Question about the Planck spaces and observable universe, .

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A Planck space is defined as the smallest measurable volume, approximately 4.222×10^-105 cubic meters. The observable universe contains about 3×10^80 cubic meters, equating to roughly 7.1×10^184 Planck spaces, which is significantly less than a googolplex. The confusion arises from the concept that a googolplex refers to the number of ways to arrange a certain number of particles, not the actual number of particles that can fit in the universe. Specifically, the number of arrangements of fine dust particles, each 1.5 micrometers in size, can reach a googolplex, but this does not imply that such a quantity of particles can physically occupy the universe. Understanding this distinction clarifies the relationship between the concepts of volume and arrangement in the context of the universe.
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From Wikipedia:
http://en.wikipedia.org/wiki/Googolplex

A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, at approximately 4.222×10^-105 cubic meters = 4.222×10^-99 cubic cm. Thus 2.5 cubic cm contain about a googol Planck spaces. There are only about 3×10^80 cubic metres in the observable universe, giving about 7.1×10^184 Planck spaces in the entire observable universe, so a googolplex is far larger than even the number of the smallest measurable spaces in the observable universe.

If the entire volume of the observable universe (taken to be 3 × 10^80 cubic meters) were packed solid with fine dust particles about 1.5 micrometres in size, then the number of different ways of ordering these particles (that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered) would be approximately one googolplex.


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So if the observable universe doesn't have enough space to contain a Googolplex of Planck spaces how come a Googolplex of 1.5 micrometres fine dust particles woud fit inside it?

Thanks in advance and sorry if I've made any mistakes, this is my first post here :)
 
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It doesn't say a googolplex dust particles fit in the universe, it says that if n is the number of dust particles, then a googolplex is approximately n factorial (the number of ways of ordering the dust particles)
 
Office_Shredder said:
It doesn't say a googolplex dust particles fit in the universe, it says that if n is the number of dust particles, then a googolplex is approximately n factorial (the number of ways of ordering the dust particles)

Awww, I feel like a noob :o I get it now! Thank you really!

And BTW this is really a great forum, thanks for the quick answer! :P
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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