Don’t expect the expected
When you roll a die, do you expect it to turn up three-and-a-half?
Hell no. But that still is the expected value of a die roll, I’m afraid.
What does that mean?
Here’s what it means. If you roll that die often enough, you’ll get 1 one sixth of the time, and 2 one sixth of the time, etc. Add those up and you get (1+2+3+4+5+6) / 6 = 3.5 and that’s what mathematics calls the expected value, or expectation (Icelandic: “væntigildið,” or “vænta gildið”) of something random.
That makes no sense, until the mathematician explains that he really means the expected average value. If you keep rolling that die until the sound of it drives you bonkers, writing down each result you get, then you should expect your average to be pretty close to three-and-a-half.
So on any one roll of a die, whatever you expect, you shouldn’t expect to get the expected value. That would be pretty unexpected.
[Incidentally, when you roll a pair of dice, you should expect to get the expected value, which is 7. That's because for a pair of dice, the expected value is both (a) actually possible, and (b) the most probable one. 6 and 8 are a little less likely, 5 and 9 still less likely, and so forth. 2 and 12 are really unlikely. If you get to gamble on a pair of dice with even odds, bet on 7 every time. Trust me on this.]
The Tower of Babel, by a 16th-century Flemish painter named Pieter Brueghel the Elder
My point? Ok, this posting is not really about mathematics. It is about language.
The term “expected value” means a slightly different thing in mathematical English than it might mean in other dialects of English.
More generally, a mathematical background changes a person’s use of language ever-so-slightly.
Still more generally, language differs with background. Culture. Upbringing. Education. Individual temperament. The way you woke up that morning. Language differs with a lot of factors. In some sense, no two people speak quite the same language.
If you do not keep this in mind when talking to someone, you will misunderstand them. Even if you do keep it in mind, you will still misunderstand them a bit. It’s a basic human function; we breathe, eat, urinate, copulate, and misunderstand.
We do have this jolly nice invention, language, for transferring ideas and concepts and feelings from one mind to another by way of speech (and writing), and that’s pretty cool, but it’s far from perfect. We do a fair job of it for simple things (“pass me the raita please”), but for anything more complex or more important (“I like you”), the message often does not get across in quite the way it was intended.
In a restaurant today, my father called for the attention of the waitress with a chipper “Fröken!” (Miss!) and I gently explained that nowadays a lot of Icelanders in service jobs find that appellation offensive. How was he supposed to know? It was the polite way to call for attention when he was growing up. Even my brother-in-law, hardly even older than me, didn’t know. But I’ve heard several people in service jobs make it pretty clear that in their language, it is plain rude.
Ask two people to define exactly what they mean by a word, and their definitions will differ. Find several people coming out of a meeting and ask them what went on, and their responses will vary, sometimes wildly, even though they all heard the exact same words spoken in there.
When someone’s attitude or opinions or reactions completely fail to meet your, hm, expectations, you may find it useful to consider the difference between their frame of reference and yours.
You might not be speaking quite the same language.
June 20th, 2005 at 11:11 am
So what on earth brought about this posting? Just curious… but I appreciated it. Strangely, it applies to a situation I’m in right now…
June 20th, 2005 at 11:41 am
Join the club. :)
June 21st, 2005 at 1:33 am
The problem that you pose becomes even more troublesome when words are used that have more than one meaning. For example: “tender”.
On the way home from work today I had a store receipt in my hand an on it said: “amount tendered”, and I asked my colleague what it meant. I had heard the term: “to tender an offer”, “this note is a legal tender for all debts” and of course – “tender loving care”. My colleague who is born in the state of Washington and has lived in the US for all his life did not know the exact meaning of the word – just how it is often used.
This example shows that effectively we need to reduce our verbal communications to a set of lowest common denominator – and that set is unfortunately not large enough to clearly elaborate ones thoughts.
June 21st, 2005 at 2:05 am
I object to that last leap of logic; we don’t need to dumb down our use of language unless we are encountering some real, painful, deleterious (heh) difficulties in communication. Your colleague may not be well-read on the etymology of the word (or two identical words) “tender” but surely he has no trouble understanding “amount tendered” in a store, and does not lie awake the whole night wondering why his dollar bills carry messages of love and care. So there is no real problem. It ain’t broke; stop fixing it!
As for this specific word, “tender,” it should hardly surprise us if it turned out to have different origins for these very different meanings. Sure enough, the dictionary says the money/business sense derives from Latin tendere: to hold forth or extend (note: ex-tend), and the loving-spoonfuls sense derives from Latin tener: soft or, well, tender. Same root as “thin” in English, they say. There you go. Sometimes different words end up with the same spelling and pronunciation. Tough! But no biggie.
June 21st, 2005 at 7:16 pm
Since your reply indicates a pompous attitude on my behalf, I would like to answer shortly.
I agree that the word tender does not keep people awake at night, at least not the dictionary definition of it. The problem I face is that I find it often difficult to understand other people perhaps that is a unique problem that I have. I do not need to dumb anything down, on the contrary.
I am not trying to fix anything, nor is there anything that needs to be fixed I was just pointing out that the only clear message we can send is by using a lowest common denominator: could you please pass me the bread?
June 21st, 2005 at 8:57 pm
Wow! The self-referentiality of it all!
I wrote some sketchy thoughts on imperfect human communications, the fact that people often read completely different things into the exact same words … and on that very posting I managed to add a comment that you took as an accusation of pomposity, where none was intended.
I had no idea my above comment could be taken as implying a pompous attitude on your part; if anything was pompous it was clearly my reply, and for that I apologize.
To beat this dead horse silly, let’s do a post-mortem dissection of the misunderstanding! :)
I was reacting (in a knee-jerk fashion, sorry) to the words “This example shows that effectively we need to reduce …” which I did not agree with. That was the “leap of logic” I objected to; “no, it does not show that” because your colleague had no real problem.
But in the process, I used the phrase “dumb down” which you presumably took to mean that you seemed to consider yourself superior to others. I was thinking of humans as a whole collectively “dumbing down” their use of language, e.g. storekeepers ceasing to use the phrase “amount tendered” on their receipts because people are not generally familiar with that sense of the word “tender” — and that is also how I thought you intended your phrase “reduce our verbal communications” (as you probably did). My point is that no such reduction is called for (fortunately, because it would have the ill effects of making language boring, and in the long run dumbing it down for real across the board, but that’s beside the point.)
So my choice of the loaded phrase “dumb down” triggered an alarm in your head saying “uh-oh, I’m being mistaken for an arrogant elitist” and you had to reply to beat that unpleasant smell off. That was not at all the spirit in which I used those words … but they sure invited that interpretation. Sorry!
My, wasn’t that a fun dissection. (If you enjoyed this, try a frog next time; click “Demos” at the top right.) But also there was an important difference between the example you took and the kind of miscommunication I was discussing.
In your example, the use of “tender” may cause someone to think “how odd that they use this word here,” but it doesn’t cause any real confusion. The exact sense of the words is not familiar to both people, but that’s OK, the context makes things clear. [And nobody reads the non-numeric parts of the store receipt anyway, but that's beside the point.]
In contrast, I was talking about the potential for real confusion: where one person emits a thought encoded into words, and the other person decodes those words into a completely different thought. Different senses of the words themselves may cause this, but even (as in our case) when the exact sense of each word is fully clear to both, still the context or spirit of the message can get scrambled in transit. A flaw somewhere in the encoding-decoding process causes real confusion.
And lo, we got a live specimen of that kind of miscommunication, right here in the comments!
I suppose the more abstract the message (discussions of emotion and attitudes and personality characteristics and such), the more likely this is to happen, because in abstract subjects context probably helps less to make things clear than in concrete subjects (such as “please pass me the bread”).
So sending a clear message is easy only when the subject is very simple … and as soon as you try to send messages whose subjects are more abstract (and thus more important or more interesting to talk about), that’s when you have to get careful about presentation; that’s when you need to consider the “language barrier” that stands — with varying height — between any two minds.
And maybe that’s what you meant, anyway. Can’t really be too sure; we were discussing abstract stuff, after all. :)
In any case, sorry I bungled into portraying you as pompous. You are just about the last person I would willingly do that to.
June 28th, 2005 at 1:51 am
To sum up bro’s last comment: He’s sorry for the misunderstanding.
Going back to the math stuff, I would like to use this opportunity to point out that the overwhelming majority of people have more than the expected number of legs.
Having said that, I expect it is necessary to clarify that it is not my intention to demean the underwhelming minority of people.
And remember: when she told you you were average, she was just being mean.
Indeed, the meaning of words is not always expected, especially when the demeanor of the utterer cannot be observed.
Never beat a dead horse on the mouth.
I guess I’m meandering.
June 28th, 2005 at 2:28 am
“Never beat a dead horse on the mouth.”
Watch your mouth, you have just been horsing around with a dead Beatle.
(No offense, George Harrison. That begged itself, punwise. I’m sure you understand.)