While I often complain about the mistakes of thought, estimation, or similar made by others, I make no claim of own perfection. On the contrary, I often make mistakes of my own. (The main difference to many others might simply be that I am aware of my own fallibility and behave accordingly, including that I am more open to revising my opinions, more likely to check my facts, more likely to double check some line of thought, and similar.)
Below and over time, I will gather some particularly interesting examples of own mistakes.
As a child, I participated in a quiz where one of the multiple-choice questions asked how many baskets of bread and fish had been left after Jesus fed the hungry masses. I reasoned that his power was very great and, therefore, the largest number must be correct. (This, obviously, was long before I became an atheist.)
This did not give me the correct answer, however.
Even accepting the premises of Christianity, there were at least two problems with my reasoning:
Firstly, no matter how many baskets had been left over, the quiz makers could always have picked a larger number. Based on the twelve that were, they could easily have picked thirteen; had it been thirteen, they could have picket fourteen; etc.
The version with twelve was the more common in my religious exposures. However, the Bible contains (at least) two such events, the other leaving seven baskets. I cannot say with certainty which of the two was used for the quiz, but the same principle hold for both events/numbers.
A more insightful quiz taker might even have speculated that the quiz makers would have made the right answer the highest with a sub-average probability, to counter exactly the possibility that quiz takers preferred the highest number. (Ditto, the lowest.) Then again, a more insightful quiz maker might have compensated for the possibility that the quiz taker would be aware of that possibility. Etc. Meta-arguments of this type can be dangerous.
Secondly, more baskets might potentially point to more power, but they would also potentially point to less precision, insight, or similar. By analogy, would we view a caterer as better or worse, if he provided far too much food? If the feeding had left more baskets than it did, this would arguably have been less impressive. If we accept the Christian framework, I might even suggest that twelve baskets were left because the near-future saw some need for exactly twelve baskets, be it for a future meal, to convince someone about some point, to be symbolic, or whatnot. (Also note that the number twelve might have had some particular significance in the context. What this would be, I do not know, but I note that there were twelve apostles, that the number twelve occurs fairly often in human conventions, and. likely overlapping, that twelve is the smallest number divisible by two, three, and four.)
I once heard the claim that Hamburg and Liverpool were on the same latitude (specifically, 53 degrees north).
My immediate reaction was “That cannot be true!”. I opened an atlas—and found that the claim was indeed ... true. (At least, with some rounding and within the tolerance of a brief eye-test relative the drawn latitudes of 50 and 60 degrees north.)
Looking closer, I found my mistake to be the accumulation of three errors:
Liverpool was further to the south within England than on my mental map. (I had it placed towards the northern reaches of the Irish Sea, while it is actually towards the southern reaches.)
Northern Germany was further to the north relative northern France than on my mental map (and southern England is, of course, slightly north of that). More specifically, Belgium and the Netherlands shot up more in the northwards direction than I thought, which indirectly affected my view of Germany relative France (and, thereby, England).
The latitude lines had a much stronger curvature (relative the implicit left–right lines on the flat page) than I had anticipated. For instance, the line for 50 degrees north approximately touches Cornwall, cuts off a small part of France, and digs down to slightly south of Frankfurt am Main (!) in Germany.
Looking at the underlying causes, this is likely mostly a mixture of problems caused by projecting something spherical onto something flat (which leads to counter-intuitive results, especially when moving from more local maps to larger global ones) and how many maps focus on a comparatively small part of (in this case) Europe.
The former is complicated by how often maps lack lines for latitude (and longitude; note that these lines do not necessarily bring much value on many maps, depending on e.g. the purpose of the map, and that the issue is an indirect effect on intuition). The latter includes maps of only one specific country or only some adjacent parts of two or three neighboring countries.
In the overlap, orientation and centering of a map becomes important. The map that I currently view, e.g., is centered on the 20 degrees east longitude (which, in a now natural choice, is oriented to have north “up” and south “down”). As a result the 50 degrees north latitude is parallel to the “left–right” of the page at Krakow in Poland (where, approximately, the two intersect). If I look at the 0 degrees longitude (Greenwich), it has a noticeable tilt relative the “up–down” of the page. If, however, the page was re-orientated to have the 0 degrees longitude match “up–down”, the perspective would shift considerably, and the lines through Krakow would now have a corresponding tilt. (We would also see Krakow higher on the page than Cornwall, while Cornwall currently is higher than Krakow.) For natural reasons, smaller maps, e.g. Germany-only, Poland-only, whatnot-only, tend to have the longitude that corresponds to “up” somewhere in the middle of the country at hand, and those who view such maps in isolation might get very wrong ideas about how a larger piece of the world might look when projected onto a flat surface. (On a globe, in contrast, all longitudes go “up” and “down” without any longitude being “preferred”, while all latitudes are “left” and “right”.)
The exact behavior of latitudes and longitudes relative up/down/left/right and similar depends on the exact projection used. I have not investigated how the various maps that I have seen over the years handle this, but other maps can have “straight lines” at the cost of distortion elsewhere, notably distances. If my exposure to different types of maps have been different in different situations, this could further explain a “geographical intuition” gone wrong, including an underestimate of the curvature on one map because of experiences with another.
(Various projections have different strong and weak points, and maps used for different purposes or with different preferences can make radically different choices.)
Above, I note how the makers of a multiple-choice quiz could always pick, as one of the false options, a number of baskets even larger than the true number, no matter how large that true number was. This leads me to a very interesting family of errors involving flawed reference frames and, especially, reference frames that are too much based on oneself and/or contain an element of (something analogous to) begging the question.
One sub-family is when I measure the difficulty of a task against how hard I find it and, in a next step, estimate my own ability more highly the harder I found the task. (Provided that I ultimately succeeded.) A trivial example is picking something up: If it feels light, I think nothing of it; if it is so heavy that I have to exert myself, I consider it heavy and come away with the feeling that “I must be strong, because I could pick up something heavy!”. However, the reason that I thought it heavy might have been that I were weak. Likewise, that I thought some other object light could have been because I were strong, in which case I might have been wrong in thinking nothing of it.
A similar idea is illustrated in an episode of “Friends”, where Chandler and Ross arm wrestle. They go at it for a very long time. Someone remarks “They must both be really strong!” and someone else notes “Or really weak.” (in both cases in an approximate paraphrase). Indeed, such a contest, whether long or short, can only tell us something about the relative strength of the two opponents, not of their absolute strength. (And even this only if we assume that other factors are sufficiently equal, e.g. technical mastery.)
With so basic tasks like lifting something, I am usually sufficiently aware of the issue that I can avoid problems; however, this does not necessarily apply to more complicated issues—if in doubt, because I rarely stop to think of the matter. (Note that I only very rarely have an explicit thought of “Yay me!”. Instead, usually, it is a matter feeling content in a vaguer and more unconscious manner. The following is a more “explicit” issue and more of a problem.)
Worse, another sub-family involves having an informal reference frame of what is hard, easy, whatnot, based on own ability, and then finding that this reference frame works poorly with others.
For instance, I have had countless situations where I have seen something (e.g. a conclusion based on some premises, the solution to a problem, the existence of a particular risk) as obvious, because it was obvious to me, but where the counterpart has failed to understand the matter unless being led by the hand—for which I rarely have the patience. (To boot, there are potential complications like a failure-to-understand going undiscovered.) In the office, in particularly in a weaker team, I have often come away feeling like a Cassandra.
For instance, in my dealings with various civil servants and customer-service workers, it often seems to me that the counterpart has problems with comprehending a perfectly ordinary text or understanding even the most basic reasoning. Moreover, these groups do, on average, have far lower IQs, education levels, whatnot, than even the “weaker teams” from the previous paragraph. Likewise, if I look back at my school years, the proportion of students that had problems in the recurring tests of reading comprehension was considerable—and chances are that this proportion overlapped strongly with future civil servants and whatnots. (Ditto, more generally, those who cause occasional headlines about how many students read well behind their “grade level”, otherwise struggle in school, and similar.)
I have spent most of my “team time” with fellow software developers. While the level of software developers varies widely, and while there are some genuinely dumb specimens among them, it is not unusual for a perceived-as-dumb-by-the-rest member of a team to be well above the population average, to fare much better by the standards of other groups in the same company, to have grown up as the “clever one” among his siblings or close childhood friends, or similar. Make the same guy a civil servant or customer-service worker and he might compare favorably to his new colleagues.
An interesting specific example in the overlap is a reading of Hemingway’s “Hills Like White Elephants” in an adult (!) reading group. (Specifically, in the context of an employer-organized English course.) We might have been half-a-dozen, including a native English speaker, who served as the teacher. Not only was I the only one who realized that the topic of the in-story discussion was an abortion, but the others, teacher included, outright denied the possibility. (Along the lines of “I don’t know what it is about, but it is not abortion”.)
Even the teacher aside, the level of prior exposure to English was sufficiently high and the text, in terms of e.g. difficult words, was sufficiently easy that I do not see “English as a second language” as a plausible explanation—it seemed more a matter of an inability to think properly about what was read. Unlike with, say, a plain business letter that is not understood, there are some textual difficulties on another level, as the text deliberately brings an idea across in an indirect manner; however, these difficulties are by no means so large that all-but-one of a group of highly educated persons should fail at deciphering it. To boot, they did not just fail to arrive at the right interpretation on their own—they outright denied its correctness when it was proposed by me.
(I also suspect that deciphering the topic is a prerequisite for even attempting to understand other aspects of the story, like character motivations and what the decisions might ultimately be made, which would make it likely that the author considered the deciphering sufficiently easy. However, I have not re-encountered the story since then, around 2000, and my memories of the story are too vague to say for certain.)
For my own part, a conclusion is that I must pay greater attention to what others might or might not understand (etc.), but this is very hard for me to keep in mind (a potential topic for this page in its own right).
In a bigger picture, a greater amount of ability testing might be needed, and this especially for often neglected positions, e.g. customer service (often hired to be as cheap as possible) and civil servants (often hired among those who could not find more challenging/rewarding/whatnot career paths, often promoted based on years of duty instead of competence, often virtually unfirable, etc.). Note how those in such neglected positions can do their employers quite a bit of harm, e.g. through the need to escalate solvable problems and through damaging a public reputation; and can do immense harm to the customers/citizens/whatnot, through enormous wastes of time, delays in performance, incorrect handling of complaints and applications, and so on.
One aspect of the issue is what causes different individuals to have different standards. Often, it is a matter of the ability to think and reason, to solve problems, to draw conclusions, whatnot, on a reasonably generic level. However, other factors can play in (notably, domain-relevant knowledge and experiences) and it is not uncommon for the same person to, e.g., see something as obvious after a few years that he did not see as obvious when a beginner. Forgetting that different causes can exist is potentially dangerous, especially, when it manifests in authority arguments (“I have ten years of experience! I am right!”) that fail to consider what difference a greater or lesser ability to actually think and reason (etc.) can make.
There is even some scope for competing ideas of what is obvious, when different persons have different priorities, focus on different aspects of an issue, or similar. (However, in my experiences, such competing ideas are much more likely to go back to one or more of the parties simply being wrong.)
There are at least two cases of naivety regarding business/economics/whatnot from my childhood that can be somewhat enlightening, but which I would view as off-topic. I include them mostly because of how many others, including many fully adult and highly educated, still seem to have a similar naivety.
In both cases, chances are that longer thought would reveal even more reasons for why my early positions were naive.
Childhood examples from other areas are plentiful and I try to limit myself to what is on-topic (in the main text) and what is truly interesting or important for other reasons (as in this excursion).
For instance, a personally interesting, but off-topic and not generally interesting/important, example is how I, as a very young child, denied the possibility that “dog” could be English for the Swedish “hund”—after all, the two words do not have the same number of letters. This, and the implication that I saw translation as a matter of transliteration, might be interesting to an expert on childhood development or a psycholinguist, for instance, but is irrelevant to my current purposes. It is, in particular, not an error of thought in the manner exemplified by the childhood quiz above—I simply had no knowledge of any language but Swedish. (A charge of “jumped to conclusions” holds, but lies on a different dimension and is unremarkable in a young child. Sufficient or sufficiently deep thought might have revealed this jump to be preposterous, but it would have required much more than for the quiz, would have been less reasonable to expect in a child, and might still have failed for want of a sufficiently developed worldview, even had the child had enough ability to think.)
When I was very young, I had a brilliant idea from reading my “Donald Duck” comics—I would invent a machine to create money so that the likes of the Beagle Boys would not have to steal!
I was very disappointed and surprised when my mother informed me that this would be illegal, but from an adult perspective:
Such machines obviously already exist: money does not grow on trees and while making money manually might once have been an option, it would be impossible to keep up even with the quantities in play back then (1980, give or take).
The issue, then, is not to have the right machine(s), but to what degree they are used. There might be situations where the government cannot keep up with printing money, but it is rare and the opposite problem has been a far more common issue where ever the connection between money and value has been weak (minting more gold coins requires more gold; printing more bank notes, more paper and ink; increasing the value of a digital account, pressing a few buttons).
Chances are that I had no awareness of non-physical money at the time, but such money obviously already existed and has increasingly been crowding out physical money. In due time, physical money might not even exist any longer. (The view of a future reader might be extremely interesting.)
When it comes to governmental (central bank, whatnot) policies, “printing money” and its variations are usually best viewed as metaphors: Physical money is still printed, but it is more a matter of having enough cash in circulation for cash-based transactions than of increasing the overall money supply. Actual increases of the money supply, in turn, tend to go other roads these days.
Unauthorized printing could lead to enormous problems, including a disastrous loss of value/confidence and the risk that too many would print for their own gain (instead of performing honest work). (Not to mention some practical complications like how to handle serial numbers.)
While I cannot rule out that I had some idea of printing for my own benefit, I have no recollection of this. My discussion with my mother definitely centered on helping others.
Generally, incentives would be perverted, even if money handouts only came from a small group of entities, say, me and the government. (As opposed to the above scenario of large scale printing for one’s own benefit.)
If the Beagle Boys get money from me without having to work, why should so many hardworking citizens still be stuck in offices, in factories, on farms, whatnot? Why should they not simply throw up their hands, refuse work, and insist on a handout? Alternatively, why not claim that “I am a crook, too! Give me my handout so that I can go straight!”. (Some might continue work through a passion, like Gyro Gearloose, who was a great inspiration for my wish to be an inventor. These, however, are bound to have been the exceptions.)
Then we have the question whether the Beagle Boys actually had to steal (even as things were)—dumber and/or physically weaker characters were regularly shown as being gainfully employed. Why, then, should they not work?
The answer is that they preferred a life of crime to honest work, making a reward through newly printed handouts a great unfairness. Worse, I strongly suspect that they would have continued a life in crime for the sheer heck of it, even had I been there with my money machine to give them handouts. (The first certainly applies to many real-life criminals; the second, likely, to at least some.)
(Executive summary: if a bank or similar entity does not receive interest, why should it lend money at all?)
Some years later, I was greatly surprised to hear that someone who borrowed money from a bank was supposed to pay back more than he had borrowed—which seemed very unfair to me.
In practical terms, we have interest, but the exact actual modalities might have been different. In my vague memory of the event, it was a case of borrowing some amount and paying back a greater balance at some later date; however, this could be the result of a faulty memory. The modalities and formalities do not matter very much, however; what matters is the principle of more money coming in than went out. A Muslim bank, e.g., might be forbidden to charge interest in the strict sense, but the principle still holds, even be it through a workaround.
(The source was, I believe, an episode of “The Little House on the Prairie”.)
Again, from an adult perspective:
Lending money comes with risks, including that the debtor cannot pay back the full amount in a reasonable time frame (or at all) for lack of income, that the debtor dies, that the debtor is dishonest, that unexpected developments gut the value of the currency, and that an own cash-flow problem causes the bank to fail (even should all borrowers be able to pay back on schedule and in full; however, “bad debt” is probably the more likely cause of failure).
Interest compensates for these risks, e.g. so that the default of one debtor is covered by the interest paid by other debtors. This removes a great disincentive to lend money and reduces the risk that a bank outright fails—which could have disastrous consequences for others.
Even short of a gutted currency, continuous inflation can hollow out the value of a certain sum. What if the bank lends an amount with a purchasing power indexed at 100 today and, a year later, receives back the same amount at a purchasing power of 98?
Here, interest does not just remove a great disincentive but also a great unfairness.
Lending money comes with an opportunity cost, most notably that the money cannot be invested in other ways. By lending money to someone, the bank loses the profit that might have resulted from such other investment.
Again, interest removes a great disincentive (and, depending on point of view, unfairness).
A bank has costs of various kind to cover and would usually wish for a profit. Staff costs money, locations cost money, safes cost money, etc. Possibly, most importantly: if depositors wish for interest on their deposits, this costs money. What is the most natural way for the bank to get this money? Lending at an interest. (Or, per the previous item, investments of other types that stand in competition with lending.)
Here, interest creates an incentive to lend, and, maybe, one without which the bank could not exist in the long term.
By no means do I deny that many banks use dishonest and/or unfair practices. This is a problem, but it is not a problem that inherently has anything to do with interest on loans or legitimate concerns (e.g. risks and opportunity costs).