|Nick contemplating the Sirag Numbers|
On Sunday, Sept 18, Nick will be the Featured Reader at Poet/Speak, a monthly event hosted by Poetry Santa Cruz. Reading will occur at 2 PM at Santa Cruz Main Library Meeting Room, 224 Church St. Santa Cruz, CA. Open Mike signup. A rare chance to experience quantum tantra live.
On Tuesday, Sept 20, MIT professor David Kaiser will describe his new book "How the Hippies Saved Physics" at the University Club in San Francisco from 6 to 9 PM. Some of the "hippies" will be present for interrogation including Jack Sarfatti, Fred Allen Wolf and Russell Targ. $25 including refreshments. For more info contact Michael Sarfatti at email@example.com.
The Sirag numbers have been partially tamed! Mark Buchanan and Dick Shoup produced a list of SN up to 2995 from which Saul-Paul Sirag extracted several quasi-periodic interval pattern of period 32. From Saul-Paul's data, Nick Herbert constructed this morning the basic equations that all Sirag numbers must satisfy. The Herbert equations classify all Sirag numbers as Primary SNs or Secondary SNs. For the Primary SNs the Herbert equations generate true Sirag numbers. For the Secondary SNs, the Herbert algorithm generates true Sirag numbers but also false ones. However the Herbert classification is exhaustive--any true Sirag number will be generated by one of the Herbert algorithms.
The Primary Sirag numbers (SPs) fall in two classes, Even and Odd. Their defining algorithms are:
SE(n) = 12 + 32n where n = 0 -> N
SO(n) = 12 + 32n - 25 where n = 1 -> N
The Even Sirag numbers SE(n) repeat with a period of 32 beginning with the first Sirag number J*(1) =12. The Odd Sirag numbers SO(n) repeat with a period of 32 beginning with J*(3) = 19. Thus the primary Sirag numbers are represented by two superposed periodic sequences separated by the interval "7". These two equations generate true Sirag numbers but fail to generate ALL SIRAG NUMBERS. For instance J*(2) = 15 is not a member of SO(n). J*(2) is a Secondary Sirag number (SS).
The Secondary Sirag numbers (SSs) fall into four classes--SS3, SS4, SS12 and SS13. These SNs are generated by the four equations:
SS3(n) = SO(n) - 3
SS4(n) = SO(n) - 4
SS12(n) = SE(n) -12
SS13(n) = SE(n) - 13
Any Sirag numbers will be found to be described either as a SP or a SS. Thus this classification is exhaustive. The first set of equations (SPs) can be used to generate Sirag numbers; the second set (SSs) are useful only for classification--some of the numbers generated are not true Sirag numbers.
As an example of this classification scheme we can now recognize J*(2) as SS4(1). The famous Sirag number "1939" representing the year of Saul-Paul's birth turns out to be the Primary Sirag number SO(61). Does the largest computed Sirag number "2995" belong to one of these sets?
The skeptical reader may wish to check Herbert's claims by testing to see if any Sirag number refuses to be pressed into one of these six classifications.
Herbert's equations for the Sirag numbers are a generalization of Saul-Paul's discovery that the intervals between consecutive Sirag numbers are dominated by "7"s and "25"s. And that these intervals are further haphazardly divided into sub-intervals "3 + 4 = 7" and "12 + 13 = 25". And these intervals are the ONLY INTERVALS that appear. No pattern has yet been discovered in the distribution of subintervals, Hence the present lack of an algorithm that will generate all Sirag numbers.
Now shout it from the rooftops:
The Sirag Numbers are (partially) tamed!