Sunday, November 11, 2007

The Abused Probability (3)

This post is a continuation of a previous post.


We often hear things like these:

The Earth is such a perfect place for us to live in. Do you know that if the Earth is 1 percent further from the Sun, or 1 percent closer to the Sun, then it would be too hot for human to live in? If the Sun is 1% hotter than it is, no human would have survived! Now, what is the probability of the Earth being located at such a perfect position? Isn't it amazing?
This universe is so fine-tuned to human beings. Do you know that if the gravitational constant was 1% different from its current value, the galaxy, the solar system and the Earth wouldn't have existed, and we wouldn't have been here? Also, the formula E=mc^2, if it isn't true, the Sun could never have produced enough power to support life!! Now, what's the probability of this universe having such a perfect condition?
Those paragraphs are usually followed by some arguments which state that since the "perfect" condition is so "perfect", and that since there must have been such an infinitesimal probability of having such perfect conditions, then it couldn't have existed by itself and hence this world must have been designed by a creator.

If you have read immature religious texts or gone to religious classes held by incompetent preachers, I am sure that you have come across the two ideas above. And building from the background I wrote in the last two parts, I would like to debunk those arguments for creators.

Before I begin, I would like to emphasize that this is not a post to disprove creator / God - nobody is able to do that, given the attributes associated with God such as omnipresence, omniscience, invisibility, being outside time-space continuum etc. On the other hand, by this post, I intend to maintain that the concept of probability is misused and doesn't help in establishing the existence of a creator God, and that evangelists should produce other arguments if they try to use logics to "prove God's existence".

As I establish in earlier posts, doing post-hoc analysis of things that have happened does not an argument make. If something has happened, then it has happened, and having a "supposed probability" which is infinitesimal doesn't mean that it could not have happened by natural means. For example, with a probability of 1 over 8.1 × 10^67, does it mean that the order of the cards must not have come about by itself, and I must have somehow doctored the orders of the card to get the pattern? No, of course, the pattern came entirely randomly through the shuffling.

At this point, some might argue, "But, hey, isn't it still such a coincidence for us to have such a perfect universe, with such perfect locations and all?"

That's a valid point; but they are missing a greater point. Say if we calculate the probability of the universe having this particular configuration, and arrived at an absurdly small number, say, 1 over 10^10000. Now, what does that probability mean?

Nothing much, actually.

That probability stands for "the probability of this Universe having a configuration such that it's good for the existence of Homo sapiens, and billions of other species on the Earth, and that the Sun doesn't collapse with Earth randomly, and that the Moon doesn't suddenly split into two". That, is the "hey-it's-so-unlikely" probability.

But, remember the example of myself munching Smith Chip, writing a blog post on IBM laptop in Melbourne? If you do the calculation, you would have a "hey-it's-so-unlikely" probability too.

So, the problem behind the apparent paradox is, we are so used to the concept of "low probability = unlikely to / will not happen", to the extent that we trick ourselves in those examples which employ probability in the wrong context.

Suppose you are the boss of a "universe factory", where there are switches that control all the configurations and parameters of a new universe. Now, a cat comes along and turns all the knobs and switches randomly, and mess up your divine plan. Now, what's the chance that with the new universe with this set of configuration, the universe will be "good for the existence of a creature like Homo sapiens, and billions of other species on the Earth, and that the Sun doesn't collapse with Earth randomly, and that the Moon doesn't suddenly split into two"?

That, is what 1 over 10^10000 really stands for. And it means nothing.

Another area where probability is often abused is in the validity of evolution. I shall ramble about it later.

[To be continued...]
[23 Aug 2008: Continued here]

12 comments:

N-C Bond said...

Wow, Chang Yang, that's probably too much, isn't that?

Interesting argument, but I still wonder where did you get all the formulae from, like the nothing-much theory 1 over 10^10000...=.= I was like "what??"

Still cann't really understand the whole thing, too deep for me. I'm not so sophisticated when it comes to maths but certainly appreciate the perfection in this world...like the 1% deviation assumption/theory ;-)

Looking forward to reading the next post - validity of evolution ;-)

WP said...

If the earth were 1% closer to the sun, the "creatures" on it wouldn't be the homo sapiens on it today, and who knows, they might be thinking hey, if the earth were 1% farther from the sun, it would be too cold to live in! But we know that's not true, since we exist! lol

bluez_aspic said...

I sort of guessed it would come to this :P I'll write a proper reply when I'm in the right mood - but:

What constitutes a 'coincidence'?

And say, if you were to get a Chor Dai Dee hand - one which is rather 'normal', one having a straight flush, and one comprising of A 2 3 4 5 6 7 8 9 10 J Q K.

I'm familiar with the evolution argument - but it's not exactly the same as the Safeway example which started the discussion (and which is the one I'm interested in :P).

bluez_aspic said...

Again, Feynman's example is also not very meaningful i.m.h.o. when placed together with the Safeway example you proposed.

Feynman's car plate example was clearly coincidence rule created after the event. I would argue that's not quite true with that serendipitous Safeway encounter.

Ok, maybe I'll make much sense next time :P

btw the chances of meeting someone you know, at some time of the day, at some location is extraordinarily high (yours probably underestimated quite a bit). Unless you were to hone it on a *particular* indiviual... but we can always appeal to the Law of Truly Large Numbers :P

youngyew said...

N-C Bond: Haha that 1 over 10^10000 thingy is just a random "very very small number" that I thought of. In fact if you read web pages talking about the arguments I stated here, you would come across numbers like this very often.

WP: That's the very point I am getting at, and you put it so concisely and precisely! You should help me write my other posts, because I am too verbose. :D

Bluez: Hah if you have read anything about evolution debates at all, you would definitely have guessed that I was coming to this topic. :)

There is no hard-and-fast criterion for a "coincidence". If I was thinking about Shou Farn one day and I suddenly bump into him, then I might be inclined to think of that as "coincidence", and some fate, karma or "yuan fen" must have been behind it. However, the thing is, if you consider all the other time where "I was thinking of someone", and where "I didn't end up bumping into that someone", you would see that it's not that much of a coincidence at all.

I do realize that the Feynman example is different from the Safeway example. Those are two different examples of how probability is abused. Feynman thingy is sort of "what is the chance of me writing a post on IBM laptop while having Smith Chip" kind of thing; while meeting OWL in Safeway is kind of the concept of "hey it's so fated for me to meet him" when it had happened. But in both examples, I was making the point that calculating probability after an event and getting a small answer doesn't imply much about the validity or the possibility of the incidence, or about whether I made up the whole thing.

Also, those small probability refers to very specific conditions, and that makes it useless as a point has zero probability of having any given value.

Speaking of zero probability, what do you think about the "perfect universe" argument?

By the way, I agree with you 100% that meeting someone we know at an unspecified place at an unspecified time is not that unlikely at all, given that we brush shoulder with so many people on the street everyday, and that the number of people we "know" is actually quite a lot.

But hey, why haven't we met in Melbourne?! What is the chance of that? Have you been avoiding me? :D

bluez_aspic said...

What's the "perfect universe" argument? :P

I still rejoice whenever I meet someone by coincidence. Even if the governing probabilities are closer to 1 than 0.

I've still got plenty of nice 'coincidental' anecdotes, which all of us would have had experienced our fair share of them. It's another thing to attribute them to FATE or DESTINY -that probably is contingent on personal beliefs and certainly lies beyond the mathematical realm.

Still, I like that sense of DESTINY whatever the Law of Truly Large Numbers might say.

And I thought YOU were the one who's been avoiding me all along, hehe.

youngyew said...

The perfect universe argument refers to the first two quotes and the paragraph that followed.

By the way, isn't this paragraph of yours a contradiction?

I still rejoice whenever I meet someone by coincidence. Even if the governing probabilities are closer to 1 than 0.

If you know that the probability is closer to 1, would those "coincidences" still constitute coincidences?

While I agree that it's up to personal belief to attribute it to destiny, fate, yuen fen or whatsoever; I strongly object to people trying to justify their attribution by the abuse of probability. That was actually my main point behind all those mindless rambling.

And hey, I don't even know your look, how do I go about avoiding someone I can't even recognize? =.="

bluez_aspic said...

I look a bit like a bleached version of Terry Tao in this picture:

http://www.wspc.com.sg/newsletter/pixjune07/0802.jpg

Unfortunately that's the only thing I share with him =(

By 'coincidence', I mean a concurrence of events which seem to be independent of each other (so it doesn't have to be surprising). I like meeting my classmate on the train although this happens with alarming frequency given that we travel on the same train line, share pretty much the same timetable, and always late for class :P

I don't read creationist stuff at all, but if a person can be logically convinced that God exists (through probabilistic arguments or otherwise), it only takes a stronger argument to reverse it. And vice versa.

I'm not saying that there's no rational basis for faith - but faith certainly goes beyond logic.

You seen Carl Sagan's Contact? Jodie Foster sums it up nicely:

"I had an experience... I can't prove it, I can't even explain it, but everything that I know as a human being, everything that I am tells me that it was real! I was given something wonderful, something that changed me forever... I wish... I... could share that... I wish, that everybody, if only for one... moment, could feel... that awe, and humility, and hope. But... That continues to be my wish."

So Jesus is more real to me than Darwin's Origin of the Species :P

N-C Bond said...

For me, believing Jesus is perhaps individual choice. what I want to point out here religion is created by humans (not by God) in the very ancient centuries as a tool to rule spirituality and define the meaning of humanity, and not really a basis of all scientific theories. Using arguments in the religion books like bible to explain scientific concepts, in this case, how this world was created or how men had come to existence is certainly not a wise idea. And I definitely don't think Bible is convincing enough to explain the creation of humans, world and stuff, for me, that's just bullshit, no offence.

Darwin's origin of species is a better theory to explain how we evolve. Jesus? Not being too sarcastic, but if time machine ever exists I really would like to see the "truth" of Jesus's resurrection with my own eyes, not reading the bible and simply take it without a thought.

bluez_aspic said...

I don't think you quite understood the point I was trying to make.

I certainly won't claim objectivity in a debate which I feel passionately about (by the same token you assume that all religions are crafted by man). But when Jodie Foster said it, the experience she had was so real that to deny it would be to deny her very own being. And for once, she abandoned the rationalism that her scientific training imbued in her.

This is not to say that the current biology curriculum should (or should not) be revamped. But anyone who's intellectually honest would confess that how creation came about is an open question - to which the answer still eludes us. And may forever remain so, in this life at least.

Anonymous said...

so many words one...who wan to read woh..

youngyew said...

While nobody knows how "the first life / cell" came about, any biologist who's not a crackpot scientist would vow for the scientific validity of evolution. It's yet to cover every inch of argument and nobody can give a 100% proof for it (nobody could, for a scientific theory); but it's the best theory human has to date which verifies and matches observations and makes the best predictions.

In any case, evolution doesn't make any claim about the first life / cell, it's only about how life diversifies once it's begun a long while ago. Many people who are against evolution got this basic point wrong, and unsurprisingly, used it as a strawman and abused probability in the process.