Episode 3: Mag Matter

Saul: Hello and welcome to Mag World, where we like to ask big questions, make wild guesstimates, and quantify literally everything on a magnitude scale.

If you want to learn more about Mag World, come visit our website at magworld.pw. I’m Saul Pwanson, your guide to Mag World, and I’m here with my friend Mike, who’s… been around.

Saul: Today’s episode is Mag Matter, where we’ll be talking about matter: stuff.

Mag Matter

Saul: So how do we measure matter? So the main scale, want to guess what the main scale we measure matter in is?

Mike: I would guess mass, kilograms, pounds.

Saul: That’s right. Mass. Uh, kilograms is the base unit for mass. So for instance, how much mass do you have Mike? In Mag World.

Mike: In Mag World? I, uh, I’m doing quick math here. [Mm-hmm.] So I’d say I’m about a mag one, mag two. Mag two.

Saul: So yes, mag two, in fact, all adults, virtually all adults are mag two kilograms of mass.

Mike: That makes sense.

Saul: So what’s neat about mass is that you can divide it up, you can divide it up into smaller bits, and then you can divide those into smaller bits. You can do this again and again and again. Is there any limit to how far you can divide up mass?

Mike: Well, I’ve taken physics in high school. And yeah, ’cause you get down to the atoms and, or the constituent parts of Atoms. I know that you can’t go all the way down.

Saul: So yes, atoms, there is, there are smallest amounts of matter.

Saul: We know now that atoms are differentiated based on their element number and their atomic mass. So we have different elements, different things that are different kinds of atoms.

Saul: Let’s talk about the smallest atom. A Hydrogen atom is generally a single proton–

Mike: A mass of one.

Saul: And it has, so it’s hard to say a mass of one because if you’re thinking in kilograms, clearly a proton doesn’t have, isn’t a kilogram right. But it has an atomic mass of one. And that is measured in a unit called Daltons. And John Dalton is the person in the modern era who introduced the concept of atomic theory into chemistry. And so it is called one Dalton, and it is in fact mag negative 27 kilograms.

Mike: Ooh, that’s tiny.

Saul: Very small.

Saul: And then the mass of a proton is mag negative 27 kilograms.

Saul: So just to establish the scale, so we’ve got mag negative 27 kilograms for the mass of a proton, which is, like you said, one Dalton. And the Earth has mag 25 mass and the sun has mag 30 mass. [And the entire universe has mag 53 mass. So that’s where our scale goes from negative 27, mag negative 27 to mag 53 in the entire universe.]

The Fermi Problem (Quiz Show)

Saul: So are you ready to play a game?

Mike: Oh, boy. Please keep it between…

Saul: This is a little quiz show. I’m calling it the “Fermi Problem” after Fermi estimations. So this, the challenge here is to estimate something, estimate these numbers without any additional information, just using your common mag sense. And so don’t worry about getting it exactly right, of, I mean, what you’re trying for is to get it within an order of magnitude in Mag World. And um, feel free to talk through your answers or your thinking process. [Mm-hmm.] And if you get it, uh, if you get it right, you’ll get a point. And if you get it wrong, we’ll talk about it and we’ll try to–

Mike: Motivate me, Saul.

Saul: Okay. Let’s do it. Yeah. You–

Mike: What do I win?

Saul: Well, number of points is…

Mike: I want listener comments.

Saul: Oh. Oh, I see. Okay. Yeah, people, please, if you think of something that I can do for Mike, given all the answers he’s going to get. Right. We’ll see then, uh, yes, I would love to hear those.

Mike: All right, now I’d better get at least one right.

Saul: Okay. Well, the first one’s pretty easy. I hope I, I shouldn’t set you up like that. Let’s find out. Okay, so the first one here, how many types of atoms are there in Mag World, like on, on a mag scale?

Mike: Types of atoms? [Yep.] Uh, there are mag two variety of atoms.

Saul: Mag two. That’s right. We can distinguish between atoms by their element. Mm-hmm. Or by their isotope. And so they could have some, it’s actually 92 natural elements. Then a handful of other ones that are man-made and we have some few hundred different isotopes of those 92 elements that are differing in mass but had the exact same chemical nature. Mike: That’s right. Mag two. Very nice. Okay.

Saul: So now let’s talk about those Mag zero, mag one and mag two types of atoms, right? Mm-hmm. So can you name a mag zero element or mag zero Dalton element besides hydrogen.

Mike: Uh, hydrogen. Helium.

Saul: Helium. Very good. Yeah.

[5m]

Mike: ..would be the next largest or next most massive.

Saul: Exactly. Helium. Good job. So now you have two points. You’re doing great, Mike. Great. Yeah. You’re gonna cruise right through this. Okay. So next, are you familiar with copper, silver, and gold?

Mike: Uh, yes.

Saul: What are, are those Mag zero, mag one or mag two elements for each?

Mike: Ooh…so are we talking about mass or atomic number?

Saul: Great question. Um, we’re gonna talk about mass.

Mike: Mass. So the number of protons and neutrons, not the atomic number, which is just the number of protons.

Saul: Right, exactly.

Mike: Okay. So copper is mag one. [Okay.] Because it is an atomic weight of over 10. Silver is mag one and gold is mag two.

Saul: Okay. That’s a good, good answer or good thinking about it. So you’re right that copper is mag one. Mm-hmm. Silver is mag two…

Mike: Is it?

Saul: Yep, I’m looking at the, at the periodic table right here. Silver is 108. Uh, mass. Yeah, just over. And gold is 196 mass [Mike: Mm-hmm.] So you’re right about gold, but wrong about silver. Silver’s also a mag two element. Okay. We’ll give you a, we’ll give you a half a point for that.

Mike: Two thirds of a point, Saul.

Saul: you want, you want two thirds of a point. Okay, fine. Two thirds of a point.

Saul: Okay. So let’s try some more advanced questions. Are you ready for this?

Mike: Yeah, I’m killing it!

Saul: You like copper, silver, and gold, right? How much copper, silver, and gold is mined each year in Mag World?

Mike: Oh my, uh, in kilograms?

Saul: In kilograms.

Mike: In How much is mined each year? Yeah. Well, gosh.

Saul: It’s more than zero.

Mike: More than zero. So. First, I’m going to say in a relative sense [Saul: mm-hmm.] Copper is going to be more, uh, abundant than silver, which is going to be more abundant than gold mining, in terms of how much we’re mining.

Saul: Do you have an idea of how much more abundant or uh, how much more we’re mining of each of those?

Mike: I don’t, so there’s two ways that I could think about this. One is value. Mm-hmm. Which is copper is expensive enough for people to steal out of abandoned homes, but cheap enough that you’re gonna throw away a pan, you’re not gonna melt it down and turn it into another pan. Whereas gold is very valuable. Mm-hmm. You never throw it out. You always remelt it into something new.

Saul: And in fact, uh, jewelers have a carpet underneath their station that collects gold dust and every few years they send that off to a place to recover the gold dust.

Mike: And there’s enough to make that–

Saul: Yeah, totally. There is.

Mike: Mm-hmm. Yeah. And I don’t see chefs holding, I don’t know, copper pieces or anything from, from their copper pots and pans. It’s, yeah, it’s not super rare. And then silver, I presume, is in between. Yeah. Yep. [Saul: Yep.] And per ounce, I have no idea what the exact price would be. Okay.

Saul: Okay. do you have an an order of magnitude idea?

Mike: Order of magnitude?

Saul: And to be clear, for this question, we’re only talking about how much kilograms of each is mined

Mike: Each year.

Saul: Each year.

Mike: I’m thinking back to an image I saw on the internet where there was a superimposed. Square showing the volume of all gold ever produced in the world.

Mike: I’m going to guess that mag three kilograms of gold are mined each year.

Saul: Mag three kilograms of gold, so that’s about a ton of gold each year. [Mike: Mm-hmm.] Okay.

Mike: A ton of gold.

Saul: Is that what you’re sticking with?

Mike: No. Okay. Because I’m trying to think about, [Saul: mm-hmm.] I’m stuck thinking about ounces versus [Saul: mm-hmm.] Kilograms, because I think of gold prices as in ounces. That’s right. 16 ounces to a pound. 2.2 pounds so we’re like 32…

Saul: So just order of magnitude. How many ounces are in a Kilogram?

Mike: ounces in a kilogram…There are mag one.

Saul: mag one, mag one.

Mike: Mag One. Mag One and a half?

Saul: Yeah, exactly.

Mike: Mag one and a half and ounces of gold in a kilogram. Mm-hmm. And let’s say gold is $200 an ounce.

Saul: You’re off by an order of magnitude.

Mike: $2,000?

Saul: $4,000 these days.

Mike: $4,000. Gosh.

Saul: Yeah, that, that’s zoomed up over the past couple of years, but yeah.

Mike: Okay. So mag 3 dollars per ounce. And that’s mag 1.5. So that’s mag 4.5. And then you said 4,000, not 1000. So add another half, let’s say. So mag 5 dollars per kilogram.

[10m]

Saul: That’s right.

Mike: And how many dollars worth of gold [Oh, okay.] are produced every year?

Saul: So you’re gonna go backwards from the amount of money that the gold produced–

Mike: Mm-hmm. Yeah. Because multimillion dollar companies mine gold. [Yeah.] But I don’t think multi-billion dollar companies would mine just gold. So we were at mag five per kilogram, a million is mag 6…If a hundred million dollars worth of gold was produced each year, that’s mag 8 dollars, and it’s mag five per kilogram. Mag eight divided by mag five is eight minus three is mag three. And that was my original guess. Okay. So, okay. I guess I worked my way back into mag three is produced a year.

Saul: This is great. So you’re way off. [Mike: *laughs*] But let’s talk about this.

Fermi Estimation Method

Saul: So this is a, this is the Fermi estimation method. And so what you wanna do is you wanna pick the range of magnitudes, right? It’s like you picked a good, a good answer. You were like, oh, I think it might be like on the order of hundreds of millions of dollars. But you wanna pick a low number and a high number in terms of magnitude. And so you think that the low number is hundreds of millions of dollars, uh, of mine each year. And the high number is what could it possibly? Like what’s the, what’s the highest amount of gold you think could be mined each year?

Mike: Uh, I’d say in the billions. Like Mag nine.

Saul: Mag nine?

Mike: Yeah.

Saul: Do you think it could be tens of billions?

Mike: I don’t know. Is our podcast sponsored by a gold company? Possibly.

Saul: Okay. Do you think it could be hundreds of billions? Okay. So you’re gonna say not hundreds of billions, maybe. Tens of billions. And then on the low side, do you think it could be less than a hundred million? [Yes] Okay. Do you think it could be 10 million.

Mike: 50 million.

Saul: 50 million.

Mike: Yeah. 10 to 50 million

Saul: So, between 10 million and a 100 billion, uh, tens of billions of dollars. Okay, so mag 10 versus mag seven. And so what you do then is you take those, that’s a huge range. It’s over a thousand. But in Mag World, there’s just three levels. And so what you wind up doing is you take the, the, it’s called the geometric mean, you average those two numbers, but when you average those numbers, you get, like I said, the geometric mean, which is, um, doing a different thing. So you’re getting the mag between them. So for instance, mag 7 and mag 10, that would be mag uh, eight and a half is halfway between those two. And so the geometric mean of those two is about about $300 million, which is what you were saying actually. Yeah. So, um, what’s interesting about this..yeah?

Mike: But I must have been wrong in some of my assumptions.

Saul: Yes. You were wrong on how much, I mean, basically your high number is right. [Mike: Oh.] It is tens of billions of dollars a year. The amount of gold mined every year is 2,800 tons of gold. Every year [Mike: (wow)] So that’s 2.8 million kilograms. That’s mag six and a half mined each year.

Back to Quiz Game

Saul: So, let’s talk about silver then. So, if gold is being mined 2,800 tons a year, how much silver is mined every year? [Mike: Uh,] We can just speak relatively too. Is it, is it, [Mike: it’s] it’s more you said, right?

Mike: Yeah. It’s a hundred times more.

Saul: A hundred times more. And what are you basing that on?

Mike: Uh, value of gold versus silver.

Saul: Okay. And you’re right, the value of gold versus the value of silver about a hundred times. I’m gonna tell you right now, you’re wrong on that. It is actually…

Mike: God, I was doing so well on the easy questions.

Saul: It’s true you were, but that’s okay. I mean, I’m curious to see what, uh, maybe it’s..

Mike: So if I’m telling you my thought process, my thought process was, well, the value of silver is like a hundred times less. So why, if demand causes the price, then that would make sense, right?

Saul: Yeah, that does, it would make sense. I have an actual answer for why that’s not the case.

Saul: Silver is an industrial metal. It is used, it is used for actual purpose, whereas gold is a value metal and it is hoarded. So it was artificially held high by the, that there’s only so much..

Mike: Saul are you telling me that the answer really is podcast ads? [Saul: Yeah.] The people telling us to hoard gold are the reason that gold prices are…

[15m]

Saul: Well, people haven’t started hoarding gold this century. This has been going on for a while. [Yeah.] I mean, dragons have been hoarding gold for millennia, right? But, yeah, the fact that gold is so precious and that people put stock in that, means that the price of gold is higher than if it were just being used, like silver is being used. We use, you know, those little bang snaps that you, uh, throw on the ground, make a…

Mike: Oh yeah. Uhhuh.

Saul: Yeah. That’s silver nitrate. They actually are using silver to make those things. Just little, little amounts, but that’s silver you’re never gonna see again.

Mike: Oh, wow, the little box, 50 cent box

Saul: They’re a buck now, but yeah, exactly. [Nice.] Yeah.

Saul: Okay, let’s talk about copper just to get the job done here. So, if we, so it’s 25,000 tons of silver are mined every year. How much copper is mined every year compared to silver and gold?

Mike: Compared to silver? [Saul: Mm-hmm.]

Mike: So my gut said that gold to silver was about a hundred times. [Saul: Yep.] And my gut is saying it’s another mag four difference.

Saul: So you think there’s 10,000 times more copper being mined than silver?

Mike: I’m trying to think about what the uses of, because silver is still valuable.

Saul: Mm-hmm. If you got a, a silver coin, you’d be like, oh, well that’s a silver coin. I’m gonna hold onto that.

Mike: Yeah. And I’ve definitely thrown out

Saul: copper coins or copper, something

Mike: Putting in penny terms, I think I’m gonna revise from 10,000 to a thousand, 1000 times more copper than silver.

Saul: Okay. Final answer? [Mike: Final.] Okay. Well you did great on that one. You’re right, it is about 20 million tons of copper are mined each year. Good job. So we’ll give you, uh, a third of an answer on that or point on that one. So between the two thirds of a point from the previous one and this one, you’ve got another point. So this is…

Mike: You can’t give me a half point on this?

Saul: I can give you a half point on this if we give you a half point on the other one. [Sure.] They’re gonna be the same thing, but, okay. Okay. That’s great! Nice job. So now, given all that, now we’re gonna talk about the total value of all gold mined ever. And we’re gonna do the same thing for silver and copper. [Mike: Oh.]

Saul: So how much of all the gold that’s ever been mined? Well, yeah. How much is that all worth if you’ve got it all in one place?

Mike: What’s the total value of all gold ever mined? So we already talked about how total value mined last year was mag 11. [Saul: Mm-hmm.] So I can add a few of those years together, but as you mentioned, it’s also been mined for eons.

Saul: Yeah. But it hasn’t been mined at the same degree.

Mike: Yes. Mm-hmm.

Saul: Like the number just keeps going up. So we mined more gold last year than we did a hundred years ago, for sure.

Mike: Mm-hmm. And so I’ve gotta think about a, a curve going back thousands of years.

Saul: So the great thing is that you can do that if you want, but you don’t have to because all those earlier years are going to be dwarfed by the current years.

Mike: Oh yeah. All the years of BC up to zero probably might equal a single year now

Saul: might, might not even, but here’s the thing. If half of the gold that’s ever been mined has been mined in the last, let’s say a hundred years, and I think it’s actually more than that, but let’s just say it’s half? Then you can basically only count the last hundred years and everything before that is a minor factor in Mag World. So. [Mike: Mm-hmm.] You don’t even have to, you mean obviously it’s more than one year’s worth, but you don’t have to like do any fancy calculus. You can just kind of eyeball it, spitball it.

Mike: Mm-hmm. Well, so let’s go with the past hundred years, mag 2 years.

Saul: Okay. Yeah.

Mike: If we just flatten everything out, say we’ve had a hundred years at mag 11 production. [Saul: Mm-hmm.] That’s mag 13 dollars, ever. [Saul: Okay.] And I think mag Thirteen’s gonna get us close.

Saul: Mag 13, is that your final answer?

Mike: It is.

Saul: The actual answer is $26 trillion of gold, and that is mag 13 and some. So nice job. That’s exactly right.

Mike: Thank you for helping me through that estimation.

Saul: I’ll still get you a third of a point. But now we gotta do silver similarly. Now, here’s the trick. There’s more silver, but it’s worth less. So you gotta take both factors into account, right?

Mike: Yes. And so, if I recall correctly, we had mag 8 kilograms annually for silver. Is that correct?

Saul: It is 25,000 tons, which is 25 million kilograms, which is mag seven and a half.

Mike: Mm-hmm. Yep. So are you asking for weight or value?

Saul: Value. Dollar Value. [Mike: value.] Yep. this is where, like you said, silver is worth a hundred. I’m sorry. It’s a hundred times less valuable than gold.

[20m]

Mike: Yeah. So the value of silver is mag three…

Saul: Uh, per kilogram, is that what you’re saying? Mag three per kilogram?

Mike: Yeah. And so we’re still talking about annually. Almost mag 11, about the same value.

Saul: Silver as gold. Wow. You’re right.

Mike: Right, So if we’re talking about the same value, I’m going to do the same math and say, mag 13 is the value.

Saul: Interesting. Well, the number that I have here. Is that there is 10 times more silver in the world, 1.7 million tons. But the value that I have written down here is two and a half trillion dollars worth, which is a 10th of the price of gold. Now this may be that my math was wrong, ’cause as I’m thinking through it, it sounds like you’re thinking right about it. So I’ll have to go back and revisit why my math is an order of magnitude off of yours.

Mike: I mean, also, I dropped a half mag for just for ease of talking about it.

Saul: Mm. And maybe there’s two half mags got dropped. Mm-hmm. And so that was what…

Mike: Yeah, because really it’s a mag 10 and a half value. [Saul: Right] So each order of magnitude is pretty big, but when talking about value of, a value of a good..

Saul: That will add up.

Mike: And so instead of doing math, I’m just gonna drop another half mag from that mag 10 and a half from silver and say, mag 10 copper is mined annually. And so mag 12 is the value of all copper mined ever.

Saul: Mag 12 would be a trillion dollars. That’s actually pretty close. It’s seven and a half trillion dollars have ever been mined. Mm-hmm. At today’s prices anyway. So it’s..

Mike: I’m within a order of magnitude.

Saul: You’re within an order magnitude.

Saul: So, good job. I, I think we give you a full point for that, that question.

Mike: I’m up to five..

Saul: up to four at this point.

Mike: I’m gonna have to listen back. Okay. I’m pretty sure we’re at six. Okay. It’s within order of magnitude. And from everything you’ve told me this episode, that’s close enough.

Saul: Okay, well, we’ll give you mag one points overall. Mag zero points overall. Good job, Mike. You’re doing great.

And so that’s this episode of the Fermi Problem. Thank you Mike for playing and we’ll let you know your prizes later.

Abundance

Saul: So let’s talk about some more scales here. [Mike: Yes.]

Saul: So I wanna talk about abundance in the world. [Mike: Mm-hmm.] So as we were saying, there’s a wide variety of abundances, like, you know, gold is, um, much more, much less abundant than silver, which is much less abundant than copper, et cetera. So what do you think, and this is, this is not in the framework of this quiz show anymore.

Saul: I’m gonna take you off the hot seat, but what do you think is the most common element in the earth’s crust? Well, first let’s take a step back. What’s the most common element in the universe?

Mike: Hydrogen.

Saul: Hydrogen, okay. Is that like, is like mostly hydrogen or is it just like a little bit more than everything else? What do you think the answer is?

Mike: I think it’s all hydrogen. And then there’s probably some other stuff, but..

Saul: Like trace elements of everything else.

Mike: Yeah. We are trace elements.

Saul: So, you’re real close. It turns out that, um, what was made at the start, at the Big Bang was hydrogen, but also helium. It was 75% hydrogen and 25% helium and some other trace elements, basically lithium. And then everything else has been made within, within the sun. Or when a sun goes nova. And in fact, thinking of mag masses? There’s mag, like I said, mag zero mass, mag one mass, and mag two mass elements? Mag zero mass things were made in the big bang mag. Mag one mass things are made in nucleosynthesis, which is when the suns burn hydrogen and helium to make other things. And mag two mass things are all produced in a supernova explosion. Like they’re basically condensed after that. And there’s a, there’s a midpoint, there’s a point right at the cusp there. It’s actually iron-56, which is the most stable. Both things that come from, that are being built up to iron-56. And they are, they are fissile or fission down or decay down to iron-56.

Mike: Mm-hmm. Iron 56 being…

Saul: The isotope of iron, which is atomic number 26, that has, is, um, the most stable.

Saul: So that was in the universe.

Mike: in the universe. yes.

Saul: On the planet slash in the earth’s crust, what’s the most common element?

Mike: Ooh. In the crust. Yeah. So the crust be, and the part we interact with, we’re not talking about our molten core of iron? Nickel?

[25m]

Saul: Yeah. And we have some ideas about that, but it’s, it’s a lot easier to, to know what’s in the crust. And it’s what we can get to. and actually in the, even in within the crust, there’s, it goes miles down. We’re not even to the bottom of the crust at all in terms of what we can mine. So there’s the upper crust that we can actually get to, but let’s just talk about in the crust in general. What do you think?

Mike: My guess is silicon. Yeah.

Saul: Really? Why would you guess that?

Mike: Because that’s sand. And there’s a lot of sand.

Saul: Mm-hmm. It’s true. I, uh, there’s a lot of rock too.

Mike: Yeah. But a lot of rock is silica.

Saul: Yeah. No, it’s funny. Um, you are exactly, well, yeah, you are correct.

Mike: Oh! Hah!

Saul: There is the oxygen is one, is more than silicon, but silicon is number two. And actually silicon is so prevalent that basically everything’s measured relative to silicon. In all my little abundance things, it’s basically per, um, million kilograms of silicon, how many kilograms are there of whatever, in the crust.

Saul: Yeah. And I did not guess that. I would’ve, I mean, oxygen makes sense. Some people would have said carbon, for instance, right?

Mike: Does oxygen make sense? It doesn’t make intuitive sense to me unless I think about geology, which,

Saul: Well, that’s the key.

Mike: Oxygen is all bound up with other elements to make the rocks.

Saul: And that’s how it works. And oxygen is a very common element to be produced in the sun. It actually is one of the more stable elements around that early zone there. And yes, then it becomes bound up in the rocks and it’s, so, it’s not that you, you don’t have oxygen, the gas hanging out. It’s all chemically involved. But yes, oxygen is the most common element in the earth’s crust and silicon is the second most. And it’s, it’s pretty close.

Mike: Yeah. Great.

Saul: Okay, so let’s talk about abundance in general here. If oxygen and silicon are–and I was tracking this–I’ve seen this done numerous different ways in the research I was doing. And so sometimes it is, versus silicon being, and basically it’s mag six, they just peg silicon to mag six and they kind of name everything else around that. Or another one I’ve seen is the mass fraction. So you see that, if you’ve got so much mass, you’ve got like a, a ton of stuff and it’s a random sample of the earth’s crust, what fraction of that is each of these things? And so it’s all below zero, but that gets, that means that mag zero is everything. And then mag negative one, uh, would be, actually, I think it’s doing less than that, is oxygen and silicon, et cetera. I prefer, this is the method, this is my own scale that I made up–and of course all these scales, they are just simply shifting, right? Like if it’s mag six is silicon or mag zero is silicon or whatever, you just kind of add six or subtract six.

abundance gold standard

Saul: So, but I think we should peg mag zero to be gold. How prevalent is gold? And that should be just be mag zero because we all know gold. Gold is a certain, known rarity, known preciousness to it? It’s, it’s almost like the most human element in a certain sense. That’s my contention anyway. And so in my numbers here, I’ve pegged it to be gold is mag zero. So how high do you think oxygen is, or silicon is compared to gold? How much more silicon is there in the earth’s crust in Mag World?

Mike: Okay, so let me make sure I understand. So you’re saying that for this conversation we’re just gonna count everything in relation to gold?

Mike: So. what’s the abundance of oxygen and silicon in the crust

Saul: compared to gold?

Mike: Compared to gold.

Saul: we already know the copper is Mag four

Mike: We know that mag four is copper.

Saul: 10,000 times more prevalent than gold.

Mike: I’m going to estimate that aluminum is therefore mag six, iron is mag eight and..

Saul: yeah, you’re real close. Aluminum is mag seven, but so is iron. Aluminum and iron are, are very both incredibly common. Aluminum is one of the most common elements in the earth’s crust also. Hmm. And uh, yeah, it’s, people are like, well why does it cost so much then? And it’s because it’s so energy intensive to extract from the ore. Like this is why recycling aluminum is actually so important. It’s because there’s plenty of aluminum around, but you gotta like put so much energy into extracting, it becomes easier just to throw a can in there and do it like that.

Mike: Yeah. That’s why there was the Iron Age, but never an Aluminum Age. You could just heat, heat up a few rocks and you get your iron out. But

Saul: That’s a good point. Yeah. We’re in the Aluminum Age now. Not quite, but [Mike: Yeah.]

Saul: This is the scale, it goes: mag eight is oxygen, down to mag zero for gold and platinum. And let’s just talk briefly about the ones below that are even less common than gold. You know, it’s all the Rs, the rhenium, the rhodium, the ruthenium, those are mag negative one. And you’ve got krypton and xenon. Those like really exotic gases, the noble gases, those are mag negative two. And you’ve got radon at mag negative 10. ’cause it’s a only, only comes from decay from another element and then it’s radioactive itself.

[30m]

So. That is the natural abundance of those elements, right? That’s one scale. We talked about the abundance. How about the price of elements? We talked about that earlier with regard to gold, right? And silver and how silver is worth a hundred times less than gold. [Mike: Mm-hmm.] So if we were to talk about the price per kilogram of these things, you already said that gold was mag five, right? [Mike: Mm-hmm.] Then the there is also, uh, iridium and rhodium are very, these are also less common than gold. They’re also mag five per kilogram. And then they, uh, if you’ve got on the scale here, we’ve got the aluminum very common element. It’s a mag zero per kilogram thing. It costs a couple of bucks per kilogram of aluminum and iron is mag negative one. It costs like 10 cents per kilogram. Yeah, I mean, you kind of think about that, right? Like if you, if you’re getting a ton of steel, it’s gonna cost you a, well, I guess maybe, I don’t know how often you buy a ton of steel, but last time I checked the price is a ton of steel, which happened to be last night. It was about a hundred bucks for a ton of iron or a ton of steel. [Mike: Mm-hmm.]

Hardness Scales

Saul: Okay. So we’ve talked about the abundance and the price of things. There are other attributes we can talk about with regard to matter. So hardness, do you remember talking about hardness in grade school? The hardness of various minerals?

Mike: Yeah. I remember doing the scratch test..

Saul: The scratch test, exactly! That’s the Mohs’ hardness scale. That’s one of the methods.

Saul: So there’s other ways of measuring hardness. There’s just, there’s a scratching that we mentioned. There’s, um, resistance to denting. You can, it’s kind of, it’s almost like not how hard it is, but how soft it is?

Saul: And, a friend of mine asked a question, how much harder is gold than a marshmallow? ’cause he’s like that. And it turns out you actually do measure the hardness of marshmallows. I, I was, I was like, oh, that’s so funny. Ha ha. But yeah. I, uh, there actually is a company out there that will measure the hardness of your marshmallows. What’s interesting about this though, is that you’re not going for the softest marshmallow. You want a certain firmness to your marshmallow. Like you don’t want it to be too soft. So anyway, there’s a, there’s a scale for measuring the resistance to denting. There’s actually this thing called the Shore Hardness scale. I, I actually, I have to go on a little rant here. It’s kind of gross. There are actually three different shore hardness scales. They all go from zero to a hundred. Each of them goes from zero to a hundred. They’re different scales. There’s one for soft things, one for medium things, one for hard things. It’s the double zero, the A and the D scale. Literally, that’s the three scales. And you measure them in the same zero to a hundred on each of them, and they kind of overlap.

Saul: Anyway, I, um, yeah, it’s kind of abominable. So that’s the, and that’s, you use a durometer to measure that as opposed to a sclerometer. And you can actually buy a sclerometer, I’m not sure if you know this, to measure fruit hardness, so for ripeness. So you can put that on a, on a peach or whatever and see how ripe your fruit is.

Mike: This, this is our next big thing. We’re going to figure out the optimal hardness for an avocado and sell an avocadometer.

Saul: Oh my God. Yes. That needs to be done. I have been warned against squeezing the avocados, but how do you tell how ripe they are until you squoze them? Right. [Mike: Mm-hmm.] Yeah. Okay. So Avocadometer, however you pronounce that.

Young’s Modulus (Pascals)

Saul: So anyway, let’s continue on. So there is one more thing on the hardness scale. We’ve talked about Mohs hardness and the Shore Hardness scale and Absolute hardness. There’s also this thing called Young’s modulus, which measures, uh, material stiffness. And that’s measured in actual force, like the force required to, um, deform. Yeah.

Mike: I think I’ve heard of this one. Yes. We talked about bike frames.

Saul: Really? Huh. I had never heard of Young’s modulus before. So, yeah. So it turns out that this is measured in Pascals, which is a certain pressure. Mm-hmm. Uh, thing that you can talk about atmospheric pressure versus whatever. And so it’s, uh, if we can actually answer this question. I’ve got the answers here. I’m not gonna make you guess this one. So, uh, marshmallow is on Young’s modulus about 30,000 Pascals. It’s about mag four and a half, right? And a diamond is mag 12 Pascals. Um, a thousand giga pascals. So mag 12 versus mag four and a half. That’s about mag seven and a half difference, right?

So it’s about 30 million times more stiff. A diamond is that much more stiff than a marshmallow. [Mike: Mm-hmm.] So that’s how we are, that’s how we’re talking about matter anyway. Stiffness, hardness, scratch ability, dent ability. So. Let’s talk about our final one here, our final category of matter. I mean, there’s all kinds of ways to measure matter, right?

Density Cubes

Saul: I mean, you can do stuff, but we’re gonna talk about the last one on my list here, which is density.

[35m]

So different things have, are more dense than others. We were talking about the density of a gold, uh, cube versus an ice cube earlier,right?

Saul: So we are gonna talk about the periodic table. And I wanted to say I’m bringing up density cubes because I have had for quite a long time, a dream of accumulating or collecting the elements of the periodic table.

Mike: all of them?

Saul: Well, there’s only 92 like we were saying. And actually it turns out that there are some 10 that you can’t collect because they’re radioactive. They don’t actually exist in nature. So I wouldn’t, I don’t think you’re allowed to get those. And so there’s really only these 82 elements that you can collect, and that’s actually very much within the scope of somebody to collect. And then I was thinking, you know what? I have a birthday coming up. I am turning 49 years old and you know what Element 49 is? You don’t know, but I do because I’m looking it up. It’s Indium, which is a soft, I’ve been calling it a soft buttery metal. That’s not quite right, but you know, it’s a soft silvery metal and it’s just, it’s, I think it’s used for LCD displays. It’s um, it’s a general technical technological element, but you can buy a little cube for like 15 bucks and it’s Element 49. And I was like, you know, what I should do is actually collect these for my birthday every year and this year I’ll get Element 49 and next year I can get element 50. I should have started this when I was one. Right? Yeah. A little bit of hydrogen.

Mike: That sounds fun.

Saul: Thank you. I agree. As a,

Mike: it means you’re not completing your collection until you’re [Saul: 92.] 92.

Saul: Well, that gives me a reason to stick around. So that’s, that’s good. Uh, I do have to also backfill a lot ’cause I haven’t started collecting yet, although. Some, and this is an open question, it’s like, do I, there’s like multiple methods of collecting elements and one of them is density cubes where you can basically, you can go online and get machine milled cubes the exact same size, and you can like, oh, here’s aluminum, here’s silver, here’s ruthenium, or whatever, and here’s gold. And you can compare how dense they’re, you can actually kind of pick them up and weigh them in your hands. Right now that’s challenging because your gold cube is going to be a lot more expensive than your aluminum cube. But, um, it’s kind of compelling and you can definitely buy that and you kinda just slot them in.

So besides density cubes, there’s also, you can collect little ampules of, uh, these elements, which works better for gases, right? I mean, you can still get the cubes of gases, but they’re definitely trying to contrive it to do that. Um, but also you can put the elements in the ampules and you’re getting more of a flavor what the element is like. It’s a lot of work to machine a metal into a cube format.

Mike: Mm-hmm. Like if you see a bismuth crystal…

Saul: They’re gorgeous!

Mike: And why would you machine down bismuth if you haven’t seen bismuth before? They make these incredible repeating fractal patterns and the color goes from like yellow, orange, purple in a gradient. It’s incredible. And to think that you would display that not as this really beautiful crystal, instead machining it down into a boring old square is ridiculous.

Saul: Okay. So the reason that we’re talking about the periodic table is that it’s kind of, uh, it’s a remarkable invention or discovery, right? Like we knew that there were different elements before we had the periodic table. We knew that they were, um, that they acted a certain way, that this was definitely, you know, this is Mercury and this is gold. And there are different things and they act different ways, but it’s the periodic nature of it that makes it so remarkable. At some point they’re like, Hey, you know what? These elements not just relate to each other, but act like each other and it’s in a periodic fashion. And so the fact that we’ve got this periodic table, and we got one right here, I can show you..

Mike: Mm-hmm. So when you talk about periodic, you mean repeating pattern, so

Saul: That there are rows and things in the same column across rows are very similar. And so if you look at here, we’ve got copper and silver and gold all in the same column. It is not an accident that we use those metals as our quote precious metals

Mike: because they all share similar

Saul: Metallurgic properties

Mike: shiny ductile, conductive.

Saul: Yeah, exactly. And there’s those. And then we can look at other, other columns in the periodic table and we can see these patterns. And not only did we see these patterns, uh, between atoms, it predicts or it predicted where certain elements would be. There are a handful of elements that don’t exist. They’re actually lower ones. So there’s this one called technetium that is, uh, element 43 and it’s the smallest one of these, or the lowest mass, one of these. It does not exist naturally. In the world, in the universe, it is only either manmade or comes from radioactive decay. And it was predicted because there, they put together this chart and there was an empty slot. There was like, oh, something should go here. And there’s something that they knew about that went there. And then lo and behold, eventually we did find out that there was a thing called Technetium, or we call it Technetium.

[40m]

Saul: So the periodic table is kind of like an atlas of elements, right? Like it is kind of a comprehensive view of the elemental world. This is actually a good analogy for Mag World. What we’re doing here is we’re coming up with a list of, uh, kind of atlas of dimensions.

Yeah, so we’re looking at the kinda map of dimensions here and just like with the whole silver, gold thing where the value of silver is 10 times less, what it should be compared to the abundance of silver compared to gold. And there’s an interesting answer to why that’s the case, but we wouldn’t have thought to look at that exact thing unless we had looked at it, and at least in terms of the actual numbers. And Mag World makes that so much easier.

Mike: I like it. Thank you for introducing me to Periodic Mag World.

Saul: You’re welcome, Mike. So, I think next time we’ll be talking about Mag Computer.

Mike: That’s great. This is really your area of expertise, isn’t it?

Saul: Oh my gosh. It’s been decades of computers, and not just for me, but for everybody.

Mike: Great. I’m looking forward to it. Yeah. And since it’s my job to ask Saul good questions about each of these topics, Uhhuh, if you think there’s things I should have asked Saul that I didn’t, or elicited reactions that remain hidden to you. Email me, mike@magworld.pw. Yeah. And tell me what I should be asking Saul, and I’ll try to make it happen.

Saul: Please do, Mike. Mike loves great questions. Thanks, Mike. Thanks for being here. It’s good talking with you.

Mike: Yeah, thanks for doing the math Saul.

Saul: See you next time. [Mike: Bye-bye.]