Episode 2: Mag Perception

[00:00:00] Saul: Welcome to MagWorld, an alternative view of science and technology and history where we explore the world in terms of orders of magnitude. In MagWorld, we don’t bother with unnecessary precision. We say mag6 and this means a million or millions. There are mag10 humans on earth, and mag16 ants. Every mag level is 10 times higher, so a thousand is mag3 and a billion is mag9, and you can see right away that there are six mag levels between them, and every order of magnitude is a whole new level. So today’s episode is Mag Perception, in which we look at the common ways we measure our experience. What’s the difference between a mag2 and a mag3 pepper, for instance?

With me today is my friend Mike. [Mike: Hey, that’s me.] And I’m Saul, and this is Mag World.

Today’s science nerd hero is Gustav Fechner, who is a German guy. He was born in 1801, and he became a physics professor at the University of Leipzig. He discovered a lot of things, though, over the course of his life, and several things are named after him. So he discovered, there’s a thing called Fechner’s Paradox. Basically, if you look at a light with a darkened piece of glass over one eye, and then you close that eye, the light appears to become brighter, even though less light is coming into your eyes, because it’s called Fechner’s Paradox. According to Wikipedia, it occurs because the perceived brightness of the light with both eyes open is similar to the average brightness of each light viewed with one eye, basically your brain compensates for the fact that you’ve got only one eye open.

[Wow.] Anyway, that’s Fechner’s Paradox. He’s also got the Fechner color effect. I don’t know if you’ve ever seen this happen, but if you get a little color wheel, I’m sorry, if you get not a color wheel, you get a black and white disc with a pattern, a certain pattern on it, and then you spin it around, it will look colorful. If we took this disc, I have a little print out here of the actual disc, it’s called a Benham’s Top on a top so you can spin it around. And yeah, if you spin it around, you’ll see colors in the black and white pattern, and this is the Fechner color effect. [Cool.]

Him, Fechner, and his mentor, Weber, who is only like six years older than him, they discovered some laws, they’re called the Weber Fechner laws, which basically say that the stimulus needed to produce a additional response is proportional to the existing stimulus. That’s one of the laws and the other one is of kind of a follow on from that same thing, but basically it’s that so the first one, the one that they discovered first was weight that if you’re holding a certain mass or a certain weight, you can’t tell that additional weight has been added below, it’s called the just noticeable difference, the JND is literally the acronym. And the just noticeable difference for weight is 5% of the weight. So if you add less than 5% of the weight to what you’re already holding, you can’t tell the difference is not noticeable.

Mike: So the just noticeable difference is 5% of the entire weight?

Saul: Yes, that you’re holding exactly.

Mike: Just noticeable difference is kind of a mouthful, Saul.

Saul: Well, it’s actually called the JND.

Mike: Since Fechner developed this, can we just call it a Fetch? One Fetch is the just noticeable difference in weight or anything that you perceive?

Saul: You know, I’m open to that. Let’s see if we can’t make Fetch happen.

Mike: All right.

Saul: Okay, so where this is going though with MagWorld is that this, the follow on thing means that the perception scale that you have is logarithmic. So that means that the levels at which you’re going to perceive different things is going to be a mag scale.

For instance, let’s talk about sound. We think about sound or we can measure sound in two different main ways. One of them is loudness and the other one is frequency, the tone. And this is actually true of any wave, right? You’ve got a wave and you have the amplitude of the wave, how high it goes, how up and down it goes. And you’ve got the frequency or the wavelength of the wave, the wavelength and the frequency are, of course, related. And those are the two things that you can measure. If you’re playing a sound or playing a sound for you, you can say, well, this is at a certain frequency that’s going to adjust the pitch up or down.

And if we adjust the loudness, obviously, it’ll become louder. If we look at the loudness, that is measured in, you might know…[Decibel.] Decibels is the unit measure the loudness of something in. And decibels are a mag scale.

Mike: Oh, decibels, I’m not a serious audiophile. The decibels have always been a little bit confusing in the way they’re numbered. Because I feel like there’s tenths and negatives and I don’t know exactly what it all means.

Saul: Okay, let’s talk about this. So decibels are very, very, very closely related to a mag scale.

[00:05:00]If you understand the mag scale, we’ve been talking about basically ten decibels is ten times. So every time you go up ten decibels, the, actually, the amount of energy that you’re, that’s been put into that sound is ten times. And so if you’ve got a twenty decibel sound and you go up to thirty decibels, the thirty decibels is ten times more energy in it.

This is just like mag world, except for in mag world, it’s one mag. Mag one is ten times. And so decibels are just ten times a mag. So ten decibels is mag one. That’s it. What’s interesting with decibels, regarding sound, is that ten decibels is ten times the energy. But it feels like twice the volume.

Mike: Oh, that’s interesting. So that’s why when, if you have something going twenty to thirty decibels, it’s ten times the energy. But it doesn’t immediately blow my ear drums.

Saul: Right. Twice as much is a lot, but it’s not, yeah, it’s just twice as much. And that registers at a different level.

Mike: Oh, I often wear hearing protection. I’m just to protect my ear when working around loud tools or the noises or when going to concerts. And for work, my hearing protection says that there are 30 decibels sound reduction.

Saul: That is great to know. Thank you. I was going to mention this in regard to different topics. So you want to know what 30 decibels actually is.

Mike: And yes, because I’m like 30 decibels. Well, that sounds great. That’s a lot better than the 25 decibel reduction in these other brand. And

Saul: how much better is it?

Mike: Well, before today, I would have thought it’s five better.

Saul: So check it out. 30 decibels. How much of a sound reduction is that?

Mike: Oh, how many times lower is the sound? Saul: Uh-huh. Mike: Wouldn’t that still depend on the source? Like if I was working with a 60 decibel versus 100 decibel.

Saul: It doesn’t cut it down at the source. It cuts it down at your ear. So no, it doesn’t matter. That’s part of the point of this decibel scale it’s all relative. And so if you’re going down 30 decibels, it’s taking the energy down some fixed proportion.

Mike: So each 10 decibels is an order of magnitude. 1,000 times.

Saul: 1,000 times.

Mike: Yes. Three zeros. 1,000 times.

Saul: So it’s 1,000 times less energy going into your ear. Mike: Then if I wasn’t wearing it. Saul: Yeah.

Mike: See, that makes the odd cut that I make with the saw after forgetting my hearing protection sound that much worse.

Saul: Yeah.

Because it’s not just a little bit louder. It’s 1,000 times louder.

Saul: 1,000 times more energy. And it’s going to sound what every level is twice as much as the sound. 8 times as loud. Sound actually 8 times as loud to your perception. And yeah, that’s going to be quite loud.

I learned the similar fact with regard to silencers on guns. It’s where part of this research went. So we think, because of movies, Hollywood, whatever, that silencers make a gun–

Mike: Oh, I know the sound of a silencer. Pew, pew, pew.

Saul: Like you can’t even hear it. Like you can have a fight in a subway as per John Wick 2, I think, right? And firing weapons at each other and everybody around you says, I don’t know. I just saw a little ping off of the wall. I was like, no, no, no. That’s not what a silencer sounds like– (Or a gun with a silencer sounds like) a gun with a silencer does take 30 decibels off of the gun. But a gun is so loud about 140 decibels, I think, that taking it down to only 110. Like it actually is a substantial reduction. It still is. But it’s still quite loud.

Mike: Wait, so a silencer reduces by 30 decibels. The sound of a gunshot.

Saul: I believe so.

Mike: So it’s the same amount as like my hearing protection will take away, which I remember I was a boy scout. We did the rifle range. And even with hearing protection, those were loud.

Saul: Yes. So basically putting a silencer on a gun is similar to putting those earplugs in. And if you did both, then it would be a 60 decibel reduction.

Mike: Mm-hmm. Saul: Yep. Mike: Wow that is fascinating and really convincing me to be more stringent about my hearing. Because a thousand times more energy. Sounds bad.

Saul: It sounds bad.

I want to get to a couple other things here, which is that the Just Noticeable Difference for sound in terms of decibels is three decibels. Three decibels is the Just Noticeable Difference for a sound. And that three decibels corresponds to twice as much.

Mike: So in order for me to discern that a sound is louder than another sound, it has to be [00:10:00] have twice as much sound energy. [Yes.] Wow.

Saul: Yeah. This is actually some good stuff to remember here. Both for decibels. And if you need to remember what mag point three is, it is double. Just like in decibels, three decibels is double and mag point three is double. They are the same thing.

Mike: Oh, so mag two is half of mag two point three.

Saul: That is 100% correct. Yes. [Great.] Well, now we’re going to talk about frequency. This is the other half of this. We talk about decibels. And that’s how loudness gets measured. And how frequency gets measured is in terms of hertz, for instance. Right? It’s the number of cycles per second. You get a tuning fork. You hit on the thing. It’s 440 hertz.

The main deal is that the frequencies fall into bands too. So what I’ve noticed here is that we have this decibel scale. And decibels can go way up in terms of loudness. And yet we kind of stop at around 150 decibels. That’s 15 orders of magnitude. So zero decibels is kind of the noise floor, the sound floor. It’s like this is quiet as far as humans are concerned. You can go negative decibels because there’s more quiet than like you think it’s quiet. But actually it’s not. There’s actually this sound going on. And so you can go negative. But zero is the human perceptual floor. And so we can go 15 or so orders of magnitude higher than that, which is amazing. But that starts getting up into ear damaging territory. I mean, it is ear damaging territory. Even above 80 decibels is ear damaging if it’s prolonged. And so if that’s 15 orders of magnitude.

Frequency wise though, all of our human perception of sound lies within four orders of magnitude. Only. Mag 1, 2, 3, and 4. And that’s it. We can’t hear higher than four. And below mag 1 frequency is actually just beats. Like if you have like five hertz, that’s like imitates drum beats like you can actually hear that as individual beats. But then once it gets above 20 hertz or so, it turns into a low, throbbing hum And then that’s the lowest notes that we can hear. And then it goes all the way up to about 20 kilohertz of frequency. And you can hear those. And above that, it’s like dog whistles. You basically can’t hear it.

Mike: So 20,000 hertz is around the top of our range for hearing. So that’s mag 4.

Saul: And that’s mag 4, exactly.

Now we’re going to listen to the frequency differences. We’re going to look at what the four different bins of sound. Actually, the fact that we can hear four different bins of sound frequencies is kind of remarkable.

Mike: Will you explain that? What do you mean four different?

Saul: So the frequencies we can hear are between 20 hertz and 20 kilohertz. Yes. It’s a thousand times difference. I am segmenting the bands by 10 to 100, 100 to 1000, 1000 to 10,000 and 10,000 and up. [Got it.] So even though yes, it’s only a thousand times difference. We’re calling it four different bands for simplicity. In mag world, it would be called four different bands. Okay. I have specially chosen these songs because of how they represent these frequencies very well. See if you can recognize the songs. Are you ready?

This one is mag one frequencies.

[Seven Nation Army clip]

Mike: That was the white stripes. That was the very first song my daughter learned on her bass.

Saul: Interesting. Yes. It’s a classic example of exactly those frequencies. And I picked it because that’s all you’re getting.

Every single note in that intro there is a mag one note there below 100 hertz. So if you want to know what 100 hertz sounds like, or I’m sorry, the notes from 10 to 100 hertz, you can just imagine the opening to Seven Nation Army by the White Stripes. And yeah, that’s what mag one frequency sounds like.

Mike: 10 hertz to 100 hertz.

Saul: Yep. So this is I was saying that mag two covers a lot of ground. Mag two is basically most things that you can make with most instruments. So every octave on a piano is double. That is, that is definitional. And so on a piano, you’ve got eight octaves, right? So that would be 200 times the difference from the very lowest note, which is around some 50 hertz, something like on there all the way up. So you do get up quite high and a little plink plink notes, what I was trying to get at is that you’re singing voice [Got it.] is only mag two.

You cannot hit–some extreme baritones can hit below 100 hertz. And the highest notes [00:15:00] that a soprano female soprano can sing are just barely mag three. High C is just over a thousand hertz. And so there are notes that can be hit, but they’re just over that. And there’s no way you’re getting anywhere close to 10,000 hertz or even 5,000 hertz.

So what I wanted to do is to illustrate this point was to play for you a song that where all of the notes, I confirm, well, I read on the internet anyway, I tried to confirm that the highest note sung here is still under, is still in the mag two range, it’s still under a thousand hertz. You ready? Let me know if you’ve heard this song.

[Bohemian Rhapsody clip]

That high note is still mag two. Wow. Yeah. And by the way, I learned that is not Freddie Mercury singing, that is Brian May. Freddie Mercury apparently couldn’t hit that note. Scandal!

Mike: Impressive.

Saul: Yeah. So every note that you heard that was sung is mag two. Okay.

So I did go and I tried to find what would mag three be. So this is a famous example of the mag three band. And basically, it’s all only instruments can hit that. I mean, some sopranos, like I said, can hit the very low end of the scale. But for the most part, this entire frequency band, mag three, between a thousand hertz and 10,000 hertz is like this.

[Stars and Stripes Forever clip]

Mike: So the piccolo.

Saul: The piccolo is mag three. Yup.

Mike: How many other instruments?

Saul: The flute, piccolo, all these little short jawnies, basically.

And that’s what it sounds like. There’s no way a human, well, like I said at the very low end of the scale, a human can sing that, but not any higher than that. And it sounds like piercing, right? It’s like a bird. A bird is mag three. Right?

Mike: Yeah. Birds are beautiful, but I don’t think that I could listen to a piccolo solo without something holding down [the lower end] Yeah, or at least the mag two.

Saul: So then that was the mag three piccolo. So mag four is not an actual instrument.

Mag four, the sounds that make up or the things that make mag four sounds are percussive. You cannot, I tried listening to mag four sounds as actual notes, like sine waves, and stuff like that, it is piercing. It is not pleasant. Listen to. And so what you actually wind up hearing in this range sounds like this.

[Rock And Roll clip]

Right? So it’s cymbols and high hats. Like you get that attack, you get it just for a brief little bit. It sounds like white noise kind of up there. It’s really high notes, or not high notes, really high frequencies. And that’s what, that’s what that frequency sounds like.

Mike: Wow.

Saul: Yeah. Here’s another one that I came up with here. This is a Chappell Roan song. And I broke it down to four segments. One each, for one for each of the mag levels. Each one is about, is a few seconds long. I’m limiting the bands just to these frequencies.

[clip starts playing]

Mike: I’m stuck on the outside of the club. Saul:Yep. This is mag 3. And that’s what’s left at mag 4. Mike: Yeah. That just sounds like, part of your cymbol hits

[clip stops playing]

Saul: Yep. And it’s the wash of the cymbol hits.

Not the attack, not anything else of that. That’s mag 4. And so that’s the range that we can hear in terms of frequency is four mag levels.

Okay.

So let’s talk about light briefly here. So we can, you can see light obviously, right? And it, the same thing is true with visual perception as with sound perception in that the amplitude of the waveform, the amount of energy in it, you can detect that’s the brightness of it, right? And that follows a mag scale. And in fact, the similar thing where you can detect changes in light with this logarithmic scale.

Now, it turns out this is actually, so this is, this is some of the things that Weber and Fechner figured out was the amount of light required to see perceptual differences. Same kind of thing. It turns out that at the lower end of [00:20:00] the scale, those laws don’t quite apply. Basically, it’s daytime light. In daytime light, this is exactly the case. It’s in nighttime light that uses the,

Mike: the rods in your eye which are more [right, exactly] attuned to low light differences, instead of the cones that are color most of your daytime vision.

Saul: Yep. So you can’t see hardly anything. You can’t tell the character difference between these frequencies with your rods. But you can tell there’s anything there at all, which is of course very helpful if any kind of night thing happens. This is actually where also the night vision, you know, it takes you a little bit of time to get used to a room. It’s because your senses have been already overwhelmed by existing light.

And the proportional difference would have to be on the same level in order for it to respond. And so you have to wait some amount of time for that to decay so that you can now respond to these much lower levels. And so that’s on the mag scale.

Now, what’s interesting though, I was going to say about this is that the frequency range for visual light that you can see is between about 300 nanometers wavelength and 700 and some nanometers wavelength. It’s entirely contained within a single order of magnitude. Not only a single order, one order magnitude, a half mag, it is contained within one half mag are the frequencies that we can see. Yeah.

So, and this is in contrast to the sound where you can hear four orders of magnitude or three orders of magnitude spread across four mags. Yeah.

Mike: What is an order magnitude up or down from our visual range?

Saul: That is a great question. Basically, mag 15 is the visible light range is just under mag 15 frequency. And mag 16 is ultraviolet and mag 14. Actually, it’s a little closer to mag 13 is infrared. Yep. Mike: So, mag 15 is the frequency of our visual range. Saul: Just under. Yep. Mike: Just under mag 15. Saul: So, mag 15 light. Mike: Mag 15 light.

Saul: Okay. So, we’ve talked about weight, right? And the perceptual difference there. We’ve talked about sound. We’ve talked about visual light.

Okay, we have one more thing to cover here. It’s what we’ve all been waiting for.

Mike: What’s that?

Saul: Mag spicyness level.

Mike: Love it. So you walk into a restaurant. And they say, how spicy would you like your wings? And you say.

Saul: Two and a half stars. Right? Is that what people say? Two and a half stars?

Mike: Well, I mean, if you’re weak. Not that strength is measured by your tolerance to spice. But there is a lot of fascination that goes around the top end of spicy, I believe.

Saul: Yes, there is. And there is a whole thing like it is a game to try to prove out that you can handle more spice. I remember seeing a chip. It was the one chip challenge at the 7-Eleven where you paid five dollars for a single chip. That was doused in, it was a Carolina Reaper, I think. And the back of the chip said, how long can you wait without eating or drinking anything? And if you can go one minute, you were a wuss. And if you could go like 10 minutes, you’re better. And if you can go half an hour, you’re a hero. And you’re invincible if you can go an hour, whatever.

So it turns out that the Carolina Reaper is one of the hottest peppers out there. Well, let’s start. Let’s go back a little bit further. So you were asking the restaurant. How spicy do things go? I think they’re generally measured on a scale from one or zero to five stars, right?

Mike: Yeah.

Saul: Peppers are measured in a unit called scovilles. And they are measuring the amount of capsicin that is in the pepper or the capacin equivalent.

Mike: I’ve heard that for sure.

Saul: And so if you look on Wikipedia or wherever else, you can find a list of all these different peppers. And how many scovilles they’re rated because of this. And the Scoville scale is a linear scale. But if you look at it in these, in these charts, it’s very clearly, at least in my mind, it is clearly it’s a mag scale. You start with banana peppers or very, very light peppers that are like 500 scolvilles. And then it goes to 2000. And then it goes to 10,000 and 50,000. And by the time you’re getting up to the Carolina Reaper, that’s in the millions.

And this is a mag scale, right? And it totally maps. If you want to talk about it like this in mag world, they would be a mag. Well, a banana pepper will be a mag two pepper. And Carolina Reaper will be a mag six pepper. And we can talk about serrano as being, I think it’s mag four. Here we go. Here’s my little handy chart.

Mike: Oh! So banana pepper would be pretty low.

Saul: So the way I think of it is that a mag zero pepper is basically not spicy. It’s not, it’s not mild or the lowest spicy. It is no spice.

Mike: That is a bell pepper.

Saul: That is a bell pepper, exactly. And even then, I’m not even sure, a bell pepper might even be mag one. A banana pepper already is mag two. And then it goes up from there.

[00:25:00] So a poblano is a mag three pepper. A jalapeno is mag three and a half.

Mike: I can tell the difference between a banana pepper and a jalapeno for sure.

Saul: Can you tell the difference between a jalapeno and a poblano?

Mike: I think so.

Saul: Yeah, I think so too.

And there’s a reason that they build the charts with the half mags separately, right? Yeah. And so then going up from a jalapeno, the next half mag up from that is a serrano. So then going up from serrano’s, you know, serrano’s are mag four. So then a mag four and a half is a Tabasco pepper or cayenne pepper. Right. So that’s mag four and a half.

And then mag five is a habanero or a Scotch bonnet. And then we do have mag five and a half Red Savina habanero basically there’s a breed of habanero peppers that are up there. And then mag six are the Carolina Reaper and the scorpion, the ghost pepper. Like that’s up there. And then there’s pepper X, which is mag six and a half.

And I just learned that there is one person who’s basically responsible for breeding these mag six peppers. And his name is Ed Currie. Smoking Ed.

Mike: No!

Saul: Yes. [Curry?!] C-U-R-R-I-E, but nevertheless, this is clearly a case of nominative determinism.

The top hot ones, pepper, the 10th wings are produced by Ed Curry’s company. So watching hot ones. Mike: There’s always the fire graphics with all these trailing zeros. Now I’m kind of like, I, I haven’t memorized how hot different things are. I just know by the number of. Like which number wing they’re on, how hot I should expect the person to react to.

Saul: So interesting. So I think in mag world, we would very distinctly say this is a mag three or a mag five or whatever pepper and organize them that way. Even. And so if you have 10 peppers and you may as well go right up the scale. But they don’t do it that way. They start at mag three because there’s kind of no point in having a bell pepper chicken wing.

I think that what’s happening here when you’re looking at that spicy level and you’re noting the the wing, the which order it is you’re literally looking at the mag level of the wing.

That’s how you how you’ve internalized you just haven’t like internalized that it’s the mag level or the half mag level.

Mike: So these are logarithmic wings

Saul: log wings! Yeah, everything looks linear on a log log scale of the fat magic marker.

So that’s hot ones that I think from now on, if you want to just call a jalapenos mag three and it’s kind of like three stars, right? If you said–if you were getting a jalapeno based dip or something like that, would you say it’s a three star dip?

Mike: I don’t know. Yes. Yeah, I think I would. Yeah. Well, I think if mag six is an irresponsibly hot pepper.

Saul: Yes. Irresponsibly hot.

Mike: Then a five scale is perfect.

Saul: Right. And you can go up to six if you really want to, but you really shouldn’t. Yep.

Mike: I think we need. Now that we’ve come up with this mag scale for hotness. We need to get all the restaurants to normalize their dishes. Because have you ever been in a situation where you’re like. Mm, Yeah. I love. I love a three star. Three star. My favorite restaurant is always good. And then you go to a new restaurant. And you order a three star. And it’s not. It’s not the three star you’re used to. [Nope] Either way is disappointing.

Saul: Right. It is. Yeah. I would love to standardize on this scale or.

Mike: Well, we pitched this hot ones and then they use their. Popularity to get this.

Saul: For sure. I, um, that’s what we’re here for. We’re trying to change the world one scale at a time, right?

Next time on mag hot ones.

Well, that’s all I have for today for mag perception. We’ve covered a lot of ground with the sound and light and spicy… Yeah, they all fit on a mag scale.

Mike: Great. Well, thank you for doing the math.

Saul: Thanks for being here, Mike. I really like talking with you about this stuff. And I will see you next time.

Mike: Bye-bye.