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On the (Small) Number of Atoms in the Universe

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Re: On the (Small) Number of Atoms in the Universe

#11

Post by lisper »

nsxwolf wrote: post #9
j1vms wrote: post #5

Here's another great one - and ballpark calculations point to it being likely true: "..the number of atoms in a grapefruit is about equal to the number of blueberries you would need to fill up the entire sphere of planet Earth." [ https://capitolhillscience8.wordpress.com/2012/10/03/just-ho... ] Edit: well, except that the Earth is shaped more like an oblate spheroid [ https://en.wikipedia.org/wiki/Figure_of_the_Eart…

That actually makes the Earth seem small to me. I wouldn't have blinked if someone had told me the blueberries would fill up a sphere the size of the Solar System. Just shows how hard it is to visualize these numbers.

The earth is small. If you build a scale model of the solar system the size of a football field, with the sun and one end and Neptune at the other (Pluto has been laid off as a planet) then the sun will be about the size of a ping pong ball and the earth will be the size of a poppy seed (and it will be about ten feet from the sun). Jupiter is about the size of a pea at this scale. Alpha Centauri is about four miles away.

And not only do you live on a poppy seed, you live on a very thin layer on the surface of this poppy seed. Blow the poppy seed up to the size of a basketball and the habitable layer is about the thickness of a sheet of paper.

Re: On the (Small) Number of Atoms in the Universe

#12

Post by amelius »

gyakovlev wrote: post #4

And it's even smaller if compared to Graham's number. Every time I try to imagine that one it feels like I'm going to mental asylum.

Related only to large numbers, but is there some theory about generalizing and extending our usual mathematical operators +, ×, and ^ (power)?

+ applied N times becomes ×N

× applied N times becomes ^N

^ applied N times becomes ...?

etcetera

And would such a theory have any practical use?

Re: On the (Small) Number of Atoms in the Universe

#13

Post by abengoam »

amelius wrote: post #12
gyakovlev wrote: post #4

And it's even smaller if compared to Graham's number. Every time I try to imagine that one it feels like I'm going to mental asylum.

Related only to large numbers, but is there some theory about generalizing and extending our usual mathematical operators +, ×, and ^ (power)? + applied N times becomes ×N × applied N times becomes ^N ^ applied N times becomes ...? etcetera And would such a theory have any practical use?

https://en.wikipedia.org/wiki/Hyperoperation

Re: On the (Small) Number of Atoms in the Universe

#14

Post by NegativeK »

amelius wrote: post #12
gyakovlev wrote: post #4

And it's even smaller if compared to Graham's number. Every time I try to imagine that one it feels like I'm going to mental asylum.

Related only to large numbers, but is there some theory about generalizing and extending our usual mathematical operators +, ×, and ^ (power)? + applied N times becomes ×N × applied N times becomes ^N ^ applied N times becomes ...? etcetera And would such a theory have any practical use?

Knuth's up-arrow notation is one of a few ways to address the addition->multiplication->exponentiation->tetration->... extensions: https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation

As for practicalities, the mathematician in me will let the scientists deal with that.

Re: On the (Small) Number of Atoms in the Universe

#15

Post by jameshart »

j1vms wrote: post #5

Here's another great one - and ballpark calculations point to it being likely true: "..the number of atoms in a grapefruit is about equal to the number of blueberries you would need to fill up the entire sphere of planet Earth." [ https://capitolhillscience8.wordpress.com/2012/10/03/just-ho... ] Edit: well, except that the Earth is shaped more like an oblate spheroid [ https://en.wikipedia.org/wiki/Figure_of_the_Eart…

whereas a grapefruit is a perfect sphere?

Re: On the (Small) Number of Atoms in the Universe

#17

Post by jameshart »

overcast wrote: post #10
j1vms wrote: post #5

Here's another great one - and ballpark calculations point to it being likely true: "..the number of atoms in a grapefruit is about equal to the number of blueberries you would need to fill up the entire sphere of planet Earth." [ https://capitolhillscience8.wordpress.com/2012/10/03/just-ho... ] Edit: well, except that the Earth is shaped more like an oblate spheroid [ https://en.wikipedia.org/wiki/Figure_of_the_Eart…

Actually the Earth is nearly perfect, far more perfect than most any sphere with interact with in day to day life. The equatorial bulge is 20 miles or so, which is approximately .33% Technically an oblate spheroid, but barely.

And for comparison, the variation in surface height relative to sealevel is over 10 miles (6 miles down to the bottom of deep ocean trenches; 5 miles up to the top of mountains)

Re: On the (Small) Number of Atoms in the Universe

#18

Post by gnaritas »

j1vms wrote: post #5

Here's another great one - and ballpark calculations point to it being likely true: "..the number of atoms in a grapefruit is about equal to the number of blueberries you would need to fill up the entire sphere of planet Earth." [ https://capitolhillscience8.wordpress.com/2012/10/03/just-ho... ] Edit: well, except that the Earth is shaped more like an oblate spheroid [ https://en.wikipedia.org/wiki/Figure_of_the_Eart…

The earth is more round than a pool ball; it'd be a perfect sphere to any human eye at virtually any scale. The bulge is too small to notice.

Re: On the (Small) Number of Atoms in the Universe

#20

Post by drjesusphd »

amelius wrote: post #12
gyakovlev wrote: post #4

And it's even smaller if compared to Graham's number. Every time I try to imagine that one it feels like I'm going to mental asylum.

Related only to large numbers, but is there some theory about generalizing and extending our usual mathematical operators +, ×, and ^ (power)? + applied N times becomes ×N × applied N times becomes ^N ^ applied N times becomes ...? etcetera And would such a theory have any practical use?

Graham's number comes from such an extension, and is about 64 such operations deeper. It's useful in the sense that it provides an upper bound for some proof that hasn't yet been proven for ALL numbers.

http://waitbutwhy.com/2014/11/1000000-grahams-number.html

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