From the September 2005 issue

Bob Berman’s strange universe: You do the math

September 2005: When it comes to math, there are three kinds of people: those who hate it, those who love it, and those who don't understand it. Most of us fit in the last group.
By | Published: September 1, 2005
Bob Berman
When it comes to math, there are three kinds of people: those who hate it, those who love it, and those who don’t understand it. Most of us fit in the last group.

That’s odd, because professional astronomers, the genuine kind who are chronically broke, are totally into math. Backyard astronomers, on the other hand, rarely need it. They exclaim, “What’s math got to do with anything, when I point my 8-inch scope at NGC 4565 using 120x?”

Well, a little math is good for the soul.

It makes the universe more amazing. It lets you answer your wife sagely when, like so many millions of others each night, she wakes you up and asks, “Honey, what’s Planck’s constant?”

Some numbers seem to repeat a lot. “1” is not among them. In fact, astronomers are forced to invent uses for 1, like defining the Earth-Sun distance as 1 astronomical unit. “2” is equally humdrum, and so is “3.” But “4” is special:

  • There are 4 cardinal directions …
  • 4 fundamental forces …
  • 4 dimensions.
  • The nearest star is 4 light-years away.
  • The solar wind gets here in 4 days.
  • The next cool number after 4 is 9,192,631,770. That’s the number of times a cesium-133 nucleus vibrates per second; it’s how we define a second. Actually, there are nice numerals in between, too. Some easily stick in the mind, like 88: the number of constellations or keys on a piano.

    Round numbers are nice, too. The average adult gives off 100 watts of energy, like a lightbulb. The Dipper stars average 100 light-years distance. Mostly, however, numerals aren’t so even.

    During this Einstein centennial year, E=mc2 pops up a lot. It’s even more meaningful when you insert actual numbers. This equation is profound because it confirms that mass is the same thing as energy. How much energy? Just weigh whatever interests you in grams (that’s m); multiply that by the speed of light (c) squared. Voilà, you’ve got its equivalent energy (E) in ergs. Einstein always asks us to express light-speed in centimeters per second, which seems as silly as posting a speed limit in angstroms per leap-year. But let’s do it.

    M31 has about the same number of stars as there are neurons in a human brain.
    Light travels about 30 billion centimeters in a second. Then, as if that isn’t big enough, we multiply that number by itself. The result: c2 is about a trillion trillions, or one sextillion.

    Go around the office and say, “Hey Mike, remember E=mc2? Well, guess what: c2 is a sextillion!” See if anyone cares. But these days, physicists do care, and they prefer to speak of particles’ energy equivalents rather than their tiny masses. It’s a great way to think of the universe, as seething with nothing but energy.

    Having reached immense numbers, let’s keep it going. How many stars are in the universe? Roughly 40,000,000,000,000,000,000,000, or 40 sextillion. Sextillion again? Maybe it’s a sexy universe after all. 40 sextillion is big, but less than the number of sand grains on Earth, including deserts and ocean floors.

    The Sun’s weight in pounds is 4 followed by 30 zeroes. 4 nonillion. It’s fun to say “no-nillion.” No joke, there’s a nonillion protons in a ton of cheese.

    The weight of the entire universe is also easy to remember: 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 tons. 50 zeros. Simple and round. What’s the highest possible number of anything? That would be all the subatomic particles everywhere: “1” followed by 80 zeroes, give or take.

    Feeling compelled to go higher? Only one way: with possibilities. The number of choices when you arrange four books on a shelf is 4x3x2 (called four factorial, written 4!), which is 24.

    If you have 9 DVDs, they can be stacked 9! ways, or 9×8×7×6×5×4×3×2, or 362,880 different arrangements. Imagine — merely going from 4! to 9! ups the possibilities from 24 to 362,880. Factorials increase wildly, crazily, like nothing else.

    So, what if each of the suns in the Andromeda Galaxy acted like a brain cell, a neuron? M31 has about the same number of stars as there are neurons in a human brain. And what if each could connect with any other? How many ways exist then? Or, how many possible ways can a galaxy’s stars be arranged?

    It’s one trillion factorial. This equals an impossible figure, with more zeroes than would fill the pages of all the books in the largest library. I don’t have a calculator that can handle it — maybe you do. The point is, if the universe’s inventory is vast, its permutations are inconceivable.

    So, if you hang out under the autumn Milky Way and a companion says, “The stars go on and on endlessly!” you can correct them: “No, babe. It’s the possibilities that are endless.”