In the city of Bayeux, France, you can see a tapestry that commemorates the conquest of England by William the Duke of Normandy in the year 1066.
According to the tapestry's narrative, Duke William had been forced to invade England because he had been betrayed by Harold Godwinson, an ambitious English nobleman. Harold had sworn to help William to become the King of England. Instead, when the English king Edward died, Harold took the throne himself. A central image in the tapestry is that of a comet. The comet was a sign that Harold's betrayal of his oath will be punished. Sure enough, Harold did die on the field of battle and William became William 1 of England.
How do read signs like the appearances of comets?
The interpretation of signs and signals from the natural world has been a human interest for as long as there have been humans. Prophets, seers, tea, palm, and the readers of auspices (the intestines of chickens) are found abundantly throughout history and in all cultures.
All cultures have developed systems of thought about how the world works and therefore how to read the signs and signals.
The systems have been designed by superior creatures such as gods, kings, or philosophers and delivered as a set of rules: "This is a sign of favor!" "Red sky at morning, sailor take warning!"
Hammurabi inscribed his code of laws on a stele (stone pillar) that included a picture of himself and the god Shamash to show that these rules were divinely inspired.
The problem has been that nature does not easily conform to the rule book and by the 16th and 17th centuries important parts of the rule books had been undermined.
Earth was no longer at the center of the Universe. Europe was no longer the whole world. New lands had been discovered. More importantly, understanding how to read nature had become a matter of practicality; for example, the need to navigate across large stretches of landmark free oceans.
Thoughtful people began to develop a new way to read the messages from nature.
Instead of beginning with the supposed rules, the approach was to observe, experiment and to derive the rules from what actually took place.
Put another way, in place of beginning with the rules; that is, with certainty about what should be found; the strategy was to begin with uncertainty. Then make an educated guess and test it against what actually happens.
According to Aristotle, the ancient authority, comets were the result of an atmospheric disturbance caused by an excess of the element "Fire" which is why they were predictors of drought and wind.
In 1577, the advent of a comet gave the astronomer Tycho Brahe the opportunity to test Aristotle's assertion.
"He triangulated the comet, by charting its position from night to night...[and] compared his data with those recorded [by other] astronomers elsewhere in Europe on the same dates." If the comet had been nearby in Earth's atmosphere, there would have been a different in the comet's position based on those data. But Tycho found no such difference, meaning that the comet was well beyond the Moon in its distance from Earth.
Less than a century later Royal Society member Edmund Halley took another step towards understanding comets when he theorized that they were simply natural objects that orbited the Sun and which followed the laws of motion and gravity established by Newton. When a comet appeared in 1682, Halley used data from historical records to demonstrate that the appearance of comets in 1531 and 1607 were likely to have been three sightings of the same comet. Halley, who had encouraged Newton to create the mathematical equations for gravitation and had paid (out of his own pocket) for the 1681 publication of Newton's Principia Mathematica, used Newton's work on gravity to support his assertion and to predict that the comet would return in 1758. (Ferris, 1988, p. 70; 112-120)
The appearance of the comet in 1065 was not a portent but a coincidence.
The experimental method raises the question of how do we know that our experiment has discovered an actual pattern? How can we be certain?
The answer, of course, is that we cannot. Instead of certain knowledge; we get reliable knowledge.
The driver-less cars being developed by Google and other companies are only possible if they can read signals from the world reliably.
They must safely navigate roads to find their way to precise destinations without the assistance of a human. They do this by collecting signals from radar sensors, laser-range finders, cameras. Self-driving cars' sensors feed information to a computer program that will make adjustments "if" the information is actually a "signal" (that is, evidence of an actual pattern) or do nothing if the data is just "noise" (evidence of a spurious pattern).
The computer programs that interpret the data from the sensors do millions of tests. Each test provides a bit of data that makes the interpretation more and more likely to be correct. The program "learns" and reduces the odds against a false interpretation.
Google self-driving cars do very well except when they are on the roadway with cars driven by humans. It is then that the self-driving cars run (literally) into trouble. The natural world behaves in ways that allow for the development of correct interpretations of the incoming data. Humans seem to misbehave in ways that pose significant challenges to the machine learning.
The extremely powerful idea that we can learn about the world by trying an idea out to see if it works has taken us from interpreting signs like comets as starry messengers to understanding that they are just comets seems to work in different contexts. For example, the idea works with machines like the self-driving cars. Computers have an advantage over humans in that they can do millions of learning computations a second and can therefore go from "just pushing buttons" to learning how to play complex games like Go quickly. We know that this powerful idea is roughly how the human mind works.
Further, we know the learning brain can use information from the environment to improve its understanding if it learns to provide itself with formative data; that is, self-regulation makes the powerful idea of making increasingly better educated guesses and then testing them in experience available to the learning wherever she or he is.
The required conditions include opportunities to learn how to identify specific learning targets, criteria for incremental success, exemplars and models. Unfortunately, in many or perhaps most classrooms, self-regulation (or learning how to learn) is not the prevailing model. Instead, the data for improvement is held to be the sole property of the teacher or the accountability system.
In the example of the self-driving car, the particles of data are each very small. What students often get in the classroom is data in huge and useless chunks. "You don't understand polynomials! Get with it!"
The teacher cannot effectively provide the appropriate level of data for the student to use.
The learner can.
Ferris, T. (1988). Coming of Age in the Milky Way. New York: Doubleday.
McGrayne, S. B. (2011). Why Bayes Rules: The History of a Formula That Drives Modern Life. Scientific American. Retrieved from http://www.scientificamerican.com/article/why-bayes-rules/
Dr. John Holton
Dr. John Holton joined the S²TEM Centers SC in July of 2013, as a research associate with an emphasis on the STEM literature including state and local STEM plans from around the nation.