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Here's another theory:
There is a 3-d shape that is the 3-dimensional equivalent of a Mobius strip; the shape, resembling a jar, has only one surface and no edges. Perhaps the universe could resemble this.
"...And the high temperature for tomorrow will be between 200 degrees F and -40 degrees F..." -- Jim Davis (Garfield)
I issue a warning to people to not try to think TOO hard about these questions.
In case anyone was wondering, yes, there WILL be more.
First Chapter: Wally Questions... beware!
1 What do you get if you cross a stream and a brook?
2 If you have an important letter to write, is it better to write it on a full stomach or on an empty stomach?
3 If humans have two hands and monkeys have four hands, what has three hands?
4 What kind of butter do you get milk from?
5 What kind of book can a writer never finish?
6 What can stand upright and lie on its face at the same time?
7 What has eight wheels but can only carry one passenger?
8 What kind of tree does a cat hide under during a rainstorm?
9 What comes after E in the alphabet?
10 What's the hardest thing about learning to ride a bicycle?
11 What comes with a motorcycle, is not needed by the motorcycle, but the motorcycle can't go without?
12 The more you take away, the bigger it gets. The more you add, the smaller it gets. What is it?
13 How do you divide 11 potatoes evenly between 4 people?
14 What has four legs and two arms?
15 There were ten cats in a boat on a lake and one jumped out. How many cats are left?
Quite right. Storms in the north, perhaps in the south, too...
I guess the positive side of all this is that if we end up like at the end of the movie, we'll be able to build all sorts of huge snow structures (tunneling through 20 feet of snow to make a huge hideout, for example). Unfortunately, we would have to wear really thick jackets to keep from freezing to death.
As a result of what I said earlier, the melting of the ice caps will accelerate exponentially. Having all this newly melted water flowing into the oceans could, like in The Day After Tomorrow, disrupt the ocean currents that stabilize our climate.
Luckily, the consequences will be slightly slower-acting than in the movie.
Unfortunately, the world could end up like it does at the end of the movie in not that long.
Actually, the Earth's orbit gets thrown of every 100 000 years, which would mean that we wouldn't see anything in our lives last time it happened being
10 000 years ago.
Unfortunately, the melting of the ice caps will, as you said, change a lot.
The ice, when it's frozen, reflects a large amount of heat away from the Earth, but when it melts, we get seawater, which absorbs all that heat. The consequences of this process are still unknown (but I think we all know that it is NOT good).
VERY well put.
By the way, in case you're wondering, I'm living in France, among many "anti-sophists".
The weird thing about global warming is that the hotter it gets now, the colder it'll get later... This year, up in the mountains, it had snowed less than it has in the past 10 years, but then, just a couple weeks ago, it snowed almost 2 feet!
Something around here is completely screwy, and it might just be the climate. This last week at school (the snow last about 2 days in the heat), the entire system has fallen to pieces... This might, possibly be related to the heat around here (I think it was about 90-some degrees F today, way more than it's supposed to be).
The main unrealistic thing about The Day After Tomorrow is the speed at which it happens, as well as the means. Otherwise, the truth is that we could end up in world at -40 C in a decade or so... kinda scary... makes you want to move to the equator, doesn't it?
Ricky,
the arrow in the notation denotes John Conway's chained arrow notation which is much much larger than knuth's up-arrow notation.
In fact, The chained-arrow notation here is pretty huge, although I'm not sure I really got the concept of the notation in full.
If I got the system of Knuth's up-arrow notation right, then I'm pretty sure that, yes,
3^^3 = 3^(3^3).
Therefore, 3^^^3 = 3^^(3^^3) = 3^^(3^(3^3))
And 3^^^^3 = 3^^^(3^^^3) = 3^^^(3^^(3^^3)) = 3^^^(3^^(3^(3^3)))
These last two are HUGE numbers.
The last one is the first step of G (Graham's number).
By the way, don't actually try to calculate the number. It would overload every single computer in the world if they tried to just calculate the first step together...
Let me see if I can explain the first steps of the number here:
1 Take the first step : 3^^^^3
2 Calculate it (it's bigger than the number of atoms in the observable universe)
3 Now go back to step 1, this time using the number you just found of up-arrows between the 3s.
Now repeat this entire process 64 times.
Thanks. I spend most of my time trying to solve thinking puzzles, so the name's appropriate.
The entire idea of Graham's number is absolutely mind-boggling! just the first two steps (out of 64) leave me pretty much gone.
In this same way, I suppose that 0.0000000000...001=0 if there are an infinite number of zeros before the 1, although anything with an infinite number is mostly theoretical (with the possible exception of pi).
I'm pretty sure the reason why people have disclaimed Graham's number is because it is the upper bound to a (rather hairy) problem in Ramsey Theory, the lower bound having been identified as 6 by the same people that "discovered" the upper bound.
As one of these people said, "there's room for improvement".
It also seems that this phenomenal number is just the upper bound answer to a problem, the determined lower bound being about 6.
By the way, in response to your question,"What an interesting comparison - which one packs the most punch?" concerning factorials and up-arrow notation, I'm pretty sure that up-arrow notation is the whopper, though I can't say for sure.
I actually heard (or read) that the number of digits in Graham's Number exceeds the number of electrons in the observable universe.
Any idea whether this is actually true?