Something I am yet to wrap my head around on this point of SHA-256 is, how do we have an estimate of atoms in the “observable universe”?
Like how the hell is anyone figuring out the amount of atomic occupied space in all that space, and doing so with any degree of confidence?
I trust that as much as I trust Covid modelling. 
Estimtes differ by about 4 orders of magnitude, all with certain assumptions about the observable universe (it is finite, flat, has a certain critical density, etc...), differing in the primary data they extrapolate from (number of galaxies, cosmic background radiation etc...).
Lots of assumptions and estimates! How accurate, I don't know. Basic process goes something like:
Estimate age of universe: 13.8B years.
Estimate expansion rate of universe, to get radius of OU. 46B light years.
Calculate area of sphere = 4π46^2.
Now estimate number of galaxies from observable size.
Now estimate the number of stars from number of galaxies.
Now multiple by number of atoms in our sun ...
Oh, and this assumes all hydrogen atoms.
You cant wrap your head around it because exponentials are inconceivable by the human brain. It's better to think of these numbers as infinity ♾️ than a concrete number.
Infinity is quite a novel concept the mathematics that go into ♾️ are pretty nuts even more nuts are the scientists who try to grapple the concept altogether.
If you've not seen the documentary called "a trip to infinity" it's a great watch.
I understand exponentials are effectively inconceivable to us, but that’s not where I get hung up on this particular case.
My issue is that it’s assumptions and extrapolations all the way down - what we define as the “observable universe” today is constrained by current technology which changes over time so the supposed measurement is entirely dependent on a point in time but that is never acknowledged, let alone how short of a time we’ve understood atomic theory for example.
Then because of the vastness of space we’re not making any real measurements of atoms in it but again, extrapolating based on other extrapolations.
Because of the nature of exponentials, one wrong input leads to exponentially wrong outputs (hence my Covid comparison) so given these are all essentially guesses based on other guesses, it seems idiotic to make a comparison which is itself entirely hypothetical and then throw a label on it like “the number of atoms in the observable universe”.
Same reason why I take all of the “age of the universe” stuff with a grain of salt - fact is we’ve got NFI. It’s all guesses and extrapolations and we don’t even understand where the boundaries of our knowledge are, we don’t know that we understand time properly, we don’t understand so much and yet we have people making claims and acting certain when we can’t even work out where humanity was at 5,000 years ago let alone 10,000 let alone 100,000..
Will watch the doco you recommended though. Always willing to try to learn more, even if I’m sceptical AF about this stuff 😂
Thanks for recommending the documentary. Veritasium on youtube has a good one on this subject if you haven't come across it. https://youtu.be/OxGsU8oIWjY
I take the point that these sorts of estimations can only have a very low degree of confidence. However, my understanding of exponents is that the estimate is wide enough to cover most possibilities.
The difference between 10 to the power of 78 and 82 makes the lower number tiny in comparison (despite it being impossibly large itself). The estimate ranges from an almost inconceivably large number or another one 10,000 times greater.
Apply it to guessing marbles in a jar, you'll get my point. - I estimate there are between 10 to the power 2 and 10 to the power 6 (I.e. Between 100 and 1, 000,000) in the jar.
Think you replied to the wrong thread but your last example shows exactly how nonsense the idea is.
A guess which lands between 100 and 1,000,000 is nonsensical. Consider how large a jar to contain 100 marbles is versus a jar to contain 1,000,000 - they’d clearly be hugely different.
And that’s the point, once you’re getting to these levels the margin of error being accepted makes the calculation essentially nonsense. It’s easier for us to understand that with small numbers but getting into exponentials it makes it, exponentially worse.
