This is the 2nd of my two-part blog on huge numbers.
In my previous blog I spoke about the number of stars in the universe.
We shall revisit that topic below but look at it in a different way.
Here I’ll address the question, “How many possible games of chess are there?”
The answer will not only surprise you, it’s sure to astound you!
Text below courtesy Wikipedia.
Almost nothing looks more orderly than chess pieces before a match starts. The first move, however, begins a spiral into chaos. After both players move, 400 possible board setups exist. After the second pair of turns, there are 197,742 possible games, and after three moves, 121 million. At every turn, players chart a progressively more distinctive path, and each game evolves into one that has probably never been played before.
According to Jonathan Schaeffer, a computer scientist at the University of Alberta who demonstrates A.I. using games, “The possible number of chess games is so huge that no one will invest the effort to calculate the exact number.” Some have estimated it at around 10^100,000. Out of those, 10^120 games are “typical”: about 40 moves long with an average of 30 choices per move.
There are only 10^15 total hairs on all the human heads in the world, 10^23 grains of sand on Earth, and about 10^81 atoms in the universe. The number of typical chess games is many times as great as all those numbers multiplied together—an impressive feat for 32 wooden pieces lined up on a board.
Scientists have detected evidence of a colossal explosion in space – five times bigger than anything observed before.
The huge release of energy is thought to have emanated from a supermassive black hole some 390 million light years from Earth.
The eruption is said to have left a giant dent in the Ophiuchus galaxy cluster.
Researchers reported their findings in The Astrophysical Journal.
“I’ve tried to put this explosion into human terms and it’s really, really difficult,” co-author Melanie Johnston-Hollitt told BBC News.
“The best I can do is tell you that if this explosion continued to occur over the 240 million years of the outburst – which it probably didn’t, but anyway – it’d be like setting off 20 billion, billion megaton TNT explosions every thousandth of a second for the entire 240 million years. So that’s incomprehensibly big. Huge.”
Stars in the Universe
Which Is Greater, The Number Of Sand Grains On Earth Or Stars In The Sky?
Here’s an old, old, question, but this time with a surprise twist. The question is — and I bet you asked it when you were 8 years old and sitting on a beach: Which are there more of — grains of sand on the Earth or stars in the sky?
Obviously, grains and stars can’t be counted, not literally. But you can guestimate.
Science writer David Blatner, in his new book Spectrums, says a group of researchers at the University of Hawaii, being well-versed in all things beachy, tried to calculate the number of grains of sand.
They said, if you assume a grain of sand has an average size and you calculate how many grains are in a teaspoon and then multiply by all the beaches and deserts in the world, the Earth has roughly (and we’re speaking very roughly here) 7.5 x 10^18 grains of sand, or seven quintillion, five hundred quadrillion grains.
That’s a lot of grains.
OK, so how about stars? Well, to my amazement, it turns out that when you look up, even on a clear and starry night, you won’t see very many stars. Blatner says the number is a low, low “several thousand,” which gives the sand grain folks a landslide victory. But we’re not limiting ourselves to what an ordinary stargazer can see.
Our stargazer gets a Hubble telescope and a calculator, so now we can count distant galaxies, faint stars, red dwarfs, everything we’ve ever recorded in the sky, and boom! Now the population of stars jumps enormously, to 70 thousand million, million, million stars in the observable universe (a 2003 estimate), so that we’ve got multiple stars for every grain of sand — which means, sorry, grains, you are nowhere near as numerous as the stars.
So that makes stars the champions of numerosity, no?
Ummm, no. This is when Blatner hits us with his sucker punch. Yes, he says, the number of stars in the heavens is “an unbelievably large number,” but then, very matter-of-factly, he adds that you will find the same number of molecules “in just ten drops of water.”
Let me repeat: If you took 10 drops of water (not extra-big drops, just regular drops, I’m presuming) and counted the number of H2O molecules in those drops, you’d get a number equal to all the stars in the universe.
This is amazing to me. For some reason, when someone says million, billion or trillion, I see an enormous pile of something, a grand scene, great sweeps of desert sand, twirling masses of stars. Big things come from lots of stuff; little things from less stuff. That seems intuitive.
But that’s wrong. Little things, if they’re really little, can pile up just like big things, and yes, says Blatner, water molecules “really are that small.”
So next time I look up at the sky at all those stars, I will be impressed, of course, by the great numbers that are out there. But I will remind myself that at the other end of the scale, in the nooks and crannies of the physical world, in the teeniest of places, there are equally vast numbers of teenier things.
We are surrounded by vastness, high and low, and either way, as Blatner’s book says, we “can’t handle the biggitude.”