Science is Strange: Part Two

Life Is Strange

1. Never Believe the Long-term Forecast

A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon” — Henri Poincare

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Edward Lorenz, a meteorologist, thought that he could predict long-term weather. If using a computer can calculate the exact flight path of a bullet or spacecraft, why not apply that to the weather? His weather program was based on twelve variables that represented temperature and wind speed.

In 1961, Lorenz was working on his weather simulation, but this time did something new. His computer program was working with an accuracy of six decimals, so the output appeared similar to 0.123456. Instead, he started the program that simulates the future weather from the initial settings, this time rounding the variables to three decimal places. According to him, the result should be the same as the previous one, and the approximated number shouldn’t make any difference. The weather should evolve in the same way every time.

Lorenz noticed that the second chart began to diverge at some point, varying from the first chart. He overlaid the two charts. The initial peaks of the charts fit together exactly, then one peak was left behind. After another peak, the similarity between the two charts was gone: a tiny difference dramatically changed the whole pattern.

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Fig. 1 – Green Line: weather pattern from the first run, red line: weather pattern with changed initial data.

2. The Butterfly Effect

Lorenz realized that the weather is impossible to predict. A small numerical error in the system of Lorenz equations completely changed the result. Lorenz called such action the butterfly effect (Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? – the smallest change in the point of entry may lead to significantly different results).

Fact: the butterfly effect first name was the sea gull effect: One meteorologist remarked that if the theory were correct, one flap of a sea gull’s wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favour the sea gulls.

Life Is Strange
Fig. 2 – Episode one – Max in the toilet sees a butterfly, but also a symbol of Illuminati. Interesting fact: one of the Illuminati’s are Thanateros Illuminati and they’re dealing with chaos magic.

Deterministic system may behave erratically if they are sensitive to the initial conditions. In this case, if the initial errors increase, the system is chaotic and we can’t predict how it will evolve. Almost every real dynamic system, adequately powered, turns out to be chaotic.

“It was philosophically very shocking. Determinism was equated with predictability before Lorenz. After Lorenz, we came to see that determinism might give you short-term predictability, but in the long run, things could be unpredictable. That’s what we associate with the word ‘chaos.’” – prof Steven Strogatz

But what is chaos? One theory says that the chaos is stochastic behavior in a deterministic system. Chaotic systems are directed by the equation, but at the same time, are sensitive to initial conditions and are not random or disordered. Therefore chaos is arbitrary behaviour completely governed by the laws of physics. Sometimes chaotic behaviour can be hidden for a long time, and a system can appear stable and predictable until boom! Suddenly everything changes. Just like the reversal of Earth’s magnetic poles that occurs sometimes. The last time it happened was 780,000 years ago and it’s a perfect example of this kind of chaos.

3. The Attractors

In addition to the butterfly effect in chaos theory, we find two additional concepts:

  • Attractor – Set of numerical values toward which a system tends to evolve. Balance within the system, represents the state in which the system finally settles.
  • Strange Attractor – Dynamic kind of balance that represents a kind of trajectory on which the system operates from situation to situation without subsidence.
A Trajectory Through Phase Space in a Lorenz Attractor
Fig. 3 – example of strange attractor when ρ = 28, σ = 10, and β = 8/3

We can use Chloe as an example to explain the strange attractor concept.

Let’s say that Chloe has roughly the same number of ideas which end up with her death (and Max will have to rewind time to save her) and the same, which don’t harm her. There is a balance – an attractor. Let’s imagine that Chloe decides to go shoot the bottles. Yay, great idea! But then Chloe shoots herself in the stomach and Max must rewind time. Then Chloe decides to sneak into the school swimming pool – fortunately Chloe lives this time. Then Chloe decides to lie down on the tracks. Great idea! But this time train kills her and Max has to save her again. Ad infinitum.

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Fig. 4 – The strange attractor drawn from Chloe’s actions

We’ve got some sort of balance and Chloe’s actions ad infinitum. Such dynamic equilibrium is a Strange Attractor: a track on which the system operates on the situation (great idea and death!) to the situation (great idea without death) but without settlement.

4. How the Butterfly Effect in Mass Culture is Wrong

The butterfly effect portrayed in mass media is not quite the same as what Lorenz was referring to. In movies, games and other mediums, the butterfly effect is a metaphor for the existence of  events, seemingly insignificant, that change the history and destiny. We have already said that that there’s no such thing as destiny and Laplace’s Demon can’t exist (as discussed in part one) but what’s the problem with butterfly effect in mass media? The thing is that according to Lorenz’s theory we can’t track cause of change. We can’t definitely say what exactly caused the storm. There’s a cause and effect but we won’t be able to find what caused it. Max, the tornado is not your fault.

5. Parallel Universes are Scientifically Possible!

Life Is Strange
Fig. 5 – Typical look of quantum physics student

Let’s go back to quantum mechanics. I mentioned earlier in Science is Strange: Part One, that this theory predicts that a particle can be in several places and states at the same time. You’ve heard of Schrödinger’s cat, right? Cat is in a box, with radioactive atom, a Geiger counter and a vial of poison. According to quantum mechanics, an atom has a 50% chance to decay. The cat has a 50% chance to survive. The cat has a 50% chance to die.

In quantum mechanics, each particle behaves like a wave. The wave: ψ presents the probability of cat’s behaviour. When a cat (particle) is closed in a box, all amplitudes occur simultaneously (the cat is alive and dead!). It is in the superposition is the sum of these two states. The superposition is the property of the wave of probabilities. Such waves, like waves on the water, can be combined – yet they can also delete themselves.

The wave function contains information on all possibilities for the behaviour of the particle. Function Ψ of a cat describes two states: alive and dead, but Ψ of electron contains a list of all the position of particle in space and time. When we open a box and observe the content, we make a reduction of quantum states and we reach only one outcome – the cat is alive or the cat is dead. What we will see is a matter of chance. We have no influence on the condition of the cat.

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The act of observation causes the collapse of the wave function and we receive the only one state, because physically, only one outcome is possible. We call it the Copenhagen interpretation. It was developed in 1927 by Niels Bohr and Werner Heisenberg. Bohr believed that the quantum world could be experienced only through the medium of an experiment: when the radioactive decay of the atom interacts with a Geiger counter. As a result we have ticking, needle to indicate a value on the scale etc. Invisible quantum event corresponds to an event in our world of classical physics.

Heisenberg, Bohr, and von Neumann separated the observer from the observed object during the measurement. But both the observer and the object is built from interacting atomic particles that at the quantum level are represented by the overlapping wave functions. So what’s the point in separating the observer from the observed things?

In the 50’s, Hugh Everett wrote a PhD where he was not impressed by Copenhagen interpretation, which required an outside observer. Everett wanted to keep the process of measurement within the system. He wondered what would happen if the observer and the observed object are bound at the microscopic level, and at which point the wave function is reduced to a small part of the whole system? Do reduction occurs when the needle of Geiger counter records an events? But if the needle is not in a superposition until it observed? And what about the eye of the observer? What if the room enters another person? Is the wave function of the observer who looks at the Geiger counter one that could collapse when another person in the room looks at them?

Over a glass of sherry he wondered, what if the wave function does not collapse? What if the superposition of states remain forever? He characterized the physical condition of the entire universe not in classical terms, but as a universal wave function. This function describes all possible superpositions of classical states that develop continuously in a linear manner. In this way he got rid of the problematic process of measuring and monitoring.

“Every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself. Here is schizophrenia with a vengeance.” ( The Everett Interpretation of Quantum Mechanics collected works 1955–1980)

The problem with the theory of universal wave function lies in the fact that in the original version, it requires an infinite number of universes, each of which splits into an infinite number of versions of reality when quantum choice is made and move forward every possible way at the same time. In the modern version of the theory of multiple worlds we are not dealing with branching universes, but all possibilities exist simultaneously – there are an infinite number of universes that “start” as identical copies.

In the next parts of Science is Strange: time travel paradoxes and how to travel to the past. How many parallel worlds Max generated?

 

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