I’m not much of a mathematician, but I’ve never been intimidated by numbers or the different ways we manipulate numbers, which is really what mathematics is all about. I’ve just never been very good at it, and that’s a large part of why I became a biological scientist because I didn’t need much higher mathematics to understand biological organisms. And if I did need higher stuff like calculus, or sophisticated statistical analyses, or differential equations, or whatever, I could always get someone in the Math Department to do the work for me.
But I have always been fascinated by numbers and how they interact. Particularly large numbers. We scientist types can wind up with some large numbers sometimes. For example, as a virologist, I frequently would have, after various manipulations in the laboratory, a test tube full of a purified virus. That’s right, a purified virus. Sometimes that was a relatively benign virus like reovirus, a virus of humans that could cause disease, but rarely did, and sometimes that would be a dangerous virus like poliovirus. I’m not talking about the vaccine poliovirus, either. I even once had a tube of purified AIDS virus. I kept that tube hidden away.
But what’s interesting about these viruses is that the numbers of them could reach very high levels. We always listed the number of virus particles in terms of ‘particles per milliliter’ (or ‘particles/ml,’ to use the common abbreviation). These suspensions of viruses were usually a milky white (except for the poliovirus) and could reach a trillion particles/ml. That’s a 1 followed by 12 zeros. We would write that as the number 10 with a superscript 12, but I can’t write it in this blog because WordPress doesn’t allow superscripts. (A glaring deficiency.) That’s only per milliliter, too, so if I had 10 ml of that suspension–and that wasn’t unusual–that would be 10 trillion particles.
But I’ve run across large numbers in more prosaic pursuits. Take for example a deck of cards. Fifty-two cards (excluding Jokers) can be played in many different games, some of which use all the cards, some of which don’t. I got to thinking about that, and wondered how many different combinations of all those cards there are. Assume you are playing a game where all 52 cards are used, like Bridge or Solitaire. How many different hands could be dealt? To figure that, you would calculate 52 factorial, which means 52 x 51 x 50 x 49 x 48… down to 1. That’s because, assuming the cards are well shuffled, there are 52 possibilities for the first card, then after it is dealt, there are 51 possibilities for the second, and so on. If you enter that into your calculator, 52, and press the factorial key, usually represented as ‘x!’ the answer comes up, 8.0658 times 10 the power 67. That means 67 digits after the first 8. That’s a huge number. No wonder all those Bridge experts like Charles Goren and Omar Sharif have had columns in the newspaper for so long. They’re never going to run out of different hands! That same number applies to any game where all cards are dealt, like Solitaire.
But an even bigger number I learned about came during high school many years ago. A speaker came to our school and challenged us to write down the largest number we could think of using only three digits. (The same digit could be used several times.) The largest I could think of was 999. But he did it differently. He wrote 9 to the power of 9, and that to the power of 9. I can’t write it here, but it’s like a column of exponents. He said at the time that number would be bigger than all the snowflakes that have ever fallen in the history of the Earth. Of course we pooh-poohed him. I couldn’t be, we said. In the history of the Earth? No way. And until calculators came along, I couldn’t evaluate that number. But now I can. I started by taking the top two nines, that is, 9 to the ninth power. That’s 387420489. Then I took 9 to that power, and my calculator gave me an “Error” message. It was too big for a simple calculator to figure. If you want to try it, you might be able to find a website that will give you the answer. I tried using logarithms, but I still got an “Error” because that number is so absolutely huge. In any event, it’s no matter. I believe now it is larger than all the snowflakes that have fallen since the beginning of the Earth. And that’s a lot of snowflakes.
Now for an even larger number. Anyone want to try to figure out the number of electrons in the entire universe?