A distinction of humans as a species is that we are overimitators. One experiment compared the behaviour of humans and pigeons. In it the subjects were displayed a random sequence of red and blue balls. The subject had to guess one at a time which ball would come next, red or blue. If they guessed correctly, they got a reward.
Pigeons eventually settled on constantly guessing red, which was twice as likely to appear as blue. An economist who knew the sequence was random would have said that this was the best strategy to maximize the expected reward. Human subjects, on the other hand, kept guessing both red and blue. In other words, they imagined themselves to see a pattern in the sequence and made their guesses accordingly. Overall, the pigeons performed better.
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Another experiment compared human babies to chimpanzees. Subjects observed through a transparent barrier an experimenter who manipulated a trick box in order to retrieve a reward, a piece of food, trapped inside. This manipulation included some abra-cadabra, movements that had nothing to do with the release of the food. When they were let to try by themselves, the chimpanzees renounced the excessive manipulation and went straight for the reward. Humans, on the other hand, repeated faithfully the entire ceremony.
This sort of human behaviour is what gave us culture. There's humility in it: I know that I do not know. I trust in my peers and follow them blindly, because there must be a reason for their actions even if I am currently ignorant about their nature. The same goes for peerless observable phenomena: I attend occurrences to see the pattern behind them, because ‘everything has a reason’.
Randomness is the frustrated attempt to see a pattern. An event occurred which was not only unexpected, but retrospectively unexplainable.
Wikipedia defines randomness as follows:
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination.
Randomness is all around us. When somebody makes a random comment, it means that we cannot see its relationship to the conversation. It did not conform to the pattern of speech that preceded it. The random might be something as non noteworthy as the height or name of a service provider we have an appointment with. We do not know these in advance, and therefore the person has a random name and height.
Wikipedia adds:
The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution.
Probability distribution, as a reminder, describes the probability of possible outcomes. For example, all the service providers in the city have a height, and in the aggregate these heights create a distribution. Heights, in other words, are distributed over the population of service providers. We do not know exactly what height the person we are meeting would have, but we expect it to be around average. If the person was 2.10 or 1.45 meter tall, it would be at least a slight surprise.
The first citation made a distinction between ‘apparent’ and ‘actual’ lack of definite pattern. The last citation used the term ‘objective’ (in scare-quotes?). Objectivity relates to the world as independent of human observers. We say something is objective if it is really there, whether we perceive it or not. For example, this pattern of human heights. And once we observe such objective things, we can describe them too. We can describe service provider heights with a probability distribution, for example. But randomness remains: the probability distribution merely gives us a probability, an uncertainty rather than a certainty.
When we say that something is random, we claim that it really is unpredictable. Objectively, as it were. But is it really?
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Let us return to the blue and red sequence of balls. One way to describe the sequence is to say that each ball is sampled, to use the statistician's terms, from a distribution where 33% of the balls are blue, 66% are red. But suppose the sequence follows a repeating pattern of blue, red, red. The above statement about the relative quantity of each colour would remain true, but we would no longer claim that the sequence is random. In fact, it's perfectly predictable: a red ball always follows a blue ball; red follows a single red; blue follows two reds, all with 100%. But if the sequence followed no pattern, then we would say that it is random. The 33-66% description admits an uncertainty about the next ball, but it's an accurate description of the objective situation — supposedly. But I claim that no, it is not. What does it mean ‘follow no pattern?’ Patterns are not directly in the world, but in their description. Randomness is not in the world, but is a product of our ignorance.
Pseudorandomness sits at the border between randomness and non-randomness. From Wikipedia:
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Pseudorandom number generators are often used in computer programming, as traditional sources of randomness available to humans (such as rolling dice) rely on physical processes not readily available to computer programs, although developments in hardware random number generator technology have challenged this.
In other words, pseudorandom number generators are pieces of programs that generate an apparently random sequence of numbers. Why is it ‘apparently’ and not ‘really’?
The computer is a machine that executes operations on data. These operations are mathematical and there's no source for surprises in it. When you sum 2 and 2 you always get 4. Therefore the execution of the program, the generation of the sequence of numbers, is deterministic. Behind the scenes it relies on a single value, the ‘seed,’ which might be itself random, in the sense that the programmer does not know in advance what it is, which determines the generated sequence of pseudorandom numbers. The sequence is derived from the seed through a complicated operation. If the programmer sets the seed for the pseudorandom generator, it would output the very same sequence every time the program is ran. You could think of the seed as the name of the sequence, not unlike the number pi, Euler's number or the golden ratio, each of which have an infinite sequence of decimal digits which are likewise ‘random.’ The alphabet, though is far from being infinite, is also in that sense a random sequence of characters.
I hope this has started persuading you that randomness is about one's state of knowledge than about the world. There isn't an essential difference between the pseudorandom generated sequence of numbers and the decimal digits of pi. You might say that there is, pi is observable in nature. Or if you measured the ratio of your desk's length and width you would get a number you did not know in advance, but it does not make it random, right? But, first, the computer and its number generator are also in nature. And, second, there was a time when you nor anybody else knew the digits of pi. Somebody could have used it to create a random number generator.
You might have noticed that reoccurrence played a vital role here. If we unwrap a freshly minted pseudorandom generator and set our birthday date as the seed, until we execute the program, nobody knows what the generated sequence would be. Doesn't it make it random? When we run it a second time we know exactly what it will be, because it has already happened before. A senselessly trivial statement might be that nothing is random because once it happened we know what it was. It's ok if it doesn't make any sense. Let's assume a random occurrence tomorrow, say the stock market movement or the weather, which we could then convert into numbers. Once it has happened, we jot down the numbers on a notebook, and then claim, no, it's not random, here is the exact sequence! My point here is not that nothing is random, but that there's no difference between ‘pseudorandom’ and ‘random.’
This is relevant to processes that we cannot repeat. A coin flip, for example. One could program a robot hand that flips coins exactly such that you can tell it to land it heads or tails. But supposing that most humans do not posses this skill, whenever they flip a coin they do not know how it's going to land. The coin obeys well described physical rules, but this does not change the simple fact that how it's going to land is unknown until the flipper makes the flip.
Nonetheless, how the coin would land is determined. We do not know how it would flip because we are ignorant about the state of the hand, the brain, the movement of air in the room and their influence on the coin. A complete physical model of the coin flipping situation would tell you exactly how it will land. Again, the randomness stems from our own ignorance rather than the world itself.
Another example. Suppose you are out in the city and you bump against an acquaintance, Alice. It's random in the sense that neither of you have expected to meet the other. But later it turns out, retrospectively, that it was not random at all. Something about your relationship made it predetermined. Some factor, say a habit of Alice, was behind both your acquaintanceship and her being there at that time and that place. You could have predicted that you would bump into each other there and then if you had only thought about it. So was it random after all?
Determinism and free will
But what does it mean to be determined?
Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way.
It seems like a meaningful statement, but it's problematic. Since ideas about determinism often clash with notions about free will, I'll touch the latter first. A decade ago I asked a good friend of mine if he believed in free will. If I remember correctly I sought to confirm to myself that others, like me, who studied neuroscience and were of a scientific mindset, held a similar view on the matter. I was therefore disappointed when he answered, after a short consideration, ‘yes.’
It was only years later that I understood that the problem was in the question itself. It was ill-posed. The question begs the clarification, ‘free of what?’ The rub is that conversations over free-will and determinism are often tied to questions about morality. For example, events within the universe can occur only in one possible way, therefore the criminal has had no choice but to commit his crime, therefore it is not just to punish him.1 There is sense in judging differentially the person who killed by mistake and the one who has planned it, but whether the person was destined, as it were, at birth, to plan a murder, or not, has no baring on whether it is just punishing murderers.
Arguments about free will boil down to language being given an undue priority over our understanding. It's the same case with paradoxes, which present the faultiness of language rather than of the world. We know that Zeno would catch up with the turtle, but when we lay it down with ‘he has to travel half the distance, and first half the distance of that, and so forth, so he cannot move’ and we submit ourselves to the logic of the words, we get perplexed.
Language reports on reality rather crudely, and often it gets conflated, whether we speak of the world as it is or the world as we should make it to be, whether we speak of the normal or the normative. If we think of the person as something above the firings of neurons in their brain, the motions of their hormones, then we'd have to say that they are shackled by their biochemistry. If the person is merely their body, we recuperate a certain freedom: the body is situated within the environment but there's a border between the two, and the body is autonomous, even if subject to external forces. Some of the many external forces are expressions about law and morality which might discourage that body from committing crime and therefore should be expressed.
Back to determinism. The problematic word in the definition is ‘can’. It's a word that expresses potentiality, that is, a contingent that is usually tied to human volition. More generally it's a word that excludes an impossibility. We would say ‘it might rain tomorrow’ to express an uncertainty, and not ‘it can rain tomorrow’ because it's trivial: of course it's not impossible that it would rain. If somebody is jumping on a chair we might say ‘the chair can break’ because the behaviour of the person suggests they think otherwise. ‘The chair might break,’ on the other hand, expresses not potentiality but a probability. If we replaced ‘can’ with ‘might’ in the definition above, we would get a very different statement: “Determinism is the metaphysical view that all events within the universe might occur only in one possible way.’ ‘Can,’ therefore, excludes an impossibility: it is not impossible that events within the universe will occur only in one way.
That already sounds very odd, and it is not how we usually think of ‘can’. Usually we think of it as a contingency. If I say ‘I can lift my arm’ it means that the lifting of my arm is possible — and contingent. For example, if you ask me to, I will lift my arm. Or: if I want to, I will lift my arm. In either case, that which leads me to lift my arm is external to my arm and uncertain in advance: the activity of my brain, my environment, however you want to cut it. If it is certain, then we would not say ‘can’ but ‘will’. If I jump with a parachute from an airplane — ‘I will fall down’ and not ‘I can fall down’.
The universe, by definition, has nothing external to it. All events within the universe as an aggregate have nothing external to them. To say that these events ‘can’ anything is simply inappropriate, and at the end of it no different than saying that,
All events within the universe will occur in one way,
which is banal.
Of course, what we really care about is whether we can predict all the events that will happen, or even all the events that we care about. The answer is no: there are limits to our knowledge. Our knowledge resides in the world too and cannot contain it. The universe is a big pseudorandom generator which we experience one digit at the time, as it occurs for the first and last time. Or is it?
Quantum physics asserts that no, the universe is not a huge pseudorandom generator but a random generator. If we ran the universe a second time, everything would happen differently. It asserts that our uncertainties about the unfolding of the physical world is not a matter of ignorance but a consequence of the its fundamentally random nature, at least where single particles are concerned.
Like the two theories of relativity, quantum mechanics presents an unintuitive picture of the world, one that has analogies to our lived experience but which is nonetheless difficult to conceptualize. This difficulty bred some misguided notions, such as the many-world interpretation. We found the limits of our measurement instruments, and, just like the navigators of old who put dragons beyond the mapped world, imagine fantasies where our ignorance reigns. If we never reached the industrial revolution we might have said that every time somebody threw a die, 5 parallel universes came into being where each of the numbers that did not turn up in our universe, did. Another notion is that consciousness affects physical reality — which is not a new notion, either. Every staunch gambler feels he might bring about a win by applying his mind. Another notion is that quantum physical effects give rise to free will — a will free from deterministic physical laws, supposedly, as if the will being random confers dignity upon it or rescue us from ethical conundrums.
Be as it may, our experience is not affected by such puzzling quantum phenomena, whether a particle went right or left. Nonetheless our ignorance is plenty. Ironically, as we quantify it, weighing probabilities, we are led to believe that we acquired certain knowledge about a chaotic world. Rather than admit we are stupid, we say it is random and investigate no further. On the other hand, how often do we say of something that did happen that it was improbable? That which is prospectively improbable becomes retrospectively improbable, even if it has obviously happened. To say otherwise is to claim undue certainty. Unless proper investigation followed? But isn't it too easy to give explanations to what we know.
This is why Martin Luther's belief that whether somebody ended up in heaven or not was unknown and anyway unrelated to their deeds in life, but only to their belief in god.