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With the global economy generally in recovery mode, nearly half of respondents to a survey conducted by Control Engineering magazine in partnership with Morgan Stanley expect sales of industrial automation equipment to increase in 2010 Source: Control Engineering.

Over the next week or so, I hope to share with you results of studies pointing the directions we can expect technology trends likely will take next year, and in the decade ahead. The good news for Americans, and for many national economies around the world, is that the recovery is exactly on track. Yammering about "jobless recovery" and doubts over the U.S. economy's ability to expand until full employment returns simply demonstrate the commentators' ignorance of how economies work.

Garden variety depressions, which is what we've experienced over the past five years, take many years to play out. Calendar year 2008 saw the acute contraction phase, but things had been unraveling since late 2005. After a contraction, comes a bottoming, followed by an expansion phase.

Economic recoveries - that is the bottoming and expansion phases of a dip in economic activity - start with stock markets, which anticipate the turn around in general economic conditions by some months. The reason stock markets anticipate recoveries is that investment professionals, unlike media commentators, do understand economics, and recognize harbingers of business improvement long before the improvement happens. Just as meteorologists know that when days start getting longer, Spring is just a few months away, investors know that economic harbingers, such as inventory levels stabilizing at high levels, pre-announce changes in economic trends by several months, and stock prices rise as these investors put themselves in a position to capitalize on the new trend.

After stock prices hit bottom and begin to rise, we start seeing signs that the downward pressure on business activity begins to ease off. High inventory levels, for example, begin to drop. Productivity begins to rise as businesses streamline to cut costs. Later, these more efficient businesses begin reporting better than anticipated earnings on still-falling revenue. Still months later, revenues begin to rise as individuals and businesses can no longer put off purchases that have been delayed since the beginning of the downturn. More months later, employment figures, which conventional wisdom seems to think should lead the recovery despite the fact that it never happens, begin to recover as the productivity gains of a few months ago prove insufficient to meet the growing demand for goods and services. Finally, very late in the recovery, large capital investments, such as in real estate, reach their bottoms and start to recover.

At present, the U.S. economy, as well as that of most of the world, is recovering nicely. Trends in measures like corporate earnings are showing the correct patterns in the correct order and with the anticipated timing. Even the jobless numbers are tracking exactly as they're supposed to. Back at the end of 2008, when the depth of the dip became apparent, knowledgeable pundits were able to predict that the unemployment rate would reach just above 10%, which is just what it did, and begin to recover in late 2009, which it also has done.

By the way, don't listen to all that emotional drivel about some fictional "real" unemployment rate being something like 18% instead of the published 10% level. "The unemployment rate" is a real, clearly defined metric that we use to compare one time period with another. The "real unemployment rate" that Chicken-Little types yammer on about is poorly defined and very difficult to measure, so it's useless as an economic metric. It's only use is to give fear merchants something to shoot their mouths off about to their poorly educated audiences.

One extremely useful metric that can provide prescience about general industrial trends is expectations among industrial automation buyers and sellers about their purchases and sales (respectively) in the coming year.

To determine whether the market for industrial automation equipment was beginning to ascend from the depths of this latest downturn, or were destined to remain mired in the muck at the bottom of the pit for awhile longer, our friends at Control Engineering magazine in partnership with analysts at financial services leader Morgan Stanley surveyed participants in the industrial automation market. The reason to look especially at sentiment in this market is that factory automation is arguably the most important trend in industrial technology of the late 20th and early 21st Centuries.

Early in the 20th Century, factory automation was generally non-existent. We (or more accurately, our ancestors) simply did not have the tools available to automate production facilities in any meaningful way.

By the middle of the 21st Century, on the other hand, we anticipate that factories will run essentially fully automatically. That is, there will be no production tasks that are not done by automated machinery. Humans will generally hold supervisory positions. There will be CEOs, managers, engineers, maintenance technicians, and such like, but the population of assembly line workers, for example, will drop to more or less nil.

So, unlike the situation a few decades ago, perhaps the best measure of industrial activity available at the start of the second decade of this century is the level of activity in the industrial automation sector. That is what the survey set out to study, and that is why it's the first thing we looking at as we peer into our crystal ball.

"I'm happy to report that the survey does, indeed, offer more than few rays of hope," wrote David Greenfield, Control Engineering's editorial director, when reporting the survey findings in his article entitled 2010 Global Automation Industry Outlook. "Overall, the findings appear to indicate that a bottom in the market has been reached, pricing is holding firm, and that customers remain loyal - all positive signs for global automation players."

Greenfield cited four key findings of the survey:

1. The automation market has already bottomed; modest growth will return in 2010;

2. There is no evidence of a price war in automation equipment;

3. There is limited differentiation between the spending outlooks for process versus discrete industries;

4. While highly cyclical, automation is a good business to invest in over the long term.

It is important to note that the second finding belies the fear that inflation might be a an immediate threat. Despite concerns over accommodative monetary policies around the world, this survey shows no sign of inflation's return in the immediate future. It's axiomatic that for inflation to appear, prices must rise. This survey of a significant sector of the economy shows no hint of rapidly rising prices.

Greenfield pointed out that the near-term trend in demand for automation equipment appears brighter than it did in early in 2009 because of the percentage of respondents expecting demand to increase, more budgets going up or staying level versus retreating, and increasing demand to replace aging equipment. In addition, pricing appears to be stabilizing in the near term. Few respondents expect to see prices fall, but neither are they expecting out-of-the-ordinary upward price moves by suppliers to help offset losses in the past year.

These results are exactly what we would expect at this stage of the present economic recovery. Pundits prophesying a double dip, an L-shaped recovery, or any similar pattern find no support for their views in this important economic indicator.

The Mandelbrot set is the most famous illustration of a fractal in two dimensions. The same mathematics can be used in one dimension to describe financial market price activity. Source: Wikipedia

The other day I caught part of an interview with a spokesperson for Elliott Wave International on Bloomberg TV. Elliott Wave International is an organization devoted to promoting the use of a market-analysis technique developed in the 1930s by Ralph Nelson Elliott, called the wave principle. The most important thing to come out of the interview, to my mind, was an off-hand comment by the spokesperson that stock-price movement "is a fractal."

A fractal is a mathematical waveform with a texture that is of the same form at all spatial-frequency scales. For example, we've all seen those neat illustrations hung in hotel lobbies and meeting rooms that include what appear to be strikingly realistic silhouettes of mountain ranges. Artists make those illustrations by simply tearing a piece of construction paper, and airbrushing past the torn edge. Since construction-paper tears and mountain-range silhouettes are both fractals, the torn paper edge bears an uncanny resemblance to a generic mountain range.

The most famous fractal illustration, and the one mathematicians use most often to illustrate the properties of fractals, is the Mandelbrot set. I think people like to use it as an illustration because it's amazingly beautiful. It also has the advantage of clearly illustrating fractal properties. Unfortunately, it has no practical value, so using it to illustrate fractals leaves the impression that fractals have no practical value.

Nothing could be further from the truth.

Like all fractals, the Mandelbrot set repeats itself on all length scales. It thus displays the property of self similarity. Similarly, if you take a typical stock-price chart covering a time span of, say, one month, and compare it to an intraday chart, the two will look remarkably similar, and will also bear a striking resemblance to the mountain-range silhouette, and the torn paper. They're all fractals.

Self-similar charts, such as stock price charts, all have two spatial frequency properties: they're combinations of "tones" at a wide range of spatial frequencies, and the amplitude of any one tone is inversely proportional to its spatial frequency. Tones at lower spatial frequencies - so they take up more of the chart horizontally - also have proportionally higher amplitudes - so they take up more of the chart vertically.

Comparison of stock-price charts covering a wide range of time spans shows that they also show self similarity, and are therefore fractals. Financial markets exhibit this behavior because they are chaotic systems. That is, there are a large number of independent actors making buy/sell decisions based on different interpretations of the same enormous, but incomplete, data set. Each actor moves the price of an individual financial instrument slightly, but none has enough pricing power to exercise significant control alone. Everyone has an effect, but nobody has a controlling effect.

That is what drives fundamental stock analysts bonkers. Each property of the underlying company, each news item about the company, each pronouncement by a politician, has an affect - often a noticeable effect - but none of them has a determining effect. There's just too much else going on that also has an effect.

It is important to recognize that there are varying degrees of self-similarity. The Mandelbrot set displays the strongest type of self-similarity (exact self-similarity), meaning that it appears exactly the same at all spatial scales. Stock prices, on the other hand, display the weakest type of self-similarity (statistical self-similarity), meaning that the figure has numerical or statistical measures that are preserved over different spatial scales. The fact that stock charts have only statistical self-similarity is what makes stock-price movements inherently unpredictable.

Because Elliott wave analysis starts from the observation that charts of financial-market prices are fractals, the wave principle, out of all technical analysis tools, has the best hope of making sense of financial-market price movements. Elliott's original work was hampered by the fact that understanding of fractals was limited in the 1930s, and understanding of chaotic systems was effectively nil until the 1960s. Some misunderstandings, such as the representation of waves as triangular, rather than sinusoidal, still persist, but anyone interested in learning technical analysis could do a lot worse than beginning with Elliott wave analysis.

Figure 1: Financial markets exhibit variations at all time scales with amplitude proportional to period. Based on data from stockcharts.com.

Yesterday kicked off the first day of the NIWeek 2009. This is the annual National Instruments user group meeting. NI to followers of this company, makes hardware and software for data acquisition and control applications. For general engineering and research laboratory software, the company's LabVIEW product enjoys a dominant position. The way the company has built and maintains this position is by working hard to anticipate major technology trends that will affect their users, and what their executives learn from this ongoing exercise comes out in comments during keynote speeches at NIWeek.

During NI Chairman James Truchard's opening comments this year, he expressed the opinion that some of the economic difficulties we have experienced globally over the past year can be traced to inappropriate use of mathematics in finance

"... Mathematics, the way it has been taught in business schools the last few years," he said, "has a serious problem ..."

Dr T, as he is known to his friends in the industry, also trotted out the oft-quoted comment by Warren Buffet: "It seems like the higher mathematics, with more false precision, should help you, but it doesn't."

This reminded me of a couple of themes I've been studying over the past few years chaos and fuzzy logic as they apply to things in general, and financial markets in particular. These are surprisingly easy to understand, easy to explain, and universal in application.

Chaos has bad connotations in western philosophy, which guides most of what we do for better or worse. In western thought, chaos is the enemy of order, and one of western civilization's stated goals is maintaining order. Eastern philosophy, on the other hand, seeks to balance the "forces" of yin and yang. These are complex concepts, but the important point for this discussion is that, among other things, yin is an order-seeking force, and yang is a chaos-seeking force. The theory is that both yin and yang are necessary for good health, and specifically must be maintained in an dynamic balance.

Mathematically, chaotic systems can most easily recognized by being in constant motion with cycles represented at all time scales, and the amplitudes of these motions are roughly proportional to their periods. Thus, weekly fluctuations tend to have an amplitude 5-10 times larger than daily fluctuations, with the largest amplitude movements appearing on decades-long time scales.

What makes chaos important is that it can be shown to govern the operation of virtually every complex system, from ocean waves to all human history. If it's a large dynamic system with lots of independently moving parts, its behavior most likely is chaotic.

Fuzzy logic, on the other hand, seems unmathematical for a different reason. The term sounds like a synonym for "fuzzy thinking," which people associate with foolishness and ignorance. Mathematically, however, fuzzy logic is a way of dealing logically with things that cannot be precisely quantified.

Humans, in fact, make nearly all personal decisions - especially life-and-death decisions - using fuzzy logic.

When you merge your car into a busy traffic lane, for example, you don't get out a radar gun to precisely measure the speeds of vehicles already in the lane, then analyze video images of the spacings between cars, then do a calculation based on the measured data plus known performance of your vehicle at various settings of throttle and steering controls. You don't have the equipment available to make the measurements, and you wouldn't have time available to make the calculations if you did.

Instead, your brain converts sense impressions and memories from previous encounters into more-or-less broad categories. Spaces between other cars, for example, are "tight," "okay," or "really big." Their speeds are "slow," "medium," or "fast." Your car "accelerates fast," "moves out okay," or "handles like a dead whale." Instead of a dozens of variables with 12-bit precision, your brain reduces the data set to a handful of variables with at most two-bit precision. It also doesn't use arithmetic to work out the answer, but a fuzzy logic algorithm that resembles a decision tree. The answer comes back as "it's safe - go for it;" "gee, it's borderline," or "that looks like a trip to the emergency ward." The final fuzzy calculation says "no" in the last instance, causes you to look further in the middle instance, and spurs you into action in the first instance.

That's fuzzy logic. It's the fastest and most reliable way to make difficult decisions when time is limited (as it always is). It's also virtually the only way to deal with chaotic systems, which, as I said above, almost all real systems are.

Probably (in a fuzzy-logic sense) the way to solve the problem Truchard and Buffet identified, is by mentally taking chaos and fuzzy logic out of the "advanced mathematics" cubbyhole, and teach it to high-school freshman. If we did that, we'd quickly have a generation with the mental tools needed to analyze and deal with the real world, rather than a hypothetical world of mathematical abstractions.

Technical market analysis applies mathematical analysis of patterns in 2-D data sets to stock market (actually, any financial market) buy, sell, and hold decisions. The two dimensions are, of course, market price and time. This entry looks at one reason such data sets should be viewed as chaotic systems.

You've all heard that the so-called Butterfly Effect is a characteristic of chaotic systems. It is the fact that small, seeming unrelated happenings can have major effects on results in a chaotic system. The classic version says that a butterfly flapping its wings in China (or some other remote location) can cause a hurricane to hit South Florida.

Since few of us have a real feel for how global weather patterns develop, we all tend to say: "Yeah, yeah. Blah, blah, blah. I've heard it before, and sure it might be real to weather patterns, but it's not real to me."

This story, however, illustrates in a way we all can relate to how the Butterfly Effect works in another chaotic system -- financial markets of all kinds. I offer it up to help unbelievers understand that these markets are truly chaotic. How chaos rules stock market price movements, and how to understand its effects, is mathematically complex, but the starting point is to accept that accurate financial market analysis is impossible without using chaos theory.

That's not to say technical market analysis based on chaos theory tells the whole story. The full development shows that fundamental stock analysis is necessary to understand the forces driving stock-price movements, which technical analysis only describes.

This story depicts characters and events that are fictitious. Any similarities.... You know the rest. That the story depicts how real people and events interrelate you can judge for yourself.

In 1992, Xin Hua was a wildlife photographer in China on assignment as part of a Peoples Republic grant to Professor Yau Khan of Beijing University to study insect flight dynamics for the purpose of improving the performance of high-speed aircraft. Prof. Yau wanted to obtain high-speed video of butterflies in free flight, rather than tethered in a wind tunnel.

Such free-flight photography is difficult because, unlike the situation in a wind tunnel where the insect is constrained to be stationary in the vision system's field of view, the insect is free to move in three dimensions, while the camera must follow it. For this reason, Prof. Yao hired Xin, reputed to be the best photographer in China for this type of assignment, rather than try to do it himself or assign it to a graduate student.

Xin spent weeks trying to obtain a few minutes of film that would meet Prof. Yau's specifications. The weeks turned into months as Xin filled dozens of CDs with hours of clips showing hundreds of different butterflies flitting across fields in rural China. Finally, he had an hour or so of video that could be used in Prof. Yau's study, along with days worth of video that was beautiful, but not quite what Yau needed.

Being one of China's hungry young entrepreneurs, Xin negotiated a contract with Beijing University and the People's Republic Central Committee that would allow him to market his excess butterfly video worldwide through stock photography service Corbis. Xin shared the royalties with Beijing University.  The Central Committee was pleased to have economic stimulus.

Akira Matsumori was an advertising executive at a firm in Tokyo, Japan. One of his firm's client's was the Japanese Tourism Bureau, and, in early 1994, he was assigned to create a wonderful new ad campaign to promote the Cherry Blossom festival to potential tourists throughout the world. Matsumori developed a campaign composed of a number of ads that all climaxed with a butterfly landing on a cherry blossom.

There was no way he was ever going to obtain actual footage of a butterfly flying in from the left to land on a cherry blossom located on the right side of the screen, with all of the action limited to the bottom third of the frame, so he hired the American film graphics company Industrial Light and Magic to create a lifelike sequence using CGI technology.

To ensure that the butterfly flight was realistic, ILM artists purchased stock video from Corbis showing slow-motion butterfly free flight. The video they studied was, of course, Xin Hua's, because it was practically the only slow-motion close-up video of butterflies in free flight existent.

From Xin's video, the ILM artists developed models of how a butterfly's wings would move if it were flying horizontally from the left and landing on a cherry blossom on the right. They then used thier models to render a butterfly animation to match Matsumori's art director's specifications. They gave the butterfly a dramatic wing coloration pattern based on stock photos of North American Monarch butterflies, with black borders and an arresting gold-color fill.

By the Fall of 1994, the Matsumori's ad campaign was ready to roll out worldwide to generate interest for the 1995 Cherry Blossom Festival in late Spring. By January of 1995, the ads were blanketing television channels all over North America, from Mexico to Canada.

Maria Delgado was a travel agent in Tijuana, Mexico. Her husband, Manuel, had a highly successful leather-goods store catering to tourists. Part of Manuel's sales strategy was to mark relatively high prices on his goods, so that he could give deep "discounts" during protracted negotiations with customers. This was lots of fun for the tourists, and gave them a sense of accomplishment by negotiating the deep discounts. Manuel's shop did very well.

Manuel brought in a large stock of handbags, boots, leather jackets, and pants to sell during the annual motorcycle run starting from downtown San Diego, California and ending in a big parade along Tijuana's main thoroughfare. It was to be a huge tourist marketing event, and Manuel's shop was busting at the seams!

The week before the motorcycle run, Maria saw Matsumori's Cherry Blossom Festival advertisement. Being in the travel business, she had arranged vacations for hundreds of tourists, but, being an aggressive Mexican entrepreneur like her husband, she had never taken a vacation herself. Matsumori's ad made the travel bug bite her hard!

She loved the exotic scenes of Japanese landscapes. She wanted to go shopping in the Ginza. She wanted to visit Buddhist temples. Especially, she absolutely fell head over heels in love with ILM's CGI animated butterfly. It was so lifelike and moved so beautifully.

Making an instant decision, she threw caution to the winds and negotiated a practically free flight for her, Manuel, and the children to go for a month-long tour of Japan during Cherry Blossom time. With her travel-business connections, she obtained cut-rate accommodations near all the great Japanese tourist attractions. It was going to be a huge surprise for Manuel when she told him at dinner that night.

Oh, it was a surprise alright. In fact, it was more of a shock. "We can't do that! My shop is full to bursting with stuff for the motorcycle run as well as the stuff for the rest of the Summer. I can't just walk away and leave it for a month."

"We can afford it," countered Maria, "We've been doing very well. We can afford to take a month off for the children to see Japan before they grow up. Besides, I can't cancel all these reservations. I had to put down deposits and everything."

"But, all our cash is tied up with this stock."

"You'll just have to sell it during the motorcycle run. Clear the store out , and we'll have cash to enjoy our trip."

During the mid-1990s, my wife, Bonnie, and I were living in western Arizona, and we attended the Tijuana Run every year with friends from the local motorcycle repair shop across the border in Needles, California. In 1995, I'd just sold a struggling magazine I'd started and been trying to keep afloat. For the first time in a couple of years, we had a little money in our pockets.

After the motorcycle run and the parade, we settled down for some serious shopping. Bonnie was still carrying around the beige handbag I'd bought her several years before. It certainly didn't go with her black leather motorcycling outfit, and was well past its prime, anyway. So, she was in the market for a replacement that would be more appropriate. She found it in Manuel's shop.

Now, I never really enjoyed the kind of aggressive negotiations Manuel specialized in. I don't much like confrontation, and don't much care whether a pocketbook costs $30 or $50 as long as I have the cash and think it's not a ripoff. Bonnie, however, likes negotiating a bargain. So, I always let her do the deals.

"You pick out anything you want, and get the price you want. I'll pay for it," is what I told her.

Because Manuel's travel-agent wife had fallen in love with an animated butterfly based on a real butterfly photographed by a Chinese wildlife photographer, the market price for that handbag in that shop at that time on that morning was $15 -- well below the $45 I'd have expected to pay for it in the States.

Notice that the handbag did have an intrinsic value based on the cost of the materials, labor, energy to make it and transport it to Manuel's shop, along with carrying costs Manuel incurred by keeping it in the store, and having a store to keep it in. That intrinsic value is the value a financial accountant would arrive at by fundamental analysis.

It is not, however, the market value. The market value is simply set by two parties negotiating one sale. It's based on a host of factors including, but not limited to, the two parties' ability to negotiate, their desire to make the sale, and the amount of coffee they'd drunk within one hour of starting the negotiations.The intrinsic value of the the item is only one factor among many.

In this case, the flapping of the Chinese butterfly's wings had a profound affect on the two parties relative willingness to make a deal, which had a major affect on the price arrived at.

The take home lesson is that hundreds of such seemingly unrelated events affect each and every sale of a financial instrument, whether the deal is struck between amateurs, professionals or 10 year olds swapping baseball cards. That fact makes stock markets -- indeed all markets -- chaotic systems.