Posts Tagged ‘MATH AND MIKE’


July 18, 2015

A bloody picture of a cyclist adorned my Facebook page.  The writer was succinct:

How I joined the walking dead:

1. Rented a bike with defective brakes.

2. Started riding through a long dark RR tunnel.

3. Encountered a multi-family group with very small children in tow coming the other way.

4. Wiped out trying to avoid scattering kids like bowling pins.

This is a classic description of a fortunately not tragic accident.  Each one of those incidents alone might not have been sufficient, but together they caused a bloody rider. There was a concatenation of events.  Sometimes, we have a concatenation of errors.

I had my own sixteen years ago this month:

  1. Took part in a long distance bicycle tour only a few months after starting to ride a road bike.
  2. Ended up on a rainy day wet, tired after crossing 3 Colorado passes, and eager to get to the school where we were going to be camping.
  3. Saw a car in the turn lane headed towards me.  I had limited experience riding a bicycle in traffic.
  4. Assumed the driver saw me.
  5. The car suddenly turned in front of me.
  6. Too late, with wet brakes, I skidded and landed on my right hip, trying to avoid him.  I wasn’t the walking dead, but I didn’t walk normally for several months, and I’m lucky I can walk today.

It’s worth discussing the concept of the expected value of an event, like the lottery.  People see 2 winners in the last lottery and buy tickets, because after all, they could win.  It has to be somebody.  This is usually true.  If not, eventually the probability becomes so high that when the lottery has an unusually large payoff somebody (or several people) almost certainly will win.

If the probability of an occurrence is extremely small, invariable, and not zero, and the number of times the occurrence may happen is very large, the expected value is their product.  A probability of 1 in 110 million of winning x 440 million lottery tickets sold has an expected value of 4 winners.  It’s that easy.  Low probability events, like automobile fatalities, occur every day, because so many people drive. Expected values are just that.  They are expected, but they are not necessarily going to occur.

Aviation, perhaps more than any other endeavor, has taken safety to heart, because aviation is so unforgiving of errors.  Additionally, aviation has a large number of events, called flights, where there is a low but non-zero probability of a crash.  Aviation has tried to improve the probabilities and in commercial aviation, there have been multiple years, often consecutive, without a fatality.

Non-commercial aviation isn’t as safe.  Nearly two decades ago, a 7 year-old was trying to be the youngest person to ever fly across the country.  Being the youngest, oldest, first, most disabled, fastest, —st is often the first cause in a cascade of events that leads to tragedy.

A 7 year-old had no business being at the controls of an aircraft.  Period.  One of the last things to mature is judgment.

  • They took off to try to beat a thunderstorm, poor judgment, because wind shear is unpredictable in thunderstorms.  One must wait.
  • They were overloaded.
  • The runway was at a higher altitude where there is less lift for aircraft.
  • Rainwater on the wings diminished lift.  Airfoils are delicate; distortions of shape diminish performance.
  • They turned to avoid part of the thunderstorm.  Turning decreases lift.  The overloaded, slow moving, distorted airfoil plane stalled and crashed, killing all aboard.

Remarkable finding of evidence and piecing it together led to understanding why Air France 447 crashed in the mid-Atlantic in 2009.  Here’s a root cause analysis:

  • Why did the plane crash?  It stalled.
  • Why did the plane stall?  It was in the nose up position for the last part of the flight, reducing lift.
  • Why was the plane in the nose up position?  Because the co-pilots had taken control and saw that the altitude was low.
  • Why did the co-pilots take control? Because the autopilot had shut off.
  • Why did the autopilot shut off?  Because it wasn’t getting useful information from the pitot tubes, like altitude and speed; the altitude reading was faulty.
  • Why didn’t the co-pilots keep on the same course as the autopilot? Because they trusted the instruments.
  • Why weren’t the pitot tubes sending useful information?  Because they were faulty and needed to be replaced, but the airline was phasing them in.
  • Why was the airline allowed to phase them in?  That ends the questions.  That’s where action needed to occur.  Additional causes included the pilot’s napping (not wrong) so he was not in the cockpit when called.  There were other crew miscommunications.
  • What could have been done?  As soon as the “stall” alarm came on, the crew needed only to push the nose of the aircraft down.  Planes stall when they climb too rapidly.


This root cause approach to errors is what medicine needs.  When a surgeon operated on the wrong side of the head, he got a letter telling him not to do it again.  Nothing changed.  Here’s what happened.

  • Patient in ED had a subdural hematoma and needed emergency surgery.  There are emergencies where one must act in a matter of seconds, and there are emergencies where one needs to act quickly, but can take a few minutes to think about the necessary approach.  A lot of people in and out of the medical field don’t understand that there is a huge difference between the two.  Unnecessary hurry is one of three bad things in medicine (others are lack of sleep and interruption).  A subdural hematoma needs to be evacuated, but unlike its cousin an epidural, it doesn’t need to be done in the emergency department, and there is time to plan the procedure.
  • CT Scans were relatively new and had changed the left-right orientation opposite to traditional X-Rays.  I practiced when CT scans showed this orientation, and it was extremely confusing.
  • Many people have trouble distinguishing left from right.  It isn’t a personality flaw, it is a biological issue, akin to being shy.  Approximately 15% of women and 2% of men have this problem.
  • Nobody spoke up to tell the surgeon they were concerned upon which side he was operating.

Without going into more detail, I reiterate the comments I made to the head of the operating room, who assured me that 99.9% of the time they did it right.

“No,” I replied.  “You get it right 99.99% of the time, and that isn’t good enough.  Counts matter, and wrong side surgery cases must be zero.”

We need better system design to decrease the probability of the wrong thing’s happening.  The stronger our systems, the more events will have to occur for something to go wrong, and that means people will be safer.

We will never know if a better system saved a life.  But probabilistically, it will increase the expected value of success, and I trust expected values.


June 2, 2015

“You guys have all given me different answers, and I don’t know what to do.”

The math tutoring room at the local community college has two parts, one for advanced math—trigonometry, pre-cal, and calculus; the other is for basic math, from carrying and borrowing up to college algebra.  I work in the latter, but as somebody with a Master’s in statistics, I am often the “go to” person for statistics questions.  The fact I have seldom used statistics in the last decade has made me rusty, but the material comes back, so long as one learns it well the first time.

When the individual came to me stating the conflicting opinions she had received, I should have either turned her down or told her she was going to have to decide up front whom to believe.  If I were not that individual, she should leave, and not waste her time.  The issue itself was a 1-sample proportion test, one of the M &M problems, where a certain proportion of different colors are put into the bag, people count out the number of each type to see if the proportion corresponds with the claimed proportion, within a reasonable margin of error.

The student had used the instructions given to her what to input into the calculator and found a probability that made no sense to me.  I looked at the question and came up with the correct probability.  The example she copied looked at the probability’s being greater than a specific number; the problem she asked me looked at the probability’s being less than a specific number.  She didn’t understand that the example given to input and the problem were asking opposite things.

I tried every way I could think to explain the issue to her.  I have become more adept at calculators, finding them fast and helpful.  This woman, as are so many students today, was faster with the calculator than I.  Her problem, however, was something that it took me some time to figure out.  I had drawn a diagram of the probability curve, the Bell-shaped normal or Gaussian distribution, and she had looked confused.  That led me to finally ask a simple question:

“Have you ever computed these probabilities using a normal probability table?”


I now understood her problem.  She was being asked to input data and push a lot of buttons.  Unfortunately, she had no idea what was being done to the data and why.  A lot of statistics is finding the difference between the sample and a postulated or known mean/average, then dividing by the standard error, a measure of variability.  The concept of variability is critical to understanding not only statistics, but everything statistics is used for, be it political campaigns or climate science.  Natural processes, like heart rate, body weight, stock market prices, or temperature, are not the same when measured over a period of time.  They fluctuate, and statistics helps us understand the fluctuation.

Dividing the mean by the standard error normalizes the data, allowing it to be compared to one standard, this instance to a table to find a probability.  By doing many problems where I had drawn a bell-shaped curve and looked at probabilities, I understood the concept well enough to teach it to undergraduates in Las Cruces for two years and in Tucson for another four.

This woman was from another generation of students, however, and in the decade where I have not been heavily involved with statistics, drawing a picture of how the data were distributed and having a sense of what the data were trying to say has atrophied, at least where I am tutoring.  The argument I was having with the student had a lot to do with the arguments I needed on the calculator;  she did not understand them, only that she was obtaining different answers.  Put simply, she did not have the background to be using a calculator.  I could say that about many students.  When I taught for a private for profit college, when a student saw a probability “6 E-4,” they wrote “6” as a probability, both impossible and showing no sense of what E-4 means, which is a power of 10 to a minus number:  6 E-4 =0.0006.  I don’t expect the average person to know that; I do expect somebody taking statistics and using a calculator to understand it.

That is only my opinion, from one who learned the material from first principles and is still slow to pick up a calculator, because I am often more comfortable performing my own calculations.  It remains to be seen whether we will continue to teach by calculator or teach by understanding the material, using the calculator as a tool to speed up the process.  I fear that in our rush to educate people, we are giving them instructions as to what buttons to push in a lot of subjects, without any idea of what is going on inside a calculator or more importantly, inside the system we are analyzing.

This is not idle philosophical musing.  When I taught, more than half the class did not understand what “the rate of increase in health care costs is declining” meant.  To them, the statement meant that the costs were decreasing, rather than the number was still increasing, but less rapidly than it was before.  This term is commonly used. The concept of statistical error to many people means that statistics is wrong, so it doesn’t matter.  Statistics is unable to tell us the exact results in a population, because from a poll, we do not know what the exact result is for the people in whom we are interested.  Where we differ from other fields is that we quantify the error in terms of confidence and probability, and we know the difference between the two terms.  We reject the concept that “anything can happen,” because we define a priori what “can happen” means.

We need to learn what calculators can do; equally importantly, what they cannot do.  Data that are not collected randomly have limitations what we can say about them.  Calculators do not have the ability to discern that. Calculators answer only what we ask them; they neither ask questions, nor do they tell us what we might want to know.

Calculators and computers are wonderful tools to get information that one needs, but education, critical thinking, and understanding remain timeless.


May 24, 2015

Quite by accident, which is how my life usually occurs these days, while tutoring at the community college, I went to an algebra site to check something.  I don’t remember what it was, but when I tutor, I frequently encounter problems I remember but don’t recall exactly how to solve. I understand ellipses and hyperbolas, but I forget how to find the foci or the latus rectum.  I have to look it up.

While on the site, I discovered the solutions were posted by volunteers, so when I had a quiet stretch, I gave myself a user name and logged in, solving a few problems that afternoon.  I found it relaxing, which I am sure would surprise many for whom math is an odious chore.  What I have learned, besides hyperbolas and ellipses, was more than math itself.  Those who do not like math might read on, for you will be surprised.  Those who do like math will likely shake their heads in agreement.

The first lesson comes early in Ringo’s and George’s lyrics:  “You’ve got to pay your dues, if you want to sing the blues.” MATH TAKES PRACTICE, just like the piano.  I practiced the piano an hour a day and took lessons for three years.  I got better.  Oh, I never got past a couple of recitals, where a dozen of us played solo to our parents and a few others.  Wow, I was nervous.  But I did fine.  I played “By the Sea,” which I had memorized.  I played it well and everybody clapped.  I never thought I had musical talent, and to be sure, I don’t have much.  But I could play the piano; I could read music and even change it into different keys.

I think latent math talent exists, too, but one has to follow the guidelines, of which practice is the most important.  Practice allows one to solve problems, but it has a bigger advantage.  When one needs such math in the future, while it may have been forgotten, it returns quickly.  I never forgot the slope of a line.  I did forget the point slope formula and quickly relearned it.  I forgot how to integrate by parts, but I re-learned it enough to astound a few people in graduate school, 30 years later, when I blurted out the integral of log x one autumn afternoon in Las Cruces.

Sit with me as I tackle online a routine problem.  Routine problems are ones I can do without pencil or paper.  People submit them to get help.  Watch my thinking, but more importantly, WATCH HOW I MAKE MISTAKES.

Joel and Nicole each together have 350 coins.  When Joel gives away half of his and Nicole a third of hers, they now have the same number of coins.  How many did they start with?

I love mixture problems; I’ve never had to review them.  It’s sort of like a guitarist who learned “Don’t Think Twice” in the 60s, never played it since, and tries to play it at a gathering.  He may not tune the instrument quite right, and he gets a few chords wrong, but he plays the song, and it is appreciated.  Math is intertwined with music; an eighth note is held twice as long as a sixteenth.

I let Joel’s coins = x  and Nicole’s = y.  I could let Nicole’s equal 350-x, a trick I use, if I choose to use only one variable.  Musicians have tricks when they play, too.  They put a song in D major, rather than in D.  They invent stuff.  I have in math, too. Back to Joel and Nicole.

x + y =350.  That is a fact.  Translate: Joel and Nicole together have 350 coins.

Joel gives away half his coins.  He has half left, (1/2)x.  I put parentheses around the numbers, because 1/2x is not the same.  Hey, you play in E minor on a piano, you may touch the D major key, same one, but it doesn’t sound the same.  (1/2)x is not the same as 1/2x.  We’re no different in math.

Nicole gives away 1/3 of her coins, so I first write she has (1/3)x.  I am not correct, and when I later check the problem, it isn’t right.  I return to the beginning, BECAUSE SOMETHING ISN’T RIGHT.  I don’t convince myself it is right, I don’t dictate it is right.  It is NOT RIGHT.  I have an open mind and start over, asking WHERE DID I GO WRONG?  A lot of politicians ought to ask themselves this question.  The guitarist knows when it doesn’t sound right, too, asking himself where he went wrong.  I and the guitarist are on the same wavelength.  WE KNOW IT JUST ISN’T RIGHT.  Oh, I discover, Nicole has (2/3)s of her coins left, not (1/3).  What was I thinking?

Can you see that somebody like me, good in math, makes a simple mistake?  If you aren’t good at math, did you ever realize how many mistakes mathematicians make?  We make them all the time!!!

OK, so (1/2)x=(2/3)y .  Now, there are at least three different ways to solve this, but I’m not going to play the song in 3 different keys, just one.  I’m lazy, and I like my math simple.  If I double (1/2)x, I get x.  If I double (2/3)y, I get (4/3)y.

x=(4/3)y,  I like this.  It feels right, just like hitting the proper chord feels right.  You sense it.  We’re brothers here.  The sense is well known in sports, where it is called “the zone”:  Bill Bradley was once interviewed during practice.  He made a 20 foot hook shot while talking:  “You have a sense where you are.”

Now instead of x+y= 350, I have (4/3)y + y=350.  One variable. But y = (3/3)y.  You’d be amazed how often we math guys multiply by 1, which doesn’t change anything.  Not only that, we multiply by really strange “1”.  Here, it is (3/3).  Sometimes, it is (√7 + 2/)(√7 +2).  That is also 1.  Even stranger, we may add 0, because it doesn’t change them.  Crazy.  Until we add 36-36 to an equation that has (x2+12x), allowing us to write (x+6) – 36.  Both of those are equivalent, but we can do things with the second that we can’t with the first.  I now add the y’s: (4/3)y + (3/3)y =(7/3)y, which equals 350.  I flip the fraction over, because (1/2)(2/1)=1 and (7/3)(3/7)=1, and I want 1y or just y on the left.  I must multiply the right by (3/7), too, and without boring anybody, y=150.

I make another mistake, a rookie one.  I usually solve for x, but if Joel had 150 coins, Nicole had 200, and one can’t divide 200 evenly by 3.  I WAS WRONG.  Two minutes later, I realized I had solved for y, and when I went to the top, I had CLEARLY WRITTEN BUT FORGOTTEN that y was Nicole’s.  She had 150; that checked just fine.

This is a simple example to a math guy.  We make many mistakes.  All of us.  We copy the problem wrong, we forget a minus sign, we add wrong.  Yeah, that too.  I’m just a guy who plays with math to relax, hitting a lot of wrong notes along the way.  Like the guitarist, I make good music, but “You Know, it Don’t Come Easy.”

I paid my dues.


May 8, 2015

A recent Facebook post showed a way to divide that the individual said “made no sense” to her.  Others weighed in with similar comments, saying they learned division differently.  They didn’t say whether they could still divide.  The complaints were leveled at Common Core, which now is to blame for everything wrong in education the way Mr. Obama is to blame for everything wrong in America.  Teachers are now getting on the bandwagon, in some instances bragging how many children are opting out of the test.  Before I tackle that problem, let me address this division problem, for there are several ways to do it.  First, if one doubles 2460 to get 4920, and divides by 10 (doubling both divisor and dividend doesn’t change the answer), one gets 492.    IMG_1117

That is how I would do it in my head.

Here, one is breaking down 2460 into numbers easily divisible by 5; namely, 2000, 400, and 60, and adding them.  Same answer.  This would be my second choice.

What I asked was how many could divide 4 into 3586.  To me, if one cannot do that problem quickly, the way they learned division didn’t work for them, and the issue isn’t with Common Core but with how to divide.   I divide 4 into (3600-14), to get 900-3 1/2= 896 1/2

As for parents not being able to do their child’s homework, my father, a science teacher, wasn’t able to help me with my geometry homework, either. That’s not common core; it’s the fact that  over time we forget how to do things.  If one learned how to divide but no longer can do it, with brief practice, one could again do it well.  I re-learned calculus 32 years after I took it.  I wasn’t brilliant, but I had once learned the concept.  When I saw it again, and saw the instructions, my ability once again returned.

One good comment posted was “how do you divide by 7?”  I answered that in my response to the original post.  Suppose we want to divide 7 into 3817:  I break 3817 into 3500 +280 +37.  If I divide 7 into each of the three dividends, I get 500 +40 +5 remainder 2, or 545 2/7.

The issue with Common Core, just like No Child Left Behind, from the “Education President,” is that American children as a whole are not doing well in math and other subjects, lagging behind the rest of the world. The rise of charter schools, the decline of public schools, the lack of funding for the latter, while we are building prisons and cutting taxes for upper income earners and businesses are all contributing factors.  The public also demands accountability.  That is fine.  The response has been to create various forms of testing to prove competence.  After all, at some point in the educational process, somebody needs to be proven competent.  How one proves such without testing I do not know; proof of knowledge has traditionally required showing one’s ability to do something, and I call that a test.  The fact a student may be nice, easy to talk to, gets along with others, gives hugs, or helps out at home or in the community is fine, but I want more from my mechanic, doctor or pilot.  I like hearing a friendly voice at Dutch Brothers.  I also want them to make change properly and serve drinks with safe water and safe ingredients.  I want my automobile properly engineered so it doesn’t break down and the seat belts and air bags work.  I want the dam up river to be constructed so it doesn’t break, which it did a while back, and lack of attention to prior broken parts caused the one of the sluices to be left open, because the motor at the time couldn’t be trusted.

We often don’t see the results of competence first hand, so we tend to disparage tests; we do, however, see the results of lack of competence.

Arizona had the AIMS test, testing English, math, and science.  The problem with AIMS was that not surprisingly, many students failed it.  If they failed it too often, they didn’t graduate.  A child’s not graduating from high school upset parents and others, because for years, children had been passed on up the line to graduation, leaving high school with the inability to do math, speak well, know geography, history, including American history, and ability to write properly.  But they graduated.  Eighty per cent failed the local community college’s math placement test.  I tutored for years in an affluent high school where students in the 10th-12th grade worked on simple arithmetic problems at the third grade level, all along being allowed to listen to music.  When I objected, stating music was a distraction, the students said they needed music to perform.  I then asked why they were in the class in the first place, since their performance to date hadn’t been acceptable.  The school allowed music to be listened to; I thought that a bad idea.  I often wonder what these students are doing now.

AIMS became watered down, so that as long as a student had a decent GPA, they could graduate without it.  Finally, AIMS disappeared altogether.  In its place, we have new national standards.  I am not saying I agree with what is on the test, and I don’t agree teachers should teach to the test.  They shouldn’t have to. Too often, math tests are written by those who want to show how clever they are.  I think we might well do better with at least two tiers of math, one for those who are likely to go to less intensive (regarding math) fields, and the other for those who are going to college and need a certain degree of math to continue.  Germany tests its students earlier in their educational career; it is clear that some should not go to college but belong in other careers, important to society, a better fit for the student, but without the math that is needed for higher level education.  I might require basic statistics, so that students would understand something about sampling, margin of error, mean-median difference, how to make and read a graph, and how to count things that matter.

Like it or not, people need to learn how to add, subtract, multiply and divide.  They absolutely need to memorize the multiplication tables, and eventually multiplication will become automatic.  They need to be able to use calculators but also understand when a calculator’s answer makes no sense.  Students must show knowledge of math for a given grade before they are promoted, the proof being one with which any reasonable adult would agree.  Some high school diplomas will not contain the same words as those for students who took four years of high school math.  Parents need to fish or cut bait.  If we want children to be properly educated for the 21st century, then we need to prove it.  It is distressing to see and hear both parents and teachers alike complain about Common Core unless they are developing alternatives.  I’m open to suggestions; I’m not open to continuing to pass students along to the next level, delaying the day of reckoning.

That day has long come.


April 27, 2015

Lately, there has been a lot of press, fanfare and pride in having one’s child opt out of testing for Common Core.  I am not a fan of standardized tests, but I took them every year in elementary and high school.  Perhaps the stakes weren’t high then, or maybe I did well enough on them so it didn’t matter.  My teachers didn’t teach to a test.  They taught material, and we were supposed to learn it.

I have taken more than one proud teacher to task for bragging about how many kids aren’t going to take the test.  “What,” I ask, “do you plan to put into place to know that a student is competent to advance to the next grade?”  At this point, I usually hear complaints about how teachers aren’t listened to, rather than specifics about how to make something better.  It’s easy to complain about something; it is a lot more difficult to put oneself on the line and offer something different.

At Lane Community College, where I am a volunteer math tutor, a recent editorial in the school newspaper suggested the school get rid of any math requirement, with the headline “Math-free degrees make sense.”  Some quotations:

  • “Many of those careers don’t require people with math skills.”
  • “For some college programs, not all, math is completely unnecessary.”
  • “However, for some students, any math is a hindrance to getting a degree.”
  • “When students have to subjects they are not suited to, rather than attending classes of…relevance…they become stressed and tired.”
  • “Granted, those going onto (sic) four year colleges would still have to study math.”
  • “What matters to employers is that job applicants have the necessary knowledge and skills to get the job done.”
  • “Choosing between a job candidate who had to study math…and one who didn’t…employers simply wouldn’t care.”
  • “These days (sic) technology handles all the math most people will ever need.”
  • “I’m not saying no to math in education altogether.  I’m saying it’s the responsibility of earlier education.   Remedial math should be the choice of the individual, not a community college mandate.”
  • “A more practical…alternative would be where students learn…how compound interest works, how monthly payments enslave people…”

My first reading of the article was that is was sarcasm, but I soon realized it was not.  The editor-in-chief of the paper has her picture present, and she looks like she is within a decade of my age.  I had a choice between a 250 word letter to the editor or a 600 word opinion piece.  I chose the latter.  I will expand upon it a little more.

It’s unfortunate that the Suze Orman Show is now gone, for Ms. Orman embodied the importance of math in finance and in life.  Those who sought help from her did not fully understand its importance, as the “Can I Afford It?” and “How am I Doing?” segments showed.  

My student who wanted to be a stockbroker couldn’t understand why he was learning logs, until I showed him how to determine the doubling time of money with 5 calculator strokes (72 divided by the interest rate in per cent is number of years), proving it in two lines (proof below).  He was amazed.  Another was thrilled to discover that by knowing the volume of a cylinder, he could determine cubic inch displacement of an engine.  I have never forgotten the look on his face, when he realized his knowledge.  Math is important, can easily be made relevant, and—yes—even fun.   Having my advisor in graduate school look at a proof of the first and second moments of a previously unknown hypergeometric function, say “Good job,” was one of my highlights of two difficult years away from home.

I grew up in an era where people did the same job their entire life.  The world is rapidly changing; multiple careers during one’s lifetime are now the norm.  At 66, I have had three.  We can’t imagine what jobs will be needed 10 years from now, let alone 50.  The winners in this new world will be those who can adapt; math is the single most valuable subject I know that increases one’s adaptability.  I taught adults in their 30s who discovered that they were wrong, when they thought in high school they knew their career path. Suddenly, they needed an MBA to advance in their company.   When faced with linear regression in a business model, knowing the slope of a line becomes relevant, as does probability, difference between a mean and a median, servicing debt, survey design, and measuring quality, to name only a few.  Without math, the glass ceiling becomes cement. 

I have heard students complain, like Ms. S., that they wouldn’t use math they were learning.  I could easily fill this paper with counterexamples, and my primary career was a neurologist.  I didn’t start my third career, statistics, until I was 49, and I had to review calculus taken 32 years earlier in order to get accepted.  Math, like learning music, chemistry, or Spanish, takes work and practice.  If Ms. S. thinks that math is stressful and makes people tired, I can assure her that I survived the stress and fatigue of reviewing calculus on my own and two years of graduate school, 300 miles commuting each way.  I didn’t remember calculus, but once I began to review it, I discovered something important: “If one learns a subject well, and doesn’t use it, he will forget it.  BUT, once he sees the subject again, it is relearned quickly.”

I have long thought we need a parallel educational pathway where math requirements vary for students.  I agree that a community college should not be a high school finishing institution, but until elementary and high schools teach students how to add and subtract, learn the multiplication tables, know when a calculator result doesn’t make sense, allowing remedial math to be the choice of a Lane student is saying math doesn’t matter at all, countering Ms. S.’s claim.  Offering math-free diplomas to increase graduation numbers is an astoundingly bad idea.  Our society needs proof of agreed-upon minimum math competence before a student  graduates from high school. Until then, Lane students must deal with the “stress” of learning math.  Life is tough. In the meantime, I hope Ms. S. understands that teaching compound interest to become financially literate requires algebra: Stating I=prt doesn’t allow one to understand continuous compounding any more than showing me middle C on a keyboard and thinking I can find D major.  For those who think math is worthless, I’m at Lane twice weekly by choice, to help students learn math.  To me, those 8 hours are almost a sacred calling.  Yes, sacred, not scared.

[A piece of wood was 40 cm long and cut into 3 pieces.  The lengths in cm are:



x+6   Add:

4x+8  = 40


x=8; pieces are 11, 15, and 14.  Even if you didn’t know this, x+7 is larger than x+6.  One piece has to be at least 14 cm, so x has to be 7 or greater.  Put in some numbers.

What is the length of the longest piece?  15 cm.  7% of American 8th graders got it right; 53% of Singaporean.]


Compound interest that can be taught for financial literacy (not difficult, but if you haven’t had algebra?):

Continuously compounded (the easiest):

P=Po exp^(rt) ; P= principal  Po=starting principal, exp= e (2.71828); r=rate, t=time. Don’t worry about e; ln takes it away just like division takes away multiplication, subtraction takes away addition.  Can you imagine doing that without knowing algebra?  Yes, e=[1+(1/n)]^n, as n gets large or ∑[1+(1/n!)] summing from 1 to infinity, but without algebra?

2P=Po e^rt; P=2Po, because money has doubled, (2Po/Po)=e^rt; ln2=rt

ln2/r= t; 0.693/r = t   69.3/r (%)  =t   round to 72/r=t, because 72 is divisible by many numbers.  That is 6 lines, but 8 small equations fit in 2 lines.


February 23, 2015

Yesterday, while looking for a pair of walking shoes, I was helped by a saleswoman who chewed an apple the whole time I was there.  I know people often need to eat while working.  I did it for years.  But eating in front of a customer one is helping seems rude.  I wondered about her education.  It was a good day to wonder, for the Sunday paper had reported that Lane Community College received a “scathing report” during their accreditation.  They are accredited, but there is a lot of work that must be done in the near future; a repeat visit is planned.

There are issues that clearly relate to Lane, regarding course structure, how students are evaluated, and a need to establish clearer goals.  There are other issues, however, not mentioned in the article, which I think need to be discussed.  I wrote a letter to the paper, but after finishing realized I had already used my allotted one letter per calendar month.

I am not an educator, only the son of two.  I have, however, taught at a community college and at a for-profit university, leaving the latter, because I thought it intellectually dishonest to pass students in statistics when they had neither the necessary math skills nor adequate time to learn it.  Not understanding the slope of a line makes linear regression impossible to learn. 6 E-5 on a calculator is not 6 but 0.00006.

I volunteer at Lane twice weekly tutoring math.  Yes, I eat lunch while there, but I put food away if a student needs help. In Arizona, I volunteered in 3 high schools for 9 years, eventually becoming a substitute teacher, because I wasn’t utilized enough as a volunteer.  I ate on the job there, too, and I barely had time to use the bathroom.  We need volunteers in the schools, but they must be kept busy.  Establishing such a system should be a national priority.

At Pima CC in Tucson, 80% of the incoming students flunked the math placement exam.  In a high school in an affluent district, I spent two years helping students do “accelerated math.”  The euphemism was an attempt to help 10th graders, with elementary school math knowledge, reach standards allowing them to graduate from high school, standards that have since been removed, after first being watered down.  We want math fluency; we just don’t want to hold students back from graduating if they don’t have it.  One may argue the test wasn’t good, but at least there was a way to evaluate students.  Now there is none.

The students I taught needed multiplication tables beside them, which I think should be known by everybody reaching junior high school, let alone 10th grade. I think students should know 8 x 6 or how to divide 3 into 12 without using a calculator.  I’m not exaggerating.  Each had been passed up the line despite their not knowing basic arithmetic.  They got “participation points,” “trying hard” was important, and some of their parents demanded they be allowed to finish high school with their peers who did know these basics.  Watch Suze Orman sometime, and it becomes clear what happens when people don’t understand finance.

Community colleges have become de facto high school finishing institutions.  I don’t know whether community colleges pass students to the next level—the workplace or a 4 year college—with the skills they need, like making basic change at a cash register.

Or not chewing on an apple when one is helping a customer.

I have three fundamental questions:  1.  What are we trying to do?  2.  How will we know we did it?  3.  What changes can we make that will solve the problem?

Funding tied to number of degrees awarded increases pressure to award degrees.  How do we know if the degree is worthwhile?  One can pass students up the line, but eventually I want a doctor, a mechanic, a pilot, or a computer specialist who is competent.  The piper must be paid.  Competence must be definable and proven.

It includes not chewing apples in front of customers.

I don’t believe a four or even a two year stint in higher education is necessary for all.  Many important jobs in our service economy don’t require college.  Education’s primary role might begin by teaching early and often that complex 21st century problems are not addressed by catchy phrases.  We need to grant meaningful degrees, not just count them, teach the myriad skills required today, pay for them, and keep education affordable.  Climate change, ocean acidification, immigration, religious fundamentalism, North Korea, Cuba, Iran, competition, environmental degradation, defense, can’t be addressed by “America first,” “boots on the ground,” “I’m not a scientist,” “deport all of them,” “de-regulate,”  “let the market do it,” or “allow parents to decide.”  None of these and other issues have clear answers.

We need to determine what courses are needed for today’s workforce and for those jobs we believe we will have in the future.  In 2045, people will be doing work that today not only doesn’t exist, we can’t even imagine what it will be.  Streaming video online, wi-fi and smart phones weren’t things I thought about in 1985.  Indeed, the words “streaming” “wi-fi,” and “online” didn’t exist, smart belonged with people, and video was defined in millimeters and called “film”.

How we certify students needs to be changed.  We need a required, sensibly structured way to state that an individual is prepared for the next step. These changes will be painful to higher education.  We have to pay for this as students and as taxpayers.  The debt load is burdensome; people need to learn what is necessary for a skill, which may not require 4 years, or even 2.  Stampers don’t need to know Chaucer, not if it is part of their $50,000 student debt at graduation, but they need to know enough math to do finance, enough English to communicate, and enough science, history and geography to be able to vote intelligently.  Professional golf management as a major once sounded like a joke, but given the popularity of golf, I’ve reconsidered my position.  By the way, learning to reconsider one’s position on a matter should be taught, too.

What are we trying to do?  Have an educated populace in the 21st century.  What is an educated populace?  I don’t know.  I offer my thoughts, and if our country were a place where we could discuss complexity with civility, not with talking points and shouting, we might be able to answer this question better.

How will we know we have done it?  We need better measurements than we have, ones that will tell us the bitter truth, which we all know exists.  We have millions of poorly educated citizens.  Let’s neither allow gaming of the system nor get hung up upon punishing schools.  The solution will be expensive, requiring money, volunteers, good ideas, but most importantly evaluating students honestly. It will be painful.  The truth usually is. We need multiple career pathways to accommodate variability in learning and intelligence.

How do we move forward?  Ask the right questions. Then answer them.  Honestly.


January 19, 2015

“Well,” I said, looking at the student’s math problem, “everything is fine until here:  you have (-14/23) + (15/23), which is correct, but you wrote they equaled 18/23.”

“What should it be?”

The student paused.  I continued,  “What is minus 14 and plus 15?”

She took out her calculator.

“No,” I said.  “No calculator.  What is minus 14 plus 15?”

She thought for a few seconds. “One”.


“I must have pushed the wrong button on the calculator.”

I tried not to cringe.  “You don’t need a calculator to add minus 14 and plus 15.  By using a calculator, you run the risk of pushing the wrong button and believing what comes out.  Use your head.  You knew what it was.”  The woman nodded.

We tutors sat alongside a wall at desks, and students, who sat at one of many tables, working on math problems, would come to any of us if they wanted help.  I spend four hours, sometimes more, two days a week as a volunteer, and I am usually busy the whole time.  A fellow tutor about my age commented how we once had main-frame computers (the adjective has now almost disappeared from the language) that took up a whole room, required air conditioning, and needed punch cards to do simple calculations.  I can remember learning BASIC, written by John Kemeny, mathematician, teacher, entrepreneur and president of Dartmouth College for 11 years, including the year I graduated.  Kemeny was a genius.

In 1969, Wang calculators appeared in a small room in the chemistry department, where I was a major.  These were slightly smaller than a laptop keyboard, and we could then do exponentials and natural logs.  We used to use log tables to do calculations. Our generation knew the word “anti-log” and the term “”. If you know what I mean, you are at least 55.  We thought these new calculators were incredible.  We could put away our slide rules.  Imagine, cube roots by pushing buttons! We played with [ln (0)], to see how the calculator handled undefined numbers.  It was fun.

Now my TI-83, a rather old calculator, can graph any polynomial I want in any size graphing window I want.  It can give me the values of derivatives, intercepts, z-values for proportions, t-tests, Chi Square values, raise numbers to the 100th power or more, which makes interest calculations easy, store numbers, do linear, quadratic, cubic, and exponential regression, has a built in z- and t-table, does binomial calculations, take n th roots of things, and fits in my back pocket.

What it cannot do IS TELL ME WHAT TEST I SHOULD USE.   Nor for that matter, can it square any number with 25  digits, all of which are 9, as fast as I.  I think I can multiply any pair of two digit numbers as fast.  Squaring three digit numbers ending in 5, I can also come close to beating it.  But graphing y= [sin x/(x-2)]^2]?  No way I can come close.  I can do logs to the base 10 of 2,3,4,5,6,8,9, and 10 to 5 decimal places faster, but I can’t do the log of 7 or larger primes. I can’t do them to six or seven places.  Nor can I do trig functions other than the simple 30, 45, 60, 90 and multiples.  But I can estimate them quite closely, which surprises people, when I say the tangent of 35 degrees is about 0.7.  The tangent of 30 is √3/3=0.5773, and the tangent of 45 is 1, so I just interpolate.  Many times, that is all I need.  I am metric fluent, but I can’t use polar coordinates well.  The TI-83 does that and shifts to radians with a couple of key strokes.

These calculators are great.  BUT THEY CAN’T THINK.  They take your thoughts and input and give the result.  They don’t say whether you asked the proper question.  They don’t tell you that a quadratic function might fit the data better than a linear function, They will tell that you inputted an incorrect formula but not a wrong number.

Nor will the calculators say if you violated the assumptions with linear regression, something that many people who argue against global climate change, for example, fail to recognize.  One cannot simply make a scatterplot, draw a line through the points, or even have a calculator do it, and conclude nothing has changed in the last decade.  A calculator can minimize the sum of the squared vertical distances of the points from the line, showing the best “fit”.  It can do it faster than I, although it can’t prove why the formula works, and I can.  A calculator can show whether the line is going up or down, even how much, and if one asks for more, the p-value for the line, the probability the occurrence is different from a fixed number’s being a chance occurrence. The calculator, however, cannot cannot tell you whether the distance of each of the points from the line follows a normal distribution with mean 0 and the same variance, without some work and judgment from the user.  Nor does it tell one whether a point should be an outlier.  That also requires judgment.

Calculators have to be used for the right things, just like computers, and one needs to have an idea when the answer makes no sense.  If I Google “East Pacific Ridge,” wondering why the Jet Stream Wave #3  has stayed stuck for so long, which is devastating the American West, I might read something that says only warm moisture from south is getting through, because of the radiation in the water at higher latitudes from the 2011 tsunami can’t, which is nonsense, akin to pushing the wrong button.  We push wrong buttons sometimes, or we forget to erase something in the calculator.  We look at an answer and should realize it makes no sense.  That ability has been greatly diminished, and in some places has disappeared, along with my slide rule.  I am not a whiz with a calculator.  But I have the ability to look at an answer, a graph, say about what things ought to be, and whether the answer makes sense.  I agree that Common Core is teaching estimation, but there are multiple ways to estimate, and children need to be taught multiple ways to do math, because they learn differently.  I estimate differently from the way Common Core does.  I learn differently.  Indeed, discovering how an individual learns is one of the most important things education should do.

A 10% increase in the likelihood of a rare disease is not 10% likelihood you will get it.

Decrease in the rate of growth does not mean the total is declining.  It is not.

Four different outcomes do not mean they all have equal probability.  They usually don’t.

There’s a place for the mean and another place for the median.  A person who uses them interchangeably to describe a set of data is either lying or doesn’t know the difference.

Finally, (-14/23) + (15/23) can’t possibly be larger than (15/23).


January 2, 2015

I was thrilled when I discovered the solution:  the student had forgotten to cube both numerator and denominator constants when she inverted 1/[(sec x)^2] to (cos x^2).  Two other tutors hadn’t seen it, and I haven’t done trig calculus in years.

When I first looked online at Lane Community College to become a volunteer math tutor, it appeared that I needed to take an 18 hour course in how to teach.  I was a bit miffed; I have taught math for years.  When I arrived in Eugene, I went to the downtown office and was given a number to call, but that didn’t help, either.  I waited, since it was summer.

In September, I called the college and this time given the e-mail address of a person whom I should contact.  To my surprise, she e-mailed me right back and said I could come over to talk at the end of September.  I did that, met her, and learned how the system worked.  She asked me when I wanted to work.  I set up some times and went to work.

The system at Lane is good, interesting, and my hours are flexible.  I often go when I have free time, for there is always a need.  The tutors have desks along the wall with a computer to look up things.  Students study in the room; if they need help, they go to one of the tutors.  If all are busy, the student waits in one of the chairs along the wall until somebody is available.  I get every math issue I can imagine, from men and women, young and beautiful; old, with a lot of miles on them; tattooed, body piercing and hair color I can’t believe.  One, 76, was recently released from prison after four years.  All are there to learn; all deserve help and respect.  Some come to me if I’m the only one free, preferring other tutors.  I don’t care. I help all comers, and if I don’t know something, I look it up quickly online.  I’m good, not perfect, but when I can explain basic algebra to somebody, lining up equal signs, balancing equations, what can and can’t be cancelled, showing short cuts, trying multiple approaches, completing squares, they are appreciative.

I’ve handled math from subtracting fractions to integral calculus.  The latter has been difficult, but I am amazed at what I have pulled out of the air.  I am the go-to person for statistics, since I have a master’s in it.  The other day, I helped a guy use a compass to make a 30-60-90 triangle.  One of the tutors asked me if I knew how.  I didn’t, but quickly figured it out.  Tutors help each other.

Every day, when I leave, I am thanked for doing what I love.  Amazing.  It works; one day I was told twice, “I saved the day” by showing up. The week before finals, I went four days in a row.  I have worked solidly for five hours.  I bring material to read and it stays unread, for I am busy. I like what I do, I am helping people, I am appreciated, I am making a difference.  I look forward to tutor day at Lane.

I also volunteer at a reading program for first and second graders.  Reading to children is important.  They need to hear the sound of words, the rhythm of the language, and discuss the book.  They begin to learn pronunciation.  They need to discover that books can take them places they can’t even imagine, and allow them to see the world without leaving a house.  I taught myself to read when I was 3.  I read the newspaper, sitting on my father’s lap.

I signed up at an elementary school that needed volunteers and was within walking distance of my house.  I was a little leery, because several years ago, I tried to teach a 35 year-old how to read, and it was extraordinarily difficult.

The school doesn’t fully buy-in to the program.  I know that as soon as I walk in the door.  I sign in at the front office and get my name tag.  Nobody greets me.  The coordinator left for another job, and nobody told me or the other readers that was going to happen.  A volunteer took it over, but she is a volunteer, not a school employee.  We start at 11, a bad time, because we may only read during lunch and recess, not at all good for students, but that is what the school wants.

I have to go to 3 rooms, get the children, who should be ready immediately, but aren’t.  Then we walk down the hall to the cafeteria, and when we should be beginning to read, we are waiting for the dietary personnel to open up the serving line, which they always do, a few minutes late.  The children go slowly through the line, then get silverware, napkins and salad dressing, FINALLY walking outdoors 50 yards, with their trays, eventually arriving at the reading room.

By the time we choose a book to read, we are 10 minutes or more late. I try to read to a child who is hungry….or not….eating, or not…., looking out the window at recess, and paying attention…. or not.  When we finish, they go to recess, we get the next group and repeat the process.  What was supposed to be an hour is an hour and a half.  Reading to kids while they should be at recess and are eating is sub-optimal, messy, with dropped food, and because the child is eating, he cannot fully concentrate.

I leave, glad I’m done, and walk home.  I don’t think I have accomplished anything, except setting a new record for the duration of a cold.  I was originally told my commitment was half a year; now I am told it is a year. When a couple suddenly left for a month because of the birth of a grandchild, I was told to read to their students, not mine, which I thought not fair to either me or my charges.

It’s a bad fit for me.  I believe in reading to children.  I believe adults should do it, and the parents should, if there are parents.  Having children brings the responsibility to read to them.  I was not put in front of a TV when I was a child. I was read to. I had to write book reports, too.  I learned to look up every word I didn’t know, to improve my vocabulary.  That’s what students need to do. I’m concerned whether computer screen reading is as effective; I know how easy it is to be interrupted on line.

I think we need those with means and time to volunteer in schools before or after classes, nights and weekends. The schools need to welcome volunteers with good systems in place to use them effectively.  Parents and the community must be involved.  This should be easy, but in my experience in high schools, it is not happening.  Why? Teaching to tests isn’t new. I grew up in the Sputnik era, however, when the world changed, and America got a dash of cold water in the face.

I tutor math where I am wanted and make the subject come alive.  For now, I read to kids who are hungry and distracted at a place where it doesn’t seem to matter.  It should.

A lot.




December 22, 2014

As I rode the bus yesterday, I happened to hear the driver say starting pay was $17 an hour, about $34,000 a year.  This is a job where one has to drive a large vehicle in traffic, keep a schedule, load disabled people and strap them in, keep order, deal with the general public, who are not generally well off, often with mental disabilities, in a place with wet, icy roads.  In short, the pay is not commensurate with the responsibility.

We don’t pay teachers well, either, a similar starting salary here in Eugene.  Sure, experienced teachers and bus drivers get more, but they top out about double their starting salary, well below six figures.  Teachers have a lot of responsibility, too.  They are educating the next generation.  They have to deal behavior problems, be surrogate parents, deal with parents, and teach to standards.  I have been a substitute, where I got paid $75 a day to teach statistics, keep order, holding my bladder 6 hours, and wolfing down my lunch in 2 minutes.  I’m literal. It was 2 minutes.

Now I read that the Business Roundtable wants to delay full Social Security from 67 to 70. They wouldn’t have this affect those over 55, but if I were 50, and I had been counting on getting SSI, I would be upset.  Indeed, far too many elderly require SSI to survive, which was never the intent, but medical and other costs don’t go away.  The group wants to decrease COLA, the cost of living adjustment, as well.

The Business Group is a bunch of super rich CEOs, many of whom have annual bonuses greater than the lifetime earnings of the bus driver, the teacher, and me.  Certainly, this is often the case with financiers, who got huge bonuses for destroying the world’s economy in 2008.  Mr. Obama oversaw the recovery, which has been remarkable, but just not fast enough for people, which is not surprising, given the total lack of Republican support, and the party of deregulation is now back in power.  If we paid teachers better, more math majors might have gone into teaching, rather than Wall Street, where they created models using the assumption housing prices would never fall.

I’d bet many of the Roundtable folks say that the climate isn’t changing, too, despite CO2 levels we haven’t seen in 600,000 years.  Yet, they will say the stock market always goes up, with 80 years’ data.

The Roundtable says that personal savings should be increased.  I agree, but it’s difficult to save when one has student loans to pay off (to become a teacher, for example).   Granted, many don’t manage money well, which these rich folks count on, so they can sell stuff at higher cost, get higher interest rates on credit cards, the fine print of which most can’t understand, and push debt instruments that practically nobody understands.  You don’t believe me, watch Suze Orman sometime.  Oh, if you don’t know what the Rule of 72 is*, you have just proven my case.

I’d like to see Common Core deal with financial management.  A hundred billion dollars a year is borrowed by students.  The amount is unsustainable and must decrease.  Here are my ideas:  one, mandatory national service (not religious) required which discharges federal student debt.  Second, no cap on withholding SSI deductions. Third, stop giving people like me SSI.  I end up donating much of it in one way or another, but if you make six figures for 10 years, you delay taking SSI for 10 years.  That is forced saving.  I’m flexible on the amount.  What we must not do is make it more difficult for the working men and women, the ones who teach our children, drive our busses, pick up our garbage, clean our buildings, to retire with less.  We find another way. If others disagree, no problem.  But I don’t want “Damned liberal socialists are stupid” comments. I want specific ideas, written with good grammar, with dollar savings, and how it deals with the poor, needy, those with bad fortune, like leukemia, or accidents.  I have been fortunate, in large part because of America, and in lesser part because who I am and my work ethic.  The idea that  people are totally self-made goes against what American government has done.

The Roundtable had the audacity to want to raise Medicare eligibility to 70, not 65, which only shifts costs to somebody else.  If you are born after the mid-60s, you are SOL.  Looked at insurance premiums on Blue Cross for a healthy 65 year-old lately?  About $2K a month. We currently have the Affordable Care Act, but that could easily be gutted by Congress.  Medical costs increase dramatically with age; medical debts are a major cause of bankruptcy.  We increase the age groups that can get Medicare, not decrease it.  Where’s the money coming from?  Why from those who make over $2 million a year, with high marginal rates on bonuses.  Tell me, please, why a football coach should make $7 million with a low marginal tax rate?  He brings money to the school by using players who get paid nothing including no degree.

The Roundtable thinks “efficient” medical care will cut health care costs.  I heard about “seamless” care 20 years ago; we still don’t have it.  I espoused quality in medicine 35 years ago, because it was better and saved money, but we still don’t have good indicators. If we did, we’d easily know the number of annual deaths due to medical errors with a reasonable margin of error.  Yes, easily.  I understand sampling.

What need to expand Medicare to include the whole country, but I’d accept age groups as a start.  This approach won’t bankrupt the country or the people; indeed, Medicare is one of the best run programs we have.  The Roundtable think we ought to have competition, because “well-informed seniors” will make the right choices.

Have any of them read the Part D drug manual from Humana?  Medicare is fine; I have issues with the number of insurance companies who generate more paper than a Douglas Fir Forest in Lane County.  Well informed?  By whom?  Brokers?  The one I had steered me in the wrong direction.  TV ads?  By whom?  I am a college educated 66 year-old former physician.  I have trouble understanding the rules.  What about the poor black woman in Arkansas who turns 65?  Or an 85 year-old with dementia, an elderly person who can’t see well, can’t think as clearly as Paul Ryan thinks he can, and doesn’t have technical skills?  Do they really think “market forces” will work?

Oh, the Roundtable is in favor of healthy lifestyles, but they object to the EPA’s reducing ozone in the air.  That is hypocrisy. They are against regulations on food, water, or emissions.  Deal with obesity?  Five years ago, I measured the number of obese 6th graders in one school district in Tucson.  The results OF THE 1100 were astoundingly depressing.  We could have obtained data for the whole county, 32,000, FOR FREE.  Nothing happened. Why aren’t we using elderly volunteers more?

We need a strong middle class.  It’s time to deal with outrageous incomes that have produced no significant value.  The Waltons have $30 billion net worths on the backs of poor people working without adequate insurance. We need a major increase in the marginal income tax rate, we need a tax on investments, higher on capital gains, which are not earned income, and a buy-sell tax of 0.125%, which would generate $1 trillion by 2024.  We need a tougher means test for SSI and Medicare than we currently have.  We don’t take down Medicare or SSI for those who need it most.

The Roundtable wants better teachers, but they somehow think that certification requirements will do it, when increased pay will lead to better teachers. Increased pay works for better CEOs, I’m told, better coaches, better university presidents, so why should it be different for teachers?

My father, who went from a high school science teacher to superintendent of schools, once told me the argument “teachers were dedicated” was the reason their pay was so low.  That would be fine, he continued, “except you can’t eat dedication.”

The Roundtable ought to see if they can compute the area of their table.  If they can’t, then maybe they ought to stay silent on matters of numbers and how to save money, when not everything comes with a dollar sign.  That is the America I want and serve today.

*Rule of 72:  The time for doubling (year) is 72/rate of increase (measured in %).  Credit card interest at 24% doubles debt in three years (72/24 = 3)

Proof:  P=Po (exp)^rt, where P is the new principal, Po the original, exp=e or 2.71828, r the rate in decimal form, and t=time in years.  [1+(1/n)]^n = e = [1 + n}^(1/n)

(P/Po)= (exp) ^ rt; ln (P/Po)= rt.  (P/Po)=2 for doubling and ln 2=0.693.

Therefore 0.693=rt.  Change rate to per cent  and 69.3=rt.  72 is easier to work with.  so t=72/r.

Tripling time is 110/r.   This is done on aTI-83 by LN, 72/rate you choose.  It is easy.  This should be in common core.


November 13, 2014

“Would you like to see the Senator’s paper on the projection for Social Security for 2035?” a student asked a statistics professor friend of mine, who taught in DC.

“Is there a confidence interval mentioned?” replied my friend.


“Then I don’t want to see it.”

Nearly every prediction we make about a parameter or phenomenon has some uncertainty.  We make the prediction based upon evidence we have gathered; the evidence we gather may not be accurate, especially predicting the future status of Social Security, which is unknown.  SSI may not even exist in 2017, for if a significant number of powerful people have their way, and enough people decide not to vote, because “it never matters,” SSI will be dumped to save money, to be used to make wealthier people wealthier, because these powerful people want no debt, believing recipients are freeloaders.  I don’t agree, but I am one person.

Even if SSI is unchanged, the funding model may, the economy will, world conditions will, and the number of people receiving it will.  Laws may modify it. All of these conditions are unknown.  They are estimated, using a variety of techniques, but these estimates have error: a word, like theory, that has a different meaning in science than it does in regular speech.

A scientific theory is a system of ideas intended to explain something.  “Your theory (thought, guess, idea) is wrong,” is in the general vernacular. Neither is wrong, except when the vernacular is used to denigrate a scientific theory.  We have a theory of gravitation, but I doubt anybody would jump off a building.

Errors in estimation occur, and they don’t mean that scientists are careless, obtain false, or don’t understand data.  Those are uses of “error” in the vernacular.  Errors in science occur because we use samples to estimate uncountable totals, like the percentage of people who plan to vote for a certain candidate, or any quantity that we may have modeled.  Let’s look at the former.  We don’t talk to every voter.  We choose people at random, and there are a variety of ways to do that.  A perfect sample is difficult to obtain; online samples, the ubiquitous surveys that B-school grads have inflicted on the country, are examples of bad sampling techniques.

If we take a second sample, we get a different result.  Same for a third and all samples we might take.  Typically, we sample only once and use the result as our point estimate, the best value we know.  Are we completely certain?  No, we aren’t, unless we take a census, measure every individual, which is not feasible.  We can quantify the error, however, depending upon the sampling approach and the sample size.  The error decreases as the sample size increases, the decrease of the error approximately proportional to the square root of the sample size.  That’s powerful stuff, done right.  A random sample of a 100 people in the nation, on a yes-no question, has an error of plus/minus 10%.

From a sample, we may construct a confidence interval, using the sample result and size.  This interval we believe to contain the exact value of what we are trying to measure.  Does it ?  We don’t know, because the true value is unknown.  Can any value be possible?  It depends upon what one considers possible.  If one considers anything possible, like the probability of winning the lottery every week for a year, then yes.  If one considers the likelihood of the sample’s being wrong at no more than 5%, typically used in science, then no, everything is not possible.

The concept of a confidence interval allows us to state a range where we think the true value lies. It is either in the interval or it is not, which is a not useful probability statement (0 or 100%).  Therefore, we call it confidence, and typically, high confidence is 95%.  It isn’t perfect, but it is considered significant evidence.

This explanation is why I was upset when the Republican candidate for the Congressional District where I live, a scientist, published the names of nearly 32,000 scientists who did not believe in global climate change.  First, scientists who matter are climate scientists (133), not people like him or me.  Second, science is not done by voting, but rather gathering evidence.  Science is not shouting at somebody, threatening them, or vilifying them in print.  One cannot discount the almost unanimity of articles that state there is manmade climate change occurring, and then use a number of disbelieving scientists to support their claim.  The database is not updated for deaths or opinion changes, which speaks to sloppiness, too, frankly.  If the database is important, it should be correct.

The publication that this candidate used to publish his list was one for which I was once a volunteer reviewer in statistics.  It is a right-wing publication, purportedly scientific, but the articles are replete with non-scientific terms and name calling.  That is fact.  I have read it; moreover, I was asked to review the statistics for articles.  If one has read this blog, one knows that I am a liberal.  I volunteered to help a right-wing journal.  I would be interested in examples where right-wing people volunteer to help a left-wing journal. I did this for free.  Truth matters.

On the basis of statistical evidence, I recommended against the publication of an article that claimed that low dose radiation was healthy (used skewing wrong), which the Congressional candidate believed in, that vaccines caused autism (regression analysis failed to check assumptions), and that the FDAs not approving drugs caused 10,000 deaths a year in the US (using correlation to conclude causation).  I stopped receiving articles for review.  I didn’t know why, suspecting that the journal didn’t like my opinion.  I cannot prove that, and I have no confidence interval.  However, I am 100% certain I stopped receiving articles to review; I later resigned.

Putting “scientist” after a name is easy; look at “creation science”.  Good science, however, is difficult.  I apply science to my life, but that is not being a scientist.  A scientist, and I will grant the candidate was once one, researches or studies something and draws conclusions, even if the conclusions are not what he hoped or expected.

Rule 2 of my approach to climate change is to look at the confidence intervals of both sides:  one side states with high confidence that their interval does not contain zero or a negative number regarding global temperature rise.  The other side does not give any such interval.  This is not scientific, and I am being polite.  If one is completely certain global climate change can’t be occurring, given the complexity of the atmosphere and oceans, such knowledge would be sought after by every climate scientist in the world.

What disturbs me is that the leadership of Congress admits they are not scientists, yet they quote both sides equally, which they are not.  They use such reasoning not to act, for acting might cost jobs, an unproven assumption.  In other words, non-scientists are deciding scientific issues in the country, and I am highly confident they threaten our future.