(September 18, 2019 at 11:07 am)Grandizer Wrote: The conventional answer is that it would never happen. But couldn't it be the case that, while it would be extremely unlikely for a broken egg to be spontaneously reassembled into an unbroken egg, there's still nevertheless this very tiny tinge of possibility that this can happen (maybe a 1 out of a googolplex probability)?

The overall entropy may be increasing, but I don't see why the atoms that constitute a broken egg couldn't, by sheer coincidence, collect together in a way that the arrangement now constitutes an unbroken egg?

There's no actual physical law against it but if we assume purely random interactions of the component egg fragments and their environment then the odds of this ever happening are so small as to be effectively impossible.

That said, purely random interactions of the components isn't a reasonable assumption and a proper examination of the probability space shows that the number of philosophers, physicists, and general contrarians involved in causality research virtually guarantees the unbreaking of an egg if it hasn't already happened.

(June 7, 2020 at 11:49 pm)Paleophyte Wrote:

(September 18, 2019 at 11:07 am)Grandizer Wrote: The conventional answer is that it would never happen. But couldn't it be the case that, while it would be extremely unlikely for a broken egg to be spontaneously reassembled into an unbroken egg, there's still nevertheless this very tiny tinge of possibility that this can happen (maybe a 1 out of a googolplex probability)?

The overall entropy may be increasing, but I don't see why the atoms that constitute a broken egg couldn't, by sheer coincidence, collect together in a way that the arrangement now constitutes an unbroken egg?

There's no actual physical law against it but if we assume purely random interactions of the component egg fragments and their environment then the odds of this ever happening are so small as to be effectively impossible.

That said, purely random interactions of the components isn't a reasonable assumption and a proper examination of the probability space shows that the number of philosophers, physicists, and general contrarians involved in causality research virtually guarantees the unbreaking of an egg if it hasn't already happened.

And if the probability is 1 in a googolplex, we don't *expect* to see actual examples in the current age of the universe (very far from it). But the probability is still non-zero.

If every fundamental particle in the universe was doing addition every Plank's time, the total computed since the Big Bang would be less than 10^135. This is *far, far, far* less than a googolplex.

I'll go further. If every fundamental particle added a total of a googol every Plank time, the total since the Big Bang would still be smaller than 10^235, which is still far, far, far less than a googolplex.

I'm standing there and an egg I just cracked accidentally reforms itself.
'Always a chance that could happen', I say to meself and carry on about me day.

In reality I'd say, 'well fuck me, god is real after all'. :-)

(June 8, 2020 at 8:21 am)Little lunch Wrote: I'm standing there and an egg I just cracked accidentally reforms itself.
'Always a chance that could happen', I say to meself and carry on about me day.

In reality I'd say, 'well fuck me, god is real after all'.  :-)

Yes, the issue then arises whether the probability of a supernatural outweighs the probability of the  violation. When talking about odds this high, almost ANYTHING can go.

(June 8, 2020 at 9:26 am)polymath257 Wrote:

(June 8, 2020 at 8:21 am)Little lunch Wrote: I'm standing there and an egg I just cracked accidentally reforms itself.
'Always a chance that could happen', I say to meself and carry on about me day.

In reality I'd say, 'well fuck me, god is real after all'.  :-)

Yes, the issue then arises whether the probability of a supernatural outweighs the probability of the  violation. When talking about odds this high, almost ANYTHING can go.

The problem is that the probability of a supernatural explanation isn't properly defined. If that probability is zero, which it likely is, then any probability no matter how vanishingly small outweighs it.

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.

The very term “super”natural is designed evade so devastating a fate For the Underlying concept as to be evaluated by a demonstrably efficacious means of assessing its claims.

*Dunning Kruger kicks in*

Quote:5 impossible things the laws of physics might actually allow

Perpetual motion machines
Teleporters
Invisibility cloaks
Negative temperatures
Matter married with antimatter

Nothing about that which is broken reforming itself, however.

(June 9, 2020 at 12:42 am)Paleophyte Wrote:

(June 8, 2020 at 9:26 am)polymath257 Wrote: Yes, the issue then arises whether the probability of a supernatural outweighs the probability of the  violation. When talking about odds this high, almost ANYTHING can go.

The problem is that the probability of a supernatural explanation isn't properly defined. If that probability is zero, which it likely is, then any probability no matter how vanishingly small outweighs it.

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.

Actually, even a googolplex is far away large enough to max out computer storage for the universe. There are around 10^80 fundamental particles in the observable universe.

If you want to get into large numbers, I would suggest the website https://googology.wikia.org/wiki/Googology_Wi.ki. Your tetration examples are big, but have you heard of Graham's number? https://googology.wikia.org/wiki/Graham%27s_number

(June 8, 2020 at 8:10 am)polymath257 Wrote:

(June 7, 2020 at 11:49 pm)Paleophyte Wrote: There's no actual physical law against it but if we assume purely random interactions of the component egg fragments and their environment then the odds of this ever happening are so small as to be effectively impossible.

That said, purely random interactions of the components isn't a reasonable assumption and a proper examination of the probability space shows that the number of philosophers, physicists, and general contrarians involved in causality research virtually guarantees the unbreaking of an egg if it hasn't already happened.

And if the probability is 1 in a googolplex, we don't *expect* to see actual examples in the current age of the universe (very far from it). But the probability is still non-zero.

If every fundamental particle in the universe was doing addition every Plank's time, the total computed since the Big Bang would be less than 10^135. This is *far, far, far* less than a googolplex.

I'll go further. If every fundamental particle added a total of a googol every Plank time, the total since the Big Bang would still be smaller than 10^235, which is still far, far, far less than a googolplex.

What do you think of ultimate reality being akin to Cantor's infinities within infinities, perhaps, our time and space being countably infinite sets within a infinitude of other countably infinite sets, across both time and space?

(June 9, 2020 at 1:39 pm)Jehanne Wrote:

(June 8, 2020 at 8:10 am)polymath257 Wrote: And if the probability is 1 in a googolplex, we don't *expect* to see actual examples in the current age of the universe (very far from it). But the probability is still non-zero.

If every fundamental particle in the universe was doing addition every Plank's time, the total computed since the Big Bang would be less than 10^135. This is *far, far, far* less than a googolplex.

I'll go further. If every fundamental particle added a total of a googol every Plank time, the total since the Big Bang would still be smaller than 10^235, which is still far, far, far less than a googolplex.

What do you think of ultimate reality being akin to Cantor's infinities within infinities, perhaps, our time and space being countably infinite sets within a infinitude of other countably infinite sets, across both time and space?

Well, we usually model things in quantum theory as operators on a Hilbert space of countably infinite dimension. The space itself is uncountable.

A countably infinite number of countably infinite sets only means countably many points. But the real line is an uncountable set, so it is much larger.

Generally speaking the cardinality of a set is far less important than the other structures put on that set (say, a metric, or a vector space structure). Cardinality is a very crude measure of the size of a set in most cases.

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(June 9, 2020 at 12:42 am)Paleophyte Wrote: 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, 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.

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.