A Reply to Someone Who's Fascinated by Mathematical Questions

Another question about math is whether it is something intrinsic to nature which people have discovered, or a very useful tool which we have invented, and which we impose upon nature. I've always seen it as the latter, which diminishes, at least for me, the intrinsic interest of those other questions you mention.

Of course, I may have been entirely wrong this entire time. I have the impression that most contemporary mathematicians and physicians and zoologists and botanists would say that I'm wrong.

Nietzsche believed we invented math. See Menschliches Allzumenschliches, vol 1, section 1, "Von den ersten und letzten Dingen," paragraph 19, "Die Zahl." Mathematicians and physicists might find this passage interesting, among other reasons for the grasp of atomic theory which Nietzsche demonstrates in something he published in the late 1870's.

But many years after I first read that, it suddenly struck me, like a hammer striking a gong, that everyone knows exactly what a circle is, although none of us has ever seen a perfect circle. This very simple fact, available to anyone who thinks about it for as long as a moment, seems to me to be a very strong argument in favor of Plato's forms, and in favor in math being something we discover as opposed to something we invent.

Nietzsche despised Plato more intensely than he did any other single human being. I went through a period of very intense admiration for Nietzsche (except for his sexism and enthusiasm for war, which I always rejected), and I adopted his contempt of Plato. But my gong-moment, my insight about circles, has forced me to reconsider Plato. And when you reconsider something as influential as Platonic philosophy, you necessarily re-consider many other things.

People Can't Do Math, Green Energy Edition

Yes, some rooftop solar installers are sketchy. But some aren't. It's like many other things, you need to do some research.

Yes, some regions get less sunlight than others, which means you'll get less financial benefit from solar, all other things being equal.

 

But, if you own the house you live in, and if your financial situation allows you to get loans, and if you get a loan to pay for the installation of rooftop solar, and your savings on your electrical bill are more than the loan payments -- sorry to break it to you Bucko, but you just got free solar. Free as in, not only is it not costing you money, it's making you some money.

 

 

I'm posting this in frustration after reading a thread on asocial media in which a few of the participants were unable to grasp that, yes indeed, in some cases, for some people, solar power can be free.

 

Actually much better than free, but one mental weakness at a time.

 

I'm autistic, and one of the aspects of my neurological condition is that I'm above average at math, so I can understand how rooftop solar can be free, or how an EV can cost the owner less than ICE over 5 years, let alone 10, despite having a higher purchase price, because lower operating and maintenance costs more than make up for the higher initial price.

 

Unfortunately, another aspect of my neurological condition is that I'm not good at explaining math to morons.

 

It's extremely frustrating. People who are too dumb to grasp the importance of polluting less, would pollute less anyway, if they were smart enough to see how much money it would save them.

True Stories From My Life. Part 4: The Mystery of Electricity

My town is in the midst of an "arctic vortex" of unusually-cold winter weather. This afternoon, I drove my 2003 Saturn Ion 1 about half a mile from my home to the Salvation Army, to see a social worker about a pair of glasses. The Major was behind the desk, and he told me that the social worker wasn't in today. I said I was surprised they were open at all today, because of the weather. He said they were open today, with a skeleton crew, precisely because of the weather: in case someone needed to get indoors somewhere and warm up.

From the Salvation Army I drove to Kroger's, about 2 miles. After I had Kroger'd, my car wouldn't start. I went back inside Kroger's, searched my wallet, and found an AARP card. (My Mom had gotten me an AARP membership, and told me that roadside assistance was the most important part of the membership.) To my surprise, the card said that my membership was still active, until May 2019. After about half an hour on the phone, I found out that my membership had been cancelled.

I went back out to the Kroger's parking lot, and this time my Saturn started. I was not as surprised as I had been when a similar thing had happened in earlier years: drove my car to a parking lot, shopped, car wouldn't start, waited about a half hour, then it started.

Since this wasn't the first time, I wasn't completely surprised. But I still don't understand what happened. Perhaps my not understanding it just shows that I know laughably little about electricity. Maybe engineers who are reading this are shouting at the screen: "It's the condensation, you idiot!" Or something else if it's something other than condensation.

I've been trying to learn about electricity, because the world is converting from petrochemicals to electricity. I can't claim to have made much progress. I open books such as this one:

-- and am immediately baffled. it maik munkee brane hert. And there are other textbooks in physics and math whose equations make my brain hurt much more than the ones in this book. I stopped studying math in the mid-1970's at age 15, as soon as I was allowed to stop, and now I'm hopelessly behind. (Also: I still don't actually like math. That's why I stopped studying it: because I hated it.) I have heard that Einstein used tensor analysis to come up with the theory of relativity. I've heard that. I don't know whether it's true, or partly true, or a misleading statement, or what.

I do know that my 2003 Saturn Ion 1, if it doesn't start on a cold day, may start a while later the same day. I know this is so, but I do not know why this is so. There's an entire world of STEM -- science, technology, engineering and math -- which is mysterious to me. And yet I know that I know much more about such things than do many poets and artists. And I know that many scientists, engineers and mathematicians are just as woefully ignorant of history and philosophy and the arts.

And so for today, grateful to be back home and grateful that the heat is on, I shall be as one crying in the wilderness for geniuses of various kinds to become less ignorant about one another.

I hope you're not too cold out there, reading this.

My 2nd Attempt To Read "Robert 's Rules Of Order, Revised"

My first attempt was when I came across a hardcover copy among my father's books. This must have been before I was full-grown, in the 1970's or even possibly the late 1960's.

It didn't hold my interest back then. I found it literally impossible to read. I was not able to maintain my focus upon it. In short, it was appallingly boring.

Decades later, disappointingly, it still is. More than that; now, not only do I find General Henry M Robert's book impossibly tedious. I am now also convinced that I would have disliked the man himself intensely. That's a rash sort of judgment in cases, like this one, where someone can't write very well at all, giving hope that there may be a personality not reflected in their writing. Still, I think that enough of Robert's personality shows here and there through the mud of his prose to allow me to make that judgment. I admit, I make this judgment on scant evidence.

Unless I have overlooked something, there is not within this entire wretched volume (Robert's Rules of Order, Revised, with a Foreword by Henry H Robert III, New York: william Morrow, 1971, ISBN 0-688-31374-4) a single reference to another written work, except in a footnote on p 300, and I quote: "Watson vs Jones, 13 Wallace US Supreme Court Reports, p 679. This case was decided April 15, 1872." Watson vs Jones was a dispute over the rights of ecclesiastical councils.

The subject of Robert's entire book, the rules and procedures by which Murrkin legislatures and other groups go about their business, is very interesting to me. This makes Robert's Rules of Order different than the Dover reprints of textbooks on advanced mathematics and physics which I got at places like Salvation Army thrift shops in recent years, hoping that perhaps I could kindle an interest in such things in myself. I held those hopes for various reasons: for one thing, as a schoolchild I showed prodigious abilities in math, up through intro to calculus in the 10th grade, after which I was not required to take any math courses. Because I hated math. I never took an elective math course, not in the rest of high school and not in college, was never even slightly tempted to do so. This was a great disappointment to my mother and to various math teachers. They thought that if my talent could be combined with an enthusiasm for math, I might do great things.

And from the time I was a small child until now, I've easily been able to see their point. And a further reason was that my brother, an engineer, has some familiarity with advanced math and physics, and I thought that if I did too, he and I might have more to talk about. So I got those Dover reprints of textbooks from the thrift store, and -- that hoped-for enthusiasm was not kindled by contact with advanced math. It seems I'll remain just something of a Rain Man-type arithmetical prodigy (although not quite as good as Rain Man), and never a actual mathematician. And of course, the Rain Man-type stuff is much less in demand these days, now that calculators are so cheap and plentiful.

On the other hand, it scarcely needs mentioning that neither I myself nor anyone at all acquainted with me and my abilities would have the slightest difficulty imaging me as a US Congressman or Ambassador to the United Nations or POTUS or Pope.

Perhaps Alice Sturgis' Standard Code of Parliamentary Procedure will prove more helpful to me, than Robert.

Or perhaps it'll be even worse, how the Hell should I know?

More From Inside My Head

In a previous post I noted that 17,153 is the product of two prime numbers, 17 and 1009. This morning I thought about some numbers near 1009, and calculated that 1007 is 19x53, 1003 is 17x59, 1001 is 7x11x13, 997 and 991 are prime numbers and 989 is 23x43. I calculated all this with the help of a pocket calculator I bought around 1992, which was not at all an advanced calculator even by 1992 standards. I got it because it looks cool and I find it very user-friendly. I divided each 4- or 3-digit number by bigger and bigger primes until I got a dividend which was either a whole number or a fraction smaller than the square root of the 4- or 3-digit number. Then I remembered that lists of prime numbers are readily available, and stopped calculating, and wondered, as I had many times previously, what possible purpose such calculations could serve.

Then I put that pocket calculator away and got out the other of the 2 pocket calculators I own. I don't remember exactly when I bought this one. I think it was closer to the present than to 1992. This other calculator is made by the same manufacturer. [PS, 8 Feb 2018: That manufacturer is Casio, a company for whom I have more respect now, after having heard about their legendary G-Shock watches.] It doesn't look nearly as cool to me. And it does much more. I don't understand what all of its functions are. I know what things like sine, cosine and tangent are, which the newer calculator features and the older one, the one I like better, which has bigger keys and a bigger screen and folds in half with the keyboard on one half and the screen on the other, does not. But I don't know, for example, what the "modes" are which are described above the keyboard of the newer calculator. Not a clue.

As far as I can remember, the only key I have ever used which the newer calculator has and the older one does not, is the X to the power of Y key. And as far as I can remember I only used that one to see whether I understood how it was to be used. I guessed that if you hit X, then the key, then Y, then =, the screen would display X to the power of Y. For example, if you hit 3, then the key, then 4, then =, the screen would display 81. My guess was correct.

So I'm looking at the newer calculator now, and I'm looking at an instrument whose purposes I am largely ignorant of, and I'm wondering how much less mysterious to me the instrument might be if I had not stopped taking math courses as soon as I was allowed to stop, after geometry in the 10th grade. I'm also wondering whether and to what extent fancy -- I'm sure it's not at all fancy to some people. I remember it wasn't the most expensive pocket calculator in the store -- to what extent fancy calculators like this one might have been rendered redundant because smart phones can do everything they do. My phone is not smart. It has a calculator on it, which I used once, but I found it excruciatingly difficult both to find and to use and I don't plan to use it again soon.

Inside My Head

Like many other autistics, I can do an unusual amount of math in my head. My abilities here are nowhere near those of Rain Man or Albert Einstein, and they might not even be above those of the average neurologically-typical PhD in math or physics, but they're above the average of the entire human population. Unlike some other autistics, I was never able to cultivate much of an interest in math. After the 10th grade and geometry, I was not required to take any more math, and it was a great relief to be allowed to concentrate more fully on subjects I liked -- literature, history: verbal subjects. (Including philosophy. Imagine my horror upon learning that some of Western civilization's leading philosophers have also been some of its leading mathematicians. Yaaargh! No escape!) My life up until now might have been very different if I had been able to become really fascinated by numbers in the way that mathematicians and physicists often are. Just recently I experienced an exception, an encounter with a five-digit number which I find interesting. The encounter, not the number per se, and so perhaps it's not really an exception. And actually, perhaps I am finally beginning, at age 51, to feel some of the fascination that mathematicians feel for numbers, specifically for factoring. Except that I'm not actually interested in factoring for its own sake, as someone who loves numbers would be, but I've begun to wonder whether there are practical applications to physical shapes which can be arrived at by factoring.

The five-digit number is 17,153. Several days ago someone I know saw this number this number on her odometer and immediately thought of someone else we both know, who is both a mechanical engineer with some knowledge of advanced math and a fundamentalist Christian with an interest in numerology.

Don't worry, this post has nothing to do with numerology.

So anyway, the lady who saw 17,153 on her odometer asked some others of us whether we saw anything remarkable in that number. Right away I could see that it was 17x1009. Then I thought about 1009 for a minute and began to wonder whether it, like 17, was prime. I could easily see that it couldn't be divided even by any prime up through 11. If 1009 wasn't evenly divisible by any prime up through 31 then it itself was prime, because the square of the next prime past 31, 37, was larger than 1009. After dividing 1009 in my head by 17, it started to become a little tedious, and I was going to fetch a calculator, but then it occurred to me that it might actually be easier to find a list of primes which went past 1009. It was very easy to find, as it turned out, and 1009 was in fact on the list, it is in fact prime. Maybe it would've been even easier to simply look up 1009. This is an an example of the kind of thing I would know -- where to look up prime numbers -- if I had been fascinated by math as a child and gotten a Bachelor's and a Master's and maybe a Doctorate or three in math or physics or engineering. If I'd taken that route I might be much more employable, but then again I might not know who Steven Runciman or Alfred Doeblin are. Je ne regrette rien.

Also, this morning it occurred to me that 1+7+1+5+3=17. Ta-daaa!

To be completely honest, what I actually find the most remarkable about all of this is that a group of people were discussing the number 17,153, and that the person who had seen that number asked what we saw in that number which was remarkable, and I got back to them right away with the info that 17,153 is the product of two primes, and no-one else seemed to find that remarkable! But maybe that's just my own ignorance showing again, like not knowing that I could just look up 1009, or where to look it up. The lady who saw 17,153 on her odometer has a PhD in math, and maybe she has a great amount of experience with five-digit numbers, and maybe stumbling upon a five-digit number which is the product of two primes -- or even a five-digit prime, for that matter -- is not as remarkable as I imagine. I wouldn't know, because I very rarely deal with math which involves five-digit numbers.

Anyway. Back to my accustomed, much-more-purely-verbal approach to stuff (except for the posts on chess) in my next post, much more likely than not. Excelsior!