Note (12/2015): Hi there! I'm taking some time off here to focus on other projects for a bit. As of October 2016, those other projects include a science book series for kids titled Things That Make You Go Yuck! -- available at Barnes and Noble, Amazon and (hopefully) a bookstore near you!

Co-author Jenn Dlugos and I are also doing some extremely ridiculous things over at Drinkstorm Studios, including our award-winning webseries, Magicland.

There are also a full 100 posts right here in the archives, and feel free to drop me a line at with comments, suggestions or wacky cold fusion ideas. Cheers!

· Categories: Mathematics
What I’ve Learned:

The birthday problem: because nobody wants (or gets) to celebrate alone.
“The birthday problem: because nobody wants (or gets) to celebrate alone.”

Birthdays often have problems. Whether it’s the annual reminder of impending mortality, Grandma getting you the totally the wrong Teenage Mutant Ninja Turtle action figure or Marilyn Monroe failing to jump out of your cake to wish you happy birthday.

(Actually, regarding that last one, it would create a whole bunch of additional problems if she did. So stop wishing for that.

There’s always Marilyn Manson, if you just can’t shake the idea. Good luck with that.)

None of these issues is the birthday problem, however. The specifically-named “birthday problem” is actually a mathematical exercise — two words which you probably wouldn’t want to hear, in any combination, on your actual birthday. Assuming it’s not your actual birthday right now, here’s what the mathematical exercise asks:

Among a group of randomly-chosen individuals, what is the probability that at least two of them will share the same birthday?

The “randomly-chosen” bit is key, of course, since including certain individuals would muck up the math. The Olsen twins, for instance, would totally ruin everything.

(Presumably, this is not something you need mathematics to tell you.)

Assuming a full-on rand-o crowd, the question gets a little more interesting — to non-probability theorists, at least — when asked in this way:

How many people do you need to have a better than 50% chance of two people sharing a birthday?

That’s a trickier question than it looks. Most people can narrow down the range of possible answers a bit. If there’s one person in the room — scary Olsen or not — then there’s zero chance of sharing a birthday with the nobody else in attendance. And if (ignoring leap days, because ain’t nobody got time for that) 366 people are mingling, then the chance is 100% that at least two of them share a birthday. There’s only so much calendar to go around.

You might think that the number to get 50%, then, would be right in the middle. You would be mistaken.

Then again, a few minutes ago you wanted Marilyn Manson to hop out of a cake and sing to you. You don’t exactly have a track record for making good decisions.

The real answer (spoiler alert!) to this version of the birthday problem is 23. According to combinatorics probability theory — and some nifty math — with just 23 people in a room, the odds are slightly better than 50% that two of them share a birthday. If you want to increase the odds to 99.9%, you’ll have to make a few more phone calls — but your meeting hall still only needs a capacity of 70 people.

That’s nothing. They get bigger crowds than that at the Pawnee, Indiana town hall. And Ron Swanson doesn’t share his birthday with anyone.

This surprising result to the birthday problem is important for three reasons. First, maybe it instills in some young minds a wonder and love for math, and they’ll go on to become professional mathematicians. Which is great, because somebody has to take that bullet. And numbers make my head hurt.

Second, there are computer hacking strategies — called “birthday attacks” — that take advantage of the math behind the birthday problem to wreak certain kinds of digital havoc. These brute-force cryptographic manipulations are often aimed at using hash collisions to the hackers’ advantage. In other words, no birthday cake for you.

And finally, this demonstrates that there’s a big difference in calculating a 50/50 that any two people will share a birthday, versus the same odds that somebody in a crowd shares your birthday. For the latter, you’d need at least 253 people, which reminds us that probability is tricky, the obvious answer is not always the right one, and for crissakes stop making everything about you, ya town hall-cramming Olsen-loving Manson-caker.

And oh, yeah: happy birthday. Freak.

Actual Science:
Damn InterestingThe birthday paradox
Better ExplainedUnderstanding the birthday paradox
NPR / Math GuyThe birthday problem
Hack This SiteHash collisions and the birthday attack
University of WaterlooInvasive species use landmarking to find love in a hopeless place

Image sources: (birthday match graph), Photobucket / taintedXarts (birthday Manson), The Gloss (Olsen twin powers, irritate!), FanShare (in Spanish!) (Pawnee powwow)

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· Categories: Chemistry
What I’ve Learned:

Enantiomers: mirror, mirror on the wall... hey, who the hell is that?
“Enantiomers: mirror, mirror on the wall… hey, who the hell is that?”

You’d think organic chemistry is hard enough already. It’s all methyl-this and hydroxyl-that; here an H2, there an O2, everywhere a hydrocarbon — just figuring out a chemical formula is exhausting. Then there’s sorting out the structure and atomic bonds, which is a whole other ball of difficult. Surely, that should be enough to characterize a molecule, right?

Wrong. It turns out you can have two organic compounds with the same formula and the same structure — but they’re mirror images of each other. Like how your left hand looks like your right hand, but they’re not quite the same thing. Or how those creepy twins from The Shining look alike, but you just know one is a little bit eviler than the other.

In chemistry, these mirror images are called enantiomers. Most of them come about because carbon is, shall we say, somewhat “promiscuous”. A carbon atom can stably bond to four other atoms at once — which, seriously, who has the energy for that? I have trouble enough keeping just one atom happy at home.

Maybe that’s just me.

In an organic molecule, two of carbon’s potential bonds might be taken up by other carbons, forming a backbone for the molecule. That leaves two other spots for hydrogens, oxygens, carbons or just about any other randy atom with a loose electron to wander by and ask, “how you doin’?”

Meanwhile, the chained-up carbon often has a kink put in the angles of its other possible bonds. So if, say, a hydrogen and an oxygen atom jump in, one of these might end up bonding on a side more “left”, while the other winds up on a side facing more “right”. But the next time around, things could get flipped — the hydrogen could wind up where the oxygen was, and the oxygen where the hydrogen ought to be.

If we were making candy, this might be a Reese’s peanut butter cup. But we’re making organic molecules instead, so the two ever-so-slightly different molecules are called enantiomers. Less delicious, perhaps — but pretty important.

That’s because many enantiomers aren’t like creepy horror movie twins, who behave in exactly the same creepy, twinny way. They’re more like celebrity twins — say, Mary-Kate and Ashley Olsen, for instance. So maybe one enantiomer goes through a little goth phase, while the other does a stint on Weeds and then dabbles with plastic surgery.

Or, you know, maybe they just have different chemical properties. It’s not a perfect analogy.

Enantiomers are a big deal in pharmacology, because many clinical drugs are made from organic compounds and synthesizing these sometimes also means dragging a mirror-image molecule along for the ride. A soup of two enantiomers in equal amounts — called a racemic mixture — isn’t always a problem. Sometimes, the “twin” behaves similarly enough to be of some benefit.

Other times, the enantiomer is completely inactive — so while the dose of such a drug might be twice as high (to make sure enough of the “good twin” is present), it’s otherwise okay. In this case, scientists might leave the compound as-is or decide to purify it further; the compound in Lunesta is an example of a drug made from one enantiomer separated from its mirror twin.

In still other cases, the unintended enantiomer actually causes harmful side effects or competes with the compound in the body. For these drugs to work, they have to be made “enantiopure” — either separated from the mirror compound, or synthesized in such a way that only one form is possible. Imagine a world with a million Ashleys, and no Mary-Kates at all.

If you can.

Actual Science:
University of CalgaryEnantiomers
Rowland Institute / Harvard UniversityMolecular chirality
ChemhelperSeparation of enantiomers
BrightHubEnantiopure medications: are chiral drugs more effective?

Image sources: Hemija u Matematickoj gimnaziji (enantiomers), Canvas, Cameras and Chianti (creepy twins), My Semi True Story (Reese’s commercial), Open Vintage (also fairly creepy twins)

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