The Mathematical Definition of the Timewave By Peter Meyer Written 1999-08-30, slightly revised 2006-03-31

The current version of HTML does not support mathematical signs (one has to use little GIFs for the infinity sign, the capital sigma, etc., which I don't have at present and can't be bothered looking for) so in this part I shall describe the mathematical definition rather than present it. Full details are given in my The Mathematics of Timewave Zero, which appeared in the 1994 edition of Terence and Dennis McKenna's The Invisible Landscape. In passing I'll note that this mathematical appendix replaced the mathematical appendices by Royce Kelley and Leon Taylor in the 1975 edition of that book. It would probably have been better to include in the 1994 version the original appendices as well as my mathematical reformulation, since the original appendices contain material concerned with the derivation of the 384 data points from the King Wen Sequence, whereas my mathematical reformulation takes the 384 numbers as primitive and simply fractalizes them in a mathematically rigorous way. This reformulation was not based upon the 1975 mathematics, and goes beyond it in a manner which results in a truly fractal mathematical object. My mathematical reformulation, and the associated lemmas and theorems, can be understood by any student of mathematics familiar with infinite series.

The timewave is defined by means of a formula (this is not the formula found by Matthew Watkins) which takes as input a non-negative real number x and gives as output a non-negative real number y. The formula is interpreted as follows: Firstly a point in historical time is chosen as, in the jargon of Timewave Zero, the "zero point". The original zero point was 6 a.m. (La Chorrera, Colombia, time) on 2012-12-21; another may be used if so desired. Then, given that x is the number (not necessarily a whole number) of days prior to the zero point, y is the value of the timewave (or the degree of Novelty) at that point in time x days prior to the zero point.

The formula is the sum of a doubly-infinite series, i.e., it is of the form:

y(x) = ... + t(-3) + t(-2) + t(-1) + t(0) + t(1) + t(2) + t(3) + ...

where t(i) is the ith term in the series, and has the form:

v(x/64^i) * (64^i)

(where 64^i is 64 — the so-called "wave factor" — raised to the ith power). When x is an integer, v(x) is simply the xth number in the set of 384 numbers (for x = 0, 1, ...; after 383 we use x modulus 384). When x is not an integer, v(x) is a value between v(k) and v(k+1), where k is an integer and k < x < k+1 (the value v(x) is obtained simply by linear interpolation between v(k) and v(k+1)).