Critical Thinking, Who Needs It?
Below are the leads to Numeracy Nuggets, our new series on critical thinking tools from the annals of numeracy. George Rebane plans to contribute fresh Numeracy Nuggets every three to four weeks and welcomes others to submit their offerings in the same vein. Each Numeracy Nugget concludes with a ‘homework problem’ for the numerate reader. The solution to each is given at the end of the next Nugget in the series.
Numeracy Nugget #1 – Critical Thinking, Who Needs It?
‘You can’t do just ONE thing.’ That bit of wisdom has now fastened itself in the heads of most thinking people in the land as they puzzle over everything from global warming to letting their teenager stay out past midnight. Every decision we act on sets in motion large and small ripples in life’s spider web of interconnections. We want to do what is good and just, but quickly discover that there is no one common set of criteria to cover ‘good’ and ‘just’ even if we were all Lutherans, or whatever.
You can download a complete pdf version of Numeracy Nugget #1 here: NN1a_17may06
Numeracy Nugget #2 – Tragedy of the Commons, Etc.
Garrett Hardin, the late professor emeritus at UC Santa Barbara, was an ecologist and world-class thinker. His long list of original ideas and writings, worth googling up on a quiet evening, pricked many sacred sentiments of the right and left. Hardin was much concerned with population growth and the kinds of decisions required in a world with too many people kind of like the decisions we are pondering here in Nevada County. ‘The Tragedy of the Commons’ , first published in 1968, is perhaps the best-known from his rich legacy.
You can download a complete pdf version of Numeracy Nugget #2, including answer to NN #1, here:NN2a_17may06
Numeracy Nugget #3 – The Shades of Belief.
What does it mean when we hold a belief? We constantly say that we believe this to be the case or that to be the case. Does ‘I believe it’s going to rain tomorrow’ mean that we are certain that it will rain and would bet the farm on it? Or does it mean that we think rain is ‘likely’ tomorrow? Dictionary definitions of ‘believe’ are all over the place from “to accept as true or real” through “to expect or suppose” to “have an opinion”. We know that to hold a belief does not have to mean that something is absolutely true since we’re used to saying things like “Seeing that strengthens/ weakens my belief in …”. About all that most people would agree on is that to believe some statement, tenet, or proposition is to behave in a way that indicates to other people that the tenet has a chance of being true.
You can download a complete pdf version of Numeracy Nugget #3, including answer to NN #2 question, here:NN3_17jul06
Numeracy Nugget #4 ‘He Probably Doesn’t Understand Probability’
‘He Probably Doesn’t Understand Probability’ – the title of this nugget is probably a true statement, but to accept that requires that you first understand some things about probability. A person for whom the concept of uncertainty and probability is foreign will have a hard time understanding or talking reasonably about social issues important to all of us.
You can download a complete pdf version of Numeracy Nugget #4, including answer to NN #3 question, here: NN4_11sep06
Numeracy Nugget #5: Influence Factors Diagrams – How to Understand and Communicate Complex Issues.
‘Influence Factors Diagrams – How to Understand and Communicate Complex Issues’ is the title of this Nugget. Almost all of us consider ourselves above average in the ability to think clearly, or more precisely, to be able to think critically. We spend our days effortlessly second guessing and pointing out the obvious foibles and missed opportunities that others, ranging from Congress to the local dog catcher, commit and cause us suffering. The right answers seem to come to us effortlessly. The only time that a doubt fleetingly darkens our brow is when someone in our presence disagrees with our conclusions or beliefs. But we quickly dispense with the annoyance by either telling the interloper that the contending view is only their opinion with the implication that it should be weighted equally with about one hundred million other such varying opinions. Most of us are fully armored to repel any inconvenient facts.
You can download a complete pdf version of Numeracy Nugget #5, including answer to NN #4 question, here: NN5_23oct06
Numeracy Nugget #6: Modeling the Future – For Whom the Bell Curve Tolls
More and more public policy is based on poorly understood computer models of very complex processes like regional air quality, local traffic congestion, and worldwide climate change. Paul Sieving wrote an excellent yet very brief article (The Union’s Other Voices, 6 March 2007) that highlighted how the output of such predictive models may lead us to wrong conclusions and, therefore, bad policy. However, it turns out the picture he painted is too rosy, this perhaps because he tried to keep the message short – a sad requirement of the times. [Read Nugget #6 for more details]
You can download a complete pdf version of Numeracy Nugget #6., including the answer to NN#5, here: NN6_8mar07
Numeracy Nugget #7: When Planning to Procure – Pick Any Two
When someone (especially in government) needs to procure some major good or service, there inevitably arise questions of what should it do, how much will it cost, and when will it be ready. And inevitably most such procurements will not meet the expectations when the procurement project was first adopted. This is so because of a number of things which come up to frustrate the original procurement plan – e.g. Murphy’s Law and all that.
In NN7 we take a look at how to avoid some of the biggest mistakes that should be known by government and also individuals who either take an interest in how government spends money or how they buy stuff for themselves or their company. NN7 also has the solution to the NN6 problem and, of course, presents a new one for your .
You can download a complete pdf version of Numeracy Nugget #7, including the answer to NN#6, here: NN7_16apr07
Numeracy Nugget #8 – The Singularity and Its Early Effects
“Understanding what the Singularity is will explain a lot of things happening in the world from here on. It early effects are felt by us all and most strongly by the world’s poor and ignorant who are already the most impacted. In this Nugget I will attempt a short explanation that will astound most people and will make many shake their heads in disbelief. Enough references will be given to enable the independent thinkers draw their own conclusions.”
You can download a complete pdf version of Numeracy Nugget #8, including the answer to NN#7, here: NN8_3jun07
Numeracy Nugget #9 – Thinking About Income Inequality
“Recent reports on the national income inequality issue (e.g. ‘A Generation of Widening Inequality’) give the casual reader the impression that something unnatural or wrong is going on in the country. In this nugget we take a look at some of the important factors that influence how wages are distributed in an advanced economy today paced by accelerating technology.”
You can download a complete pdf version of Numeracy Nugget #9, including the answer to NN#8, here: NN9_31aug07
Numeracy Nugget #10 – The WoRm Formula
If you like hiking, golfing, camping, hunting, boating or any other activities that take you out of doors, then you will find the WoRm Formula, borrowed from the military, to be a useful tool to have in that toolcase you carry between your ears. For you investors, this nugget also contains the solution to the inflation adjusted return problem given in NN9.
You can download a complete pdf version of Numeracy Nugget #10, including the answer to NN#9, here: NN10_18dec07