Atheism 32.Probability Arguments

What are we to make of the theist assertion that all these contrived events required together means god is implied? Firstly,god is not the default explanation in lieu of one,and certainly not the Christian god as others exist. So what are the actual explanations? We are at the right distance because life exists in the goldilocks zone of stars,and it is unsuprising to find life there. Any planet not having the conditions for life to thrive won't have life,so water being at the right pressure,just means life happened here,as opposed to somewhere pressure was incorrect. Needing heavy elements is a red herring,they are produced in stars and will be found on planets. Oceans and land are not needed in a given ratio,life exists in oceanic sulphur vents without light. Life was not always here,man is a recent evolutionary development.

The idea that things are a very small probability because events are required in conjunction does not in itself negate an activity and often the argument is set up in such a way that the  "infinitesimal" amount referred to has been falsely manufactured. For instance - if in fact as many seem to believe,the events science proposes for how the universe came to be has low probability - then it is still possible that a low probability event can occur - this does not really mean one should disbelieve it - if one understands how those events conspired to come to pass - it maybe that there are resonances or other forces enhancing the way low probability events come together - or it maybe that one's understanding of probability is poor in the first place. The archetypal probability argument for Evolution is that of a jet plane being thrown together from spare parts in a scrap yard by a hurricane - this is supposed to represent the small probability of the chance of life being thrown together by randomness - but it is a straw man argument - that is NOT how science proposes that life came to be. Similarly,the argument about the start of the universe says that the universal constants are so fine-tuned that to think this is not the work of a designer is absurd - it has so low a probability of happening by chance that God is the only solution - again the argument is a straw man - it is not chance alone that is operating with respect to the universal constants. For those who think that resting cases on probability arguments is fair game - I would ask that they investigate the subject further - In my Booklist - I have Eugene P.Northrop's "Riddles in Mathematics" - if one reads Chapter 8 it is evident how easily the mind can be tricked and persuaded by misuse of probability arguments.If one multiplies any number of probabilities together that are less than one - eventually one will make a very small number if enough events are used IE: P(x) * P(y) * P(z)....... The more events one uses the smaller the number gets - and this can be used as a ploy to show something as untenable by exploiting people's ignorance of probability - or used in all sincerity by someone who does not understand how to wield it properly.Sometimes people do not know when events are mutually exclusive and when they can run concurrently in parallel and may compute likelihoods in error or be using warped logic to arrive at what variables should be considered when computing a probability,and in the end - even if something is unlikely - it is not impossible - only improbable. One of the most notable mistakes in probability is "The Prosecutor's Fallacy"  - where even lawyers make mistakes - and more recently even mathematicians had to update their ideas of the probability of the outcome of a gameshow,which only comprised the choices made by a contestant from 3 doors. Note that any probability by definition is always less than 1 -and so multiplying them makes the resultant number get smaller and smaller the more terms are multiplied if the conditions are reliant upon each other - that is the probability of throwing a 6 on two die is 1/6 * 1/6 = 1/36 when the condition is that we require the single event to be mutually conditional.This is because there are 36 possibilities and only one outcome that is the case of BOTH die being 6 AT THE SAME TIME. Contrariwise,if we were looking for the condition of a single die being 2 or 3 then the outcome is that of two mutually exclusive events - that is - a die cannot be both 3 and 2 at the same time.The probabilities are additive. 1/6 + 1/6 = 2/6 or 1/3 What people do not seem to understand is how such events build on top of each other - once one unlikely event HAS occurred - and given eons of time - even improbable events can happen - it may make other events more likely - ie AUTO CATALYTIC processes such as the one shown in Frontiers of Complexity may need only singular bootstrap sequences to initiate or may make use of catalysts which may enhance the chances of other events ocurring.What one sees from this and other books - such as Figments of Reality - is that no matter what the probabilities - a consistent story of evolution and chemistry exists that can get started without recourse to a creator. An RI lecture once had all the audience flipping coins,at each turn sitting half the remaining audience down,upon subsequent flips being heads or tails,until one person was standing. That person had a unique series of heads and tails that led to them,but it could have been any person in the audience,with another unique series. Evolution isn't a series of unconnected events done at random,which can be exploited as independent events to render an unlikely possibility. This is a rouse used by innumerate creationists who ill understand the theory to try and make God the more likely explanation. But it is not a matter of likelihood,it is a matter of proof and evidence and God fails and evolution doesn't,on that score. INNUMERACY - John Allen Paulos 7. Conditional Probability,Blackjack,and Drug Testing One needn't be a believer in any of the standard pseudosciences to make faulty claims and invalid inferences.Many mundane mistakes in reasoning can be traced to a shaky grasp of the notion of conditional probability. Unless the events A and B are independent,the probability of A is different from the probability of A given that B has occurred. What does this mean? To cite a simple example,the probability that a person chosen at random from the phone book is over 250 pounds is quite small.However,if it's known somehow that the person chosen is over six feet four inches tall,then the conditional probability that he or she also weighs more than 250 pounds is considerably higher.The probability of rolling a pair of dice and getting 12 is 1/36.The conditional probability of getting a 12 when you know you have gotten at least an 11 is 1/3.( The outcomes could only be 6,6;6,5;5,6 and thus there's one chance in three that the sum is 12,given that it's at least 11.) A confusion between the probability of A given B and the probability of B given A is also quite common. A simple example:the conditional probability of having chosen a king card when it's known that the card is a face card - a king,queen,or jack - is 1/3.However,the conditional probability that the card is a face card given that it's a king is 1,or 100%.The conditional probability that someone is an American citizen,given that he or she speaks English,is,let's assume,about 1/3.The conditional probability that someone speaks English,given that he or she is an American citizen,on the other hand,is probably about 19/20. Consider now some randomly selected family of four which is known to have at least one daughter,Say Myrtle is her name.Given this,what is the conditional probability that Myrtle's sibling is a brother? Given that Myrtle has a younger sibling,what is the conditional possibility that her sibling is a brother? In general,there are four equally likely possibilities for a family with two children - BB,BG,GB,GG,where the order of the letters B (boy) and G (girl) indicates birth order.In the first case,the possibility BB is ruled out since Myrtle is a girl,and in two of the three other equally equally likely possibilities ,there is a boy,Myrtle's brother.In the second case,the possibilities BB and BG are ruled out since,Myrtle,a girl,is the older sibling,and in one of the remaining two equally likely possibilities,there is a boy,Myrtle's brother.In the second case,we know more,accounting for the differing conditional probabilities. Before I get to a serious application,I'd like to mention another con game which works because of confusion about conditional probability. Imagine a man with three cards.One is black on both sides,one red on both sides,and one black one one side and red on the other.he drops the cards into a hat and asks you to pick one,but only to look at one side;let's assume it's red.The man notes that the card you picked couldn't possibly be the card that was black on both sides,and therefore it must be one of the other two cards - the red-red card or the red-black card.He offers to bet you even money that it is the red-red card. Is this a fair bet? At first glance,it seems so.There are two cards it could be;he's betting on one,and you're betting on the other.But the rub is that there are two ways he can win and only one way you can win.The visible side of the card you picked could be the red side of the red-black card,in which case you win,or it could be one side of the red-red card,in which case he wins,or it could be the other side of the red-red card,in which case he also wins.His chances of winning are thus 2/3.The conditional probability of the card being red-red given that it's not black-black is 1/2,but that's not the situation here.We know more than just that the card is not black-black;we also know a red side is showing. Conditional probability also explains why blackjack is the only casino game of chance in which it makes sense to keep track of past occurrences.In roulette,what's occurred previously has no effect on the probability of future spins of the wheel.The probability of red on the next spin is 18/38,the same as the conditional probability of red on the next spin given that there have been five consecutive reds.Likewise with dice: the probability of rolling a 7 with a pair of dice is 1/6,the same as the conditional probability of rolling a 7 given that the three previous rolls have been 7's.Each trial is independent of the past. A game of blackjack,on the other hand,is sensitive to its past.The probability of drawing two aces in succession from a deck of cards is not (4/52 x 4/52) but rather (4/52 x 3/51),the latter factor being the conditional probability of choosing another ace given that the first card chosen was an ace.Likewise,the conditional probability that a card drawn from the deck will be a face card,given that only two of the thirty cards drawn so far have been face cards,is not 12/52 [The probability of pulling any face card from a full pack-LB] but a much higher 10/22 [The probability of pulling a face card from a pack consisting of 52 - 30 = 22 cards,with 12 -2 = 10 face cards-LB].This fact - that (conditional) probabilities change according to the composition of the remaining portion of the deck - is the basis for various counting strategies in blackjack that involve keeping track of how many cards of each type have already been drawn and increasing one's bet when the odds are (occasionally and slightly) in one's favour. I've made money at Atlantic City using these counting strategies,and even considered having a specially designed ring made which would enable me to count more easily.I decided against it,though,since unless one has a large bank roll,the rate at which one wins money is too slow to be worth the time and intense concentration required. An interesting elaboration on the concept of conditional probability is known as Bayes' theorem,first proved by Thomas Bayes in the eighteenth century [Ref:Fisher Dilke "The Numbers Game:Lies,Damn Lies & Bayesian Statistics" Video N30].It's the basis for the following rather unexpected result,which has important implications for drug or AIDS testing. Assume that there is a test for cancer which is 98% accurate; i.e.,if someone has cancer,the test will be positive 98% of the time,and if one doesn't have it,the test will be negative 98% of the time.Assume further that .5% - one out of two hundred people - actually have cancer.Now imagine that you've taken the test and that your doctor sombrely informs you that you've tested positive.The question is:How depressed should you be? The surprising answer is that you should be cautiously optimistic.To find out why,let's look at the conditional probability of having cancer,given that you've tested positive. Imagine that 10,000 tests for cancer are administered.Of these,how many are positive? On the average,50 of these 10,000 people (.5% of 10,000) will have cancer,and so,since 98% of them will test positive,we will have 49 positive tests.Of the 9,950 cancerless people,2% of them will test positive,for a total of 199 positive tests (.02 x 9,950=199). Thus, of the total 248 positive tests (199 +49 =248),most (199) are false positives,and so the conditional probability of having cancer given that one tests positive is only 49/248,or about 20%! ( This relatively low percentage is to be contrasted with the conditional probability that one tests positive,given that one has cancer, which by assumption is 98%.) This unexpected figure for a test that we assumed to be 98% accurate should give legislators pause when they contemplate instituting mandatory or widespread testing for drugs or AIDS or whatever.Many tests are reliable: a recent article in The Wall Street Journal,for example,suggests that the well known Pap test for cervical cancer is only 75 % accurate. Lie-detection tests are notoriously inaccurate,and calculations similar to the above demonstrate why truthful people who flunk polygraph tests usually outnumber liars.To subject people who test positive to stigmas, especially when most of them may be false positives,is counterproductive and wrong. [Not in J.A.P's opinion but absolutely-LB] .

Evolution myths: Evolution is just so unlikely 18:00 16 April 2008 by Michael Le Page For similar stories, visit the Evolution Topic Guide By weeding out harmful mutations and assembling beneficial ones, natural selection acts like an "improbability drive" that can, given enough time, produce results that appear utterly impossible at first glance. In a recent TV special shown in the UK, called The System, a mother with big debts was persuaded to borrow even more money to bet on a horse race. Having been sent correct predictions of six previous races, she believed illusionist Derren Brown really had come up with a foolproof system for predicting the outcome of races. In fact, the producers of the show started by sending different predictions to nearly 8000 people. After each race, those sent predictions that turned out to be wrong were eliminated and another set of varying predictions sent to the remaining participants. What appears utterly extraordinary at first - sending someone correct predictions of the winners of six races - seems very ordinary as soon as you understand that thousands of people got wrong predictions. Confronted by the marvels of the living world, many people jump to the same conclusion to the woman in the programme: they cannot be the result of chance alone. But what we don't see are all the failures: the countless numbers of creatures that died in the egg or in the womb, or hatched or were born with terrible defects, or fell victim to predators or disease because of some weakness. In the wild, most individuals die long before they get a chance to reproduce. The living organisms on Earth are the result not just of six rounds of selection, as in the TV programme, but of trillions. This, not chance, is the crucial factor in evolution. Three steps to evolution To understand evolution, you need to appreciate three things. Firstly, that quadrillion-to-one chances actually happen all the time. Secondly that, while mutation is random, which mutations survive often is not. And thirdly, given enough time, the accumulation of one beneficial mutation after another can produce amazingly complex systems. Natural selection can be seen as a kind of improbability drive that - given enough time - makes the apparently impossible extremely likely. If you pick even the simplest creatures alive today and calculate the odds of getting their genome by randomly shuffling DNA sequences, you'll find they are pretty astronomical. Even matching the sequence of the simplest virus is stupendously unlikely. Does this prove evolution is impossible? Try this: get a pack of cards, shuffle it well and spread it out so you can see the sequence. Now try to generate the same sequence by shuffling another pack. Done it yet? The universe might end before you succeed. If shuffles are truly random, the chance of generating any particular sequence of 52 cards is 1 followed by 68 zeroes - and yet such an incredibly unlikely event happens each time any pack is shuffled. Shifting genes In all living creatures, the "pack of cards" is constantly being shuffled. Damage to DNA or mistakes in replicating it generate random mutations, ranging from changes in single "letters" to duplications or deletions of huge chunks of DNA. The vast majority will be either harmful or neutral - only a few will be beneficial. But as the card example shows, even if all beneficial mutations are highly unlikely, this doesn't mean they cannot happen. In fact, the odds of a beneficial mutation occurring are higher than you might think. One recent study of the E. coli gut bacterium puts the rate as high as 1 beneficial mutation for every 10,000 new bacteria. That might not sound like much but populations of many simple organisms can number in the trillions, with new generations appearing every hour or less. Do the sums. What really matters, though, is what happens after mutations appear. That's when natural selection kicks in. Each new organism's life is essentially a rigorous testing process. Those with a harmful mutation will tend to die out, while those with a beneficial mutation that gives them a competitive edge will thrive and produce more descendants. This means that beneficial mutations will become more common in a population, while harmful mutations disappear. This process happens over and over again. If individuals with one beneficial mutation thrive and multiply, eventually another beneficial mutation will occur in one of them. Over time individuals with both beneficial mutations will come to dominate a population, making it likely for yet another beneficial mutation to appear in one of them... Benefits of sex What's more, in species that can swap genetic material, for instance by reproducing sexually, beneficial mutations that occur in separate individuals can be combined in their descendants. In this way, natural selection can create the astonishing organisms we see around us, the result of countless trillions of beneficial mutations slowly assembled over billions of years (see Mutations can only destroy information). It's true that how the process got underway in the first place is still something of a mystery. We won't begin to know just how likely or unlikely the origin of life was until someone manages to get life to evolve from scratch in the lab or discovers life that originated independently, perhaps on another planet. What is clear, however, is that as soon as the first primitive entities capable of replicating themselves emerged, further evolution was inevitable. And the more evolution there is, the faster it may become. In fact, evolution might produce "evolvability". For instance, as organisms evolve systems that can cope with a wide range of environmental conditions, further evolution might become more feasible - an idea backed by recent experiments showing evolution can be speeded by varying the environment. Such ideas remain controversial. What is indisputable is that while the end results of evolution might appear utterly impossible, once you understand the way in which natural selection can collect and distil the results of chance events, there's nothing impossible about it at all. Read all the myths in our Evolution Special http://www.newscientist.com/article/dn13694-evolution-myths-evolution-is-just-so-unlikely.html

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