INTEGRATING LOG X


On an autumn day 15 years ago in Las Cruces, New Mexico, I sat in a Math Stats graduate class.  The teacher was discussing some function and came to the part where he said, “Oh, now we have to get the integral of log x.  I can’t remember what that is.”

With that question, my stats teacher had just opened a life changing door that neither he nor I knew existed.  The class, mostly in their 20s and early 30s, was silent.  I was the oldest person in the room, even having four years on the professor.  I quietly said,

“It’s xlog x – x”.  I continued, “you integrate it by parts.”  My classmates and professor looked at me as if Einstein had been reincarnated.

The class moved on to other subjects that day, about which I knew nothing:  moments of functions, and other aspects of beginning graduate level statistics.  I would have many difficulties in the coming 20 months, but that day changed my life, and my teacher’s, too.

He later became my advisor, and said when I left NMSU that it had been a long time since he had enjoyed a graduate student as much as he had enjoyed working with me.  I had a very difficult two years at New Mexico State, but I did pass with a 3.89.  I took graduate level statistics starting at age 49, and I got through the program in two years.  The last semester wasn’t pretty, but I finished it.  My advisor helped me finish in two years, when many stayed longer to finish their thesis.  I was grateful to him for that.

My advisor told me that the day I knew the integral of log x was the day he realized I was for real.  He did not give out praise often.  When I determined the mean and variance for a godawful hypergeometric function using a technique that I was frankly quite surprised I figured out, I showed it to him.  He agreed, and as I walked out the door, called to me: “That was a slick piece of work.”  I remember that as one of the top 5 compliments I got in grad school.

Chance occurrences one might say.  Perhaps.  I have, however  been amazed at how often supposedly “chance occurrences” appear.  I was volunteering in a calculus class when limits of the function: y= x squared, was discussed, when x was 0.999999.  The teacher said, “I need a calculator for that,.   From the back, I stated “no you don’t,” and gave the answer, exactly, to 12 decimal places.  The year before, I had seen that problem, wondered if there were a pattern to squaring numbers that were all 9, found it, and happened to be in the class the following year.

Or the day in a quality improvement course in Salt Lake City, where the discussion centered upon diseases common in “the three Scandinavian countries.”  Without thinking, a major flaw I have, I blurted out, “There are four.”  The teacher looked at me and said, “Name them.”  There was no problem with Denmark, Norway, and Sweden, I suddenly realized Finland wasn’t one, and somewhere from the recesses of my brain, I dredged up “Iceland.”

Why?  Am I unusually intelligent?  No, I am not.  Plenty of people are a lot smarter at many things than I, including math.  What I have learned over the years are two fundamental facts about learning:

  1. If you learn something really, really well, you will eventually forget it if you do not use it.  But if you ever need it again in the future, with a little reading, it will come back quickly.  It doesn’t matter if it is math or playing the piano.  I  had to relearn calculus after 30 years of never seeing a derivative or an integral.  One day, I happened to see the integral of log x, and for whatever reason, it stayed with me.
  1. Know your learning style, which is how you learn best.  Do NOT let teachers tell you,”You don’t have to write this down,” if you feel you should.  Write it down.  Do not let people say that we learn like children or “adult learning theory says…..”  We are not children, and adults have different learning styles, too.  Mine is very different from most adults, and I have struggled a good share of life until I understood what my learning style was.

I am a slow processor.   When a financial advisor explains a trust, a company’s prospectus, or a host of other issues, I cannot understand what they are saying.  I need time.  I understand numbers quickly; finance is a different matter.  I was also an average medical student in gross anatomy.

Being a slow processor, however, comes with a big, big advantage.  Once I learn something well, I keep it forever.  The first time I knew that was in my clinical rotation in surgery when somebody asked me where the nerve that eventually caused tearing left the skull.  “The hiatus of the facial canal,” I stated, and the expression on the surgeon’s face was priceless.  Nobody had answered that question right the whole year.  In anatomy, I was average; the following year, I had the same knowledge I had before, but the fast learners had forgotten it faster.  Both groups have advantages and disadvantages.  It isn’t only fast or slow processing, either.  It is a matter of vision, hearing, touch, taste, and smell–our senses–that help us learn, too.  Some are primarily one, other a combination.  It is useful to know what works for oneself; no, it is more than just useful.  It is essential.\

Education is never wasted, said Moira Gunn, when she was once told that a woman engineer from Purdue should not host a radio show about technology and science.  Today, her “Technation” show is arguably the best show-podcast for science information.  She knew how to interview people, and her life took a direction I don’t think she ever dreamed it would.

Jay Anderson was a Winnipeg meteorologist whose interest in solar eclipses and weather were melded into a climatology page for very solar eclipse.  Every “chaser,” and the number is increasing, knows who he is.  His page is free; the information astoundingly good.  He never would have believed he would be a household name in the eclipse chasing community.  I will be doing ground views of the eclipse path in Oregon the next three years, before the 2017 eclipse. I never thought I would chase solar eclipses; now I am helping a little with the climatology for the next one to cross North America.

Integral of log x? Something odd that you learned that you think is worthless?  Perhaps. Maybe, however, it will be life changing.  Keep your mind open to opportunities.  You can sometimes log a few more than you thought.

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