# huge numbers into perspective



## countdavie (Mar 9, 2011)

So we know that that the total number of configurations for the 7x7x7 cube is 19.5*10^160. I was only able to find one example that can somewhat put this into perspective: that is more combinations than 8 independent 3x3x3 Rubik's cubes. 

I was just wondering if anyone else has ideas about how to put that number into perspective? You know, how there are many examples of how 43 quintillion is put into perspective, kind of. I wonder how 19.5*10^160 could be put into perspective.

If you have any ideas, that would be great!

Thanks


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## Kenneth (Mar 9, 2011)

1 molecule of water, how big container would you need to keep all of those?

Edit : hmm, it is depandant on temperature, say +4 Celsius, that is the temperature where water have the greatest dencity...


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## qqwref (Mar 9, 2011)

Considering there are "only" roughly between 10^72 and 10^87 particles in the universe, you probably won't be able to find a lot of useful physical comparisons 

Assuming a 7x7x7 is roughly 6cm cubed, if you made a gigantic cube out of all the possible positions, it would be about 10^36 light years on a side... or about 4.5 * 10^25 times the diameter of the observable universe. And that's still a really big number.


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## theace (Mar 9, 2011)

That's just scary...


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## aridus (Mar 9, 2011)

If my math is right... if you were to actually produce each combination at 1 per second, it would take you 6.18340945 × 10^153 years to do them all.


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## cmhardw (Mar 9, 2011)

Best... Huge numbers into perspective site... EVER

The final note on the page sort of gives you an idea of how to perceive any larger number in general, but this site will not necessarily well handle your larger number.


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## ben1996123 (Mar 9, 2011)

cmhardw said:


> Best... Huge numbers into perspective site... EVER
> 
> The final note on the page sort of gives you an idea of how to perceive any larger number in general, but this site will not necessarily well handle your larger number.



Awesome page 

A cube with side length 12,756.2km (the diameter of the Earth):
3,602,928,135,411,117,047,808,000,000 cents, 3.6 octillion cents.
Height stacked is ~3.554*10^21 miles, just over 600 million light years
 thats an alot of moneys 

If I did it correctly.


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## Ordos_Koala (Mar 9, 2011)

ben1996123 said:


> Awesome page
> 
> A cube with side length 12,756.2km (the diameter of the Earth):
> 3,602,928,135,411,117,047,808,000,000 cents, 3.6 octillion cents.
> ...


 
I don't like that big numbers so I'll just state, that money doesn't have plural... but yes, it's an alot of money


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## Rinfiyks (Mar 9, 2011)

Imagine every cube is the size of a proton. You could fill the observable universe with no gaps with roughly 10^125 cubes. (Thanks wolfram alpha for proton radius and universe volume.)
Now we still need to find a way to visualise 10^35 times this number.
A quick (and probably very inaccurate) estimation of the number of rain drops that have ever fallen on earth:


Spoiler



Assume the average diameter of all raindrops is 2 mm. Volume is then about 17 mm^3.
Average precipitation: 990 mm.
Assuming it's been around 1000 mm for all of Earth's history won't make more than 1 or 2 factors of 10 difference.
Surface area of earth * 1000 mm = 5*10^23 mm^3.
(5*10^23)/17 = 3*10^22 raindrops per year.
Assume it's been raining for 4 billion years.
3*10^22 * 4000000000


That makes about 10^32 raindrops. Still need another 10^3, so just stick 1000 universes in each rain drop.

tl;dr: If every drop of rain that ever landed on Earth contained 1000 universes each filled with proton-sized 7x7x7s, you'd have roughly enough space to fit every position.


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## Godmil (Mar 9, 2011)

Agh, even if I think of the cubes as being as big as 1mm and try to imagine them filling the universe it really freaks me out, and that's seemingly so far from all of them. Is the number definitely right? It does take into account the interchangeable identical pieces? It's just such a big number.


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## cmhardw (Mar 10, 2011)

Godmil said:


> Agh, even if I think of the cubes as being as big as 1mm and try to imagine them filling the universe it really freaks me out, and that's seemingly so far from all of them. Is the number definitely right? It does take into account the interchangeable identical pieces? It's just such a big number.


 
I definitely get the same number:

7x7x7 has the following number of combinations:

\( \frac{8!*3^7*12!*2^{10}*(24!)^8}{24^{36}} \)

And that equals:
19500 551183 731307 835329 126754 019748 794904 992692 043434 567152 132912 
323232 706135 469180 065278 712755 853360 682328 551719 137311 299993 600000 
000000 000000 000000 000000 000000




ben1996123 said:


> Awesome page
> 
> A cube with side length 12,756.2km (the diameter of the Earth):
> 3,602,928,135,411,117,047,808,000,000 cents, 3.6 octillion cents.
> ...


 
If this is for the 7x7x7 this doesn't seem right. If Michael used a shape that was 6cm cubed for every possible combination of the 7x7x7 cube and it ended up being a factor of about 10^25 times the diameter of the observable universe, then scaling the shape down to a penny (0.576 cm^3 compared to 216cm^3). This is a difference in volume of a factor of 375, then we should still be measuring the volume in terms of massive magnitudes larger than the diameter of the observable universe.


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## mr. giggums (Mar 10, 2011)

I found this it's very intersting especially towards the end of the article.


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## cmhardw (Mar 10, 2011)

Wow, that article was really cool! I had heard of Turing machines, but didn't really know how they worked until reading that.

This thread really reminds me of epsilon-delta proofs for limits, and having to invoke the Archimedean property to do so


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## amostay2004 (Mar 10, 2011)

Ordos_Koala said:


> I don't like that big numbers so I'll just state, *that money doesn't have plural*... but yes, it's an alot of money


 
Oh yes it does. Though it's 'monies', not moneys.


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## aridus (Mar 13, 2011)

Godmil said:


> Agh, even if I think of the cubes as being as big as 1mm and try to imagine them filling the universe it really freaks me out, and that's seemingly so far from all of them. Is the number definitely right? It does take into account the interchangeable identical pieces? It's just such a big number.


 
I'm pretty sure it's right, but it is also non intuitive a bit because I'm sure like the 3x3x3 it does not take into account abstraction, it is speaking of very literal, technical combinations. I'm sure that as with the 3x3x3 many of them are theoretically "the same" when abstracted but are technically unique because they involve different colors and even orientation of the whole cube might be counted.


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## whauk (Mar 13, 2011)

if you compose a song by hitting any keys on a piano you would have to play at least 83 notes to beat the possible states of a 7x7.
if you count the possibilities for an arrangement of different elements in an order you would need at least 104 elements to beat the possible states of a 7x7.
if you throw coins and note down every result for every throw you would have to throw at least 536 coins to beat the possible states of a 7x7.

these were the first few examples that came into my mind. its hard to find sth that is imaginable for us.


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## ben1996123 (Mar 13, 2011)

Rinfiyks said:


> If every drop of rain that ever landed on Earth contained 1000 universes each filled with proton-sized 7x7x7s, you'd have roughly enough space to fit every position.



O_O


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