Category Archives: Math

Getting Serious About Mathematics

You may have noticed that I haven’t posted to this blog for a while.  It’s not because I’ve stopped writing, but because I haven’t been able to get WordPress to accept Word documents.  Although I’ve had minor problems before, the first major problem came with Rambling #2 comparing the Pirahã and Sirionó languages of the Amazon basin, when WordPress dropped all my references and formatting near the end of the article.  When I wrote my last post in December of 2015, it wouldn’t even accept input from Word.

That seems to have been fixed, so I’m going to give it another try.  I’ve been looking at mostly third-party vendors who provide direct editing inside WordPress using drag-and-drop plug-ins.  Along the way I discovered that to install plug-ins, you’ve got to use self-hosting, which is expensive and requires changing from WordPress.com to WordPress.Org, making continued blogging more difficult in the short-run.  For now, I’m sticking with trying to use the free Word converter in WordPress and not make major changes.

Sorry about getting side-tracked.  As you may have guessed, I have a real interest in math (and if you’re British, that’s maths).  I’ve decided to write about topics that you may not have seen unless you’re a math major.

There are two major problems:  Microsoft Word is deficient in fonts needed for mathematics, and I have a real paranoia about someone stealing the original work that I did and publishing it as their own.  This last concern isn’t unfounded, and I personally worked with a physicist whose work was successfully plagiarized by a senior researcher in whose lab she worked.  Of course there are many classical examples from mathematics such as Tartaglia and Cardano and Grassmann and Cauchy.  I couldn’t find anything that was both simple and relatively complete about these two examples.  Where Grassmann thought that Cauchy had plagiarized his work, everything I could find was dry and technical.

As a result, I’ll describe results without going too deeply into how it was done (in most cases).  I’m slowly writing a book that does get into the bloody details, and if I live to 120, I may even finish it and publish before I start pushing up daisies.

I’ll describe some of my early work from 50 or more years ago.  Back then, I had no problem remembering the details, so I had no reason to write anything down.  Senility does nasty things to details, and trying to recreate what I did has been fun.  In all that time, no one else has duplicated some of the things I did (as far as I know).

The first thing I want to talk about in a later post is the gulf between mathematics and science, which is really surprising since math seems to be part and parcel of understanding science.  At times there are philosophical dilemmas in trying to distinguish the two.  In Newton’s three laws of mechanics, and depending on how you look at it, parts of the laws seem to be either definitional or axiomatic.  The original edition of Resnick and Halliday’s Fundamentals of Physics discussed this at length.  (Back then the book only costed me $5, and now, it’s over $200 for just the first volume.)

A related topic is the queen of the sciences.  As everyone knows from Thomas Aquinas, it’s without a doubt, theology.  Stephen Hawking disrespectfully thinks it’s physics.  The final word (at least for mathematicians) comes from Carl Gauss.  (You only need to follow the link on the unlikely chance you’ve never heard of him.)  Every mathematician definitively knows that “Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank”.  Only she’s not a science, which I’ll talk about in my next post.

Eugene Wigner wrote an influential paper in philosophy a few years before becoming a Nobel Laureate.  It’s entitled The Unreasonable Effectiveness of Mathematics in the Natural Sciences.  I found this reprinted in a humanities magazine in the 1970s, long after thinking many of the same things that Wigner talks about.  Be sure to read this article; there will be a test on it later.

I thought I had resolved this issue in 1962 in my sophomore year and only 2 years after Wigner published it, but I had no idea that anyone else was thinking about the problem.  The fact that it was my sophomore year seems almost ironic, given the British folk etymology (at the end of the definition) of meaning “wise fool”.  Of course I won’t talk about my solution until my next post on mathematics.  Even then, it will only be about the solution without divulging some specific details.  It’s my paranoia kicking in again.

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Five More Problems

When I was in eighth grade, one of our local newspapers would occasionally publish a math problem and wait for at least a week for someone to write in a solution.  I know better than to try that here, since the people I thought might read my last set of problems apparently didn’t.  Since the previous problems were more logic than math, I promised one actual math problem.  Three of the five here use math.  Since the last group was such a dud, I promise no more problems after this. Continue reading

Answers to Logic Problems #1

I was a little disappointed that so few people are interested in mathematics (or in this case, logic).  My next problem will be pure mathematics, just in case it’s logic that people don’t like, but I’m still not optimistic.

Before reading the answers, be sure you’ve read the original post:  Logic Problems #1. Continue reading

Logic Problems #1

I’m finally getting caught up on my e-mail; I need to quit spending so much time away from home.  One of the things I used to enjoy back in junior high (before they invented middle schools) was that one of our local newspaper columnists would throw in a math problem from time to time.

I’ve pulled 3 problems off the Internet and reworded them slightly to make it harder to find the answers with Google.  The answers will come in the next post.

  1. A guy goes to a hardware store to buy a common item found in any hardware store.  He asks the clerk what 1 costs – 20 cents.  12 would cost 40 cents, and 128 would cost 60 cents.  What was he buying?
  2. When a mathematician asks a second mathematician the ages of the second’s three children, he answers that the product of their ages is 72 and the sum is equal to the number of dollars he pulls from his billfold. The first mathematician comments that the information is insufficient to solve the problem, and the second adds that his oldest child likes butterscotch, and the answer is then obvious.
  3. Fred and George have just met Hannah, and they want to know when her birthday is. Hannah gives them a list of 10 possible dates, shown in tabular format:
May 15 16 19
June 17 18
July 14 16
August 14 15 17

Hannah then tells Fred the month and George the day of her birthday.             Fred: I don’t know when Hannah’s birthday is, but I also know that George doesn’t either.
George: At first I didn’t know Hannah’s birthday, but now I do.
Fred: Then I also know her birthday.
So when is Hannah’s birthday?”