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# ID and statistical coincidences

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A friend writes to say that Scientific American provides an adapted excerpt from statistician David J. Hand’s new book, The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day:

A set of mathematical laws that I call the Improbability Principle tells us that we should not be surprised by coincidences. In fact, we should expect coincidences to happen. One of the key strands of the principle is the law of truly large numbers. This law says that given enough opportunities, we should expect a specified event to happen, no matter how unlikely it may be at each opportunity. Sometimes, though, when there are really many opportunities, it can look as if there are only relatively few. This misperception leads us to grossly underestimate the probability of an event: we think something is incredibly unlikely, when it’s actually very likely, perhaps almost certain.

Hand offers, for example, a really clear explanation of the birthday coincidence: “If there are 23 or more people in the room, then it’s more likely than not that two will have the same birthday.” (Hint: The probability isn’t that you have the same birthday as someone else but that any two people in the room share a birthday. See the calcs.)

Our friend wonders whether Hand will be misunderstood when he writes,

This law says that given enough opportunities, we should expect a specified event to happen, no matter how unlikely it may be at each opportunity.

Visions of checkout counter mag headline: Flimflam rescues Darwin in high stakes drama!

For what it is worth, when defining the complexity of an event, ID theorists take interesting stuff like the birthday coincidence into account, but our friend worries that Darwin’s defenders may not grasp the fact or encourage anyone else to: There is no free lunch.

selvarajan thanks for trying but I'm ignorant on all math. I don't see how this could be true and don't think testing would prove it true but i might be very wrong. It seems something is wrong but maybe I'm just wrong about a instinct. thanks again. Robert Byers
Robert @ 22,
selvarajan I can’t follow the math. Lets use common sense or logic. I say any testing of this would not produce two mutual birthydays from just 23 people
The total probability is always 1. The probability that none of the 23 people share birthday will be 364/365 x 363/365 x 362/365 x 361/365 and so on for 23 people. If you multiple all those, you will get probability of NOT SHARING birthday (which is 0.49). Just subtract that number from 1 and you get probability of sharing birthday. (1-0.49). If you want to do it exactly, you will need to take leap year days into account and the births in each month - births in each month differs and it differs in different countries! So the math given is the simplest possible math.
365 options for each person makes it seem impossible .
365 is the number of days. The possible pairs for 23 people is 253 `((23-1)/2) * 23` selvaRajan
This issue reminds me of an evolution debate I heard on NPR a few years ago. The ID critic (Shermer, if memory serves?) was making the standard silly argument to try and rescue the materialistic creation myth from the awful probabilities: "But improbable things happen all the time." It seems like he went on to say something like "What are the odds that both of us would be here on this particular day debating this issue? A year ago no-one could have predicted this, and -- yet -- here we are. Improbable things happen all the time." The problem with this example is that we, by intentional activity, bring about improbable things all the time. So the speaker, as so often is the case when the Darwinists give examples of improbable things happening (think about Berra's Blunder, for example, or Peter Ward's debate in Seattle), inadvertently referenced something designed as though it were an example of happenstance. In that particular case, yes, it is indeed improbable that two particular individuals would show up at a radio studio on a particular day at a particular time to debate a particular topic. At least initially. But as soon as a decision is made by the studio to host such a debate, the probability of the event increases. Later, when the two individuals are invited and then accept the invitation to appear, the odds of them appearing spike dramatically. Once the date and the time and the topic are set -- all by design -- we approach certainty that those two individuals will appear at a particular moment on a particular date at a particular location to discuss a particular topic. It is not at all improbable anymore; indeed it approaches certainty. What the example in fact demonstrates (as usual, and contrary to the Darwinist's intent) is that intelligent agents have the ability to search through a vast space of possibilities to cause a particular outcome. It is an example of design, not happenstance. ----- As to the other improbable things that happen in life, I don't want to suggest that truly improbable things can't happen. They do. Indeed, some things that are improbable and meaningful happen, and I am open to the possibility of real miracles in life, particularly where inspiration, or intuition, or spiritual guidance, or whatever you want to call it is concerned. However, there are many other "improbable" things that occur in life that, when carefully examined, aren't really all that improbable. That seems to be partly what David Hand's book is about. The birthday coincidence is one example. Other things like that happen rather often. "Guess who I ran into at the store?" Is a common one. Improbable? It seems like it at first. But when we consider the number of people we could have run into at the store who would produce a similar response, the number of times we've been to the store without seeing anyone in particular, the fact that no particular date, or place, or location, or time, or even person was specified, then it becomes almost certain that over the course of several weeks or months, in all our shopping experiences, given everyone we know, that we'll run into someone we haven't seen for ages and think it is a remarkable coincidence. Again, I'm not suggesting that real, remarkable, meaningful events don't take place. Just that we have to distinguish between such events and other events that really aren't all that improbable. Distinguishing between these kinds of events, at least for the believer, is a necessary part of drawing the line between coincidences and miracles. But that is a topic for another time . . . Eric Anderson
Second to last paragraph should say "you could spend you afternoon..." punching away at a keyboard/calculator to get the product of the series. wd400
Robert, I don't knwo what bits have to do with it, bu I'm sure you can follow the math for this problem. It's easier to work it out backwards and ask "what is the probability that we have no coincidnces". In a group of two people this is straightfowrard enough - the first person can have a birthday on any day. If we aren't to have a conicidence then the second's birthday must be any other day (i.e. 364/365 days work). So the probability of no coincidence with just 2 people is 364/365 ~ 0.997. If we then add a thrid to the group, and presume we haven't yet hit a conincidence, then there are only 363/365 days left avaliable if our run is to continue. To get the probability of no-coicidences after two runs we can just multiply our 2-person result but the 363/365: (364/365) * (363/365) = ~0.992 As we keep going we just need to add a new term, subtracting one from the denominator to reflect the number of non-coinciental dates left as our run continues. You spent the afternoon punching away at a keyboard but it's easier to express it the product of a series. When you add the 23rd person here's the result: http://www.wolframalpha.com/input/?i=Product++%7Bx%2C1%2C23%7D+%28365-x%2B1%29%2F%28365%29 The probability of no-match drops below 50%, and we are indeed more likely to have a match than not. wd400
selvarajan I can't follow the math. Lets use common sense or logic. I say any testing of this would not produce two mutual birthydays from just 23 people. 365 options for each person makes it seem impossible . No math. If no actual testing, like in evolution, then use words. Something fishy here. Robert Byers
PS: with 367 people, it is certain that at least 2 will have the same birthday. 20 - 30 is a typical number for a class, a School Staffroom, etc. I recall being one of the lucky pair in a group in my uni days, and in one of my high school classes, someone was born two days before I was. kairosfocus
Folks: Just remember there are 366 possibilities for birthdays [~ 8.52 bits], but 1,000 bits has 1.07 * 10^301 possibilities. A crowd of 20 - 30 people is easy to observe, and there is no significant needle in haystack, blind search challenge. Where also for every additional bit [y/n decision node] the config space DOUBLES, and just the genome for a simplest cell based life is credibly in the range of 100,000 to 1 mn bits. The needle in haystack blind search challenge is pivotal. KF kairosfocus
I listened to a story on radiolab recently. It was about a ten year old girl named Laura Buxton who released a balloon with her name on it in England, asking anyone who found it to mail it back to her. The balloon traveled 200 miles and ended up on a farm of a man whose ten year old daughter was named Laura Buxton. He almost threw it away as trash until he noticed the name on it. The two girls eventually met, and they both not only looked remarkably alike, they were wearing the same clothes when they met, they both have a 3 year old black lab dog, and both own a grey hamster. Now a statistician was on the shown and he remarked that although it seems crazy, he claimed that although the girls shared some similarities, there were other things about them that are not similar, so its really just a case of selectively choosing the coincidences, so in fact the odds are almost certain that this would happen one time. To which I say...bunk! How many people actually ever send up balloons with their names in them, and how many of those balloons ever get recovered. And how common is the name Laura. And how common is the name Buxton. You then have to put layer upon layer of other things that almost never happen for these all to come together and form the coincidence. There may have only been ten ballons in all of history that kids have written their names on and someone found and sent back. If you say this is not so surprising to happen, then how about the possibility that this would happen twice? With four different Laura Buxtons? Or how about 6 times with twelve Laura Buxtons on the same day? At some time a coincidence becomes too unlikely to ever occur. How do we know when that is. The same problem happens with the multi-verse nonsense, which says there is another copy of you somewhere in another universe. Well, then how about ten more copies of me, and also ten more copies of me, except with exactly one less hair on my arms. And ten more copies with two more hairs on my leg, and ten with one more freckle, ... Eventually you can say bullocks. phoodoo
Greetings. I asked the following before to a friend: If there are no cards, what are the chances one will pull an ace? This is a new question I thought of: Suppose I have a pack of cards in a locked room with no one inside. What is the probability that an ace will drawn by anyone who does not have the key to the room? I do not know the what is the revealed value for the probability of a Boeing 747 plane being built by a tornado from junk. But I see it as zero for one simple reason: System controls need to exist in a plane, which tornadoes cannot build. How is it related to the examples I have stated? So far one thing is lacking (cards in the first example, and a person with a key in the second example), the probability is not improbable, but zero. It should be shown that there is something necessary which is lacking in unguided evolution. Of course, from what I see, it is being done. seventrees
A true miracle would be if only we could never again hear the classical nonsense about improbable things happening every day. It is really the most stupid "argument" I ever heard in the context of the ID debate. It is usually "proposed" in the form of the "hand of cards" argument: a specific hand of cards is absolutely unlikely, and stille one of them happens each time you shuffle your cards. What a paradox! How will poor ID survive such stringent logic? gpuccio
"More than likely" having same birthday means 50.x% chance or better. 49.x% chance of no match. Odds of matching "Un-Birthdays" improve dramatically. ppolish
Robert @14, It is simple to calculate. Assuming 365 days P(n,365)>=1/2. You get n=23. You can also look at the link in OP You could look at the link near the OP end for more details. selvaRajan
Prove that 23 people in a room will produce the same birthday for two! i say it will not. odds stuff never works. Robert Byers
'Quick question – how many dogs have to give birth, before one gives birth to an octopus?' - #4 drc466 Depends on which universe of the multiverse is concerned. Axel
So what's more probable: 1/10^500 probability or God? Which takes more faith to believe in? -Q Querius
Joe, I believe in miracles. Especially the real ones:) ppolish
A miracle occurs when the impossible happens. Water into wine, walking on water, and so forth.
USA amatuer hockey players beating the Soviet Union's premier hockey team (the spirit of winter olympics past) Joe
Folks: It so happened we were selected (with 149 others) for a Tablet giveaway today. A welcome surprise. As part of the setup, I found and put on a HP 48 emulator, and ran some numbers on: 10^80 atoms, each observing 1,000 fair coins flipped every 10^-45 s, for 10^25 s, giving 10^150 observations. Then, compared to the 1.07 *10^301 possibilities for 1,000 bits. Using the usual comparison of 10^150 is as a 1 g straw, we end up dealing with a cubical haystack that seems to be ~ 2 *10^33 LY across. Or, about 2 * 10^21 times the diameter of the observable cosmos. [Fairly sure these results are at least rather roughly right. of course a cross check is always going to be done later on before finalising confidence on specific values. Measure twice, cut once etc.] Toss in the observed cosmos into the stack, even millions of such cosmi. Now, your mission, should you choose to accept it, is to pick a single straw-sized sample from the whole. With all but certainty, you will pick straw and nothing else, none of the millions of cosmi being anywhere near likely to be spotted. The relevance of this is that there are some things which are needle in haystack challenges and it is not reasonable to expect any blind search of small scope relative to the field of possibilities to spot anything but the bulk of the distribution. Yes, rare things do happen, but when we have narrow hot zones and a lot of haystack, blind search runs into the no free lunch effect. With all but utterly complete certainty under such circumstances, if you pick up other than straw, the search was not blind. The relevance of this to the challenge of getting to FSCO/I by blind watchmaker mechanisms should be obvious, especially as the rabbit trail on how you cannot be sure that functional clusters are not isolated is long since gone cold. KF PS: And yes, lotteries are very carefully designed to be both winnable and very profitable. If the odds run too long, you are looking at a needle in haystack problem. kairosfocus
A miracle occurs when the impossible happens. Water into wine, walking on water, and so forth. ppolish
Miracles and rare events - why does one preclude the other? RexTugwell
Rob Sheldon at 1: What nonsense you talk! In a science-based model, no Darwinists have brought lunches. Lunch is free, remember? Note: At 3:00 pm, the Darwinists are proven right. The lassie from the Sally Ann drops by, scoop bonnet and all, with a cauldron of soup and a satchel of free temperance tracts. News
Just because improbable events happen every day that doesn't mean our existence is due to some just-so accumulations of improbable events. Joe
--Slightly off-topic point follows-- Quick question - how many dogs have to give birth, before one gives birth to an octopus? Some things are mathematical, logical or physical impossibilities, regardless of how "truly large" the number is. It helps to identify whether something is impossible or improbable before you start calculating... drc466
The other day I watched the following hold-em poker hand play out: Player A raises with KK. Player B calls with Q4 (a terrible play mathematically). The flop came QQQ. There are 19,600 possible combinations for the three card hold-em flop. There is one and only one way to get QQQ. Therefore, the probability of this flop coming is 1/19,600 or .0051%. Yet it happened. The really interesting thing is that the probability of QQQ coming on the flop is exactly the same as any other three-card flop -- .0051%. Barry Arrington
At the base of his argument is the assumption that unguided 'chance' has causal power all by itself. But when 'chance', as a causal agent, is pushed to the extreme of trying to explain the universe then 'chance' undermines any coherent epistemological basis it might have had as to having true explanatory power:
The Absurdity of Inflation, String Theory and The Multiverse - Dr. Bruce Gordon - video http://vimeo.com/34468027 Here is the last power-point slide of the preceding video: The End Of Materialism? * In the multiverse, anything can happen for no reason at all. * In other words, the materialist is forced to believe in random miracles as a explanatory principle. * In a Theistic universe, nothing happens without a reason. Miracles are therefore intelligently directed deviations from divinely maintained regularities, and are thus expressions of rational purpose. * Scientific materialism is (therefore) epistemically self defeating: it makes scientific rationality impossible. BRUCE GORDON: Hawking's irrational arguments - October 2010 Excerpt: For instance, we find multiverse cosmologists debating the "Boltzmann Brain" problem: In the most "reasonable" models for a multiverse, it is immeasurably more likely that our consciousness is associated with a brain that has spontaneously fluctuated into existence in the quantum vacuum than it is that we have parents and exist in an orderly universe with a 13.7 billion-year history. This is absurd. The multiverse hypothesis is therefore falsified because it renders false what we know to be true about ourselves. Clearly, embracing the multiverse idea entails a nihilistic irrationality that destroys the very possibility of science. Universes do not “spontaneously create” on the basis of abstract mathematical descriptions, nor does the fantasy of a limitless multiverse trump the explanatory power of transcendent intelligent design. What Mr. Hawking’s contrary assertions show is that mathematical savants can sometimes be metaphysical simpletons. Caveat emptor. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/ God Is the Best Explanation of the Fine-Tuning of the Universe for Intelligent Life - William Lane Craig - video http://www.youtube.com/watch?v=VMBcc2aTqcE But Who Needs Reality-Based Thinking Anyway? Not the New Cosmologists - Denyse O'Leary January 2, 2014 Excerpt: Logic and reason are likewise irrelevant. Consider the multiverse claim that there are "infinite copies of you and your loved ones leading lives, up until this moment, that are absolutely identical to yours." Mathematician George F. R. Ellis notes that, if so, the deep mysteries of nature are too absurd to be explicable and that the proposed nine types of multiverse in one scheme are "mutually exclusive." True, but in a multiverse, "inexplicable" is okay. "Absurd" and "mutually exclusive" are meaningless concepts. It is equally meaningless to assert that one event is more probable than another. As David Berlinski puts it, "Why is Newton's universal law of gravitation true? No need to ask. In another universe, it is not"(Devil's Delusion, p. 124).,,, http://www.evolutionnews.org/2014/01/but_who_needs_r080281.html
i.e. Either everything since the creation of the universe, no matter how mundane, painful, or joyful, is a miracle from God, or else all rationality and reason is lost!
"There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle." Albert Einstein (GodWinks) SQuire Rushnell & daughter of Emmett Kelly on FOX & FRDS 6/16/13 http://www.youtube.com/watch?v=RvdkCJgRzEk&list=UUhhpzDrOSynYa9xPfNtbrqw Mark Burnett says 'weird things happened' on 'The Bible' set by Grady Smith “The hand of God was on this…. the edit came together perfectly, the actors came together perfectly, it just comes to life.” But Burnett wasn’t just speaking about how well the practicalities of production had gone. “Weird things happened during filming,” he said. “Everybody would look at each other like, “Whoa.”,,, A mighty desert wind “There’s a scene with Jesus and Nicodemus, when Nicodemus comes to Jesus in the night. It’s a very still night, not a breath of wind, and we’re on the edge of the Sahara desert in a palm grove in an oasis… Jesus says, ‘The Holy Spirit is like the wind.’ At that moment, a wind, like as if a 747 was taking off, blew his hair, almost blew the set over and sustained for 20 seconds across the desert, and the actors didn’t break — they kept going. And everything stopped. Everyone just looked at everyone like, ‘What just happened?’”,, http://insidetv.ew.com/2013/03/06/mark-burnett-bible-set/
bornagain77
But Denyse, you didn't read the book! If there are 23 Darwinists in the room, each with a lunchbox, there is 50/50 chance that one of them will get his lunch stolen because morality isn't naturally selected. Which is to say, Darwin doesn't just allow, but predicts free lunches. Robert Sheldon