Humans are Way Gullible

In units of Kelvin per cubic meter, or other forms of temperature per unit volume, the average human is hotter than the center of the sun.

This is, of course, completely ridiculous, completely true, and completely useless. And arguably meaningless. To start with, here’s the explanation.

The solar core (which I often referred to as “the center of the Sun” because it would make more sense to most people) has a temperature of about fifteen million Kelvin. This is known colloquially as “really hot.” And it is the center layer, with 24% the radius of the star itself. So it has a volume of about 2*10^25 cubic meters. (Numbers pulled from Wikipedia.) This is known colloquially as…no it isn’t. There is no comprehensible term for how big this is. Thousands of times the size of the Earth. Now that means that if you measure temperature per unit volume, you get about 7.5*10^-19 K/m^3. A small number.

Now do the same thing for a human. Temperature: 98.6 degrees Fahrenheit, 37 degrees Celsius, 310 Kelvin. Volume of a human body is a bit trickier, because who the heck knows the volume of a human body? I sure didn’t, but average weight is 136.7 lbs (or 62 kg if you prefer more sensible units). Since the human body has about the same density as water, that means the average human takes up 62 liters of space, or .062 cubic meters. xkcd verifies that this is about right. Google tells me that’s 16.4 gallons. So if you could liquefy your body, that’s what it would fit in. Also, ew.

Anyway, for the number we’re looking at, we want Kelvin divided by cubic meters. 310K/.062m^3 is five thousand Kelvin per cubic meter. (Yes, it just happened to be a round number. Don’t blame me.)

Sun: 7.5*10^-19.
You: 5*10^3
The ratio between those is 6.67*10^21. In other words,
In Kelvin per unit volume, you are six point six sextillion times hotter than the solar core.

(A sextillion, or 10^21, is better known as “big enough that when you say it people will only hear it as “too big.”” As a general rule, if a number ends in -illion preceded by anything except a boringly small consonant, nobody even heard it.)

There are a few problems with this statement. First: temperature per unit volume isn’t something anyone cares about. (Power per unit volume sometimes is, and humans still win that comparison against a type G star. But I was using temperature instead because it’s simpler and more people are familiar with it.)
The second problem is worse. What does “Kelvin per cubic meter” even mean? Watts per cubic meter would be the power output of an average cubic meter from the Sun, but if you want the temperature of an average cubic meter you just use regular temperature measurements. K/m^3 doesn’t even represent a physical quantity.
And if that ratio did mean something, “hot” is probably not the right adjective to describe it. “Hot” means high temperature, so calling this number heat would be like finding something with high pressure and saying that that must mean it has a lot of force. Which would be bad.

So what does all this have to do with humans being way gullible? A friend and I disagreed about this claim. I thought that most people would, if they understood how the math worked, not bother questioning it, accept it as true, and then proceed to ignore it. It’s what people do with most random factoids they hear. She had more faith in normal people, and thought they would notice how Kelvin per cubic meter is absurd and that temperature per unit volume is useless anyway. The numbers may work out, but they don’t matter in any meaningful way. The question was, would they bother to think of that?

Clearly this is a job for science. Or at least for uselessly informal semi-random sampling. Since I obviously don’t have the resources to conduct an actual survey, I just went and asked people. I was wandering around the engineering section of the university, because that way they’d have the best chance of actually understanding the question. Lots of them still didn’t (I had no way to make sure everyone walking down that street was an engineer, after all), so I just didn’t count those. After throwing those out, five accepted it as true without criticizing it and three pointed out that K/m^3 is weird, or that it’s a physically meaningless quantity, or whatever other legitimate point. No data on how many thought “your body is a sextillion times as hot as the center of the sun” was supposed to be a pickup line.

Obviously, eight people is such a small sample as to be almost useless. I don’t get to say that “sixty-two and a half percent of people believed me.” I can’t even declare myself to have been right. But it does show that it’s at least close, and that you can’t count on people to reject something backed by numbers even if it sounds off.

Also I think I might have accidentally convinced someone that the sun was very cold. I marked him down as not understanding the question.

OK, so people don’t pay attention to  math and so they’ll believe whatever you say. That doesn’t prove gullibility, or much of anything else. And you probably all knew that already. And it’s not even much of a big deal: If you tell me some counterintuitive but interesting fact about something I’m not familiar with, and give me the reasoning, I’d just file it away. Maybe people simply aren’t interested in numbers and units and the temperature of the Sun, which is still disappointing but for a different set of reasons. It’s not like “Kelvin per cubic meter? What does that even mean?” is a thought that comes naturally to normal people.

But, since I was asking strangers questions anyway, I went and did something I’ve wanted to do for a while now. I included the following question:

“Why is it that you can’t see the moon during the day? Is it because,
A: The sun is brighter and drowns it out, or
B: The moon is over on the other side of the world where it’s night, so the earth gets in the way?”
The correct answer is “You can see the moon during the day.” When people answered why it was impossible and seemed confident in their answer, I rather enjoyed seeing their faces when I pointed up. To where the moon was clearly visible. As pretty much the only object in that side of a blue sky.

The whole time I was asking these, I was thinking about how in the backstory my dad tells me to remember to use my powers for good. This “lying for fun to see if they’d notice” thing seemed a bit evil, but I wasn’t about to stop. It was too fun. And I have plausible philosophical arguments for why there’s nothing wrong with it as long as I show them the moon afterward. (If I ever show up laughing maniacally while villainously twirling the ends of an unexplained black mustache, tell everyone not to trust anything I say with numbers. Take that, potential evil future self!)

By an odd coincidence, the moon happened to be in conjunction with Jupiter at the time. So while the moon unfortunately wasn’t the only visible object in the sky, I did enjoy the fact that if it weren’t for making fun of people for not looking up, I probably would have missed it.

So they’d look up and, by Jove, they’d see the moon. Of course, they probably didn’t see Jove by the moon, and I didn’t know it was Jove until later that day. I could probably have convinced them it was a star that was visible in the day time because of something or other.

There were exceptions. One particularly clever person said that it was neither A nor B, but it was actually caused by Rayleigh scattering (better known as the thing that makes the sky blue). After agreeing a few times that because of Rayleigh scattering it was impossible to see the moon during the day, he added “also, you can see it.” He then said that Rayleigh scattering is actually the reason why the moon appears less bright during the day. I don’t know if he’s right or not (I suspect not), but he did beat the question.

Another person said, as soon as I had asked the moon question, that it is possible to see the moon in the day and she looks for it every day. But then, that person was wearing a “you are here” map of the galaxy on a T-shirt, so not exactly representative. I had some faith in humanity restored, until I got the next few wrong answers.

Of the fifteen responses I got, five called me on the trick question and the other ten were more or less evenly split between the two fake answers. It’s probable that some of the people who answered mistook the question for “when the moon is not visible, is it because A or B.” But judging by the looks on some of their faces when they saw the moon, there was at least a sizable minority who honestly did not expect to see a moon in a blue sky. Even though they had seen it loads of times before. Either I just radiate scary amounts of credibility, or people are ridiculously easy to fool. I’m guessing it’s the second one.


One thought on “Humans are Way Gullible

  1. anna

    “This is, of course, completely ridiculous, completely true, and completely useless.” This sounds like something the Doctor would say. And you lost me at useless. I tried to keep going, but woosh! it went right over my head. Good job!


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