Pulsar Network Transmission of the
Fibonacci Series and Golden Mean Ratio
Paul A. LaViolette, © April, 17 2007
Update for the book Decoding the Message of the Pulsars
(reproduction of the following page is restricted, personal download is permitted)
In the book Decoding the Message of the Pulsars, from more than 1775 known pulsars a half dozen pulsars were singled out as possibly conveying an intelligent message. Three of these are the Crab pulsar, the Vela pulsar, and the Vulpecula pulsar, whose periods and period derivatives are listed in the table below.
Period and Period Derivatives for Three Unique Pulsars Measured in May 1992
(From Table 3 of Decoding the Message of the Pulsars)
Pulsar Period (seconds) Rate of Change of Period (s/s) Crab Pulsar 0.033648365 4.20 x 10-13 Vela Pulsar 0.089298530 1.258 ± 0.008 x 10-13 Vulpecula Pulsar 0.144457105 5.75318 x 10-14
A Brief Review About the Significance of this Tri-Pulsar Subset
All three of these pulsars are among the very few that are found to be associated with supernova remnants. The Vulpecula pulsar is distinguished as being the one pulsar that happens to be positioned closest to the Galaxy's northern one-radian point meridian and which makes a key trajectory sighting with the Millisecond Pulsar (see the book DMP for the full significance). The Vela and Crab pulsars are very distinctive. Not only are they respectively the brightest and most luminous of all pulsars, as well as among the few known to emit optical pulses and giant pulses, but they also mark the two young supernova remnants that reside closest to our solar system. The supernova explosion dates of the remnants they mark coincide with the time when the 14,150 year BP superwave cosmic ray volley was impacting their progenitor stars. The Vela pulsar marks a location near our solar system while the Crab pulsar marks a location 6,585 light years away toward the Galactic anticenter and the superwave cosmic ray volley that impacted us about 14,150 years ago is currently seen impacting the Crab remnant. As described in Decoding the Message of the Pulsars, the Vela pulsar's period is gradually increasing and if we project this period change back in time, we find that 14,100 ± 100 years ago Vela's period would have equaled the Crab pulsar's current period. It was suggested that this gradually changing period was intentionally engineered as a chronometric indicator of the date when the last major Galactic superwave passed through our solar system.
Furthermore as discussed in Decoding the Message, if we map out these three pulsars on a log-log plot with their period derivative coordinate plotted vertically and their period coordinate plotted horizontally, the three appear to form a map of the Sagitta constellation, the Celestial Arrow. The Crab pulsar represents the star Delta Sagitta, the Vela pulsar represents Gamma Sagitta, and the Vulpecula pulsar represents Eta Sagitta, the "target star" toward which the Arrow is flying.
Encryption of the Fibonacci Series and Golden Mean Ratio in Pulsar Periods
Recently, Dietmar Wehr was reading Decoding the Message of the Pulsars and noticed something quite astounding which he shared with me. He noticed that the periods listed for the above three pulsars match three of the numbers in the Fibonacci series. The Fibonacci series is a mathematical number sequence that begins with zero and one and then adds the sum of the previous two numbers to obtain the next number in the sequence, hence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... The sequence converges on the golden mean phi ratio phi = 1.6180339887. For example taking the ratio of two successive numbers of this sequence 144 ÷ 89 we get 1.61797753 which in this case is within 5 X 10-5 of being exactly equal to the phi ratio. As the sequence proceeds, this ratio comes closer and closer to phi.
The golden mean ratio is frequently observed in nature in the morphology of living organisms as in the occurrence of the golden spiral in sea shells. It also characterizes the height to width ratio of the golden rectangle known in art and architecture for its pleasing appearance. The ratio was also known to ancient Egyptian and ancient Greek geometers and employed by these civilizations in the construction of their temples. In mathematics phi has the unique property where its inverse is equal to phi minus one: 1/phi = phi - 1. Because of the mathematical and geometric uniqueness of the phi ratio and the Fibonacci series and because of the ubiquitous appearance of the ratio in nature, the Fibonacci series and phi become candidates for use in extraterrestrial communication. Like the one radian angle concept and the number pi, they are part of the universal language that any civilization in the Galaxy would recognize and would be understood by any civilization as being a hallmark of an intelligent communication.
The table below compares the pulsar periods given in milliseconds with three numbers from the Fibonacci series. The Vela and Vulpecula pulsar periods particularly stand out in that they deviate by just 0.3% from two consecutive numbers in the series. In fact, the ratio of the Vulpecula pulsar period to the Vela pulsar period calculates to be 1.617688 which is within 3 X 10-4 of the phi ratio. So this more recent discovery that the periods of these pulsars fall close to numbers in the Fibonacci series lends support to the suggestion proposed earlier in Decoding the Message of the Pulsars that these pulsars may be of artificial origin and are conveying an intelligible message.
Pulsar Period (milliseconds) Fibonacci Number Percent Deviation Crab Pulsar (9/2010) 33.648365 34 -1.03% Vela Pulsar 89.298530 89 +0.34% Vulpecula Pulsar 144.457105 144 +0.32%
So that we, the pulsar signal recipients, would note this golden mean correspondence, the pulsar message authors would necessarily have to properly configure the periods of these pulsars in terms of units that measure time in durations close to our own millisecond. Otherwise the millisecond value would not approximate the whole number values in the Fibonacci series. But regardless of what time standard may have been used by the alleged transmitting civilization, the particular units intended for time measurement would not affect the number ratio. In all cases, this Vulpecula/Vela ratio would come out close to the golden mean. Another factor to consider is that the periods of these pulsars are constantly changing and changing at differing rates. So we would necessarily have to be observing the pulsars at a unique time in their history in order to appreciate this golden mean correspondence. One could make the argument that the observed correspondence is just a coincidence, although a very peculiar one.
The Crab pulsar period exhibits the greatest deviation from its corresponding Fibonacci number 34. This number is not adjacent to 89 in the sequence but is separated from it by the number 55 which does not correspond here. A look at the first table indicates that the period of the Crab pulsar changes most rapidly of the three. Projecting its period change into the future we find that the if the Crab pulsar period continues to change at the above recorded rate observed in September 2010, its period should equal 34 milliseconds on May 7, 2037 AD, precisely matching its corresponding Fibonacci number in that year. Alternatively, if we use a time unit that is 0.32% longer than our standard millisecond time unit, so as to bring the periods of the Vela and Vulpecula pulsars closer to their corresponding Fibonacci numbers, then the Crab pulsar's target date will be moved up to September 2045 AD. Is the Crab pulsar period intended as a future date chronometer? Is it intentionally using the universal knowledge of the Fibonacci series as a way of marking a significant event that is to take place in the future? If so, is this event to take place in our Galactic vicinity or in the vicinity of the Crab Nebula? At this point we can only guess.