The Butterfly Effect

The Gifts of Chaos

Chaos theories offer us 3 totally new and innovative tools.

These 3 tools are:

• The strange attractor
• The Butterfly Effect
• Fractal images

Let’s take a closer look at the butterfly effect.

Edward Lorenz and the Weather Forecast

Edward Lorenz, a mathematician and meteorologist working at MIT in 1961, used state-of-the-art computers to try to predict the weather.

The weather was already a tricky problem. While events such as the return of Halley’s comet could be accurately calculated decades in advance, and tides and eclipses had long yielded to scientific prediction, the weather remained elusive.

Lorenz hoped that the new technology would allow him to find a similar level of mechanical determinism in Earth’s climate.

He thus created computer simulations to better visualize trends and hoped to develop a reliable forecasting model.

Lorenz once took a shortcut to reexamine a particular simulation. Instead of running the entire calculation sequence from the start (computers were much slower than today), he started halfway through. So he entered the numbers from a previous simulation himself to make sure the initial conditions were exactly the same, then went for a cup of coffee, giving the machine time to spit out his new predictions (in other versions of the story the calculation lasts all night …)

 

The recalculation should have exactly reproduced the previous results, as Lorenz had not made any changes. But when he saw the new result, he was very surprised: it had nothing to do with the previous results!

Lorenz looked at his results, then looked for an error somewhere in the code or in his computer.

After weeks of analysis, he found the culprit. It wasn’t in the code or in the machine, it was in the data. The two identical simulations he had performed were actually very slightly different.

In the original sequence, computer memory stored six decimal for each value, but Lorenz had only entered three for the new simulation assuming that the difference, for example, between 0.506127 and 0.506 would be of no consequence.

In a world of watchmaking, that would have been irrelevant. The calculations that had succeeded in predicting eclipses, tides and the passage of comets behave in a simple way: a small error in the input data would result in a small error in prediction.

 

 

But Lorenz’s tiny rounding error existed in an environment more interdependent than the vacuum through which Halley’s comet orbit. Tiny eddies of air can be influenced by an almost infinitely small event – something like the flapping of a butterfly’s wings – and these eddies can affect larger currents, which in turn alter the way cold fronts and hot ones are building – a chain of events that can magnify the initial disturbance exponentially, completely preventing attempts to make reliable predictions.

Lorenz thus discovered that in meteorological systems, one will never be able to predict the weather precisely because a variation of a few harmless phenomena, such as the beating of the wings of a butterfly, alter the initial parameters sufficiently to cause huge changes after a while.

When, several years later, Lorenz presented an article on his findings, he titled it Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?

It was the birth of the butterfly effect.

The analogy should not be taken too seriously. Because at this scale in the real world, there are so many processes involved that it is unlikely that a butterfly flapping in Brazil could ever be identified as the cause of a specific tornado in Texas.

What Lorenz and other chaos theorists who followed actually demonstrated was not simply the temporal or practical limits of the predictability of natural phenomena, but their impossibility.

No advance in scientific equipment or methodologies will ever allow us to accurately predict all natural phenomena.

It’s mind-blowing!

If classical mechanics taught us that the same causes produce the same effects, chaos theories teach us practically the opposite!

The same causes do not necessarily produce the same effects!

Or more exactly, the slightest difference in the initial conditions can lead to a completely different result.

Thus, to the quote generally attributed to Albert Einstein:

Insanity is doing the same thing over and over again and expecting different results

Chaos theories answer:

Insanity is doing the same thing over and over again and expecting the same results!

 

 

The term butterfly effect thus covers two phenomena:

• Sensitivity to initial conditions
• Self-amplifying effects

Let us return to each of these phenomena.

Sensitivity to Initial Conditions

We see with the experience of Edward Lorenz that an important point that teach us the theories of chaos, and that we will also find with the fractal images, is the sensitivity to the initial conditions: the least small change to the initial conditions can lead to a very big change on arrival.

I insist: this is again almost the opposite of the deterministic view. It is therefore sometimes impossible to predict the final result as the slightest deviation can have very important consequences in the final result.

The union of sperm and egg is a good example of sensitivity to initial conditions: if another contender had won, you wouldn’t be here to read this 🙂

 

 

Likewise, even the slightest small change in the yet very simple mathematical formula that creates a fractal image will result in a completely different image upon arrival.

Self-amplifying Effects

The other important aspect of the butterfly effect is self-amplification.

Let’s look at three examples.

One day in India, King Belkib, who was bored, demanded that a game be invented to distract him. The wise Sissa then invents the game of chess, which delights the king. To thank Sissa, the king asks him to choose his reward, however lavish it may be.

Sissa chooses to ask the king to take the game board and, on the first square, put a grain of rice, then two on the second, then four on the third, and so on on the 64 squares, doubling each time the number of grains of rice.

The king and the court are amused by the modesty of this request.

But when it is implemented, they find that there are not enough grains of rice in the whole kingdom to satisfy it.

This in fact represents 2⁶⁴-1 = 18 446 744 073 709 551 615 grains of rice.

That is more than 18 thousand trillion grains!

 

 

In the same way with the so-called compound interest: a dollar placed at 1% interest per day which accumulates makes nearly 4000 dollars after a year …

The mind has great difficulty in apprehending nonlinear growths, geometric series, or exponential functions…

We can also take the example, perhaps simpler, of the so-called snowball effect: the more the ball grows … the more it grows and faster and faster!

 

 

Self-amplification, the snowball effect, is an important driver of so-called herd behavior. For example, if a person suddenly starts running in a street screaming in terror, it is possible that one or two people will start running as well. If this is the case, there is a good chance that more people will start running (ten, for example), and seeing this, other people on the street will have a probability of adopting the same behavior the greater the number of people who have already adopted it. The phenomenon is self-sustaining and therefore tends to increase more and more quickly.

So imagine, if it doesn’t happen in the street but rather on Facebook, Twitter, Instagram, or Tik Tok!

Note that this is sometimes referred to as a domino effect. However, this is not quite the same as there is not much of a self-amplifying effect in the domino effect.

A domino usually causes only one to fall, the next one, which itself causes another to fall, etc.

 

 

A Self-amplified World?

As I show in this webinar, because we have never been so many on earth and never so connected, there has never been so many self-amplifying effects around us.

This is also called crisis … especially when we don’t like the results of the self-amplifying effect.

Anyone who understands that the world is far from balanced, that its functioning is no longer linear and binary but chaotic and turbulent, knows now that a single action, a single project, a single individual transformation can change the world.

Suddenly, never in the history of humanity has a single human being had so much power!

You never had so much power!

All this put the power to change the world at our fingertips because, as we have seen, in a chaotic world, a tiny modification can turn everything upside down.

In a linear world, you have to be powerful enough to change the world.

In a turbulent and chaotic world, a simple individual action can change everything!

Before, to change things, you had to be very powerful: either very rich, or the president of the country or a great number of people to start a revolution.

Today a few words on a smartphone can spark a revolution …

Because the world has become more chaotic, thanks to the butterfly effect, you never had so much power!

Now check out the other gifts of chaos: the Strange Attractor and Fractal Images.

Take care of yourself,

Bruno Marion, the Futuristic Monk