Illusion of Free Will

By the now most accepted belief, we are a part of the physical world, and we are governed by the laws of physics at the fundamental level. This leaves no room for real, or actual, free will.

This poses a kind of a paradox, given the strong conviction that we can decide about ourselves autonomously. Let's take the following laconic formulation: Contrary to our conviction, we cannot affect the way how the Universe evolves just by using our minds. And the Universe contains our minds, then also all decisions we make. The name for something that exists subjectively, but not objectively, is illusion. So I will name this effect the Illusion of Free Will (IFV). I will be also using the IFVH acronym, for the Illusion of Free Will Hypothesis.

Let me write yet another formulation, in a way that will be useful for the later discourse.

IFV: "It is an illusion to think that I can decide today what I will be doing tomorrow". Instead, it will be decided by the laws of physics. I can only hope that my current state of mind  will be retained long enough that I will take the action that I wish for today. A side note: if I really care about assessing the probability of me taking the action, I should rather use indirect methods, like judging from my decisions in the past in similar circumstances. Or look at other people, possibly -- similar to me, and see what actions they usually take. Another side note: it does not matter if the physical world is deterministic, or if it has quantum nondeterminism built-in, or if it is chaotic, etc. If only our understanding of the physical world is correct and more or less complete, I cannot influence these processes just using my mind.

IVFH: I fully recognize the above.

Update for Marek -- and thank you for the comments!

Indeed, "free will" is a very good abstraction to describe actions of an agent without going too much into details. Similarly, we talk about temperature of a macroscopic object without analyzing energies of its atoms individually. Certainly, as it happens with abstractions, it has limits. It would be a little bit awkward to say that a dice has free will, or that it wants to pick a number, and that it finally decides the outcome. Just like we cannot measure the temperature of a vacuum -- the abstraction breaks down there. Importantly, this is our description of the whole system observed from outside.
If we look from inside, we may have a very different picture. Let us imagine a person who has just committed a crime. They may have at least three explanations for their actions:
"I did it, because I concluded that... etc."
"I did it, because voices in my head told me to do it!"
"I don't know why I did it. It was as if someone else took control..."
(I think most of us have read the phrase "He heard himself say..." at least once. Some might even have experienced it).
Why the differences? We usually tend to give all these voices a collective name, "I". Sometimes the agent responsible for the task just cannot cope, for many reasons.

The impact of IFV and IFVH

The paradox doesn't go without practical consequences. If a mind makes IFVH a firm belief, it may end up ignoring its core values and following the easy path every time. Let's consider the following internal dialogue as an example:
"I definitely should go on a diet!"
"I can let it go... My dietary decisions are determined anyway"
"But what if I get fat?"
"Yup, it may happen. But there is really nothing I can do about it; we'll just see. By the way: how many people happen to be successful with their diet, long-term? Do you have some statistics? Have you done any research? If you do, I can tell you the probability"

Let's decompose the consequences, step by step

First, I dare say that our core values are just solemn disguises of our needs. What makes them special is that at some level we give them more priority, or more meaning. This usually follows from their emotional significance. By the occasion: contemplating them in this way may reveal what we are really attached to, in the Buddhist sense of attachment. Why do I need to be fit? Do I want to feel attractive? Does it mean that I feel unattractive, to start with? Or do I want to be healthy? Maybe the root is then the desire to live forever? Is it about the fear of death?

If we feel the drive to do something against ourselves, this just means that we witness competing needs. If we look carefully, it will turn out that we even cannot do anything against our wishes! We just choose to suppress some of them, treat them as less valuable, or even evil. But they have been generated by the very same mind that gave us our highest and most precious aspirations.

Maybe it is a good time to look from the other side. Namely,

What difference does IFV make?

As of now, I can only rely on my own introspection to tell about the nature of these conflicts. The interfering goals I witness when accepting IFVH are short-term. Following them would give me immediate gratification. I think they are instinctive. The goals that have been disturbed are, on the other hand, long-term. Usually they are a result of planning, deliberate or not.
Let us consider another example. Imagine someone who goes to university wishing to graduate in five years. This is really a long-term perspective, but with predictable big benefits: good job career, higher salaries, prestige, to name a few. To achieve this goal, one needs to make a lot of austerities. Let us take waking up in the morning every working day as an example (especially in case of someone who really hates it).
Now: I take the decision to graduate in 5 years. I have to wake up today. And tomorrow. And the day after. And all the days of the university course.
 

If we have no free will and we fully realize it, it is rational that our mind tends to make choices giving immediate gratifications. This is because we can only guess what choices it will make, day after day, during the very long period. This is the central point: we cannot decide now what we will do tomorrow, things will just "decide themselves". We can only assess probabilities. Hence we need the illusion that we can make the decision, just to increase our belief in the final outcome, and, thanks to that, indeed increase the probability of meeting our long-term goal. This works like a self-fulfilling prophecy. We can also see it as tricking our own mind.

In technical terms, it's all about increasing the famous discount factor, γ.

Why did IFV evolve in humans?

I speculate that the free will issue can only concern species that developed the long-term deliberate planning ability, and humans is the only known to me. (I think we can skip the squirrels hiding nuts during autumn. They probably do it instinctively. This instinct has evolved under pretty stable climatic conditions, and my guess is that they will not be able to rethink their behavior as the global warming progresses). It would be extremely interesting to know the steps of IFV evolution. I can only put highly speculative hypotheses here, but let me try.

For IFV to evolve, we need at least the following prerequisites:

• Species that needs to live in conditions far from those it evolved to. We may think about a tribe that spent thousands of years on an African savanna, without witnessing harsh winters every year. They would not have the instinctive need to stockpile up for the winter, or spend time and energy on looking for shelters, or building them.
• Ability to predict the future and imagine (albeit vague) the result of various strategies.
• Limited resources, so that hard decisions need to be made for survival.

Following one's instinct would be to eat the available food immediately, and conserve energy. The winning strategy is to limit daily rations and expend energy to find or build a shelter, which may take days or weeks of continuous effort. This strategy is risky: the daily shortage of energy may be lethal in many ways. So: maybe it is better to eat what we have? We would then protect the food from fellow tribesmen and spoilage, we would increase our chances of successful hunting, and escaping predators. One of the risks is also that we would consume our supplies on the next day anyway, but with reduced chances to live even that long. By the way, I strongly recommend the reader to go on a three-day fast and re-read this paragraph, to appreciate the arguments better.

For our considerations, the last item on the list is important. Let us imagine putting ourselves in the position of the mind module responsible for assessing odds of various scenarios outcomes. First and foremost, the module does not have advanced mathematical tools for calculating probabilities. It also operates in a highly uncertain environment. This means that it needs to simplify things and use approximations. In other words -- it has to apply heuristics. Maybe the simple but powerful "today's weather principle": given no better data, we assume that our temptation to consume the supplies tomorrow would be similar to what we experience today. Let us also assume that we face the "all or nothing" decision every day. Admittedly, this is an oversimplification, because our supplies usually can be split. This makes the optimization problem harder, but it does not change the outcome. We may think about it as about opening This Jar of a jam (and then consuming it fast, until it turns bad). Finally, we get the Bernoulli scheme with N equal to the number of critical days when we need to preserve the jar,  p equal to the probability of keeping the jar intact on each consecutive day, and with our survival guaranteed if we success every time. This gives us the (very simplified) formula

P(survival) = p^N.

Since we have the exponent there, the final estimation is very sensitive to a change of p. Even a slight increase of the estimation of p increases our chances of actual survival. This means that I need to change my belief in my decision tomorrow. This is where a special mental shortcut comes in handily; let us name the shortcut strong will. We know we have it, don't we?

Two important notes: firstly, the updated estimation does not have to be realistic. It is enough that it promotes survival. Secondly, the whole consideration doesn't even have to be conscious. The whole thought process may as well execute in the subconscious mind, including the vote: eat it now? Or wait till the doomsday?