Largest Meaningful Number

[u/vondee1]

It’s easy to describe large numbers, but wouldn’t the largest meaningful number (that is, a number that describes either our universe or something within the universe) be the number of cubic Planck lengths in the universe? i.e., the size of the universe expressed in cubic Planck lengths.

Yes, one could easily craft a larger number (e.g., the number of cubic Planck lengths in the universe to the power of the number of cubic Planck lengths in the universe) but that number wouldn’t really represent anything meaningful. Is there a larger meaningful number?

And a side question… As the universe expands, does the number of cubic Planck lengths in the universe increase or do the cubic Planck lengths themselves expand while the number of cubic Planck lengths in the universe remains constant?

[u/Hairy_Cake_Lynam]

I don’t know. But when you’re thinking about entropy and trying to work out the number of possible microstates corresponding to a particular macroscopic state, you get some ridiculously large numbers!

The universe is about 10⁶⁴ Planck lengths across. This number is vanishingly small compared to the number of possible arrangements of the air molecules in your room!

[u/datapirate42]

What qualifies a number as "meaningful"?  is the volume of the universe in Planck volumes meaningful? And even if it is, is it actually very big?

https://www.wolframalpha.com/input?i=volume+of+visible+universe+%2F+%28Planck+length%29%5E3

10¹⁸⁵ is not particularly big in terms of big numbers.  I'm sure you could easily come up with something bigger if you were trying to do statistical mechanics on  any macro scale object.  What is the number of microstates for the molecules in 18g of water?   the first term in the equation is (10^23)! Which is pretty much 10^ (10^23).  On the scale of big numbers this makes that other one look miniscule

[u/bsievers]

Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe.

[u/StopblamingTeachers → u/bsievers]

I think they’re specifically not interested in this

[u/HoldingTheFire]

A Planck length is not the smallest length, and I wish that misconception would die.

As for your largest number: The multiplicity of microstates in a handful of matter can easily exceed your example.

[u/Nicholas-DM → u/HoldingTheFire]

Might it be the smallest measurable length?

[u/HoldingTheFire → u/Nicholas-DM]

No

Edit: Elaborating, people often cite that this is the wavelength of a photon that would make a black home.

But a) that isn't true, the Schwartzchild length is like 1.7 Planck's lengths and b) I can measure lengths much smaller than the wavelength of light I use. Look at LIGO.

[u/Nicholas-DM → u/HoldingTheFire]

Fair enough. Thank you for the clarification.

[u/Final_Character_4886]

Check out how many QR codes there can be.