Basically what Iβm asking is if there is an equation, a mathematical way to represent the likelihood probability of everythingoccurring by chance. Which is the position that scientists have that everything is just a random occurrence of chance, correct?

Sorry, but that wasnβt coherent enough to respond to. Who in the world thinks that everything happens by chance? What do you mean by βchanceβ?

Thatβs not possible because we donβt know everything about the natural world. Furthermore, it seems like that would be very susceptible to the fallacy of thinking that this is the only way things could be. The chance that a shuffled deck of cards has its exact configuration is 1.24 * 10^-68, but that doesnβt mean someone must have guided it to that configuration. Likewise, the chance that this exact configuration of things is as it exists is undoubtedly miniscule, but we have no idea how else things might have turned out, or how life may exist under a totally different set of circumstances.

There are, within the field of Statistics, probably thousands of equations, which are *each* mathematical ways βto represent the likelihood probability ofβ *something* happening. Examples include:

the binomial distribution:

and the normal distribution:

Knowing which formula to use requires having sufficient information about the chance event in question β there is no βone formula to rule them allβ. And there are many situations for which we have insufficient information to estimate the probability with any real reliability.

I would be speaking as someone who has a background in statistics, rather than as a scientist, and would probably agree with this statement β *but probably not for the reasons you think*.

βChanceβ includes *everything* that doesnβt have a probability of *exactly* one or *exactly* zero.

I may βknowβ that the Sun will rise tomorrow β but there is still a tiny, but non-zero, probability that (for example) the Sun may explode tonight.

A scientist may βknowβ how an experiment will proceed, but there will always be a non-zero probability that something will happen (e.g. a power surge) that ruins the experiment.

Iβm not sure that this includes βeverythingβ β but (i) itβd come very close, and (ii) Iβd want to look very carefully at any exceptions before admitting to them.

Is there an equation or a numeric way to express the probability that the universe occurred randomly (i.e. no conscious creator involved)?

The reader of the essay entitled

Is There A God (What is the Chance the World is the Result of Chance?)may be interested in knowing some hard numbers with regard to the probability that the universe occurred randomly (i.e. no conscious creator involved). Oxford University Professor of Mathematics John Lennox quotes renowned Oxford University mathematical physicist Roger Penrose:

βTry to imagine phase spaceβ¦ of theentireuniverse. Each point in this phase space represents a different possible way that the universe might have started off. We are to picture the Creator, armed with a βpinβ β which is to be placed at some point in phase spaceβ¦ Each different positioning of the pin provides a different universe. Now the accuracy that is needed for the Creatorβs aim depends on the entropy of the universe that is thereby created. It would be relatively βeasyβ to produce a high entropy universe, since then there would be a large volume of the phase space available for the pin to hit. But in order to start off the universe in a state of low entropy β so that there will indeed be a second law of thermodynamics β the Creator must aim for a much tinier volume of the phase space. How tiny would this region be, in order that a universe closely resembling the one in which we actually live would be the result?β

Lennox goes on to cite Penroseβs answer:

βHis calculations lead him to the remarkable conclusion that the βCreatorβs aimβ must have been accurate to 1 part in 10 to the power of 10 to the power or 123, that is 1 followed by 10 to the 123rd power zeros.β

As Penrose puts it, that is a βnumber which it would be impossible to write out in the usual decimal way, because even if you were able to put a zero on every particle in the universe, there would not even be enough particles to do the job.β

No. There would appear to be insufficient information or clarity as to the earliest states of the universe for that question to have even the glimmer of hope of being meaningful. As I said above:

Those numbers are meaningless without the assumptions underlying them. I could as easily state:

The probability of making a good cup of tea is one in a million billion trillion gazzilion.

It also should noted that:

- John Lennox is an apologist, not a cosmologist. Therefore his aim is not to understand the universe, but to win arguments.
- He appears to be quoting from Penroseβs book
*The Emperorβs New Mind*β which is the starting point of Penroseβs transformation from renowned physicist into purveryor of fringe Quantum Consciousness claims. Its claims therefore need to be taken with a pinch of salt.

And so the claim that these are βhard numbersβ also needs to be taken with a heavy pinch of salt. The number lacks any corroborating evidence, is made by somebody who has gained a reputation for making claims that are outside the scientific mainstream, and has been filtered through two apologists β first Lennox and then Scott Youngren.

I find Lennox interestingβsometimes I listen to interviews/lectures/debates at the gymβbut I remain constantly aware of a fact that I regularly reiterate here (no doubt to the boredom of all): **Philosophical discussions which happen to deal with science topics are still philosophy and do not involve the rigor and methodology of the scientific method.** Thatβs not necessarily a criticism of Lennox. It is a simply a reminder of the field of inquiry.

Philosophy has great value, especially as it is the very foundation and source of the historical development of science. But especially when I hear or read mathematical arguments from apologists, I keep a salt shaker and its many grains within reach.

Hmmm. I kinda like that last paragraph. I may put that one on my tombstone. Of course, considering the charge per letter, I may not want to reduce the value of my estate all that much. What the heck. Here goes:

HERE HE BE DEAD

THIS IS WHAT HE SAID

OF THE LIFE HE LED

AND WHAT LIES AHEAD.βπ»πππππππππ πππ πππππ πππππ, ππππππππππ ππ ππ ππ πππ ππππ ππππππππππ πππ ππππππ ππ πππ ππππππππππ πππππππππππ ππ πππππππ. πππ ππππππππππ ππππ π΄ ππππ ππ ππππ ππππππππππππ πππππππππ ππππ ππππππππππ, π΄ ππππ π ππππ ππππππ πππ πππ ππππ ππππππ ππππππ πππππ.β

Yeah, I guess the fancy font didnβt help all that much. (I had hoped it would make it sound more profound.)

It will probably need a β(Continued on back of this tombstone)β to make room for all that text.

POSTSCRIPT: The monorhyme quatrain at the top of my toomstone probably deserves a fifth line just below it: βBurma Shave.β

@Puck_Mendelssohn and others of my generation will get it.

Hmmm, perhaps I just found a sponsor for my tombstone lettering.

That is not what Penrose was calculating. Lennox is being disingenuous, as is usual for anyone connected with the Discovery Institute. Anyone interested can read the full context of what Penrose wrote here:

Spacetime, Relativity, Quantum Physics, and Quantum Gravity (ws5.com)

Thank you for reaponding. So 1. There is insufficient information and that would mean the exclusion of the possibility of βhard numbersβ or any reliably accurate data. 2. Philosophical inquiries are not necessarily scientific nor do they adhere to the scientific method.

As far as the number itself is concerned would it be an astronomically high number if we were able to ascertain it? Perhaps even higher than the apologist Lennoxsβ claim? Although the exact number may not be obtainable currently, could there may arise new data or new data collection methodologies that may bring us closer to the possibility of a βhard numberβ?

Until such time would it be safe to assume that the number(whatever it may be) is a very large number?

No, it would not be.

So then by your rationale itβs safe to assume that itβs a very small number that doesnβt make sense at all?

It could be. It could also be far lower. *We have no way of knowing*.

*Any* number, *even an approximation*, is currently unobtainable β and may well remain so indefinitely.

Lennoxβs conclusion based upon Penroseβs line of argument rests upon an unsubstantiateable implicit assumption: that all points in his βphase spaceβ are equiprobable.

To have any idea of the probability of any of these points (and even whether they are all *even possible*), we would first have to know the state of the system immediately prior β i.e. the state of the universe immediately before the Big Bang. This is currently impossible.

Therefore this conclusion is nothing but *wild speculation*.

No β that assumption is **grossly unsafe**, for the reason I gave above.

This is the problem with this line of Apologetics argument. Apologists find or confect a large number/small probability and then sit back and expect people to be impressed. But *inevitably* the number falls apart on closer examination.

No. Itβs not safe *to make any assumption at all.* The only reasonable response is that we have no idea how big the number is.

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