Monday, March 21, 2011

Pi Day Pie

Check out the pie my wife made for Pi Day.

Pi i = Log(-1).  Get it?  If this appeals to your geeky and foodie side, please vote for it here!  Tell your friends!  Voting closes on March 23 (Wednesday at midnight), so vote ASAP.

UPDATE: We finished second!  Thanks to everyone who voted for us!

Saturday, March 19, 2011

Death and Presidents

A few years back, an older friend told me a story about her grandmother.  It was November 1963, and her grandmother had just turned 105.  My friend went to visit her grandmother in the hospital.

Friend: "Grammy, the president's been shot!"
Grandmother: "Another one?!"

It was then that I realized her grandmother had lived (and was old enough to remember) every presidential shooting from Lincoln to Kennedy.  It blew my mind.

It's amazing how much can happen in a lifetime.  This point was driven home in a recent post on Reddit.  As of March 2011, our 10th president John Tyler (born 1790) had two living grand children!  This got me thinking: If you passed a baton from person to person, what's the least number of hands it could touch and reach the first even human?

According to Wikipedia, modern humans showed up about 200,000 years ago.  If you passed the baton from a centenarian to a new born that would live to be a centenarian, it would take only 2000 people.1   This is roughly the number of people attending my high school.  If you wanted to go back to the time of Christ, it would only take 20 people. 

[1] Some people will no doubt quibble that the average life span was in the 30s for much of our history.  True, but this neglects two points.  First, we're doing an order of magnitude estimate and this fact won't change the answer by an order of magnitude.  More importantly, "life expectancy" is the average life span.  Life expectancy may have been low, but this was largely due to high infant mortality rates.  Back in the day, if you were lucky enough to make it to adulthood, you stood a good chance of making it to old age.  Since we're only looking for the oldest person at any one time, there's a good chance there was centenarian somewhere in the world.

Sunday, March 13, 2011

Chalk Hell

Wright Laboratory of Physics Room 201 at Oberlin College.

"Begone, Ye Accursed Chalk!  I banish thee and thy vile and insufficient yield strength to the depths of Chalk Hell!!!"
Most colleges have at least one big lecture hall with chalk boards that slide up and down.  To make space for the boards to slide underneath, there's usually a small gap behind the wall.  This gap is Chalk Hell: a black hole out of which no chalk ever emerges.1   How long would it take for Chalk Hell to over flow with chalk remnants?

A brief glimpse into the horror that is Chalk Hell.
Chalk Hell is about 1.0 m deep,  10 cm wide, and 3 m long giving a total volume of 0.3 m3.  Much of the chalk in Chalk Hell is about 0.8 cm thick and 6 cm long giving a total volume of about 3.8×10-6 m3.  I drop at least 1 piece per lecture and over the course of a year there might be 300 lectures in a room.  From this we can estimate that there are

0.3 m3 / [ (3.8×10-6 m3 per piece) · (1 piece per lecture) · (300 lecture per year) ]
= 263 years.

It would take over 2.5 centuries to before Chalk Hell flows over.

[1] Unless you duct tape the long erasers together to make a giant set of chop sticks that you can use to pick them out of Chalk Hell.

Sunday, March 6, 2011

Death Statistics

There was an interesting post on Reddit a couple of days ago:

"After your death, what kind of statistics about your life would you like to know? ... Let's just say you get a sort of 'post-game' screen, like in a videogame. What kind of statistics (numbers, percentages, etc.) about your life would you like to know?"

I love this idea.  Here are my estimates for some of the statistics Redditors wanted to hear.  I’m assuming an 80-year life span. 

“Gallons of liquor consumed”: If you average 3 beer cans worth of liquor per week, you’ll consume 4.4 m3 in a lifetime. 

“Number of lies I told/was told”: Lies come in a variety of forms, but let’s not get too pedantic.  No matter how you define it, telling ten lies per day seems like a lot and telling one lie every ten days seems like too few.  I’ll assume people tell one lie per day on average.  This gives about 30,000 lies in a lifetime.  By symmetry, you might expect the number of lies told to equal the number of lies heard, but this is not necessarily the case because lies can be told in parallel.  For example, when a politician lies, he’s usually lying to huge crowds of people.  Assuming the average number of people who hear a lie is 10, you would hear about 300,000 lies in your lifetime.

“Number of biblical sins committed”:  Minor sins are pretty common.  If you average two sins per day, you’ll total about 60,000 sins.

“Percentage of time spent sleeping”: If you average 8 hours per night, you will have slept 33% of your life.

“Time spent on the Internet”: If you average 2 hours per day, you’ll spend about 7 years on the Internet.

“How many hours I've spent fapping”:  This varies a lot from person to person depending on gender and how fast your Internet connection is.  If you average 5 minutes per day, you’ll spend almost 100 days of your life fapping.

“Amount of semen expelled”:  Assuming each—er—deposit contains about 1 tablespoon, and you make a deposit once per day, you’ll have about 0.4 m3, or roughly about 1 bathtub full. 

“How much money I made in my lifetime (including all the money I earned when I was little)”:  The money you made when you were little is probably not a significant figure, but if you average a $50K salary from age 25 to 65 and manage to spend all of it, you’ll have spent $2 million.

“Time spent on videogames”.  If you average 2 hours per week, you’ll spend about 1 year of your life playing video games.  (Note: Hardcore gamers will average much more that 2 hours per week.)

“Time spent playing sports”: If you play a couple hours each week, you’ll have played a year worth of sports.

“The percentage of how many people I came into contact with out of the people who lived on Earth at the same time as me”: There are about 7 billion people in the world right now.  From this, we might estimate that in your lifetime 14 billion people have been alive at one point or another.  Even if you average 100 new contacts per day, you’ll still only meet 0.02% of the people whose lives overlapped yours.

“Number of heartbeats and breaths taken”: Heartbeats and breaths happen about once per second and once every three seconds, respectively.  That means you’ll have about 2.5 billion heartbeats and 840 million breaths.

“Number of pens lost”: I lose one at least one pen per month.  That gives about 1000 pens lost.

“How many words I typed”: If you type at a computer for 0.5 hours per day and type 30 words per minute, you’ll have typed 26 million words.  (The 0.5 hours per day number might seem small, but I’m only counting the time spent actually typing.)

“How many letters I typed”: If each word averages about 5 letters, you’ll have typed 130 million letters.

“How many words I said”: If you talk for an hour per day at a rate of 3 words per second, you’ll utter 300 million words in a lifetime.

“How many hours I slept”: Most people sleep about 8 hours per night, which means 27 years of sleep.

“How many times I had sex”: If you average once per month, you’ll have sex about 960 times.

“How many times I ate burritos”: If you eat one burrito per week on average, you’ll eat 4200 burritos in a lifetime.

“How many times I said the word [expletive]”:  Some people never curse while others curse every other word.  If you lie somewhere in the middle, you likely curse about 5 times per day which would mean about 150,000 curses in your lifetime.

“Amount of time spent on Reddit”:  If you average 10 hours per week, you’ll spend almost 5 years on Reddit. 

“Number of witty remarks made”: It’s hard to define a metric for witty, but I like to think I make at least one quip per week giving a total of 4200 witty remarks.

“Amount of time spent in the air”: I’m assuming we’re talking about riding an airplane rather than time spent in the air jumping.  If you fly 4 hours out of the year, you’ll be in the air a total of 13 days.

“Fastest overall speed”: This question is not well defined, since speed has to be measured relative to some point.  If we’re free to measure in any reference frame, then your fastest speed would be close to the speed of light since we could always choose a reference frame that was moving close to the speed of light relative to you.

“Number of farts”:  This depends on your body chemistry.  Most people probably average at least 1 and less than 50 farts per day, so I’ll assume 5 per day on average.  This means you’ll have about 150,000 farts.

“Total volume of gas farted”: If each fart contains 50 mL of gas, the total volume of farts in one lifetime would be 7.5 m3.  That’s about the size of an office cubical.

“How many total inches of [penis] I have taken. Each sexual encounter counts (not only each partner)”: If you assume one sexual encounter per month and a 6-inch average, you’ll have “taken” 150 m of penis or about 1½ football fields.

“Total miles walked”: I calculated this in How Many Licks?  It’s about 23,000 miles.

“Number of laws I've broken”:  I jaywalk at least 5 times per week.  This means I will have broken the law at least 21,000 times.

“Number of times I said ‘I love you’”: Between family and my wife, I probably say it about 10 times per day which gives about 300,000 proclamations of love.

Friday, March 4, 2011

Death Star Physics Revisited (part II)

Saturn's moon Mimas looks eerily like the Death Star.
Given the very in depth analysis some of my readers sent me after the last Death Star post, I hesitate to follow up with this one since there's clearly some Star Wars physics that should to be debated before we continue.  However, I'm posting this any way because (1) I already typed it up and I'm pretty lazy about these kind of things and (2) if you allow my initial assumptions, there's still at least one more question that begs to be asked: how is all that laser energy stored?  Is there some giant car battery hidden somewhere?  After all, it would take 40 million years to collect enough solar power to blow up a planet.  Wouldn't one shot sap all the energy out of the Death Star?  According to relativity, one could very efficiently store energy as mass.  If that were the case, what percentage of the Death Star's mass would be lost with each shot?   

Luke mistakes the Death Star for a small moon, which suggests the mass of the Death Star is about that of a moon.  I'll assume the Death Star's mass is equivalent to that of Saturn's moon Mimas (M=3.7×1019 kg) since it kinda looks like the Death Star.  As we calculated before, the total energy required to blow up a planet is E = 2.1×1032 J.  According to relativity, the amount of energy stored in a piece of matter with mass m is given by the equation

E = mc2,

where c = 3×108 m/s is the speed of light.  If we solve for the percentage of mass lost with each laser shot, we find

fraction of mass = m / M = E / (M c2)
= ( 2.1×1032 J ) / [(3.7×1019 kg) (3×108 m/s)2]
= 0.0063%.

It's a very small percentage.  At this rate, the Death Star could blow up over 15,000 planets before it ran out of mass.  This of course assumes that the energy is directly transferred to the planet without loss.

Wednesday, March 2, 2011

Death Star Physics Revisited


I've been thinking more about the "Death Star Physics" problem from last year in which I estimated it would take about 2.1×1032 J of energy to blow up a planet.  It strikes me that I should have taken this problem even further.  How many photons were in the laser beam that blew up Alderaan?

As you can see from the video, the laser is green.1 Green light has a frequency f = 5.6×1014 Hz.  Using Plank's constant h = 6.6×10-34 J·s, one can compute the energy of a single photons by using the well known formula

E = h·f

From this we can compute the total number of photons,

number of photons = (total energy) / (energy per photon) =  ( Etot ) / ( h · f ) 
 = ( 2.1×1032 J ) /[ ( 6.6×10-34 J·s ) · ( 5.6×1014 Hz) ] 
= 6×1050 photons

This is a huge number. It's a 6 with 50 zeros after it. I'd have to go back and check, but I think this is the biggest number I've posted on this blog.

[1] At least the visible part of the laser is green.  It's possible the are also UV or other high frequencies of light coming out of the laser.