Fractal Sensitive Dependence to Initial Conditions and Butterfly Effects

The butterfly effect on financial market is a term that has been misused by many people in the past. The term was fist attributed to Edward Norton Lorenz to describe why it is difficult to observe every minute factor that might affect or change weather condition in the future. For example, a butterfly flapping its wings (an almost imperceptible influence) could contribute to the development of a hurricane on the other side of the globe. Edward Lorenz did the first computer simulations in the 1960s that demonstrated dynamical instability of weather systems with actual equations and data.

What he was really trying to say was why it is difficult to capture or mimic chaos system with 100% accuracy.  First, we should understand that his experiment is a laboratory simulation of real life event – “weather system” which in turn, is influenced by many environmental variables including temperatures, air masses, pressures, ocean currents, geographic locations, landmasses, vegetal covers, including human impacts and impacts of other living things such as butterflies.

Just a small change or error in the measurement of one of the above initial conditions or variables can drastically change the results of our laboratory experiment (not the real life behaviour of the natural weather system we are simulating or mimicking). This natural weather system cannot change by just because of our failure to accurately capture every variable in our experiment. The weather system is indpendent or unawaver of our laboratory experiment. In other words, our inability to correctly simulate weather system has no effect on whether the weather pattern will occur or not. The result of our experiment will just not be accurate.  However, the more precise our data is, the closer will be our prediction of the real -life weather system.

In attempt to explain the impact of error of measurement on the outcome of his result Edward Norton Lorenz delivered a speech in 1960 titled, “Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texa?” This has been misquoted and misinterpreted by different people since then. Here is a popular misinterpretation of Lorenz original idea of butterfly statement:

The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)

We know by now how God’s pattern works – everything works according to their    cycles as ordered by God (see http://www.geocities.com/forexchaos/gd.html ).

What we should really say, or Lorenz was try to explain is that if we set up two experiments in one place to forecast God’s weather system based on all our initial known variables; and if one experiment differ only in measurement of one of the variables e.g. air pressure, by an amount so small as comparable to the difference caused by a butterfly flapping its wings, then one experiment might predict a hurricane down the road, and the other not or may be significantly wrong in predicting the weather system as ordered by God. 

Here is how another author tries to misinterpret financial chaos system using the butterfly effect in order to sell their fractal software:

“The software or (technique) is also extremely sensitive to what Edward Lorenz (1963) terms the Butterfly Effect. That is, even the smallest change in initial conditions will show up as a huge change in conditions down the road.”

This is very confusing because whether your software is sensitive to the initial conditions or not, it has no effect on the direction of the market itself. The software and your chart is a laboratory for observing the market and cannot change the market. Therefore, your software’s ability to spot the initial condition cannot show up as a huge change in condition of the market down the road.  If the software spots the condition correctly you will be rewarded with profits, and not the actual market itself. Markets will always follow their paths as ordered by God whether our experiments (software) designed to predict markets are right or wrong.

This is just the same case with two people trading with the same software but from two different platforms. If one is inappropriately set up to get accurate data about the market, one might predict bearish market behaviour and the other a bullish behaviour.

I discovered too that due to the problem of precision no two platforms or people are able to correctly display the same market information with the same exactness. You will be surprised to see how price patterns of same instrument may differ from one trading platform to another, from one broker to another, and from one computer to another due to Internet connection.  

What the butterfly effect theory is all about is that the prediction of the behaviour of any large system is virtually impossible unless one could account for all tiny factors, which might have a minute effect on the system. Thus, large systems like weather financial, or any chaotic systems for that matter remain impossible to predict to 100% accuracy level because there are too many unknown variables to account for. This again brings us to the issue that all things are ruled by God and we are incapable of knowing what next He want to do with the system we are trying to predict. God rules all things including the hearts of the largest market participants (e.g., Ps 103:19; Dan 4:34-35; Eph 1:11; Lam 3:37-38). 

For this reason too, this is why retail traders are unable to exactly speculate the behaviours of largest market participants. And for reasons explained above, no matter how careful retail traders maybe, there will always be some errors in our measurement or judgements, experiments, models, techniques design to imitate the largest market participants. Your broker’s platform or trade station and desktop computer becomes the laboratory while the inter-bank markets becomes the system or field or real life behaviours we are trying to imitate. If we have the right techniques we may be able to imitate or approximate the inter-markets correctly and win against our brokers.  

In other words, if you know your chaos phase space, you know the edge of chaos you are trading, and you enter the market at the right the edge of chaos, such that there is a fundamental change in market sentiments (may be as tiny as the flapping wing of a butterfly or as great as tsunami wave) that would have adverse negative effect on the direction of the chaos, you cannot suffer losses beyond your entry point at the edge of chaos assuming you did set up stop losses and trailing stops correctly with your trade.

Does this mean the concept of butterfly effect has no relevance in financial chaos trading? It thus, but this depend on its application. The concept of small variations producing the butterfly effect was actually first cited by Henri Poincaré before the works of Lorenz, when he (Henri Poincaré ) wrote:

1.    “But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena.”

2.    “A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”

Without knowing it, Henri Poincaré was actually rephrasing what God has already warned us about:

Deuteronomy 4:19

 And when you look up to the sky and see the sun, the moon and the stars—all the heavenly array—do not be enticed into bowing down to them and worshiping things the LORD your God has apportioned to all the nations under heaven.

Whether used in science or financial markets the butterfly effect remains a warning  that need to be applied with care. It offers some reasonable explanations while we should not expect to predict the market with 100% accuracy. It does not say we cannot imitate some part of the market with reasonable result. For example, if a market has potential to give 120 %  in a day, due to some tiniest error on our part  the concept is only saying, maybe we could only estimates or harvest 100% instead of the exact 120%  profit the market can offer. This is different from saying that tinest errors caused by our software may have significant magnitude on the market down the road.

However, if we take our main reason for trading financial markets as only to speculate the behaviour of the largest participants (central banks, commercial banks, large hedge funds) then the theory is relevant to some degree and does suggest that:

“if we fail to accurately observe the initial conditions, even the smallest errors on our part may have some consequences on our profitability and our ability to harvest the maximum pips the market has to offer for that day.”

That is where it ends. Errors on our part no matter how small – as tiny as the flapping wings of a butterfly, or as big as the entire universe, has no consequence on the actions of the largest market participants  we are speculating. In other words, our errors cannot affect the main market  we are trying to simulate, just as any error committed by Lorenz has no effects on the weather systems he was trying to forecast.

In the financial market the closer we are correct to the actual behaviour of the largest participants, the more pips we could approximates or harvest out of the market, and the more wins we could have against our brokers.

Common Errors that can cause negative butterfly effects

1.    inaccurate specification of phase spaces;

2.    insufficient variables use to describe deterministic behaviours in different space phases;

3.    wrong timing of initial contions;

4.    not following formalized laws governing price behaviour in phase space;

5.    not staying in the market till the end of markets’ chaos or cycle;

6.    Own fear, self satisfaction, greed, influence of external factors not part of chaos systems, and self distrust in chaos phase space.

To read more on how to corrrectly apply the concept of fractal sensitive dependence to initial conditions and butterfly effects  in financial chaos  click here.

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Fallacies of Wave Theories and Fibonacci Numbers

How God Brought Order out of Financial Chaos

Self-Similarity Behaviour of Financial Fractals 

Fractal Sensitive Dependence to Initial Conditions and Butterfly Effects