This number can only ever be WAG[sup]WAG[sup]WAG[/sup][/sup]

Still, it’s a finite number.

So, to arrive at even a theoretical number, how many calculations would you have pile on each other?

-number of snowflakes per volume of snow
-volume of snow that falls on the earth in a year
-variables for ice ages? or is that asking too much?
-an estimate of when the first snow fell; when the Earth had cooled sufficiently, etc.

Is anyone crazy enough to tackle this, as an exercise in the wasting of time and energy?

OK, that was funny. And obscure; I can’t believe I got it, and I have no memory of when or where I picked up that bit of cultural flotsam. In fact, it’s mostly funny just *because *it’s obscure. How obscure does a reference have to be before the obscurity itself is what makes it funny?

Well, I’m sure records are kept on how much snow falls, in inches. So let’s say that there was an inch of snow, over a 1-square-mile area. What volume of snow is that? That must be fairly easy to figure out, although obviously snow doesn’t simply fall at a certain rate within an area, and then not fall at all outside that area. Still, that’s something that could be looked up, so it would get you closer to finding a real answer.

Any reason you want to know, or just one of those wondering thoughts that pops into your head?

Just to arrive at an upper boundary estimate for the number, you can use these figures (unit conversion and actual calculation left as an exercise for the reader):

Interestingly, I found a page where people have attempted a similar calculation, and have arrived at a figure of approximately 10[sup]30[/sup] snowflakes. Here is the (crappy) page. Go there and search on 1030 to find the relevant text. I wasn’t able to find the worksheet or calculations to which they refer, but it gives us something to go on.

It may interest you to know that Archimedes attempted to answer questions of this sort over 2000 years ago, and was able to come up with an answer more specific than “a lot” or “WAG”. His book, on the subject, The Sand Reckoner (He was attempting to figure out how much sand there was omn earth) is extant:

Ah yes, Graham’s number - so mindboggling big that you can’t represent it with exponents, not even with exponents of exponents, nor even with a tower of exponents the size of the Empire State Building. Even bigger than moser, which itself is so big that it can’t be adequately represented except in terms of the notation made up specially to represent it.

Even the Shannon number is laughably inadequate compared to the number of possible arrangements of the DNA molecule, IIRC, which is of the order of 10[sup]32,000[/sup]. That’s a big number, but small compared to the googleplex (1 followed by 10[sup]100[/sup] zeroes) which, however, is piss easy to write down if you use a mere two levels of superscripting.

A square mile of snow an inch deep (reference TJdude825’s post) would be about 4 billion cubic inches, btw. In terms of the numbers we’re talking about, that’s such a small number it can hardly be said to exist.