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What To Do When The Trisector Comes claims that most cranks (for lack of a better word) are old men (trisector refers to a specific type of crank):

One obvious characteristic of trisectors is that they are old. The typical trisector heard of the trisection in his geometry class, but did not succeed with his construction until many years later, usually after retirement. "His" in the last sentence is not sexist because almost all trisectors are male. From the two female trisectors I know of, it follows by an invalid statistical calculation that we can be 95% sure that the proportion of female trisectors is less than .04. Women have too much sense to waste time on such things. Trisectors are old men.

(Can't tell if "invalid statistical calculation" is a typo in the source)

I'm looking for:

  1. A more detailed explanation for why cranks tend to be male (more detailed than "Women have too much sense to waste time on such things"). References would be even better.
  2. An explanation for why cranks tend to be old.
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    So, I think it’s okay to use the term crank for the purpose of this question and maybe mark that it’s for lack of a better word. The important thing is that we do not denote any particular individual as crank. Compare to the use of troll. Calling some user of this site troll is offensive; but when discussing how to deal with trolls (in general) on Meta, it’s okay to use the term troll. – Wrzlprmft Mar 10 '20 at 7:19
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    Comments are not for extended discussion; this conversation has been moved to chat. Please read this FAQ before posting another comment. – Massimo Ortolano Mar 11 '20 at 18:43
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    The phrase "invalid statistical calculation" is exactly what was meant. It succinctly expresses the facts that (a) the author knows full well that their data sample is too small to conclude anything useful with 95% certainty, (b) they proceed to do so anyway, so (c) you should not take the following figures too seriously. – Adam Chalcraft Mar 12 '20 at 7:50
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In order to assess this claim, it is important to first bear in mind that classification as a “crank” theory actually requires a reasonably high level of technical development. For example, in the linked article on trisection of an angle, it actually takes quite a bit of skill and work even to come up with a plausible-sounding false theory of how to do it. There are almost certainly millions of adolescents in geometry classes around the world who would think that you can trisect an angle using straightedge and compass, and are willing to give it a go. You would probably find thousands who think they have figured out how to do it. The reason we don't class these kids as “cranks” is not because they are any smarter than the “cranks”, but just because they lack the time and technical skill to put forward a plausible-looking method, backed up by technical argumentation. Even if they did, you wouldn’t tend to call an adolescent a “crank”, since the expectation of knowledge is lower.

Secondly, one should consider the likely preconditions for spending a large amount of time trying to prove something that professionals in the discipline assert to be false. This will generally occur only if: (1) the person is of the view that these authority figures are fallible, and there is some reasonable prospect of success; or (2) the person gets direct enjoyment from the challenge, regardless of its impossibility. Therefore, a “crank” is more likely to emerge among people who are either sceptical of institutional and professional authorities, or among people who get direct enjoyment from playing with technical problems. Having then found a “solution” that appears plausible to them, what are they supposed to do? Keep it to themselves?

Thus, assuming that your hypothesis is true (i.e., that most “cranks” are indeed older men), I would posit that the most likely explanations are probably a combination of the following factors:

  1. There are far more men than women in technical professions that give them the requisite skill to develop a “crank” argument (ergo more men than women);

  2. There is strong evidence that men score lower than women on the personality trait of “agreeableness”, and they are also much more interested in things in the people–things dichotomy. There is some psychological evidence that men are more sceptical/resistant to institutional authority. They are therefore much more likely to satisfy the preconditions for gaining utility from working on a problem that is asserted to be impossible by professional authorities (ergo more men than women);

  3. In order to develop a theory in sufficient technical detail to be considered a “crank”, one needs a substantial amount of technical training, e.g., in engineering, mathematics, physics, etc., and there are more men and older people with this technical training (ergo more men and more older people);

  4. In order to develop a theory in sufficient technical detail to be considered a “crank”, one needs a substantial amount of time, such as would be available in retirement (ergo more older people);

  5. Even under equivalent circumstances, an older person is more likely to be classified as a “crank” than a younger person, due to the fact that certain younger people (particularly children, adolescents, and young adults) are not expected to have a high level of technical knowledge, and are generally excused for making assertions that are belied by expert knowledge (ergo more older people);

  6. The context for discussion of “cranks” often tends to be technical disciplines like mathematics, engineering, physics, etc., which are heavily dominated by men. There are many other fields of interest dominated by women, where silly ideas are ubiquitous, but these tend not to be raised as examples of “cranks” in these kinds of technical discussions. For example, for every male “crank” in the field of mathematics, there are probably a hundred woman who believe in crystal healing or tarot cards, or some other scientifically baseless idea in a field that is more popular with women (ergo more men than women);

Incidentally, these are exactly the same reasons why the vast majority of correct technical methods in the fields of mathematics, engineering, physics, etc., are developed by men, with a reasonable representation of older men – for every few “cranks” that put forward asserted proofs of false theories, we get an innovator who breaks new ground with a correct theory that extends existing knowledge. In any case, these are just hypotheses, but they seem pretty plausible to me, and I am not aware of any literature that attempts to study this problem. Personally, I find it unlikely that a gender imbalance is due to women “having too much sense”. Both sexes can lay claim to a great many people with very little good sense, and in my observation, various women spend absurdly large amounts of time on activities that are no less ill-advised than trying to prove/disprove difficult/impossible technical theories.

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    To strengthen your case for Point 6 and your last paragraph: There is an armada of “child-pedagogy cranks” trying to sell books advocating their theories. As this is a traditionally female topic, most of the authors are women. (How do I know they are cranks? Well, only a fraction of these books can be correct as the proposed theories blatantly contradict each other.) Also strengthening your argument is that due to the age factor (and the fact that Dudley’s paper is from 1983), this is not about the current gender imbalance but the one from half a century ago. – Wrzlprmft Mar 10 '20 at 7:48
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    TL;DR: women are just as dumb as men, but usually in other disciplines, and we reserve other disparaging terms for them. – user108403 Mar 10 '20 at 8:22
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    I think there's a serious error in this answer? A key characteristic of cranks is that they cannot be convinced. Students learning geometry might "find" a way to trisect the angle, but most of them should be quickly convinced that they were mistaken, and therefore are not cranks (as opposed to not being cranks because they lacked the training necessary to be one). – Allure Mar 10 '20 at 11:25
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    @Allure: Surely the "cranks" can make the exactly same claim about you ---i.e., no matter how clearly they set out their brilliant theory of phlogiston, you are not convinced by their argument either. Ultimately, what tends to happen in these situations is that neither party convinces the other, because the underlying premises and knowledge are so substantially different that neither is convinced of the argument of the other. – Ben Mar 10 '20 at 13:00
  • Comments are not for extended discussion; this conversation has been moved to chat. Leaving these top few comments to summarize the discussion. Please read this FAQ before posting another comment. – cag51 Mar 16 '20 at 4:23
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Interesting that all of the responses so far seem to be from men. I believe that the extreme gender-skew among math and physics cranks is the flip side of the cult of genius, which is deeply entrenched in mathematics and theoretical physics, and also heavily gendered.

"Genius" in the sense of having brilliant insights into an abstruse field is almost exclusively conceptualized as male. As a result, men are far more likely to imagine themselves as possessing undiscovered or unappreciated brilliance. This delusion either intensifies with age or retirement provides more opportunities for indulging it.

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    This is a great response, and a view point that is very underappreciated and probably uncomfortable for many to accept. It seems easy to attribute this whole thing to male dominance of fields. Being in academia, it is increasingly clear the cultural forces present in male behavior. And these male cranks usually tend to respond highly to attention, whether it be positive or negative attention. Crank-like behavior among men is more common than many would think. It's quite literally outstanding when women display this behavior (i.e spiritual women, and/or anti-vax moms). – Sprinkle Mar 14 '20 at 16:17
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"Old men" have a lot of accumulated knowledge and experience, and have usually developed a lot of wisdom.

We can often look at a situation, immediately know what superficial details to ignore, and then quickly assemble and analyze the fundamentals.

Unfortunately, we sometimes look at situations outside of our expertise, where our knowledge is less than it should be, and then we develop amazing answers that are totally wrong.

I myself learned about trisection from my grade 10 teacher, who had the patience to read my proof and point out that "draw a line connecting points A, B, and C" made an unwarranted assumption.

I later learned that when a soft-science expert says something is impossible, it really means that it goes against all common knowledge and reasoning, but when a mathematician says something is impossible, it really does mean that it is impossible.

Those that grew up in non-mathematical fields tend not to be aware of this distinction, and so see impossible as a challenge, not as an absolute fact.

(E.g. it used to be impossible to transmit a signal of much more than 5 kHz over twisted pair telephone wires.)

For the sexist part of the question, all I can suggest is that males tend to be more aggressive, challenging the status quo, and women tend to be more conciliatory, working for compromise. E.g. an "old man" would say that trisection is possible, and here's why, while an "old woman" would say, if she said anything at all, that trisection might be possible, and here's why.

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Old men in general don't work anymore, which means

  • They have plenty of time on their hands.

  • They don't have employers/ bosses/clients/subordinates anymore for which they have to behave (normally)

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Perhaps there is something psychometrics can tell here. I suggest it here as a possible perspective into the question.

This wikipedia article claims:

Previous research has found evidence that most adults become more agreeable, conscientious, and less neurotic as they age.

with this reference.

And it further claims

For example, women consistently report higher Neuroticism, Agreeableness, warmth (an extraversion facet) and openness to feelings, and men often report higher assertiveness (a facet of extraversion) and openness to ideas as assessed by the NEO-PI-R.

with this reference.

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    Interesting, but wouldn't that be a reason to expect less "cranks" to be older people? – Ben Mar 10 '20 at 19:33
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    @Ben-ReinstateMonica probably yes. Perhaps this is a counter-evidence. – Boaty Mcboatface Mar 10 '20 at 20:26
  • People that are weak become agreeable because really, they can't afford to contradict. That's why everybody likes trained dogs, children, (really) old folks, etc.: They are no opposition. Women are also weaker in many ways, be it physically or because of culture, so that fits the picture, although mostly the hormones will determine your aggressiveness and thereby your willingness to contradict. This will also determine your certainty about you being right and exceptional (which I guess refers back to original question). – Radio Controlled Mar 11 '20 at 9:10
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    @Ben-ReinstateMonica younger ones simply aren't called cranks. Just idiot, awkward ++++ard, and so on. – Will Crawford Mar 12 '20 at 2:40
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    @RadioControlled The hormones are certainly a point, but there is definitely an sizeable overlap in the "agressiveness ranges" of the sexes. There is however zero overlap in the testosterone concentration of healthy adult males and females. The average in men is a factor five or so higher I believe. (And it goes down by a factor two from dawn til late afternoon.) – Karl Mar 12 '20 at 18:02

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