Month: March 2013

Science as Cumulative Cultural Evolution

According to this article, historians of science have demonstrated that science is a process of cultural acquisition:

A well-documented example of cumulative cultural evolution is seen in the growth of scientific knowledge. Historians of science have detailed how scientific knowledge has gradually accumulated over successive generations of scientists, with each new generation building on the advances of previous generations. To paraphrase Isaac Newton, each new generation of scientists can only see further by “standing on the shoulders of giants”. Mathematics, to which Newton himself contributed, is an illustrative example of how scientific knowledge slowly accumulates over successive generations and thousands of years. Only after Babylonian scholars invented numerical notation and basic arithmetic in around 2000 BC could Greek and Arab scholars subsequently develop geometry and algebra respectively, which then allowed Newton, Liebniz and other Europeans to invent calculus and mechanics in the 17th century, through to present-day mathematics.

The author relies heavily on Derek de Solla Price’s Little Science, Big Science (New York, 1963) for this and subsequent claims about the “exponential increase in scientific knowledge over time.”

For the author, mathematics is the paradigm for cumulative scientific knowledge and for the acquisition of that knowledge. A cultural version of Haekel’s phylogeny recapitulates ontogeny undergirds the article:

…individual learning recapitulates history, in other words, that people learn during their lifetimes a sequence of concepts or skills that have previously been accumulated historically. While this assumption may not apply to all cultural domains, certain domains of scientific knowledge do appear to show this recapitulation. While this assumption may not apply to all cultural domains, certain domains of scientific knowledge do appear to show this recapitulation. Figure 2A shows how present-day mathematics education during a single lifetime recapitulates the order in which concepts were discovered in human history ….

Here is Figure 2A, with its wonderfully convincing linear fit:
130331math

A few difficulties spring to mind:

  • Empirically, many sciences don’t seem to show a cumulative evolution in the way described. Humans did not have to perfect Ptolemaic astronomy before developing Copernican astronomy, which was not necessary for Tychonic.
  • Typically, science curriculum does not reflect the recapitulation theory. As a necessary step in their science curriculum few students, for example, have to learn alchemical reaction theories before learning stoichiometry; in biology, understand earlier theories of transformationism before learning modern theories of evolution; in physics, master Aristotelian physics before learning Newtonian physics.
  • Finally, historians of science as well as philosophers of science have detailed the difficulties in the older “scientific knowledge has gradually accumulated over successive generations of scientists, with each new generation building on the advances of previous generations” model. Way back in 1962 even Thomas Kuhn tried to distance himself from that overly simplistic, cumulative model of scientific progress.

Oh well, the numbers, equations, and graphs in the article more than compensate for any empirical or conceptual worries I might have.

Complex and Mysterious Mechanism

In 1938 when Dr. Jayne’s used the Mensch als Industriepalast image, the company was recycling an image it used at least as early as 1934.

At least as early as 1934 Dr. Jayne’s used the Mensch als Industriepalast  in its almanac.
At least as early as 1934 Dr. Jayne’s used the Mensch als Industriepalast in its almanac.

The description at the top emphasized modern, mechanized picture of the human body: “A picture of the World’s most complex and mysterious mechanism.” By 1938 the image had lost that description. In 1934 this mechanized picture shared space in the almanac with a detailed description of, among other non-mechanized practices, “Fortune Telling by Tea Leaves.” There we read:

In using this method, much depends on the imagination and natural aptitude of the reader. You must have the “seeing eye” which will interpret the formation of the leaves correctly, but this readily comes with practice.

The reader must interpret the “emblems,” including:

  • anchor—This is the sign of trade and travel. If standing alone at the top of the cup it indicates true love.
  • coffin—This may mean, as it does in dream, and in other methods of fortune telling, death or serious illness either to the hearer, or a friend. Closely surrounded, it means an inheritance.
  • lion—(or any wild animal) Good fortune to eminent persons, if clear and distinct. Envy and jealousy if in the thick.
  • mouse—Standing alone it is an omen of recovery of a lost object. Almost indistinguishable among other leaves, you must prepare for disappointment in this respect.

While it seems incongruous to read modernist descriptions of the human machine sandwiched between fortune telling practices illustrated by mysterious, exotic men gazing into crystal balls, Dr. Jayne’s must have been confident that it would not seem so to its customers.

Johannes Schöner—Neither Medieval nor Modern

Johannes Schöner will never be a household name, but it’s nice to see him get some attention in John Hessler’s A Renaissance Globemaker’s Toolbox.

John Hessler’s A Renaissance Globemaker’s Toolbox
John Hessler’s A Renaissance Globemaker’s Toolbox

Schöner attracted Hessler’s attention less for his own work than his compliations of material, which included the now famous 1507 Waldseemüller map of the world. Hessler seems to have combed through Schöner’s various Sammelbänden to reconstruct how Schöner put together his intellectual world, from how he read maps and learned to build globes to how he studied the stars. An excerpt from Hessler’s book concludes:

More generally, however, by looking closely at what Schöner thought important enough to preserve in these collections of mathematical, geographical, astrological, and astronomical information, and how he might have utilized it in his work, we will gain deep insights into the epistemological revolutions that occurred at the end of the fifteenth century and the beginning of the sixteenth. The years between the amazing discoveries of Columbus and Copernicus saw the beginnings of the birth of modern scientific thought and in the chapters that follow we will see Schöner fully engaged in the intellectual transitions from the science of Aristotle and the geography of Ptolemy, to that of Copernicus and Ferdinand Magellan (1480–1521). The dates of the materials that Schöner compiled are mostly from 1475 to 1540 and represent a cross-section of central scientific materials from pre-Copernican science. Each of these books and manuscripts is interesting in its own right but taken together they provide a case study for the use and transmission of scientific information in the Renaissance through the eyes of a contemporary consumer of these materials. Schöner’s toolboxes are nothing short of encyclopedic and his use of them helps us understand in a unique way how our modern scientific worldview came into being.

John Wilford reviews A Renaissance Globemaker’s Toolbox in Why is America Called America?. Wilford finds the book generally lucid and facinating, except those pesky parts of the technical chapters that “appear to be written more for the author’s academic peers than for many laypeople.”

In the excerpt and more markedly in the review Schöner becomes an important transitional figure in the development of modern science. Both associate him with modern geography—an understandable point considering this book began in the Waldseemüller map of the New World— and link him to Copernicus and Copernicanism. The reviewer seems to overstate things when he says:

Nothing in the book points up more clearly Schöner’s pivotal place in a world in transition from the medieval to the modern than his residual interest in astrology and his awakening curiosity when he apparently heard reports of a new theory being formulated by a Polish Catholic cleric.

Schöner’s interest in that “new theory being formulated by a Polish Catholic cleric” probably owed more to his interest in astrology and making astrological prognostications than the modernity we see in Copernicus’s theory. Along with his prognostications and calendars, Schöner also wrote books on astrology before and after Copernicus’s De revolutionibus was published, notably his Opusculum Astrologicum in 1539 and De iudiciis nativitatum Libri Tres in 1545. Schöner might also have been the author of a horoscope cast for Copernicus. Judging from the table of contents, Hessler spends some time assessing Schöner’s astrology.

Copernicus’s horoscope attributed to Schöner (photo of BSB Cod. lat. Monac. 27003 from R. Westman, The Copernican Question, p. 116).
Copernicus’s horoscope attributed to Schöner (photo of BSB Cod. lat. Monac. 27003 from R. Westman, The Copernican Question, p. 116).

Schöner’s interest in astrology shouldn’t diminish our interest in him, but it should, perhaps, prompt us to wonder about the labels “modern” and “medieval” and the work they do for us (on the force of the medieval label, again see Elly Truit’s posts).

Hessler’s A Renaissance Globemaker’s Toolbox looks like it will be interesting and a nice complement to Monika Maruska’s dissertation, “Johannes Schöner — ‘Homo est nescio qualis’.”

Dr. Jayne’s Mensch als Industriepalast

In 1926 Fritz Kahn created his famous “Mensch als Industriepalast,” a fascinating, modernist depiction of the human being as a chemical factory, staffed with industrious little workers, replete with control centers, machines, conduits, communication wires (see the copy at the NLM).

Fritz Kahn’s Mensch als Industriepalast (1926)—see a larger version here.
Fritz Kahn’s Mensch als Industriepalast (1926)—see a larger version here.

In an impressive display plagiarism, Dr. Jayne’s almanac for 1939 included a strikingly similar image:

Dr. Jayne’s Mensch als Industriepalast (1939).
Dr. Jayne’s Mensch als Industriepalast (1939).

Although Dr. Jayne’s illustration was meant to explain “A few of the mysteries of the human body,” it adopted the same factory rhetoric and imagery that marked Kahn’s original poster: bile is manufactured; the bladder is a tank; nerves are like telegraph wires; the eye is like a camera, the ear like a microphone; the spinal cord is “the main cable of electric wires;” the heart is “a powerful pumping station.”

Workers and control centers are arranged and many of the details are labeled just as they are in Kahn’s original image.

Imitation is the purest form of flattery.

Math is Always a Weapon

The authors of “Justices Flunk Math” worry that math—or more narrowly, statistics and probabilities—is being misused in the courtroom. After looking at a few examples, they conclude:

The challenge is to make sure that the math behind the legal reasoning is fundamentally sound. Good math can help reveal the truth. But in inexperienced hands, math can become a weapon that impedes justice and destroys innocent lives.

Inexperienced and experienced hands use math as a weapon. Let’s take, for example, the analogy they use in the article.

The appellate judge in the Amanda Knox case refused to retest the murder weapon for traces of the victim’s DNA. According to the article, the judge claimed that if there was too little material to provide a reliable result the first time it was tested, in 2007, then tests on less material in 2011 would be no better.

Although the authors claim that the judge “demostrated a clear mathematical fallacy,” they describe a simple flaw in reasoning and then use a misleading mathematical example to make their case. They are right. Repeated tests of the same material in comparable conditions can confirm or disconfirm previous results. And the greater number of confirming or disconfirming results should influence the conclusions we draw from those results. But their analogy, while superficially persuasive, doesn’t necessarily apply to the judge’s decision not to perform additional DNA tests.

They say:

Imagine, for example, that you toss a coin and it lands on heads 8 or 9 times out of 10. You might suspect that the coin is biased. Now, suppose you then toss it another 10 times and again get 8 or 9 heads. Wouldn’t that add a lot to your conviction that something’s wrong with the coin? It should.

According to the article, the judge’s decision was based on there being less material to test. How much less? We are not told. But less. So a better analogy might be (my changes are in bold):

Imagine, for example, you toss a coin and it lands on heads 8 or 9 times out of 10. You might suspect that the coin is biased. Now, suppose you then toss it another 3 times and get 2 heads. Would that add a lot to your conviction that something’s wrong with the coin? Maybe.

We can play with the numbers for that second coin-toss series, but a useful analogy here is not 10 tosses followed by another 10 but followed by some smaller number. How much the second coin-toss series will add to our conviction that the coin is biased will depend on how many times we toss it and how many times it comes up heads.

At first glance their math looks persuasive. The information they present in the article, however, does not allow us to assess the relevance of their analogy or evaluate the judge’s decision. We are being asked, on the strength of their mathematical analogy, to accept their criticism of the judge. In this case, their math distracts us from asking about why the judge made his decision and whether or not that was a reasonable decision. But this is nothing new. People hoping to achieve certain ends apply the math they think will be most persuasive. Math is always a weapon.