link to a Feynman video (and a 2nd (distantly related) video)
This may be the best one of all the Feynman videos. He explains how physicists do mathematics and distinguishes how physicists do math from how mathematicians do math. He describes the two flavors as Greek and Babylonian.
The money quote if you don't have time to watch it: "Physicists do Babylonian mathematics and pay little attention to precise reasoning from fixed axioms."
Comment number 1; the quality of the video ain't all that great--in particular there is an annoying very small synch error which is just large enough to be definitely noticeable. Nevertheless it is absorbing because of the power of his presentation. The occasional audience shots show an audience transfixed. They also show the majority of the people wearing eyeglasses.
Comment number 2; in his earlier days his working class New York accent seemed far more obvious. I am reminded of Art Carney from The Honeymooners. (That is a four minute clip.) Feynman was born in Queens in 1918. Carney was born in Mount Vernon in 1918.
Deviant argumentation regarding Monty Hall problem
In class number four of the online Artificial Intelligence course from Stanford, Peter Norvig explains "one of the most popular problems in the subject of probability theory, the Monty Hall problem". His presentation was exactly what I have always been taught, and I got the right answer on the quiz.
Hold; P(goat) = 2/3; P(car) = 1/3;
Switch; P(goat) = 1/3; P(car) = 2/3.
Since the last time I looked at that wikipedia article, a number of qualifications and stipulations and elaborations have been added. Apparently this problem has kept its popularity and controversy with undiminished vitality since around 20 years ago, when it was popularized by a national Sunday newspaper magazine columnist Marilyn Vos Savant. Her answer is the one above, which is also what I would call the least complicated wikipedia page answer (as the page sits today.)
Now there is one probable error in Norvig's lecture. He claimed that Monty Hall didn't know the answer to his own problem, and quotes a letter he says was written by Monty Hall in 1990. If this is true, I find it impossible to follow the following New York Times story, from 1991 where Monty explains all the subtleties of the problem in much shorter order than all of the complications on wikipedia. To summarize Monty's take: he is the carnival barker; it's his game; and he can change the rules in the middle of the game if he feels like making it more complicated than your five minute presentation for your students.
But there is one critical element missing from all of the discussions I have seen to date, except for one which was told to me by a playfully deviant fellow many years ago. His argument is simple: if by this strategy a player can double his chances of winning, the players would have figured this out forthwith; everybody would have switched every time; and the drama and the fun would have been drained from the game. The fact is the show was the most popular game show in it's hay day. Ergo there cannot possibly be an easy way to game this strategy. My deviant probability theorist pal had confidence in Monty's game players to find any available edge.
Also the data is in the archives. All you have to do is watch every episode and count the holds and switches and wins and losses and you will have a really high confidence estimation whether the correct answer is closer to 2/3 and 1/3 or is closer to .5 -- .5. If no statistician is interested in researching this, surely some enterprising historian of science or sociologist of science ought to be up for it.
Ig Nobel for the anti-akrasia guy
The Improbable Research folks have awarded an Ig Nobel prize to John Perry (previously on Less Wrong) for his work on how to procrastinate and still get things done.
(edited to fix the link)
Meditations on first philosophy
I put this post up on my blog this morning (link) and some here might like to see it or discuss it.
Meditations on first philosophy is the title of the first book ever written in contemporary western Philosophy, according to the university course I took. It was written by Rene Descartes in the seventeenth century, who began with the premise that he wanted to find true factual indubitable knowledge and that the way to find this was to begin by doubting everything, and retaining only what could be defended by rigorous logic. So by these meditations he reasoned to such respected elements as "I think, therefore I am." This short book continues to be relied on hundreds of years later and modern (especially French) philosophers such as Sartre, Foucault and Derrida all explicitly acknowledge the importance of Descartes' achievement.
I am occupied with a similar project. This was not entirely a conscious choice or any sort of Cartesian magnum opus. In the past five years I have slowly realized that almost nothing I think or do is too trivial to closely examine, and I am now of the attitude that I am willing to examine anything and everything, taking absolutely nothing for granted.
The first major recent instance changed my note taking practice. This happened in 2005 and was entirely accidental. I found myself in a seminar that did not absorb my entire attention, and to entertain myself I experimented with notation methods. It is no understatement to say that I learned how to take notes all over again as if for the first time in my life, which is a little odd considering I was over forty years old at the time. By the end of the seminar, I still was not engaged in it very attentively, but everybody else in the seminar felt they had to have a copy of my notes. One of my fellow attendees referred to them as the Golden notes. I later learned that a similar system was employed by Michel Foucault, which he referred to as hypomnemata.
The second big event concerned my vocabulary. In 2006 I thought I had almost as much vocabulary as I was ever going to need, that this was a basic skill like tying one's shoes or riding a bicycle that you learn once and don't worry about it after. In retrospect, that was obviously a silly attitude, but it was not until I took a vocabulary test which I thought I had aced and found out I had not aced it that I realized this. Details are here.
It was the third of my discoveries which shook me to Cartesian doubting level. This was months in the making, and thanks to my hypomnemata I have exact records of its genesis and development. On the 31 March 2010 I became self-employed, and one of the first tasks I embarked upon was an overhaul of my diet and workout practices. I took advantage of the freedom to ignore the clock, eat when hungry, and sleep when tired. Things seemed great in the beginning and actually for several months when I noticed that I had lost quite a few pounds. I bought a scale and weighed myself and was surprised at how little I weighed. It was actually a little bit alarming.
This was in late September. I began weighing myself daily. Within a couple of weeks I concluded that eating when hungry was not consistent with the level of working out I was doing, that I had to eat breakfast immediately upon waking and continue to feed myself as soon as possible in order to maintain weight. After a couple of months (and gaining weight very slowly) I did the numbers. It was a revelation. Here are the constraints:
Eight hours sleep per night.
Three meals per day.
Ninety minutes workout per day.
Five hours to fully digest dinner before laying down to sleep.
To my amazement this sums up (including to the minute how much time is required to prepare and eat breakfast, lunch and dinner) to 24 hours within 2%; i. e. there is virtually no slack time in my schedule at all. After six months and nine days of thinking I was indulging myself in complete freedom, on the 10th of November 2010 I discovered that the simple mechanics of running my organism in its proper operational fashion requires rigid adherence to a fixed daily schedule. Up at 6:00 A. M. every single day without fail. Directly to the kitchen to ingest my breakfast. After four hours digestion, directly into workout with no delay. After workout, directly to the kitchen to prepare and consume lunch. After four hours digestion, directly to the kitchen to prepare and consume dinner. Five hours after dinner, directly to bed to sleep for eight hours. I am self-employed and I have no boss.
Ha! My body is the most rigid task master I have ever known. A fact which I could have, should have known my entire life but it took me six months of being unemployed or self-employed (however you prefer to frame it) to figure it out. And so now I am wondering what else is ripe for making over, and I am inclined to consider anything--speaking, reading, walking, standing, sitting, listening. Even breathing.
Theory and practice of meditation
This is a (slightly revised) concatenation of three of my blog posts which I wrote after reading:
Understanding vipassana meditation by Luke Grecki in October 2010. The originals may be seen here (part I), here (part II) and here (part III).
I posted some comments myself in the original thread, but after giving it some thought I have decided to write a little more systematically on the topic.
There are three parts: one theory part and one part each on descriptions of the two techniques in my current practice.
Part I, a theory
I have been meditating daily for over thirteen years and did it sporadically for fifteen years or so prior to that. My menu of tried protocols is wide: vipassana, zen, transcendental, Gurdjieff self-remembering, Jung active-imagination, Erickson self-hypnosis, Loyola spiritual exercises, and probably a couple others I have totally forgotten about. The common thread through all of these techniques is mental health benefit, or spiritual benefit, or stress relief through calming mental processes. It is a purging of obsession and compulsion and anxiety and worry. Don Juan advises Carlos Castaneda the way to become a sorcerer is to learn to make one's mind perfectly still. (Castaneda's regimen may be the only one that I have heard about that I have not tried--I have seen people under the influence of deliriants and that is definitely not for me.)
There is modern scientific research in support of this, most notably in the work of the psychologist Albert Ellis and the psychiatrist Aaron Beck. Their therapy techniques are based upon the idea that our problems of mental life are twofold: first there are the human stressors which plague all of us to one extent or another--family problems, relationship problems, money problems, diseases--what Zorba called the full catastrophe; second there is the stuff which we tell ourselves on top of these typical and normal human stressors.
"This always happens to me."
"Nobody loves me."
"I am a freak; I am a loser; &c."
We could make a very long list. Ellis and Beck say you may be unable to eliminate the family problems and whatnot at the source of your grief, but you surely can quit telling yourself the exaggerated and goofy crap you pile up on top of it. Their experience (and a large amount of subsequent clinical experience) is that modifying the self-descriptions will benefit mental health. This can involve work, and sometimes a lot of it. This is the scientific research behind the psychobabble in the self-help books regarding being a friend to your self.
Meditation provides the ancient path towards quieting these activities of our minds which can be such a burden. There are two basic techniques: a technique of concentration and a technique of emptying. In the technique of concentration you focus your awareness as completely as possible on one stimulus. It can be listening to a mantra as in the example of the hare krishnas or the transcendental meditation. It can be staring at a mandala or a crystal ball or a blue vase or a saucer of ink. It can be saying a rosary. In the technique of emptying you focus your awareness as completely as possible on the minimum possible field of concentration; this is usually the breath. You simply follow only your breathing as purely as possible for a period of a few minutes. A hybrid of the two is use of the minimum possible sense stimulus, the mantra Aum.
In this attention to nothing, or attention to as little as possible, time and space is provided for the mental burdens of anxiety and such to run their course and escape from our attention center. This is the process by which meditation leads to better mental health. This apparently is not the intent the innovators who developed these procedures were going for, however. They were aiming at something much more profound.
If you participate in meditation practice for a very long time (like, thousands and thousands of hours), you may have an opportunity to attain a state of being where you are connected link-pow-one-with-the-universe. Samadhi. You attain Samadhi, and presumably you never again need care about all the girls thinking you are too short.
Part II, my (shorter) daily practice
This is adapted from a self-hypnosis relaxation script I obtained from the book Mind-Body Therapy: Methods of Ideodynamic Healing in Hypnosis, by Ernest Rossi and David Cheek. I call my variation the homunculus meditation. The name is taken from a neuroscience figure, a homunculus, which is made by inflating anatomical parts in proportion to the amount of the somatic sensory cortex which are involved in our sense of touch for the particular anatomical part.
The script is very simple. You sit quietly in a relaxing posture and invite yourself to sequentially relax different portions of your body. There are thousands and thousands of terms which pertain to various anatomical structures, so you cannot name them all in one single meditation (or self-hypnosis) session. The ones I routinely use are (in order): eyes, optic nerves, visual cortex, cerebral cortex, limbic lobes, hindbrain, throat, spine, median nerves, fingertips, (back up to) limbic lobes, hindbrain, throat, spine, sciatic nerves, toe tips, foot soles, ankles, calves, ankles, shins, ankles, fibulas, knees, hamstrings, knees, quadriceps, knees, femurs, glans, testicles, anus, lumbars, navel, seventh thoracic vertebrae, nipples, seventh cervical vertebrae, shoulders, elbows, thumbs, index fingers, middle fingers, ring fingers, little fingers, elbows, wrists, thumbs, index fingers, middle fingers, ring fingers, little fingers, wrists, fingertips, wrists, elbows, shoulders, seventh cervical vertebrae, nipples, seventh thoracic vertebrae, navel, lumbars, anus, testicles, glans, testicles, anus, lumbars, navel, seventh thoracic vertebrae, nipples, seventh cervical vertebrae, spine, throat, tongue, palate, gums, lips, nostrils, nasal cavities, sinuses, eyes, temples, ears, eustachian tubes, ears, temples, eyes, forehead.
On average this takes about twenty minutes to work all the way down and back up through these features of my anatomy. There are three additional important details:
1.) In the Rossi-Cheek recipe they instruct us to instruct ourselves "Relax eyes, &c." There is an old philosophical conundrum here regarding who is talking to who when we are talking to ourselves. When you sink a long basket and you say to yourself "Good shot!", who is talking to who there? There is some implicit dissociative model like perhaps Freud's--and perhaps it is your superego talking to your ego, or something similar to that. Anyway, what I do instead of commanding myself to relax, is to invite myself to relax. I substitute "I may relax my eyes, &c." for the literal instruction provided in the Rossi-Cheek recipe.
2.) A few of these invitations are repeated, sometimes over and over. Roughly, I devote the proportion of the session along the proportions in the homunculus diagram, hence my name of homunculus meditation. I invite my fingers and my lips and my tongue to relax far more than I invite any other portion of my anatomy to do so.
3.) The other weighting is toward the eyes and ears; a large fraction of our brain is allocated to the processing of visual and audio sense information. By concentrating on the parts of the body that involve the largest brain fractions, the given twenty minutes (or whatever) of meditation can have the largest total brain footprint! That is one theory.
I have been using this meditation (or one close to it) on a nearly daily basis since 1997, since I first read Rossi and Cheek's book. I will be using it for the foreseeable future.
Part III, my (longer and at least) weekly practice
This one takes me about forty minutes.
Step one is to sit still in a comfortable position with eyes closed. Breathe slowly and count, one count for each breath to one hundred. For each breath, I visualize a sphere which looks like, or almost like a billiard ball, with the number of the breath inside the little white circle area (like on a standard billiard ball that is numbered one to eight.) The spheres alternate on an interval of ten in color and in spatial position. This sequence is patterned after a common representation of the Kabbalah Tree of Life.
1, 11, 21, 31, &c are a white sphere on the crown of my head;
2, 12, 22, 32, &c are a gray sphere on my right shoulder;
3, 13, 23, 33, &c are a black sphere on my left shoulder;
4, 14, 24, &c are a blue sphere on my right elbow;
5, 15, 25, &c are a red sphere on my left elbow;
6, 16, 26 &c are a yellow sphere on my crotch;
7, 17, 27, &c are a green sphere on my right fingertips;
8, 18, 28, &c are an orange sphere on my left fingertips;
9, 19, 29, &c are a purple sphere between my knees;
10, 20, &c are a brown sphere between my feet.
I used to play a lot of billiards so visualizing billiard balls is quite easy for me. A million other things do cross my mind during this forty or so minutes of meditation, but I try and hold my attention as closely as possible to my breath and to the billiard ball images. After, I make notes of: how many minutes (37 - 51 is the range in recent memory); if I lost count at any point (if I lose the count, I just guess where I was and continue from there--this is an excellent marker for me on how well I am attending to the meditation); if I had a hiccup or a cough or a saliva swallow or a saliva drool (I prefer not to, and sometimes I will stop meditating if any of these occur.)
Sometimes I will try and extend this to an even longer meditation. About once a month I will go for 200 breaths, and about once a year I will go for 300. 300 breaths is the longest I have ever gone. If I am going for a long meditation, I always stop if I lose count or if I hiccup or if I drool or if anything is not perfect.
Human performance, psychometry, and baseball statistics
I. Performance levels and age
Human ambition for achievement in modest measure gives meaning to our lives, unless one is an existentialist pessimist like Schopenhauer who taught that life with all its suffering and cruelty simply should not be. Psychologists study our achievements under a number of different descriptions--testing for IQ, motivation, creativity, others. As part of my current career transition, I have been examining my own goals closely, and have recently read a fair amount on these topics which are variable in their evidence.
A useful collection of numerical data on the subject of human performance is the collection of Major League Baseball player performance statistics--the batting averages, number home runs, runs batted in, slugging percentage--of the many thousands of participants in the hundred years since detailed statistical records have been kept and studied by the players, journalists, and fans of the sport. The advantage of examining issues like these from the angle of Major League Baseball player performance statistics is the enormous sample size of accurately measured and archived data.
The current senior authority in this field is Bill James, who now works for the Boston Red Sox; for the first twenty-five years of his activity as a baseball statistician James was not employed by any of the teams. It took him a long time to find a hearing for his views on the inside of the industry, although the fans started buying his books as soon as he began writing them.
In one of the early editions of his Baseball Abstract, James discussed the biggest fallacies that managers and executives held regarding the achievements of baseball players. He was adamant about the most obvious misunderstood fact of player performance: it is sharply peaked at age 27 and decreases rapidly, so rapidly that only the very best players were still useful at the age of 35. He was able to observe only one executive that seemed to intuit this--a man whose sole management strategy was to trade everybody over the age of 30 for the best available player under the age of 30 he could acquire.
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