World’s Tallest Comedian.Matt is bringing An Evening of Unnecessary Detail to New York! The Bell House, Brooklyn on Sunday 12th July. Tickets can be found here: https://www.ticketmaster.com/event/300064B84CCCF567Matt has extended his tour - and he’s filming the show in London in October - all the dates, venues and tickets can be found here: http://standupmaths.com/shows Join us on Patreon for early releases and our monthly bonus podcast I’m A Wizard!If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post!  If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with a friend, or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

Hey Matt here from the podcast that you're about to, and I swear we'll shortly listen to. I'm doing a show in New York on a Sunday, July 12th. It's an evening of a necessary detail. Tickets on sale now. We'll link to them below. Me and a bunch of my nerdy friends. Sadly, Beck can't make it. But, you can hear more Beck on this episode.

Hello, and welcome to a problem square, the podcast, which is a lot like springtime. Great idea for an intro. Thank you. Thanks. It's like I had written it for the last one. Ah. And then someone else decided to steal it. Nah, it doesn't feel right.

Let's hear it. Let's hear it. So in this analogy, life is a big, bright, beautiful flower that everyone just wants to enjoy. However, life is full of problems, just like flowers are full of pollen. And right now, that proverbial pollen is everywhere. This was true at the time that I wrote this for the last episode. Yep. So you, our listeners, employ us as your allergy treatment. Matt Parker is a mathematician YouTuber and author who is a lot like Optrex eye drops,

in that he allows us to see things more clearly, is fast acting. And a rare trait for a mathematician does not cause drowsiness. Oh, dang. I feel like I still caught a stray in there somehow. Well, the maths community did, but you survived. Yeah. Yeah. Yeah.

I'm negging the mass community. I got hit with some shrapnel off the recoil from that. I am Beck Kill, a comedian, writer and presenter who is more like Beccanais and that my name is Beck and I am Nasal. Wow. On this episode, I'm going to explain E to an eight-year-old. I'm going to explain relationships to probably grown-ups, to be honest. And there will be any other blow your noseness.

It's the best I can do. Any other bless you. Great sneeze. Great sneeze. Hello Matt. Well, I'm here enjoying the very end of Aussie autumn. And the big news, I've done my bike ride. Yes, I was excited to hear about it.

Tell us more. So, number one, did not break my hands. hand shortly before the bike ride. That's pretty exciting. I'm very pleased I did that. I was very tempted to text you and say like, did you fall off and your teeth got knocked out, which is something that we discussed on the last one. And then I thought, don't ruin it now, Beck. Wait to see if he's got teeth when you talk to him. Got teeth, got all my limbs, everything intact. I did gently come off the bicycle about a week before because my brother and I went and cycled around some gravel trails up in the hills outside Perth.

You know, it's Pratt. And we both, both of us came off on this one just particularly a slippery bit of gravel. But we're both fine, we got up, moved on with our lives. As I went down, I'm like, oh, great, this again. But it's fine, did not break my hand this time. For new listeners, I attempted this gravel race a year ago, and I broke my hand like a month out. And then I couldn't do it. So I was able to go back now and successfully do it.

Finished the gravel race, did not come off my bicycle during the race. I managed to go around all 56 miles, roughly 90 kilometers, in a mere 5 hours, 43 minutes and 46 seconds. That's very impressive. It's adequate. It's up and down on gravel, 10 miles an hour. I think that's very impressive. Yeah, yeah, yeah. I was 10 miles, and that includes breaks.

Like, that includes stop each time. I was a little generous on the stops. I came 19th in my age and distance category, albeit out of 26. I'm still taking that. Yeah, I would. I was probably less healthy, less fit than last time. And I was doing the longer course

because I could upgrade to the full course next year or I could do this one again. This is like I'm in the second top one now. So I'm torn between doing it again and getting a better time. The last quarter was pretty tough going. On like the second last hill, my left leg started cramping up. But I had a plan. I ignored it.

And I kept cycling. And then on the next hill, my right leg started cramping. I'm like, come on. But by then I had a winning strategy, right? So I just carried on. So I definitely couldn't. There's room for improvement on that distance. I think I could do a lot better.

Yeah. So I'm undecided. For those of you following my cycling career, if I will Career Look, I career into a lot of things including curves I decided to take a sip of coffee

just as you said that and I regretted it because that's a great joke and I'm very like, well done Great, great great Did anyone show up pre 6am to say hello to you and have a calculator signed? Would you believe one person

Yes, that makes me so awesome An electrician named Matt was like, hey, I'm doing the seven. I'm going to be there. And they didn't say, can you sign my calculator? They said, would you like a calculator? They said, hey, do you want an Adler calculator? The Adler 81. And I was like, oh my goodness.

Yes, I would like. The Adler 81. Can I just stop you there? Yeah. Adler is definitely the name. that I would make up if I invented a calculator. I'd be like, it's a ad... A fake, oh, you know, an adulator, whatever.

Summonator. So, you know, I'm not going to bury the lead. Do you want to see it? I've got it. Of course I do. It's from 1972. I'm holding it up in its case. Oh, it's got a lovely leather case. Like, I don't think it's original leather, but it's a fantastic case.

Open the case up. Make sure it's facing the right way. Are you ready? Oh, my God. Is that not like the ultimate 70s calculator? This looks like a calculator. It's very similar to a calculator that my grandpa had that he used to let me play with. Because am I correct in thinking that the display is like red LED?

Like it's light. It's not like a LCD. No, we're well before that. Look at that. So Matt, the electrician's dad was a cabinet maker and he used this. His dad's calculator. from doing the accounts in his home office. And he had, he was doing a clear out.

I know, he's doing a clear out. It's been so looked after. You know, you sometimes just got to clear out. He's like, you know, I think I want to donate this to the Matt Parker calculator collection. And so. Yeah. The amount of times I've sent you photos of like calculators that I've found like in

shops or in, you know, family cupboards and stuff like that, there's some that you might already. There's some we're like, oh yeah, they show up a lot, all that sort of thing. So it's very nice to see you excited about a new calculator. Well, there's also a high bar because if I wasn't careful, I would have nothing but calculators in my life. So I've got to have some, not quality control, but I've got to be a little discerning. So they've got to be cool, like this one.

They've got to be a little bit rare. This one's not particularly common. And they're going to have a good story. So this one just ticked all those boxes. And poor Matt brought it down. We weren't able to find each other on the day. So on the day, poor guy, he didn't have to like cycle it around the whole course. But he had it in his car.

We didn't end up crossing paths on the day because there's a lot going on. We were starting at different times. And so we actually, this afternoon, before this recording, I went and met him at a pub near he lives. And we did a calculator handover. And I signed a copy of one of my books for him. So we did do the whole thing. It was started because of the gravel race. He had a great time.

He did the full course as well. It was his first time doing it and just absolutely smashed it. Got on him. I'd like to show you it working. But as you can see, if I slide at the back here, I'm just showing you the battery case is empty. There's no batteries in there at the moment. So it'll make it hard to do calculations, were it not for the fact.

I've also got the plug-in power adapter. Wow. There. This is a chunky individual. Look at that. to run a calculator. The adapter is bigger than the calculator. So let's have a look here.

I can switch it from AC to battery on this. And on the calculator, there's a switch. Can you see there's a switch that's a picture of a plug and a picture of a battery? Yes. And I've got it on plug setting at the moment. So what I'm going to do now, let me get my cable. All right. Matt is holding an extension cord and the plug for the adapter,

much like Doc Brown in Back to the Future. Yeah, it's got a real... I feel like he's about to get struck by lightning. Now, I haven't tested this, but also it was given to me by an electrician. So I feel like they cancel that. So I'm going to... First of all, I'm just going to... I haven't plugged it into the calculator yet.

I'm just going to power up. It's got a custom plug. Oh, it's so great. Wow. And then there's a sock on the top of the calculator. Okay, we're going in. I guess it only plugs in one way. Yeah, it does.

Oh, look at that. clever. Oh, it's on. It's on. It's on. It's on. Look at that. You got a little light up zero. You now have to use that for any calculations you do in this episode. It's working as well. I'm just typing, oh, I'm going to type in pie. You're going to write boobies? 1,4, 15, 9, 2, 6. Oh, look at that. Look at that. Pie. Yeah. Great. So any, any maths I'm going to do in this, in this episode, I will, um, I will type it straight into this. Into the Atlas 81.

It's got a lovely sort of silvery metal casing with then a black front and the buttons are round and a sort of grey colour. The font used for the buttons is really like, I mean, it's very 70s. It's so nice. Imagine the sort of font that Wes Anderson would use. Yeah, it's like not Art Deco, but it's clearly, you know, a post-art deco. eco world. Yeah, those buttons are properly raised so I feel like you'd get some nice. Yeah, they're real tactile. The five looks like it's got places to be. Yeah. It's great. Oh, I love this. This is really very enjoyable. Yes, photos on, we'll put photos on socials. Not to, not to say this is my big news,

but I did recently treat myself to a creamy keyboard to encourage me to answer my emails more regularly and so far it is working. I sit down and then I start typing and I'm like oh yeah I get to type on the fun keyboard. It's very nice. I'll leave it plugged in for the duration of the recording and I'll report back with any temperature changes. It's running pretty cool at the minute and I haven't checked what its power drawer is. I don't know how many how many watts it takes and if that changes when I'm calculating but this is the beginning of the journey of discovery. So they why that's my adventures cycling and Beck, how are you doing? I'm doing well.

Two things have happened. I did a spot at the Bill Murray. You're a friend of mine, got old Barry, runs the R. Yes, of Barry's economics. They did a street party at the Bill Murray. Oh, can I just ask you one question before you carry on? Because I've got a note I've written down here that just says legs, question mark. Because I had a meeting yesterday with James Grime,

Katie Stakeles, Elyann MacDonald, the mass YouTubers, people who know them, we were catching up and Aalian said to me, hey, what's it like to no longer be the tallest comedian? Was Aalian there? How does she know about this? What are you talking about?

She's like, ask Beck about her legs. So I've written legs as a note to myself. And now, Beck, I am asking you about your legs. So, Barry asked me, during the week just beforehand, if I wanted to do a spot. And when they do the show, because it's a street party, everyone's outside,

and the performers perform either on the roof, there's a little roof terrace bit. So the roof terrace is kind of like first level, because it's one of those buildings where it's like a three-story building that then has like a little one story bit that goes for a little bit longer. So on the roof, you're sort of standing on the second story, if you know what I mean. or you could perform from one of the windows. And I thought, well, you want to make the most of that scenario. So I was like, if I was performing out the top window of a three-story building, rather than just looking down and yelling at people, what would I do with that?

And I was like, well, what if I'm the world's tallest comedians? So I. And this is a classic Beck thing where I think, where I spent more time in the prep on the visuals rather than on the material. The jokes, they'll follow. I spent like two days building these like 10 metre long legs and three meter long arms. And there's footage, we'll put it on socials so you can see. I would love to see it.

And then I wrote five minutes of material about what it's like to be the world's tallest comedian. which was really fun. Great. The arms were so heavy, Matt. They were so heavy. Because the problem is, is everything was so long. I couldn't rehearse the bit because no room was big enough for me to put my arms out and to see how heavy they were after a prolonged amount of time.

So I wore out very, very quickly. What were the legs and arms made of? Tights with rolled up cylinders of paper and stuffed it with newspaper just to, bulk it up a bit so that it wouldn't crumple too much. That said, the bottom four, because Barry thought that I was only going to perform from the second floor. So initially, I only made like five metre long legs, but I did have spare tights and some of that like big brown paper that comes in Amazon packaging. And I'd packed it with me just in case. And I'm glad I did because when I got there, Barry went, oh, I didn't think, I thought that would be too high. And I was

like, the higher, the funnier. So I. quickly whipped up another five meters of legs. More legs. But they're so much slimmer and they're really noodily. So like when their legs first come out, they're super noodly and then they start to become a bit more leg-like. I now know how I would do it in the future. Look, I'm just saying that if you book anything that has a balcony or any opportunity where I can perform as the world's tallest comedian again, I've got an idea of how to make it safer. and easier to transport.

And could the legs and arms move, or they just dangle there the whole time? The legs dangled. I needed someone to spoon me from behind to hold the legs up. A lovely volunteer who blessed his heart. He's just a big comedy fan. And so we've only ever spoken in occasion.

And then suddenly I was like, I need you to stand behind me and put your arms around me like right where my legs on my hips are yeah and hold on to my legs for dear life because they cannot fall out this window they will hurt someone and then I had someone else holding the microphone for me but the arms were so my arms got so tired so the arms moved but a lot less as time went on in the end they sort of just started to droop yeah wow and my one addition is and I just wanted to mention this. While I was in Australia, my fridge broke. And lovely Barry from

Bill Murray was doing a lovely job looking after my house plants, popping in, making sure everything was okay in my flat while I was away. And he noticed that the fridge had broken, bless his heart. And so being the wonderful person he is was like, she can't come home to a bunch of off stuff. So he cleared out the stuff that's like unnecessary. And then he brought the little bar fridge, a spare bar fridge from the Bill Murray to my place and then put anything left over I had in there just so that when I came back it wasn't like I had some refrigeration. I got my new fridge yesterday.

I'm very happy, but it only just occurred to me yesterday that in that original fridge was a lemon. I was about to say the lemon. No. And it only just occurred to me and I was like, oh, bless his heart, Barry would have been like, what's this old lemon?

Beck doesn't need an old lemon in her fridge. Petrified lemon. And he would have just like put it in the compost. And my plan had been to try and get the seeds and plant my own lemon tree. Yep. Which I should have done way earlier. And maybe the seeds wouldn't even work because of how old that. You only had a swift three or four years in which to do that.

I know. So just to say if you happen upon any other lemons. Now, for anyone who wasn't listening to the original Lemon Saga, that was a lemon tree that was in my brother's backyard. And I brought a lemon. I forget why we were even talking about the lemons, but we were. And I brought one back for you. He has since moved house. So I no longer have access to the original lemons.

Dang. But I will keep an eye out and see if I can give you a new. new lemon for a new fridge. I mean, I can get lemons here. I will say that. No, no, no. It's not the same. I will find something that can live on perpetually in your fridge.

Thank you. Okay. We should get on with the episode. We should do an episode. And our first problem comes from Barney. Good old Bonnie. Barney wrote into the problem posing page at a problemsquare.com and said, this is a problem on behalf of Phoebe age eight, who was playing with a calculator app on a parent's phone

and asked what does the E mean? Also, when they said on a parent's phone, which does make me wonder, what is Barney's relation to Phoebe? I'm not sure. I don't know. All the parents. Could be a parent, could know the parents. Could be talking about themselves in the third person.

Yeah, potentially. Barney is a person of mystery. Barney goes on to say, I did Mass A level a few decades ago. I know it has something to do with natural logarithms, exponentials, and is 2.718 blah, blah, blah. But I was at a loss as to how to explain it to an eight-year-old. How would you to approach this? Now, before you start answering this, Matt, funnily enough, I saw this problem and thought, if I can find this out myself and figure it out, then I'll definitely be able to explain it to an eight-year-old because I understand it.

And how'd that go? And I don't understand it still. I know it has something to do with like, I understand the power of 10 stuff, but I do remember sometimes you do something and it just says E as the answer. Like you don't get any other information. So that's probably the E for error. So sometimes on a calculator, if you mess up, it just says error. So E, the number E.

E is a number in the same way that pi is a number. So instead of always having to say 3.14159, etc. For pi, we use the Greek letter pi. And instead of saying 2.718, blah, blah, blah. For E, we use the English letter E to stand for the number E. So it's a bit like pi in that it is a number, but it's not a whole number. It's got a whole lot of decimal places. And on, you won't get it on old calculators like the Adler here, but on a new calculator, like a scientific calculator, just on an iPhone, if you go to scientific mode, there will be a key.

And I'm just holding one up and I'm pointing at it with a pen there. It's literally a button with the letter E on it. Oh, it's a little E. It's a little E. But if I push that, oh, unhelpfully, it just puts a little E on the screen. Producer Laura is showing us on. There it is. The phone?

Put E in the phone calculator and there it is. 2.71. When the Simpsons did a Sesame Street parody, at the end it was brought to you by the number E. Not the letter E, the number E. So it's a number. It's a number. It's a number is a very short, the short thing.

It's a bit like saying what is pie, but there are lots of numbers. Why does this one get a special name? and why is it on calculators? Yeah, because with pie, I can be a bit more like, oh, it's to do with circles. Exactly. So, here's an explanation for why this number exists. If you had, let's say, a pack of cards and you were to shuffle them and pick one at random

and you want to know if you're going to get a red card, you know the probability of getting a red card is one in two. because half the cards are red, half a black, probability is one in two. Whereas if you're like, oh, I wonder if I'm going to get clubs, well, now the probability is one in four, because only a quarter of it are clubs. Or if there was this particular card, like, you know, the ace of spades, one in 52. And so you can do probabilities kind of a one in, like, well, what's my chance of getting it, there's one in whatever. But let's say you take off 10 cards numbered 1 through 10, 8th through 10.

So you shuffle them up, and then you're like, Well, hang on, what's the chance I've moved every card? What's the probability if I have a look at these and the ace is no longer in the first spot and the two is no longer in the second spot and the three is no longer in the third spot? Because there's a chance, just randomly, the six might end up back in the six spot. So you're like, oh, what's the probability that they've all moved? It's one in E. It's the probability that if you mix something up, nothing goes back to where it started.

is a one in E probability. And that's where the number E comes from. Okay, that is, that's something that I can start to wrap my head around. Thank you. And that's the case for anything. Yeah, it's often called the coat check problem, where the original phrasing was, you know, you got 100 people at a party.

And each time they show up, they hand their hat in to the hat person who looks after them. But the hat person's just chucking them. in a pile. They're not keeping track of who's is whose. And then when everyone leaves, they just get given a random hat. What's the probability? No one gets back their hat. One in E. So actually, on your calculators, if you do one divided by E, you'll get that as a percentage. So one divided by E equals 36.79%. So just over a third. Huh. Like how was that answer arrived at?

Good question. Maths. A bunch of working out. Now, here's the thing. E actually appears a lot of different places. And I've just picked one. And I've tried to pick the one that's the easiest to explain and the most intuitive for an eight-year-old.

It's a bit like when people first meet pie, they meet it as the ratio of the diameter of a circle to the circumference of a circle. They don't meet it with people going, oh, there's this infinite C. a reason it converges to pie or oh if you're doing a thing with a normal distribution there's a pie in there or all these other weird places pie shows up everyone starts with hey it's a circle because it's the easiest thing to understand is nice of intuitive and then the reason we love pie

is because it unexpectedly appears in other places right e is a similar deal okay because this is actually a bit mind-blowing for me because i've never thought of pie as not being in relation to a circle but now that you mention it, I can now see why you get excited by it because it is something that shows up when it's not necessarily circle related. Correct. That's why mathematicians,

if pie was just circles, we wouldn't care about it. Like we'd probably wrote it down somewhere it would be in a book, but it wouldn't be like the poster child, like the mascot of mathematics, if it was just circles. It's like a mathematician superstition type thing

where it's like, this number is. It shows up everywhere. Yeah. I'm so excited. It feels like a conspiracy. Yeah. Yeah. And that's why we like it.

Yeah. Because math is about finding patterns and unexpected links and all these things. And it's like, oh, what's the logic behind? Yeah. I imagine sometimes if you find it somewhere, then it could also suggest that it is linked to the other things. Exactly that. Like, if you were to find it somewhere, you'd be like, oh, oh, okay, this actually relates to circles and I hadn't considered that circles would be a part of this. And I'm using circles as an

example because that's like the only one I know. But I'm sure that's the case for like other things. When we talk about a ridiculous place where pie shows up, the question is always, where's the circle? Because, you know, and it's just a catchphrase way of saying it, I mean, more accurately should say what is the bit of mathematics that is common between this and circles? Like what is happening here? That also happens in circles or is similar and like, why is Pi showing up again? And Pi is the undisputed champion of this, but E might be the second placeholder for a number that appears when you least expect it in loads of different places. In maths, people be like, oh, I got a puzzle for you.

And if the puzzle at all involves what are the chances, the answer is always 1 over E. If someone's like, oh, what if you're rolling a dice and there's a one and six chance getting the number you want and you roll it six times. What's the chance you didn't get the number you wanted? You're like, it's one over E. It's always one over E. All these puzzles, it's one in E. So I like it because it shows up in all those places. Is it a bit like the Fibonacci sequence is something that shows up a lot?

Yes. Yes. So actually, really good point back. The golden ratio, which is the Fibonacci sequence. 1 plus 1 plus 1 equals 2, 2 plus 1 equals 3, 3 plus 2 is 5, 5 plus 5 plus? plus three is eight. You add the previous two terms to get the next term. As you do that, if you look at the ratio between one number and the next number, that approaches the golden ratio.

So the golden ratio suddenly shows up as the limiting ratio for Fibonacci numbers, and it shows up in lots of other places. So a lot of people are probably saying, no, E isn't second place. The golden ratio might be second place for a number that shows up when you least expect it. and I would entertain that notion. They might be correct. But it's not represented by a little symbol or is it? Yeah, phi.

It gets Greek letter phi. Phi is in Fibonacci. Fy as in Fibonacci, yes. No, it's not that. Oh, it's right there, guys. The pie is pie as in from perimeter, which is ridiculous. Okay, one thing to come clean on, the probability thing, the shuffling cards or getting your hat back, that's not why E is on a calculator.

It's for one of the other places where it shows up. And if it was primarily about shuffling things or probability, we probably wouldn't have it on all our calculators. And a lot of people, when they heard the thing about E, were thinking, oh, it's for exponential growth. And that's how we first discovered E was through exponential growth. Right. So way back, in the 1600s, a guy called Jacob Benoulli, who's not. Benuli of the Benuli effect. There's so many Benouli's. Benoulli effect, that was Daniel Benoulli in the 1700s. This is Jacob Benoulli in the 1600s,

who also did a bunch of calculus stuff. Jacob was wondering, hey, hypothetically, like let's say you invested some money at a hundred percent interest rate. At the end of a year, you would have doubled your money. So if you started with like $1 or whatever and you get a hundred percent interest, that means at the end of the year you've got $2. He's like, well, hang on. Banks don't just pay interest once at the end of the year. You can get it during the year. So in fact, you can get your interest paid. You could get half your interest halfway through the year and the other half at the end of the year. So you'd get 50% interest part way through and 50% at the end. But because you've got 50% halfway through, you've now got $1.50, and when you get 50% on that at the end, that's an extra

75 cents, you're now $2.25, you made more money. Or you could do interest every single month and get even more money, or you could do it every day. Or like, how far can you go? Is this an infinite money glitch? It turns out no. As you go to smaller and smaller intervals, like you split the interest up into smaller and smaller bits and collect it more often, it turns out the limit is E. You will get E times your original money in the extreme version of compound interest. So you'd get $2.70, if you're around it, I guess,

72 cents. So that was where E was first discovered was that question of what's the limit if you compound interest in, you know, incredibly small intervals? And this was the era of calculus showing up. So this is why people would think about these things. and Benulli did a bunch of probability stuff as well

it's very interesting character so Benuli came up with E in the context of exponential growth and because of that and because it's kind of like the ultimate form of exponential growth like the purest one and you can use it to get any other

interest rate like it's a really nice way to understand it using E and then you can kind of scale to whatever interest rate you're actually getting like it's like the underlying logic of growth. And it's not just interest rates. It'd be like bacteria growth,

you know, things that... Anything that increases proportional to its current size, E will explain that growth. And that it's used as a base for logarithms. So it's often... It's the natural logarithm is base E.

And that's why you get it on calculators because it's a super useful thing both in terms of growth, be it scientific, things or finance or the like, or you're doing logarithms back in the day, E was a really handy base for your logarithm. So I maintain, like a lot of people, everyone opens with that. Normally you first learn about E the way we first discovered it with interest rates, but

eight-year-olds aren't going to care about interest rates and limits and all of this. And Pye worked out well historically because we discovered it in circles and then we found all the other places. but circles are still a great starting point for learning about pie. I would argue E, even though we discovered it in interest rates first, other places it appears are way more interesting and more accessible. So I don't think we should teach it first with interest rates. I think we should teach it first with like combinatorics or probability.

I think that's a lot more fun. And so that's why I thought I would pull that out as the circles of E as to what you'd show an interested eight-year-old. So, as your proverbial eight-year-old, which I am, by the way, I would say that Phoebe and I are on the same level. You're not a bad approximation. I'm a great approximation. So I find that really useful. The idea that E is the number you would use to help calculate the chances of essentially something not happening.

The name for it, because when you rearrange something, lots of rearrangements, the case where the real arrangements, the case where the real arrangements, arrangement has nothing back where it started is called a derangement. So it's the probability of getting a derangement. That's nice. Fun, fun word. I like that. So yeah, the probability of a derangement. Now that I can wrap my head around. I'm sure there are eight-year-olds who can wrap their minds around it, although I wouldn't judge any eight-year-olds who can't. Because I turn 40 this year, and I am still just wrapping my head around it. But is there any situation where I who only tends to use my calculator for very simple arithmetic. Yep.

Like, at what point would I use an E button? You wouldn't. Oh. It's not a particularly useful. It used to be more useful when we had to use log books and doing log things as a shortcut for calculation. But calculators do that for us now. I have never used the E button on a calculator. calculator for something practical.

I've definitely done things with E and log and everything else when I'm, you know, doing physics or maths or something like something academic. And in my practical life, I've definitely used pie. I've used square roots. I've used a bunch of other stuff on the calculator. I don't think I've ever used E in anger. I'm just thinking I've definitely done a bunch of spreadsheet simulations for mortgages. And even then I didn't use E. I just worked out because banks don't compound interest constantly.

I've just used the discrete version of compound interest. So I don't think I've ever, if people out there, if you've practically used E, and don't be like, oh, I'm a cell biologist. Yeah, I know. I get that. Not in science. If anyone's practically used E in their everyday life, I would love. In something that the everyday person might use it for.

Yeah. I like your explanation for what E is, and especially like how E represents a number. I think for me that is definitely something like, okay, it's a shortcut. It saves me from having to type out a very, very long number to help me do a thing. It's a nickname. Like, I can use the letter E and the calculator knows what I'm referring to. You know, someone should make a calculator that has like one, two, E, three, five, four. All of them. Yeah. Yeah. Yeah.

Like in the, it's set out in numerical order. 1. Route 2, 2, E, 3, pi. And you'd work your way up. Oh, golden ratio would have been between root 2 and 2. So put that in there as well. If anyone's drawing this as we go, I'm sorry. It's another number that isn't a whole number. No.

And would come in handy if you were doing very specific calculation. You don't need to worry about it right now, but it might be useful to know in the future. A lot of people are like, oh, but it's useful for complex numbers and electrical engineering. And I know, I know that, but an eight-year-old, like, it doesn't help by saying, well, it's useful for complex numbers. You're just, you're raising more questions than you're answering at that point. Yeah, exactly. And this is the other thing. And as someone who writes for children, like, which is partially because I think like a child, when you're a kid,

your brain is still so spongy. And so you are learning so much constantly. Like every day you are experiencing something that you have never experienced before. And the older you get, the less that that occurs. And that's why you have to do like things like brain training or like try different hobbies or things like that. Because otherwise that plasticity starts to like solidify essentially. And so when you're taking in that much information on a daily basis, I think you're

it is really important to both appreciate where the curiosity is coming from and the wanting to understand and to not patronise by saying, just don't worry about it, which is what happened with me. I was just told to ignore it. And that was it. And at the same time, also be able to say, like, this is something that you don't necessarily need to need to know right now. but you'll start to learn enough

that it will make more sense if you need it later. But yeah, you don't want to overwhelm. No. You don't want to overwhelm a child was so much information that then they overload and they're like, well, I don't care about any of this, which is what I do. You're back out, yeah.

The fuse breaks and then I'm like, well, I'm not interested now. It's difficult to explain something like E, without referring to other concepts, the child also hasn't met yet. Because the moment you're doing interest or this or the other or whatever. Yeah, they're like, oh, what's that then? And you're like, ugh, like to be able to build it up just from things they already probably understand is a fun challenge. But yeah, even just the knowledge of it represents a number that is useful to have essentially a short handful.

Yeah. For other calculations. If, let's say Barney has a relationship with Phoebe such that it's appropriate to find them and try out the explanation, I'd love to hear how it goes. Yeah, yeah, I would too. Or get Phoebe's parents to do that. whatever works. Yeah. It's useful to know what's landing.

Oh, Phoebe knows way more than we gave Phoebe credit for. Yeah, exactly. Yeah, yeah, yeah. This is still slightly a bit too confusing. Phoebe's like, but how does that apply to my stock portfolio? I'm like, okay, fine. I misjudged. Yeah, yeah, yeah.

And then I'll email Phoebe and ask for some advice. No, love this, love the curiosity. And also really appreciate Barney wanting help to take a question seriously rather than to fob it off because it's too difficult to answer. Yeah. Well, I'm going to give it a ding from me, because that's helped me. Great. I understand a bit more about why that's there.

But if we could get a potential ding from Phoebe or Barney or Phoebe's parents, then that would be great. Anyone with access to an eight-year-old who's curious about the E? The number, the number. Next problem was sent in by PAV-Pav, who went to the problem posing page at a problemsquared.com and said in episode 134, recent. That was like two ago. Pav says Beck was talking about her teeth collection she was and mentioned in the intro banter that she is seeing someone new. What is your rule of thumb on when to disclose more unusual facts or hobbies to a new slash potential partner and where does it fall on other milestones? So e.g. going abroad to visit family. First of all, great to hear

that what we have is banter. That's fun to know. I feel like we're fulfilling the podcast requirements. Like PAB's use of calibration, because there are obviously other milestones. I don't know, every relationship's different.

Things happen at different times, but often typically in a semi-similar order. And we're going to use it to calibrate, hypothetically, if you had a hobby, such as collecting other humans, teeth, or when would you bring that up in casual conversation? Beck, you've got a unique amount of experience in this area. Yeah, well, I'm a big fan of front loading any new interaction with someone with like anything

that could put them off. Like get it out the way at the top because you don't want someone who's wasting their time. who can't handle you at your weirdest. I don't know what phrasing you'd use for this, but I use the notion of credit in the bank when I'm talking to people about public speaking or comedy or whatever. I'm like, sometimes you've got to do some good material, you've got to get some credit in the bank with the audience

before you do something different or weird or experimental or all the like. To be fair, I'm not going to go in and say, hi, I'm back, I collect human teeth, as the first thing I say to each person. I'm pretty sure I've seen you do that. I'm the world's tallest comedian. Yeah, yeah, exactly. I need you to hold my legs on for me.

Yeah. Now, yeah. What I'm saying is, like, it may not be a deal breaker if you've got a couple positive stacked up, but if you're coming in neutral and you're like, hey, by the way, I have a toilet seat stuck to my living room wall. I don't know if that would be like. The first. I'm saying it because I can see a toilet seat behind back on her living room.

Yeah, and I've done business zooms with this as my background. This is the first thing that most people see if I'm meeting them for the first time on a Zoom. Yeah, exactly. It is relevant and appropriate for your business, your career. So yeah, you're right. You are a, let's get the speed bumps up first kind of person. Yeah, yeah, exactly. I appreciate that like there are scenarios where,

it might be unprofessional to start something that way. Right. And I suppose, all right, here's the thing. Okay, it's not necessarily that I would lead with saying I collect human teeth, but the way I present myself, if I am to say it, by the time that someone hears it, they're in no way surprised. Oh, yeah, it checks out. Yeah, yeah, that's it.

So I, and I think I like to think that I'm pretty upfront with like the type of person I am right at the top as much as I can. I can corroborate that. Yeah. Yeah. And if it's someone who I think that I can't say that to, like if I was meeting someone and considering being in a relationship with them and I felt that I couldn't tell them that part, if I was after like a serious or like some level of romantic relationship with someone, then I would be like,

okay, I'm noticing that I'm feeling self-conscious about talking about this. And I don't want to be with someone who I feel self-conscious around. Yeah, it's more of an insight. It's a raw shark test into your own subconscious. Yes, yeah. The person I'm seeing at the moment has a jar of some of their extracted teeth in their bathroom on a shelf. Right. And I noticed it when I used their bathroom and I came out of their bathroom.

This was quite early on. And I said, are those your teeth? Yeah. And he went, yeah. And I went, can I buy them? and he went, what? And I think he was embarrassed that I'd noticed that, because he just sort of didn't know what to do with them

and had just had them sitting there. So I think he was embarrassed. I'd noticed them. And then very quickly went from feeling embarrassed to feeling like, oh, okay. And actually, he's, he, later I said, are you scared of selling your teeth to me in case we break up? And then I've got your teeth. And he was like, yeah.

And I was like, that's, fair. That's a really fair reason to not sell me your teeth. It's always the teeth would get hurt. Weirdly, it's less weird to own like strangers' teeth than it is to own teeth of like non-blood relatives. Just staying together for the teeth. Yeah, yeah. You don't want to have to hand the back at the end. That's weird.

Yeah, that's a weird hand. He's your teeth back. Leaving out on the front lawn. Get out. Yeah. But it has got me in trouble in some. Not so much with that, but there are certain personal aspects of my life where I assumed family members would be absolutely fine with it. And then, you know, ended up making jokes because I'm a very open person.

I talk about stuff on stage again because I'm like, well, this is me. and if they don't like it, they don't have to come. There's a lot of comedians out there. They don't have to see me if I'm not their piece of cake. And then it's turned out that those family members felt very uncomfortable with the fact that I was talking about those things on stage. They're personal things. I wasn't talking about other people.

They're my own things. Yeah, you're not talking about the family members. No, no, no, no, no. It's all related to me. You're talking about you. Yeah. Yeah. But even then that struck up conversations that I probably needed to have with those family members.

And, you know, it ended up, that we're much closer for it in the end. But I do think it is worth, like, being open and honest with people. Do you have any strange things that you were unsure about telling Lucy? No, I don't think so. I mean, in a similar vein, like, when we first met, she already knew that I had a watch that told the time in binary. Like, that was our origin story.

This is what I mean. I think sometimes the weird things are sometimes the things that actually help you, bond with someone as opposed to something you should hold off from them. Yeah. I think I still not drip fit. Like I don't want to overwhelm someone as well. Like you need to give people processing time per thing. Yeah.

And yeah. So I think I'd probably stagger things a bit more than you, but not in a, I'm nervous about telling them a thing, but more they need processing time per thing. And that's the whole point of a relationship, right? you discover about the other person to learn about them. When I met Lucy, I didn't make my own salt or ride bikes or working comedy or, you know, all these other things.

So, you know, there's a lot of stuff I didn't even know as I was hiding from her until after the fact. I was hiding them from me. But they're things that, again, it's that similar thing, isn't it? It tracks. Like, they're not surprising. None of them were off brand. Yeah. Yeah.

And I think that's the thing. if you're the type of person to indulge in those sorts of things and they're already aware that you're that type of person, anything that you either reveal or later on decide you want to do or something isn't necessarily going to come as a big surprise to them because it's on brand. Be true to yourself. Yeah. And in terms of other milestones, that's a tricky one. It's a tricky one when you introduce them to family members or go on a... Oh. Travel abroad or that sort of thing.

The trick is to keep your family in a different hemisphere. Yeah. Weirdly, I had met my partner's mother when he and I were just friends. Ah. Oh, that's one way to do it. She doesn't live in London and she was popping by his place and he was like, oh, my, my mum's coming over. And I was like, oh, okay. And so I got to meet his mom.

She's lovely. Really like her. And then found out via his brother later that apparently his mom was giving her approval of this woman that he had over at his place. And he had to say, oh, we're, I mean, it's not okay. Well, she was right. So I knew I had the approval before we went into anything, which is nice. Great. Yeah.

I mean, that's handy to have as well. So, I don't know. I think those things are a lot more. That depends on the nature of the relationship and the person. For some people, might be quite quick. For others, they might not feel comfortable. You know, I think the introduction to the family, once in a partner, as a partner, is something that does tend to step it up because,

then if things end, it's some people that you need to tell. Yeah. So the conclusion, and correct me if I've got this wrong, is tell them about the teeth very early on. Yeah. But don't actually buy their teeth until much later. I don't think there's a world where that would be a great idea. Don't put your money Where your partner's mouth is Got it, okay

Yeah Let's catch you Yeah, nice Path I don't know if it's appropriate to report back But whatever's happening in your life Would love to hear about it

Yes Yeah I would love to hear a bit more context As to why you needed to know this information Now on to any other business Also known as Allergy Of blocked noses

So in this section, we go back and respond to previous problems or things that people sent in regarding episodes that we have done before. And we've got a bunch of dings. Yeah, we are downtown in Dingsville this time. Yeah, we've got a whole bunch of things that we solved in the past. We asked people to let us know if they ding it. And now we've got a bunch to catch you up on. So, Matt, would you like to take us away? Absolutely. The first one was from someone named Matt. Great name. They want a ding.

Us solving their icy snack problem from episode 117. They say even though we didn't ask for it, they're going to go ahead and ding it anyway. Matt, we always enjoy a dinging. This was the ice-lolly problem where Matt asked us to find the name of the shape. Matt says they enjoyed learning that it's called a disfanoid. And they want to be the first to see a person. suggest a more household-friendly name, the frism, as in your frisom. Your Friesom, the Frism. Matt, I'm going to put that on the table as an option. No promises. I love Frism. I'm all for it. I've taken it on. You would. Yeah, yeah, I do. I like it. Thanks, Matt. I'm going to give you a ding for that. We also heard from Stu and then in brackets from Stu and Angus. Ah, the famous stew.

Stu says it was to do with our episode about Pythagral Dimensions. They said, that's a ding in all dimensions. We're on the way home from the night away and saw the episode titled Pythagral Dimensions. Immediately I said to Gus, as in Angus, that sounds like it could be ours. We resisted the urge to fast forward and the patience was truly rewarded. Good work. Well done. So this was to do with the hypotenuse being.

A squared plus B squared equal C squared and then does it go up a power when you go into another dimension? In higher dimensions. Yeah, and the space diagonal does Pythagoras does work in higher dimensions. Yes. As does the ding given to us by Stu from Stu and Gus. Yeah. He says it's nice to know that sometimes what seems like a pattern actually is a pattern

and doesn't go off in some weird tangent as it goes through. We hope you both bring shows to Melbourne and or Geelong at some stage. You know there is a salt, like a salt factory in Geelong, like a salt. refinery. Oh really? And in the meantime, keep up the great work. We will. Thanks again from the Coldwell family. You're welcome. Jethro says hi, Beck and Matt. Thank you for investigating and solving my microwave conundrum. Ah, this is what we were talking about microwaves, how they work. And Beck brought

all the answers. So, Jethro has recreated some of the experiments you talked about in that episode. They say they use thinly sliced stale bread and they can confirm a similar result to Beck's Mum's microwave. This is like laying the pattern out to see where the hotspots form. They then did attempt, as you suggested, to make a 3D map with a lattice of marshmallows on cocktail sticks, but the result was a collapsed, gooey, pointy mess. I see they didn't say delicious in that sentence.

interesting. So their experimental method needs some work. That's their words, not mine. And so anyway, they would like us to please accept this ding, which is vastly inferior to Beck's mum's microwave's ding. And their gratitude. Oh, and there's a link to a SoundCloud. Oh, they've got a ding from their microwave.

That's great. So here it is. We're going to play it in. This is the ding from Jethro's microwave. That is a terrible ding. I mean, thanks, Jethro, but look. And quite pleasingly, both, Both the Pythagoreal dimensions and the microwave conundrum were from the same episode.

That was 131. Fully dinged. Yes. I love a total dingage. Love a ding sweep. We also heard from Josh, we're going to the Jays now, who says, ding! I ask the egg-shaped question, which was from episode 133, and later remembered the word ovoid and figured that question wouldn't be worth podcast content.

Could have saves a lot of work there, Josh. Also, that does say a lot about the sorts of questions that I decide to answer. Once they could just be remembered. Yeah. But then Josh says your answer could not have been more satisfying. The etymology nerd enjoyed the now obvious fact that Oval and Ovoid come from the word for egg. Truly a satisfying answer. Thanks.

Ah, and finally, you have to blow the dust off this one. It's an ancient ding. The biggest delay between the... solving a problem and receiving the ding. This is from someone. They put their name in as user bin Pearl. It's a UNIX programming joke, as they point out. And they say, hi, Beck and Matt.

Listening to some of your recent podcasts, I realized that I never gave you a ding for previously answering my problem. And then they point out in their defense, the whole concept of dinging wasn't about at that point in the podcast history. Good point. We brought dinging in. I forget when, but it was a little way in. But user Bin Perl, their problem, we solved in episode zero, zero one.

Yeah. The first episode. Wow. The refrigeration question about how efficient fridges are. Why, that was the first episode? Refrigeration. Just the other day, I was thinking, because I did an analysis of, if you were to buy a new fridge,

how long would it take to like save the money it cost you to buy the fridge on the efficiency savings of having a new fridge? And this would have been back late 2019. Goodness. So given it's now, wait, where are we now? Oh goodness, like six and a half years later? We've had more fridge development. I saw a conversation about fridges online the other day,

about buying a new one or keeping the old one. And I was like, I thought I settled that. Oh, wait, seven years ago. So there's probably another generation of fridges. So if there's demand, let me know people. I can dust off the spreadsheet from episode one. I mean, I'm definitely a buy-up for life

a kind of repair things kind of guy. But fridges are an interesting edge case because new ones are so much more efficient that I think it outweighs trying to repair older ones. So there you are. Anyway, as agreed from old Yuzabin Pearl, who's now offering us a ding, a ding on them. Love the show. Blah, blah, blah. I love this. Thanks, user bin, Pearl.

And as we come to the end of this sunny, flowery episode, I'm trying to stay on brand. You're succeeding. Like you would offer a bunch of flowers to someone who has done something kind. we would like to offer our thanks to our Patreon supporters, of which you can become one too. Go to patreon.com forward slash a problem squared. You get a bunch of bonus stuff for being a Patreon supporter. And one of the things you get is the chance to have a special little mention at the end of each episode.

We will choose three Patreon supporters at random to mispronounce their names at the end of every episode. And on this episode, those Patreon supporters are... E.V. Ant. Uh, why? Gar. Rear. Thur. My char.

Elk rock. Thank you very much to all of you and to the other Patreon supporters as well as our listeners. Of whatever support you offer, it could be financial. It could just be the fact that you live. listen. It could be emotional. It could be emotional support. It could be technical support. We appreciate all of your support, but especially I appreciate the support of my co-host, Matt Parker. Hey, that's me. I'm Beck Hill, and I'd especially like to thank the person who puts the spring in our step. That'll do our producer, Laura Grimshaw. But bye for now. Bye. Now, I believe it's my turn on the

Connect Four. It's Connect Four over the internet. This is the thing. theme for Internet Connect4. Oh, okay. Now, last time, Beck, you went far right. Yes. And Laura's now holding up Connect4 the other way around. So it's from my point of view. Now, if, I'm not saying this is what I've been doing the whole time, but hypothetically,

given it's flipped, and if I want to always do the mirror image of what you just did, I'm also going to have to go far right. Ooh. Yeah, look at that. Oh, the free market has spoken.