The Law of Small Numbers: What Do 'Breaking the Silence' and Alternative Medicine Have in Common? (Column 38)
With God's help
For some time I have been wondering about the phenomenon of 'Breaking the Silence.' Despite my disagreement, and although the phenomenon seems outrageous to me, I find it hard to accept that they are all self-interested Israel-haters funded by the European Union and Hamas. In fact, my feeling is that most of them are actually good and honest people who are genuinely protesting wrongs they saw, wrongs that trouble them and touch their hearts (and who are indeed funded by the European Union and perhaps Hamas as well). I assume their feeling is that these wrongs are not being meaningfully addressed within the IDF and the state, and therefore they are forced to take their complaints outside—to the press, and at times even to the U.S., Europe, and the UN.
On the other hand, from my reserve service and from conversations with other people I get a different picture of the army's mode of conduct. It is clear to me that there are such cases here and there that require treatment, and it is clear that power can sometimes lead people to behave insensitively; still, the overall picture I get is completely different from the one described in the statements of the people from 'Breaking the Silence.' I myself encountered problematic attitudes toward Palestinian civilians and was angered by them, but the descriptions by 'Breaking the Silence' people of deliberate shooting merely in order to kill and other deranged events sound unreliable to me, if only because the norms in the IDF are different and it is reasonable that every soldier and commander fears punishment in such a situation (on the contrary, there are quite a few claims about excessively severe restrictions that prevent soldiers from taking obviously necessary steps in difficult situations they find themselves in). Even a very unruly soldier does not want to be court-martialed and sent to prison, and it is clear that even if they are right that there is weakness in dealing with such phenomena, a soldier who decides to do such a thing has no assurance that he will emerge unscathed. Therefore, even if there were a few such cases, I find it hard to accept the picture that holds that this is the prevailing norm.
So now I ask myself: where does the picture described by the people of 'Breaking the Silence' come from? How is it formed? It is important to understand that beyond complaints about one case or another, they operate under the banner that the occupation corrupts. This is a sweeping general statement, not a claim about this or that case. They are not working only to eradicate a local injustice, that is, to deal with soldiers who went astray (and also those who did not), but to end the occupation. Here they move beyond the moral question into the political realm (this is not an accusation; it is entirely legitimate, I am only sharpening the discussion). They claim that there is a significant phenomenon here, beyond isolated cases that are not handled properly.
My purpose here is not to investigate the complaints of the people from 'Breaking the Silence,' but to derive an important methodological lesson for all of us (for me and for them) in many varied fields. Is it possible that people who rely on their own personal experiences and those of their friends can develop an incorrect, even distorted, picture of reality? This question is relevant to all of us, and 'Breaking the Silence,' whether they are right or wrong, is at most one example of it.
The justifications: between Israel and Switzerland
Just to clear secondary claims off the table, I will add here that unequal and inconsiderate conduct toward Palestinians has various justifications. Some are substantive (that this is indeed how one ought to act), and some are psychological (that it is natural to act this way even if it is not proper to do so).
The substantive justifications are connected to our security needs. Sometimes there is no way to defend ourselves and prevent violence without harming people, even innocents (such as standing at checkpoints and various inspections). Moreover, our need to control them stems from their ongoing refusal to negotiate, which began already with the refusal to accept the Partition Plan and with the hope of annihilating us all. Therefore I have never understood, and certainly never accepted, the claims about the corrupting 'occupation.' It can indeed corrupt (as noted, I do not know to what extent it does so and to what extent the phenomenon is general), but it is hard to see what alternative we have.
The psychological justifications are connected mainly to the background of the conflict and to the way it has been conducted. We have been experiencing ongoing Palestinian violence for more than a hundred years. That violence enjoys broad public support among them (this is not an 'extremist minority,' but entirely the mainstream). They rejoice and exult every time a Jew is harmed, and they encourage violence by means of lies, incitement, and ridiculous propaganda that spreads various fabrications about us and our deeds (plots to take over Al-Aqsa, etc.). If one understands that one is facing a people whose entire essence and very definition is the desire to annihilate us (they do not have many other things in common), it is very easy to understand why an Israeli civilian or soldier does not see them as ordinary people entitled to fair and humane treatment. If they had succeeded in their schemes in 1948, today we would be at the bottom of the ocean. If one sees what happens in places under their control (including the Palestinian Authority), it is hard to develop a burning love for their primitive, corrupt, and violent culture. If one sees the zero contribution of them and their cultural kin to world culture (apart from terror and murder accompanied by whining about discrimination and Orientalism), it is hard to expect sympathy toward them. All this even though, of course, there are good and intelligent people among them on the personal level. For all these reasons, it is hard to see how one can expect an Israeli civilian or soldier to behave toward them in a moral and balanced way, even if ordinarily that would indeed be proper. We are all human beings, not ministering angels, and turning the other cheek is not exactly normal human nature. Therefore it seems only natural to me that the attitude toward them is not like the attitude toward equal-rights citizens, and the concern for them is not like the concern for other civilians. And again, these are psychological justifications, even though the rules rightly determine that every civilian deserves equal treatment.
But all of this is written only to remove those considerations from the discussion. Here I am not discussing whether the criticism of the people from 'Breaking the Silence' is justified and why (although, of course, my position on that matter is not hidden), but rather how I explain to myself the phenomenon of 'Breaking the Silence' and the overall picture that emerges from their statements, which to my impression is plainly incorrect and whose reality on the ground seems to me entirely different. As noted, the easiest thing is to attribute it to schemes, wickedness, and hatred of Israel (the European Union, cringing 'ma yafit' dances, and the like). Even if there is some truth in that with respect to some of them, it seems to me difficult to attribute everything to interests and plots. But if not that, then a very significant question arises here, one we must think about: can people who base themselves on personal knowledge arrive at an incorrect picture of reality, and how does that happen?
Daniel Kahneman on fallacies and biases
Nobel Prize laureate in economics, the psychologist Daniel Kahneman, together with his partner Amos Tversky, identified several fallacies and biases in our statistical thinking and in our evaluation of reality. Many of them are described in Kahneman's book, Thinking, Fast and Slow. From p. 99 onward in his book he describes the fallacy he calls WYSIATI (= 'what you see is all there is'), whose meaning is jumping to conclusions on the basis of scant data and limited evidence. We reach conclusions on the basis of partial information, even when it is clear to us that it is partial, simply because this is the information we encountered and experienced. Kahneman states there (p. 101) that people's confidence in their conclusions is not built on the quality and quantity of the sample and the evidence, but on the quality of the story constructed from them.
There are two features of limited information sets: 1. Precisely because of their limitation, small bodies of information usually create in us a picture that is more coherent than pictures formed on the basis of large samples. In a large sample the chance that we encounter examples that contradict our theory is greater. Therefore the picture will be less extreme and also less coherent, but clearly more correct. The conclusion is that the smaller the number of examples we have encountered, the more the story created from them will generally be, on the one hand, more extreme, and on the other hand, more believable and coherent. The combination of these two is a knockout blow to inference, and that is really what I am dealing with in this column. Kahneman explains that when the story formed in our minds is consistent, we tend to believe it, because in our psychology consistency is more important than reliability. Small samples create a more consistent story and therefore, ostensibly, a more reliable one, even though it is more extreme and less true.
Once one thinks about it, the phenomenon is very simple, but Kahneman would not have received a Nobel Prize if what he said were self-evident. It turns out that many of us are led captive (or duped) by these biases. To see why this is not entirely trivial, I will now bring a few examples.
On generalizing from isolated examples and nice stories: kidney cancer
Kahneman opens chapter 10 of his book with a study that examined the mortality rate from kidney cancer in various counties in the U.S. Of the 3,141 counties examined, it turned out that the counties in which kidney-cancer mortality is lowest are rural counties with sparse populations, located in the Midwest, South, and West of the U.S., and having a tradition of support for the Republican Party. What do we learn from this? I assume we would agree, even if we are ardent Trump supporters, that support for Republicans is not a relevant shield against cancer mortality. The conclusion is that the root of the matter is probably rural life. Country people who eat healthy fresh food, drink unpolluted water, live calmly and not in urban neuroticism, enjoy better medical resilience.
As responsible people, we now move on to examine the counties in which the mortality rate from cancer is among the highest. It turns out that these are… rural counties with sparse populations, located in the Midwest, South, and West of the U.S. (and Republican leanings—I mentioned that already, didn't I?). Well then, the obvious conclusion is now that poverty, lack of education, lack of access to medical centers, alcohol consumption, and the like are what cause kidney-cancer mortality.
We see that each such sample gives us a good and coherent story, and therefore it is easy for us to adopt the conclusion (an extreme one, as we will see immediately) that it seems to demand. But clearly these are two contradictory conclusions. So which of the two is the correct story? What is the truth? You are surely expecting me to say, 'somewhere in the middle.' But no: neither is correct. The truth is somewhere else entirely.
First, among the different counties, probably most are rural counties with sparse populations (a large city contains many residents who together are one county), so it is no wonder that among the multitude of small counties one can find diverse characteristics. One can find everything there. But beyond that, the root of the matter is not rurality, nor only the number of counties, but rather the sparse population in each such county. In small groups one can find more extreme results in any sample, because group size moderates deviation from the average (the law of large numbers). When there are many small groups, then among them there will be groups characterized by extreme properties in every direction. The conclusion is that the extremes (especially high morbidity and especially low morbidity) will usually be found in the group of sparsely populated counties.
The sentence 'large samples are more accurate than small samples' sounds plausible to all of us (the law of large numbers). But the following sentence—'small samples yield extreme results (and also more coherent and less correct ones) more often than large samples'—which is completely equivalent to it, sounds much less intuitive to us. But as noted, this statement is equivalent to the first, and therefore it too is correct.
On generalizing from isolated examples and nice stories: where did Bill Gates go wrong?
On p. 133 there, Kahneman brings the story (which I myself heard only a few days ago from my father-in-law) about the Gates Foundation (a huge philanthropic foundation established by Bill Gates to advance education). The foundation invested about 1.7 billion dollars in tracking the characteristics of the most successful schools. They tried to identify the excellent schools with the best results, and found that on average these were small schools. No wonder the foundation decided to invest a fortune in establishing small schools, and sometimes did so by splitting large schools into small units. Other philanthropic and research institutions joined this effort, as did special programs of the American Department of Education. Notice how easy it is to build a coherent and persuasive story around the success of small schools. There is personal investment in every student; he is not lost inside a large class; every teacher and principal knows him and is aware of his situation. Every student can receive the kind of treatment and program suited to him. No wonder, then, that small schools do better, right? It seems to me that these arguments are familiar to all of us inhabitants of the Holy Land, but now they also have scientific validation. Even our great friend wise Bill Gates reached these simple and obvious conclusions.
But as people schooled by experience, we immediately turn to examine the less successful schools. Astonishingly, when one does so one discovers that they too are generally small schools. The explanation here is exactly as in the previous example. Small schools have greater variance in results. Both the good and the bad will generally be small, just as in the case of kidney cancer. There are additional biases here as well, since wealthy homes can afford to establish and send children to small schools. Students from wealthy homes will succeed more in their studies because they have more means. One can say that school size is a result of success and not its cause (alternatively, there is a third factor, household wealth, that is responsible for both).[1]
The law of small numbers
In chapter 10 Kahneman speaks about the law of small numbers, which states that: 'the law of large numbers applies to small numbers as well' (p. 129). This is, of course, a fallacy—that is, a law in psychology and not in statistics. You encountered a few cases of violence by soldiers, so apparently the occupation corrupts and our army is violent. It may be that if you conduct a broader survey you will discover that the rate of violence among soldiers is rather small, but small samples give us a more coherent and persuasive story. A soldier who has undergone a few difficult experiences develops a coherent story, and in his mind a picture is formed that this is the general state of affairs.
Definitions and the meaning of data
So far I have not yet addressed the question of the meaning of data. Even if we are indeed careful to collect them systematically, and work according to the law of large numbers rather than the law of small numbers, we must still ask ourselves: what counts as 'a lot of violence' in this context? To what should we compare these data? To the number of violent incidents in the Swiss army? In ISIS? In a Trappist monastery or Ponevezh Yeshiva? To violent incidents in our schools or in the street? After all, the claim that the occupation corrupts must be tested against violence in those same contexts without occupation (assuming that without occupation we would still be here and not under the ocean).
And what does all this have to do with alternative medicine?
Similar questions arise for me when I hear enthusiastic reports about the wonders of alternative medicine. My impression is that this is pure hokum: baseless nonsense that benefits no one except the therapist's pocket and the patient's mood (and I am not belittling that, of course). Simon Singh (the one from Fermat's Last Theorem, The Big Bang and The Code Book) wrote another book, I think less well known, titled Trick or Treatment? There he goes through the various techniques of alternative medicine one by one, reviews the systematic studies that were conducted on them, and arrives at the conclusion that these techniques have not a shred of research-based confirmation. They have never shown statistically significant results; that is, there is no indication whatsoever that this works. That, of course, does not prevent millions of people around the world from flocking to such 'healers' and filling their pockets with great wealth. Today one can receive such treatments in hospitals and in the health funds, which teaches you that the facts and the law of large numbers do not really matter much in our public discourse—certainly not when facing the law with the draconian force of small numbers).
What is the secret of this stupidity's success? When I direct such questions to various people, I immediately receive answers based on personal and immediate knowledge: 'My grandmother reached a point where all the doctors had despaired, and then she took Bach flowers and after a few days the cancer disappeared.' Or: 'The son of my cousin's sister-in-law fell ill with an incurable disease, went to a therapist who gave him homeopathic drops, and lo and behold, after some time the disease disappeared.' The scrupulous add: 'You should know that this was a person who himself did not believe in any of this. But he came to see that these are facts.' And so too with reflexology, various needlings, holistic treatments, communication with aliens, incantations of babas, prophecies of Oren Zarif, and assorted nonsense. The deep feeling of all those who spoke with me is that personal information has greater value than studies or hearsay. After all, this is verified information. I know the people in question, and they are not lying. The scrupulous further add that they have no trust in conventional scientific research because it is funded by self-interested pharmaceutical companies. And from this, of course, the conclusion logically follows that alternative medicine is pure truth, doesn't it? You would be surprised how many times (for example, in the days before I despaired and still bothered to warn about it on the bulletin board of the Torah nucleus in Lod) I received similar reactions from people of demonstrably academic education.
And indeed, if these are reliable people, there is no reason to assume that they are lying. But we need to examine two things: 1. What the Talmud calls, with regard to witnesses, in solitude—witnesses sometimes do not say what is true not because they intend to lie, but because they imagine that this is indeed what they saw (but it is an interpretation, not facts). 2. As we saw in the previous sections, isolated facts can create a false appearance (the law of small numbers). In fact, we saw that they generally do create a false appearance. A small number of cases can demonstrate very high or very low mortality from kidney cancer, or tremendous success or colossal failures in studies, and so too enormous success in alternative medicine. The story appears coherent and reliable, and therefore we adopt it, even though it is quite clear that it is extreme and incorrect. The law of small numbers in psychology overcomes the law of large numbers from statistics.
It is precisely for these reasons that responsible medical research (that is, research not funded by pharmaceutical companies, of course) insists on systematic, controlled, double-blind studies. Such research insists on a sufficiently large sample, on a test group and a control group, on double blinding and systematic method, in order to neutralize situations of spontaneous healing (that is, illness that heals on its own, for unknown reasons), and of course our friend the placebo (psychological healing due to trust in the medicine or the healer). Statistics is intended precisely to neutralize the biases of the law of small numbers—but what is statistics in the face of psychology?
How does it work? Ali Baba and the Forty Thieves
Think about the divine kabbalist Baba Oren Zarif, or any one of his colleagues in this lucrative profession. A hundred people come to him each month, each with his own problem. This Zarif gives each of them a prophecy or healing mechanism, and in the way of the world, for about forty of them it even works (let us assume that this roughly reflects spontaneous healing + placebo + cases in which the people are not ill at all but merely delusional + cases in which they were not healed at all but are merely deluding themselves that they were healed and have not yet understood that they were conned). What 'healed' them was not, heaven forbid, the mechanism they received from the wizard, but the wonders of chance (or the wonders of lack of intelligence). The prophecy was fulfilled not because of Zarif's wondrous abilities but because of statistics. The forty wondrous ones who were saved thanks to Zarif's superpowers go out resolutely and sensitively to the media and recount his wonders to anyone who asks, and especially to those who do not ask. The other sixty return disappointed and silent to their homes ('We tried,' they say to themselves. 'Sometimes doctors do not succeed either, and after all there are forty who were healed, aren't there? Probably our bad luck caused it, or perhaps the sins in our hands').
What picture is created in the public? Of course—that Oren Zarif has superpowers. The media echo is created by miracle stories from a small sample. Who pays attention to the day of small things, that is, to the other sixty who went home mournful and downcast and tell no one anything at all? Believe me: if you dispense enough prophecies/remedies to enough people, there will always be a small sample among them who will enthusiastically testify to your magical superpowers. From here on, the law of small numbers will arrange your bank account for the rest of your days. Every person on the street will meet at least one person who reports to him a prophecy of yours that came true or a healing that succeeded, and from there the road is short to the general picture of kabbalistic superpowers. This report will be based on personal knowledge. After all, he himself experienced these amazing results on his own body (not from the newspaper and not from pharmaceutical companies), so will you not believe him?
The law of small numbers turns the small sample you encountered into a general law. This is how the alternative healer works, the common baba (the divine kabbalist), and above all the forty thieves (or the forty who were robbed). I will now bring a few more stories that illustrate the phenomenon of the law of small numbers.
'Choose a Number'
I once read a book called, in Israel, 'Choose a Number.' It tells there (this is a reconstruction from memory; I am not responsible for the details, but that is not important) about a man who received an envelope in the mail from an unknown sender and found in it a letter and a smaller envelope. In the letter he is asked to choose any number he wants between 1 and 1000, and then to open the attached smaller envelope. The letter informs him that inside the envelope he will find exactly the number he chose. He contemptuously chooses 734, opens the small envelope while merrily whistling 'We're walking down the road, hopa hey,' and to his astonishment discovers that indeed the small envelope contained exactly the number 734. He is further told in this wondrous letter that if indeed the number he found is the number he chose, he is advised to send 10,000 dollars to the sender, and the sender will tell him everything he wants and needs to do in order to be healed, succeed, get rich, get married, and the like. This is really the phenomenon of the baba—except that here it is verified, no? No wonder the young man immediately sends the requested sum to that all-powerful prophet, and of course waits to this very day for the promised salvations that will never come.
What is the secret? Very simple. The sender took a thousand envelopes and sent them to a thousand people. Into each one he inserted a different number between 1 and 1000. On average, he stands a reasonable chance of matching the guess of one of the recipients and receiving 10,000 dollars. What is bad about that? Repeating this once a month gives you a handsome monthly salary. In fact, this is a successful branch of alternative medicine, because it does exactly the same thing to many of us. I promise you that if the letter also said that the reader would be healed on the spot, there would be 400 among them for whom that would indeed happen.
Why is this connected to the law of small numbers? Because if I build a picture of reality on the basis of a single case, astonishing as it may be, I am risking foolish conclusions. Even if I see that the sender was right in my case, in order to reach a general conclusion about his abilities I must test him systematically against additional cases and additional guessers (a sufficiently large sample) in a controlled way, and not assume WYSIATI.
to thank and praise Your great name: Michael Abraham and the celebrity hairdresser become religious
Another story happened to me personally (prepare the envelopes). One night I was returning in my car with my entire extensive family (I had a wife and six dwarfs in tow) from a family event in Kfar Chabad (yes, yes, you read correctly) back to Yeruham. And suddenly, from the side, there appears unexpectedly a sweet young thing who had just received her license; the car in front of me brakes, and I ram into its rear end with due ceremony.[2] Our car fell silent, and as became clear to me immediately afterward, it was not drivable. It was 1:00 at night in Gedera, with the whole family (eight people) stranded on the way to Yeruham. What does one do? How does one transport eight people at such an hour to Yeruham and still have enough money left over for alternative medicine and Oren Zarif? But do not worry—the story has only just begun.
We had not yet managed to digest that there had been an accident, and already (!) a neighbor from Yeruham passes by us (!) with a large (!) empty (!) vehicle. He stops (!) and gathers us all into it, and after we left the key for the tow-truck driver, we drove with him happily and comfortably home. Every exclamation mark in the sentences above marks yet another miracle, as will become clear. During the drive it became clear to us that this man, a local political activist from Yeruham who traveled to Jerusalem every few days and knew the road well, had nevertheless somehow lost his way on the way back (!), missed the Latrun interchange (!), and found himself against his will in Ramla (!). He had no idea how to drive from there or where to go (still before the age of Waze), and found himself in Gedera (!). As he passed by us (!) at exactly the right time (!), his wife said to him, 'Arie, look, there's the Abraham family; stop, maybe they need something' (!). He told her that he saw no reason to stop, because it was not yet clear that there had been an accident and that we needed help (it was literally the very second of the event). She persuaded him (!) and he stopped (!), and the rest is history (?).
Your faithful servant arrived at the yeshiva in Yeruham and did what is customary in such cases: a Sabbath evening gathering for his students over bland cookies and Crystal Cola. There he explained to the astonished ears of the listeners that he saw in this no miracle or wonder at all, but a completely statistically possible event. After all, there were thousands of people who got stuck at night on the way home and were not rescued. There is a small chance that in such a situation one of them will be rescued by chance, so that one happened to be me. What does that prove? It seems to me that mainly it proves that statistics works. So long as I have not checked, over a broad sample of events, how many times people got stuck and were not rescued, I cannot say anything about the probability of such a thing happening and whether there was anything surprising here (the hand of God, providence, or Mame Ruchel).
I am sure many of you would run outreach seminars together with a celebrity hairdresser saved from a flying razor, and a paratroop officer who became religious because a Book of Psalms in his pocket miraculously saved him from a bullet fired at him point-blank. This too is again the law of small numbers, since the enthusiastic returnees to religion infer a general conclusion on the basis of one example.
From Delphi to Bar-Ilan: on futurology and economics
One final example is the new 'scientific' field of futurology, which tries to compete with Oren Zarif without joining his professional guild and receiving from him approval and certification.
A little over ten years ago I received an article by an academic scientific futurist who predicts, by means of systematic academic tools, economic and social forecasts about the State of Israel. It turns out that futurology is a developing and flourishing academic field. Truly messianic days: prophecy has returned, and the oracle of Delphi has arrived, in our very own times, at the university. Reading the article (along with a few others) made it clear to me that this is an oracle in every respect, and he can certainly join the said guild (if they will admit him). In most cases these are sufficiently vague predictions (for example: 'Sometime between a decade and five decades from now, there will be significant economic success for the State of Israel') such that one can always explain that they have indeed been fulfilled, or will be fulfilled very soon, or will be fulfilled after none of us is still here. When needed, one can add a few more predictions, some of which will come true, and thus, by the law of small numbers, this field too will acquire at least the halo of Oren Zarif and a respectable academic position alongside researchers of women's poetry in the Middle Kingdom of China in the tenth century BCE. Just so as not to mislead the reader interested in a career in this field, I must add that the academic salary given to a Delphic futurist cannot really compete with the private market, so I recommend to the futurists among us not to go in the academic direction, but to turn instead to the economic college for money-printing named after Oren Zarif and Scheherazade. The admission requirement is growing a braid—nothing more.
Three additional biases
At the foundation of the law of small numbers stands the power of personal encounter and personal experience. Kahneman explains that what I myself saw appears to me reliable and persuasive (WYSIATI). But to understand the force of the phenomenon we need to add to the discussion three more biases: the first is the bias of emotion, the second is degree of presence in the public discourse (the press), and the third is the a priori conception with which we come to the discussion.
Many people will tell you that plane crashes are more dangerous than asthma, despite the fact that the latter kills twenty times more people than the former (see chapter 13 there). Likewise, people's fear of terror attacks is far greater than their fear of traveling by car, even though the number of casualties in car accidents is much greater (there too in chapter 13), and this is both because of the emotional intensity attached to the matter and because of the prominence and force of media descriptions[3]. Incidentally, strokes kill more people than terror attacks and accidents combined, yet I think very few people go through daily life fearing strokes.
So too, the emotion and the difficult experience of a soldier who experiences violent behavior, as well as the prominence of such cases in the press (which does not usually deal with ordinary normative behavior by soldiers), lead him to infer that this behavior is widespread in the army. In his view, this is what characterizes the overall picture, even if in the bottom line there is a rather small number of soldiers who experienced several cases of violent behavior around them. It is very important to understand that statistically it is clear there will be such soldiers. Out of hundreds of thousands of soldiers there will probably be some soldiers who saw, during their military service, several incidents of violence (the number of such soldiers, of course, declines as the number of incidents rises). Those few soldiers will develop a picture of reality (a story) according to which this is the prevailing state of affairs throughout the IDF. Other soldiers—that is, the overwhelming majority, who did not experience this, or saw one case and perhaps not even a particularly extreme one—are the ones who represent the more prevalent state of affairs. But they do not establish organizations and go to the media, because who is interested in the fact that IDF soldiers behave properly? Therefore the overall media picture is created on the basis of reports by a few soldiers who, by chance (a chance that is very statistically predictable), experienced several incidents of violence and improper behavior during their service (exactly like the resolute group of forty thieves in the alternative-medicine and Oren Zarif stories above).
Now we have reached the third bias. These things are intensified sevenfold among soldiers who arrive with an a priori worldview according to which the occupation corrupts. Those among them who experience such situations (and sometimes even those who do not) see those cases as clear confirmation of their conception, and then the story formed from those cases they experienced falls on fertile soil. It is a good and coherent story, and therefore from their perspective it is very reliable and persuasive. No wonder there is violence, they say to themselves, since it is known that the occupation corrupts. As we learned from Kahneman, the question of the quality and quantity of the evidence is not always as important as the consistency and persuasiveness of the story. On the contrary: even if the army presents statistical data showing a relatively small number of such cases, this will be suspected by them as a tendentious false appearance (like the studies that are always funded by pharmaceutical companies, and like the stories of 'Breaking the Silence' themselves, which are rejected because they are funded by the European Union). It does not fit the story that developed in their minds, and therefore they see it as a biased picture. The large sample, which yields a more balanced picture, does not accord with the picture or story formed in their minds.
My claim, in effect, is that the phenomenon of 'Breaking the Silence' arises more easily among soldiers who come in from the outset with a worldview of 'the occupation corrupts.' It can of course intensify through soldiers who came with a different starting point but themselves experienced cases of violence and converted properly to the religion of 'the corrupting occupation' on the basis of the law of small numbers.
Those soldiers inspire great trust throughout the world, since their testimony is based on first-hand experiences. They did not hear about the events; they experienced them themselves. The question of sample size loses importance in the face of the credibility of personal reporting and a coherent story (and, of course, also an extreme one). Again one can easily see the similarity to the examples of alternative medicine and Oren Zarif. All these are results of the law of small numbers, which says that in a small sample the results will always be more extreme, more coherent (and trust-inspiring), yet at the same time also less true.
Conclusions for the issue of 'Breaking the Silence'
If we return to our matter, it is no wonder that soldiers who experience events of violence and/or come with a convenient infrastructure for the story that 'the occupation corrupts,' and certainly those endowed with high moral and human sensitivity, will develop for themselves a very coherent 'story' regarding the moral state of the IDF, irrespective of the scope and reliability of the evidence in their possession. On the contrary, the fewer the examples they possess, the more extreme the picture will be on the one hand, and the more coherent it will be on the other (that is, there will be more isolated soldiers in whose minds a coherent picture is formed). It is worth noticing that there are conclusions here in both directions: on the one hand, the picture presented by 'Breaking the Silence' is not necessarily correct. On the other hand, it does not necessarily stem from self-interested plots, but quite possibly from a sincere picture formed because of human and moral sensitivity (perhaps over-sensitivity). Therefore the way to deal with it is not through accusations but through an attempt to accumulate and present reliable information, and no less importantly, through developing statistical understanding and an understanding of the psychological fallacies that interfere with our ability to work with it. One can also infer from here that the less we resort to alternative medicine and to Oren Zarif and the rest of the charlatans, the slightly less healthy we will be (because of the placebo), much wealthier, and also less likely to suffer from phenomena such as 'Breaking the Silence.'
It is important to emphasize that my remarks deal solely with the general question of what the character of the IDF is, and to what extent one can answer that question from personal impressions. This has not the slightest connection to the question of whether the IDF in fact deals with the (few?) cases of violence and improper behavior, nor to the question of what is correct and proper to do if I feel that the IDF is not dealing with those cases properly (to go to the UN and the newspaper, or not). Even if the IDF is the most moral army in the world, and even if the number of exceptional cases is very small, there is still room for discussion about ways of dealing with these cases and whether the IDF does so properly. A soldier who saw this or that case perhaps cannot generalize from it and create from it a complete picture, but that particular case and its treatment he did see. He can and should ask himself whether the treatment in that case was proper or not. But these questions are unrelated to the larger picture on which I focused here.
Conclusions about me: Objectivity is my middle name
I am sure that many of my intelligent readers are already snickering and directing these same claims at me. After all, I too am a human being with all the same flaws. Those who think otherwise regarding the character of the IDF and the occupation (like me) can also be emotionally biased, nourished by a priori worldviews and, of course, by the media (even opposition to the reports of the 'leftist' media or opposition to the descriptions of 'Breaking the Silence' because of the funding they receive from the European Union are an excellent basis for biased thinking). Their conceptions too are fixed on the basis of a story that sounds persuasive to them, and perhaps also on the basis of personal experiences. I confess with shame that my own claims about the state and conduct of the IDF are not based on systematic sampling but on impressions, and it is clear that hasty generalizations are not the property of one population group or one worldview. The law of small numbers has universal force, exactly like its cousin that deals with large numbers—and perhaps more so (almost like Murphy's unified field laws).
And indeed I am not sure that my story is more reliable (although of course I tend to think it is). What is important to me is not to go out against 'Breaking the Silence,' but to point to a human failure that exists in all of us and that it is important to be aware of and try to neutralize as much as possible. These arguments do indeed arouse a need, for me no less and perhaps more than with others, to examine myself. The conclusions and positions regarding the substance of the claims of 'Breaking the Silence' I leave to each of the readers. Here I wanted only to describe how I explain to myself this strange phenomenon: assuming that I am right in my analysis of the facts and the reality, I must examine how it happens that others see a completely different reality. But the implications of the explanations I propose for the behavior of others are much more relevant with respect to myself.
It is easy and convenient for us to accuse others of irrationality,[4] but sometimes that is a mirror image of ourselves. I of course do not intend here to convert stringently to postmodernism and claim that everyone is right and there is no truth. The lesson for me is that when one approaches the clarification of truth, one must do so honestly and courageously, and be prepared to examine oneself as well. The concentrated attack I have carried out here on 'Breaking the Silence' has far more methodological than political conclusions. And these concern me no less than they concern my fellow man (and for me, even more).
At this point, during the Swords of Iron war (2023), I found it appropriate to add an important note.
The discussion in this column was conducted under two assumptions regarding Breaking the Silence: 1. That their testimonies are true. 2. That their testimonies present serious acts. It turns out to me that both of these assumptions are problematic.
As for assumption 1, see here: https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.adkan.org.il/BreakingthesilenceRe-he&ved=2ahUKEwjNyoOnlv-BAxWO7qQKHak1DwIQFnoECAsQAQ&usg=AOvVaw1e5oQirKtCvwkuO1ZZioiA
As for assumption 2, I have now seen a concentrated file of testimonies about Protective Edge, and I was astonished to discover that it describes policies and acts that are, almost all of them, entirely sensible and reasonable. Which did not prevent them from seeing all this as war crimes. Bizarre. Here is the file:
https://acrobat.adobe.com/id/urn:aaid:sc:EU:7a5ee6c0-62ad-4b96-82c8-add564ee31e4
Read and judge for yourselves.
[1] Kahneman claims that it is actually more likely that we would find an advantage specifically for large schools, since they can offer their students more varied educational and instructional options. That is, in our case the second story (that the small schools are less successful) is actually more correct, and not that both are mistaken. But even if this is true—it is not necessarily for the reasons taught by the story we constructed for ourselves.
[2] Lest you ask how it is that I failed to keep my distance: surprise—I did keep it, and afterward I even won in court. I leave that as homework for the reader.
[3] Here there is also the sense of control that we have (not always justifiably) with respect to road accidents as opposed to terror attacks.
[4] I will only note that these matters are also connected to column 31, in which I discussed rational thinking among believers and non-believers, and to the same extent one can ask about the degree of emotionality among them, as well as about the left-right axis. But I will not enter that discussion here, since I do not wish to examine the questions of 'the occupation corrupts' on their own merits, but rather to focus on the methodological lessons that are relevant to all of us, right and left alike.
Discussion
What a useless site! They philosophize and philosophize, and by the time they get to one practical point, it gets left as homework!
With God's help, 23 Heshvan 5777
On the contrary, that is the good thing about this site: it awakens and sharpens questions, 'attacks' the subject from an unusual angle, and thereby stimulates the reader to reexamine his initial position. In most cases the reader will remain with his original position, but after the renewed challenge and clarification, his position will be more refined and tempered.
Of course this is not suitable for everyone, nor at every stage and situation in life. It is advisable for a person, before approaching a site of this sort, to have some basic knowledge in Jewish thought and halakhic thinking; then he will be able to cope with and weigh what is offered here, to refute, build, and be built!
Regards, S.Z. Levinger
Regarding the "miracle" in Gedera:
What difference does it make that statistically such a case can happen? Why does the fact that this happened to so-and-so not obligate him, as a religious person, to thank God that this is what happened to him, when statistically it could have been much worse?
Is this different from saying that because the splitting of the Red Sea can be explained scientifically, that detracts from its being a miracle—because that scientific event happened precisely when it happened?
Levinger,
You have got to take a course in recognizing humor. Until then, make do with looking up what the homework in the post actually is, and see whether what you wrote about it is relevant.
With the blessing of get yourself a life,
Yishai
Hello.
First, my remarks were made in the context of proofs for the existence and providence of God. If I am looking for evidence of God's hand in the world, then an event that is statistically plausible does not testify to that in any way. The miracle in Gedera or the rescue of the paratroop officer because of the book in his pocket are not miracles, and therefore there is no indication whatsoever that the Holy One, blessed be He, intervened and did this. It can be explained by the laws of nature and statistics.
By contrast, if you already assume from the outset that the Holy One, blessed be He, is involved in the world and does everything that happens in it, then of course you are right. But in such a worldview (which I do not agree with) you must also give thanks for recovery from a cold by natural means, or simply for the fact that you get up in the morning and manage to walk ("Modeh Ani"). Therefore, on your view there is no need at all to resort to a definition of miracle. On your view, even if the splitting of the Red Sea had happened because of ordinary tides, and Moses our Teacher had actually planned in advance the tactic of reaching the sea exactly at low tide, we would still have had to thank the Holy One, blessed be He, to the same extent. In such a picture of the world, you empty the discussion of miracles of its content. There is no such thing as a miracle, because everything is a miracle. Likewise, there is no need to discuss whether something is a miracle, because one must give thanks for everything. The issue of thanksgiving for a miracle implicitly assumes that I am thanking for miraculous intervention and not for assistance from the laws of nature. Hanukkah and Purim were established in memory of miracles, but no festival was established for the fact that we are alive one more day ("for Your miracles that are with us every day"). But in order to thank for a miracle, I must reach the conclusion that there really was a miracle here. To the best of my judgment, in these cases there was no miracle. And here we have returned to the starting point.
In my post and in my comments thus far I discussed the question whether it is indeed correct to see this as a miracle. My answer is no (at least I have no indication for a positive answer). As for the very question of God's involvement in the world, I have already written here that I tend to think there is almost no such involvement (if any at all). Once there apparently was, but it seems that He changed policy.
At the Red Sea there was a prophet who informed us that there was intervention here and that a miracle occurred. If so, who am I to deny the words of Moses our Teacher? But in Gedera no prophet stood there to tell me whether this was a miracle or not. Since that is so, I am left only with my tools of observation and interpretation. And these, to the best of my judgment, yield the interpretation I wrote. And where there is no miracle, the people will pay the price (a play on words there, there). I cannot give thanks for a miracle when no miracle occurred.
Hello to Rabbi Michael,
A minor point mentioned at the beginning of your article:
A bit about the Palestinians you referred to at the start. Did you mean Israeli Arabs as well? (Those who define themselves as Palestinians? when it suits them?)
What I am trying to say is that, at the very least, from my acquaintance with Arabs (I teach at a bilingual high school, meet Arabs at the hospital, at the garage, at the mall, in cleaning at my son's school, and more), even on days when arson attacks are looming, they are no happier than we are about our downfall.
I may be suspected of bias, since who are the Arabs who come to a bilingual school? A tiny few who do not reflect the overall picture.
Still, I do not think so and do not feel so. My eyes are not blind to the many problems in this sector, but it seems to me that just as, in the depths of your heart, you incline toward kindness regarding Haredi society because of the values it preserves and because of its healthy humor and its reverence for the word of God and Torah study, so too there is room to view Arab society with a less extreme eye, and not only because of its hummus and maqluba.
And as for "It is hard to develop an intense love for their primitive, corrupt, and violent culture. When one sees the near-zero contribution of them and their fellow culture-members to world culture (apart from terror and murder accompanied by wails about deprivation and Orientalism)":
I think we have things to learn from them, including those who are our neighbors. Their attitude toward the elderly (who are not cast into nursing homes, and in general honoring parents); concern within the family (I have not forgotten the murders over family honor) and, generally speaking, less alienation and cynicism.
In short: you can go on voting Likud, but remember that the primitives are not flocking to the polling stations in droves.
And thank you for the posts. They uplift the soul.
As for Singh's book, I remember that at least in a very tiny fraction of the cases, acupuncture (and some additional herb whose name I don't remember) had small effects that could not be explained by placebo.
(This writer thinks alternative medicine is a fraud.)
As far as I remember, even in the best cases it was still very close to placebo, and one cannot draw clear conclusions. But the principle stands (the public trust these methods receive is not higher than the trust given to the other methods).
Hello Shlomi. You remind me of the speeches we got day and night about the residents of Yeruham, how much one can learn from their warmth, etc. I am not really impressed, and it seems to me that even those who said this did so merely as lip service. Obviously there are good, nice, and warm people, and still on the collective plane this is a primitive and violent culture. By way of distinction, even a gang of robbers has rules of ethics and mutual aid (I am not comparing—this is only an example to sharpen the point). One can also learn a great many things from Hamas (such as devotion to a goal, burning faith—some would say to their discredit—help for the weak (sometimes), etc.). Does that mean their culture contributed anything to the world? Very doubtful, and certainly that does not suffice to reject criticism of their violence and primitiveness).
When speaking about a society, one always deals in generalizations, and therefore the claim that you know other examples falls under the law of small numbers (though, as I noted, it may be that I too fall into it; hence what is important to me is the methodological remark and not the content). You yourself said that the sample you know is hopelessly biased and unrepresentative.
I am not one of Likud's voters (and usually not a voter in elections at all), but saying that they are flocking to the polling stations was a completely legitimate statement without a trace of racism or any other problem. Bibi has enough real problems; there is no need to go after him for things that are not there.
I wrote an answer here and for some reason I cannot find it. The spaghetti monster is intervening here again. I will try to reconstruct it briefly.
The question is very good, and I considered addressing it in the post itself, but I decided not to get into side corners.
As for the matter itself, I am not arguing that one should not seek explanations and draw conclusions from low-probability events. Certainly, if some event has a low probability, it is reasonable to assume there is a guiding hand behind it (this is really the second law of thermodynamics: in a system in which entropy decreases over time, an external factor is involved. In the language of physicists: it is not a closed system). My claim is that in the cases under discussion, this is not a low probability. Probability is a function of the number of trials, and these must be taken into account in the calculation. The probability of getting a 6 in the roll of a (fair) die is 1/6. But if the number of rolls is a million, it is almost certain that in one of the rolls you will get a 6.
Hundreds of billions of galaxies is an utterly negligible number in view of the chance of the formation of life (lower by many, many orders of magnitude than 1 in hundreds of billions). In my book God Plays Dice I presented a calculation of bounds on these probabilities (originally done by de Duve, a Nobel laureate in biology if I recall correctly), and showed this.
Take into account that we do not know random processes of the formation of life at all. This is a large scale compared to quantum scales, and therefore there is no real randomness in it. It is a deterministic process that we merely handle with statistical tools because of its complexity (this is what most biologists do not understand, because they do not know physics). I explained this in my aforementioned book and in the aforementioned booklet.
Moreover, even if the probability of the spontaneous emergence of life were reasonable, that would be within the laws and not outside the laws (see my book there, and even more so the third booklet here). The probability that such laws would arise at all is not even defined until we see that there are mechanisms that generate universes with different systems of laws (this is the problem with the anthropic principle; see there and there). And even if we assume there is such a mechanism (a bizarre and utterly baseless assumption. Even physicists who speak about multiple universes do not speak about universes with laws of nature different from ours), the probability of a system of laws that permits life is zero to all intents and purposes (this is the fine-tuning argument).
With God's help, 24 Heshvan 5777
There is an advantage to a large sample when we come to define what the rule is that reflects 'the way of the world.' But since there are also exceptional situations and exceptional people in the world, we must also provide an answer for such situations or such people. The citizen who suffers from improper treatment by people in power, or from an illness for which regular medicine finds no remedy, is not comforted by the fact that this is not a 'common affliction.' A decent society must care even for the 'tiny minority of a minority,' for each individual is an 'entire world.'
In the end, science too is built from focusing on exceptional cases; the attempt to understand what causes this exception leads us to a more precise and complex definition of the rule, a definition that can explain under what conditions the rule will operate and under what conditions there will be an exception. Scientific thinking aspires to a state in which it has a solid explanation both for the rule and for the exceptions to it, and a true scientist will devote great attention to a thorough examination of exceptional situations.
Regards, S.Z. Levinger
The cases in which conventional medicine does not succeed in coping with the problems, whereas traditional means of treatment do succeed, have long ceased to be 'exceptional cases'; the experience of many people attests to this, and today even 'conventional' institutions make room for 'complementary medicine.'
I would prefer to define natural medicine as 'early-stage medicine.' Before the 'creaks' in the 'machine' arise that require an expert 'mechanic,' it is worth investing in proper and balanced nutrition, physical activity, and cultivation of mental balance. When there is physical and mental resilience, the body will know how to cope with disease factors on its own.
When the natural dams have been breached, whether by improper use or by a strong external factor, then scientific medicine must come in, adding tools both for diagnosing and precisely defining the problem and for powerful means of treatment, such as drugs or surgeries, whose severity requires using them while coping with their not-so-simple side effects.
The ideal, in my humble opinion, is to act under the guidance of a physician with full conventional scientific training who, on the other hand, also has openness and broad knowledge in various natural treatment methods, and according to his knowledge and experience will know when and how each method can be used in the most intelligent and effective way.
Regards, S.Z. Levinger
By analogy, in problems of proper treatment of a civilian population under our responsibility, there is value in policing and judicial oversight, and no less important is preventive treatment through explanation and education, and through the personal example of commanders—how not to give up one jot on either the demands of security or the demands of human and Torah morality, which obligate us to act fairly and responsibly; to be careful with 'honor him' just as we are careful with 'suspect him.'
As for your previous remark, here is a passage from my words in the post:
It is important to emphasize that my remarks deal solely with the general question of what the IDF is like, and to what extent that can be answered from personal impressions. This does not have even the slightest connection to the question whether the IDF is in fact dealing with the (few?) cases of violence and improper behavior, nor to the question what is right and proper to do if I feel that the IDF is not handling these cases appropriately (to go to the UN and the press, or not). Even if the IDF is the most moral army in the world, and even if the number of exceptional cases is very small, there is still room for discussion regarding the ways of dealing with these cases, and whether the IDF is doing so properly. A soldier who saw one case or another perhaps cannot generalize and create a complete picture from it, but that case itself and the way it was handled he did see. He can and should ask himself whether the handling of that case was proper or not. But these questions are unrelated to the larger-picture question on which I focused here.
S.Z.L., this is part of the standard propaganda methods of alternative medicine. As far as I know, there are no indications that it works, neither on the preventive/early-stage level (as you suggested) nor on the curative level. And just because you transferred those techniques to another plane, is no evidence needed that they are useful there? Or is that transfer itself some sort of evidence in your eyes?
To my mind this is similar to Reuven claiming there is some physical law X, and when Shimon replies that there is no evidence whatsoever that the law works, Reuven answers that maybe it works on the moon. And that requires no evidence? What did you gain by redefining alternative medicine as "early-stage" medicine? Definitions are not a substitute for empirical testing.
The fact that the service is provided by health funds and hospitals adds nothing to the discussion. They are yielding to public pressure. This is a commercial question, not a factual one. As far as I know, these services cost a lot of money even through the health fund, so there is an economic consideration here with no connection whatsoever to the medical facts.
As for conventional doctors who provide alternative medicine services, the only advantage is that perhaps they will make sure you are not harmed by this nonsense (for such treatment can also cause harm. Not homeopathy, of course, because that is just water, but other things perhaps. It seems to me that most of them have no harmful potential because they simply do nothing to the body). But the fact that the practitioner is a doctor does not help cure you. When a certified doctor whispers voodoo incantations, that does not turn them into an effective remedy. At most he wants to make money, or he too is an idiot, or he is providing a service to people who ask for it without there being any scientific backing whatsoever.
To Michael,
The approach that says: I have a position and an opinion, but I would be happy to "step out" of it for a moment and examine from the side what it is based on—whether perhaps on an error, faulty data—is worthy of all praise. Since I regard myself as a rational creature, I have no choice but to change my mind.
Among pedagogical methods, the strongest is personal example. It would have been nice, in my opinion, had you shown how, in the course of the analysis, you might discover that "Oops, actually…"
Kahneman describes another bias as well, the "halo effect": take a bowl of juicy red cherries. Tempting to scoop up and swallow. Then discover a cockroach among the cherries. The cockroach creates a halo effect (evokes disgust) over all the cherries. You are invited to add the example to your arguments against Breaking the Silence. One ugly act by a soldier who got up on the wrong side of the bed creates a halo effect over the entire army. But this effect is false.
But a juicy parable is no substitute for a valid argument. It is easy to persuade through examples; we use this device a great deal. It helps persuade, but the problem is that it interferes with making a valid judgment. So please—no parables! (I found in your books several times parables that divert the discussion from the issue itself to a discussion of the parables, which is a pity.) Even so, I was persuaded that Breaking the Silence's shining of the flashlight on isolated incidents does not provide a true and general description, and it definitely changes the way I look at the army, at the question of how moral or not the army is. Following your arguments, I know that I have no idea how much "our army is moral." Certainly not on the basis of Breaking the Silence testimonies.
The main problem I found in your remarks, in my humble opinion, concerns the essence of Breaking the Silence. The message of Breaking the Silence is not that the army is immoral. The message is that there is a kind of repressed violence in each of us. Our psyche is a sea of emotions, impulses, tendencies, memories, genetics, evolution. Because of the occupation, the control over a population group that is "different," acts become possible that do not happen in "normal life." Elor Azaria, were it not for the situation of occupation, would never have imagined shooting an mortally wounded man lying on the ground in the head. Even if he were a despicable criminal. The point is indeed political, relating to the situation of occupation, not to the character of the army.
The real, existential question, as you too point out indirectly, is whether we have no choice—war is war—or whether in the present situation the price we pay is unbearably heavy, and the testimonies of Breaking the Silence bring to the surface a kind of heavy price that is usually not taken into account, and we must recruit not only force but also mind in order to break the cycle of hostility. A hint toward the right way: stop dividing into "us" and "them." Among the Palestinians there are primitives and bloodthirsty people, and there are such among the Jews too.
The true, right, and also effective division is between good people and bad people.
A footnote regarding the example about the Arabs in the bilingual school: the Jewish answer is not "they are a minority," but rather
"'Far be it from You to do such a thing, to kill the righteous with the wicked, so that the righteous should be as the wicked—far be it from You! Shall not the Judge of all the earth do justice?' (Genesis 18:25)
One must elevate those who seek the good, recognize their healing power. By their merit the world is redeemed.
Hello Haim.
Thank you for your remarks. A few comments:
1. I will try to think of a personal example. On this specific issue I saw no reason to retract, but I did note that perhaps my own remarks too suffer from the law of small numbers fallacy (I assume you do not expect me to retract without justification just in order to serve as a personal example).
2. The spirit blowing from your words is that because of the law of small numbers fallacy or all the other fallacies, there is no truth and everyone is right and it is not correct to sort and classify. I completely disagree and do not want to arrive at that desperate and despair-inducing conception. What I hope for is caution in drawing conclusions, not giving up on conclusions. Caution in distinguishing between groups (us and them), not ignoring differences between them (and moving to a distinction only between good and bad). For this reason I refuse to make comparisons (such as that there are bloodthirsty people among us and among them alike, and the like. That is true in small numbers, not in large ones; on the personal plane, not the collective one (hence my remarks about the bilingual school).
3. In general, I refuse to subordinate the true to the useful, as you do here. Even if some approach is more useful (and I do not think you are right even regarding the question of usefulness), I refuse to adopt it as though it were operating on the plane of truth and falsehood.
4. Regarding Elor Azaria, see my remarks in column 1.
With God's help, 26 Heshvan 5777
Indeed there is no room for comparing an organization that spreads lies and slanders IDF soldiers by claiming they fire machine guns at a civilian population and the like, with mistakes of the 'law of small numbers.' These are not 'mistakes' but libels. Complaints that have a basis regarding IDF soldiers are examined and handled by the authorized bodies and also reach the courts. Baseless accusations—there is no choice but to 'distance their testimony' to audiences that will buy them uncritically.
Regarding your remarks about the need for a systemic solution:
A corrupt dictatorial regime needs perpetual war in order to distract its people from the oppression and corruption at home. Both the Fatah state and the Hamas state strive for perpetual war. A democratic regime, in which the government needs the trust of the people, naturally strives for calm.
This situation often plays into the hands of the terrorists, because leaders of democratic states prefer to give in to aggressors in order to buy quiet. The problem is that every concession to terrorists is perceived as weakness, and increases their appetite; their demands continue to grow.
That was the case in Europe in 1939. They thought Hitler would calm down if Czechoslovakia were abandoned into his hands, and he conquered almost all of Europe, and later turned also against his ally the USSR and the neutral USA. And so today. The success of Arab and Muslim terror in Iran and the Middle East is bringing about an expansion of terror toward Europe and the USA as well. When the world understands that there is no escape from eradicating terror and from establishing democratic regimes in Arab countries—there will be someone to talk to!
Regards, S.Z. Levinger
With God's help, 26 Heshvan 5777
The data brought by Prof. Kahneman—that both peaks of medical success and peaks of medical failure are found in small, peripheral communities, and that both peaks of success and failure in education are found in small schools—perhaps do not stem from a measurement failure due to small numbers, but from the fact that a small place really does have advantages and disadvantages.
In a small community there is more social support, but on the other hand less ability to find high-level services, if any. Likewise, in a small school there is the advantage that the student can receive personal attention, but on the other hand the disadvantage that it is impossible to offer a variety of clubs and subjects.
Perhaps the solution is in frameworks that allow the existence of small frameworks within a large umbrella framework. For example, in a large city, to maintain autonomous neighborhood administrations that will enable greater connection with the individual without giving up the advantages of the large city. Or, on the other hand, to maintain in every area of small communities a regional center that will support the small communities.
And likewise in a large school, to maintain small classes (as the Sages required, that there not be more than 25 students in a class), and for each age group to have an educational director who will coordinate it, guide the classroom teachers, and give each student a personal response to his educational needs!
Regards, S.Z. Levinger
Prof. Kahneman apparently holds the view of his relative, the great Rabbi of Ponevezh, R. Yosef Shlomo Kahaneman zt"l, who advocated establishing a giant yeshiva 🙂
S.Z.L., what you are writing is merely an explanation of Kahneman's words (the other one). The phenomenon he is speaking about is a statistical fact (that in small samples there is a larger standard deviation and more extreme results). Your explanations at most explain how it comes about. At the end of the day, it is still not correct to rely on these findings in order to conclude that we need small schools. One can present plenty of stories that explain these results (I too wrote a few of them inside), but as I said, these are only explanations of what he said.
The fact that there is an exceptional case requires an explanation and a definition: in what situations and under what conditions is there an exception to the rule. If we dismiss all exceptions as mere 'standard deviation,' we will get nowhere.
Many of the great scientific discoveries grew out of discovering exceptional cases that did not 'fit' the rules. Researchers tried to propose a logical explanation for the phenomenon and suggested a more complex rule that explains why in certain cases there is a deviation from the known rule. Once the logical explanation was proposed, the way was opened for researchers from around the world to conduct many experiments that verified the hypothesis.
Silencing in advance a logical explanation for an exceptional phenomenon because it has not yet been measured in large numbers is the premature strangling of all scientific progress. Let the logical analyst offer his explanation, and let the testers come and test it.
Regards, S.Z. Levinger
As for the suggestions I raised for combining the advantages of a large and a small framework, I did not develop them from the survey discussed by Prof. Kahneman, but from some experience I accumulated in my life.
My remarks about a regional framework supporting small communities—I see this with my own eyes both from my period of residence in Nokdim and from my period of residence in Kokhav HaShahar. Suffice it to mention the pediatrician under whose 'care' my children grew up, Dr. Mati Erlichman, who was a regional pediatrician in the Binyamin communities, and from that position was promoted to become director of the pediatric emergency room at Shaare Zedek. If there had not been a regional framework, and each community had had to find its own doctor, it is likely there would have been far less chance that everyone would get a doctor of that caliber.
The source of inspiration for my remarks about educational coordinators for age groups in a large school I drew from the figure of Rabbi Yehuda Gabrieli, head of the middle school at Ulpanat Ofra. During the period my daughter studied there, I went in to see him at one of the parent meetings, and I was astonished that the principal knew in detail my daughter's educational and academic situation (there were four classes in the cohort!). R. Yehuda explained to me that because he was not burdened with administration and budget, he was free 'neto' to be an educational director who gave thought to each student as to an 'only daughter.'
Anyone who wishes is invited to test my insights statistically. For me, what my eyes see is enough.
.
Michael, apparently I erred in my formulation, if one can understand from my words
A. that because of the law of small numbers fallacy there is no truth. On the contrary. No one believes in truth and in holding fast to truth more than I do! Even so, there is no connection between holding fast to truth and validating every classification. There are classifications that distance one from the truth, and therefore in my eyes they are invalid.
B. I never subordinated truth to the useful. Truth is above all. I wrote that the division into good and evil is a true and correct description, and also—how nice—effective. Even if it were not 'effective,' it would still be correct and true. And it is the basis of everything; it is the precious souvenir we carry from the Garden of Eden: knowledge of good and evil. (Of course, the subject of distinguishing between good and evil, i.e., ethics, is a vast sea).
Hello Haim.
You are moving the discussion onto the political plane, and there is no avoiding recourse to it.
Our discussion is not about whether the division between good and evil is true/useful. You made life easy and comfortable for yourself. We all agree that it is both useful and true.
The more difficult question I asked, which arose directly from your words and which for some reason you did not answer here, is this:
You wrote that in your opinion the distinction between Arab culture and ours is not effective and not useful (and therefore it is preferable to distinguish between good and evil). Are you claiming that it is also not correct? That it distances from the truth?
Now note the meaning of your answer:
If you claim that it is not true—then you have a problem with the law of large numbers. And if you say that it is true—then it turns out that the useful is not the true (and from this it follows that in your remarks you did subordinate the true to the useful. Indeed you did so despite your denials).
Alternatively, you could say that it is both useful and correct, and then we have no disagreement and your identification between the useful and the true has not collapsed. But unfortunately, that goes against what you wrote in your first comment.
S.Z.L.,
It seems to me that logical analysis cannot precede statistics. It itself is based on accumulated experience, which itself presupposes statistics. You are right that there is significance also to prior experience and common sense, not only to current statistics.
My claim is that one must still beware of stories that sound good (fit our current perceptions), because they have a problematic tendency to subordinate the statistical findings to themselves.
In short, even if we have a thesis that sounds logical, when one comes to support it with findings one must do the statistics with due caution. One may simply make a claim by force of common sense (as you did here)—and that is perfectly fine. I deal only with situations in which statistics are brought to support such a claim. Here caution is important (do not use small numbers, like the examples you yourself brought. That is a classic case of small numbers).
To sharpen the point: if there is someone who does not agree with you about the basic assumption, a statistical finding from small numbers (like your examples) will not persuade him. And if he agrees with you, then the examples are unnecessary because he already agrees. My claim is that day in and day out people bring such findings to persuade those who hold opposing views (as with alternative medicine and the other examples I brought). Note this well.
To complete the clarification, which in my opinion is the center of the discussion. Correct: the argument is not philosophical. Breaking the Silence is not the Central Bureau of Statistics; rather, it is political-moral.
Perhaps "on average" the level of primitiveness among Jews in Israel is lower than the level of primitiveness among Arabs in Israel. Suppose so. If so, one can declare that "on average, in a sample of large numbers, the level of primitiveness is such-and-such." You attribute to me the following claim: "…you wrote that in your opinion the distinction between Arab culture and ours is not effective and not useful (and therefore it is preferable to distinguish between good and evil). Are you claiming that it is also not correct? That it distances from the truth?…" But I, nowhere (you are welcome to check), assigned grades either to Arab culture or to Jewish culture. Even if under a statistical test the claim is 'true,' in my opinion it is a claim of the type 'the average depth of the water in the pool is 30 cm.' Even if that is correct and the claim is 'true,' it still does not prevent drowning. To prevent drowning, the datum of the average depth of water in the pool may be a 'true' datum, but it is not important. (And forgive me for using an analogy to demonstrate my argument, despite declaring that I am against analogies as arguments…)
I argue that the claim is true (perhaps), but not useful. It is precisely this possibility that you do not mention. And that was already my claim in my original comment.
And one final note. At the beginning of your original remarks you write—by way of disclosure—that you do not support Breaking the Silence. You write that the descriptions regarding soldiers' behavior "are not credible." To the best of my knowledge, no testimony of Breaking the Silence, not even one, has been refuted on the spot. So there is no room here at all for credible or not credible.
When eradicating evil, there is no room to do statistics according to the law of large numbers, nor according to the heuristic of small numbers. One must shine light on evil, denounce it, and eradicate it. And let our camp be holy.
You wrote that your remarks are both true and useful, and that you do not subordinate truth to the useful. Now you are doing exactly that. If you write that a claim is true and not useful, and I write that the claim is true and do not address the question whether it is useful, then what are we arguing about? It is hard for me to discuss claims that are both a thing and its opposite.
The claim about culture is in no way similar to the claim about the average depth of a pool. The difference is that culture always characterizes a collective and collective behavior, and therefore there the discussion is inherently about collective characteristics, not about individuals who can be of all sorts. Therefore, to say that there are Arabs of all sorts is actually a statement (true but) irrelevant to the discussion.
A comprehensive review, based on studies that have been conducted, of the various fields of complementary medicine, and an examination—out of appreciation, openness, and criticism—of the efficacy and safety of the treatment methods offered by a range of its approaches, can be found in Prof. Yonatan Halevy's book (director-general of Shaare Zedek Medical Center), 'Complementary and Alternative Medicine—All the Facts' (2005). Studies on complementary medicine were collected in the journal of the Israeli Medical Association, 'Harefuah,' issue 154 (January 2015).
Regards, S.Z. Levinger
Hello, tzaddik (with the stress on the first syllable, of course)
I very much enjoyed reading your column about Breaking the Silence and the rest of the vegetables.
The lethal combination of Litvak–Chazon-Ishnik, Gushnik, and physicist leaves no oxygen to breathe for a Hasidic soul.
Two light remarks:
1. The accepted term for what you call a "story" is "sippar"—narrative.
2. Placebo is 40% (as you wrote), not four! Therefore, out of a thousand who recover, four hundred recover, not only forty as you wrote. This improves your argument tremendously! I was delighted to catch you in a mathematical error.
Be healthy, a healthy winter
Hello, our rabbi.
I was glad when they said to me that Rabbi Yehuda HaNasi is among my readers. And if I have managed in my way to destroy yet another Hasidic soul—let that be my reward (as it is said: let Hasidism come to an end, but not the Hasidim). 🙂
I pulled the number 4% out of my stomach (at first the example dealt with a group of a hundred, and then I enlarged it to a thousand without changing the number of people cured), merely as an illustration. If it is 40%, then indeed the argument improves tremendously, although I am skeptical about the ability to set such a number, since in every type of illness the percentage changes. I assume advanced cancer is not cured in high percentages by placebo.
As for the "sippar," I considered using the term and decided not to surrender to the winds of the times. Though I must note that the meaning is not exactly the one accepted among our postmodern cousins, but perhaps some generalization of it.
Fine and good.
I know a Jewish woman, a doctor from Hadassah, whose research work was on placebo and came to 40%.
Of course, the main point is that it makes no difference at all whether we are talking about a runny nose or cancer of the left kidney.
I fished this from Wikipedia:
Placebo effect
In the 1950s a new surgery was introduced to treat coronary heart disease and those suffering chest pains as a result of this disease. In the new surgery an artery in the chest was tied off. About 40% of the patients who underwent the surgery reported the disappearance of the chest pain, and their physiological indicators also improved.
A group of skeptical doctors thought the surgery did not help and performed the following experiment: they divided patients who were designated to undergo the surgery into two groups at random. Members of one group underwent the surgery. Members of the second group were brought into the operating room and anesthetized; an incision was made in their chest and then stitched up, without operating on the artery. Both groups showed identical improvement in their condition after the surgery. The use of the surgery was discontinued, after between 10,000 and 15,000 such surgeries had been performed in the United States.
Be healthy,
Yehuda
I have to say that it seems completely implausible to me that the rate of recovery by placebo does not depend on the illness. I find it hard to believe that placebo healing cures severe cancer (I am not talking about improvement in feeling but about cure. Therefore the report you sent does not really impress me).
If you take placebo healing as indicating that there was no illness in the first place, then of course you are right (because there is no difference between a severe and a mild "non-illness"). But that is only one of the cases that fall under placebo. There are cases of actual sick people being cured by placebo. It seems to me that if you were right, then this is really a startup, and I do not understand by what right they stopped those surgeries. In severe situations they perform surgeries whose success rate is lower than 40%. So why not keep tricking the patients and doing all kinds of nonsense to them (perhaps less significant than tying off an artery, just anesthetizing them and waking them up and telling them stories).
In short, implausible. I would be glad if you asked her again whether indeed the cure rate does not depend on the type of illness. After all, there are diseases whose cure rate under full and correct medical treatment is lower than 40% (there are even some for which the rate is 0 because they still do not know how to cure them). Are you/she claiming that placebo will work there too in 40% of cases?
Surely it is not even plausible that they tested this on all diseases. So how can one determine that the effect does not depend on the illness?
I am betting this is nonsense, but perhaps I too am captive to conceptions.
With your permission I will also connect this column to your remarks about providence.
Here we have a case, highly exceptional statistically, and there is no way to rule out that it happened because of providence.
How will you know? We will not know. On that we both agree.
My question is: if even such a highly exceptional case we do not ascribe to providence, why not exempt providence from practical discussion and discuss it only by means of outlook and belief?
After all, a religious person claims there is providence because of the assumption that we have a tradition for it. If you undermine the tradition, fair enough. If you prove otherwise from the Tanakh or from Hazal, fair enough.
But to move to the practical plane? I do not understand.
After all, there is almost no case that you would ascribe to providence, so why not simply give up on the empirical test in this matter?
Every scientific law is the product of observations + common sense. You can always find excuses that explain the findings otherwise. Common sense says that the simple explanation is the correct one. Therefore I do not accept the excuses that the Holy One, blessed be He, hides every time one tries to see Him; rather, apparently He is simply not there, and that is that. Nor can you deny that I have next to me a fairy with three wings and two horns, when every time you look she hides. So is it 50-50 in your view? That is Russell's celestial teapot.
The important point is that Hazal also knew no more than you and I do on this subject, and therefore I do not see them as a source of authority for these questions. They looked at reality and at the Torah and drew conclusions. I do that too. Therefore I see no pressure in the fact that I do not accept the words of Hazal on factual and theological questions, and I have no reason to look for excuses.
You are entirely right that in my worldview it will be very hard for me to detect a miracle even if it occurs before my very eyes (there will almost always be another explanation available to me). On the other hand, what can I do—this is the truth. Because it is hard to detect it, should I therefore accept that it happened even if I did not detect it? That logic is very problematic.
I think I finally understood the disagreement between us; I understood where the somewhat dialogue-of-the-deaf feeling I had was coming from.
I come from the assumption "we have a tradition that there is individual providence," and I thought you were claiming that nature proves there is no providence, whereas you come from the assumption that there is no tradition about this and ask whether we should innovate and say there is providence; therefore you rightly argue that there is no reason to introduce something like providence in today's information age, when there are not many puzzling phenomena that cannot be explained.
Therefore I want to steer the discussion in a different direction.
Let us begin by asking for your agreement that I have indeed understood you correctly: in the rabbi's view, is individual providence (and I assume also Messiah, resurrection of the dead, and so on) a principle that Hazal conceived on their own?
Assuming the answer is yes, I will continue and ask:
Assuming that individual providence is from the prophets, or alternatively a halakha given to Moses at Sinai, do you still think your arguments suffice to refute it?
From here I come to my main request: does the rabbi have a source showing that this is not a halakha to Moses at Sinai?
Because I too agree that reality does not compel one to create(!) a novelty of individual providence, and the only reason I believe it exists is because of Hazal, on the assumption that it did not come only from looking at the world.
Hello Netanel.
That is almost accurate, but the description is a bit too dichotomous. I do not know whether there was a tradition here or not. It is possible that this is a reasoning, and it is possible that it is a tradition. In addition, the reality around us plainly shows that there is none (though one can reject this with great strain). In addition, there is the possibility that God's mode of conduct in the world changed, and therefore even if once there was individual providence (like prophecy or miracles), nowadays that could have changed.
The only thing that would force me to strain my perception of reality is if you show me that there is a tradition (from Sinai or from a prophet, and not from reasoning) that this exists, and that the tradition also establishes that it continues forever. I greatly doubt that you can show this, and therefore common sense (to the best of my judgment, and I understand that you agree) remains as it is.
Again, you are thinking from a somewhat different angle than I am, so it takes me time to sync up.
This is also the place to apologize for scattering my comments over several places on the site; I thought I was asking from different angles, and now I understand that it all converges.
I am trying for a moment to think about the development of the principle of individual providence.
In the period of prophecy, I think we both agree that there was providence, rather densely, certainly at least on the national level of the people of Israel.
And then we went into exile.
Who innovated that providence diminished?
Would it not be more correct to assume there is providence until proven otherwise?
And when speaking of a reduction of providence, it would be proper to put this into a clear process; after all, we are taking away a principle that existed. One ought to rely on the Song of Ha'azinu or something of the sort; to invent from the heart that it does not look as though there is providence sounds strange to me.
Why is it that with providence you 'dare' to say it has lapsed, whereas regarding the effect of the mitzvah of Sabbath observance you do not?
If God's modes of conduct have expiration dates, then where do you stop?
I do now understand your opinion more clearly, but the way you chose to raise it strikes me as odd and really grates on me.
I would have expected, and forgive me if this sounds insolent, that the article would be directed to proofs that there is no source in the Tanakh for providence, that there is no biblical reason to assume there is providence today, to prove that Hazal innovated from their own hearts that there is providence in exile too; after the table is clear, one can begin to discuss.
And even when discussing, looking at reality through overly scientific glasses gives an incomplete picture. One must factor in parameters such as 'religious overarching goals,' 'national overarching goals,' 'advancing divine processes,' and I do not know what else.
All this was missing for me; pardon me, but it sounds to me like the atheistic question: if there is a God, how could there have been a Holocaust?
I would be glad for a reply,
despite the insolence with which this comment was written,
I will comment again, just in a less emotional summary form.
After you admit the existence of providence in the time of the prophets, let us ask: were there not laws of nature then? Certainly there were. Would not all your difficulties have existed then as well? Certainly they would. So use your answers there for today's reality.
Second, whence comes the innovation of the cessation of providence and the cessation of the power of prayer? I am speaking on the plane of authority: after the authority of the prophets, who said it exists, by what right do you deny it?
Continuing this comment, according to the explanation you gave, the case that happened to you on the way back to Yeruham should be interpreted as a miraculous case. Granted, if out of 1,000,000 trips to Yeruham such a case happened once, I would say fair enough, but even out of all the trips you made in your life, the probability that such a case would happen still sounds implausible, and therefore it seems that there is nevertheless something miraculous here.
Not at all.
First, there are others who travel too, so the overall space is not only my trips but all the travelers who got stuck at night. There are many such cases.
Second, regarding the accident in Gedera, I know that there are many other cases of people traveling and many who got stuck, and therefore I say that the determination that this is a miracle requires checking how many such cases there were and how many of them were "saved" in this way. By contrast, I have no information at all about the spontaneous formation of many other worlds and many other universes, or attempts of chains leading to the creation of life. Therefore here it is not enough to say that one needs to check whether the number of "successful" universes or chains is reasonable relative to the total number; one must add the assumption—a baseless speculation—that indeed there were many other such universes/attempts (universes, each with other laws of nature).
Hello Rabbi,
As a continuation of the discussion with "Elad Sh" and "Oren": in response to the question why there is no connection between the law of small numbers and the physico-theological proof, the rabbi answered: "My claim is that in the cases under discussion this is not a low probability. Probability is a function of the number of trials, and these must be taken into account in the calculation."
My question is: which trials should be included in the calculation? To the best of my understanding, logic says to include in the calculation only the trials whose outcomes I know. If additional trials were made but I have no way of measuring their outcomes, I do not see a reason to include them in the calculation, or to reduce the degree of reliability of the calculation I obtained. Of course, if I examine additional cases, my accuracy and reliability are expected to improve, but insofar as these data are unknown to me, I must draw conclusions from what is known to me (with the awareness that there is a certain statistical chance that perhaps I happened to fall upon unrepresentative data), and the degree of reliability of my calculation does not depend on the number of trials in the world but on the number of trials I measured, as an absolute rather than a relative value.
Therefore I did not understand why it is relevant how many other people also got stuck at night (as the rabbi wrote in his reply to Oren)? Ostensibly this is similar to someone who conducted an experiment with all the required conditions and in the results there was clear statistical significance, and then it became clear to him that this experiment had been performed in history (or will be performed later in the future—I see no difference) such a great number of times that it is plausible that one of them would emerge with statistical significance of this sort, even if the results do not reflect reality (the results of the other experiments are unknown to him). In other words: although it is known that if everyone follows such a path of drawing conclusions, it is certain that there will be a minority whose conclusion will be incorrect (if they are not aware of others' results, of course), still, ostensibly this does not change the reliability of my calculation. As far as I understand, there are two ways to calculate the probability of error, but their result will be identical: whether we calculate the chance that I am the one who errs and not the others, or whether we calculate the chance that I fell upon unrepresentative data.
If I return to the examples from the post, then in some of them I do not disagree, but in all the examples involving a one-time experiment with an exceptional outcome (in the example of alternative medicine the rabbi simply explained that the result is not truly exceptional, so that example is not relevant to my point), I indeed do not understand why it is not logical to draw conclusions from it. In the example of the letters and the numbers, admittedly one of them will have a chance match, but what is the probability that I am that one? Likewise in the accident story. It seems to me that the real reason not to assume the above conclusions is that although we are dealing with a very exceptional result, the conclusion that the sender of the letter has supernatural powers is less plausible than that he is a charlatan and a coincidence happened here, because of the paucity of people with supernatural powers and the abundance of charlatans. I think that if this happened to me three times, I would believe it, and likewise regarding the accident (there too it seems to me that the discussion is whether, after a careful assessment of the probability that such a case would occur [which of course is very difficult to assess], the more plausible conclusion is that this is a miracle or not. If there is no external reason to assume that it is not a miracle, then ostensibly that is the required conclusion [except that I assume there are people who have other reasons to assume that it is not a miracle]. But on second thought I think this really is a good example of erroneous inference, for here the number of trials is indeed enormous—but the trials, in my opinion, are not the number of other travelers who got stuck, but essentially the entire life of the person as one huge sequence of trials in this sense [and some might say not such a successful one]; I mean: since the 'experiment' here is to prove a 'guiding hand,' which is not such a well-defined thing and can operate in varied ways, at almost any moment such a story could arise, one upon which some sort of 'guidance' could be imposed. In other words—the probability that in the course of a person's life nothing of this sort will happen to him seems to me very small indeed]. In the example of 'Breaking the Silence,' to the best of my understanding we are dealing with quite a different inference. Of course it is not correct to draw decisive conclusions about the general picture on the basis of one case, for the simple reason that even a minority is still quite a common thing.
I disagree. Take, for example, the case of Gedera. Suppose you know that there were many other such cases in the past but do not know the outcomes (whether a neighbor with a large empty vehicle passed by there or not). The assumption is still that this is normally distributed, and therefore my case does not raise a probabilistic difficulty. True, one cannot establish this positively, but one also cannot raise a difficulty (how did this happen? a statistical miracle).
Regarding the formation of life, I discussed this in the booklet and in the article and in the book. Estimates of the number of trials lead to results with a tiny number of trials relative to what is required (de Duve's estimate). Beyond that, the laws of nature are the same in all galaxies, and the argument from the laws remains intact.
Thank you for the quick reply. [Regarding the rabbi's reply I did not understand what he meant by "True, one cannot establish this positively" (establish what?), and regarding the second paragraph about the formation of life I did not understand what he meant to defend, since what follows from my remarks only strengthens the physico-theological argument, and I did not come to challenge that at all (indeed, from what I remember the rabbi touches on a point similar to the one I raised in my comment in his book, but I read the book several years ago and do not have it at hand to consult now).]
Regarding the subject itself: indeed, the assumption is that this is normally distributed, and there is no 'probabilistic difficulty' that it happened in the world (!) since one would expect this to happen somewhere, but what is the probability that I (!) happened to fall upon the measurement of a minority by natural means? The rabbi answered "statistical miracle," and I do not understand, for this is precisely my claim: that the probability of falling upon the minority is sometimes smaller than the probability of a guiding hand; that is, if there is good reason to assume that the guiding hand is interested in the minority and there is no other reason to assume there is no guiding hand, then it is more logical to assume there is a guiding hand than that I fell upon the minority, unless I myself measured additional results (though the probability of the minority would have to be small enough to overcome Occam's razor; I agree that not every minority meets that requirement, of course [otherwise every trial whose outcome was a minority would be proof of some entity that for some reason is interested in that minority, which is of course absurd]).
I would be glad if the rabbi could address the analogy I gave earlier regarding the experiment; I thought it was a good example. I can give another example: if a person conducted an experiment to test whether a certain die is biased, he would almost never be able to achieve sufficient statistical significance, because in history there has been an enormous number of die rolls. Likewise, if he had done precisely the same experiment in the year the die was invented, the experiment would have been crowned with tremendous success. This seems patently unreasonable. (The alternative, that future experiments also diminish the importance of the experiment, seems to me no less unreasonable; go out and see that no one is concerned about the possibly infinite future before us in which all sorts of experiments will be conducted, etc.) And even "in reason" I cannot understand why, if someone else also conducted an experiment like mine, that changes anything in my experiment; after all, the probability of being the exception among the testers equals the probability that my data will be exceptional relative to the data of the other testers, as I already argued. Thank you in advance.
If you did an experiment of 200 die rolls now, and what came out was a sequence of 200 consecutive 6s, that is a statistical miracle. It makes no difference at all that there were many experiments in the past, or that there will be in the future. Only if you did many experiments and then, in a tendentious way, selected from among the results before you some special sequence—only then can one not raise difficulties from the uniqueness, because out of enough rolls there will almost always be such a sequence. But there is no difference whatsoever between past and future in this respect.
To my understanding, up to here I agreed with every word the rabbi wrote in the last reply. The rabbi writes that only if the selection is "tendentious" can one not draw conclusions from it, of course. If I examine all the results known to me, is that a tendentious selection? As I understand it, a tendentious selection is only one that knows the other results and deliberately chooses to analyze only part of them. It follows from this that if something happened to a person as a single case, and he has no other data (even though it is known that there were additional cases like his but the results are unknown to him), and he chooses to infer from the case that happened to him, his choice is not tendentious and therefore his conclusion is valid.
To sharpen the point: I do not understand whether the rabbi claims that the case mentioned in the post of the book "Think of a Number" (the letter in which there was a match in numbers from one to a thousand) is not a "statistical miracle" [and if that is his intention I would ask what the difference is between this and the die experiment that the rabbi mentioned in the last reply, which he said is a statistical miracle], or whether the rabbi admits that this is a "statistical miracle" and nevertheless claims that no conclusions may be drawn from it [and here I ask why, for ostensibly if the solution of the sender's "supernatural powers" were not itself a poor explanation, then ostensibly it is preferable to the explanation that a "statistical miracle" occurred here, and that would be the required conclusion]. Likewise regarding the Gedera case.
I do not understand the question. And the yeshiva-style 'inquiry' whether it is called a miracle but one cannot learn from it, or whether it is not called a miracle at all, also seems to me mere wordplay.
If you want to discuss, please formulate briefly and clearly the current question. I lost you.
(This is not an inquiry at all; all I was trying to do was raise sides in order to understand what the rabbi agrees with and what he disputes, since I did not understand how he addressed the point I raised.)
My question is utterly simple: how is the number of trips made by others at night relevant to the question whether the Gedera case is a miracle? Ostensibly, since the outcomes of their trips are not known to us, and we included in the calculation all the trips whose outcomes are known to us, this is a non-tendentious selection of data and we should draw conclusions from it. (And therefore one should weigh how likely it is that this happened by chance against how likely it is that there was a guiding hand.)
A successful trip selects itself, as in the example 'think of a number.' Everyone for whom it did not work, of course, pays no attention to the matter; the one who points to a success is only the one for whom it succeeded. Therefore there is nothing to wonder at here. De facto, this is a situation in which you choose the successful outcome from among them all.
As in the argument against the anthropic argument: we live in the successful case because in all the others we could not have lived. The problem there is that there is no reason to assume that there were additional attempts, unlike the accident in Gedera.
Why "pays no attention to the matter"? I pay very close attention to the fact that nothing unusual happens to me; it's just that there is no conclusion to be drawn from such events. Only when an unusual event happens do I have something to infer from it. But my claim was that the trials included in the calculation are only the things known to me and not to others, and I should calculate only the number of trips I myself took at night (including some ordinary trips too, of course, but there is still clear statistical significance here), and not those of others. Of course I, from the rabbi's case, cannot infer that a miracle happened there, because there was a reason that people would tell me specifically about unusual trips that happened to them and not about ordinary trips; therefore there is indeed no surprise that from time to time I hear about events of this sort. But my claim was that the rabbi himself should infer this [were it not for the reservation I presented in my first comment]. That is: one must distinguish between the case of a person who observes only himself—then an exceptional event should lead him to infer a conclusion, because it is surprising that it happened to him (since this is an exceptional event out of a small number of trials)—and someone observing all people together, for whom there is no surprise that one of those observed had an exceptional event happen to him (because this is one exceptional event out of a large number of trials).
Again, I did not understand the relevance of whether trials are being made in additional universes or not, since with respect to us, who conducted only one experiment, this is not relevant.
To sharpen the point: my claim was that a person who made one trip and was saved has no reason to assume that if he checks all the other trips he will discover that no one else was saved and that he is the ordinary statistical minority; rather, it is more reasonable to assume that it is a miracle, and that the statistical minority is within the majority group whose outcomes he did not check (because the probability that the statistical minority would be specifically he himself is very small, whereas in the majority group it is almost certain that it will be there).
I am ending this pilpul here with one last attempt.
The person who was saved knows that there were many other cases. The normal distribution is known; the probability that there will be a successful case is 1 in a million.
Now he was saved. Is that wondrous? No. He is the one case. You write that there is no reason to assume the others were not saved, and I claim there is. The known probability is that the chances of such a case are negligible. That is all.
I understand that the rabbi does not wish to invest more of his time, and I am somewhat sorry, because I felt that we had finally begun to communicate a little. In any case, it seems to me that what the rabbi has written now is the very mistake taught to every beginner in statistics: namely, that the fact that on the first roll a six came up on the die does not lower the probability that in the next five times a six will come up. Therefore, in the rabbi's example, the fact that I got the rare result of one in a million is not a reason to assume that not one of the other million people who performed the experiment also got such a result (even though the probability is tiny, nevertheless the group whose results I do not know is large enough), and on the contrary, the probability says there is an excellent chance that one more person got such a result (the statistical minority). Therefore there is no reason to assume that I am "the only case," which is rare; rather, it is more logical to assume that the statistical minority fell to one of the others and that I am a miracle. I will understand if the rabbi does not respond; sorry for the audacity, and thank you for the time and patience.
It really is not. But indeed we have exhausted it.
Let not the rabbi be angry with me, and let me speak but this once more (I undertake not to trouble the rabbi anymore, except that I think I have found a short parable that encapsulates the matter well. I am sorry that the rabbi sees this as pilpul, since I really only asked one genuine question in search of truth, and I think the matter fell victim to a communication shortcoming).
Given the following data: there is a city with 1000 gates. Inside the city there is known to be one male and 999 females. At a known moment, all the inhabitants leave it, each through a different gate. I observe only one gate, and at every other gate there is another observer. In addition, I have a prior doubt: there is a probability of one in 100 that my body has a special property that causes anyone who goes out through the gate I observe to turn into a male one second before I observe him. These are the preliminary data. The result was that indeed a male came out of the gate and not a female. My question is: what is the more reasonable conclusion—that I do not have the aforesaid property and this is a coincidence, or that I do have the aforesaid property? My assumption was that the required conclusion is that I have the aforesaid property (with a probability ten times greater than the alternative). I think the analogy to the Gedera accident (and also to the physico-theological proof, even given that there are attempts to create life in additional universes) is clear (the analogy: the property = the guiding hand). I would be glad to know where the rabbi disagrees: does he disagree with my conclusion in the parable, or is there no connection between the parable and the analogy.
Yehuda,
In your parable, if the chance that you have this ability is 1/100, and the chance that a male would come out just like that is 1/1000, then I agree that it is more likely that you have this property.
I did not understand the analogy to the Gedera accident or to the proof. In my opinion there is no connection whatsoever. In accidents, with respect to all of them there is the question of a guiding hand. There is nothing special about this accident. It is not like the gate, which is special in that you are standing next to it.
But indeed I am done. Forgive me.
Thank you very much. All the best
([For clarification, I do not ask/expect a response to the following text, or even that the rabbi read it {both because I want to keep my word and because "the time" begins today…}:]
The analogy is perfectly exact. I do not understand the intention of the rabbi's rejection that the gate is special in that I am "standing by it," unlike the trips:
Possibility A — in the parable, only the possibility was given that I have the special property and not the others, unlike trips, where all trips are candidates for a miracle [up to here]. My reply: and if we add to the parable the datum that if I have this property then certainly all the other observers have it too [and the probability remains 1 in 100], would that change anything? Of course it would not change the conclusion of the parable at all, so long as I do not know what the others saw [therefore I did not see any need to add this to the parable].
And if someone asks that now there is no longer any resemblance to the analogy, for surely if one miracle happens, not everyone experiences a miracle, as our eyes plainly see—his reply is: the assumption of the discussion was that the rabbi's rescue is more plausible if there is a guiding hand, but not certain. So too in the parable: if we assume the property does not always transform a female into a male, but only in fifty percent of cases, the conclusion remains the same [not with the same probability, of course]. And in the analogy—if we assume that specifically the rabbi's rescue fits a guiding hand and not another person's rescue [or fits to a lesser degree]—then the rabbi's distinction does not get off the ground. If we assume that everyone is equally eligible for rescue like the rabbi [which seems to be the rabbi's opinion], then there is no reason to assume that the unchecked trips are distributed normally according to nature, since if there is a guiding hand, the assumption of the discussion is that this is not so; and since that is precisely what is under discussion, whether there is or is not a hand, if the rabbi assumes the rest of the trips are distributed normally—then the rabbi has committed the fallacy of *begging the question*, namely, that there is no guiding hand.
Possibility B — the rabbi means to distinguish on the grounds that the gate is special in that I came to measure only it and not the others [without connection to the special property in the parable. Up to here]. My reply: of course there is no distinction, because as I wrote, a person measures only the trips he knows [that is, his own trips] and not those unknown to him [the trips of the whole world], in a way completely parallel to the gate. [The fact that he can check the results of additional trips changes nothing. Of course, in the parable too, if we add the datum that he can now ask his friends what they saw but does not ask, this plainly does not change the conclusion of the parable].)
Not at all from a place of criticism, only striving for truth. The book you mentioned is called "Think of a Number."
First, criticism is excellent too. Second, why think there is criticism here?!
In any case, thank you.
If the miracle of the ride from the trip by car had repeated itself another 5 times, would the rabbi still not see it as a miracle?
In practice you have eliminated every possibility of a miracle.
Why is it so important to the commenters here to define and recognize the "miracle"?
Apparently it is the longing to break through the limits of reality. A dream. A fantasy.
To overcome gravity and fly.
Who knows, perhaps even to overcome the unavoidable decay whose end is unavoidable death.
Sunday morning. On Kol HaMusica they are broadcasting Glenn Gould playing the Goldberg Variations. If the word miracle has any meaning, that is it.
In reply to Adi.
The remark is correct. If there is an indication of the relation between the probability and the number of cases that occurred, one can speak of miracles. If not—then indeed it is very hard to argue for the existence of a miracle in the statistical sense. There are miracles that are against nature (not statistics), and that is something else.
There he explained to the astonished ears of the listeners that he sees in this no miracle or wonder whatsoever, but an event that is entirely statistically possible.
??????????????????
Ramban, at the end of Parashat Bo, chapter 13 verse 16: …for a person has no share in the Torah of Moses our Teacher until we believe that in all our affairs and all our occurrences, all of them are miracles; there is no nature in them, nor the ordinary course of the world—whether for the community or for the individual. Rather, if one fulfills the commandments, his reward will cause him to succeed, and if he transgresses them, his punishment will cut him off—all by the decree of the Most High!!
Come on. There isn't a single person from Dan to Mozambique who doesn't know this Ramban. What is the point of quoting it again and again?
More power to you for these remarks!
A question that came to me בעקבות reading the article: in your book "God Plays Dice" you present an argument according to which the probability that life developed without divine creation is so low that it pushes us to explain that the world was most likely created by God. In this article, by contrast, you argue that the attempt to look for an explanation for phenomena whose probability is low is mistaken, since according to the law of large numbers even low-probability phenomena are realized at some point, given a sufficiently large sample, and one should not look for an additional explanation for this, as in the story of the "miracle."
My question is why similar things cannot be said about the creation of the world. A quick check on Wikipedia reveals that according to estimates there are hundreds of billions of galaxies (and many times that number of planets). Why, then, should we not say that the fact that there is life on Earth is simply the realization of a low probability in light of the law of large numbers, given the enormous sample of planets?