Episode 01: Mag Cosmos

[00:00:00] 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’re new here, you should know that on a magnitude scale, every mag one means times 10. So a hundred is mag two, and a thousand is mag three, and a hundred times a thousand is mag two times mag three. To multiply numbers in mag world, you just add them together to get Mag five, which is a hundred thousand. That’s really all the math you need to know to start learning about Mag World. Just remember that every order of magnitude is a big deal because as we say in Mag World, quantity has a quality all of its own. I’m Saul Pwanson, your guide to Mag World, and I’m here with my friend Mike, who loves learning and making witty observations. Today’s episode, we’ll explore the bounds of space and time. How big and how small are the universe, really? If you want to learn more about Mag World, come visit our website at magworld.pw.

Archimedes

Saul: So first I wanna talk about my new math nerd hero: Archimedes. Archimedes…yeah?

Mike: New on the scene, huh?

Saul: New from, well, I’ve heard of him. Most people have heard of him from like grade school or whatever, but like I didn’t realize how much of a math nerd this guy was. So he’s kind of the OG big thinker.

He lived around 250 BC in Greece and he figured out that bathtub displacement thing, trying to figure out whether people were being ripped off in terms of coins, whether it was really silver or some fake metal or something like that. And he was saying things like, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world”.

Mike: Not just a good thinker, but that’s like, a banger.

Saul: That’s a banger of a line, right? [Mike: Right.] Anyway, he was most famous for his inventions, but he also wrote a few books, one of which is called The Sand Reckoner, in which he tries to figure out how many grains of sand can fit in the universe. This is an absolutely audacious undertaking in 250 BC.

Mike: Was sand a way that they measured things, or did he just say, I don’t just wanna know how big it is, I want to have a number…

Saul: What he did, he took the biggest thing he could think of–the universe–and he took the smallest thing that he knew about–grains of sand–and tried to put the smallest thing into the biggest thing and to count them all. Archimedes trying to count the number of grains of sand that can fit in the entire universe.

For one thing, he only has words for numbers up to 10,000. In old Greek, that’s a myriad. That’s where we get the word myriad from. 10,000 things, right? [Mike: 10,000 is a myriad.] And, what’s that in Mag World, Mike?

Mike: 10,000 is Mag four. [Saul: Mag four.] One followed by four zeroes.

Saul: That’s right, Mag four is a myriad. Mag four things. And so, okay. So Archimedes doesn’t even have numbers to talk about bigger than that. So he defined a myriad myriads, basically 10,000 ten thousands. Right. Which of course would be Mag eight.

Mike: Mm-hmm.

Saul: Are you with me on that? [Mike: Yes.] So where does mag eight? [Mike: It’s a hundred million.] A hundred million.

’cause mag nine–mag six is a million, mag nine is a billion. It’s 10 off of a billion, so a hundred million, mag eight. And you can get there also. Well, this is how I got there anyway. You know mag four times mag four, you add the two fours together, you get mag eight. That’s how this math works. So he made a myriad myriads. That’s Mag eight, mag four plus four.

Mike: Did he have words for this?

Saul: He didn’t. He just called it a, well, actually what he called it was, he called it a second order myriad. So there’s myriads and then there’s second order myriads, and those are the hundred million. And then he’s like, okay, well I need bigger numbers than that even. So he’s got, now he’s got second order myriad of second order myriads, that’s mag eight times mag eight. That’s mag 16, right? So. Do you know what Mag 16 is?

Mike: No.

Saul: So it’s billion, trillion for Mag 12, quadrillion for mag 15. And so Mag 16–[Mike: quintillion] mag 18 would be quintillion. ’cause every three, you get those numbers, the, you know the [Mike: Oh yes.] The quad, quint, whatever. And so [Mike: Mag 16 is 10 quadrillion.] 10 quadrillion. That’s exactly right. No, that’s fine. That’s good. [Mike: Yeah.] This is why we’re, why we’re here. And so, so we get second order myriads and third order myriads, and we’re up to Mag 16 now, and then fourth order myriads would be Mag 32 in our nomenclature, right. He only, he goes up to doing myriad-order myriads. He goes all the way up to 10,000 of these damn things, which is basically–

Mike: a myriad-plex.

Saul: Yeah. No, exactly, right? It’s like a, a googol is–I’m not sure if you know this, a googol is literally mag 100. [Mike: Is that?] That’s what Google means. Yeah. [Mike: Oh,] and then a googolplex is a mag googol. Mag mag 100. [Mike: Yeah] Which is nuts.

So our friend, Archimedes is making a myriad-order myriad, which is Mag 80 quadrillion. Which is utterly bonkers, like that number doesn’t even deserve to exist. It’s just, it’s so, and this is what we’re getting into with this exact episode here, is what are the literal bounds of Mag World?

[00:04:58] Okay? So not only does he do this with the number system. He also discovered and improved the law of exponents, which we’ve been using right here. When I say, you know, mag four times, mag four is mag eight. The fact that you just add those two numbers together in order to get the the mag number.

That’s the law of exponents. And so the roots of Mag World really extend all the way back to 250 BC with Archimedes.

Mike: That’s a little incredible.

Saul: That’s what I’m saying. He’s my new math nerd hero because it’s not that he like understands this stuff. It’s that he made this stuff up! Like he was working with nothing, everyone around him is still counting–the maximum number of sheep they can count is 10,000. He’s like, what? What if we had a mag 80 quadrillion sheep?

Okay. So anyway, over the course of this book, The Sand Reckoner, he makes a bunch of wild ass guesses and approximations and eventually estimates that the diameter of the universe is about, in our lingo, mag 14 stadia, and one stadium is about the length of a stadium, which makes sense, maybe 200 meters. We don’t know the exact number ’cause we didn’t have standardized, they didn’t have standardized units then. And so that would make the universe about two light years across.

Mike: Mm-hmm.

Saul: Now the universe is much bigger than that, of course, but I mean, major props to this guy for trying. How many light years across do you think the universe actually is? Archimedes guessed two.

Mike: Well, okay. Talking through the problem.

Saul: Okay, great. Yeah.

Mike: The universe is about 6 billion years old.

Saul: Okay. Do you want real numbers for that? Because I have a real number for that too. [Mike: Nah.] Okay, great.

Mike: I’m gonna [Saul: wing it], tell me if I’m more than a order of magnitude off [Saul: Great, perfect!] with any of this.

The universe is about 6 billion years old. I know that one of the things that scientists study is the cosmic background radiation. Which, cosmic background radiation is background. It’s everywhere. It’s from the beginning of the universe, so that means we’re getting radio signals from the beginning of the universe. [Saul: Mm-hmm.] 6 billion years ago, those radio waves have traveled at the speed of light. [Saul: Yeah.] So we’re talking 6 billion miles. Well, 6 billion light years. [Saul: Okay, good idea.] And then double that for [Saul: the diameter.] For the diameter that, [Saul: Yeah. Okay.] from Earth that we can see. But the universe is constantly expanding, at a greater and greater speed. So there must be universe beyond the observable universe. [Saul: Okay.] So minimum 12 billion light years. And I don’t know, let’s [Saul: not bad!] increase it by 10% for error.

Saul: 10% sure, sure. Okay. Yeah. Uh, not bad actually. Yeah, we’ll get there. The actual answer is about a hundred billion light years, but we’ll get there and talk about why your math is a little off.

Mike: So by the end, I was an order of magnitude…

Saul: or, you’re one order of magnitude off. [Mike: Mm-hmm.] Yeah.

Mag Distance

Okay, so, let’s talk about space, size, distance, length, whatever this, this dimension is, right. So of course, Mag World encompasses all kinds of different dimensions, but this literal size, distance, length is the original dimension used to illustrate magnitude thinking.

Like there’s this classic Powers of Ten, uh, short film from ’68, 1968. Have you seen this one? Probably, where it starts with a picnic, a woman on a picnic blanket, and it zooms out. Order of magnitude 10, you can see the park that she’s in, and another order of magnitude, you can see the city and just so on and so forth, all the way out to the edge of the universe?

Mike: I’m not sure if I’ve seen this particular one, but I’ve absolutely seen..

Saul: variants of it. [Mike: Yeah. Mm-hmm.] So now in math world, and this is like the normal math world that we’re used to being taught in school. A logarithmic scale is like any other number line, and is thought of as stretching infinitely in both directions.

But in Mag World, there are real limits to the mag scales and they aren’t nearly as large as you might think. I mean, we’ve just seen Archimedes way over-engineer numbers to construct mag 80 quadrillion, but the real size of the known universe is “just” mag 27 meters. Mag 27. That’s as big as the universe actually is.

So you don’t need anywhere near, I mean, you don’t need mag 80, much less mag 80 quadrillion. So now, yeah. So how about on the small side? If we go below zero, we can, we can get a 10th of a meter. Mag negative one is a centimeter. Sorry, mag negative one is a decimeter. It is a 10th of a meter. Mag negative two is a centimeter. Mag negative three is a millimeter, and then mag negative nine is a nanometer.

You know how the scale goes? It’s like mag negative three is milli, mag negative six is micro, mag negative nine is nano, and those are very consistent. [Mike: Mm-hmm.] And then of course, on the positive side, mag three is kilo, so a kilometer is mag three, mag six is mega. So we don’t actually say a mega meter, but we could.

So a thousand kilometers or a million meters is mag six and then etc. Then mag nine is giga, mag 12 is tera.

Okay, well, how far down the scale does it go? Like we’ve already established that Mag 27 is the size of the known universe, the observable universe. So how far down the scale does it go? Any guess?

Mike: How far down the scale does it go?

[00:10:00] Yeah, like we’ve had negative nine is an nanometer, mag negative 10 is an angstrom or the size of a hydrogen atom. So the smallest possible length that we can even think about in our standard model would be, what do you think?

Mike: Well, you’ve got your hydrogen atom.

Saul: Mm-hmm.

Mike: Just the proton. And then…

Saul: so the hydrogen atom has electron spinning around it. That’s mag negative 10.

Mike: That’s, so that’s the entire volume of the atom.

Saul: and then a proton is mag negative 15 or mag negative 16. That’s just the proton.

Mike: Mm-hmm. So what’s the smallest distance a thing can be?

Saul: or that we can even conceive of in our system? [Mike: we, yeah. Uhhuh.] Yeah. So I’m gonna tell you, [Mike: tell me] it’s mag negative 35.

This is called the Planck Length.

Mike: That is way smaller than a proton.

Saul: It is! Now, there’s two sides to this. One is like, that is, yes, that is a huge distance there.

Mike: Mm-hmm.

Saul: But also the scale only goes down to negative 35. Like that is a huge amount and we don’t need any more than that. Like the scale for stuff, for literal physical space, runs from mag negative 35 to mag 27.

That’s where you’re, how big things can be. You have no right saying anything like mag negative 50 or mag positive 50. That’s outside of the bounds, even if it exists in math world, because everything exists in math world, and you can make stuff up and you can have mag 80 quadrillion if you’re so inclined, but in the real physical universe, at least according to the standard model, that’s it.

That’s the range. [Mike: Mm-hmm.] I have these anchors: mag negative 35 for the bottom of the scale, mag 27 for the top of the scale, the size of the universe, and I have a few other anchors I keep in my head for mag space.

Okay. So you remember how Archimedes was trying to take the smallest thing that he knew about and then count how many would fit in the universe?

[Mike: Yes.] So we now have the smallest thing we can talk about–the Planck length–and we can try to fit how much, how many of the smallest things can fit into the entire universe.

Mike: So Planck length is a distance. The Planck volume would be a square or a circle, one Planck length in diameter.

Saul: That is totally correct. And so to convert a Planck length into a Planck volume, which is the smallest three dimensional grain of sand, I guess, we would take the Planck length, which is mag negative 35 and triple that. That’s times three for the three dimensions [Mike: Mm-hmm.] taking the volume of something, and I guess it’s kind of more like a cube than a sphere, but it turns out that a sphere is only half the size of the equivalent cube, so in Mag World, they’re basically the same. So, if we take negative 35 times three. Imagine that you’ve got a cube, a thousand, I don’t know, miles or a thousand meters. Doesn’t matter. A thousand somethings on a side, right? What’s the volume of the cube?

Mike: Mag three times mag three times mag three.

Saul: Yes. And so what’s that?

Mike: Mag nine.

Saul: Mag three cubed. And so mag negative 35, cubed…

Mike: Negative 35. Oh, got it. So you’re adding your 35 three times. [Saul: Yes, exactly.] You’re cubing. [Saul: Yes.] So that is mag 105.

Saul: Mag negative 105.

Mike: Mag negative 105

Saul: for the volume of a, I’m sorry for the Planck volume, the smallest grain of sand that we can talk about here.

Mike: Mm-hmm.

Saul: And so let’s see how many we can fit of those into the entire universe. So the universe is size… [Mike: Mag] 27 for the universe. [Mike: 27.] Okay. And then, so if the diameter of the universe is Mag 27, then the volume of the universe…

Mike: is 27 plus 27 plus 27. [Saul: Yes.] ’cause when you use it as exponent, you add the mag number together. [Saul: Yes.] 27 plus 27 is 54, plus 27 is 81.

Saul: 81. So mag 81 volume, meters cubed, for the volume of the universe. And then if we’ve got the volume of a Planck length, which is mag negative 105, [Mike: Planck volume.] Planck volume, thank you very much. How many Planck volumes can fit into the volume of the universe?

Mike: So Planck, number of Planck volumes per universe. [Saul: Yep.] So 105 per 27. Negative 105 per 27.

Saul: I think you want the other way around. Right.

Mike: Yes. And so, [Saul: but it’s actually not 27, it’s 81.] 81, right. Okay. So. You’re taking 81 divided by negative 105. [Saul: Yep. Mag 81 divided by mag negative 105.] And when you divide mag numbers, you subtract one from the other.

[00:15:01] [Saul: Yep.] So it’s 81 minus negative 105. [Saul: Yep.] So the number of Planck volumes that will fit in the universe is…mag 186.

Saul: That’s right. That I think is the number that Archimedes was looking for all along: Mag 186 smallest things in the largest thing. And I think we can call this an episode of Mag Reckoner here. His book was of course called The Sand Reckoner, and I actually really like the word “reckon” for what we’re doing here. [Mike: Mm-hmm.] I reckon this size we’re, uh, you know, it’s not like, it’s not calculation exactly. I mean it is calculation, but it’s, it’s very, um, hand wavy in some ways…we’re reckoning. You know? [Mike: Mm-hmm.] So, yeah, [Mike: I reckon you’re right.] Totally. Thanks Mike. So the big one for me is a light year. Do you wanna guess, given those numbers, how big a light year is?

Mike: A light year is 3 million meters per second. Is that correct?

Saul: So you’re thinking of the speed of light.

Mike: Uh, yes.

Saul: And you’re actually pretty close. Well, actually you’re way off. But…

Mike: Wait, three point oh times 10 to the 12th, is that right?

Saul: Here’s, this is actually the exact problem. You’re trying to remember the numbers and you’ve got the three, the three is a hundred percent right. Well…

Mike: And it’s the least important number! Is this…

Saul: and you’ve missed. Completely.

Mike: Because, uh, this is taking me back to, I don’t know, at least 20 years last time I had to do anything with these numbers.

Saul: Yeah, totally. Mag 16 is a light year. That’s one of the anchors that I have in my, in my head.

Mike: Oh, I was gonna work it out from… [Saul: the speed of light.] the speed of light. But–

Saul: We’re gonna do it backwards. [Mike: Cool.] Because we’re gonna hit, we’re gonna hit space, time and speed today. And then [Mike: So mag 16,] it’s big. It’s a lot. And it’s literally mag 16 meters. Yeah. And it’s not Mag 16.2 or Mag 15.8. It’s like Mag 15.976. It’s like really close to Mag 16. Just Mag 16. [Mike: Yeah.] It’s a light year. [Mike: Wow.] That’s fine. Meters. Yeah. And a lot of these numbers, they’re surprisingly close to the, either the whole or the half. And it’s like, ah, good enough, you know? Like I don’t… So Mag 16 is a light year. The other anchors that I have, mag 27, like I was saying, for the universe, the moon is mag six and a half.

Otherwise, the earth is mag 7.1. Jupiter is mag 8.1, the sun is mag 9.1. They’re just 7, 8, 9. So the earth is mag seven, Jupiter is mag eight, the sun is mag nine in diameter. And so those are my anchors. Sun is mag nine. Do you know what an AU is? An astronomical unit.

Mike: That’s the distance from the sun to the earth. [Saul:** Yes!] On average.

Saul: Totally. And that is mag 11. And so those are my anchors.

Mike: So the distance from the earth to the sun [Saul: Yep.] Is about mag two suns.

Saul: That’s correct. It is 100 times the size of the sun. From the sun to the earth.

Mike: Mm-hmm.

Saul: Yeah, that’s completely correct.

Mike: Cause that’s a mag 11 Astronomical Unit. [Saul: Yep.] And a mag 9 diameter of the sun.

Saul: Yeah. [Mike: Cool.] Really nice, [Mike: huh] Exactly. [Mike: That was easy.] Right? The moon is mag 8.5 or so distance away from the earth, which means that you can fit a Jupiter between the earth and the moon.

Mike: A Jupiter, which is 10 Earths.

Saul: and a Jupiter, which is 10 Earths. Exactly. Yeah. So it’s 10 times the size of the earth to get to the moon.

So we’ve talked about the sizes here. We’ve got, like I said, the Earth is mag seven, the sun is mag nine, an AU is mag 11. The light year is mag 16, the universe is mag 27. That’s my own sense of size in my head. At least astronomical size. 27 for the universe, and a light year is mag 16 and the sun is mag 9, and that’s how the scale looks.

Okay. So, and, and it’s mag 16 meters, but in Mag World we always use the base SI units just because it gets really confusing. And in fact, I have a quote here by Richard Feynman.

Feynman: Before I begin the lecture, I wish to apologize for something that, uh, is not my responsibility, but as the result of physicists all over the world of scientists so called, have been measuring things in different units.

And cause an enormous amount of complexity. So as a matter of fact, nearly a third of what you have to learn consists of different ways of measuring the same thing, and I apologize for it.

Saul: Yes, you’ve got electron volts over here and joules over here and megatons over here, and they’re all the same thing and they’re all on the same mag scale.

But we’re trying to, I mean, obviously you don’t talk about atom bombs in terms of electron volts and you don’t talk about atoms and their power in terms of kilotons of TNT. In Mag World, we actually can talk about ’em all on the same scale and I want to do that. And so when we use–when we talk in Mag world, we’re always talking in base SI units.

Mag Time

[00:19:59] Let’s talk about mag time.

Mike: Everyone is into time.

Saul: People have been wondering about the age of the universe for about the same amount of time, as the age of the universe. Right? Science has figured out that the age of the universe is 13.8 billion years. [Mike: Cool.] Yeah. Mag 10.1 years for the Universe.

Mike: Universe, mag 10 years old.

Saul: Yep. Okay. So the year is not the SI base unit for time. [Mike: No.] What is, do you know?

Mike: If I had to guess it would be the second, because I feel like. A lot of things are defined by…decay per second.

Saul: Yep. Meters per second. A hundred percent. Second is the, the only one that everybody seems to agree on we’re SI units.

The base units for everything is seconds. So let’s talk about the age of the universe in terms of seconds. Okay. For me, this is the bounds of the time scale. So, basically the one number that I latch onto in terms of time, my anchor for time is a year. A year is mag 7.5 seconds. But it is 7.499, I’m sorry, mag 7.499 seconds, like it is so close to Mag 7.5–it’s just Mag 7.5. And that is the anchor that I have for time. If you remember that one–all these different people converting, you know, oh, it’s the, the universe is mag, I’m sorry, is 10 billion years old or 13 billion years old? It’s like, oh Mag 10.1 times a year is seven and a half.

Mike: So seven and a half times 10.1. [Saul: Yep. Mag] Mag. Mag seven and a half times mag 10.1. [Saul: Yep.] Add those together. Mag 17.6.

Saul: That is how old the universe is in seconds. Mag 17.6. Yup. Okay, well let’s talk for just, just a split second here. Besides the smaller times, like millisecond and nanosecond of course, which I know because of their other SI prefixes, I only have this other last little number here, which is the bottom of the scale.

Mike: Mm-hmm.

Saul: Uh, a Planck time is the smallest unit of time we can possibly even conceive of measuring. And the Planck time is mag negative 44. [Mike: Wow.] Yep. So that scale runs all the way down to mag negative 44. Now it’s, I mean, it is way debatable whether there’s any even reasonable thing you can do at that side of the scale, both for space and for time.

But that’s, like I said, the, the Standard Model’s, smallest possible conceivable unit of time.

Mike: Mm-hmm.

Saul: Okay.

Mike: Is there a benchmark for smallest, useful amount of time?

Saul: You know, I think that we are at femtoseconds now, which I think is, there’s nanoseconds. Picoseconds and I think Femtoseconds is after that. So that would be mag negative 15?

I think there are femtosecond lasers. Where you can pulse them on and off and that–which is mind blowing that you can even do that. So I would say Mag negative 15 might be where we’re at in terms of time, actually being able to control something. Which is again, on the order of the mag negative 15 of space of the proton.

Mike: I’m finding these, these limits, fascinating.

Saul: A hundred percent. Me too. And one thing I wanna do actually with Mag World in general is produce kind of like a poster. Of all these things. You put it on our wall here, right? Where it’s each individual scale and it runs the actual length of the scale. Like it actually stops, at negative 44 and stops at 17.6 or maybe even a little higher because of time. But I wanna make that poster I think that’d be actually super useful for people just to see so they can ground themselves in Mag World. Okay, so one more thing I wanna say about mag time, running from mag negative 44 to mag 17.6.

So how long do you think it’ll be until we get to mag 18 time, seconds? We’re mag 17.6 now, that’s gonna be mag 0.4 to get to mag 18.

Mike: I’m thinking in seconds, but the question is not seconds. It’s age of universe [Saul: times], yeah. So four tenths of the age of the universe?

Saul: close. It’s actually 10 to the 0.4.

And that’s gonna be–if it was 10 to the 0.5, it would be 3.16 times the age of the universe. And so since it’s 10 to the 0.4. It’s a little less than that. It’s more like two times, two and a half times, something like that? And so it’s two and a half times the existing age of the universe, which is already 13.8 billion years. So it’s on the order of 30 billion years from now to get to mag 18 seconds.

Mag Speed

Saul: I want to talk about one last thing before we go, which is speed, mag speed. Velocity. Right?

Mike: Mm-hmm.

Saul: Because we’ve been talking about distance and time and we should all know, or sorry, we shouldn’t–we all know, I think, that speed is distance divided by time, like miles per hour, or fathoms per fortnight, or in Mag World, as in much of science, it’s meters per second, right? So you mentioned earlier here that

[00:25:00] the fastest speed is the speed of light, and they actually mentioned it in the Galaxy Song, the speed of light, you know, 12 million miles a minute, and that’s the fastest speed there is. I have a hard time computing 12 million miles a minute, but I know that the speed of light is mag 8.5 meters per second.

And I actually know that number better than I know the literal speed of light, which is, you were trying to say it. It was, I dunno what your number was. The actual speed of light is 300 million meters per second. And often it gets confused because people say 300,000 kilometers a second, and of course they’re the same number, but whether it’s 300,000 or 300 million, you actually, I think, wound up saying 3 million…

I don’t know. It’s mag eight and a half. [Mike: Mag eight and a half.] If you just log, latch, whatever, mag, eight and a half in your brain, you will go far in this world. Because. Let’s think about this. Mag eight and a half is the speed of light, meters per second. What was a year? [Mike: A year was mag seven and a half.] Mag seven and a half for a year.

The speed of light is mag eight and a half. A year is mag seven and a half. What’s a light year?

Mike: Light year is, well, I’ve got eight and a half mag. Mag eight and a half meters per second. [Saul: Yep.] I’ve got mag 7.5 seconds. [Saul: Yep.] If I multiply those together, it’s 8.5 plus 7.5. [Saul: Yep.] So mag 16

Saul: Mag 16 meters is Lightyear.

Mike: And I feel like you said that number minutes ago.

Saul: Yeah, it all adds up. Or it all multiplies up. There’s three numbers: mag seven and a half for a year, mag eight and a half for the speed of light, and mag 16 for a light year. If you remember any two of those, you can get to the third one with just a little bit of small arithmetic.

Okay, so if the speed of light, the fastest speed there is, is mag 8.5 meters per second, let’s go down the scale. Let’s talk about other speeds. Now, speed is interesting. Because it’s divided by time it’s, it feels like…this is what I’ve come across anyway, it feels like it’s more compressed, that it’s not that every mag, every whole level is a whole other level. It actually seems like more, like every half level is more like a, is a whole level. And so for instance, the speed of a human running or walking is mag zero. [Mike: Yeah.] And that’s whether you’re running or whether you’re walking, there is not a, a factor of 10 difference between those two.

Like if you’re running, you’re not running 10 times faster than you’re walking. Now, you can take a bike, for instance, right? And if you’re taking a bike, you can go 10 times faster than you can walk. You can go mag one on a bike. [Mike: Absolutely.] And if you’re taking a car, you can also go 10 times faster than you can walk.

And you can kind of go like as a bike, you can go mag one; as a car, you can go mag 1.5.

Mike: Mm-hm. You’re not getting to mag two.

Saul: If you’re in a race car, you can go to mag two, right? Let’s not, let’s not tell humans they can’t do something like that. But you’re right. If mag two is like a, whoa, what that–

Mike: A hundred meters per second is flight speed.

Saul: Yeah, actually you’re totally right. That’s exactly a flight speed. So an airplane goes mag two meters per second. A bullet goes mag two and a half meters per second. Like neutrons, like fast neutrons versus slow neutrons are mag three and a half or mag four, like when we’re getting up in this size, this side of the scale is things that are subatomic particles.

And then finally you get to mag eight and a half, which is the speed of light, and that’s the cap of it. But there’s this kind of like dead zone here where it’s, you know, things just don’t go that fast.

Mike: Celestial bodies will move that fast, and that’s pretty much it.

Saul: Celestial bodies, I will, I’ll research that too because they quote a lot of ’em in this song, The Galaxy Song, and I’m actually very curious how fast they actually are. [Mike Well, we,] I’m not sure because they’re so big!

Mike: we can figure out, ’cause we know the magnitude of an AU, so we can figure out the circumference and we have the time that it takes to complete that, right?

Saul: Yeah! Okay, great. Let’s do this m–this is perfect. Let’s do this math. [Mike: Let’s.] Okay, so an AU is Mag 11. Now the great thing about Mag World is that the circumference only adds 0.5 because it’s basically pi times the diameter. And when you multiply something times pi, you’re effectively multiplying it, you’re multiplying it by a half mag, right? Because 3.14 and 3.16 are really close.

Mike: but we’re playing multiplying it by two pi. Because AU is the radius. [Saul: Oh, look at you. Yeah! Thinking!] Tau. Multiply by tau, man.

Saul: Okay great. So yeah, so, um, you’re right, then AU is the radius of our orbit. And times two pi would be times pi, which is a half, adding a half in Mag World. And then times two is actually 0.3, adding another 0.3. So you’re right, we’re adding a 0.8 onto this. So it’s a mag 11.8.

[00:30:00] Let’s say. For the circumference of the Earth’s orbit. So Mag 11.8 for that. And then we have the speed–the year, mag 7.5. And so we subtract those things out.

And what do you get here? I get Mag 4.3 for the speed of the earth, going along it’s little orbit. Look at that. We just did some mag math and that’s gonna be around [Mike: 10,000.] 20,000. [Mike: Yeah.] Meters per second. Nice math.

Mike: Well done us. [Saul: There you go. Yeah.] So yeah, celestial bodies, at least the one we are on, moves at mag four.

Saul: and I’m gonna, I’m going to verify that because that like, doesn’t sound right to me, but we just did the math. If the math is wrong, I gotta figure something else out here. That’s gotta be right. Yeah.

Mike: I liked that use of the mag.

Saul: Awesome. Anyway, just to wrap things up here, let’s talk about the slow end of the spectrum.

Mike: Mm-hmm.

Saul: Have you heard of, uh, snail’s pace? Sloths move slow? Sloth, snails, glacial pace, right? A sloth is mag negative one speed. A snail, I believe is mag negative two.

Mike: Yes.

Saul: And then a glacial pace. The glaciers move at mag negative six meters per second. Continental drift?

Mike: Oh wait, so it’s gotta be slower than glaciers.

Saul: Yeah. How much slower do you think it is?

Mike: I, so a glacier is a large geologic feature.

Saul: But it’s liquid. It’s ice. and it’s on top.

Mike: And it’s so much smaller than a continental plane.

Saul: Yeah.

Mike: So if a mount, the order of magnitude between a mountain and a continent is, I mean, that’s a thousand times. So that’s mag three, let’s say mag three under the speed of the glacier.

Saul: Very nice. That’s exactly right. It’s either mag negative nine or mag negative 10. You’re totally right. Nice job, Mike. [Mike: Cool. I like this.] Yeah, exactly. Yeah. So anyway, so today we’ve been exploring the range of some fundamental physical scales like the size of the sun at Mag nine, a light year at mag 16, the galaxy at Mag 21, the universe itself at Mag 27, all the way down to a hydrogen atom at mag negative 10, and then the smallest theoretical Planck length at Mag, negative 35.

And that’s the range of distance and time and speed. Mag Cosmos.

Mag World Plugin

Well, first of all, I wanna pitch my mag plugin. I wrote a Firefox plugin that will convert all numbers on your web pages to Mag World. It’s pretty fun. [Mike: Oh no.] Oh yes. Oh yes.

Mike: Oh no. Even your bank account? That sounds terrible.

Saul: (cackles) Yep. So there’s that.

And that’ll be on the website, of course, as soon as I get that up. The other thing I wanted, oh, for next session, next episode, I was thinking of talking about mag perception. So, log scales are all around us because that’s how we perceive things. You’ve heard about Scovilles for peppers? For instance.

Well, I mean, we talk about them in terms of 20,000, 300,000 scovilles. That’s just a mag scale. We have mag peppers in our future.

Mike: Ooh. Mag Hot Ones.

Saul: Mag Hot Ones, exactly.

Mike: Love it.

Saul: Okay. Thanks a lot, Mike. I’ll see you next time.

Mike: See you next time. For Mag Hot Ones.

Before I begin the lecture, I wish to apologize for something that, is not my responsibility, whether it’s the result of physicists. All over the world, scientists, so called, have been measuring things in different units and cause an enormous amount of complexity. So as a matter of fact, nearly a third of what you have to learn consists of different ways of measuring the same thing. And I apologize for it. It’s like having money in francs and pounds and dollars and so on.

With the advantage over money, however, is that the unit, the ratios, don’t change as time goes on. But, for example, in the measurement of energy, which is indicated up here, the unit we use here is the joule, and a watt is a joule per second. But there are a lot of other systems of measuring energy depending upon what it is, and I’ve listed three of them up at this thing for engineers. Now the physical chemists do something else, and the physicists do something else when they want to talk about the energy of a single atom instead of the energy of a gross amount of material. The reason is, of course, that the single atom is such a smaller thing that to talk about energy with all those 10 to the minus God knows what joules would be inconvenient.

But instead of taking a definite unit like 10 to the minus 20 joules or something in the same system, they have unfortunately chosen, arbitrarily, a funny unit called an electron volt, which is the energy needed to move an electron through a potential difference of one volt, and that turns out to be 1.6 plus a few more figures times 10 to the minus 19 joules, For which I am sorry that we do that, but that’s what they do. And, now that’s the physicist. Now the chemists, the physical chemists, when they deal with, atoms and talk about the energy per atom, they since they don’t use the atoms individually but in large blobs of them in cans and barrels, they have chosen a certain number of atoms as a unit. And this number of things is called a mole and it’s 6.023 times 10 to the twenty third objects, is one mole of objects. The more precise definition which is coming, which is either present now or will soon be correct, is that one mole is defined so that a mole of carbon 12 atoms, that’s a particular isotope of carbon, will, have a mass of exactly 12 grams, but what of it?

The mole is a certain number of things so that when they want to talk about energies per atom instead of giving the energies per atom they give it per mole. It’s good therefore to know how much energy is a mole of electron volts. In other words, if each atom had one electron volt of energy a mole of these atoms would have a reasonable amount of joules instead of such a small decimal, namely 96,500 joules per mole. Incidentally, just for interest the charge on an electron can be remembered this way that a mole of electrons, that universal number, six times 10 to the twenty third electrons, has a total charge of 96,500 coulombs. Those numbers are the same for a reason you’ll have to figure out.

Now there’s an additional unit that the physical chemists use in measuring energies of an atom, which is called a kilocalorie per mole. And 23 of those is an electron volt per atom. Finally, unfortunately, we have another system for measuring masses. The mass of an atom from the chemist’s point of view is measured by giving the mass of a mole of atoms. So that for example, the mass of carbon 12 is called 12 units or 12 atomic mass units means that a mole of carbon 12 weighs 12 grams or rather has 12 grams of mass.

And one atomic mass unit then represents one gram for every mole of objects, if a thing, gram per mole. Now, we can measure that in electron volts also. You can’t measure mass in electron volts, sure you can, because if the relation energy equals mc squared it’s useful to know how much energy corresponds to the emission or consumption of one atomic mass unit of material. And that turns out to be nine thirty one million electron volts. MeVs are simply million electron volts.

Incidentally, to annihilate a proton, the proton mass corresponds to an energy of 900 and the rest mass corresponds to a rest energy, mc square, of 938 MeV, when an electron is 0.511 MeV. The nine thirty eight differs from the nine thirty one because a proton is not one unit atomic mass unit but is 1.008 something, I can’t remember. So it’s a little higher and it makes nine thirty eight. I’m sorry for the confusions produced by all the systems of units. I left out obviously a large number of different things.

For example, in measuring radiant energy light, the lumen is used and a lumen is one and a half milliwatts of, energy milliwatts. That’s the power from a light. One and a half milliwatts in the most visible light, namely 5,500 angstrom light. It’s all very annoying. But when you get to measuring light, you look up in a book what a lumen is.

Don’t worry about it now. Okay, that’s the end of the unfortunate fact that we measure things in a whole series of different kinds of units, which causes a lot of confusion, but it’s too bad. But I’ve already apologized for my colleagues, and there’s nothing else I can do.

    Whenever life gets you down, Mrs. Brown
    And things seem hard or tough
    And people are stupid, obnoxious or daft
    And you feel that you've had quite enough.

    Just remember that you're standing on a planet that's evolving
    And revolving at nine hundred miles an hour
    That's orbiting at nineteen miles a second, so it's reckoned,
    A sun that is the source of all our power.
    The sun and you and me and all the stars that we can see
    Are moving at a million miles a day
    In an outer spiral arm, at four hundred thousand miles an hour
    In the galaxy we call the Milky Way.

    Our galaxy itself contains five hundred billion stars.
    It's a hundred thousand light years side to side
    It bulges in the middle, six thousand light years thick
    But out by us, it's just a thousand light years wide
    We're thirty thousand light years from galactic central point
    We go 'round every two hundred million years
    And our galaxy is only one of millions of billions
    In this amazing and expanding universe.

    The universe itself keeps on expanding and expanding
    In all of the directions it can whizz
    As fast as it can go, at the speed of light, you know
    Twelve million miles a minute and that's the fastest speed there is.
    So remember, when you're feeling very small and insecure
    How amazingly unlikely is your birth
    And pray that there's intelligent life somewhere up in space
    'Cause there's bugger-all down here on Earth.