Is it ever physically possible for a broken egg to reassemble into an unbroken one?

[Paleophyte]

In practice, people tend to be exceptionally bad at properly examining the probability space. Probabilities lower than 1 in a googolplex happen every instant of our lives but we fail to recognize them because of the stochastic nature of the universe that we inhabit. In the instance of the egg the rational course of action is not to start worshipping Gawd AllMighty Mender Of The Yolk but rather to look for the Gallifreyan pankster who has been unscrambling your omelettes.

On a side note, googol and googolplex have always failed to impress me. They're stunt numbers based on the number of fingers on your hands. If really big numbers is all you want then 4^^4 is a bit better than 50% more digits than a googolplex and 9^^9 should be more than sufficient to tie up any computer from now until the end of time.

I think you might find it more difficult than you imagine to get odds of 1 in a googolplex.

So, for example, the radius of the observable universe is about 13 billion light years

46.5 billion light years last I checked.

which is around 10^26 meters, or 10^38 femto-meters.

So, the number of cubic femtometers in the observable universe is around 10^114.

The number of fundamental particles in the universe is around 10^80, so the odds that the specific arrangement of particles in the space of the universe (up to femtometer accuracy) is about (10^114)^(10^80), which is less than 10^(10^83). This is assuming the position of each particle is independent of every other particle. This is *far* less than a gogolplex.

Now, the odds for every fundamental particle in the universe *randomly* and independently happening to be in the specific cubic femtometer they are, independently for each femtosecond n a second, would be less than (10^10^83)^(10^12), which is about 10^10^95. This is still far smaller than a googolplex.

In fact, one in a googolplex would be worse odds than the odds of every particle in the universe randomly and independently being in the precise cubic femtometer, independently for each femtosecond in 100,000 years.

So, no, we do NOT see events with a lower probability happening every instant of our lives.

Not when you math it like that, no. However:

- Femtometer resolution is ridiculously coarse right out of the gate. You won't even be able to predict if two protons are on course to fuse into a deuteron or not at that resolution.

- You've neglected to account for all the various different properties that each of those fundamental particles can have. Those are going to be important.

- The whole mess is iterative, which means that each ridiculously improbable configuration follows from an equally preposterous configuration. That means that if you don't have extremely good resolution the errors compound very quickly. Given that the large-scale structure of the universe originated as quantum fluctuations during the universe' inflationary era you're probably going to need Planck-scale resolution in all four dimensions.

If you want to know the probability of these exact sodium ions being pumped in and out of my neurons, to send exactly these electrons and photons bouncing around the pinball game we call the internet, to eventually light up exactly these atoms in your display, trigger precisely these opsins, and fire exactly these sodium-ion gates in your neurons, yadda, yadda, yadda, blah, blah, blah... requires calculating all the intermediate and preceding states and their improbabilities. If just one proton had been a bit to one side rather than the other 10 billion years ago then stars in our distant history would have blown themselves apart very slightly differently, our constituent atoms would never have been formed, and somebody very different would be having a very different conversation.

PS: We *do* see events with probabilities lower than 1 in a googol every instant. But a googolplex is much, much, much larger than a googol.

Yes, you can beat a 1 in a googol if you have $3.33 in pennies and that's doing it the lazy way. Or a couple well-shuffled decks of cards.