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/ The Bell Curve / Computers / Fractals, Fractality / Fuzzy Logic / Hackers and the "Hacker Ethic" / Science, Rationalism, and Critical Thinking /
/ Statistics, Numeracy, Probability, Mathematics /
This page has been spun off from the site
http://doggo.tripod.com/
Links to other pages on this site are being gradually updated,
but this is a low-priority task, especially for less-important or less-used pages.
Links in the form doggfoobar.html
should work when kludged to http://doggo.tripod.com/doggfoobar.html
- New Algorithm Offers Ability to Influence Systems Such as Living Cells or Social Networks
14 MAY 2011
"... an MIT researcher has come up with a new computational model that can analyze any type of complex network -- biological, social or electronic -- and reveal the critical points that can be used to control the entire system."
- Correlation and Causation -- Misuse and Misconception of Statistical Facts
- the Math Mistakes Website: Reader-Submitted Examples
"A) The Japanese eat very little fat and suffer fewer heart attacks than the British or Americans.
B) On the other hand, the French eat a lot of fat and also suffer fewer heart attacks than the British or Americans.
C) The Japanese drink very little red wine and suffer fewer heart attacks than the British or Americans.
D) The Italians drink excessive amounts of red wine, and also suffer fewer heart attacks than the British or Americans
E) Conclusion: Eat & drink what you like. It's speaking English that kills you."
- the Math Mistakes Website: Reader-Submitted Examples
"I read an article in the Deseret News about a ninth grader in Idaho who did a study on critical thinking. He asked 50 of his classmates if they would be willing to sign a petition calling for the elimination of dihydrogen monoxide. ...
The Dihydrogen Monoxide facts sheet can be found at http://extlab1.entnem.ufl.edu/IH8PCs/humor/water.htm. According to an article in the Skeptical Inquirer (Jan 1998 pg. 13) the survey was done by Nathan Zohner, 14, of Eagle Rock Junior High. Economist James K Glassman wants to coin the term "Zohnerism" defined as the use of a true fact used to mislead a scientifically and mathematically ignorant public.
- Dihydrogen Monoxide: Unrecognized Killer
by James K. Glassman
Copyright 1997 The Washington Post Company"The implications of Nathan's research are so disturbing that I've decided to coin a term: "Zohnerism", defined as the use of a true fact to lead a scientifically and mathematically ignorant public to a false conclusion."
- Glossary of Mathematical Mistakes
by Paul Cox
Most of these seem very elementary to me, but there are some good links.
- What is "Math Literacy"? AKA "Numeracy"
by Paul Cox
"...here is my list of minimum math skills every adult should possess.""I know what most readers will be saying: 'I understand that you are simply trying to list the bare minimum amount of math people should know, but it is simply not enough. People should study Algebra and Calculus, Differential Equations, and advanced Geometry...." The truth is that I agree with this sentiment.
My philosophy behind the list is not what we should be schooled in. It has something in common with an old Saturday Night Live sketch where comedian Father Guido Sarducci described a Five Minute University. In five minutes he would teach you everything that you would remember from college five years after graduation. Like Economics class would be the phrase "Supply and Demand", and business class would be "buy low, sell high", etc. The math literacy list above does not represent concepts to cram in to you head, spew them out on a test, then forget them. These are the concepts you should remember years later. They are the foundational concepts for all higher level math."
And... (one of my pet peeves here) this stuff isn't particularly difficult.
Cox lists as his topic headings Arithmetic, Measurement, Algebra, Geometry, Probability, Statistics, and Logic.
In the USA, a typical academic year runs about nine and a half months including holidays, or about nine months not counting holidays, or 180 days. (Many other countries have longer academic years.)
I would expect all elementary school students to learn basic mathematics, and have a good foundation in the basics of measurement and geometry.
IMHO we could then cover all of the sub-topics that Cox lists under Measurement, Algebra, Geometry, Probability, Statistics, Logic in one year, say when students are twelve years old. One month each for Cox's Measurement, Probability, Statistics, and Logic, and we have five months left for Algebra and Geometry -- maybe 3.5 months for Algebra and 1.5 months for Geometry.
The order is probably Measurement (we're going to ease into this, the first unit here is very simple, concrete, hands-on, and practical), Geometry (the visually-oriented are still not going to find this too esoteric), Algebra (this is the tough one, but we'll need it to do some of the later work), Probability, Statistics, and we probably wind up with Logic (including critical thinking -- gives a bit of a rest from the math grind and we'll be talking about the real-world relevancy).
Again, there's a lot in these subjects that we won't be covering under Cox's curriculum -- this is just the "five minute" version.
Students who don't pass the course at age 12 will repeat it as necessary, while those who do can either go on to higher maths or drop math in favor of other interests. (Though I'd require a checkup exam every few years, with a refresher course for those who need it.)
- Another of my pet peeves -- what Cox calls the Rare Scare:
Anthrax Anxiety Spreads in America, UNNECESSARILY!
"A Rare Scare - A media report of a probable disaster (i.e.. death, earthquake, cancer risk from eating apples, etc.), where the probability is considerably lower than risks taken everyday (i.e.. getting in a car wreck on your way to school).""Before the September 11th attacks, the big headlines were about shark attacks. So widespread were reports of shark attacks, Congress was looking into the matter. After September 11th, we did not hear anything about sharks again.
There are two kinds of risks reported in the media: those that really matter and those that sell papers. Reports of shark attacks disappeared because they were the latter, they sold papers.
... this is truly a rare scare. In the month of October, sixteen people have contracted anthrax and four people have died as a result. In the same month, an estimated 3400 new cases of HIV have been diagnosed, and an estimated 1400 people have died from AIDS or AIDS-related causes in the United States. Also, in the same month, approximately 200,000 cases of influenza or pneumonia were diagnosed by doctors and approximately 2200 people died from influenza or pneumonia in the United States alone.
The chance of being killed by an anthrax terrorist attack is so small, you have a better chance of getting struck by lightning than getting anthrax from reading the mail."
And -- my typical example here -- Americans are terrified of terrorists. The government has pretty much carte blanche to do whatever it likes, as long as it mentions that it's doing so to protect Americans from terrorists.
Over the past quarter-century, the number of American civilians killed by foreign terrorists has been on the order of 5,000 -- I would even be willing to go as high as 10,000 for rhetorical purposes, although I think that that is in fact a great exaggeration.
But I've got news for you -- "death from terrorist action" isn't among the top ten causes of death worldwide (and plenty of countries have a worse terrorism problem than the USA does).
Here are the top ten causes of death in all developed countries combined in the year 2002, according to the World Health Organization (per Wikipedia):Ischaemic heart disease ("Heart attack": death caused by problems witht the flow of blood to the heart.)
Stroke
Chronic obstructive pulmonary disease(Mostly caused by cigarette smoking)
Lower respiratory infections (Chiefly pneumonia)
Lung cancer (Again, chiefly caused by smoking tobacco)
Car accident
Stomach cancer
High blood pressure
Tuberculosis
Suicide ("In the United States, suicide ranks in the top ten causes of death, accounting for about 1.5 percent of all deaths. The annual number of suicides has averaged about 30,000 since the late 1980s ..." -- Suicide Facts, Encarta Encyclopedia.)
In other words, in the USA we lose at least as many people from suicide every four months as the total from terrorism over the last twenty-five years -- more probably as many people every two months.
In the USA, there were over 500,000 deaths from ischemic heart disease in the year 1999. That's about 10,000 people per week.
What should we really be focussing on?
Yes, it is true that the government has been working to contain dangers from terrorism during those twenty-five years, and that deaths from terrorism could otherwise have been higher (though personally I don't think by much if at all).However, the government has also been working to contain dangers from other causes (requiring seat belts, requiring air bags, drunk-driving arrests, cigarette package warning labels, public health programs, etc, etc, etc), and those might also have been higher otherwise.
- The Most IMPORTANT Video You'll Ever See (part 1 of 8)
I don't know if I'd quite go that far, but this is a very good short introduction to doubling times and incremental growth.
(Take home message, as always in discussions of this kind: We are totally screwed.)
(Part 2) -- IMHO better than Part 1
- Law of Truly Large Numbers - Wikipedia
- Littlewood's law - Wikipedia
- Good Math, Bad Math blog
by Mark Chu-Carroll ( MarkCC )
- Innumeracy
Copyright © 2001 Mikolaj "Mik" Sawicki. All rights reserved.
Good examples of numeracy mistakes in the media.
- Visualising sorting algorithms
Fascinating
- Is the Universe Actually Made of Math?
"Unconventional cosmologist Max Tegmark says mathematical formulas create reality."
16 JUN 2008
- Innumeracy: Mathematical Illiteracy and Its Consequences
by John Allen Paulos
- How do I estimate the probability that God exists?
01 MAY 2011
- Some good introductory info on estimating probabilities here.