Introduction

Abstract games, traditional puzzles and mathematics are closely related. They are often extremely old, they are easily appreciated across different cultures, unlike language and literature, and they are hardly affected by either history or geography. Thus the ancient Egyptian game of Mehen which was played on a spiral board and called after the serpent god of that name, disappeared from Egypt round about 2900–2800 BCE according to the archaeological record but reappeared in the Sudan in the 1920s. Another game which is illustrated in Egyptian tomb paintings is today called in Italian, morra, ‘the flashing of the fingers’ which has persisted over three thousand years without change or development. Each player shows a number of fingers while shouting his guess for the total fingers shown. It needs no equipment and it can be played anywhere but it does require, like many games, a modest ability to count [Tylor 1879/1971: 65].

As, of course, do dice games. Dice have been unearthed at the city of Shahr-i Sokhta, an archaeological site on the banks of the Helmand river in southeastern Iran dating back to 3000 BCE and they were popular among the Greeks and Romans as well as appearing in the Bible.

The earliest puzzles or board games and those found in ‘primitive’ societies tend to be fewer and simpler than more recent creations yet we can understand and appreciate them despite the vast differences in every other aspect of culture.

‘Culture’ is undoubtedly the right word: puzzles and games are not trivia, mere pleasant pastimes which offer fun and amusement but serious features of all human societies without exception – and they lead eventually to mathe- matics. String figures are a perfect example. They have been found in northern America among the Inuit, among the Navajo and Kwakiutl Indians, in Africa and Japan and among the Pacific islands and the Maori and Australian aborig- ines [Averkieva & Sherman 1992]. This is not necessarily evidence of ancient exchanges between cultures. It could just be that people everywhere tend to fiddle with bits of string – and the results can be very pleasing, like the Jacob’s ladder in Figure 1.

Figure 1 Jacob’s Ladder

String figures are extremely abstract. Although usually made on two hands, or sometimes the hands and feet or with four hands, Jacob’s ladder would be recognisably ‘the same’ if it were fifty feet wide and made from a ship’s hawser, yet these abstract playful objects can also be useful. The earliest record of a string figure is the plinthios (Figure 2), described in a fourth-century Greek miscellany. It was recommended for supporting a fractured chin, and much resembles the Jacob’s ladder figure [Probert 1999].

Figure 2 Plinthios string figure

No surprise then that string figures are more than an anthropological curios- ity, that they are mathematically puzzling, related to everyday knots – including braiding, knitting, crochet and lace-work – and to one of the most recent branches of mathematics, topology.

The oldest written puzzle plausibly goes back to Ancient Egypt:

There are seven houses each containing seven cats. Each cat kills seven mice and each mouse would have eaten seven ears of spelt. Each ear of spelt would have produced seven hekats of grain. What is the total of all these?

This curiosity, paraphrased here, is problem 79 in the Rhind papyrus which was written about 1650 BC. Nearly 3000 years later in his Liber Abaci (1202), Fibonacci posed this problem:

Seven old women are travelling to Rome, and each has seven mules. On each mule there are seven sacks, in each sack there are seven loaves of bread, in each loaf there are seven knives, and each knife has seven sheaths. The question is to find the total of all of them.

It is tempting to suppose that these puzzles are related. If they are, could there be a historical connection across 5000 years with this riddle from the British eighteenth century Mother Goose collection?

As I was going to St. Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits;
Kits, cats, sacks and wives,
How many were going to St. Ives?

Another widespread puzzle concerns a man, a wolf, a goat and a cabbage, to be transported across a river in a small boat, never leaving the wolf alone with the goat or the goat alone with the cabbage. It first appeared in a collection attributed to the medieval scholar Alcuin of York (735–804), Propositions to Sharpen the Young [Alcuin of York 1992].

Tartaglia (1500–1557) who famously solved the cubic equation and then gave the solution to Cardan who scandalously broke his solemn agreement not to publish it, printed a version featuring three brides and their jealous husbands who have to cross a river in a boat that will only take two people. If no bride can be accompanied by another women’s future husband, how many trips are required?

Essentially the same puzzle is also found in Africa, in Ethiopia, in the Cape Verde Islands, in Cameroon, and among the Kpelle of Liberia and elsewhere. Since these African versions are often logically distinct from the Western, they may well be entirely independent: the difficulty of transporting uncongenial items across a river used to be universal [Ascher 1990].

Read the entire excerpt from Games and Mathematics here.

What is resilience?

Most of us at some point will be struck by one or more major traumas: violent crime, domestic violence, rape, child abuse, a serious automobile accident, the sudden death of a loved one, a debilitating disease, a natural disaster or war. If you are very lucky, then you have never encountered any of these misfortunes; but most likely you will someday. It is estimated that up to 90% of us will experience at least one serious traumatic event during our lives (Norris & Sloane, 2007 ).

Traumatic events throw our lives into turmoil in unpredictable ways; no two people will respond to them in exactly the same manner. For some, the stress of the event will become chronic, lasting for years. They may undergo a dramatic change in outlook, becoming sullen, demoralized, withdrawn, cynical, and angry. Some will become depressed or develop post-traumatic stress disorder (PTSD). Horrific, intrusive memories and nightmares will haunt them for days, months or even years, and they will feel unsafe in the world – hypervigilant – as if another serious danger lurks just around the corner. Some will take up drinking or drugs to numb their pain and dull their memories .

Nevertheless, many people will fi nd ways to meet the challenge and continue with purposeful lives. For a period aft er their ordeal, they may become distressed, but in time they will bounce back and carry on. For some, it will be almost as if the trauma had never occurred. For others, the distress will persist, but they will fi nd healthy ways to cope. Some survivors will even grow stronger and wiser because of their trauma. Th ese survivors may report that their tragedy has helped them to appreciate life more, to become closer to family and friends, to find greater meaning, and sometimes to embark on a new mission in life.

In the words of Elisabeth S. Lukas, a protege  of the neurologist;  psychiatrist and Holocaust survivor Viktor Frankl, “Th e forces of fate that bear down on man and threaten to break him also have the capacity to ennoble him ” ( 1984 ) .

Read or download the entire excerpt here.

In this cleverly constructed book, several of the puzzles of present-day neurology are considered alongside accounts of the lives and times of those with whom they are eponymously associated. Parkinson’s disease, Alzheimer’s disease, and Korsakoff’s, Tourette’s and Asperger’s syndromes feature among the better-known instances, but lesser-known syndromes such as the those of Clerambault and Capgras (perhaps more psychiatric than neurological) are also considered. Each receives a chapter to itself.

The author’s particular skill is in making his subject matter interesting at several levels and to different groups of readers. His accounts of the successes and sorrows of those who are seen (not always accurately, as he points out) as the discoverers of these well-known diseases are historically vivid without resorting to hagiography; and the story of the fortunes of their brain-children as they negotiate the fluctuations of medical and social fashion since their conception is absorbing.

The reader need not be a professional medic or psychologist to appreciate these accounts, but nor will the relevant professionals be bored or disappointed by them: Douwe Draaisma’s research is thorough and his treatment of the issues penetrating as well as clear. He has a rare talent for writing informatively and entertainingly without losing depth.However, this is not just a historical account, and Draaisma does not merely record events. One of the more fascinating aspects of the book is the clarity with which it demonstrates that what were (in the main) neurological puzzles in the past remain neurological puzzles today. We are no clearer now about the significance of the tics and compulsive imprecations shown by his patients than was Gilles de la Tourette when he first described them more than a century ago; controversy over the origins of “childhood autism” is no more resolved than it was in Hans Asperger’s and Leo Kanner’s heyday; the sombre tale of Alzheimer’s disease highlights the frustrating lack of progress in understanding the processes involved, let alone treating them successfully. The advance, if one can call it such, of medical science is a halting and uncertain affair…

Keep reading at the Times Higher Education >>

A stethoscope amplifies inaudible heart and lung sounds in a very satisfying way. If, however, the owner of the organs under evaluation decides to make a comment during the exam, what results is a painfully loud, unintelligible blast of noise directly into the doctor’s head.

It was during such an interruption almost 30 years ago that Dr. Richard Baron, a Philadelphia internist, grumbled at his patient: “Shhhh. I can’t hear you while I’m listening.” The phrase has undoubtedly been said by many, but Dr. Baron was the one with the wit to stop and laugh (and reflect at length in a classic medical article), realizing that he had enunciated in pure koan form probably the single greatest tension in modern medical practice.

Against the siren song of all those beautiful instruments and machines, whatever the patient has to say is sometimes just an annoying interruption. Medical technology is addictive; it is exclusionary and expensive, and it begets versions of itself like the sorcerer’s brooms. It complicates everything, and yet from X-ray and M.R.I. to the stratosphere of gene analysis, only a simpleton would opt to fly without it.

Dr. Stanley Joel Reiser, a physician, historian and medical ethicist now at George Washington University, has been ruminating on these matters in scholarly circles for years. His latest collection of essays escapes the ivory tower and resonates precisely with today’s headlines. Anyone with more than a passing interest in our present health care logjam will be intrigued and enlightened by Dr. Reiser’s painstaking retracing of its origins.

He begins with the stethoscope, the greatest medical hit of 1816. “Before stethoscopes, the coin of evaluation was words — the doctor learned about an illness from the patient’s story.”

Then, suddenly, the doctor was paying attention to something else.

Keep reading at the New York Times >>

Americans have expressed their displeasure with House 3200 and the Senate health care bill because both contain bad economics and bad ideas.  Why does extending good insurance coverage to all Americans require socializing American medicine, reducing doctors to having the state look over their shoulders, and telling our seniors that the nature of their care is conditional on the number of quality life years remaining to them?

Economists such as myself are dismayed at the bills put forward.  Congress has had years to consider health care yet still does not show understanding in its legislation of even the most basic features of the subject.  For example, the distinction between health insurance, which insures against treatable events in the coming coverage year, and reclassification risk insurance (sometimes called health status insurance), which insures against a change in the insured’s risk classification that carries over into later periods seems to have been ignored by the writers.  Nobel laureate Kenneth Arrow wrote about this distinction in 1963.  How could Congress fail to understand it in 2009?  The re-insurance mechanism that supports insureds’ ability to change their health insurance company at any time and pay no more than the standard premiums paid by others of their same sex and age could also have been adopted by the House or Senate.  The Senate also shows ignorance of the importance of homogeneous risk pooling when it requires by law that men and women must be grouped together for insurance.  Why should a man pay for breast cancer or a woman for prostate cancer?  What if the treatment costs are radically different?  Are teen-age women required to pay the same for car insurance as teen-age men who are known to have more accidents?

Keep reading at the Galen Institute >>

The New York Times has a front-screen story this morning about Bob Collier, a 62-year old American from rural Georgia who, according to the Times, was moved to speak out at a recent town hall meeting about his worries concerning health care reform.

Here’s what appears on the Times’ front-screen:

Calm, But Moved to be Heard on Healthcare

By KEVIN SACK

In the health care discussion, the respectful questioners like Bob Collier — those expressing discomfiting fears and legitimate concerns — may have the most impact.

So, the set-up is clear — Bob Collier is respectable, not like those gun-toting, Nazi name-calling crazies who’ve been showing up to town hall meetings. And he’s got “legitimate concerns” about health care reform.

Sack tells us in the opening grafs that Collier was never interested in politics. Instead, he’s built a “quiet life” for himself in rural Georgia, involving family, church, hunting and fishing.

So, what “legitimate concerns” moved Bob Collier to speak, “to his wife’s astonishment,” at a recent town hall meeting? Well, his wife of thirty six years, Susan, survived breast cancer through “early detection and treatment” and, in Collier’s considered opinion, none of that could happen if health care reform with a public option passed Congress.

Instead, Collier’s wife would be on a “waiting list.” And this calm, considered, thoughtful citizen firmly believes that everything is at stake in the debate about health care reform:

“This is about the future of our country as we know it,” Mr. Collier warned, “and may mean the end of our country as we know it.”

You can argue that part of the Times’ responsibility to its readers is to provide a panoramic view of public opinion on this, as on other issues. But you cannot argue that that’s really what they’re doing here. Instead, the main outcome of this article is to portray Bob Collier as the reasoned everyman, offering good old common sense in a plain old vernacular that egghead Washington politicians have a hard time answering.

It’s almost too tiresome to point out that Collier is entirely uninformed about the issues. But because he did not articulate this utter nonsense in a “high decibel rant,” the Times saw fit to put his version of health care reform on the front page of its newspaper.

Continue reading at The Huffington Post >>

It may seem that the doctors of New York today are a far cry from the old-fashioned country doctors of mid-century Middle America.

Or are they?

The New York Times this week has pointed out the growing popularity of “patient centered” practices in the city. These doctors make house calls, give their cell phone number to patients for after-hours consultations, and handle many patient issues without the help of a specialist. Doctors of the “patient centered” movement are redefining the doctor-patient relationship and recreating the personalized attention given by country doctors decades ago.

But how, in our age of overcrowded doctors’ offices and an overburdened healthcare system, are doctors able to give more attention to patients?

The answer, as it so often is, is technology. Doctors of the “patient centered” movement have invested thousands of dollars into the technology for online appointment setting, the possibility of virtual meetings with patients, and digital health records, allowing them to streamline administrative processes and spend more time with patients.

~ ~ ~

It’s not the first time technology has revolutionized the relationship between doctor and patient. In his new book TECHNOLOGICAL MEDICINE: The Changing World of Doctors and Patients, medical technology expert Stanley Reiser shows that technology has been dramatically changing the way doctors interact with patients since the invention of the stethoscope in 1816.

But the change hasn’t always been for the better.

This Side of the Pond caught up with Dr. Reiser to ask him about his upcoming book and the influence of the stethoscope on modern medical practice, as well as his thoughts on the technology-savvy doctors of the “patient centered” movement and the future of technology in medicine.

THIS SIDE: Your upcoming book describes the changes in patient care that have been brought about by the introduction of new technologies into medicine, beginning with the invention of the stethoscope. How did that technology change the way doctors interacted with patients?

STANLEY J. REISER: The stethoscope, introduced in 1819 by the French physician René Laennec, was the first widely used technology to diagnose illness, and introduced doctors to the concept of using technology routinely in evaluating a patient’s illness. The information the stethoscope gave doctors about the condition of the patient’s heart and lungs by listening to the sounds they made was so compelling, that doctors began to pay more attention to the sounds of the body than the words and thoughts of the patient.

TS: Have more recent technological inventions in medicine – the X-ray or ultra sound, for example – continued that trend?

The problems of health care delivery require a focus on basic matters such as why doctors use technology to excess, what is needed to strengthen the quality of the doctor/patient relationship…

The attraction to technological evidence such as given by the X-ray and ultrasound continues today to create challenges to a robust and sensitive doctor/patient relationship. Is it not a common experience today to spend 5-10 minutes with the doctor and many times that waiting for and receiving technological examinations? Images of the body produce important evidence, but there is a compelling need to link them to a thorough understanding of the context in which illness exists – the life of the patient.

TS: What do you think of the “patient centered” movement? Is it possible to improve the doctor-patient relationship by increasing the use of technology?

SR: The more focused we can become with the patient, the better. I think it’s a worthy movement. And communication technology has an important role to play in facilitating patient-centered practice. But it is an adjunct to, and cannot be the core of, any movement which seeks to know the patient more.

TS: The digitization of health records is a real hot-button issue right now. How would the creation of a nation-wide computerized health database affect the doctor-patient relationship and the state of healthcare in the US today?

SR: The health record is the principal synthetic technology of medicine. It stands alone as the technology that weaves together the patchwork quilt of medical interventions received by each patient. It thereby is highly significant. The technology of the computerized health record, which is being promoted to replace the paper record, facilitates more rapid and less erroneous transmission of the doctor’s orders and prescriptions, improves the legibility of the data it contains, improves the passage of medical data among the various health care providers seen by a patient at different times and in different places, and so forth. For all of these possible benefits the computerized health record is still a work in progress. Some studies find it will not be a great source of reducing the cost of care. And it can negatively affect the medical relationship, when doctors spend important time with patients concentrating on the computer screen and not on them. Of equal significance, the computerized health record diffused throughout our national health system is not a panacea for curing its problems. The problems of health care delivery require a focus on basic matters such as why doctors use technology to excess, what is needed to strengthen the quality of the doctor/patient relationship, how to reduce the costs of medical care without diminishing its quality. More than technologies are needed to deal with such matters, even one as promising as the computerized record, and what this more is, is what I have striven to provide in my book.

Stanley J. Reiser

TECHNOLOGICAL MEDICINE: The Changing World of Doctors and Patients

“If All Doctors Had More Times to Listen”, New York Times, June 7, 2009

]]> http://www.cambridgeblog.org/2009/06/country-doctor-city/feed/ 0 http://www.cambridgeblog.org/2009/04/wired-recalls-the-last-swine-flu-outbreak/ http://www.cambridgeblog.org/2009/04/wired-recalls-the-last-swine-flu-outbreak/#comments Mon, 27 Apr 2009 19:07:54 +0000 CambridgeBlog http://www.cambridgeblog.org/?p=2026 WIRED posted an article last year about a 1976 swine flu outbreak. One casualty, and mass vaccinations, having recalled a deadly Spanish flu from after WWI. Read it here >>