If One Learns by Memory, and Does Not Think, All Remains Dark. Confucius

Probability

- If one learns by memory, and does not think, all remains dark. Confucius

In the mid-1980’s, the ten states with the greatest longevity were Hawaii, Montana, Iowa, Utah, North Dakota, Nebraska, Wisconsin, Kansas, Colorado, and Idaho. During the same time period, these same states except for Hawaii, were the states that consumed the most animal fat per human diet. Does this mean eating large quantities or even ridiculous amounts of animal fat prolongs life? An inference such as this from the data seems ridiculous and for a dairy company to propagate such lies to the American public would have all the indecency of two priests swapping stories they heard from confessionals. So what would be a more appropriate interpretation of the data? It also turned out that there was another occurrence in these same states, again except for Hawaii; these same states had the highest rate of graduation from high school. Thus, one could infer, the population’s demographics with regard to education may have played a significant role in longevity. A greater percentage of people who had more advantages, maybe better health insurance, maybe better living conditions on the whole contributed to greater longevity in these states.

There is a fundamental difference between correlating a relationship, which just means drawing a parallel between the states where people lived the longest and states the consumed the most animal fat, versus inferring causation, deducing from the correlation that eating animal fat makes one live longer.

It is said the ordinary chess player’s eyes roam over the entire board while the great grand masters scan the few squares that really matter. Let’s examine your eye. Again, in the mid-1980’s there was a correlation between the thirteen states that were voted to be the most scenic, WY, NV, CO, NM, MT, AZ, FL, OR, OK, CA, VT, AL, and WA according to the Automobile Association of America (AAA) and those states whose residents commit the most suicides. Should we conclude that beautiful scenery surrounding a neighborhood is a risky venture because it increases the rate of suicide? Is there perhaps a more reasonable explanation? Unlike the above data, the insight we need to see is not in the form of another set of hidden data. Rather, it is in the interpretation of the data it self. Do you see it? If not, we will tell you at the end of this opening section. Think about it. Scan the few squares that really matter.

Statistics you may not have heard.

While 79 out of 1000 people are injured at home, it is a surprise that nearly 58 out of 1000 are injured at work.
In this country, there are roughly two suicides for every murder.

Surprising, only because we tend to focus on injuries at home, or worry about our loved ones being in mortal danger, but rarely do we fixate on injuries at work or the possibility that suicide can take a loved one.

And why do we talk about so many people out of 1000? Because, raw numbers, when shown in a comparative light, give you a perspective of the world around you. For example, we know there are roughly 6.3 billion people living around the world, but since this number is to big to comprehend we use proportions to visualize a smaller number to represent the whole, say 1000 people. These 1000 people are assumed to provide an average slice of the greater population, preserving proportions to the world’s true demographic profile. This method is no different than shrinking the earth’s age to week’s time or shrinking the sun down to the size of a soccer ball to visualize the age of the earth or the vastness of space. Now, let’s examine the world around us through these 1000 representatives of the earth’s human population.

By continent, there are

570 Asians
210 Europeans
and just 60 North Americans

By religion, there are

300 Christians
175 Moslems, the fastest growing religion on earth
55 Buddhists
33 Jews

Literacy,

700 would be illiterate

By income,

60 people would own half the world’s wealth

Poverty,

167 would earn less than 1 dollar per day

Hunger,

500 would go to sleep hungry.

On the surface of the data, things may look really awful. Well, not really. A slight perspective change could show that as bad as things seem on a global level, it was far worse in the past. For example, in the 1700’s half of the world’s population died before they were eight years old.

You may be thinking, well, yes, while this is interesting in a trivial sort of way, maybe even eye opening if I was to stretch it, but to be honest, so what? How can a ‘feel’ for numbers, basic numeracy in a literate society be of help to me. Well, we all walk around in darkness on many subjects, but with a smidge of numeric awareness, maybe every now and then a little light may shine through.

For a moment, let’s just examine one of those conversations parents of teenagers must be prepared to convincingly win. Their adorable child who they have protected from the dangers of the cruel world says to them, “Why should I work hard in school, pops? I’m gonna be a professional athlete after high school. My future is in the NBA (or NFL or Major League Baseball or on the LPGA Tour… ).” Well, let’s reply in a way that would make even the Huxtable’s proud by simply examining the dream through a numerical argument. The parent’s reply, “Junior, what is the greatest number of high school athletes you believe could actually make such a leap? Is it reasonable or even generous to assume that at most there are 50 players per high school graduating class in the United States that can conceivably make the NBA by way of the draft? With the influx of European players, non-senior NCAA athletes and some high school ballers tossed into the NBA draft, this 50 is actually quite optimistic considering each draft has 32 teams and only 3 rounds. Moreover, did you know only 1 out of every 50,000 high school athletes go on to play a professional sport and this includes bowling. The odds are not in your favor. Try altering your dream. Why don’t you aim for a Ph.D? Last year, there were roughly 44,000 doctoral degrees conferred in this country. Do you think the odds against each of those newly appointed Dr.’s were bordering on 1 in 50,000? That would mean for their high school class, if we multiplied 44,000 by 50,000, 2.2 billion students in that high school class must have set their sites on a Ph.D too. Does this seem reasonable? Of course not, this number is absurd, it is 7 ½ times the size of our country, for goodness sakes. Set the Ph.D. in your sights. It’s a more realistic dream. Pick a book. Study … “

Now, to formulate that argument, you would have to know some of the figures quoted. We easily researched ours and found the “1 out of 50,000” portion of the argument was formed by Art Young, the director of Urban Youth Sports at NortheasternUniversityCenter for the Study of Sports in Society. And the 44,000 doctorals degrees was actually a modest adjustment of the true figure, 44,1660, according to the National Center for Education Statistics (US Department of Education). The point is, mathematics and the ability to be comfortable with numbers and the use of logic with the ability to draw proper inferences, does not exist independently from us. Rather, mathematical reasoning can enhance your life and with it sharpened, you’ll be a better decision maker. The statements, symbols and methods we will study are not meaningless statements governed by rules, but rather a way of viewing life around us. The trick here is to understand how to work with numbers, and at the same time to not have the personality of an accountant.

Back to the correlation between the thirteen most scenic states and the same thirteen state’s with the highest rate of suicide. Is it reasonable to infer that nature’s beauty causes one to ponder whether of not to end their own life? Of course not. But, it does seem reasonable to conclude that a larger number of transient people move to those same scenic states seeking to start over, picking scenic states as a place because the state offers nature’s comfort. Many are looking for a new job, new life. Unfortunately, for a percentage of these people, their dreams don’t come true.

Exercise Set

Ratios designed to help you understand the world around you and allow you to

make forecasts

1. Internet Project: The World Population compressed to 100

If we could shrink the Earth's population to a 100 people, with all the human ratios remaining the same; what would this collection of people look like? How many would be …

Asians
Europeans
From the western hemisphere (north and south)
Africans
Female
Male
Non-white
White
Non-Christian
Christian
60 % of the entire world's wealth would be in the hands of this many people
from the United States
live in substandard housing
unable to read
suffer from malnutrition
be near death
be near birth
have a college education
own a computer

For problems 2 – 9, use the following data from Table 1.

The following data can be found at at the US Census Bureau web site.

Table 1. Population of Selected States in the years 1990, 2000 and 2003.

Fill in the remaining information for your home state.

State / 1990 / 2000 / 2003
Florida / 12,941,197 / 15,982,378 / 17,019,068
New York / 17,987,163 / 18,976,457 / 19,190,115
California / 29,816,592 / 33,871,648 / 35,484,453
Arizona / 3,665,228 / 5,130,632 / 5,580,811
Your home state

2. Fill in the table below by finding the numeric population growth (actual difference in population) for each state for the indicated time period.

State / Numerical Growth
from ’90 – ‘00 / Numerical Growth
from ’00 – ‘03
Florida
New York
California
Arizona
Your home state

3. Fill in the table below by finding the average annual population growth (population growth per year) for each state for the indicated time period.

State / Average Annual Numeric
Growth from ’90 – ‘00 / Average Annual Numeric
Growth from 00 – ’03
Florida
New York
California
Arizona
Your home state

4. Fill in the table below by finding the percent growth (ratio of 2000 to the 1990 population or ratio of 2003 to the 2000 population respectively)for each state for the indicated time period.

State / Percent Growth
from ’90 – ‘00 / Percent Growth
from ’00 – ‘03
Florida
New York
California
Arizona
Your home state

5. Population Forecast for each state. Predict the each state’s population for the year 2010 based on the annual numeric growth for the indicated time period.

State / Predicted 2010 population
based on Average Annual
Numeric Growth from ’90 – ‘00 / Predicted 2010 population
based on Average Annual
Numeric Growth from ’00 – ‘03
Florida
New York
California
Arizona
Your home state

6. Population Forecast for each state. Predict the each state’s population for the year 2010 based on the percent growth for the indicated time period.

State / Predicted 2010 population
based on Percentage of
Growth from ’90 – ‘00 / Predicted 2010 population
based on Percentage of
Growth from ’00 – ‘03
Florida
New York
California
Arizona
Your home state

7. Why are the population projections for the year 2010 larger when based on the percent change?

8. Which of the four predictions, Annual Numeric Growth from ’90 – ’00, Annual Numeric Growth from ’90 – ’00, Percent Growth from ’00 – ‘03 or Percent Growth

from ’00 – ’03, do you feel is the most accurate? Why?

9. For which of the states is the projected predictions the largest and why?

Introduction to Probability, Coincidences

- I don’t know what’s the matter with people; they don’t learn by understanding; they learn by some other way – by rote, or something. Their knowledge is so fragile! Richard P. Feyman, winner of Noble Prize in Physics. 1985. “Surely You’re Joking, Mr. Feyman!”, WW Norton & Company, Inc.

I had a friend in college who had the world’s worst pick-up line. He would set his eyes on some gorgeous co-ed and amble over to her. In a dead pan voice he would ask, “have you ever been to Africa?” The co-ed, with eyes rolling, would reply, “no” and he would say, “what a coincidence, never have I. See, we already have something in common.”

The fact that two events coincide means nothing. Situations where two events coincide gives us the root of the word coincidence, right? My own wife routinely has said over the years “you and I were talking about so and so last night, and guess who I ran into today? So and so. What’s the odds of that?” This time, my eyes would roll. When one considers all the names spoken between a couple each and every day, all the tens or even hundreds of conversations they have each week, all the hundreds or even thousands of conversations they have each month, sooner or later, one of the people discussed, on one of the many days, weeks, months, and years they have been together, would show up somewhere in the presence one of the spouses. The spouse should not be stunned by this occurrence. But, that is not how my wife feels. Life can sometimes seem like photographs in our minds and we crop away the edges of anything we do not want to see. What is construed as a coincidence with some special meaning assigned to it is nothing more than basic probability presenting itself. As was my friends pick up line. “Well, what are the probability she has been to Africa,” he would say after his personalized probability lecture with respect to being so cheesy. “At least I have a can’t miss opening.” Can’t miss, no. But, it is more likely than not that the unknowing woman will have that ‘something uncommon in common’ my friend.

We are all familiar with the bizarre coincidences between the Kennedy and Lincoln presidencies, and these Kennedy/Lincoln coincidences certainly make interesting reading. They captivate us all, filling chat rooms and web pages. Let’s pick one of the chat rooms and glance at the coincidences. We choose snopes.com because they choose to discuss the coincidences in a manner befitting this discussion; they analyzed each coincidence thoroughly. Source:

Abraham Lincoln was elected to congress in 1846. John F. Kennedy was elected to congress in 1946.
Abraham Lincoln was elected president in 1860. John F. Kennedy was elected President in 1960
Lincoln's secretary was named Kennedy. Kennedy's secretary was named Lincoln.
Andrew Johnson, who succeeded Lincoln, was born in 1808. Lyndon Johnson, who succeeded Kennedy, was born in 1908.
John Wilkes Booth, who assassinated Lincoln, was born in 1839. Lee Harvey Oswald, who assassinated Kennedy was born in 1939.
Booth ran from the theater and was caught in a warehouse.
Oswald ran from a warehouse and was caught in a theater.
Booth and Oswald were assassinated before their trials.
The names Lincoln and Kennedy each contain seven letters.
Both names contain fifteen letters
Both wives lost their children while living in the White House.
Both Presidents were shot on a Friday.
Both were shot in the head.
Both were assassinated by southerners.
Both were succeeded by southerners.
Both successors were named Johnson.
Both assassins were known by three names.
Both were particularly concerned with civil rights.

And on the darker side, A week before Lincoln was shot, he was in Monroe, Maryland. A week before Kennedy was shot, was he was with Marilyn Monroe?

Hain’t we got all the fools in town on our side? And hain’t that a big enough majority in any town?

- Mark Twain, Huckleberry Finn

Conspiracy Theories or Coincidences What do all these seemingly unrelated coincidences mean? Anything? we say, “no.” Any two particular events have an extremely high number of associated facts, events and meanings associated with them. The fact that some of these occurrences appear to overlap or coincide should not surprise us. It is just a reflection of the multiplication principle discussed in the previous chapter. The events that coincide are as the term suggest, coincidences, not anything more. They do not conspire something dark and dangerous, they are not conspiracies.

Take this example. Two people meet on a plane, they find they have a common acquaintance. So what? I know 100 people, who know 100 people, who also know 100 people means 100x100x100 = acquaintances. She knows 100 people who each know 100 people who also each know 100 people. And one person is an acquaintance of both of us. Big deal. It’s just a consequence of the multiplication principle. It does not mean there exists a special significance between the two of us.

Don’t believe it? Take any two seemingly unrelated events, ‘google’ the topics on the Internet, and you will uncover just as many “coincidences” or “what’s the odds of that” as the Kennedy/Lincoln coincidences. You try it. Start benignly. Pick any two unconnected presidents, Millard Fillmore and Harry Truman or Grover Cleveland and James Buchanan. Google. Then spin your own conspiracy theories about two presidents. Write a book, if you want. We often thought a good book could be written if we employed the same notion with the vice-presidents. Common thread or little known conspiracies about those really in charge. From John Adams to Dick Cheney. Certainly, Dan Quayle and Levi Morton must have had inconsequential commonalities that may be cleverly exploited into something more.

Enter these three seemingly unrelated items into google.com: December 5th,,boats, sinking. And then search. And search. And search. The result: You could find that on December 5th, 1664, a ship off north Wales with 81 passengers aboard, sank. There was one survivor. A man named Hugh Williams. On the same date, December 5th, 1785, a ship sank with 60 passengers aboard. There was one survivor. A man named Hugh Williams. On December 5th, 1860, a ship with 25 passengers abroad sank. There was one survivor. A man named Hugh Williams. Going into this venture, we didn’t know the coincidence we would find, but we believed a coincidence could be put together. By only telling you the three facts by themselves, we could easily extol this coincidence as something meaningful. And if the point has yet to be made, coincidences are not meaningful.