Monthly Archives: March 2014

Heisenberg Hilarity

Werner Heisenberg is pulled over by a police officer. After checking his license and registration, the cop asks “Do you have any idea how fast you were going?”

“Not at all,” replies Heisenberg, “but I know precisely where I am.”

The cop says “I clocked you doing eighty miles an hour.”

“Oh great!” says Heisenberg. “Now I’m lost!”

Werner Heisenberg was a central figure in the development of quantum mechanics, the branch of physics that deals with the strange comings and goings of the subatomic realm. His name is connected most frequently with the Uncertainty Principle; more about that in a moment.

There’s a lot of history behind the development of the modern atomic theory and quantum mechanics, not all of which is relevant to this joke. Still, I would be remiss not to include some links so you can refresh your knowledge about how scientists know what they know about impossibly tiny subatomic particles.

  • First, spend four minutes with this video to get acquainted with the origins of quantum mechanics.
  • has an incomplete “Who’s Whom?” of atomic philosophers and physicists spanning from ancient Greece to modern times.
  • David Harrison of the University of Toronto provides a brief but somewhat academic narrative of the birth of quantum mechanics through the work of Heisenberg and Erwin Schrödinger, with a smattering of Eastern philosophy thrown in for good measure.
  • Todd provides a decent introduction to some principles of quantum mechanics.
  • And finally, if you don’t feel like reading the rest of this article (or even if you do!) spend four more minutes with this video that brilliantly demonstrates the Uncertainty Principle in a simple experiment.

In the first decades of the 20th century, physicists were making enormous strides toward understanding how protons, neutrons, and electrons work together to make atoms. It was becoming apparent, however, that subatomic particles still had a few closely-guarded secrets. Werner Heisenberg, a German theoretical physicist and the star of today’s joke, voiced an argument that there was a theoretical limit to how precisely we can measure the speed and position of an electron (or any other particle, for that matter). According to the Uncertainty Principle, the more precisely we know an electron’s speed, the less precisely we will know its position, and vice versa.

Unlikely press conferences, Figure 1.

Unlikely press conferences, Figure 1.

The reason for this intractable uncertainty has nothing at all to do with scientists’ instruments. Even if scientists could use perfectly precise instruments (which don’t exist anyway), they would never be able to break past this barrier. No matter what, nature prevents us from knowing both the speed and location of an electron with exact certainty.

Unlikely press conferences, Figure 2

Unlikely press conferences, Figure 2

Of course Heisenberg couldn’t really use his Uncertainty Principle to claim ignorance about the location or speed of his car. The Uncertainty Principle doesn’t really apply to objects above the atomic scale. Heisenberg would have known this: I think he was just trying to get out of a ticket.


Binary Befuddlement

There are 10 kinds of people: those who understand binary and those who don’t.

This joke really only works in writing. I’ll explain why later.

Binary (also called base 2) is a number system; a way of counting. It’s really not that different from the decimal number system (base 10), which is the system that most of us know and love from our days in elementary school. Still, binary feels unintuitive because we’re used to thinking in powers of ten, not powers of two. But maybe I’m getting ahead of myself.

Before I jump right into binary, it might be educational to review base 10 first. As you know, the base 10 number system uses – wait for it – ten digits. You’ve probably heard of them: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The first nine counting numbers are each represented by a single digit, but when you get to ten, you have to switch to two digits. Why, you ask? Because there’s no digit in base 10 that represents the number ten. Instead we use a new “place”…a place where the digits 1 through 9 represent multiples of ten instead of one. So 10 can be read as “1 ten and 0 ones” and 11 as “1 ten and 1 one”. Whenever we accrue ten ones, we roll it over and bump up the tens column by one. Easy peasy so far, right?

And so it goes until we reach 99 (9 tens and 9 ones). Adding one more causes the digits to spill over into a third place, which we call the hundreds place. The number 100 could be read as “1 hundred, 0 tens, and 0 ones”, although we normally forego mentioning the tens and ones if there aren’t any to speak of. Up through the three-digit numbers we climb until we reach “9 hundreds, 9 tens, and 9 ones”, or 999. Adding one now will cause the digits to spill over into the thousands place, and four-digit numbers are born.

If you’re particularly math-savvy, you probably noticed that each of the “spill-over” numbers is a power of ten. The first two-digit number is 10, or 101. The first three-digit number is 100, or 102. The first four-digit number is 1000, or 103. That’s no accident; our number system is built up from multiples of powers of ten, hence the name “base 10”.

Perhaps the following illustration will help. The number one hundred seventy-five may be thought of as 1 hundred, 7 tens, and 5 ones.

A picture is worth 103 words.

A picture is worth 103 words.

Okay, okay, I hear you object, I know how to count. Indeed you do, gentle reader, perhaps too well. Most of the time when we think of numbers, we think of them in sort of a holistic sense; rarely do we stop to consider how they are put together. But now that you have considered the construction of numbers, you’re ready to tackle binary.

See, binary uses the same rules as decimal, except you get only two digits: 0 and 1. Instead of being based on powers of ten, the binary number system is based on powers of two. You don’t have a tens place, a hundreds place, a thousands place, etc; you have a twos place, a fours place, an eights place, a sixteens place, and so on. The first counting number is written as 1, just as in decimal, but when you add 1 to that, you don’t get 2. Instead, the numbers spill over into the twos place, and you get 10. Don’t read that as “ten”, because it isn’t. It’s “1 two and 0 ones” in binary. The next counting number is 11 (1 two and 1 one), which we would write as 3 in decimal. Next comes 100, or “1 four, 0 twos, and 0 ones”. Hopefully you get the drift.

For your edification, here are some numbers of interest in both the decimal and binary number systems.

Description Decimal Binary
The loneliest number 1 1
The loneliest number since the number one 2 10
Blind mice, wishes, bears, etc 3 11
Pi, approximately 3.14159265359 11.0010010000
Number of seasons 4 100
Bo Derek 10 1010
Candles 16 10000
Days of summer vacation 104 1101000

And just to utterly drive home the point, here’s a visual representation of the same number as above (one hundred seventy-five) but in its binary form: 10101111.

A picture is worth 1111101000 words.

A picture is worth 1111101000 words.

Now I said before that the joke really only works in writing. If you try to say it out loud, you run into a problem or 10. First, you wouldn’t read it as “There are ten kinds of people” because then the rest of the joke doesn’t make sense; your listener would be justified in expecting you to describe eight more types of people. You could read it as “There are one-zero kinds of people”, but that makes the joke awkward and telegraphs the punch line. You could just say “There are two kinds of people” but then it sort of becomes an anti-joke, and not a very funny one at that. Sorry, aspiring math-based stand-up comics; you’ll have to leave this one out of your repertoire.

In closing, I’d like to offer this follow-up funny, which I’m sure will leave you in stitches.

There are 10 kinds of people: those who understand binary, those who don’t, and those who didn’t realize that this joke is actually in base 3.

Paleontological Precision

A man is touring a natural history museum, admiring the dinosaur reconstructions. He spots a curator and asks him: “How old are these fossils?” The curator replies: “They are one hundred million, four years and six months old.”

“That’s amazing!” says the visitor. “How can you know their age so precisely?”

The curator explains, “When I started working here they told me those bones were one hundred million years old, and that was four and a half years ago.”

When somebody is dealing with a situation that demands approximations rather than precision, he might say “it’s not an exact science.” Well the truth is that there are no exact sciences – at least, none that involve taking measurements. All measurements include some kind of error, and error has an adverse effect on precision.

If you ask most scientists to define “precision”, they’ll say that precision is synonymous with “repeatability”; in other words, a measurement is precise if you can take the same measurement over and over and get the same result. In laboratories, where scientists can carefully control their experiments, precision is roughly proportional to the cost of the instruments. No, really. But what about the scientists who work in nature, which is the antithesis of a controlled environment? How do they achieve precision in their measurements?

If you’re a paleontologist – that is, a person who digs up ancient fossils and tries to piece together their life history – precision has a somewhat looser definition. Finding the precise age of dinosaur fossils is impossible. Mother nature was not kind enough to timestamp each dinosaur bone when the animal died. Even if she had, the bones have been exposed to every weapon in nature’s arsenal – heat, pressure, chemical attack, gravity – for tens of millions of years. Despite the fine detail preserved in some dinosaur fossils, finding their age still involves a lot of detective work and the answers are not always satisfyingly precise. HowStuffWorks has a really great set of pages about how scientists determine the age of dinosaur fossils, if you’re interested.

When a paleontologist says that a dinosaur bone is one hundred million years old, he doesn’t mean that the animal died exactly 100,000,000 years ago today. He really means that the animal died somewhere between, say 103,000,000 and 97,000,000 years ago (and even those bookends are not all that precise). That’s a huge window of time, but it’s the best you can do when you have to rely on the clues that nature deigned to leave behind.

Our naïve curator was obviously unaware of the imprecision inherent in paleontological ages. He inappropriately added two values with different degrees of precision, and obtained a useless result. Here’s a similar situation: suppose you know that your SUV’s curb weight is 4,700 pounds. Now let’s say you place a U.S. penny (weight = 0.0055 pounds) on the roof of the vehicle. Does the vehicle now weigh 4,700.0055 pounds? Doubtful, because there are a lot of variables you probably haven’t considered: how much gas is in the tank; how many empty McDonald’s wrappers are in the back seat; etc. Without taking great pains to measure the weight of the SUV to the nearest ten-thousandth of a pound prior to adding the penny, you won’t be able to give an precise accounting of its weight after adding the penny. You cannot add numbers with different degrees of precision and hope to obtain a useful result.