Archive for January, 2015

Perceptions of Economic Mobility

January 29, 2015

The immediately preceding blog post raised the question of large pay inequities.  So the obvious question is why are such large pay inequities tolerated?  This post addresses that  question and it is due to  perceptions of economic mobility.  This post is based on the article, “Building a More Mobile America—One Income Quintile at a Time,” By Shai Davidai and  Thomas Gilovich has revealed a marked discrepancy  between people’s beliefs and economic reality.  One of their findings is that whereas the bottom two quintiles (40%) own 0.3% of the total wealth in the country, they are thought to possess about 10%.

A World Value Study found that 71% of Americans (compared with 40% of the Europeans) believe the poor have  a reasonable chance of escaping poverty.  The remainder of this post addresses the beliefs of people cast agains the economic reality.  A nationwide cross-sectional sample of 3,034 Americans was surveyed online between February 21st and February 25th, 2014 by the Harris Poll on behalf of the Northwestern Mutual financial services organization.  To elicit their beliefs about either upward or downward intergenerational  income mobility, respondents were asked the likelihood of a randomly selected American born to a family in the poorest or riches quintile ending up as an adult in each of the five quintiles.  For example, in the upward mobility condition participants were asked to imagine a randomly selected American born to a family in the lowest income quintile and to estimate his or her likelihood of either remaining in this quintile as an adult or rising to each of the four higher income quintiles.  In the downward mobility condition, respondents estimated  the likelihood an an American born to a family in the richest 20% would either remain in the top quintile or drop to each of the four lower quintiles.  Their assessments needed to total 100%.

Overall, respondents thought that a randomly selected American  is significantly more likely to experience upward mobility than downward ability.  Whereas respondents believed that an individual born into the bottom quintile has a 43% chance of moving up to the middle quintile or higher, they thought that someone born in the top quintile has only a 33% chance of dropping to the middle quintile.

So, how accurate were these estimates when compared to actual upward and downward mobility rates provided by the Pew Research Center in 2012?  Respondents overestimated the amount of upward mobility, estimating a 43 %  likelihood of a person born into the poorest quintile rising to the top three quintiles whereas the actual likelihood of 30%.  Estimates of downward mobility were somewhat more accurate as 37% of the individuals born into the richest quintile drop to the middle quintile or lower with participants estimating only 33% do so.

It is interesting to note that  low-income respondents (those with an annual income lower than $25.000) believed that moving more than one quintile from the top or bottom is significantly more likely 44% than high income respondents (annual income more than $100,000) who estimated 33%.  So poor income respondents perceive more mobility than there richer counterparts.

It would appear then that it is correct that this belief in upward mobility that leads to tolerance for income inequality.

A Universal Desire for More Equal Pay

January 27, 2015

This post is based on the Perspectives on Psychological Science article (November 2014), “How Much  More  Should CEO’s Make:    A Universal Desire for More Equal Pay,” by Sorapop Kiatpongsan and Michael J. Norton.  They used a survey based on 55,238 respondents in 40 countries.  These respondents estimated the wages of people in different occupations–chief executive officers (CEOs)—cabinet officers—and unskilled workers and also provided their estimates of what their pay should be.  Data from 16 countries was used to show that the respondents were dramatically underestimating actual pay inequality.  Although the specific magnitude of the pay estimates differed across countries and across specific demographic groups, the clear conclusion is that people underestimate actual pay gaps and their ideal pay gaps are even further from reality  than those underestimates.

This underestimation was most conspicuous in the United States where the actual pay ratio of CEOs to unskilled workers (354:1) far exceeded the estimated ratio (30:1) which in turn exceeded the ideal ratio (7:1).  The United States presents an interesting case where the ratio of the average CEO to an average employee increased from 20:1 in 1965 to 354:1 in 2112.  Peter Drucker, the management guru, suggested that exceeding this 20:1 ratio would increase employee resentment and decrease morale.

An interesting question is how all this came about.  There was a business professor, whose name I have unfortunately  forgotten, who published an  article he intended to decry the gross overcompensation of CEOs, but the law of unintended consequences was at work.  These data were used as a basis for pegging and increasing CEO compensation.  A candidate could use these data to estimate what the going rate was and boards of directors felt a need to be competitive and kept increasing the offers.

The obvious question here is what can be done about it.  The passing of laws or regulations is one idea, but there are probably creative ways to circumvent them.  I believe that the problem stems from corporate structure.   Currently there is a CEO and a Board of Directors.  They take good care of each other.  This is not good for the company, the company ‘s stockholders, the company’s employees, or the company’s customers.  Elections usually consist of a ballots distributed to stockholders with one list of candidates for the Board of Directors.  This board selects the CEO and they take good care of each other.   Elections with one set of candidates is what is used by totatalitarian states.  I never respond to these elections.  I demand viable competitive candidates before I vote in any election.
I think corporations should be required to issue ballots where there are at least two candidates for every available position.   Then shareholders could vote for candidates who committed to reeling in CEO compensation and perhaps even their own compensation.
I know that the argument against this is that shareholders are not knowledgeable enough to vote, nor do they want to extend the effort to familiarize themselves with the candidates.  I would argue that in our democracies there is ample evidence that voters not only frequently do not know the candidates, but also vote against their own interests.  Although our democracies might not function effectively, they usually manage to minimize the subversion of power.  In others words, they do have some level of control that is absent from corporate governance.
© Douglas Griffith and, 2015. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and with appropriate and specific direction to the original content.

Food for a Healthy Memory

January 24, 2015

When I saw the lead article in the Washington Post Health & Science Section (6 Jan 2015) by Bonnie Berkowitz and Laura Stanton titled “Food for thought: Is your brain missing something?” I felt obligated to pass it on to my healthymemory blog readers. The neuroscience professor Gay Wenk, author of Your Brain on Food: How Chemicals Control Your Thoughts and Feelings, notes “Our brains need certain nutrients to keep us happy, focused, and functioning at our best. But moderation is key, and gobbling more of a particular nutrient helps only if you are making up for a deficiency.” Now on to substances that are good for the brain.

Antioxidants are important because they delay cognitive decline by neutralizing free radicals, which are by products of our oxygen guzzling metabolism that damage cells by causing inflammation. People who exercise a lot tend to eat more and breathe more heavily, which results in more free radicals. Flavonoids, one type of antioxidant, improve blood flow to the brain and enhance its ability to form memories, especially in conjunction with exercise. Antioxidants can be found in colorful vegetables and fruits, red wine, cocoa, calf and beef liver.

Caffeine seems to protect the brain, although scientists are not sure exactly how. Caffeine is found in coffee, many kinds of tea, cocoa, many sodas, and dark chocolate.

Omega-3 fatty acids are anti-inflammatory and an important component of brain cell membranes. A deficiency has been linked to brain disorders such as depression. Correcting a deficiency can boost the brain’s plasticity enhancing cognition and learning. Omega-3 fatty acids can be found in salmon, tuna and other fatty fish, plants such as flaxseed, walnuts and other nuts.

Tryptophan is an amino acid used to make seratonin, an essential mood-regulating neurotransmitter. The brain can’t store tryptophan, so we need to get a regular supply from protein in our diets. Tryptophan is found in eggs, nuts, spinach, meat, fish, and poultry.

Curcumin has anti-inflammatory properties. It is found in the spice turmeric and seems to protect the brain against Alzheimer’s and possibly Parkinson’s disease. Turmeric has been used in Asian herbal remedies for centuries to treat inflammatory diseases such as arthritis. Curcumin is also a powerful anti-oxidant. Curry and sine mustards contain, and turmeric can be added to many foods. My wife uses it and it is delicious.

B vitamins, folate, or folic acid is needed to keep the enzymes related to energy metabolism humming alone. If a woman is deficient, additional folate may improve memory and ease depression. Studies indicate it may also help protect the brain from dementia. It is found in fatty fish, mushrooms, fortified products, milk, soy milk, cereal grains, orange juice, spinach, and yeast.

Shortly after reading the Washington Post article I received the January 7th Scientific American article, “Get the New Skinny on Dietary Fat.” It included the following quote from David Perlmutter, the author of Grain Brain. “The brain thrives on a fat-rich, low carbohydrate diet, which is unfortunately relatively uncommon in human populations today.” Mayo Clinic researchers showed that individuals favoring carbohydrates in their diets had a remarkable 89 percent increased risk for developing dementia as contrasted to those whose diets contained the most fat. Having the highest levels of fat consumption was actually found to be associated with an incredible 44 percent reduction in the risk for developing dementia.”

The article goes on to state that certain types of fats are more beneficial than others. “Good” fats include monounsaturated fats, found abundantly in olive oil, peanut oil, hazelnuts, avocados, pumpkin seads, and polyunsturated fats (omega 3 and omega 6), which are found in flaxseed oil, chia seeds, marine algae oil and walnuts.

Olivia Okereke of Brigham & Women’s Hospital tested how different types of fats affect cognition and memory in women. Over the course of four years she found that women who consumed high amounts of monounsaturated fats had better overall cognitive function and memory. Similar findings resulted from a study by researchers in Laval University in Quebec. They found that diets high in monounsaturated fats increased the production and release of the neurotransmitter acetylcholine, which is critical for learning and memory. The loss of acetylcholine production in the brain has been associated with Alzheimer’s.

Although canola oil, which is high in monounsaturated fats in its natural form, is often hydrogenated so that it can stay fresh longer in processed foods. Partially hydrogenated foods, also known as Trans fats, were shown to be detrimental to memory in a University of California at San Diego study. According to Beatrice Golomb, “Trans fats increase the shelf life of the food, but reduce the shelf life of the person.”

The article concludes by noting that “a well-rounded diet with plenty of fruits and vegetables may still may be the best way to stay healthy. But it’s good to know that a little fat here and there won’t kill you. In fact, it might well help you live a healthier, more productive life.”

© Douglas Griffith and, 2015. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and with appropriate and specific direction to the original content.

How the Illusion of the Present is Created

January 20, 2015

This blog post is based in large part on an article in New Scientist (10 January 2015, 28-31) by Laura Spinney. Although we feel like we are living in the present, we need to construct the present from what has happened in the recent past. First of all, we need to work with data processed by our senses. Different senses process information at different rates. For example, the auditory system can distinguish two sounds just 2 milliseconds apart, whereas the visual system requires tens of milliseconds. It takes even longer to detect the order of stimuli. There is evidence that even at the subconscious millisecond level, our brains make predictions. For example, when we watch a badly dubbed movie, our brains predict that the audio and visual streams should occur simultaneously, but if the lag between them does not exceed 200 milliseconds we stop noticing that the lip movements and voices of the actors are out of synch. Our brains need to blend these different sources of information coming in at different rates into a coherent present, so we can deal with what is happening in what appears to be now, but is actually the future.

Marc Wittman of the Institute for Frontier Areas of Psychology and Mental Health in Freiberg, Germany has developed a model of how this process occurs by drawing on a very large mass of psychophysical and neuroscientific data (Frontiers in Integrative Neurosciece, vol. 5, article 66). He believes that there are a hierarchy of nows, each of which forms the building blocks of the next, until the property of flow emerges into an the illusion of the present.

Virginie van Wassenhove and her colleagues at the French Medical Research Agency’s Cognitive Neuroimaging Unit in Gif-sur-Yvette have been investigating how the brain might bind incoming information into a unified functional moment. They exposed people to sequences of bleeps and flashes. Both occurred once per second, but 200 milliseconds out of synch. Brain imaging was used to reveal the electrical activity produced by these two stimuli. This consisted of two distinct brain waves, one in the auditory cortex and the other in the visual cortex, both oscillating at the rate of once per second. At first the two oscillations were out of phase and the research participants experience the light and sound as being out of synch. But later they reported starting to perceive the beeps and flashes as being simultaneous, the auditory oscillation became aligned with the visual image. So our brain seems to physically adjust signals to synchronize events if it thinks that they belong together (Neuroimage, vol 92, 274). So it appears that even at the subconcious level our brains are choosing what it allows into a moment. But according to Whittman this functional moment is not the now of which we are conscious. This comes at the next level of his hierarchy, the “experienced moment.”

This experienced moment seems to last between 2 and 3 seconds. David Melcher and his colleagues at the University of Trento, Italy provided a good demonstration of this moment. They presented research participants with short movie clips in which segments lasting from milliseconds to several seconds that had been subdivided into small chunks that were shuffled randomly before presentation. If the shuffling occurred within a segment of 2.5 seconds, people could still follow the story as if they hadn’t noticed the switches. But the participants became confused if the shuffled window was longer than 2.5 seconds (Plos ONE, vol 9, pe102248). So our brains seem able to integrate into a cohesive, comprehensible whole within a time frame of up to 2.5 seconds. The researchers suggest that this window is the “subjective present,” and exists to allow us to consciously perceive complex sequences of events. Melcher thinks that this window provides a bridging mechanism to compensate for the fact that ourackf brains are always working on outdated information. Our brains process stimuli that impinged on our senses hundreds of milliseconds ago, but it we were to react with that lag we would not function effectively in the world. Melcher goes on “Our sense of now can be viewed as psychological illusion based on the past and a prediction of the near future, and this illusion is calibrated so that it allows us to do amazing things like run, jump, play sports or drive a car.”

Wittman acknowledges that it is not clear how all this works. The biological of the experienced moment has yet to be found, however neuroscientist Georg Northoff set of the University of Ottawa has proposed one possibility in his 2013 book, Unlocking the Brain. He speculated that implicit timing could be related to slow cortical potentials that provide a kind of background electrical activity measurable across the brain’s cortex. Wittman notes that it’s telling that these waves of electrical activity can last several seconds. He also notes that consciousness itself is kind of filter because it focuses our attention on some things to the exclusion of others. It could be influenced by factors such as emotion or memory, it might tag or label a subset of functional moments as belonging together, to create an experienced moment.

What about meditators who say they are “in the now?” It is clear that it is impossible to be “in the now.” But is it possible that although they appear to be fooling themselves, they are actually accomplish something good? Data indicate that the answer is yes. Wittman did research in which meditators were able to maintain one interpretation of an ambiguous figure longer than non-meditators. Meditators also tend to score higher on tests of attention and working memory capacity. Wittman notes, “If you are more aware of what is happening around you, you not only experience more in the present moment, you also have more memory content.” He also notes, “Meditators perceive time to pass more slowly than non-meditators, both in the present and retrospectively.”

The final paragraph of the New Scientist article merits direct quotation. “This suggests that with a bit of effort we are all capable of manipulating our perception now. If meditation expands your now, then as well as expanding your mind, it could also expand your life. So, grab hold of your consciousness and revel in the moment for longer. There’s no time like the present.”

Memory Health and Technology

January 18, 2015

Memory Health and Technology is the subtitle for this blog. One of the primary themes of this blog is that we are not victims of technology. Rather, technology provides a means for cognitive development and growth throughout the entire lifespan. Thirteen of the previous fourteen posts were based on Daniel J. Levitin’s The Organized Mind: Thinking Straight in the Age of Information Overload (the odd post was on tips for fulfilling New Year’s resolutions). The reason for this is that the book directly addresses the goals of the healthy memory blog. It was not possible for my posts to do justice to the entire book, so I would recommend reading the book itself.

Another outstanding book that addresses the goals of the healthymemory blog is The Distraction Addiction by Alex Soojung-Kim Pang. I strongly recommend this book. If you do not read the book, I urge you at least to read the healthymemory blog posts based on the book. You can find these posts by entering “contemplative computing” into the healthymemory blog search box.

© Douglas Griffith and, 2015. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and with appropriate and specific direction to the original content.

Everything Else: The Power of the Junk Drawer

January 14, 2015

The final chapter in Levitin’s The Organized Mind: Thinking Straight in the Age of Information Overload is “Everything Else The Power of the Junk Drawer.” He begins by reiterating the most fundamental principle of organization, the one that is most critical to keeping us from forgetting or losing things is this: “Shift the burden of organizing from our brains to the external world. If we can take some or all of the process out of our brains and put it into the physical world, we are less likely to make mistakes. But the organized mind enables you to do much more than merely to avoid mistakes. It enables you to do things and to go places you might not otherwise imagine. Externalizing information doesn’t always involve writing it down or encoding it in some external medium. Often it has already been done for you. You just have to know how to read the signs.

Levitin then uses the example of the numbering ot the U.S. Interstate Highway System. Frankly, I have only understood a portion of this numbering system and not the whole system. So I learned something here. It is quite ingenious.

He then goes on to discuss the periodic table of the elements. This ingenious organization of the chemical elements has led to the discovery of new elements. Moreover, given this ingenious organization, there are already defined places in which they fit.

Next he discusses mnemonic systems for remembering names. You can find the technique he discusses in the healthymemory blog post “Remembering the Names of People.” (Use the healthymemory blog search block to access it).

Now the power of the junk drawer can be found as the result of browsing and serendipity. Browsing should be slow and leisurely. You need to be able to assess the content and potential value of what you are browsing. The reward might be the very real phenomenon of serendipity in which you discover something valuable that was not the objective of your original search. I suppose we can leisurely browse with the objective of some serendipitous finding. is one of a number of websites that allow us to discover content (new websites, photos, videos, music). Try it, you just might experience a serendipitous finding.

What to Teach Our Children

January 11, 2015

The penultimate chapter in Levitin’s The Organized Mind: Thinking Straight in the Age of Information Overload is titled “What to Teach Our Children.” He considers the world into which today’s children are born in contrast to the world in which we older adults were born. In that world information was both hard and slow to come by. In contrast, today’s world information is much easier to come by. But although vast amounts of information are easily and quickly accessible, this can make finding the exact information needed difficult. And there is the question of assessing the veracity of the information. I would wager that today the most commonly used encyclopedia is the Wikipedia, but anyone can make an entry to the Wikipedia. The vetting process is that the entry can be corrected or elaborated, but the vetting process can produce errors and the original author can change reintroduce the original error. Nevertheless, the Wikipedia works pretty well and I am a frequent user, although I always try to keep these caveats in mind.

Levitin recommends comprehensive instruction in critical thinking for our children, and I would add also for ourselves for the process of critical learning should not end, but should continue as long as we live. So children should be taught how to think critically about an article. They should also consider sources of possible bias. Some journals and websites do make an effort to identify political sources as being conservative or liberal and might even go on to assess the extremity of the political belief. Of course political leanings are not the only source of bias, there are also religious biases, academic biases, and even strongly held biases within different fields of endeavor. For healthymemory blog posts on critical thinking, enter “critical thinking” into the healthymemory blog search box.

Levitin also recommends understanding orders of magnitude to aid understanding how large or how small an object or quantity is. Being able to understand orders of magnitude estimates is important. Basically these are estimates of how many zeroes are in the answer. So if you were asked how many tablespoons of water are in a cup of water. Here are some “power of ten” estimates: 1,10, 100, 1000,etc etc. There are also fractional powers of ten such as 1/10, 1/100, 1/1000, etc. Basically these estimates help us understand the magnitude of size under consideration.

Enrico Fermi was a famous physicist who was famous for making estimates with little or no actual data. This involves sophisticated approximating sometimes called guesstimating. Regardless of its name, it is an important creative thinking skill. Examples of Fermi problems are “How many basketballs will fit into a bus?” “How many Reese’s Peanut Butter Cups would it take to encircle the globe at the equator?” and “How many piano tuners are there in Chicago?” Here is a four step solution to the last problem.

  1. How often are pianos tuned (How many times per year is a given piano tuned?)

  2. How long does it take to tune a piano?

  3. How many average hours a year does an average piano tuner work?

  4. How many pianos are in Chicago?

One can find the answers to these questions and come up with an approximate answer. Then one can criticize this analysis and propose a different solution. This is a good exercise for developing both creative and critical thinking.

© Douglas Griffith and, 2015. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and with appropriate and specific direction to the original content.

Organizing the Business World

January 7, 2015

“Organizing the Business World” is another chapter in Levitin’s The Organized Mind: Thinking Straight in the Age of Information Overload. It provides a nice historical overview of how organizations have developed driving down to technologies of organizations such as filing systems. There is a large amount of material, and I am going to attempt to focus on portions that I think will be of special interest to readers of the healthymemory blog.

One of these topics of interest I think will involve Area 47 in the lateral prefrontal cortex. It is an area no larger than a pinky finger that contains prediction circuits that it uses in conjunction with memory to form projections about future states of events. If we can provide some, but not all aspects of how the job will go, we find it rewarding. However, if we can predict all aspects of the job, down to the tiniest minituae, it tends to be boring because there is nothing new and no opportunity to apply discretion and judgment. Opportunities to apply discretion and judgment have been identified by management consultants and the U.S. Army as components to finding one’s work meaningful and satisfying. If some, but not too many, aspects of the job are surprising in interesting ways, this can lead to a sense of discovery and self-growth. Levitin writes that finding the right balance to keep Area 47 happy is tricky, but that most job satisfaction comes from a combination of these two. We function best when we are under some constraints and are allowed to exercise individual creativity within those constraints.

Levitin discusses the toxic consequences of negative leadership that can result in the collapse of companies or the loss of reputation and resources. He notes that this is often the result of self-centered attitudes, a lack of empathy for others within the organization, and a lack of concern with the organization’s long-term health. The U.S.Army has recognized this in both military and civic organizations: Toxic leaders consistently use dysfunctional behaviors to deceive, intimidate, coerce or unfairly punish to get what they want for themselves.” The latest version of the U.S. Army’s Mission Command manual outlines five principles that are shared by commanders and top executives in the most successful multinational businesses:

  • Build cohesive teams through mutual trust

  • Create shared understanding

  • Provide a clear and concise set of expectations and goals.

  • Allow workers at all levels to exercise disciplined initiative

  • Accept prudent risks

Levitin returns to multi-tasking in this chapter. He notes that we do not multi-task. Rather what we do is rapidly switch our attention from task to task. Consequently two bad things happen:we don’t devote enough attention to any one thing, and we decrease the quality of attention applied to any one task. Doing one task results in beneficial changes in the brain’s daydreaming network and increased connectivity. He notes that, “Among other things, this is believed to be protective against Alzheimer’s disease. Older adults who engaged in five one-hour training sessions on attentional control began to show brain activity patterns that more closely resembled those of younger adults.”

So people should not be forced to multi-task. But why, then, do we multi-task ourselves? Levitin attributes this to a cognitive illusion that sets in, fueled in part by a dopamine-adrenaline feedback loop, in which multi-taskers think they are doing great. Levitin writes that we are Balkanizing the vast resources of our prefrontal cortices, which has been honed over tens of thousands of years of evolution to stay on task. He further writes, “This stay-on-task mode is what gave us the pyramids, mathematics, great cities, literature, art, music, penicillin, and rockets to the moon. Those kinds of discoveries cannot be made in fragmented two-minute increments.

He notes that companies that are winning the productivity battle are those that allow their employees productivity hours, naps, a chance for exercise, and a calm, tranquil orderly environment in which to do theit work. Research has found that productivity goes up when the number of hours per week of work goes down.

© Douglas Griffith and, 2015. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and with appropriate and specific direction to the original content.

Organizing Information for the Hardest Decisions

January 4, 2015

“Organizing information for the hardest decisions” is a chapter in Levitin’s The Organized Mind: Thinking Straight in the Age of Information Overload. The primary focus of this chapter is on medical decisions. The subtitle is “ When Life is on the Line,” but Levitin structures the decision making in terms of probabilities and statistics. Given that we live in a world of uncertainty and constantly deal with, whether we realize it or note, probabilistic information, the advice in this chapter can be generally applied to the vast majority of decisions we need to make.

Levitin begins by discussing objective probabilities, probabilities regarding things we can count. For example, what is the probability of drawing an the ace of spades out of a pack of 52 playing cards. This can be computed by dividing the number of aces of spades in a legitimate pack of playing cards, but the total of number of cards in the deck, that is 1/52=0.019. The probability of drawing an ace from the deck of 52 cards requires that the 0.019 probability be multiplied by 4, as there are four aces in a deck of cards to yield 0.076.

Or consider the probability of rolling a six on a fair die. As there are six sides to a die the probability wold be 1/6=0.0967. To compute the probability of rolling two sixes, we need to multiply this probability by itself to get 0.0082.

To compute the likelihood of winning a pick three lottery you divide 1 by the number of numbers in the lottery, 1/1000=0.001, 1/10000= 0.0001, 1/100000=0.00001. 1/1000000=0.0000001.

Remember that in these rollover lotteries, where the winnings can assume astronomical amounts, the reward will be shared among the winners. Moreover, very often the prize is paid out over time, which effectively reduces the amount of the earnings. I remember one of these times when the prize had reached some astronomical amount and people were waiting in line for hours just to buy a ticket. When one woman was asked what she thought her chances of winning were, she answered, “about fifty/fifty.” Although she might represent an extreme case, few people can understand these extremely low odds. First of all, they would not waste their money. But it is also a waste of effort and time. Nevertheless, it keeps a fantasy alive for some. There is a term for this phenomenon and it is known as denominator neglect. People ignore the magnitude of the denominator, when evaluating risk or a bet.

There is an error most people commit when dealing with objective probabilities that is known as the gambler’s fallacy. This stems from a failure to appreciate how random random really is. For example, when people are asked to write down what they think a random sequence would look like for 100 tosses of a coin. Rarely will anyone put down runs of seven heads or tails in a row, even though there is a greater than a 50% chance that they will occur in a 100 tosses. Statisticians have argued that there is no such thing as a hot hand in basketball or other sports because hot streaks are likely just as a matter of random chance. The gambler’s fallacy is related to the notion that something is due. For example, if a fair coin is tossed five times and comes up heads five times, people will think that the sixth toss will be tails because it is “due.” Well each of these coin tosses is independent, so the probability that the sixth toss will be a tail is 50%, just as it was for the first toss. Now it is true that the probability of six straight heads is 0.008.

The preceding were objective computable probabilities. Whenever possible or relevant, you should be familiar with or compute them. However, we must also deal with subjective probabilities. Subjective probabilities are estimates, or guesses, regarding the likelihood of particular events or outcomes. We need to deal with these subjective estimates all the time. For example, how likely is it going to rain? How likely is it that I could get a job offer? What is the probability that my car will break down. What is the probability that I’ll miss my flight? I hope when you do this you are better calibrated than the lady who thinks she as a 50/50 chance of winning the lottery. And you need to combine these subjective probability estimates with respect to both favorable and unfavorable outcomes.

Levitin divides decisions into the following four categories:

  1. Decisions that you can make right now because the answer is obvious. (Here I would add that it is a good idea to do a mental check to see if you are overlooking any relevant information or risks. In retrospect you might find a risk that was obvious that was initially overlooked.)

  2. Decisions you can delegate to someone else (your spouse, perhaps?) who has more time or expertise than you do.

  3. Decisions for which you have all the relevant information but for which you need some time to process or digest that information. This is frequently what judges do in difficult cases. It’s not that they don’t have the information—it’s that they want to mull over the various angles and consider the larger picture. It’s good to attach a deadline to these.

  4. Decisions for which you need more information. At this point, either you interest a helper to obtain that information or you make a note to yourself that you need to obtain it. It’s good to attach a deadline in either case, even if it’s arbitrary, so that you can cross this off your list

Much medical decision-making, particularly important medical decisions, falls into category 4. You need more information. Doctors can provide some of it, but doctors have their own biases, are usually poor at computing or expressing probabilities. Moreover, much of this information is wrong (see the healthymemory blog post “Most Published Research Findings are False.”). If you read that post you should remember that many doctors cannot inform a woman who has tested positive, the probability that she actually has cancer. The probability is still only 10%. The reason for this is that the base rate of cancer is quite low. So many mammograms result in false positives. If you have read that blog post you should also realize that the successes of cancer screening are reported via cancer survival rates. There has been no analogous improvement in mortality rates. When making decisions you should not overlook the option of doing nothing. Ignoring base rates is an all too common human fallacy. So determining accurate base rates is critical to many decisions.

Making decisions regarding conditional probabilities involves using Bayes Theorem. Levitin provides a simple example that can be used as a template. That example follows.

Suppose that you take a blood test for a hypothetical disease, blurritus, and it comes back positive. However, the cure for blurritus is a medication called chlorohydroxelene that has a 5% chance of serious side effects, including a terrible, irreversible itching just in the part of your back that you can’t reach. Five percent doesn’t seem like a big chance, and you might be willing to take it to get rid of this blurry vision.

Here is the available information.

The base rate for blurritis is 1 in 10,000 or .0001.

Chlorohydroxelene use ends in an unwanted side effect 5% of the time or .05.

What we need to know is the accuracy of the test with respect to two measures

The percentage of the time the test falsely indicates the presence of the disease, called a false positive.

The percentage of time that it fails to report indicate the presence of the disease when the disease is present, called a false negative.

Draw a table of two rows and two columns, a fourfold table.

The columns represent the test results, positive or negative.

The rows represent the presence of the disease, Yes or No.

There are test results for 10,000 people. There is one positive test, and no negative tests for people who did not have the disease. So in the first row of the table there is a 1 in the left portions and 0 in the right portion.

In the “No” row there are 200 positive tests and 9,799 negative tests.

So to determine the probability that you have the disease, you add up the total positive test results and find that there is only a 1/201, 0.49% that you have the disease. So there is a 9.51% chance that you do not have the disease. Levitin provides an appendix in the book elaborating on the development and use of these fourfold tables. They are absolutely essential when conditional probabilities are involved and there are always conditional probabilities involved in medical tests. No medical test is infallible and it is important to have data regarding both false positives and false negatives.

Biopsies provide a good example of the fallibility of medical tests. They involve subject judgment in what is basically a “Does it look funny test.” The pathologist or histologist examines a sample under a microscope and notes any regions of the sample that, in her judgment, are not normal. She then counts the number of regions and considers them as a proportion of the entire sample. The pathology report might say something like”5% of the sample had abnormal cells,” or carcinoma noted in 50% of the sample. Pathologists often disagree about the analysis and even assign different grades of cancer for the same sample. So always get, at least, a second sample on your biopsy.

These medical decisions are example of making decisions are the basis of expected values and expected costs that can be generally applied. Suppose you need to decide whether you should pay to park your car. Suppose that the parking lot charges $20 and the cost of a parking ticket is $50, but there is only a 20% chance that you’ll get a ticket. So the expected value of paying for parkins is a 100% chance of losing $20 (-$20). Not paying for parking has a 25% chance of losing $50 (-$12.50). So for today the smart money says do not pay for parking (excuse me for avoiding the ethical problem of disobeying the law and inconveniencing workers by parking in a loading zone. This is only being done as an illustrative example).

What is current in the news is a big problem, because often we are lacking information regarding the frequency of events and confuse the frequency and urgency of reporting with the actual frequency of occurrences. One of the best examples of this occurred after the 9/11 tragedy many people decided to drive rather than fly. As driving is more dangerous than travel by commercial aviation, this resulted in an increase in deaths due to changing modes of transportation. People are alarmed by crime and envision frequent shoot outs between criminals and police. They feel a need to arm and protect themselves. Well check the actual frequency of crime in your neighborhood versus basing it on the programs and news reports on television. You probably are much safer than you think you are. In contrast to what we see on television, it is my understanding that the majority of police retire from their jobs without ever having fired their weapons on duty. And guns are used in more suicides than in homicides, to say nothing of accidental shootings.

This post has probably been disturbing for many readers. Well unfortunately, there is much missing information, much misinformation, and problems in accurately computing probabilities in making decisions. It is hoped that this post will inform on what to worry about and what to ignore, on what questions to ask, and how to combine probabilities to make decisions.