One of the points where mathematics and day-to-day intuitions jar is in estimating numbers of combinations and similar combinatorial problems. I’ve just made a booking on Eurostar, and my confirmation code is a 6-letter code. Surely, my intuitive brain says, this isn’t enough; all of those people going on all of those journeys on those really long trains, day-in, day-out. Yet there are a vast number of possibilities; with one letter of the 26 letter alphabet for each of the 6 letters in the code, there are 26^6=308,915,776 possible combinations. Given that there are 10 million Eurostar passengers each year, this is enough to allocate unique codes for passengers for around thirty years. It then makes you wonder why some codes are so long, like the 90-digit MATLAB registration code that I had to type in by hand a couple of years ago.
Archive for the ‘Psychology’ Category
We all seem to have tiny little mental blocks, micro-aphasias, things that we, try as dammit, cannot learn. My mother couldn’t remember the word “volcano”—she was a perfectly fluent native speaker of English, with no other language difficulties, but whenever she came to that word it was always “one of those mountain-things with smoke coming out of the top” or similar, followed by several seconds until the word came to her. I have a block on the ideas of “horizontal” and “vertical”. Whenever I read these, I feel my mind blurring; I know which two concepts they map on to, but for a second or two (which feels like an eternity in the usual flow of thought) I cannot fluently map the words onto the concepts. Usually I break the fog by making a gesture with my fingers—somehow, this change of mode (moving my fingers from left to right strongly associates with the word “horizontal”) dispels the confusion, it must trigger a different part of my memory associations. Quite where these odd little blocks come from—and, why we can’t just learn them away—is fascinating.
Here’s an interesting phenomenon about memory. I sometimes remember things in an indirect way, that is, rather than remembering something directly, I remember how it deviates from the default. Two examples:
- On my father’s old car, I remembered how to open the window as “push the switch in the opposite way to what seems like the right direction.”
- On my computer, I remember how to find things about PhD vivas as “really these ought to be classified under research, but there’s already a directory called ‘external examining’ under teaching, so go in there and look for the directory called extExams and then the sub-directory called PhD“.
It makes me wonder what other things that I do have a similar convoluted story in my memory, but where the process just all happens pre-consciously.
Here’s an interesting situation. Several times a year, I take part in university open days, where I sit behind a desk answering questions about courses from prospective students. Typically, at the undergraduate open days, the punters consist of a shy 16/17 year old and one or two rather more confident parents.
Here’s my problem. I don’t want to make the assumption that the older person is the accompanying parent and the younger person the prospective student. I’d be mortified if I made that assumption on the day that a parent, bringing their child with them for moral support or lack of childcare, was the prospective student. But, this happens so rarely that the parents and student just sit down assuming that I am going to read the situation as the obvious stereotype.
How should I react in this situation? Asking “which of you is the prospective student?” is treated as a joke or, more troublingly, as evidence of density or weirdness on my behalf. But I still feel uncomfortable making the assumption. I’ve taken to starting with a broad, noncommittal statement like “So, what can I do for you?” or “What’s the background here then?” and hoping that it will become obvious. That isn’t too bad, but there might be a better way.
More abstractly: we try to avoid stereotypes and making assumptions about people and situations based on initial appearance. But, what do you do when the stereotype is so commonplacely true that even the people being stereotypical are expecting that you will react using the stereotype as context?
Get to the bus stop to find that someone is waiting at the wrong end of the stop. Stand at the correct end of the stop, a few other people come to the stop. The bus arrives, both of us want to get on the same bus, I let them get on first, get a slightly strange look from them, like I’ve broken some taboo about having paid enough attention to someone in a public space to recognise them a few minutes later. But, I didn’t want to barge on in front of them in case they felt I was being boorish by not recognising that they had got to the stop before me.
One difficulty that I have when place in a new environment, e.g., travelling to a new country or working in a new place, is adapting to day-to-day norms. Travel books are full of advice of the “always insist on taxi drivers using the meter” kind, but I always find it difficult when the reaction of the local is a slightly shocked-bemused look and a comment like “really?”. One problem is that the travel books tend to be quite stiff and risk-averse, for good reason. We don’t want to be taken as a rube or tyro, and so we go along with “what seems normal” in a particular situation, rather than being the stiff outsider who seems to be the first person in a century to insist on rules being followed to the letter.
I wonder if this sort of thing happens at all levels of engagement with novelty. We sometimes here of a senior politician who is railroaded along into carrying out some corrupt or biased action. The common response to this is to say “come on, you were the Prime Minister, how could you have been so ignorant/allowed yourself to be taken along for a ride”? But, I don’t think it is as easy as that; I can readily imagine a situation in which you are told “actually, minister, we don’t really do things like that” by some adviser or civil servant, and exactly the same kind of psychology as above kicks in. However experienced a politician you might be, being Prime Minister (or whatever) is still new, for quite a while, and I can imagine that the pressure not to look like some uptight noob is very influential.
I came across a pair of cod-definitions a while ago (I can’t find the reference), along the following lines:
- A jerk is someone who, because their attention is elsewhere or they don’t know the consequences of their actions, messes up things for other people
- An asshole is someone who knows that their actions will mess things up for other people but goes ahead anyway
Would you rather be seen as a jerk or an asshole? Probably neither! But, if you screw up in public—say by tripping someone or bumping into someone in public—you would rather that this be seen as an accident rather than a result of you (say) thinking that you need to get somewhere quickly as so you are going to push your way through the crowd regardless of whether you trip or bump other people.
How do we try to achieve this? We usually do this by following up an apology with an explanation, whether a real one or a made-up one: “sorry, just got new glasses yesterday and I’m still adjusting”. By giving this explanation, we are trying to change the perception of the person we offended by moving from the (seeming default) asshole category to a position that we might called “justified jerk”, where we messed up because we weren’t sensitive enough to realise that our situation (say, the new glasses) required more care, but at least we have some reason for it. We are essentially sending out an appeal for empathy.
Usually, though, this doesn’t work. The explanation gets taken as an “excuse” and just harrumphed off. I wonder why? Perhaps this is a variant on the Dunning-Kruger phenomenon, where people who are bad at some task overestimate their ability at the task. I imagine that when we ask for empathy in the situation, the other person thinks “if I’d just got new glasses, I’d have been more careful and slowed down my pace of walking etc.”. As a result, we get bumped back into asshole territory: because we have tried to give an explanation, we have shown some awareness of the situation, and therefore given evidence that we had some understanding that we could have used to anticipate the problem, so the problem is because of our arrogant disregard rather than because of casual error.
Perhaps just an apology is better? But then, we don’t move they person away from their default position that we are doing this for assholey reasons. Perhaps there is no way out of this bind.
Here is something that I have observed, which has interesting implications for memory problems like Alzheimer’s disease. My father has some memory problems, and what is interesting is that he can recall some facts learned a long time ago, but some of the deductions from that knowledge aren’t readily recalled. For example, he can remember each of his two marriages, but when asked “how many times were you married?” he doesn’t know.
Here is my hypothesis about what is happening. He has a clear memory of the two marriages as specific sets of events, but has not “bothered” to learn the fact “I have been married twice” as a specific propositional fact, as this can be deduced immediately from the memories of those two specific facts. However, as he has lost speed of access to specific memories, the ability to make that link from particular pieces of knowledge to a new “deduced” piece of knowledge has declined, and so he has trouble accessing the pieces of knowledge that were never stored as explicit propositional knowledge but which were always present as immediate deductions from readily recalled facts.
Do we not bother learning some things because we can instantly deduce them from other knowledge, and then if we have memory problems we actually end up with this being a problem?
There is an interesting rhetorical move that I notice increasingly, which we might refer to as self-reinforcing criticism. An example of this is given in one of Edward De Bono’s books: a caricature of a Freudian analyst argues that some negative trait that someone has is due to their repressing some aspect of their personality. The person being criticized has very little in the way of response. Either they agree, or they disagree. If they disagree then that can itself be used as evidence of even deeper repression!
A common use of this is in planning processes in organisations. A complex proposal will be presented, which is roundly criticized for a number of reasons. However, rather than taking on the criticisms, the person presenting the argument counters with the argument that the critics are just “afraid of change”.
We need a term to “call out” this kind of specious argument. I have experimented by called out the emotional aspects of it: “why are you in a position to know how I am feeling?”. But this isn’t ideal. We need a term of art to describe this, and then to create a pejorative sense to that term. Perhaps a term for this already exists in rhetoric somewhere?
Relatedly, there is a phenomenon where a complex proposal will be presented and, if it is attacked, the proposer will say “well, what do you suggest instead?”. This is difficult to respond to, as the proposer is in the position where they have had days, weeks or months to prepare their proposal, whereas the off-footed opponent has a matter of seconds or minutes. I wonder if we should be working harder to make multi-alternative proposals to be both normal (so that proposals with only one alternative are seen as weak) and acceptable (so that presenting proposals with multiple alternatives are not seen as being weak and indecisive).
Thinking about the basis for moral action as a result of Stuart Sutherland’s interesting lecture earlier this evening on “Hume and Civil Society”. Hume skeptically examines various putative bases for moral action, and finds many of them wanting—religion, social norms, rational thought.
I was wondering whether, in practice, there is a single “base theory” like this, though. Perhaps there are a number of different bases, and the consequences of these all largely coincide. Groups might seem to be acting in a coherent moral fashion, but each individual’s morality might have a different basis; or, more likely, combination of bases. Some might be driven by emotional repugnance, some by rationally thinking through the consequences of their action, some by social norms, some by fear of (spiritual or temporal) authority, most by some mixture of them all. In the end they all do more-or-less the same thing. This has a flavour of the “swiss cheese” theory of risk: most of the time at least one of our moral bases kick in to prevent us acting immorally, and it is only when all of the bases are absent, or else miscued in a particular context, that morality fails.
A project to enumerate unusual forms of embarrassment (part 1).
One particular form of embarrassment that catches me by surprise is when people think that I have said something much more shocking/out of character than I actually had.
For example, a couple of years ago I was talking about hash tables and dictionary lookup in a lecture and used an example of animals and their names. One example pairing was (Panda, “Eats, shoots and leaves”). I was familiar with a version of the joke about a panda who eats a meal, shoots the waiter and then walks out of the restaurant; I was not familiar at the time with a variant in which the “shoots” refers to ejaculation. As I began to tell the joke, a few members of the audience (should I really be thinking of students as “audience”!) began to titter or look shocked that their lecturer was going to tell an off-colour joke. I found out after the lecture by talking to students what had caused this.
Of course, it is a shocking indictment of our society’s values that a joke about someone being murdered in cold blood is inoffensive, whereas the slightest sexual reference is shocking.
Momentform is a description of a style of musical composition devised by Stockhausen and first used in his piece Kontakte. The key idea is that a piece is constructed so that each moment is appreciable in its own right; by contrast, most traditional musical forms are based around the idea of some kind of temporal structure such as narrative or development.
I wonder if there is some scope for this as the basis for a musical form that would be appreciated by people with memory problems and dementia. One of the features of many kinds of dementia is that patients find it difficult to form a coherent structure from what is happening in the world. Perhaps, rather than trying to force a narrative-based musical form on such a person, we should be inventing forms that are appropriate for them.
From time to time I wake up in the morning (or in the middle of the night) convinced that I have, either in some dream or in some hypnopompic reverie, come up with a really hilarious joke. In the cold light of 20 minutes later, they reveal themselves to be utterly un-hilarious but nonetheless having some joke-like structure.
Here is the latest example: “I hear that the Gibb brothers, Geri Halliwell and Mel B. are going on tour? What’s the name of the band? The Spice Gees.”
They have the flavour of the computer-generated jokes found in Graeme Ritchie’s work (except that the jokes generated by his system are actually funny!).
There seem to be two meanings to the word “confident” in English. The first is the idea of confidence as a generic motivational aspect; we should learn to put aside our inhibitions and then we can tackle a problem with confidence. Call this motivational confidence.
The second is the feeling that you have been able to calibrate your actions against experience. this is the kind of confidence where you know, and know you know, when you have got something correct. Perhaps we can call this calibrational confidence.
It seems that we confuse the two fairly readily. When I say that I am not a confident singer (which is true), I am saying that I cannot calibrate my attempts at singing against the world. I don’t feel that I am singing wrongly, but I wouldn’t bet any amount that I am not awful. When I try to correct this, I am frequently told that I should be more confident; this is clearly a references to motivational confidence, as this can be summoned by willpower, whereas calibrational confidence can only be gained by skill and knowledge. However hard I might say that I am going to sing out with confidence, if I am unable to calibrate my efforts then I am not going to improve—by contrast, I’ll be like one of those godawful people at karaoke who belt out a song with great will but little skill.
I wonder why these two contrasting concepts have the same word? And, why many people conflate the two, and believe that the second will follow automatically from the exercise of the first? Clearly they are not entirely unrelated; but the link is fairly slim.
Lotteries are often described as “a tax on people who are innumerate”. The idea is that any rationalist would not play a lottery, because the return on investment is shoddy—negative, indeeed, stunningly so. Back to the post office savings account then.
But hang on there! Is this really why people play lotteries? Often the driving force is the remote chance of a truly life-transforming event, which is not adequately measured by the ROI.
The interesting observation is that this argument also works for events with negative consequences. Indeed, we are accustomed to this kind of reasoning about negative events. For example, people will readily argue that, whilst they know that the chances of a plane crash are minuscule, nonetheless they aren’t going anywhere a damn plane—because the consequences of being in a plane crash, however remote, are horrifying. Again, a life-transforming event, but one with bad rather than good consequences. The behaviour seems to be controlled by the same mechanism—I wonder if a carefully controlled experiment would show that the underlying structure of thought is basically the same?
My elderly father has to take pills twice a day, and frequently forgets to take them. What he doesn’t forget are routines that he has been doing for all of his adult life. Is it worth me establishing a habit of taking no-effect sugar-pills twice a day from a marked container, so that if I get into that state the pill-taking habit will be thoroughly engrained by then, and I (or a weekly helper) can just substitute real pills for the sugar pills?
As I have improved my typing skills over the years, I have noticed that I increasingly make errors at the whole word level rather than at the wrong-letter or transposed-letter stage. For example, when I try to type the word “universe” I frequently find that I have typed the word “university” before I realise that I have made an error. “University” is a word that I type many times a day; “universe”, perhaps once a week or less. This would seem to relate to the idea of “chunking” in memory—instead of controlling each individual letter being typed, instead I am chunking together the typing activity of whole words as “basic units”. There is an argument (from Rumelhart and McClelland, Parallel Distributed Processing) that when experienced typists type a word like vacuum, where the first three letters are all in the left hand, the right hand is moving towards the letter ‘u’ before the left hand has finished the “vac” part of the word.
Another piece of evidence for this: a colleague of mine has said in an email: “slip of the fingers: Venue for the meeting will be S122A, (*not* S110B)”. Fingers would have to slip very precisely to type the exact sequence of letters required to type the name of one room rather than another; the slip is at a much earlier stage in the cognitive process! It would be interesting to do a proper study of this kind of mistyping, perhaps this would make a good student project.
When I was a teenager my mother won a mint set of coins in a display case; a neat prize. Something that surprised me when I looked at it in detail was that the coins with the Queen’s head on were described as the obverse of the coin, and those with the distinctive design the reverse. This contradicted something that was part of my (mistaken) tacit knowledge about the world, i.e. that the distinctive side was the front, and the Queen’s head the back (probably being rooted in learning about coins by looking at the side on which the amount was displayed so as to learn the denomination).
Bizarrely, I’ve never been able to square this objective knowledge with my tacit feeling that the Queen’s head is on the back. I have known objectively that the Queen’s head is the front of the coin for around 25 years. However, I still basically grok that the Queen’s head is on the back. I wonder if this kind of conflict between tacit and explicit knowledge is a known and studied phenomenon?