Statistics sounded extremely interesting to me before I had taken it.
Afterwards (and during), not so much.
mmm
I had two semesters of calculus in college, but they were special classes, designed for business majors, and were mostly there so that anyone who worked with financial models had some clue as to how they operated (as opposed to teaching the theory behind things).
As I specialized in market research, I think I had four semesters of statistics, between my undergrad and graduate work.
In my four years of High School, my math classes were, in order: Algebra, Geometry, Trigonometry (not in the poll), and Calculus.
Turns out only three years of math were required (the counselors at my HS were not very good communicators), and all the Calculus did was drag down my GPA.
I was done with math after that. No college courses.
We touched on graph theory in a computer science class, but I haven’t taken a full-blown graph theory class.
As a bonus, we have a remarkably good set of data about undergraduate tears. Did you know that the volume of tears produced is a bell curve (A+ and F students produce the fewest tears)? It’s actually a really important tool for tracking grade inflation, because while the numbers go up, the tears remain constant.
I had pretty much the opposite experience. Even though I was a math major and went on to get a Master’s in math, I never took a class in Statistics and/or Probability, and part of the reason was my perception of Statistics as boring number-crunching and record-keeping.
But later I studied it on my own and eventually ended up teaching Statistics classes, and I found it to be much more interesting (both from a pure mathematical standpoint and from a practical application standpoint) than I had expected.
Weirdly, now that I am many years distanced from my statistics class, it now seems interesting to me again.
mmm
I love Lewis Carroll’s book “Symbolic Logic”
Oh, and in my probability and statistics class, while we learned to calculate lottery odds, the professor said “Improbable in NOT the same thing as impossible”
Funny how that works.
It is true of 72.7% of folks who have taken a statistics class, according to my calculations.
mmm
Isn’t it also true that 81.4% of statistics are simply made up on the spot?
I believe it’s more like 86.3%, which is a statistically significant difference.
I’m an English major (-type - I dropped out of college before actually declaring a major), but I understood algebra. You might even almost say that I enjoyed it. Then I hit geometry, or, more accurately, it hit me. I took it, but I failed the first round and squeaked by with a D in the second. However, I took statistics in college, at the beginning when I was considering psychology as a major, and I loved it. It just made sense to me.
Nowadays, I’ve forgotten most of my algebra and can just barely understand statistics. But, man, am I ever competent at basic operations!
I didn’t know it existed!
– having spent three minutes looking it up: I might have had a different attitude to the class if we’d used it. We had a very dry text – which had been written by the professor giving the class. That fact rather put me off attempting to discuss with the professor my reaction to his example for the either-or principle; and my serious doubts about the either-or principle resulted in my scraping through the (required) course by memorizing the answers considered correct while disagreeing with the axioms they were built on.
I still think that the either-or principle needs to be approached with great caution, and that using it in the way that text did is the source of a whole shitload of problems in the actual world.
I imagine the problem you had is due to the fact that the English word “or” is ambiguous. It often means what logicians call “exclusive or” (“For dinner you can have chicken or steak”) but sometimes may mean “inclusive or” (“To pass airport security you need a driver’s license or a passport”). The problem is not with logic but with the English language.
What is the “either-or principle”? I’m not familiar with the name, and googling just beings up references to Kierkegaard.
Sorry. Law of the excluded middle. Either A or not-A.
The problem I have with it is that it’s often used for things that are nowhere near that simple. It’s not just the English language; it seems to be a common human tendency – in the really nasty form, it turns into ‘the way I live/the way I believe is right, therefore the way you want to live/believe must be wrong.’
The example in the logic book was ‘Either it is raining or it is not raining.’ I opened the book and read that on a day in Rochester, NY on which it was not raining in any standard sense – there were no distinct raindrops hitting the ground – but nevertheless if you stood out there more than a few minutes you were going to get wet. I then started thinking of all the other examples of what’s wrong with that statement, including but not limited to the time it poured on half of my back yard and not a drop on the other half. “It’s raining” and “it’s not raining” are both useful statements, and they don’t mean the same thing – but “either it’s raining or it’s not raining” is pure bullshit unless you specify in detail both what you mean by “raining” and exactly what spot you’re talking about.
Oh, excluded middle. The problem here is “raining” is not strictly a boolean predicate, so the logical operations don’t apply to it. Many things that refer to the real world are of this type. Predicates that are strictly boolean with no possibility of quibbling are things like mathematical statements: an integer is even or not even; a line in the Cartesian plane is vertical or not vertical; a natural number is prime or not prime; etc. When you try to treat predicates like “helpful”, “desirable”, “intelligent” as boolean, you do indeed run into trouble.
Yes, exactly. Once you’ve specified a predicate with enough precision that it becomes boolean then you can apply boolean operations to it. That doesn’t mean that logic is bullshit, it means you need to specify precisely what you’re saying, which is a useful principle in a lot of situations, not only mathematics and logic.
It means that the way the professor who wrote that book and was teaching that class was using logic was bullshit.
And that particular bullshit way of using logic is very common, and IMO does a lot of damage.
Of course the principle can be used properly, and isn’t bullshit when so used.
I don’t completely agree with this. I think it’s ok to make simplifying assumptions and idealizations for pedagogical purposes, and to use examples from everyday experience. If the topic is logic rather than meteorology, it’s fine to say “it’s either raining or it’s not raining”. Everyone knows what that means.
For example, in a discussion about fractions, the teacher may say “take a rod 3 feet long and cut it one foot from one end; now one piece is 1/3 the original length and the other is 2/3”. It’s not useful to object “But how could be sure that you’ve cut it exactly one foot from one end? There are no measuring tools accurate enough to do that, or knives sharp enough! And some atoms will be lost in the cutting process…” This is just quibbling for the sake of quibbling, and diving into such arguments does not help in understanding the topic. If you can’t imagine a world in which it is always either raining or not raining, substitute some other process for which you can accept that happening and not-happening are mutually exclusive. Certainly such situations exist even if not every situation is an example.
Not me, apparently. Or at any rate, what you think it means and what I think it means aren’t the same thing. Because what it means to me is that the person saying that isn’t looking at the world; they’re looking at the inside of their own head, and the inside of their head is really limited.
I don’t think the fractions example is at all the same thing. Maybe it’s even the reverse – you’re taking something that works as a practical matter and imagining someone complaining because it doesn’t work as an abstract. The either-rain-or-not-rain is saying something that doesn’t work at all as a practical matter and trying to use it as an example of an abstract.