A Certain Book

A little while ago, I noticed a book cover that had a major problem. The book was the UK edition of Dr. Chad Orzel's How to Teach Quantum Physics to Your Dog, which sports a couple of scientific formulas on its cover... and one of them didn't look right.

"Ah-Ha!" I said in an accusatory manner to the imaginary publisher sitting in front of me. "Did you think your mistake would go unnoticed? Ghosting the equation back to a 30% gray has failed to mask your egregious error, you cretinous lackwit!"

But before transmitting a scathing missive to the real publisher like an annoying little know-it-all douche, I decided to check and make sure I was remembering things correctly. As a reflective, self-aware, highly insecure individual, I felt it was important to make sure *I* wasn't the one who was "Wrong, wrong, wrong!"

The equation in question was for the position-momentum form of the Heisenberg uncertainty principle. It's named after Werner Karl Heisenberg who developed the theory in the late 1920s/early 1930s. I've said it before and I'll say it again: When your peers are naming stuff after you, you know you're good. Heisenberg died in 1976 with a Nobel Prize on his shelf and a place in history for helping invent the field of quantum mechanics.

In retrospect, the uncertainty principle seems pretty obvious: Light is energy and we need light to see things, but at the subatomic level, you can't shine a light on something without giving it energy thus changing the nature of the subatomic thing you're trying to look at. One way of expressing this idea is with the equation "delta-x times delta-p greater-than-or-equal-to h divided by two pi", or

This equation describes what we think is probably happening to some subatomic particle we're interested in. Delta-x and Delta-p can be thought of as measures of probability. Delta-x represents how sure we are a particle is in a certain position. Delta-p represents how sure we are about a particle's momentum. But momentum (p) is equal to mass (m) times velocity (v), typically written as p = mv. So, since the mass of the particle doesn't change, you can say that Δp is really a measure of how sure we are about a particle's velocity.


That "h" is Planck's constant, a number related to the energy and frequency with which a particle oscillates. It was discovered by Max Karl Ernst Ludwig Planck around 1900. (When people start naming stuff after you...) In the uncertainty equation,

h = 6.626 x 10^-34 J•s

The units for Planck's constant are "Joule-seconds" (sometimes I will willingly stress over detailed explanations of what the units mean, but not today). The quantity [h/(2π)] turns up so often in physics that it was given a special symbol (called h-bar) which is why you sometimes see the uncertainty relation written as

Since the quantity [(h)/(2π)] is always the same and multiplying Δx by Δp always gives you something greater than or equal to [(h)/(2π)], if Δx increases then Δp must decrease. In other words, the more certain we are about where a particle is, the less certain we are about how fast it's moving and vice versa.

In Germany, there was even a Heisenberg stamp with the equation on it, fer chrissakes! So that's what I thought the uncertainty equation was, meaning the equation I saw on the book cover was wrong. Except it wasn't.

Placenta is Awesome!

A few weeks ago, I picked up a free copy of what has to be one of the world's geekiest newsletters: Fields Notes, a magazine-style publication about the mathematical research and activities at the Fields Institute in Toronto. One small article caught my eye -- a short blurb about something called the Placenta Modeling Group. In a couple of paragraphs, one of the group members (all students, supervised by a mathematics professor) described how human placenta was being used to study something called "Murray's law" (not to be confused with Murphy's law) and how it was involved in creating mathematical models for blood flow and vascular branching -- basically, how blood vessels grow and spread throughout an organ. I admit, I had never imagined connecting placenta and math, but it made so much sense. Here's an organ, perfectly healthy in most cases, that is simply "ejected" by a woman at the end of her pregnancy, typically without a whole lot of fuss -- why not use it for research? It's not like anyone was planning on doing anything with it, right? I became so curious about the "placenta + math" concept that I had to look into it further.

I'd heard the terms "placenta" and "afterbirth" tossed around, but when they show a baby being born on television, usually the most you ever see is part of the umbilical chord and no one ever seems to talk specifically about the placenta. And since I have no interest in being a father or getting anyone pregnant, learning more hasn't exactly been on my "To Do" list. But I'm here t' tell ya:

Placenta is awesome!

Do you have any idea how *awesome* placenta is?? Why does no one ever talk about how awesome placenta is? Is it one of those things where men who aren't doctors dismiss it as unimportant because they don't have to deal with it directly? Or maybe it's because placentas look like bloody, disgusting raw liver when they come out a few minutes after the baby. Or maybe it's kind of like the Opening Act Syndrome: people only care about the headliner (the baby) and are off buying t-shirts when the opener is on stage (in the case of the placenta, I guess it would be Closing Act Syndrome).

And, as I'm sure you've heard, there really are people who eat it. More on that later.

The placenta is formed by the trophoblast, a layer of tissue that surrounds the fertilized embryo and also forms the outer membrane that the baby sits in. Lots of proteins working at the molecular level interact to dig into mom's uterine wall and anchor the little parasite into place. Tiny tendrils called microvilli reach out like tree roots and hook the fetus into the mothers plumbing. But the placenta does way more than just hold the fetus in place. If pregnancy were a car, the baby would be in the passenger seat... the placenta would be the driver.