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Old 09-04-2012, 12:04 PM   #1
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Default A mole of moles

What would happen if you were to gather a mole(unit of measurement) of moles (the small furry critter) in one place?
—Sean Rice
Things get a bit gruesome.

First, some definitions. A mole is a unit. It’s not a typical unit, though. It’s really just a number—like “dozen” or “billion.” If you have a mole of something, it means you have 602,214,129,000,000,000,000,000 of them (usually written 6.02210^23). It’s such a big number because it’s used for counting numbers of molecules, which there are a lot of.



"One mole" is close to the number of atoms in a gram of hydrogen. It’s also, by chance, a decent ballpark guess for the number of grains of sand on Earth.

A mole is also a type of burrowing mammal. There are a handful of types of moles, and some of them are truly horrifying.


So what would a mole of moles—602,214,129,000,000,000,000,000 animals—look like?

First, let’s start with wild ballpark approximations. This is an example of what might go through my head before I even pick up a calculator, when I’m just trying to get a sense of the quantities - the kind of calculation where 10, 1, and 0.1 are all close enough that we can consider them equal:

I can pick up a mole (animal) and throw it. Anything I can throw weighs one pound. One pound is one kilogram. The number 602,214,129,000,000,000,000,000 looks about twice as long as a trillion, which means it’s about a trillion trillion. I happen to remember that a trillion trillion kilograms is how much a planet weighs.



… if anyone asks, I did not tell you it was ok to do math like this.

That’s enough to tell us that we’re talking about pile of moles on the scale of planets. It’s a pretty rough estimate, though, since it could be off by a factor of thousands in either direction.

Let’s get some better numbers.

An eastern mole (Scalopus aquaticus) weighs about 75 grams, which means a mole of moles weighs (6.02210^23)75g≈4.5210^22kg.

That’s a little over half the mass of our moon.

Mammals are largely water. A kilogram of water takes up a liter of volume, so if the moles weigh 4.5210^22 kilograms, they take up about 4.5210^22 liters of volume. You might notice that we’re ignoring the pockets of space between the moles. In a moment, you’ll see why.

The cube root of 4.5210^22 liters is 3,562 kilometers, which means we’re talking about a sphere with a radius of 2,210 kilometers, or a cube 2,213 miles on each edge. (That’s a neat coincidence I’ve never noticed before—a cubic mile happens to be almost exactly 4/3 π cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that’s X miles on each side.)

If these moles were released onto the Earth’s surface, they’d fill it up to 80 kilometers deep—just about to the (former) edge of space:



This smothering ocean of high-pressure meat would wipe out most life on the planet, which could—to reddit’s horror—threaten the integrity of the DNS system. So doing this on Earth is definitely not an option.

Instead, let’s gather the moles in interplanetary space. Gravitational attraction would pull them into a sphere. Meat doesn’t compress very well, so it would only undergo a little bit of gravitational contraction, and we’d end up with a mole planet a bit larger than the moon.



The moles would have a surface gravity about one-sixteenth as strong as Earth’s—similar to that of Pluto. The planet would start off uniformly lukewarm—probably a bit over room temperature—and the gravitational contraction would heat the deep interior by a handful of degrees.
But this is where it gets weird.

The mole planet is now a giant sphere of meat. It has a lot of latent energy (there are enough calories in the mole planet to support the Earth’s current population for 30 billion years). Normally, when organic matter decomposes, it releases much of that energy as heat. But throughout the majority of the planet’s interior, the pressure is over a hundred megapascals, which is enough to kill all bacteria and sterilize the mole remains—leaving no microorganisms to break down the mole tissues.

Closer to the surface, where the pressure is lower, there’s another obstacle to decomposition—the interior of a mole planet is low in oxygen. Without oxygen, the usual decomposition doesn’t happen, and the only bacteria that can break down the moles are those which don’t require oxygen. While inefficient, this anaerobic decomposition can unlock quite a bit of heat. If continued unchecked, it would heat the planet to a boil.

But the decomposition is self-limiting. Few bacteria can survive at temperatures above about 60 C, so as the temperature goes up, the bacteria die off, and the decomposition slows. Throughout the planet, the mole bodies gradually break down into kerogen, a mush of organic matter which would—if the planet were hotter—eventually form oil.

The outer surface of the planet radiates heat into space and freezes.

Because the moles form a literal fur coat, when frozen it insulates the interior of the planet and slows the loss of heat to space. However, the flow of heat in the liquid interior is dominated by convection. Plumes of hot meat and bubbles of trapped gases like methane—along with the air from the lungs of the deceased moles—periodically rise through the mole crust and erupt volcanically from the surface, a geyser of death blasting mole bodies free of the planet.

Eventually, after centuries or millennia of turmoil, the planet calms and cools enough that it begins to freeze all the way through. The deep interior is under such high pressure that as it cools, the water crystallizes out into exotic forms of ice such as ice III and ice V, and eventually ice II and ice IX (no relation).

All told, this is a pretty bleak picture. Let’s try an alternate approach.

I don’t have any reliable numbers for global mole population (or small mammal biomass in general), but we’ll take a shot in the dark and estimate that there are at least a few dozen mice, rats, voles, and other small mammals for every human.

There might be a billion habitable planets in our galaxy. If we colonized them, we’d certainly bring mice and rats with us. If just one in a hundred were populated with small mammals in numbers similar to Earth’s, after a few million years—not long, in evolutionary time—the total number which have ever lived would surpass Avogadro’s number.

If you want a mole of moles, build a spaceship.

Attached Thumbnails
A mole of moles-moles_too_many.png   A mole of moles-moles_star_nosed.png   A mole of moles-moles_number_length.png   A mole of moles-moles_layers.png   A mole of moles-moles_scale.png  

A mole of moles-moles_rocket.png  

Last edited by Joe Perez; 09-04-2012 at 12:58 PM. Reason: Fixed notations
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Old 09-04-2012, 12:05 PM   #2
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We should have a "Insert Joe Perez here" section
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Old 09-04-2012, 12:07 PM   #3
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Moles live underground.

Much like a troglodyte.
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Old 09-04-2012, 04:05 PM   #4
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Oh the days of stoichiometry and the mole train...
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Old 09-04-2012, 04:29 PM   #5
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Quote:
Originally Posted by 18psi View Post
We should have a "Insert Joe Perez here" section
We do have a good "Insert Joe Perez here" thread, for lack of an actual section...

https://www.miataturbo.net/insert-bs...favorite+rants
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Old 09-04-2012, 04:37 PM   #6
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Joe, do you have a blog? If you do not you should.

You are probably the first person I have ever said that to. You are also the first person that I have come across on the web that is entertaining enough for me to just read the random **** you think about. I think it is not only the thoughts but the way in which you express them with the accompanying pictures. It is just entertaining in the purest sense of the word.
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Old 09-04-2012, 04:39 PM   #7
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so he can copy and paste stuff from other blogs?
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Old 09-04-2012, 05:00 PM   #8
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Haha.

Yeah, most of the stuff I post is original (including all of the rants) but these past few (the ones with XKCD-style illustration in them) are just taken straight from XKCD. Trust me- I absolutely suck as an artist. So if it has pictures, I probably didn't create it.

I'm merely copying-and pasting the work of others, just as JasonC does with his political and economic philosophy.

If you're not familiar with XKCD, it's a very amusing webcomic that tends to skew towards the higher-geek audience: http://xkcd.com/ (eg: past punchlines have included string theory, the personal life of Mr. and Mrs. Heisenberg, accidentally taking the Fourier transform of a cat, etc.) It's written for mass-appeal, though. You don't have to have a PhD to understand it.
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Old 09-04-2012, 06:04 PM   #9
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Quote:
Originally Posted by Joe Perez View Post
Haha.

Yeah, most of the stuff I post is original (including all of the rants) but these past few (the ones with XKCD-style illustration in them) are just taken straight from XKCD. Trust me- I absolutely suck as an artist. So if it has pictures, I probably didn't create it.

I'm merely copying-and pasting the work of others, just as JasonC does with his political and economic philosophy.

If you're not familiar with XKCD, it's a very amusing webcomic that tends to skew towards the higher-geek audience: xkcd: Nine (eg: past punchlines have included string theory, the personal life of Mr. and Mrs. Heisenberg, accidentally taking the Fourier transform of a cat, etc.) It's written for mass-appeal, though. You don't have to have a PhD to understand it.

Your vaccum-source-for-wastegate writeup had some cute anime pictures.
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Old 09-04-2012, 06:09 PM   #10
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Quote:
Originally Posted by Faeflora View Post
Your vaccum-source-for-wastegate writeup had some cute anime pictures.
Hehe. Yeah, I almost forgot about that. Those images were lifted from some random webcomic and edited to fit the context. I think one of them had sexynurse leaning seductively against the curve of a line-chart if I recall correctly. Just a lot of searching for the correct images to fit the context of the posting.

But the text of that one was all original. So I guess that kills the "If it has pictures then I didn't write it" rule. That's probably not a reliable rule at any rate, as I try to interject cat-based (and now pony-based) humor into serious technical postings to lighten the mood.
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Old 09-05-2012, 11:07 AM   #11
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Joe's antics are half the reason I read every thread on this forum. Even ones that I don't care about. There is Joe Perez gold spread out everywhere, just waiting to be discovered.
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Old 09-09-2012, 04:16 AM   #12
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Was the hello kitty/***** crank trigger a Joe original?
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Old 09-09-2012, 12:04 PM   #13
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Was the hello kitty/***** crank trigger a Joe original?
Haha.

Yeah, that was mine. I'm perfectly capable of slapping together clipart from different sources, I just can't draw for ****.
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Old 11-06-2012, 04:28 PM   #14
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This one had me rolling. Any electoral analysis in which the density of cocaine is a variable is just too good to not pass on.


What if there's LITERALLY a tie?
—Nate Silver, Twitter, January 4th, 2012

In most states, a popular vote tie is broken by a coin toss or drawing names from a hat. The odds of a many-state tie are slimmer than the odds of the hat being hit by a bale of cocaine dumped from a drug-smuggling airplane.

Nate Silver flippantly posted his 'tie' question on Twitter during the tallying of the extremely close 2012 Republican Iowa Caucus results. In that case, an exact tie was averted—Santorum ended up winning by 34 votes out of 121,503. And since it was a non-binding nominating vote, the Iowa Republican Party could handle a tie any way they wanted.


But since it’s Election Day, let’s apply his question to the current contest. What will happen if there's a tie?

I don't mean an electoral college tie. There’s probably about a 1 in 500 chance of one of those this year, and the consequences are thoroughly explored. I mean both candidates getting the same number of votes in a swing state. How unlikely is it?

Several researchers—including Silver himself—have calculated the odds of a state winner being decided by a single vote, which is effectively the same as the probability of a tie vote. For typical close states, the linked article calculates the probabilities to be in the neighborhood of 1 in 100,000—which makes intuitive sense, since 100,000 is the sort of vote margin by which swing state elections are typically decided.


But what if the tie happens anyway?


For that matter, what if there’s a tie in every close battleground state?


Well, for starters, recounts happen. But since recounts happen in close elections in general, these are just as likely to create ties as to break them. They don’t change the underlying probability. So let’s assume that after all recounts, there’s a tie. What then?

The short answer is that it’s up to the state’s laws.


I went through the general laws of nine competitive states to see how they handle popular vote ties. In most of them, the tie is broken by “drawing lots”—that is, randomly. (If you’re curious, here are links to some tie vote laws in each state: Virginia, North Carolina, Florida, Ohio, New Hampshire, Wisconsin, Colorado, Iowa, Nevada).


“Drawing lots” can mean a coin toss, drawing straws, or picking a name from a hat. Most states leave the details up to the Secretary of State or an electoral board, although Iowa Code 50.44 specifies that the names be written on pieces of paper and placed in a “receptacle”. In North Carolina, however, a tie vote (when more than 5,000 votes are cast) results in a new election. (Which could potentially itself result in a tie ...)

But let’s imagine that there’s not just one state that’s tied—instead, the nine most competitive states are tied (and the rest go as expected). If North Carolina held a runoff to break the tie, and the other eight states flipped coins (or picked from Iowa’s receptacle), Obama would be reelected in 431 out of 512 cases—about 84% of the time.


But how likely is a nine-state tie?

If we ballpark the odds of a tie vote in each close state at 1 in 100,000, then the odds of a tie vote in all nine states is in the neighborhood of one in a quattuordecillion—1 followed by 45 zeroes. (This ignores vote correlation between states, but it’s good enough for a first-order estimate).

Florida is hit by an average of 66 tornadoes per year. If each tornado is 50 yards wide and has a path 1.5 miles long (which is typical, if not necessarily the mean), we can calculate that a typical location in Florida experiences an average 1.4 picotornados per second:


66 (tornadoes / year) ((1.5 miles50 yards) / Area of Florida) 1.41012 tornadoes / second


Astronomer Alan Harris calculates that a person’s lifetime odds of death from a comet or meteorite impact are about 1 in 700,000. If a typical person in the calculation lives 70 years, this suggests a Florida resident suffers an average of 0.64 femtodeaths per second from meteorite impacts:



(1/700,000) deaths) / 70 years 6.41016 deaths / second


In 1994, drug smugglers fleeing the authorities dropped an estimated 20 bales of cocaine from an airplane over Florida—one of which crashed through the roof of a Crime Watch meeting and narrowly missed the Homestead Chief of Police. If Florida has been hit by 20 bales of cocaine over the last 20 years, then the average person in Florida is struck by an average of 29 zeptobales of cocaine per second:



(20 bales / 20 years) (((75 kg / Density of cocaine) 2/3) / Area of Florida) 2.91021 bales / second

(By the way—this means that given a street price of $20,000 per kilogram, a typical acre of Florida land produces an average revenue of three cents per year in falling cocaine bales).


Putting all this together: The probability that every battleground state is exactly tied is roughly equal to the probability that, when one of the Florida electors reaches into the hat to draw a name, he or she is struck by a falling cocaine bale, the hat is hurled away within the next few seconds by a tornado, and the elector is obliterated minutes later by a meteorite impact.


If you’re in the US, don’t forget to vote—your vote could make or break a tie.

And if you’re voting in Florida, keep an eye on the sky.
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A mole of moles-tie_map.png   A mole of moles-tie_map_all.png   A mole of moles-tie_coin_toss.png   A mole of moles-tie_catastrophe.png  
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Old 11-06-2012, 04:47 PM   #15
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Shouldn't it be "a mol of moles"?
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Old 11-06-2012, 04:51 PM   #16
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Quote:
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Shouldn't it be "a mol of moles"?
Then we have no meat for the joke.

edit: bah I have it backwards, we still get our mole meat.
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Old 11-06-2012, 05:17 PM   #17
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I propose a tie breaker of the following fashion:

All registered nonvoter names are put into a hat and one is drawn at random. That person is contacted and allowed to vote.

Then that individual are allowed to have secret service for life to prevent their early demise from the slightly-less-than-50% minority.
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