Cycles, fractal patterns, and exponential functions
If you want to understand the world as a system then you need to investigate three key components.
 Cycles
 Fractal patterns
 Exponential functions
Here are some of the authors I have studied
 Fred Harrison(18 year land price cycle)
 Nokolai Kondratieff (60 year price/debt cycle)
 Oswald Spengler – book: "The Decline of the West" (15002000 civilisation cycles)
 Martin Armstrong (8.6 year PI cycle, fractal patterns)
 Robert Prechter (Elliott waves, fractal patterns, 300 years)
 Chris Martenson (exponential functions, 10,000 years)
Most authors try and model the world with only one of these components. Martin Armstrong was the exception as he used 2 components (cycles and fractal patterns)
Winston Churchill said, "The further back you look, the further forward you can see."
So why not create a model that incorporates all three components and goes back as far as the Big Bang.
This is exactly what Dr Carl Calleman has done in his 2 books and Ian Lungold presents in his Google videos.
I would go as far to say that Calleman’s model is so powerful that it can unify the 6 author’s works listed above. His model has metaphysical qualities too
It goes much further than the book Waking Up In Time in that he pinpoints the date evolution completes – 28 October 2011 – 3 years away.
Sounds completely crazy? Most people would reject this concept. But when you really start to think about an evolution of consciousness model, this is exactly how it would work. We only realise right at the end what it was all about.
PS. Not sure where chaos theory fits in with Calleman’s model but one person I have blogged with managed to reconcile his model with chaos theory
Hi S2r1, I agree that cycles are an important study, I have been following the subjects for 30+ years as an analyst and financial cycle historian, and have been able to pick tops/bottoms, and trends along the way. If the US Fed bought the Prechter’s Elliott Wave Theorist newsletter, ($19) the whole crisis could have been avoided, or if the read Conquer the Crash – the esential 2003 book on this crisis. Amazing, Bernanke saved $19 and lost over $1,000,000,000,000 – ???
I suggest it all fits under Cycles. Cycles more often than not have sub waves, which covers the entire fractal aspect that large waves can be broken down into smaller component (fractal) subwaves. And as for exponential, that is simple math. By the way, the credit for exponential math goes back before Chris’s time, (he borrowed it from Dr. Albert Bartlett), I am sure you know that, but that is not the way it is written above. Same with Elliot, the credit belongs to Ralph N Elliott from the 192060s work, prior to Robert Prechter Jr. or Glen Neely – Could you edit your list please? (There are a few others that were left off, but you already have a couple obscure ones – more will not make this thread better IMHO).
Elliott has been applied to long periods, I have some ‘Millennium Wave’ charts that deal with a five wave movement beginning before Jesus came. I question the need to reinvent the wheel on the life works these people gave on cycles. Frankly, we don’t have time, and it already exists.
What you have missed has been Fibonacci, the numbers we find in all of Gods the Creators intelligent design, from cycle relationships, time intervals, retracements and expansions; – to DNA, and socioeconomic movements of crowds from euphoria to extreme pessimism. Elliott and Fibonacci math are interlinked and supportive. Did you chosse to omit ‘Fibo’ for a reason?
I will post some charts as background where we are in these cycles, and we can begin to debate how that applies to our present Crash Course situation.
Leonardo of Pisa (c. 1170 c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages". (Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).)
Fibonacci is best known to the modern world for:
 * The spreading of the HinduArabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.
 * A modern number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci (1)
In the Fibonacci sequence of numbers, each number after the first two, is the sum of the previous two numbers. Thus the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.
The higher up in the sequence, the closer two consecutive numbers of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1)
source: http://en.wikipedia.org/wiki/Fibonacci
[(1) Note: It is nice to be known as a genius and given credit for something considered important, as was the case with both Fibonacci and Charles Darwin cases.]
Robert Prechter Jr, and Ralph Elliott bio summaries are here, if you are interested:
The green squiggles were my own informal annotations of the expected next move down. Wave 4 may be complete now, with wave 5 already in the early stages moving down to complete Cycle degree (1) of [C] (4 more waves coming, up and down). While a temporary bottom may be near at the end of October, and a rally will follow trapping bulls, the next cycles down will crush any lingering bullish delusion for a return to the past cycles soon.
Bear market final bottom is estimated around 2014 based on Elliott, a study of Bear Market history from Morgan Stanley, and a Demographic study of stock net selling in the DJIA, that has been demonstrated in Japan’s ‘lost decade’.

Thu, Nov 10, 2011  06:56am
#7Peak Prosperity Admin
Status Bronze Member (Offline)
Joined: Oct 31 2017
Posts: 1612
count placeholderexponential functions
I have been working on this integral for a long time ,however i still can’t solve it because of the comlicated index of logarithm Exponential Functions . So if any of you have any idea,please tell me ,thank you so much~~
Thu, Oct 16, 2008  01:47pm
#1Cycles, fractal patterns, and exponential functions