John Pierce writes:
>the numerologists are at it again...
>
>http://www.nature.com/nsu/030317/030317-13.html
I have a cold, which is making me grumpy. Of course, stuff like
this only tends to put me even further into Alexander Pope mode:
>Kumar's team looked at the increments in the intervals between
>consecutive primes. For example, the intervals between the first
>few are 1, 2, 2, 4 and 2. The increments are the differences
>between these successive intervals: +1, 0, +2 and -2.
>
>These increments are not random, the physicists conclude:
>they have a rough-and-ready predictability. "Positive values
>are almost every time followed by corresponding negative values,"
>explains team member Plamen Ivanov. That is clearly already true
>for the third and fourth increments above: +2 and -2.
...so it must by extension hold for all primes, right? Seriously,
based on the way they characterize things, i.e. as the difference
in length between successive prime gaps, it seems this is like
saying about a sequence of coin tosses: "Anomalously long runs of
all heads or all tails are almost invariably followed by shorter
runs of heads or tails." Well, of *course* they are - that's what
makes them anomalous, innit?
>The researchers are not experts in number theory, the relevant
>branch of pure mathematics.
Glad the author cleared this up - would've never guessed that
from the nature of the work.
>While probing the variations of the gaps between heartbeats, the
>researchers found something else. A plot of the number of increments
>of different sizes shows oscillations with a period of three.
>
>That is to say, increments of plus or minus 6, 12, 18, and so on,
>are statistically less likely than increments of other sizes.
>
>This finding is less surprising. Previous studies found period-6
>oscillations in the histogram of distances between consecutive primes.
Consider a sequence of successive odd numbers, starting with an odd x:
x, x+2, x+4, x+6, x+8, ...
Without losss of generality, assume x is divisible by 3. Knocking
all multiples of 3 out of the sequence leaves gaps of length 6. Sure
looks like a signal of period 6 to me. Of course the other odd primes
will leave a similar imprint, but since 3 is the smallest odd prime
(of course, this latter finding is not supported by any kind of
rigorous mathematical proof - can some of the number thoery experts
help me out here?), it will leave the densest imprint on the sequence.
>Increments, remember, are differences between consecutive distances.
Again, thanks for setting us straight on that.
While investigating this stuff exhaustively, I discovered an even
more remarkable property of the primes: ALL BUT THE FIRST ONE ARE ODD.
Isn't that spooky? It's like reading the mind of God, I tellya.
Oh wait, I see the cosmologists have trademarked that line. My
most humble apologies.
"I hate numbers. There's, like, too many of them." - Beavis & Butt-Head
