WhiteLion said:
"RANDI: One cannot fail, given enough time and opportunity, to find correlations with obscure elements. Pseudoscientists have wasted their entire academic lives finding repeated series of digits in the irrational number "pi" for example, and assigning significance to those discoveries."
"VERITAS - Actually, many distinguished mathematicians have searched for a possible order in the digits of pi - to our knowledge, none has found a repeating order to date. Could it be that pi is random? Or, could it be that we have yet to discover how the digits in pi unfold (the more humble position)?"
Is this above an erroneous statement by Randi? Or does Gary Schwartz express a factual error? Or are they both correct with different experiences in their investigations?
[begin math mode]
Schwartz is wrong here, as far as pi goes.
First, some background:
It has been proven (repeatedly

) that pi is irrational. This means that there is no regular repeated series of digits in pi.
Let me try to be clearer: pick any finite series of digits (314). You will find it somewhere in the digits of pi (here, right at the start, for instance), and further down. However, the distance between the occurances of the series will change. You could have 1000 digits go by - in fact, if you wait long enough, you *will* have 1000 digits go by exactly before 314 repeats.
One thing that is certain is that you will never have your series repeat at the same interval forever (so you won't have 314 happen every 296 digits after the millionth digit, for instance).
At the same time, pi is defined, and is not random (pi is never 4, despite what some people may claim).In fact, there are formulas that can be used to compute pi, to any desired number of digits, relatively quickly. It's one of the common tests for computing power.
End of background.
Claims:
Randi states that pseudoscientists have looked for repeated digits and assign meaning to them.
For instance, "1" is the 2nd and the 4th digit of pi, so a pseudoscientist could somehow link "oneness" with 2 and 4 (or some convoluted computation based on this). This is meaningless pattern seeking, and can be used to prove anything - because pi is irrational, so any series you desire will occur.
If your proof requires that pi contains the series "101001", it will occur, because every finite series will occur. Period.
Hence Randi's statement (that by studying pi you *will* find patterns, though they are meaningless) is correct.
Schwartz does not contradict Randi's statement, and says that mathematicians have looked for an order to the digits of pi, without finding a repeating order.
This is dishonest reasoning. First of all, the proof that pi is irrational is fairly old, and since it was made, only cranks have tries to find repeating series in pi (i.e. a series, say "12" that occurs at regular intervals). Second, devising faster ways to compute the digits of pi is an interesting mathematical and computational challenge, so mathematicians have been working on it. The dishonesty lies in implying that studying pi is the same as looking for repeated series.
Schwartz then establishes a false dichotomy, between pi being random (it isn't, or it would sometimes be equal to 4), and us being unable to predict the digits of pi yet (we can - it just takes computing power, and we can only find a finite number). Both of the positions he suggests are wrong, which implies that his knowledge of mathematics is pretty low.
To summarise, in this case, Schwartz has shown blatant ignorance of mathematics, and used at least two fallacious arguments when trying to make a point. Advantage: Randi.
[/end math mode]
[begin stats mode]
And this brings me to one of my favorite anecdotes (experienced by yours truly, rather than word of mouth).
My first econometrics class, the professor told the tale of an experiment: a group of researchers created 20 random, independent series with 1000 elements each (so the value of one is unrelated to the value of the other), and then tried to find correlations between them, by expressing one series as a linear combination of two others. Something along the lines of A = 2B - C, where A, B and C are distinct series.
In 75% of the cases, they found a strong correlation, though by definition and design, there shouldn't have been any.
The moral?
Use enough variables (here, express one series as a linear sum of two others, rather than as a multiple, or offset, from one), you will "find" correlations even if they don't actually exist.
And that's what Randi was saying.
[/end stats mode]