The Meaning of Collective Determinism (Column 539)

Dedicated to my dear son Shlomi,

a Facebook employee. Wishing him success.

In column 335 I discussed the impact of social networks on all of us and the deterministic feelings these effects arouse in many. On Friday I spoke with my son Shlomi, who works at Facebook, and received a direct impression “from the horse’s mouth” of how we all look from there (hint: not great). This stirred a few thoughts in me—naturally, in an ipcha mistabra (i.e., contrarian) spirit—about each person’s freedom. Although the basic idea was already said in that column, I wish to present it here more fully and clearly, with an additional novel point.

The picture from the horse’s mouth: humanity as ant swarms

Shlomi told me about the phenomenon of our collective behavior. He claims it is truly astonishing how precisely we behave according to expectations, and always in the same way. Peak hours, the distribution of visits and ad clicks, etc., etc.—everything looks the same. Even if you change the conditions and examine it week after week or year after year, the behavior looks exactly the same. As if there were a big engine driving us all and making us behave like a trained, obedient herd. There can be differing characteristics in different countries and places, but those particular patterns are also preserved everywhere. Likewise, there are characteristics common to all places and groups, and of course they too are preserved.

It is important to understand that in every such behavior the individuals change each time, yet the collective phenomenon remains exactly the same. Let us take, as an example, the Mahane Yehuda market. Every Thursday the market is flooded with people, even though each Thursday they may be different people. But a similar number always arrives at similar hours and on similar days, and the change in presence at the market throughout the hours of Thursday is very similar from week to week. Although each of us conducts himself according to his own decision, and it is certainly not the same population every Thursday, it does not happen that on one Thursday the market is suddenly empty or half empty. Somehow a certain percentage of Jerusalem’s residents will be in the market at those hours, even though the individuals are replaced.

From the vantage point of the algorithmic ivory tower, his impression is that all humanity looks very much like swarms of ants or bees. The collective picture is entirely identical, even if the individuals are replaced. This, of course, enables those who control the media to maneuver this herd and change the distribution, or to exploit it for commercial needs (when and where to place which ads, and the like). Thus they lead these flocks and swarms wherever they wish, as if we were all marionettes.

The dissonance with the sense of freedom

Needless to say, precisely in this era each of us has a sense of freedom and full information, and each of us is sure that his decision-making is entirely in his own hands and done freely. It is obvious to us that never has man been as free as in this generation. Yet at the same time it keeps becoming clear that somehow we are all manipulated by our environment and of course by the algorithms that operate within it and even change it. Many claim that the global village may give us an illusion of freedom, but in truth it is one big slave farm. A significant part of that slavery is its success in hiding from us and preserving the illusion of freedom. Just as in Orwell, they keep drumming into us that slavery is freedom, and it seems we are buying it.

Indeed, the dissonance between our personal feeling (and also the real freedom each of us has) and our collective behavior is very troubling. Yet I wish to argue here that this nagging feeling need not truly trouble us. It is not correct to conclude from this that we are all living under the shadow of Big Brother (=the algorithm). Our freedom is real. My claim is that our collective behavior not only does not contradict it, but to some extent even reflects it.

The law of large numbers

It is worth beginning the discussion by looking at the statistics of dice throws. Think of a fair die, that is, one built uniformly on all its faces. With such a die, the chance of getting any particular outcome on each throw is identical for all faces. We have six faces, and if the chance for each is equal, then the chance of any result is 1/6. What does it mean that the chance for each outcome is 1/6? There is no bar to getting the same result on three consecutive throws. That option occurs from time to time, and therefore one cannot give a reliable forecast for a small number of throws. Probabilities give us a tool for predicting the outcome for a large number of throws.

The expectation is the average result over many throws, and an experiment that performs a large number of throws will yield a result that approaches the expectation more and more. If we throw the die 1,000 times, it is likely the result will be about 160–170 times for each face, but there is a non-negligible chance that some faces will still appear a different number of times (150 or 200). If we increase the number of throws, the distribution of outcomes will more and more approach the a priori probability, namely 1/6 of all throws. This is the law of large numbers.

The role of independence

However, even if the die is fair, this is not necessarily the result one gets with a large number of throws. There is an additional condition: independence between the throws. If the angle at which the die is thrown or the initial speed I give it does not change randomly from throw to throw—that is, if there is dependence between the various throws—then the result obtained, even with many throws, will be different. For example, if a person throws the die at some angle and this, for some reason, causes him to throw it next time at some other particular angle, this means the angles are not chosen randomly in the different throws. There is dependence from throw to throw. In such a state the result obtained will not necessarily express an equal distribution among the faces. One must understand that dependence between throws effectively causes a non-uniform distribution of outcomes on each throw (there is a bias toward a certain direction). Even if the die is fair, if the present throw depends on the previous ones, then the chance of each outcome is no longer equal. To achieve an equal distribution the die must be fair and the throws must be independent. If either of these conditions fails, the distribution is not uniform, and then the results for each face will not be even.

At first glance, this condition is very unintuitive. It would seem that if, in a large number of throws, one gets the result expected in advance, this actually indicates dependence between throws—for if we got many more 5s and fewer 2s, that gap should balance out later. There must be something ensuring that, and that “something” (the invisible hand) actually expresses dependence between the different throws. The outcomes of later throws depend on earlier ones; otherwise how does the ‘miracle’ occur that, in the end, the overall numbers balance?! If each throw does not “know” what happened before it, then the outcomes expected of it split equally among the six faces anew each time, and therefore there is no reason the result would balance what has happened so far. It seems the law of large numbers expresses dependence between throws.

Well, it does not. It turns out the opposite is true. Precisely when there is complete independence between throws, only then will we necessarily get outcomes that match the expected distribution. If there is dependence between them, the distribution can be different.[1] There are fairly simple mathematical explanations for this, but in practical terms we can explain it as follows: when there is absolute independence between the throws—that is, each throw is free to yield any of the six results equally—there is symmetry among the faces, and then there is no reason to suppose any face will occur a different number of times than its peers (at least when dealing with a very large number of throws). In contrast, when there is dependence between throws, that dependence creates an effect on the results and can thus create asymmetry in the outcomes.

Examples

The clearest example here is the shell-hole fallacy. Soldiers under artillery bombardment tend to enter a crater created by a shell that has already fallen, on the assumption that the chance another shell will fall in the same place is lower (because the distribution of impact points is supposed to be uniform over the shelled area).[2] But statisticians will tell you this is a mistake. Since the impact point of each shell is independent of its predecessors and is uniformly distributed over the area, its chance of falling in the existing crater is exactly equal to its chance of falling anywhere else. That is the meaning of independence between shots. And yet, when we examine the distribution of impacts at the end of the barrage, we are indeed supposed to find a uniform distribution over the area, and very few places in which two shells struck. You can fairly easily see why: if each shell can fall anywhere with equal probability, the shells will be spread evenly over the whole area (assuming there were many shells, so the law of large numbers applies), and consequently two-shell craters will be rare. But this happens precisely because of the independence between the shots. If there were dependence between them, many situations could arise in which two shells fall in the same place. Of course this depends on the nature of that dependence. If each shell falls in a region close to its predecessor, then obviously that is what will happen. But it is important to understand that in many other types of dependence we would also get such a situation. Independence creates symmetry among locations, and therefore it is a condition for obtaining results uniformly distributed over the area.

Another example can be seen in basketball games. Suppose a team, in the first half, shot much worse than its average. Basketball commentators tend to say that this should balance out in the second half, and therefore the expectation is that they will shoot better to reach their average by the end of the game. This is exactly like the shell-hole effect, and thus clearly a mistake. So too with dice throws: even if we got the result 6 ten times in a row, the chance of getting it on the eleventh throw is 1/6. There is no bias toward balancing, because there is no dependence between events. So how does the balance happen? After all, in the end the results do distribute according to the a priori probability, and therefore some balancing must occur at some stage. It will indeed occur, but precisely because of randomness. That is, it may be that the balance will be achieved in the final game of the season, in which the team shoots a very high percentage, or in the fourth game from today. There is no way to claim the balance is expected specifically in the second half of this game. Because of independence, there are possibilities for games with low results and with high results, and precisely because of that the overall situation balances out. Not because there is a dependence whereby, if the first half yielded a low result, an invisible hand will ensure a high result in the second half. There is no such invisible hand and no dependence between events, and therefore there is no guarantee of balance in the second half. And yet, it is precisely the absence of an invisible hand that ensures that, in the long run, balance will indeed be achieved and the expected result attained.

The way to influence results

Now think of a person who wants to influence an experiment of dice throws. He has control over the die—he can make a different, unfair die—and slip it into the game and thereby influence the result. Let us assume, for the sake of discussion, that he holds the outcome “5” dear (he has financial profit depending on the number of 5s). He wants to reach a state in which 80% of the throws yield 5, and for that purpose he constructs the die so that it has probability 0.8 of landing on 5. Is that sufficient to determine the outcome of the game?

The answer is, of course, no. If there is dependence between the throws, this will spoil his prediction. For 80% of the throws to yield 5—even if the die has been constructed accordingly—there must also be no dependence between the throws. Imagine a correlation between throws such that each throw must be one more than the previous one. Then on the first throw it is likely that 5 will come up (even that is not certain), but from then on the results are dictated by the correlation. To ensure that 80% of the throws land on 5, he must ensure that each throw is independent of its predecessors. This again is not intuitive, but the explanation is exactly as in the previous cases.

The conclusion is that what we saw above is not unique to a uniform distribution of outcomes. Independence is a condition for the realized results to reflect the a priori distribution (the probability arising from the die’s structure), whether the distribution is uniform (1/6 per face) or something else (such as 0.8 for outcome 5 and the rest equally—0.04 per face).

Is a die throw a random process?

I have pointed out here more than once (see the series of columns 322–327) that a die throw is not a random process at all. It is an event that is entirely Newtonian mechanics. If the die’s shape and structure, the initial speed and direction of the throw, air density, temperature, the height of the release point above the ground, and perhaps one or two other parameters are given, the outcome is determined completely deterministically by those parameters. There is nothing random here.

So why do we use probability to analyze and predict the outcomes of such a non-random event? Because the direct calculation, despite being conceptually simple (this is dynamics according to Newton’s second law), is very difficult and complex in practice. This is mainly due to the sensitive dependence of the outcome on the initial conditions, meaning that a small change in them will alter the outcome very sharply (as in chaos). That is what makes such problems very difficult to compute and predict (if only because we do not know the initial speed and direction precisely enough to predict the outcome). This is why we prefer to use probabilistic or statistical tools instead of performing a direct calculation.

It is important to understand that this is the main reason for using statistics in our lives. In our world there are no random processes at all (perhaps except for quantum theory at very small scales—but that gets washed out and fades at large scales). Therefore the use of probabilistic and statistical tools appears only in situations that are not random. In those columns I pointed out that biologists who deal with evolution are not always aware of this, and thus see genuine random aspects in evolution, whereas in the vast majority of cases, if not all, we are dealing with entirely deterministic processes whose complexity compels us to use statistical rules.

Surprisingly, it turns out that statistics indeed works even when we are not dealing with random processes. Complex calculations that depend very sensitively on some parameter also respond to statistical calculations as if randomness were involved.[3] As noted, in our lives this is always the case: statistics is not applied to random processes but to complex ones.

In those columns I distinguished between ontic uncertainty (that is, uncertainty in reality itself) and epistemic uncertainty (uncertainty in our knowledge). Ontic uncertainty stems from vagueness—i.e., a non-single-valued state—in reality itself, whereas epistemic uncertainty stems from a lack of information due to our cognition. Ontic uncertainty corresponds to genuine randomness, whereas epistemic uncertainty stems from our lack of information even when reality is defined unambiguously. One must understand that statistics always deals with situations of lack of information, but such lack can arise either from a state in which reality itself allows several possibilities, or from a state in which reality itself has one outcome but I do not know which of the possibilities has been realized or will be realized in the future. In quantum theory, at least according to the accepted interpretations, we speak of situations in which reality itself allows several possibilities, and hence prediction of the future must use statistical tools. But this is the only known example in physics of true randomness (and even there there is an interpretive debate not yet resolved). By contrast, in classical physics (relevant at large scales—that is, the phenomena we encounter) there is only one possible outcome, but I do not always know which will be realized. The use of statistics regarding dice throws, like everything else in our world, is an example of the second case. The present circumstances dictate a single outcome, but I cannot know in advance what it will be.

Human behavior

We are now almost at the heart of the matter. It turns out that human behavior, whether you are a determinist or a libertarian, obeys statistical laws. In column 405 I noted that all scientific psychology is based on this surprising fact. The laws of psychology describe the average behavior of large human groups. They cannot predict the behavior of an individual person, but they can state what will happen on average—that is, the average behavior of a large group.

Note that something very similar to what I described in the previous section occurs here. Each person, individually, behaves in the way he decides, and yet at large scales it is possible to predict what the collective will do (i.e., what percentage of it will act in a certain way). This is the law of large numbers. Note that this fact does not depend on our metaphysics. Determinists will say that a person acts in a way determined by the sum of influences upon him, but even though, in their view, these are deterministic processes, the complexity of human behavior compels us to use statistical tools to describe and predict human behaviors. And surprisingly, this works. Libertarians, on the other hand, claim that a person acts freely—that is, decides his path and actions in a way not determined by the collection of influences—and thus it is necessary and justified to use statistical tools to describe and predict his behavior. But it is important to understand that even according to the libertarian picture we are not dealing with random processes. Contrary to Peter van Inwagen’s mistake, free choice does not reflect determinism (as compatibilists think) and is not a random lottery either (see my essays here and here, and column 376). It is a third mechanism. Therefore, even in the libertarian picture there is a certain ‘miracle’ in the fact that statistical tools work well. Here too we are dealing with processes that are not random (and not deterministic either), and yet statistical tools are applicable to them.

The libertarian picture of free will: the topographic model

In my book The Sciences of Freedom (and more briefly in my essay here) I describe the libertarian picture of free will via what I there called “the topographic model.” In this model, I gather all the influences upon a person—genetics, brain, education, home, environment, and so forth—and depict their sum as a topographic landscape within which the person operates. Toward certain directions it is harder for him to go (i.e., to decide to do something in that direction), which means that on the topographic map there is a mountain in that direction (it is hard for him to climb it). In other directions it is easier for him; there is only a hill. There are directions that are a plain or a valley, toward which it is easy and perhaps even natural to roll, and there are directions that are an abyss (representing an irresistible impulse—he has no ability to resist falling there).

The basis of this model is the assumption that a libertarian picture does not deny the existence of the set of influences acting on the person (contrary to the caricature painted by determinists, whereby any correlation between data and behavior contradicts libertarianism). It only claims that they do not determine the person’s decision, but only influence it. Returning to the topographic depiction: the determinist sees the person as a small ball rolling over the topography I described, and the topography determines for him, deterministically, the entire route and of course where he will end up. If there is a mountain before him in a certain direction, he will of course not climb it, but will fall to the lowest valley. By contrast, in the libertarian picture, the one moving on that landscape is a person with choice. He makes decisions freely whether to climb a mountain or descend to a valley. Of course it is harder for him too to climb a mountain than to go down to a valley (for the person too is subject to the laws of physics), but it is still in his power. Thus, for example, a person with a tendency toward violence (from environment, genetics, or his education) will tend to respond violently in situations of provocation or frustration. A person without such a tendency will respond less violently. For the first person there is a valley in the direction of a violent response, whereas for the second there is a plain or even a mountain in that direction.

One must understand that even if you give me a person’s psychological structure, I cannot predict his behavior unequivocally. The laws of psychology are statistical and not deterministic (and determinists concede this too, though in their view it is merely a complexity problem), and therefore they allow me to state that in a group of one hundred people of the first type there will be a higher percentage who respond violently than in a group of one hundred of the second type. We have again arrived at the statistics of a collective composed of individuals. A person’s psychological structure corresponds to his probability of responding violently in the given situation (just as a die’s structure reflects the chance of each outcome), but his actual behavior is the realization of those probabilities—that is, it is the experiment’s result (the counterpart of the outcomes of the actual throws). Hence it is clear that, for a single person, I have no way to predict what will happen, just as in a single throw of a die I have no way to predict it. But a sufficiently large group of people will come closer and closer to the a priori probability dictated by the topographic structures of their psyches. This is the use of the law of large numbers in psychology.

Example: the Holy One, blessed be He, and Pharaoh

In column 76 (see also column 335), I brought an example from Maimonides, Hilchot Teshuvah chapter 6. In halacha 3 there he writes:

It is possible that a person will sin a great sin or many sins until the verdict is rendered before the True Judge that the punishment for this sinner, for these sins he committed willingly and knowingly, is that repentance be withheld from him and permission not be granted him to repent from his wickedness, so that he will die and be lost in his sin which he will commit—this is what the Holy One, blessed be He, said through Isaiah: “Make the heart of this people fat,” etc. And it says [in Chronicles], “They mocked God’s messengers, despised His words, and scoffed at His prophets, until the wrath of the Lord rose against His people until there was no remedy”—that is, they sinned of their own will and multiplied transgression until they became liable to have repentance, which is the remedy, withheld from them. Therefore it is written in the Torah, “And I will harden Pharaoh’s heart,” for he sinned of his own accord initially and did evil to Israel who dwelt in his land, as it says, “Come, let us deal wisely with them.” Justice therefore required that repentance be withheld from him until retribution was exacted from him; therefore the Holy One, blessed be He, strengthened his heart. And why would He send to him by the hand of Moses and say, “Send [My people] and repent,” when the Holy One, blessed be He, had already said to him, “You will not send,” as it says, “But as for you and your servants, I know…” and “But for this I have made you stand [i.e., preserved you]”—in order to make known to the inhabitants of the world that when the Holy One, blessed be He, withholds repentance from a sinner, he cannot repent but will die in his wickedness which he did initially of his own will. So too Sihon, by reason of his sins, became liable to have repentance withheld from him, as it says, “For the Lord your God hardened his spirit and strengthened his heart.” Likewise the Canaanites, because of their abominations, had repentance withheld from them until they made war with Israel, as it says, “For from the Lord it was, to harden their hearts to meet Israel in battle, to utterly destroy them.” Likewise Israel in the days of Elijah: because they multiplied transgression, repentance was withheld from those who multiplied transgression, as it says, “You turned their heart backward,” meaning You withheld repentance from them. Thus you find that God did not decree upon Pharaoh to do evil to Israel, nor upon Sihon to sin in his land, nor upon the Canaanites to commit abominations, nor upon Israel to worship idolatry, but all of them sinned of their own accord, and all of them became liable to have repentance withheld from them.

The Holy One, blessed be He, hardens Pharaoh’s heart as punishment for his prior sins. In Maimonides’ words it seems that this hardening was deterministic—that is, Pharaoh could not avoid enslaving Israel. From this it would follow that his punishment did not really come upon him because of those deeds, but because of earlier deeds. But in my opinion it is more reasonable to interpret the verses (and perhaps Maimonides himself) differently: this is not a hardening that dictated Pharaoh’s decisions, for otherwise it has no meaning (God could have punished him directly for the earlier sin—“he will die in his wickedness which he did initially of his own will”—rather than harden his heart and punish him for that). It seems more reasonable to interpret it as a hardening that influenced Pharaoh’s actions (but did not dictate or determine them). This is a state in which, in the topographic landscape around him, a fairly high mountain grew in the direction of freeing Israel and a valley in the direction of enslaving them. But his actions were still of his own choosing (he could have decided to climb the mountain and avoid sliding into the valley) and therefore also his responsibility, and hence he was punished for them too (and not only for the earlier sin). If we place Pharaoh in a hundred such situations, or take a hundred Pharaohs to make such a decision, the collective result is known in advance and is determined by the distribution (the weights set by God). But the particular Pharaoh in this particular case acted by his own choice. Thus, although the hardening was a punishment for his earlier sins, the punishments described in the Torah came upon him because of his responsibility for his deeds (despite the hardening).

And now, in halacha 5 there, Maimonides asks:

[…] But is it not written in the Torah, “They will enslave them and afflict them”?—behold He decreed upon the Egyptians to do evil; and it is written, “This people will rise and go astray after the gods of the strangers of the land”—behold He decreed upon Israel to worship idolatry. Why then is retribution taken from them? Because He did not decree upon a particular known individual that he would be the one who goes astray; rather, each and every one of those who go astray to worship idolatry—if he did not want to worship, he would not worship. The Creator informed [Moses] only of the way of the world. To what is this similar? To one who says: in this people there will be righteous and wicked. One should not say, “The wicked was already decreed to be wicked” just because He informed Moses that there will be wicked people in Israel—as it is said, “For the poor will never cease from the land.” So too the Egyptians: each and every one of those who oppressed and harmed Israel—if he did not want to harm them, permission was in his hand. He did not decree upon a particular person; rather He informed [Abraham] that ultimately his seed would be enslaved in a land not theirs. And we have already said that a human being has no power to know how the Holy One, blessed be He, knows the things that will be in the future.

Maimonides asks here why the Egyptians who enslaved Israel harshly were punished, since God had decreed in advance that they would do so (in the Covenant between the Parts). He answers that the decree was upon the Egyptian collective and not upon a particular Egyptian, and therefore each individual Egyptian had free choice; having chosen to enslave Israel, he is punished for it. So too regarding the punishment of Israel for idol worship. This is precisely the law of large numbers regarding human behavior: although each person had free choice, the collective behaves in a way that is predictable and predetermined. God decrees upon the Egyptian collective to enslave Israel—that is, He tilts their balance of choice (as with the hardening of Pharaoh’s heart)—and still each of them has freedom to choose good or evil. The flip side is that, even if each Egyptian freely chooses, in large numbers it is almost certain that enslavement will occur (as with dice throws). Thus the objections of the Ra’avad there are also resolved (see the columns cited).

Now I will add another important point. The collective behavior of the Egyptians is predetermined, and as we have seen this result is realized despite the freedom each individual Egyptian has. But now we can say even more: this does not happen despite each individual’s freedom, but because of that freedom. The freedom of each Egyptian to choose whether to enslave Israel or not (when the options are weighted unequally—that is the hardening of the heart) is what creates the collective phenomenon. The independence and freedom of each individual Egyptian not only do not impede the realization of the expected collective result; they are a condition for its realization—exactly as we saw regarding dice throws.[4]

Back to social networks: the meaning of collective determinism

We are now ready to return and examine the meaning of collective determinism as it appears from the perspective of Facebook employees (humanity as a swarm of bees or ants). We saw there that these companies manage us, at the collective level, like marionettes on a stage. Presses on different buttons at their disposal change our collective behavior in a deterministic way that can be predicted almost completely in advance. Does this mean we lack choice? In essence, the question is: what does this say about each human individual’s freedom nowadays?

Those who infer deterministic conclusions from this picture assume that collective determinism necessarily expresses determinism at the individual level as well. But we have seen here two reservations: (1) there is no such necessity; (2) in fact, the assumption that each of us has freedom to act not only fails to contradict collective determinism—it can actually be the very basis that establishes it. I will now elaborate a bit more on these two reservations.

1. Why is it not necessary?

We saw that, because of the law of large numbers, even in a libertarian picture you get collective determinism. Even if each private person freely chooses his path, the collective picture reflects the a priori probability distribution regardless of each individual’s choices, which are truly free. The collective behavior will appear in the same form, but the people who compose it in practice change each time. The same percentage of all people will always click on the Facebook ad button, but each time they will be different people—exactly as we saw above regarding attendance at the Mahane Yehuda market. Even if the ability to influence our collective behavior does not indicate control over the private person’s decisions, it will nonetheless affect the collective result in an almost deterministic manner. As we saw, changing the weights of the die’s faces will change the result even if each throw is free and independent of the others. The same goes for human behavior. Pressing the buttons that move us is essentially a change of weights, or of the topographic landscape within which each of us operates. Such a change will alter the collective result even if each of us chooses freely.

In columns 126–131 I noted the distinction between freedom and liberty. Our degree of freedom is determined by the number of constraints within which we operate, with absolute freedom being the absence of constraints. But our liberty is the ability to act autonomously within that system of constraints, and therefore the existence of constraints does not affect it (on the contrary—it constitutes it). In this terminology, Facebook’s control over the weights and the frame within which we operate limits our freedom (the number and shape of the constraints within which we act), but it does not touch our liberty, i.e., our ability to act autonomously within that frame of constraints. What is surprising is that, despite liberty, the frame within which we operate will deterministically determine (at least if a group large enough is involved) the result—that is, our collective conduct—but this does not contradict each person’s liberty.

Up to this point the conclusion is that even if one sees deterministic conduct at the collective level, it does not necessarily indicate determinism at the individual level. We will now see that deterministic conduct at the private level even somewhat contradicts collective determinism.

2. Individual freedom is a condition for collective determinism

We can go one step further and argue that, in the libertarian picture, it is precisely the individual’s freedom and independence that bring about deterministic phenomena at the collective level. Assuming we have free choice, the collective picture we described can reflect the fact that we are independent of others, and only this leads to the results of the law of large numbers. As we saw with dice throws, if there is dependence between throws and if each individual throw is not free, the law of large numbers will not hold—that is, the collective outcome will not necessarily reflect the individual’s a priori probability distribution.

If so, when a company like Facebook expects a certain collective outcome and accordingly sets the weights within which each of us will operate as an individual, it will not obtain the hoped-for outcome at the collective level unless each of us acts freely within the constraints (is a person of liberty, even if not of unbounded freedom). The conclusion is that not only does collective determinism not necessarily indicate determinism at the individual level; to some extent it indicates individual freedom. Without this freedom, the hoped-for, pre-calculated outcomes would not be obtained.

You surely noticed I am using qualifying expressions, since this claim is of course not necessary. Even if there is dependence between individuals’ choices, there is still some expected collective outcome. It will not be the outcome expected from the individual’s a priori distribution, but if one also accounts for the dependence, it is still possible (by a much more complex—and typically impossible—calculation) to predict the collective outcome. Dependence of one person’s choices on another’s can also lead to uniform, stable outcomes of some sort, and perhaps what we are seeing are such outcomes. Therefore, uniformity of outcomes does not necessarily indicate independence and libertarian conduct. But note that the companies’ control over the collective outcome does presuppose that they can calculate in advance where they want to get—i.e., change the weights acting on us as individuals in order to reach, deliberately and under their control, the collective results they desire. Such control is not possible (at least not fully) when there is dependence between individual choices and/or when each of our choices is not free.

I will add again that there are dependencies that will reinforce these collective phenomena. If we suppose that people’s consumption affects other people, then there is a dependence whereby, if a drift begins toward some product, it will strengthen via its influence on additional people. A company like Facebook can, therefore, benefit precisely from dependence among people’s behaviors. But here too there are two reservations: if we are speaking of people and groups with no direct connection between them, the picture is as I have described—there is independence, and the company’s control stems precisely from individual freedom. Moreover, even when there is influence and dependence among people, this too does not contradict each person’s freedom. That influence is merely another addition to the system of constraints and influences within which each individual acts, but within it he acts in a libertarian manner. This takes us back to the topographic picture above.

The conclusion is that although there is no necessity to the claim that individual freedom is required to create collective uniformity, it is clear that the converse is not necessary (i.e., that there must be determinism at the individual level). And we have further seen that, to the extent collective determinism has any significance for the philosophical question of determinism versus libertarianism, it is more correct to say that collective determinism actually tilts us more toward the conclusion that there is freedom at the individual level than toward the opposite conclusion. Not so intuitive, but I think that, at least in this qualified formulation, it is the correct conclusion.

In column 335 I already noted conclusion (1): collective determinism does not necessarily indicate individual determinism. What has now become clear to me is conclusion (2): if collective determinism has any significance at all, it actually tilts us more toward the conclusion that there is freedom at the individual level. That is what I have shown here.

[1] Of course, this depends on the nature of the dependence. For example, if the next throw’s outcome is always one more than the previous, even then, in many throws, we will get a uniform distribution. The precise claim is: when there is no dependence one necessarily obtains a uniform distribution; when there is dependence, one is not compelled to obtain it (though it is possible for certain dependencies).

[2] By the way, this is not entirely accurate, but for our discussion here I will assume it.

[3] My apologies to mathematicians of ergodic theory (like Bnei Nachman) who will surely want to storm Habima Square in protest at this sweeping statement. But as a physicist I can reassure you: although certain mathematical conditions are required for ergodicity, in real life it usually works not badly.

[4] In column 76 I noted some halakhic ramifications of this picture regarding public pikuach nefesh considerations. And in columns 529–531 I added further ramifications regarding laws of the public.