This is the video of a HS female basketball player who made a half court and full court baskets to help her team win! What is the odd of this happening? Probably one out of millions!
Chess Daily News from Susan Polgar
An amazing feat!
Now that it has happened, the chance is 100%!
Seriously, note that the shots were actually made two days apart (December 12 and 14). While still very impressive, it is not nearly as improbable as it would have been had the shots been made back-to-back.
This actually raises some deep and cryptic questions about the nature of reality, with quite possibly different answers on the macro-scale of the “Real World” versus the micro-scale of the quantum world, and versus small-scale digital simulations. A “miracle” half-court shot to win a game, following an amazing full-court
heave two nights before. The natural but “paranormal” question is: (*) Did the success of the first shot influence the probability of the second shot?
Susan asks, “What are the odds of this happening?”, and commenter Tony emerges to reply, “Now that it has happened, the chance is 100%!” And adds that the shots would be more impressive if made back-to-back…so let’s put them that way, and with the easier half-court shot first. I am a true expert in only one of the several fields needed to understand question (*) fully, yet my understanding is that the answer can be Marv Albert’s “yes!”—but only as a matter of perception and under circumstances like the following:
() The basketball is a “Buckyball”, with regular structure and a tiny blueprint;
() The net has a tiny formula, like the Mandelbrot Set;
() The shooter really is determined completely by a few strands of DNA;
() There are no other players, no audience, no noise, not even any lines on the floor.
Then the first shot may be a witness that the numerator of the
probability of the second shot is a whole number different from zero.
And that may already make the second shot’s probability higher than expected merely because in such a constrained world the denominators of these fractions
cannot be large enough to match the expectation we transfer from the “real” world. Moreover, equivalence relations that knock out other possible combinations may come into play, making the denominator even smaller or the numerator even larger.
The bare fact is that in a constrained world, you may be unable to make the assumption that the two shots are independent events. Conditioned on the first one going in, the second may depend only on an alignment factor of the system itself, making it a coinflip. In a world with so little choice on where things
can go, the basket may be the fore-ordained only place that the full-court heave can go. And more successive shots may have the same kismet.
But put back in the flesh-and-blood, the players, the crowds, the
noise, the warts-and-all, and then you may assume the shots are largely
independent. Then you can use tools such as the Diaconis-Mosteller paper on “Coincidences”, which appears in the 1996 Encyclopedia of the Paranormal, but in view of this review, you may prefer to pay-download or look up the 1989 journal version. (And look up its 1996 successor, “Metrics on compositions and coincidences among renewal sequences” on Diaconis’ page.)
Then even with independence,
Diaconis-Mosteller will tell you that after you count how many thousands of courts there are, how many millions of shots, and how many spectators have vidcams, you should expect to see a fair number of events like this on TV news. This is true even without something systematic like autistic
Jason McElwain hitting 6 three-point shots in a row, because he sees the basket differently and people didn’t run him over.
YouTube videos.
Moreover, pervasive noise is also what assures that when Erwin
Schr”odinger lugs out his box to center-court for the halftime show,
his macro-world cat is certainly either stone dead or definitely alive, before you open the box. Stephen Hawking says he’ll pull a gun on anyone who doesn’t get that right, so I hope I don’t need a bullet-proof vest now :-). Our macro-scale real world does muffle the ideas of “synchronicity” and “series” which appealed to Jung and Kammerer (as you can compare in Diaconis-Mosteller, Koestler’s “Midwife Toad” and some other book(s), and even in a recent major research paper also discussed here.) But in the micro-world, not only may “God play dice”, but if we try to graft our perceptions from the macro-world, the dice may even appear loaded and to re-load themselves before each roll! This is all controversial even in basic science, and may involve connections between “emergence” in nonlinear dynamics (aka. “chaos theory”) and notions of probability—this is where it gets beyond my prior knowledge of the latter in “Kolmogorov Complexity.”
I can simplify some of the concepts above by presenting the basic Einstein-Podolsky-Rosen (“EPR”) Paradox with the same basketball analogy. Wikipedia’s EPR article still calls it a “thought experiment.” However, it has been experimentally verified now on large scales, not just in the 1982 “Aspect Experiment” (for which see Roxanne’s EPR pages), but recently in a series of experiments led by Dr. Nicolas Gisin of CERN over progressively longer distances: 1997, 2003, latest word here. But you don’t have to read deeply into these articles—let’s play some more hoops!
Two shooters stand back-to-back at midcourt, facing opposite baskets. Each will shoot with either a rightward spin or a leftward spin on the ball. The spin is not conscious, just an accident of how they happen to shoot, and “right” and “left” each have a chance of 50%. If the shot has a rightward spin, it will go in the basket; if it has a leftward spin, it will miss.
At the start, there are four combinations: (1) right-right (so both shots make), (2) right-left, (3) left-right, and (4) left-left. The two balls are independent of each other, so in what is technically called a “binary Hilbert space”, the system has 2 degrees of freedom.
But now suppose the shooters each hold their ball over their head before shooting, so that the balls touch. At that moment, an “entanglement operator” can be applied. This operator “knocks out” the possible combinations (2) right-left, and (3) left-right—and per my words in my first article, this can be regarded as “modding out by an equivalence relation.” This leaves only possibilities (1) right-right, and (4) left-left, each still with 50% probability. The shooters lower their balls and prepare to shoot, in a system that now has only 1 degree of freedom.
Now suppose one shooter shoots first…and hits the shot. This means that the second shooter will make the shot, with certainty! Yes, “tony”, 100% probability before the shot is taken! (It is possible in labs to entangle more than 2 particles—though how the effort scales with the number n of entangled particles is still controversial—thus also giving an example of my words “successive shots may have the same kismet” above.)
Well, I would need to qualify “before” and “first” with knowledge of relativity which I don’t quite have, and there is also some ongoing controversy about the mechanism behind all this. But my understanding is that the causality issue which troubled Einstein, and the difference between “micro” and “macro” world views (even over “macro” distances under Lake Geneva), have been established beyond doubt. Hence if you originally had the macro view (of the shots as independent of each other), then you might perceive the success of the second shot as a case of “100% emergent probability.” Now emergence has many vague, roughly-consonant meanings, but in chaos theory it is a technical term, and a good place to look for both research and popular exposition is chez Professor Steven Strogatz, whom I knew well as an undergraduate and may need to link up with again…
To bring this back to chess a bit, see recent comments by Jon Jacobs (whom I knew well from the 1970s chess scene) toward the bottom of this itemin Mig Greengard’s blog at http://www.chessninja.com. Yes, Jon, inside the basketball there is a marble, and I have no clue what the marble is…maybe because I’ve lost all of mine :-).