Hi, Reddit.

My name is Aaron Santos, and I’ve made it my mission to teach math in fun and entertaining ways. Toward this end, I’ve written two (hopefully) humorous books: How Many Licks? Or, How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. I also maintain a blog called Diary of Numbers. I’m here to estimate answers to all your numerical questions. Here's some examples I’ve done before.

Here's verification. Here's more verification.

Feel free to make your questions funny, thought-provoking, gross, sexy, etc. I’ll also answer non-numerical questions if you’ve got any.

Update It's 11:51 EST. I'm grabbing lunch, but will be back in 20 minutes to answer more.

Update 2.0 OK, I'm back. Fire away.

Update 3.0 Thanks for the great questions, Reddit! I'm sorry I won't be able to answer all of them. There's 3243 comments, and I'm replying roughly once every 10 minutes, (I type slow, plus I'm doing math.) At this rate it would take me 22 days of non-stop replying to catch up. It's about 4p EST now. I'll keep going until 5p, but then I have to take a break.

By the way, for those of you that like doing this stuff, I'm going to post a contest on Diary of Numbers tomorrow. It'll be some sort of estimation-y question, and you can win a free copy of my cheesy sports book. I know, I know...shameless self-promotion...karma whore...blah blah blah. Still, hopefully some of you will enter and have some fun with it.

Final Update You guys rock! Thanks for all the great questions. I've gotta head out now, (I've been doing estimations for over 7 hours and my left eye is starting to twitch uncontrollably.) Thanks again! I'll try to answer a few more early tomorrow.

Comments: 4344 • Responses: 24  • Date: 

kipz0r2013 karma

If I gain a kilo of weight here on earth, how much more will my wife be attracted to me?

aarontsantos2767 karma

Assuming you're 80 kg and she's 60 kg and you're standing 1 m apart, she'll be attracted to you with an extra 4x10-9 Newtons of force. That makes you about 1.2% more attractive to her.

shakadan1826 karma

How fast do you have to throw a burrito so it catches on fire?

aarontsantos2001 karma

Ooh...me gusta. I'm gonna guess a burrito has a similar flashpoint (i.e. the temperature at which it ignites) to wood, which would put it around 300 degrees Celsius (~570 Kelvin). There's a lot of water in food, so I'll assume they have similar heat capacities (~4 J/g K). As such, a 0.5 kg burrito would need to gain 500 kJ of heat energy to ignite. The energy lost due to friction for a burrito will be about the same magnitude as that for a baseball. I'm assuming all the energy lost to friction goes into heating the burrito. (Numerical Assumptions: Drag coefficient ~ 0.3, Area ~ 9 square inches, air density 1.2 kg/m2, burrito catchs on fire in 1 second.) This will be about (0.0003 kg s/m) x (velocity)3. This gives about 1000 m/s.

oldmanjank1586 karma

This is great; hooking the minds of young scientists with hilarious, gross, and risqué calculations can't be understated.

Two questions: 1) How many semesters would it take to gather enough pubes from a dormitory floor to make a size large sweater? 2) I think you're great, can I send you a sweater?

aarontsantos1497 karma

OK...now this is my kind of question. I'll assume 1 cm long pubes spaced 2 mm apart covering a total area of 20 square inches. Laid end-to-end, that gives a total pube length of about 60 m for each person. At about about 10 microns thick with a density of 1 g/cm3, you'd have a total mass of about 64 mg of hair. The mass of a sweater might be 0.3 kg. From this, you can see that you'd need about 5000 people or roughly 100 dorm floors assuming 50 people per floor.

If only for shock value...yes, I'd love a sweater....

JonathanZips703 karma

Is it more dangerous to own and regularly ride a motorcycle, or regularly use cocaine?

aarontsantos1013 karma

A quick web search shows that in the U.S., about 4000 cocaine-related deaths occur each year. There is a similar number of motorcycle related deaths. The fraction of cocaine users over the age of 12 is about 0.7 percent. There are about 6 million motorcycle riders in a U.S. population of 300 million, meaning that roughly 2 percent of Americans are motorcycle riders. Given a similar numer of deaths, but about 3 times as many riders as cocaine users, it's likely that cocaine use is more dangerous.

Sources: http://schansblog.blogspot.com/2009/05/cocaine-deaths-statistics-lies-and.html http://en.wikipedia.org/wiki/List_of_motorcycle_deaths_in_U.S._by_year http://www.drugabuse.gov/publications/drugfacts/cocaine http://wiki.answers.com/Q/How_many_Americans_ride_motorcycles

khudgins701 karma

You're on a westbound train out of Novosibirsk that has just left the station with a 3rd class ticket that doesn't guarantee you a seat. You're travelling with a standard steamer trunk full of old magazines left to you by your recently deceased eccentric grand-uncle. It will take 42 hours, including stops, to reach your destination on the Black Sea. Assuming you can find somewhere to sit, do you have enough reading material for the trip?

aarontsantos951 karma

Love the detail in this one. Let's see. It takes me about half an hour to read through a magazine. (I'm a slow reader, but I tend to skip pages.) This means I'd need about 80 magazines for the whole trip. If magazines are 0.5 cm thick, you should be able to stack at least 100 in your steamer trunk. BTW, sad to admit I had to look up what a steamer trunk is :(

wheelis607 karma

How many Hot Pockets would you need to burn to release the amount of energy released by a standard US issue hand grenade?

aarontsantos691 karma

I do a similar problem to this one in How Many Licks? (though mine is with McDonalds Burgers and nuclear bombs.)

I'm going to assume the source below is correct. (Not necessarily a safe assumption.) It lists about 800 kJ of energy for the grenade. A hot pocket has about 300 Calories. A Calorie is just another unit of energy. 300 Calories equal to about 1kJ of energy. (Food calories are 1000 times bigger than the physics calorie.) You'd need about 800 hotpockets to equal 1 hand grenade. If this number is surprisingly low, remember you have to consider rate. All the energy of a grenade is released instantly, were as it takes a while to burn all the hot pockets.

Source: http://answers.yahoo.com/question/index?qid=20090911051703AAazjAr

No_9593 karma

A physicist! I've been waiting for one. I've been wondering this for a while, but can't come up with a solid answer.

If I was in space and I attached an LED light to one corner of a cube, is it possible for me to push/toss/throw/rotate the cube in such a way along a linear path that the LED light's pattern would never repeat itself (aka, there would never be a period)?

EDIT: Forgot to include my thoughts: assume we are dealing with only two different spins upon two different axis... Normally we'd say that these two axis could combine to form a new axis upon which our cube is rotating. Therefore if one of the original axis has an irrational period, then there is no net period, right? However, I have trouble convincing myself that it would be possible to have an irrational period in the first place... blargh.

EDIT2: "Trouble convincing myself", because my question was if YOU (not a machine) can push/toss/throw/rotate the cube.

aarontsantos757 karma

Oooh...you want me to do real physics. This one deserves an answer, but it'll take more time than the AMA. I'll play around with it and PM you if I come up with something good.

andrewsmith1986564 karma

airspeed velocity of an unladen swallow

[deleted]715 karma

What do you mean? African or European swallow?

aarontsantos663 karma

Dang...you beat me to it.

AverageGatsby91432 karma

What is the kinetic energy of a growing finger nail?

You may have heard of
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin by Laurence Weinstein

It sounds quite similar to your book. I used this book as a text for an Estimation Course. It was incredibly fun and thought provoking. We talked about everything from mass and energy estimations, to human senses, scaling and extraterrestrial life.

aarontsantos587 karma

I use that book in one of my classes! (My books are more general audience, while Larry's is better as a textbook.) If you like it, he has another one coming out this fall.

I'll assume the fingernail has a thickness of 0.2 mm and an area of 1 cm2. If it's about as dense as water, then this would make its mass 20 mg. My nails grow about 2 mm per week. Using these, you can estimate a kinetic energy of 10-22 Joules.

aarontsantos499 karma

Words cannot express the awesome feeling one gets after having a GGG meme with your name attached to it :)

rorcuttplus425 karma

How large would the wings of a pegasus have to be to allow a horse to actually fly?

aarontsantos401 karma

We need to consider two things here: wing area and wing flapping rate. I did a similar problem for Mothra's wingspan. Horses weigh about 500 kg, which gives a downward gravitational force of about 5000 N. If you assume her wings flap 2 meters down and do so once every second, she'd need winds that were about 1000 m2 in area. A 2 meter wide wing would need to be about 5 football fields long.

lubriciousbears377 karma

How many house cats would it take to crush an average man?

aarontsantos477 karma

Let's assume 2000 kg (roughly the mass of a car) can crush a man. If your cat weighs 5 kg, it would take 400 cats to crush a man.

ItsPhysics304 karma

The entropy change in the universe when a 200 lb human is vaporized (assume no molecular fragmentation occurs).

aarontsantos562 karma

If we're talking vaporized "out in space", then the entropy increase is infinite since the molecules can literally be in anywhere in an infinite volume. To make things easy, I'll assume a room with a volume of 1000 ft3. If we grid up the room into molecule-sized boxes, we'll have about 1029 boxes. (This assumes boxes are 0.5 nm in width.)

To within an order of magnitude, there are about 1027 molecules in a 200 lb human, (you can find this by assuming we're mostly water and using 18g/mol as the molecular weight.)

There are 1029 !/[(1027 !)x(1029 -1027 )!] ways of arranging the 1027 molecules in 1029 boxes. Taking the log of this times Boltzmann's constant will get you the entropy increase (very approximate.) By my estimate, that's about 80,000 Joules per Kelvin.

edit: formatting

Somthinginconspicou276 karma

This should be fun, alright my question is this Reference In that picture, Superman is carrying about 13 planets attached to a giant chain with one arm. How much approximate weight is he lifting with these planets, how heavy/strong does the chain need to be and how much force is he exerting with that one arm. Thanks, and I hope finding the answer was fun :P

aarontsantos425 karma

You asked for "weight", but I'm assuming you mean that in the coloquial sense of how massive something is. (If I'm wrong, let me know and I'll compute the physics weight.) OK...there are 13 planets. Assuming them to be Earth sized, that would be a total mass of about 8x1025 kg. I'm assuming each link in the chain is 1 ft long and 25 pounds and that the total length of each connecting chain is about the diameter of the Earth. That would give a total chain mass of 6x109 kg.

The force is a bit harder. Assuming he's pulling against the gravitational force of the Sun and he's located around the orbit of the Earth, it would take about 5x1023 Newtons of force to pull all the planets.

rawdoglife227 karma

Hopefully this one gets an answer. If I am a poor college student trying to donate blood/plasma/sperm for food money, how much should I make per year if I attend the maximum times?

aarontsantos288 karma

I hate using Yahoo answers (notoriously unreliable), but here goes. Assuming the source below to be accurate, you can make up to $50 per for blood/plasma donations. Let's assume you donate once per month. I've also seen sperm donation banks that pay up to $1000 per month (assuming you've got that kind of genes they're looking for.) The catch is you can't masturbate of have any other type of sex. If you meet all the criteria, you've got yourself about $17,000 per year. Most of that comes from the sperm.

Sources: http://www.mayoclinic.org/donate-blood-rst/faqs.html http://answers.yahoo.com/question/index?qid=20090303103113AANKEVc

scottswan167 karma

The last physicist I asked this question got really mad at me. Fortunately you have the option to just ignore it and I won't blame you one bit. :)

If the rotation of the earth were to slow down would I weigh more, or less?

aarontsantos439 karma

Technically, you would weigh the same since weight is just related to the gravitational force. Physically, if you stepped on a scale you would see a larger number since it's like the Earth is trying to throw you less. It's kind of like a fat kid being thrown off a merry-go-round. The faster it spins, the more there appears to be a force pushing you away from the center.

mcaffrey163 karma


aarontsantos206 karma

This is the one I've been thinking about during lunch. It's a hard problem because you're not just concerned with conserving mass, you need the energy requirements of recreating all that blood. Since these are only order of magnitude estimates, I'm gonna say 2% of your energy consumption goes into replacing lost blood. I could be way off on that (I'm definitely not a biologist), but I suspect the actual number lies somewhere between 20% and 0.2% of your total energy intake. Let's say you regenerate that blood in a four days. That's 2% of your 1500 Calories per day for 4 days, which would give 120 Calories (about the equivalent of a small energy bar), though it could be as high as 1200 Calories if you take the 20% figure instead.

Take home message: If you don't know how to calculate something, try to make some upper/lower bounds. Choose ones that seem unrealistically high/low to you. You may not be able to find exactly what the answer is, but you'll get a range of possible answers and, perhaps more importantly, you'll have a good idea what the answer is not.

Airazz144 karma

OK, a tough one here:

Moving air is used to cool many things, but mostly car and bike engines. Air is moving around the engine itself or the radiator and it brings the temperature down.
However, jet fighter wings heat up a lot because of this fast moving air, rather than cool down.

The question is: what's the speed at which a thing would neither heat up, nor cool down, if the air temperature is 25C, the item temperature is 37C and we're at sea level?

aarontsantos114 karma

I love this problem (very hard), but I'm not sure I'll be able to do a good job with it. I think the best answer I can give for this one is that it really depends greatly on what the object is (its heat capacity, shape, etc.) Here's what I do know: Things heat up because of friction between the air and the moving object. However, convection (i.e. moving air currents) also carry some of that heat away.

Let's start with this. The drag force of a fast moving object grows proportional to the velocity square (~v2). The energy loss due to friction would be this times the velocity, which would scale proportional to v3. Since convection works only for slower speeds, it must scale as the velocity to some power less than 3 (so that the heating can grow faster than the cooling.) The convection is really the tricky part of this one. There's a differential equation you can use, but I'm not going to be able to solve it quickly.

I'm gonna cheat on this one a bit. We know things traveling at the speed of sound (~300 m/s) heat up but small amounts of moving air (<~1 m/s) cool things down. As an order of magnitude estimate, I'm gonna guess 50 m/s because it's an order of magnitude thats somewhere between the two.

J00nj00n140 karma

Just wanted to say I'm thoroughly impressed by your skills!

Also, as soon as I opened this page I searched "swallow" but it was asked already =(.

Now calculate the mass of the Death Star, in its incomplete form please.

aarontsantos113 karma

Thanks for the kind words! Now to fun Star Wars problems...

Luke mistakes the Death Star for a small moon, so it's probably about the size of Europa. This would be about 5×1022 kg (~0.008 Earth masses). If we assume it's made of steel, that ups the mass a bit to about 1×1023 kg.

For some extra fun, here's some other Death Star problems:

http://diaryofnumbers.blogspot.com/2010/04/death-star-physics.html http://diaryofnumbers.blogspot.com/2011/03/death-star-physics-revisited.html http://diaryofnumbers.blogspot.com/2011/03/death-star-physics-revisited-part-ii.html

edit: spelling

TheTrinketWeasel128 karma

If I bend over at 90 degrees, facing north, and pass wind on 1/1/12 at midday at Alice springs, Australia, how will the orbit of neptune be affected? Assume average fart density, speed.

aarontsantos203 karma

Hmm...Neptune is probably not going to be affected very much since the fart gas won't make it out of the atmosphere. The land mass of Earth on the other hane will gain a small amount of angular momentum. In Ballparking, I estimated that continuous flatulence will produce a force of about 0.01 Newton. (It turns out this would not significantly help you in a weightlifting meet.) Bending over at 90 degrees, that would give the Earth a torque 64 Newton kilometers. For a 3 second fart, the length of a day would change by 10-31 percent.

ghostdog20117 karma

How often do you use Wolfram Alpha?

aarontsantos280 karma

I use WolframAlpha occasionally and Mathematica a ton. I normally just use Google to do my calculations. It's great for doing conversions quickly. It's only drawback from what I can see is that it doesn't work with some of the esoteric units I use (e.g. "teeth per hockey player.")

ChiralAnomaly106 karma

Consider a super awesome race. A proton in the beam of the LHC and a photon. How much would the proton lose by (in distance) if they raced across the milky way galaxy?

ColdFire75182 karma


Says the protons reach 0.999999991 times the speed of light.

The milky way is about 9.5x1020 meters in diameter.

So the difference is 9.5x(1020) -9.5x(1020) *0.999999991

Or just 9.5x(1020) x(1-0.999999991)

Which is 8 550 000 000 000 m

Or about 60 times the distance from earth to the sun, or 1.4 times the distance from the sun to pluto

aarontsantos179 karma

ColdFire75 beat me to it, but I agree.

Yum_Krill95 karma

How large would a creature have to be to make a sound like The Bloop? The largest creature on earth, the blue whale, would not be able to.

aarontsantos72 karma

I had to look up what the Bloop is. Interesting...This one will take longer than I have now. Let me play around with it and get back to you.

Edit: It's a week later, but I finally got around to this. I estimated it here: http://diaryofnumbers.blogspot.com/2012/06/holy-flaming-burritos-batman.html

For the lazy, it woud be about 30 km long.

maltin56 karma

As a fellow physicist, I will send you one of my favorites. There is a portuguese poem, due to Fernando Pessoa, that reads:

Ó mar salgado, quanto do teu sal

São lágrimas de Portugal!

Por te cruzarmos, quantas mães choraram,

Quantos filhos em vão rezaram!

Quantas noivas ficaram por casar

Para que fosses nosso, ó mar!

Valeu a pena? Tudo vale a pena

Se a alma não é pequena.

Quem quer passar além do Bojador

Tem que passar além da dor.

Deus ao mar o perigo e o abismo deu,

Mas nele é que espelhou o céu.

The version in english should be:

Oh salt-laden sea, how much of your salt

Is tears of Portugal!

To cross you, how many mothers wept,

how many sons in vain prayed!

How many brides-to-be brides remained,

So you were ours, oh sea!

Was it worth? Everything is worth,

If the soul is not small.

Whoever wants to go beyond (cape) Bojador,

Has to go beyond pain.

To the sea gave God peryl and the abyss,

But in it He also mirrored heaven.

After this introduction, I ask you: Oh salt-laden sea, how much of your salt is tears of Portugal?

aarontsantos30 karma

Cool...what type of physics? Nice poem by the way...kinda makes me feel like a should have learned Portugese.

For simplicity, I'll assume that all tears eventually make their way into the Mediterranean Sea. Portugal's population is about 10 million people. Some people never cry while others cry every day. I'll assume the average person cries once per month, and when they do they lose about 2 mL worth of tears. If the average age in Portugal is 30 years, you've got yourself 7200 m3 of Portuguese tears. Someone once told me Gatorade is basically chemically-synthesized sweat. (Disgusting, but this makes sense if you're trying to replenish electrolytes.) If this is so, then you're getting about 200 mg of salt for every 355 mL. This gives about 4000 kg of salt.