A number of things from Innumeracy, by Paulos

March 12, 2008 at 12:46 pm 2 comments

Innumeracy, by Paulos

Mathematical Illiteracy and its consequences

Contents

Introduction

Ch. 1 Examples and Principles

Ch. 2 Probability and Coincidence

Ch. 3 Pseudoscience

Ch. 4 Whence Innumeracy?

Ch. 5 Statistics, Trade-offs, and Society

Close

 finger-numbers.jpg

P13  Put huge numbers in context, e.g. eleven and a half days is a million seconds. Thirty-two years is a billion seconds.  Homo sapiens is probably less than 10 trillion seconds old….writing has been around for only 150 billion seconds; rock music for only one billion seconds….the nuclear weapons on board just one of our Trident submarines contains eight times the firepower expended in all of World War II.

P22 Used quite a bit throughout the book: if some choice can be made in M difference ways and some subsequent choice can be made in N different ways, then there are M x N different ways these choices can be made in succession.

P29 …one runs about a 50% chance of not contracting AIDS by having unsafe heterosexual intercourse every day for a year with someone who has the disease….?!  With a condom a 1 in 50 million chance – you are more likely to die in a car crash on the way home from such a tryst.

P32  What are the chances that you just inhaled a molecule which Caesar exhaled in his dying breath?  99%!

P37 The paradoxical conclusion is that it would be very unlikely for unlikely events not to occur.  If you don’t specify a predicted event precisely, there are an indeterminate number of ways for an event of that general kind to take place.  Enter medical quackery and television evangelists.

P39 Chance encounters…If each adult knows 1500 people and these individuals are spread out around the country….99%, almost certain that two people chosen at random will be linked by a chain of at most two intermediates.  Milgrim found the links to average about 5.

P44 televangelists…there’s always enough random success to justify almost anything to someone who wants to believe.

P45  Pre-Anderson Long tail comment.  Before the advent of radio, TV, and film, musicians, athletes, etc. could develop loyal local audiences since they were the best that most people would ever see.  Now audiences, even in rural areas, are no longer as satisfied with local entertainers and demand world-class talent.  In this sense, these media have been good for audiences and bad for performers.

This was published in1990

P56 Countless…oddities result from our conventional ways of measuring, reporting and comparing periodic quantities…

P60  Stock analysts….Almost never does a commentator say that the market’s activity for the day or even the week was largely a result of random fluctuations.

P67 Asimov – Inspect every piece of pseudoscience and you will find a security blanket, a thumb to suck, a skirt to hold.  What have we to offer in exchange?  Uncertainty!  Insecurity!  From the Skeptical Inquirer.

Cowper – to follow foolish precedents, and wink with both our eyes, is easier than to think.

P69  “Whatever God wills, happens.”  People may be able to take solace from it, but it’s clear that the statement is not falsifiable and hence…not part of science.  “Plane crashes always come in threes.”  You always here that too, and if you wait long enough, of course, everything comes in threes.

P73 Firewalkers and mind over matter debunked: What makes this phenomenon less remarkable is the relatively little known fact that dehydrated wood has an extremely low heat content and a very poor heat conductivity.  …Of course, quasi-religious talk about mind control is more appealing than a discussion of heat content and conductivity.

P75 The probability of a monkey accidentally typing out Shakespeare’s Hamlet is (1/35)^N, where N is the number of symbols in Hamlet, maybe 200,000 and 35 is the number of typewriter symbols, including letters, punctuation, spaces…This number is..zero for all practical purposes.  Though some have taken this tiny probability as an argument for ‘creation science,’ the only thing it clearly indicates is that monkeys seldom write great plays.  If they want to, they shouldn’t waste their time trying to peck one out accidentally but should instead evolve into something that has a better chance of writing Hamlet.

P79 The best antidote to…pseudoscience in general is, as Carl Sagan has written, real science, whose wonders are as amazing but have the added virtue of probably being real.

P108 Most priesthoods (mathematicians included) are inclined to hide behind a wall of mystery and to commune only with their fellow priests.

P120 …what about students who don’t care enough to focus any of their energy on intellectual matters? Their problems are an order of magnitude more serious than math anxiety.

P126 Vagueness is at times necessary and mystery is never in short supply, but I don’t think they’re anything to worship.

P127 a proposed logarithmic safety scale: if one person out of X dies as a result of some give activity each year, the safety index…is simply the logarithm of X.   The bigger the number the smaller the risk, and with every unit the risk decreases by a power of ten.  E.g. kidnapping is 1 in five million for a safety index of 6.7.  Automobile driving and smoking have values of 3.7 and 2.9, respectively.  Russian roulette played once a year has a 1 in six chance of danger, for a safety index of 0.8.  These safety index values could be reported along with a sensational news story:  “Yes, this was a dramatic event, but with a safety index over 6, you’re pretty safe.”  Anything less than 4 and you should start getting wary.

Since perceptions tend to become realities, the natural tendency of the mass media to accentuate the anomalous, combined with an innumerate society’s taste for such extremes, could conceivable have quite dire consequences.

P139 a discussion of the Prisoner’s Dilemma.  I forget where I first hear about this – in Smart Mobs, Rheingold; thanks Pet Brain

P147 There is no such thing as a free lunch and even if there were, there’d be no guarantee against indigestion

P153 to publically obtain private information in a questionnaire-type format, flip a coin without letting anyone see the outcome, if it lands on heads, answer the question honestly yes or no; if it comes up tails, answer yes.  Yes responses mean either tails, or a real yes.  If 620 out of 1000 answers are yes, 500 are due to getting tails, 120 are real yes answers so 120 out of 500 are real yes answers.

P178 Zealots, true believers, fanatics, and fundamentalists of all types seldom hold any truck with anything as wishy-washy as probability.  May the all burn in hell for 1010 years (just kidding), or be forced to take a course in probability theory.

In an increasingly complex word full of senseless coincidence, what’s required in many situations is not more facts – we’re inundated already – but a better command of known facts, and for this a course in probability is invaluable.  Statistical tests and confidence intervals, the difference between cause and correlation, conditional probability, independence, and the multiplication principle, the art of estimation and the design of experiments, the notion of expected value and of a probability distribution as well as the most common examples and counter-examples of all of the above, should be much more widely known.  Probability, like logic, is not just for mathematicians anymore.  It permeates our lives.

P179  The discrepancies between our pretensions and reality are usually quite extensive, and since number and chance are among our ultimate reality principles, those who possess a keen grasp of these notions may see these discrepancies and incongruities with greater clarity and thus more easily become subject to feelings of absurdity. I think there’s something of the divine in these feelings of our absurdity, and they should be cherished, not avoided.  The provide perspective on our puny yet exalted position in the world and are what distinguish us from the rats.  Anything which permanently dulls us to them is to be opposed, innumeracy included.

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Line from Dark Matter, Kerr First Wikipedia Edit

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