POETICKS

The sentence below this one is false.

The sentence above this one is true.

What can we now say about the two sentences above?  That, if we dispense with the false true/false dichotomy, neither is either true or false: each is true/false or paradoxical.  Parodoxes are inevitable in any human language, which in my thinking includes the language of mathematics and all the sciences.  It seems to me they never occur in nature.  That is, nothing in reality except our attempts to describe is ever paradoxical.  Hence, two parallel lines can meet each other in Non-Euclidean geometry, but not in the real world.

An aside: I’ve always wondered at the fact that many intelligent people with scientific backgrounds find the idea that parallel lines that meet will exist if the universe were the surface of a sphere.  Only in geometry.  In the real world nothing that has less spatial dimensions than two can exist.  Start drawing a line on your universe as the surface of a sphere and your first tiny dot with burst out if it on both sides.

Related to this absurdity is the idea of curved space.  But that’s just an absurdity of expression–saying, for instance, that a curving ray of light curves due to the effect on space of gravity rather than due to the effect of gravity on it.

It applies, too, to the idea of transfinite numbers.  The idea behind that, according to George Gamow is that you can’t form a list of infinitely-repeating decimal fractions that contains them all as shown by the fact (and this is true) that if someone brings up a fraction he claims is not on your list, giving you the first ten digits, say, and you show him it is on your list, he can show it isn’t by showing you the eleventh digit on his is different the eleventh digit on yours,  or–in the one in ten chance thatthe digits match, that some other later digit on his fraction is different from the one in that spot on yours.

But that procedure can work oppositely: you can make a list of all possible decimal fractions including infinitely-repeating ones and challenge him to find an infinitely-repeating decimal fraction of a given length that’s not on your list.  If you take all the integers in order, reversed, and make them infinitely-repeating decimal fractions by putting a point in front of each one as here:

.1 .2 . . .  .9 .01 .11 .21 . . .  .91 .02 . . .  .99 .001 . . .

he will not be able to give you any decimal that you can’t immediately indicate the location of on your list of a decimal fraction matching whatever string of digits he gives you.  Say it’s 00958746537 . . .  That will be the 73564785900th number on your list.  He can’t then say his number’s twelfth digit is different from your number’s because you can honestly say you don’t know what your number’s twelfth digit is.  But that his second number can be as easily found as his first.

So you have two true statements about mathematics that contradict each other.  I say they are therefore true/false statements, or paradoxes.

I don’t believe any real object can be infinite.  Space may be said to be, but it doesn’t exist, in my philosophy.  But I doubt that there’s any way of testing the truth of what is just my opinion.

Note to anyone concerned about my health: I managed to get through a stress test yesterday without having a heart attack or stroke.  I’m now wearing a heart monitor that will come off in three hours, at ten a.m.  I felt peculiar a few times while wearing it.  I hope they don’t turn up as problems on the monitor’s record.

I had trouble walking properly on the stress test treadmill.  My doctor and the woman overseeing me got quite frustrated.  I felt incredibly stupid.  I think I know what happened: there are rails to hold onto that I couldn’t grip without slightly stooping because I’m tall but have the arm-length of a 5′ 9″ white man, so I felt very awkward–until I just let my fingers touch the rails.  I also tried too hard because I thought I was going to be tested with stress.  When it was over, I asked why they’d never speeded it up.  No stress at all except the stress of feeling physically incompetent.

Hmmm, my spell-checker doesn’t like “speeded up.”  But surely “sped up” is not correct.  Weird.  I’d automatically say, “I sped home,” not “I speeded home.”  But that’s great.  The language should be crazy–as long as it tries for maximal stability.

I have opined on occasion that people who can remember rules of usage like sped/speeded may be use them to show their superiority to those who can’t–in other words, the lay/lie distinction that I hold to, for example, I hold to partly to show I’m not low-class.  But I hope my main reason is that I like ways to break out of universal rules as a literary artist.  I do believe in social classes, though.  It slightly simplifies relating to people, which is incredibly complex.  Not that my believing in it matters since a classless society is impossible.

This entry was posted on Thursday, April 21st, 2011 at 12:00 AM and is filed under Philosophy. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.