A Math Dream That Was Not a Nightmare

Why would my dream life be invaded by a geometry problem? The setup was a line segment, and the question that invaded my dream life was, how many lines could intersect that line segment? At first I imagined the intersecting lines to be all perpendicular and parallel, and my dream thinking was that the number of possible intersecting lines could not be infinite because (1) the original line was only a line segment, and so not itself infinite; and (2) while lines have no breadth or thickness, it seemed to me (but this could be only commonsense thinking, which doesn’t always translate to mathematics) that there would have to be space between the lines or they would simply fill in -- ??? But they would not turn the group of lines into a solid, because there would still be no thickness, or depth.... Does plane geometry care at all if a surface is blank or filled in, or (and if I had to bet, I’d put my money on this second disjunct) does it only care about lines and points?

Ah, but points have no length, breadth, or thickness! A point is not an object but a location. So even the line segment could have, it seems, an infinite number of intersecting, parallel, perpendicular lines. Do you buy it?

Next (still in my dream) I started wondering about intersecting oblique lines. (What would be the smallest conceivable angle? Would there be such a thing?) Would this generate a larger infinity of intersecting lines? Can infinity come in different sizes, bigger and smaller, or is infinity just always that -- infinity?

Finally, dragging myself out of the dream and into wakeful consciousness, I searched around for a way to ask the question that my geometry dream had posed, and here's what I came up with: What is the maximum number of lines that can intersect any given line segment?

Here’s a question and answer I found online that has bearing on my dream, but before following the link you might enjoy thinking about the question yourself. I mean, there's no exam involved here, not even a pop quiz.

Income Gap? How About the Interest Gap?

Has anyone given any attention to the huge gap between interest charged and interest paid? An 11% interest rate on credit card debt is now considered low. At the same time, savings accounts that had a yield of only half a percent a couple of years ago have now fallen to 2/10s of a percent. Is it any wonder Americans are saving so little?

Why don't Americans save more? The inflation rate for 2013 was 1.5%. One hundred dollars in savings in 2013, at .02%, earned 2 cents in interest, but by the end of the year the buying power of that $100 had declined by $1.50.

Someone needs to leak this information to the politicians and pundits.

Two Political Proposals

(1) The amount of the bailout to the banks should be deducted from money the government has borrowed, thus reducing the principal, cutting down interest owed, and substantially reducing the federal debt. If (a) Tom has borrowed from Harry, and (b) Harry goes subsequently broke, and (c) Tom bails him out, how can Tom still owe the full amount of the loan? 

(2) In addition to an increase in the minimum raise, how about a maximum cap on compensation --not just salaries of CEOs but also their bonuses, stock options, etc. Taking into account experience, expertise and accomplishments, merit could still be recognized.

All Cranked Up: The Trouble with Leaving Out Commas

Might as well accept it: this blog is my cranking place! Sigh! Well, it is what it is, so here are a couple of peevish items for December:

First, here’s a sentence quoted from an advance reader’s copy of a novel reviewers are asked not to quote (and I take the liberty because I am not reviewing the book, and it came out in 1996, anyway): “The olive-green river slid smoothly between the high ochre buildings and the soaked terracotta roofs seemed luminous.” And yes, I would have used a comma before the “and” that joins the two independent clauses of this compound sentence. Why?

A visiting writer-researcher in the midst of a book she intends to self-publish told me recently, very, very firmly, that a comma was not necessary in a compound sentence. Oh, really? Well, here’s my problem: I’m reading along and I see the subject-noun phrase “river slid,” the preposition “between,” and then along comes “buildings,” obviously an object of the preposition, and there’s that conjunction, and then there’s another noun, “roofs,” and without no comma between the two independent clauses, I’ve been set up to read “roofs” as a second object, i.e., “between the buildings and the roofs,” which doesn’t make much sense, but that’s where the punctuation leads me – and then along comes another verb, signaling a second independent clause, and I have to backtrack and re-read the sentence! Damn, that’s annoying!

Two paragraphs down the problem occurs again:

“It was the ideal time to walk about and look at the city and the Marshal and his wife were always saying....”

You see what I mean? “It was ... time to walk .. and look at the city and –.” Huh? Look at the city and the Marshal and his wife? No, not at all. Well, how much trouble would it have been to use a comma before “and the Marshal”?

Writers who omit the comma in the compound sentence are probably the same people who come to an intersection and fail to signal their turns. Even if you are “following the highway,” how are other drivers supposed to read your mind and know that? Which way are you going? Give me a clear indication! Don’t leave me standing here on the curb when I could have crossed safely, and don’t make me read every one of your brilliant sentences twice, please.

The woman determined not to use commas in her compound sentences was also planning to write a history book without an index. Need I say more?

Too Busy

Forgot what I was going to say....

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What Should Men Be Doing?

Yet another man is upset that women are not staying home with the kids. That’s where women belong, he tells us, not working outside the home to contribute financial support to the family.

Why isn’t this man out in the forest with a spear, hunting game? What is he doing all dressed up in front of a television camera? Is that the place Nature or God intended for a man? Mouth, mouth, mouth – where’s the muscle work?