Innumeracy

Innumeracy is "the mathematical counterpart of illiteracy," says computer scientist Douglas Hofstadter. It describes "a person’s inability to make sense of the numbers that run their lives." Although Dr. Hofstadter coined the term, mathematician John Allen Paulos made the word part of the common vocabulary with his book, Innumeracy: Mathematical Illiteracy and Its Consequences. Since its publication in 1989, it has been translated into thirteen languages.

Dr. Paulos is not saying that everyone needs to be a mathematician, but rather one must be able to understand the consequences in everyday life of how our society uses numbers. The consequences of innumeracy are not as visible or obvious as the consequences of illiteracy. Nonetheless, they can be just as profound when they contribute to "confused personal decisions, muddled governmental policies, and an increased susceptibility to pseudoscience." He wonders if this is why people would buy a home having a $2,000 monthly mortgage when they only make $4,000 a month? Or why a person might borrow money at thirty percent interest in order to buy a large screen plasma television?

The difference between illiteracy and innumeracy is that the former affects mostly uneducated people whereas the latter affects people who are both intelligent and well-educated Many people who are extremely competent in many fields of knowledge and can understand complicated issues may tremble when confronted with numbers or probability.

For example, some people won’t travel to other countries because they are afraid they might be killed by a terrorist attack. Yet, they continue to travel locally in their car. The odds? Your chances of dying overseas by a terrorist attack is about 1.6 chances out of a million, yet you have a 1 chance in 5,300 of dying in the family car.

Journalist, Chip Scanlan, tells about his innumeracy and what negative effects it had in his professional career as a writer. "In high school and college, I was a terrible math student. I flunked geometry, was totally bewildered by algebra. Trigonometry I ran from. I had trouble balancing a checkbook. As a reporter, I was painfully aware of my innumeracy every time a percentage appeared in my story. Budget stories made me cringe. Without math skills I was not as effective a journalist, and my readers weren't as well-served as they could have been. It wasn't just the mistakes I made or the agonies I went through trying to figure things out. As a reporter I regurgitated statistics without understanding them because I didn't feel capable of interpreting them. I'm sure I missed stories and screwed up others because of my weak math skills." He goes on to say his dilemma is not uncommon in the journalism business.

Sometimes, people can make numerical claims that are publicly embarrassing. Years ago when the speed limit debate was taking place in America, a Washington lobbyist, Clarence Ditlow, made a public, numerical goof. He published an article explaining why he believed raising the speed limit above 55 miles per hour would be dangerous.

His heart was in the right place because he was trying to educate people against driving too fast by explaining how far a car can travel in one second. He made the following calculation: "A vehicle traveling 55 mph covers 807 feet in one second, almost three football fields. At 70 mph, a vehicle covers 220 feet more or 1027 feet in one second." Anyone who has driven a car knows they are not going the length of three football fields each second. If you care to do the calculations, you will find that at seventy miles an hour you only travel 103 feet each second.

Innumeracy has many faces for many people. One such face is seen when people say that "there is no such thing as a coincidence" — a belief that philosopher Sigmund Freud held dearly to his heart. By underestimating the likelihood of coincidences, people believe that something strange or mystical must be afoot when a coincidence happens. For example, most people would consider it a coincidence that if in a room of only twenty-three people any two people would have the same birthday. "Common sense math" appears to support this notion. Most people would calculate it this way. Since we would need 367 (counting a leap year) people in a room to be absolutely certain of two people sharing the same birthday, then it seems "obvious" that there is only a 6% change of this happening with only 23 people in a room (23 divided by 367).

Innumeracy can also raise its head in financial matters. Assume your friend invested $1000 in the stock market and the next day her investment went up 60%. Yay! The next day the price dropped 40%. Your friend might shrug and say "Great, I’m still 20% ahead in my investment." "Wrong," you would say. You would tell her that she actually lost $40 of her original investment. Here’s how you would explain it to her. Her 60% gain the first day would leave her with $1600. The next day when this $1600 went down by 40% she was left with only $960. If this doesn’t make sense you can easily check it with a simple calculator.

Statistics is one of the fastest ways for innumeracy to come bubbling to the top in any conversation (if no mathematicians are present). Although developed in the eighteenth century mainly for the purpose of developing a theory of gambling games, statistics today are the mainstay of pollsters. Commonly, innumerate people decry the results of polls because they don’t understand how it is done. The statistics that comprise polling can be baffling because it seems impossible that enough people could be polled to account for a country’s entire population. How can asking a small group of people what they think of an issue be used to say that a certain percentage of all Americans believe something specific about that issue?

Additionally, we know that people are not honest all the time so how do we know that people being asked personal questions by pollsters are going to be honest? Mathematicians have come up with a clever solution to the problem of lying that could be used by pollsters to account for any lying from the people they question. Dr. Paulos gives an example in his book of how someone could estimate the number of people in this country who might engage in a potentially embarrassing sex act (use your imagination here). Suppose you randomly asked 1000 people whether or not they engaged in this unusual sex act. Just asking the question is useless because there obvious reasons why a person would avoid being honest about their sexual behavior.

However, let’s say that each person is asked to flip a coin of their choosing. Before the question is asked they are told to flip the coin and privately look at the result of the coin flip. If the coin lands on heads, they are supposed to answer "yes" to the question being asked even if they have to lie. If the coin shows tails, they are to answer truthfully. Now the person being polled knows that nobody will ever be able to know if he or she answered the question honestly or not.

Next, each person flips their coin and looks at it in secret prior to being asked the sex act question. Some say "yes ," others say "no." When we have finished asking the thousand people let’s say we find that 620 of them answered yes. So, how do we interpret the results? Simple. We know that 500 people answered yes because odds of getting heads is 50%. We throw out these answers. Now we know that of the 500 people left who answered truthfully, 120 people, or twenty-four percent, answered "yes"honestly about their sexual behavior.

One of the ways that statistics teachers teach numeracy in an introductory statistic course is to have their students solve the well-known Birthday Problem mentioned above. With simple math tools of probability, it can easily be shown that there is a 50% chance that a room of 23 people will have the same birthday. Gamblers have used this fact as a "bar bet" for years by betting someone with odds in their favor. The gambler would rig the odds so that even though they lost half the time, they would win more money when they won the bet than they would lose when they lost the bet. There are many variations of this non-obvious observation. Dr. Paulos notices that "at least two people living in Philadelphia must have the same number of hairs on their heads." Figure that one out.

There is an interesting stock market scam that is based on innumeracy but isn't legal so you may not run into it. It goes something like this. Let’s say you received an unsolicited email from a person claiming to be a financial advisor and he was predicting the direction a particular stock would take in the following week. The week goes by and the prediction comes true. Your next email explains his company can do this because of their just-developed proprietary computer model. This email also makes another prediction of the same stock. Surprisingly, they are also correct on this prediction. This happens six weeks in a row and by now you are becoming interesting in how they can do this and seeing mega-dollar signs in your eyes. You are hooked because now the "advisor" tells you that for a reasonable sum of money you can buy into their program and become wealthy in a matter of months. Most people would jump at the chance.

Here’s the problem. What you would not know is that this person sent out the same first letter to 32,000 people. Half of these letters told people the stock would rise, the other half are told the stock would drop. This means that 16,000 people would have gotten an email with the correct prediction. Which ever way the stock actual goes, these 16,000 people who got the correct prediction would get a second letter with a new prediction. The "advisor" would use the same principle: 8,000 people would be told the stock would go up while the other half that it would go down. This pattern continues until 500 people have been given six correct "predictions" in a row for the stock.

These are the "marks" for the scamer. They are all now sent the "if you pay a fee you will have untold wealth" letter. They are told that they only have to pay $500 in order to win big next week. They each figure they can easily get their $500 back in just a week. Since you don’t know 499 other people just got the same letter you send in your money and start planning for retirement. Since everyone sends in the money, the stock "advisor" is now $25,000 richer in just six weeks. Of course, nobody ever hears from this miraculous advisor again.

Belief in predictive dreaming and precognition is also enhanced through innumeracy. How many people have you heard say something like this? "I dreamed my brother, who lived in another country, died one night and when I awoke I received a phone call saying he had had a heart attack in the night and died." This experience can feel spooky to both the dreamer and people who hear the story.

Simple math can easily explain this precognition. I won’t bore you with the calculations but the numbers show that of all the people in the world who remember their dreams (we usually have more dreams than we can remember) about 3.6 percent of all the people will have a predictive dream on any given night. Although that number seems small it is significant because there are so many people in the world. We can expect that millions of people would have at least one precognitive dream every year while hundreds of thousands would do so each night.

When innumeracy and human emotions are combined (which invariably they are) we find that most people make many decisions that are wrong -- especially when it involves risk. It has been shown many times that people will avoid risks when seeking gains, but choose risks to avoid losses. This principle was co-discovered by Daniel Kahneman, a psychologist and Nobel prize winner in economics.

Let’s say you had the choice of winning $30,000 or making a bet that has an 80% chance of of winning $40,000 or a 20% of winning nothing. Most people would take the thirty grand even though the average gain from the second choice would be $32,000.

If the scenario were changed so that you it was certain you would lose $30,000 or given a second choice where there was an 80% of losing $40,000 or a 20% chance of losing nothing. In this case, most people would take the second choice even though it would be wiser to take the 80% change of losing $40,000.

Numbers are a part of who we are because we live in a world saturated by numbers. Technology, which is all about numbers, is advancing exponentially as is information from our technology. Thanks to the ubiquity of computers and the Internet, we are bombarded hourly with information and we have to decide whether to accept new information or reject it. Fortunately, we don’t have to make all the choices by ourselves.

We can make wise choices by using numerate people who understand numbers and know how to do legitimate research. One such example is the team of Barbara and David Mikkelson. They are excellent researchers and are experts at sniffing out rumors, urban legends and new myths. Their website, Snopes, often uses mathematics to find out the truth of dubious claims wending their way through cyberspace.

Numeracy is also required of all scientists since mathematics is the language of science. We need to listen to scientists for getting through the daily barrage of fluff, lies, and half truths poring forth from media outlets and their so-called experts. Even well-meaning and smart people can be propagators of nonsense by being innumerate. Scientists, mathematicians and engineers can help us get clarity on many issues. For example, Peter Aczel, is an audio engineer who has debunked nonsense in the world of high-end audio. His online magazine, The Audio Critic, is the place to head if you plan to spend any significant amount of money on new or even used high-end audio equipment. His back issues begin in 1991 (even though he began his magazine long before then) and well worth the read. His no-nonsense intelligence and sharp wit that does not suffer fools gladly will keep you entertained for hours.

Religion and innumeracy are common bed fellows. America is the most religious country in the world, yet for all its popularity, religion can promote certain myths as absolute truth. For instance, some religious people believe in a literal Flood as described in the book of Genesis. Fortunately, most religious people understand this story as a metaphor with much deeper meaning than can be had from a merely literal rendition.

Why is it difficult to accept this story literally? That is because the story is loaded with numbers — numbers that some people don’t take seriously or avoid even if they take the story seriously. The writer of this Genesis story says that ". . . all the hills that were under the whole heaven were covered . . ." Taken literally, this means the entire surface of the earth was covered by at least 20,000 feet of water which would make the water about four miles deep (the deepest part of our planet’s oceans in the Mariana Trench which is over 6.8 miles deep). That was a deep flood. Even worse, the Flood Story tells us that it rained steadily for 40 days and nights for a total of 960 hours. Doing the math tells us that the rainfall was at least 15 feet per hour! This is enough of a downpour to sink an aircraft carrier, let alone a small wooden ark with thousands of animals on board.

Mathematician John Allen Paulos wrote his book on innumeracy because, in his words, "I'm distressed by a society which depends so completely on mathematics and science and yet seems so indifferent to the innumeracy and scientific illiteracy of so many of its citizens."

Resources:

Best, J. (2001). Damned Lies and Statistics: Untangling numbers from the media, policians, and activists. Berkeley, CA: University of California Press.

Dewdney, A.K. (1996). 200% of nothing: An eye opening tour through the twists and turns of math abuse and innumeracy. New York: Wiley.

Paulos, J. (2001). Innumeracy: Mathematical illiteracy and its consequences. New York: Hill and Wang.

Illiteracy

Webster's New Third International Dictionary defines "illiteracy" as "The inability to read or write, or the actual or perceived state of being uneducated or insufficiently educated."

When we think of illiteracy we immediately think of people in third world countries or the few dirt-poor areas of highly educated countries. Since the United States puts so much emphasis on education we don’t see illiteracy as a major problem in this country. We are leaders in research and educational opportunities. Our scientists have received over 130 Nobel prizes in the last hundred years. Americans have also received a number of Nobels for literature and economics.

Britain has some of the most prestigious universities in the world with Oxford and Cambridge. California has ten world-class campuses in its system — more than most countries have universities. This is not to mention the multitude of California State University campuses. Add to all this the multiple universities almost every state in America offers in addition to private universities in many states and you can begin to see why American is a leader in education and research. The University of California has produced 65 Nobel laureates with the Berkeley campus, alone, having twenty-five faculty who have won the prize.

So what does illiteracy have to do with America? Unbeknownst to many, we have forty-two million adults in our country who simply can’t read. That is a lot of people! Surveys have found that another fifty million people read no better than a 5th grade reading level. Is this just a passing problem? Not really. Twenty-five percent of all teenagers drop out of high school. Even sadder is that of those who do graduate, another twenty-five percent are at the same educational level as someone who stopped their education at the eighth grade. These numbers are huge. To illustrate the size of the problem, there were fewer people who voted in the 1980 presidential election than there are illiterate people in America. How few? Sixteen million fewer voters than those who cannot read or write.

Most of us don’t know about nor do we want to think about the appalling amount of illiteracy in this country. How can a society that is becoming more dependent on increased technology hope to find enough workers with these rates of illiteracy. One of the assumptions of our founding fathers was that a democratic society would be based on generally high levels of literacy.

In 1955 Rudolf Flesch stunned this country with his book, Why Johnny Can’t Read. Time magazine called his book "the outstanding educational event of that year." Since then, experts have found out that American illiteracy is still growing at an unacceptable rate. We are told that every year 2,250,000 more adults are added to the rolls of functionally illiterate people in this country.

I am going to do a series of blog articles on illiteracy, but not the kind that has been identified above. There are other kinds of illiteracy that involve people who can read and write just fine. There are several types of illiteracy that apply to educated people. For the next several weeks, I’m going to write an article on each one of these.

One type is called" innumeracy." It is a word devised by a cognitive scientist, Douglas Hofstadter, who used to write a column for Scientific American. In the early 80's he used this word to describe the inability of anyone who could not understand the basic numbers that are used in our society. Then, in the late 80's, a mathematician, John Allen Paulos, wrote a book entitled Innumeracy. Is not knowing how to use numbers really a big deal? According to the experts the answer is "yes," because struggling with numbers has a high social cost such as wasted money, bad social policies, and unnecessary risks.

Somewhat related to this is another kind of illiteracy called scientific illiteracy. Mark Twain spotted this problem a century ago when he said, "The trouble with the world is not that people know too little, it’s that they know so many things that just aren’t so." We live in an age of science yet surveys have shown that many people have not shed the baggage of superstition. We are a people who have a very long list of things we believe in that "just aren’t so": lucky numbers; healing through pyramids, mind power, crystals, homeopathy, etc.; extrasensory perception; subliminal learning; biorhythms; astrology (55% of American teenagers believe in astrology; 75% of people in Great Britain believe it is scientific); UFOs. Much of scientific illiteracy occurs because people don’t understand what science is, what it is supposed to do, and how it is done.

Cultural illiteracy was a problem E.D. Hirsch identified about twenty years ago. Dr. Hirsch taught us that reading was not enough. We must also understand what we read and this can only be done if we have a basic fund of knowledge that we bring to our reading. Cultural literacy is only obtained when a society shares a basic knowledge of geography, history, literature, politics, and democratic principles. When Jay Leno finds random people on the street who cannot give him the name of the current Vice President of the United States, then something is wrong. Recently, we had the sad experience of someone who aspired to this office who had appalling gaps in her understanding of the world. She even relished in the idea of calling herself a "rogue." Perhaps she might have been more reluctant to do so if she knew the definition of the word. The dictionary says it means (1) a dishonest, knavish person; scoundrel. (2) a scamp. (3) a tramp or vagabond. (4) in biology it refers to an usually inferior organism.

Have you ever heard of religious illiteracy? It has come to light that many religious people are not well-versed in their specific religion. For Christians to whom the Bible is the foundation of their faith, a recent survey discovered that only thirty-three percent of Evangelicals actually read the Bible; only twelve percent do so daily. Professor Stephen Prothero is chair of the religion department at Boston University. He has found that "Americans are both deeply religious and profoundly ignorant about their religion." He gives examples:

• Protestants who can’t name the four Gospels
• Catholics who can’t name the seven sacraments
• Jews who can’t name the five books of Moses

His research has shown him that faith in American is "entirely devoid of content." His conclusion is that America is "one of the most religious countries on earth and also a nation of religious illiterates."

Although I may throw in a few more examples of different types illiteracy, the final blog will be on financial illiteracy and will be authored by a guest. He is Jason Kelly, whom I greatly admire as a person of substance and highly knowledgeable when it comes to understanding the market and other financial concerns. He is the best-selling author of five books on investing and personal finance. I think you will really enjoy his article on this blog. Prior to his blog article, you can check him out at http://www.jasonkelly.com/

The Amazing Story of Dr. Katze

Most of you know that psychotherapists need to be approved by a state licensing board in order to ply their wares. In California this means that after graduation from graduate school, a person needs to get three thousand hours of experience as an intern under the supervision of a licensed psychotherapist. They must then pass an exam in order to be licensed to practice.

Most states believe that the licensing of psychotherapists will "safeguard the health, safety and welfare of the citizens" of the state. This is a nice thought but does licensing really work this way? As far as I know, there is no research that has unambiguously found that licensing promises professional competence.

This is not true of all professions. For example, if your physician is what is called "board certified" there is a very good chance that she has passed some difficult requirements to reach this level. Psychologists have to jump through demanding hoops to obtain the level of Psychology Diplomate which is equivalent to a board certification.

Even these diplomas on the wall, however, can be bogus. Earlier this year the Attorney General of Connecticut issued an urgent warning to the public about the sale of bogus medical board certifications. Certification boards keep springing up around the country. For example, the Science-Based Medicine website has identified a "Pseudomedical Pseudoprofessional Organization" called the US Autism & Asperger Association (USAAA). The site identifies this organization as a scam because

USAAA Staff, Board of Directors, and Advisory Board rosters are filled with physicians and other professionals who, for the most part, lack real credentials in biomedical research related to autism. What do they have to recommend them? Overwhelmingly, they are parents of children with autism. I find it hard to muster the contempt that I usually feel for people whose pseudoscientific eruptions contribute to horrible outcomes. Instead I feel an almost futile sense of sorrow.

I remember a time in the 80s and 90s in California when increasing numbers of Master’s level students were being certified to practice psychotherapy. Soon, there were too many psychotherapists for the population and these practitioners had to find other ways to stand out from the crowd. To find ways to have an edge over the consumer’s dollar, many psychotherapists signed up for any therapy du jour class that just happened to be available. Many of these new approaches were based on pseudoscience. With more than five hundred unproven therapies available for psychotherapists, it was easy for these psychotherapists to slip into believing they were receiving training in legitimate therapies. The pull of the dollar got them to overlook the fact that there was no evidence their new therapy technique really worked. They believed in it because it seemed to make some of their clients better. These psychotherapists didn’t understand the power of the Placebo Effect and other reasons why people can get better in spite of the specific therapy.

This sad state of affairs came about because many Master’s level training programs gave short shrift to the science of psychotherapy. In a two year degree program there is often not enough time to educate students on the importance of critical thinking and the underpinnings of science for helping people. Consequently, there is wide variability among training programs so it is possible for a person to be poorly trained and still pass a licensing exam. There are psychotherapists today who are licensed and practicing who don’t think that science has anything to contribute to the field of psychotherapy.

In 1991, I presented a paper at the 99th Annual Convention of the American Psychological Association about "psychology, mysticism, superstition and the paranormal" in the field of mental health. One of the examples I gave of bogus offerings to the public by psychologists was a licensed psychologist in the San Francisco Bay Area who was advertising her services as a "Critter Consultant." If you had a problem with your pet you could take your beloved animal to this person and she would use her special supernatural powers to telepathically deal with your pet. My paper was called, Hungry People Who Buy Imaginary Food with Real Money (let me know if you would like a copy and I can send you a PDF version of it).

All of these bogus therapies, offered by equally bogus credentialing boards, became an irritant to a psychologist by the name of Steve K. D. Eichel. Dr. Eichel came up with a creative way to show the public how prevalent phony credentialing had become. He thought it would be interesting to see if his female companion (who had no college degree or any association with the profession of psychotherapy) could get some fancy psychotherapy credentials. He decided to see if "Dr. Katze, Ph.D." could get some bogus credentials.

Dr. Eichel found a website for credentialing lay hypnotists, paid the application fee and waited. Within a couple weeks his companion, Dr. Katze, was a certified lay hypnotist. The reason they decided on starting with this credential is that most lay hypnosis associations agree to accept without question certifications from other, similar organizations for lay hypnosis.

By using these reciprocity agreements, Dr. Katze was on her way to filling up a wall with impressive sounding and fancy looking certificates. By doing nothing more than sending organizations checks she was able to get certificates from the National Guild of Hypnotists, the American Board of Hypnotherapy, and the International Medical & Dental Hypnotherapy Association. She also became a Professional Member of the American Association of Professional Hypnotherapists.

A dream came true with so little work. If it was this easy, they decided to check out the next level called Board Certification. Now, this is serious. Physicians can practice medicine as soon as they are licensed. If they become "board certified" they are saying to the public they have achieved additional expertise in a specialty field like pediatrics or surgery. We psychologists go to the next level by working for Diplomate status which indicates we have reached the top of our profession.

An organization called the American Psychotherapy Association was originally established "to advance the profession of psychotherapy." Dr. Eichel discovered they offered the powerful credential of Diplomate. When Dr. Katze applied for this certification the American Psychotherapy Association requested both a resume and what is called a curriculum vitae (a listing of graduate classes and post-doc experience). After very little effort the computer was fired up and was able to print out some very impressive looking documents to comply with these document requests. The fake documents provided a long list of previous jobs such as having been a consultant for the bogus "Tacayllaermi Friends School" in New Castle, Delaware.

At this high level of certification, it is customary for the licensing body to request copies of corroborating documents. Although this request was fully expected, the association never asked for transcripts for the universities listed or copies of all the certificates listed, or for any copies of state required licenses to practice. This information is basic and required when applying for Diplomate Status. Additionally, after a licensing board reviews these documents, the candidate is then examined by other professionals in a face-to-face context. None of these were ever asked for. The credentialing board never met Dr. Katze.

The check went out and another certificate came in the mail within a couple weeks — and a very impressive certificate it was. Dr. Katze was now a certified Diplomate because she had passed "rigid requirements" for this status. The certificate was accompanied with a letter of congratulations for her achievement. The letter told her she belonged to a "select group of professionals who, by virtue of their extensive training and expertise, have demonstrated their outstanding abilities in regard to their specialty."

It is hard to believe that anyone without any expertise could accumulate these credentials by merely asking and paying for them, but this is what happened. It is even more inconceivable when the applicant is not a human. Yes, Dr. Katze was the name Dr. Eichel gave to his cat. His last application even gave the organization a hint to this effect by imbedding a clue. Look at the name of the Friends School in the third paragraph above this one and read the name of the school backwards. If you are interested in reading Dr. Eichel’s original article you can find it here.

Living In La-La Land

Sit in reverie and watch the changing color

of the waves that break upon

the idle seashore of the mind.
—Henry Wadsworth Longfellow—

If all humans daydream, why is it seen in such a negative light? Why is something so easy and natural seen as a waste of time? How can something so universal to the average human be considered pathological?

It appears that daydreaming can have real benefits:

• It can make us feel active and energetic by relieving boredom.
• It can be similar to meditation by activating our parasympathetic nervous system.
• It might help us be more aware of who we are.
• It may be a key for researchers in understanding consciousness.
• It can organize our conflicts into meaningful solutions.
• It helps to enhance social skills and relationships.
• It appears to be a wellspring for creativity.

I was trying to daydream, but my mind kept wandering.
—Steven Wright—

One of the first psychologists to scientifically study daydreaming is a retired Yale professor. Dr. Jerome Singer surveyed many different groups of people and found that most people’s daydreams are quite ordinary and not at all unusual. Dr. Singer’s book, The Inner World of Daydreaming, discovered that often daydreaming was a way for the brain to map out goals and doubts. Daydreaming as mental rehearsal can actually help you to be more effective in dealing with what is to come in the days ahead.

I remember years ago working with a woman whose husband was an NFL quarterback playing for a team that had surprisingly made it to the Superbowl. The other team was odds on to win the game easily. However, just the opposite happened. The underdog won the Superbowl game much to everyone’s amazement. Much of the credit went to this quarterback who had the best game of his career. He later told me that he had spent about twenty-four hours prior to the game thinking about nothing but throwing perfect passes. His "perfect" passing, which was not one of his strong points, carried his team to victory.

Sometimes, in a summer morning, having taken my
accustomed bath, I sat in my sunny doorway
from sunrise till noon, rapt in reverie.
—Henry David Thoreau—

The amount of daydreaming varies a lot from person to person. Some people daydream as seldom as 5 times a day while others might daydream over 175 times a day. One finding of researchers is that people who daydream more than the average person tend to remember more content from their dreams at night.

Creative people also tend to daydream more than the average person. Daydreaming is usually a stream of consciousness that randomly moves from topic to topic. This randomness combined with high frequency is one of the determinants of creativity.

Every child knows how to daydream.
But many, perhaps most,
lose the capacity as they grow up.
—Dov Frohman—

It seems that daydreaming happens more often when we are bored or have no need to focus on the task at hand. How does this information apply to the real world? Some psychologists believe that we might be stifling creativity in our children by over programming their time. One study found that children who watch television at least three hours a day are less imaginative than children who watch only one hour a day. Of course, this study does not tell us which is the chicken and which is the egg.

The increasing use of drugs for children decreases daydreaming. For example, children with ADHD who are taking Ritalin are less creative than ADHD children who are not taking Ritalin. On the other hand, people with severe ADHD may daydream so much that they cannot focus on simple but necessary tasks.

"If I were not a physicist, I would probably be a musician.
I often think in music. I live my daydreams in music.
I see my life in terms of music.
... I get most joy in life out of music."
—Albert Einstein—

What drives the brain to daydream. It seems that daydreaming and night dreaming have something in common. It is a time when the brain assimilates the millions of data bits it continually receives. It must make sense of this chaotic, rambling information and does so during sleep and daydreaming. As with night dreaming, daydreaming helps the brain to solve problems and connect seemingly unconnected pieces of information. This latter function is what creativity is all about — finding the new by connecting pieces of the old. Various studies have shown that highly creative people from Albert Einstein to Walt Disney spent a lot of time daydreaming.

Active daydreaming can help us overcome personal problems. I had a therapy client who came to me because he had become sexually impotent in his marriage. This was before Viagra so we had to find a non-medical solution to his problem. His job was demanding and also involved a lot of daily driving. We found that during these drives, he spent a lot of time daydreaming about this problem and the negative effect it was having on his marriage. Wondering if changing the focus of his daydreaming would work, I asked him if he would like to spend his mental down time daydreaming about seducing and making love to his wife. His answer was not surprising. After doing this assignment not only faithfully but with gusto, he called me back in two weeks and told me he and his wife were having the best sex of their lives.

Reverie is not a mind vacuum.
It is rather the gift of an hour
which knows the plenitude of the soul.
—Gaston Bachelard—

It appears that there is a place in the brain called the "executive network." This area of the brain acts like a switchboard by combining the activity of different brain structures. This network is more sophisticated in adults than in children because it is not fully formed and operational until the early to mid-twenties. Neuropsychologist Dr. Karen Spangenberg Postal claims that we now know enough about this area of the brain so that parents can actually learn how to increase their children’s academic performance.

You can also use daydreaming to help yourself. Since you may already daydream, on average, about one-third of your waking day, why not use it to your advantage? The first step is to reinterpret the value of daydreaming. Instead of seeing it as a sign of laziness or time-wasting, view it as a way to enhance the quality of your life. Once you have given yourself permission to daydream, you no longer have to feel guilty for doing so. After this, you can anticipate and look forward to times of daydreaming. Some people actually schedule daydreaming times – these times can be as short as a few minutes to as long as you want. One final word. Let yourself get lost in your daydreams so that you are the passenger, not the driver. Some research has found that people who are not aware of the daydreaming content can be more creative than people who actively monitor their daydreams.

Thought is the labor of the intellect,
reverie is its pleasure.
—Victor Hugo—

Happy dreaming.