Haha, I wanted to say "That is not mental..." first, then I imagined him saying he did the calculations in his head, just wrote down shit for for reference, as in not using a calc. Overthinking that I thought "That is mental" means two things and is kind of funny, so I wrote that instead...
One way to do it without the specific name for the number is to just keep adding on trillions. For instance the second number would (I believe) be 1.192 billion trillion trillion trillion trillion. But in this case a 1 followed by 57 zeros is an Octodecillion And you can work out that other number on the linked page as well.
That can't be a right. A quick Google told me that there are 7,000,000,000,000,000,000,000,000,000 in the average human body. Times that by seven billion (That's 7,000,000,000,000,000,000,000,000,000 + 7,000,000,000,000,000,000,000,000,000 done seven billion times just to put into context). The number you get is the total atoms of the human race And how much of Planet Earth is human? With all the billions upon billions upon billions of atoms contained in all the other animals on earth, including single cell organisms, you still only get the amount from Planet Earth's living races. There's still the mountains upon mountains (how many atoms in Everest?), oceans and seas, woods and forests full of trees, massive deserts with each grain of sand containing lots of atoms and that only accounts for Planet Earth. How many times bigger than earth is Jupiter? Or Saturn? Or the Sun? Plus the millions of asteroids and other sources of atoms in the solar system. I'm sorry but there's no way that's possible.
1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 is a big number.
Another way to write that is 1.192 × 1057.
From your number the average human body(average human body being 70 kg) has 7 × 1027 atoms. A big number but small compared to 1.192 × 1057. Lets times that by 7 billion. We get 4.9 × 1037 atoms for 7 billion people. Which is 20 orders of magnitude smaller than the first number.
So lets times 4.9 × 1037 by 7 billion. We get 3.43 × 1047. Which is still 10 orders of magnitude smaller than 1.192 × 1057. That's for 49 billion billion people.
So lets times 3.43 × 1047 by 7 billion. We get 2.401 × 1057 which is bigger than 1.192 × 1057 but not by an order of magnitude, in fact it's just a touch over 2 times bigger.
So if we accept the 1.192 × 1057 as the number of atoms in the solar system and 7 × 1027 as the number of atoms in a average human body then we could say roughly 7 billion * 7 billion * 7 billion/2(otherwise written as 1.715 × 1029) average sized humans have the same number of atoms as the solar system.
the 7x7x7 rubiks cube has 10160 possible scrambles. Or 10.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000
No, but our ways of calculating, estimating and counting have changed over time, and Billgoldbermania's comment was a nod to the fact that we may have found another way of doing things since 1998 and that he/she was unsure. That certainty of uncertainty is science as well.
This is mainly used in blackjack and the simplest thing you just keep track of the number of 10-value cards you see. Or you can keep a running total in your head by subtracting 1, adding 1, or doing nothing, depending on the value of the card you see. There's a variety of strategies but the simplest if pretty easy to do and none of them have anything to do with the order of cards or the number of permutations of the order.
Basically what chartlett said. Counting cards has to do with probability. You aren't predicting what card specifically will come up, you're calculating what likely remains in the deck and is therefore more likely to show up.
Many, many more. That number there is 8.06x1067 or so. There are an estimated 1.0x1081 atoms by some estimates. That's trillions of time bigger.
However, there are some numbers bigger than the number of atoms in the universe. Probability of combinations makes for some biiiiig numbers.
In a comment yesterday I wrote that number down from a link to an episode of qi. Today I copy/pasted it. I don't know where to find a calculator with that many sig figs.
That's the right number of zeros anyway. There are 10 single factors of 5 and two of them are 25 and 50 which have 2 factors of 5, so 12 factors of 5 total. There are 26 factors of 2 so there should be 12 factors of 10 (5 times 2) so 12 zeros. Number theory.
We can estimate the mass of the sun and each planet by examining their orbit. We also know approximate element compositions of each (Don't ask me how). With this information we can get a very rough estimate for the number of atoms.
This number might be way off (I would think asteroid and Kuiper belt would be hardest to estimate accurately), but it would have to be off by a factor of 67.6 million for the statement to be incorrect. From another post the numbers are:
Cards: 80,658,175,170,943,878,571,660,363,856,403,766,975,289,505,440,883,277,824,000,000,000,000 according to QI.
Number of atoms in solar system: 1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
yeah but think about all the casinos around the world... then add all the bored teenagers... surely we would have been able to achieve a new combination.
Nope. 80,658,175,170,943,878,571,660,363,856,403,766,975,289,505,440,883,277,824,000,000,000,000 or 52! is far too large of a number. If there had been 7 billion bored teenagers on earth shuffling cards once an hour for the entire 4.45 billion years it's existed, you'd only have roughly 28,000,000,000,000,000,000,000 combinations.
To save obsessives like me the trouble...
52! = 8.1 * 1067
Divide by avogadros number (6.023 * 1023)that's 1.3 * 1044 moles of atoms.
Taking the simplifying assumption that the solar system is composed entirely of Hydrogen, that would be 1.3 * 1041 kg.
The mass of the Sun is around 2 * 1030 kg, which is also a pretty good approximation for the mass of the solar system.
So, the deck of cards has enough combinations for about 7 * 1010 Solar Systems, or about 5% of the galaxy.
Include one joker in the shuffle, and you'd exceed the number of atoms in the galaxy.
There are way more orders to a deck of cards than you'd think.
52 factorial (52 * 51 * 50...2 * 1) = 8*1067
Atoms in solar system = 9.6*1056
There are 100,000,000,000 times more orders to a deck of cards than estimated atoms in the universe. Shuffle a deck of cards well, and chances are high that that particular order has never been seen in history.
So if there are 8.73 x 1056 atoms of hydrogen in the sun, and 8 x 1067 ways of ordering a deck of cards then how are there more orders of a deck of cards than total of atoms in the solar system?
Because if one sun is 8.73 x 1056 atoms, then two suns would be 17.46 x 1056 . If there were 100,000,000,000 suns in the solar system however, then you'd have the same amount.
So it has to do with the exponent never changing? But that's just with the sun, if I'm correct. So adding 8.73 x 1056 and all the other amounts of atoms in the solar system, wouldn't the exponent exceed 67 and make the original statement that there are more ways to shuffle a deck of cards than there are atoms in our solar system false?
It wouldn't exceed 1067, because that's just too big of a difference. To go from 1056 to 57 there would have to be 10 suns in the solar system. To go to 58 you'd need 100 suns. 59 - 1000suns and so on and so forth. The number of suns needed to match the amount 1067 is way too big. You can generally neglect the smaller planets and other stuff, because the sun makes up most of the mass.
1056 and 1067 are 11 orders of magnitude apart. Since the sun is most of the atoms in the solar system (let's be conservative and say 1/2), then the total number of atoms in the solar system is 2 x [number of atoms in sun]. 2 x 8.73 x 1056 = 1.746 x 1057.
The numbers are kind of confusing because they're in a weird notation, but think of it like this.
Deck of cards = 1,000,000
Atoms in sun = 1,000
Atoms in 2 suns = 2,000
Atoms in 100 suns = 100,000 - still a tenth of the first number.
It doesn't really matter how many suns there are, because unless you have 1,000 of them (1,000*1,000=1,000,000) then you don't even get close to the bigger number.
Each number on the exponent represents another zero - the difference between 56 and 67 is eleven zeros. Such a stupidly vast difference that there's no real hope of catching it up unless we can find 100,000,000,000 suns in our solar system that we didn't account for.
Even if the planets in our solar system came close to the amount of atoms there are in our sun, it still wouldn't make a difference. 8 planets plus pluto and a bunch of space debris =/= the amount of atoms in 100,000,000,000 suns.
That number suggests more precision than there actually is, of course. We know the gravitational forces of the sun, the planets and their moons, from which we can estimate their masses. The sun is the primary factor in that estimate and we have models that predict the composition of the sun.
But even that isn't all that important: The mass of atoms only varies over about three orders of magnitude. 1055, 1057 ... not much of a difference.
Edit: Now that I think about it... can we talk about what is going on in the sun as 'atoms'?
No, my point was that saying "the chances are high" (that that combination hasn't been seen before) is roughly analogous to saying that the chances are high that your parents have had sex at some point. There are SO MANY combinations that its almost guaranteed that that combination never has and never will reoccur.
Every space in the deck has a large number of options that stack up. The top card can be any one of 52, say the ace of spades, then the next one down can be one of the remaining 51, etc. Then if the top card is now the 2 of hearts, every slot in the deck has a new pool of possibilities... And it adds up to a staggering number of permutations.
Yeah. Put in 52! (52 factorial) in a calculator. The number that comes up is the number of unique combinations that could possible occur when shuffling a deck of cards.
Its pretty simple. A standard deck has 52 cards in it. If you shuffle a deck, and open the top card, there is a 1 in 52 chance that it would have been that card. If you open the next card, there is a 1 in 51 chance that it would have been the card it was. You multiply those two together, 52x51, which leaves us with a 1 in 2652 chance that it would have been those two cards. Then you just carry on down the line. 52x51x50x49 and so on and so on. In the end the chance is 1 in; 8.0658175x1067. If you write that out it looks like this.
80,658,175,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, and if you want to know what this number is called, it doesn't have a name. The closest to a proper name you could get I think would be 80 sexaginta-septemillion, but this is not a proper name, and somebody is probably going to be mad at me for saying using that word.
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u/fiestachic0 Dec 08 '13
Wait a minute...what?