Friday, June 29, 2007

It is ALL My Fault!

I've been getting emails from people who claim to have posted Comments that I could not see.


I had improperly understood the "Blog Moderation" settings.


A bunch of new Comments should have just appeared.

SORRY (this is my first Blog as Administrator)

AND, THANKS to all who have posted Comments.

Ira Glickstein

Tuesday, June 26, 2007


All about the abuse of anecdotal math to falsify the truth and truthify falsehood.

This is the second part of my "presentation" on the topic of "Lies, ..."

Click here for the first part:

In this part, we will explore "truth and consequences" and "playing the percentages."

EXAMPLE #1: What did I say?

This year is 2007. If I told you I was born in the year 2000, how old am I?

Well, 2007 - 2000 = 7, so, I guess I am seven years old. Right?

All right, not necessarily. This is the month of June 2007, so, if a person was born before June 2000, he or she would be 7, but, if after June, he or she would only be 6. So the answer is six or seven years old. Right?


Sorry, nope! No matter what I told you, I am the age that I am. That happens to be 68 years old. I am sixty-eight years old!

LESSON: No matter what someone may say, that does not change the truth of the matter.

EXAMPLE #2: Let us move on to playing the percentages.

From now on in this posting, let us assume (for the sake of this discussion) anything in purple bold italic type font is a literal truth.

Poupon University has five academic departments. Four out of the five have more male than female professors. Thus, 80% of the departments at Poupon U. are male-dominated.

The percentages of Male/Female are as follows:

  • Engineering: 90% male / 10% female.
  • Physics: 80% male / 20% female.
  • Philosophy: 65% male / 35% female.
  • Foreign Languages: 60% male / 40% female.
  • Humanities: 25% male / 75% female.

If you average the percentages of the five departments, you get 65% male / 35% female.

That would seem absolute proof that old PU is discriminating against female professors! Right?

Not necessarily! Here are the numbers for each department, and the sum of the numbers for Poupon U. as a whole:

Note that there are EXACTLY 200 female professors and 200 male professors at old PU! The genders are EXACTLY 50/50!

What happened to the discrimination? (The same thing that happens to your fist when you shake hands!)

THE LESSON: Beware of percentages, particularly when they are averaged.

EXAMPLE #3: Percentage Increase and Percentage Decrease

In 1980, gas in the US cost about $1.50 per gallon and now it is up to about $3.00 per gallon, which is a 100% increase.

If gas prices should drop back from $3.00 to $1.50 per gallon (I'm not predicting that, just suggesting it for the purposes of illustration), that would be a 50% decrease.

What is going on? When prices go up by $1.50 we get twice the percentage increase as when they go down by the exact same amount!

If we look at the historical record, US gas prices peaked in 1980 when they were about $1.50 per gallon. Considering inflation from 1980 to 2007, that is about $3.00 per gallon in constant dollars! If you calculate the gas price as the number of minutes the average US worker must devote to earn the price of a gallon of gas, the current price is less than the historical peak in the 1980's!

The same percentage increase and percentage decrease confusion holds for unemployment, crime rates and all things that are bad.

As an example, in the Orlando Sentinel for June 26th 2007, there is a report on the increase in Florida gun crimes, based on data for 2005 and 2006. Gun Murders in Florida went from 521 in 2005 to 740 in 2006, an increase of 42.0%

What if they happen to decrease in 2007 to the same number as in 2005. That is, if they went down from 740 in 2006 to 521 in 2007? That would be a decrease of only 29.6%, 12% less of a decrease than the increase reported above.

If the number of Gun Murders in Florida happened to be 521 in odd years and 740 in even years for a decade, and you averaged the percentages, that would show an average increase of 6.2% per year while, in truth, the rate was unchanged for the decade!

THE LESSON: Beware of percentages, particularly when percentage increase and percentage decrease are compared.

Please comment on this material. (Stay tuned: I plan to post yet another part of this "presentation" in a week or so.)

Ira Glickstein

Monday, June 25, 2007


As a thinking machine, the human brain leaves a lot to be desired. Living is about making decisions, most of them binary choices. Do I go left or right? Do I eat this plant or not? Do I release my arrow now or do I wait for a better shot? We seem to have evolved special mechanisms for making this type of survival related decision. Those mechanisms often get in the way of complex thinking. In fact, I'll propose to you that what we call thinking is only an artifact of our primitive decision making skills, creating the illusion that we can reason. Our ability is so faulty that large fractions of the population, given the same facts about a situation will still come to quite different conclusions as to what to decide. That's why on almost every public policy issue, the population will split very roughly in half, and each half will think the other is mad. With Respect -Joel

Friday, June 22, 2007

The Purloined Letter by E.A. Poe (was Lies, ...)

[Edited by Ira for paragraph structure of long quotes and more specific Title]

Recently, Stu Denenberg got me to reread The Purloined Letter by E.A. Poe. If you recall, the story centers around the search for a stolen letter secreted in the home of a court schemer. The chief of police has failed to find the letter, yet it must be there. He comes for help to Dupin, an amateur sleuth. Dupin discusses the matter with the narrator (his "Dr. Watson.")

The particular part relevant to Ira's presentation is as follows below, in which Dupin speaks about the court schemer and why the chief of police's (the Préfet) disdain for poets has caused him to underestimate the schemer's reasoning power.

"You are mistaken; I know him well; he is both. As poet and mathematician, he would reason well; as mere mathematician, he could not have reasoned at all, and thus would have been at the mercy of the Prefect."

"You surprise me," I said, "by these opinions, which have been contradicted by the voice of the world. You do not mean to set at naught the well-digested idea of centuries. The mathematical reason has long been regarded as the reason par excellence.

"'Il y a a parier,'" replied Dupin, quoting from Chamfort, "'que toute idee publique, toute convention recue, est une sottise, car elle a convenu au plus grand nombre.' (trans: I would wager that every popular notion, every convention, is a bit of stupidity that exists only because it is useful to the majority.) The mathematicians, I grant you, have done their best to promulgate the popular error to which you allude, and which is none the less an error for its promulgation as truth. With an art worthy a better cause, for example, they have insinuated the term 'analysis' into application to algebra. The French are the originators of this particular deception; but if a term is of any importance — if words derive any value from applicability — then 'analysis' conveys 'algebra' about as much as, in Latin, 'ambitus' implies 'ambition,' 'religio' religion or 'homines honesti,' a set of honorable men."

"You have a quarrel on hand, I see," said I, "with some of the algebraists of Paris; but proceed."

"I dispute the availability, and thus the value, of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation uponform and quantity. The great error lies in supposing that even the truths of what is called pure algebra, are abstract or general truths. And this error is so egregious that I am confounded at the universality with which it has been received. Mathematical axiomsare not axioms of general truth. What is true of relation — of form and quantity — is often grossly false in regard to morals, for example. In this latter science it is very usually untrue that the aggregated parts are equal to the whole. In chemistry also the axiom falls. In the consideration of motive it falls; for two motives, each of a given value, have not, necessarily, a value when united, equal to the sum of their values apart. There are numerous other mathematical truths which are only truths within the limits of relation. But the mathematician argues, from his finite truths, through habit, as if they were of an absolutely general applicability — as the world indeed imagines them to be. Bryant, in his very learned 'Mythology,' mentions an analogous source of error, when he says that 'although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.' With the algebraists, however, who are Pagans themselves, the 'Pagan fables' are believed, and the inferences are made, not so much through lapse of memory, as through an unaccountable addling of the brains. In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x squared + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x squared + px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down."

Before we get too upset with what seems like an unfair attack upon mathematicians, we should remember the Pythagoreans who made trigonometry into a religion. As Ira has demonstrated, it's necessary to set up a problem "correctly" before one can use mathematics to find a solution.

With respect -Joel

Saturday, June 16, 2007


All about the abuse of anecdotal math to falsify the truth and truthify falsehood.

Mark Twain famously wrote:

Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics." [from the Autobiography of Mark Twain]

He was implying that, of the three classes of lies, statistics were the worst. Others have added to the list, in order of falseness:

  1. Lies
  2. Damned Lies
  3. Statistics
  4. Politicians Quoting Statistics
  5. Journalists Quoting Politicians Quoting Statistics

This new topic posting (like a presentation at a physical club meeting) gives some examples of how anecdotal math and statistics are used to confuse the public.

A large percentage of the population is “mathematically challenged.” Their eyes glaze over like deer caught in headlights whenever someone uses numbers and mathematics to argue for their version of the truth. Some even proclaim their innumeracy as if it was a badge of honor!

The result is that many educated people are convinced to accept falsehoods as truth and to discard truths as falsehoods.

This first example has to do with the need for reason as well as mathematics.

Please read this poem:

When I was going to St. Ives,
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits,
Kits, cats, sacks, wives,
How many were going to St. Ives?

Can you figure out the answer? If you think you know the answer, or how to figure it out, write it down on a scrap of paper. Then, please scroll down and continue reading.

OK. Here is one approach. The poem says: I met a man with seven wives, so at least seven wives are going to St. Ives. Right?

The poem continues: "Each wife had seven sacks," so, that would be 7 x 7 = 49 sacks. But, should we count sacks in our total? The last line of the poem asks: How many were going to St. Ives? It does not ask how many people or how many living things are going, just "how many".

Therefore, let's count the sacks. We have 49 sacks going to St. Ives.

The poem goes on: Each sack had seven cats, so, that would be 49 x 7 = 343 cats going to St. Ives.

The poem adds more information: Each cat had seven kits, so, that would be 343 x 7 = 2401 kits going to St. Ives.

Adding them all together, Kits, cats, sacks, wives, we get 2401 + 343 + 49 + 7 = 2800 total items going to St. Ives. OK, so that is the answer. Right?

Think about it, then scroll down and continue reading.

OOPS, we forgot the man! We were so engrossed in mathematics we only figured the Kits, cats, sacks, wives and forgot all about the man who had the seven wives. So let us add him, and we get 2800 + 1 = 2801. OK, so that is the answer. Right?

OOPS again! The first line of the poem says: When I was going to St. Ives, so we need to add the author of the poem to get the answer to "How many were going to St. Ives?" We get 2801 + 1 = 2802 people and sacks and cats and kits going to St. Ives. OK, so we finally have the answer! Right?

Think about it, then scroll down and continue reading.

2802? No we don't! Read the poem again. All it says is When I [the author of the poem] was going to St. Ives. That is just one person we know of who is going to St. Ives.

All the others, including the man, his wives, the sacks, the cats and the kits could be coming from St. Ives or coming or going to or from any other place!

So, the correct answer, based on the facts in the poem, is ONE is going to St. Ives. All the rest is unsupported conjecture.

THE LESSON: Don't jump in and work the mathematics until you understand the logic and reason!

Please comment on this posting!

I plan to post the next part of "Lies, Damned Lies, and Statistics" in a week or so.

Ira Glickstein

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