I'm not happy with the way science is usually taught in secondary school. It is rendered boring - memorize a number of "facts" and either replay them on a test or use some recalled formulae to plug in a few numbers to find an answer. It completely misses the fun of science and also something rather fundamental about how new knowledge is found and why, at least to a scientist, answers and fact aren't the real product - even though they may be useful and advance knowledge. It also creates a view of science that has opened a divide between scientists and non-scientists - something that in a society that depends so much on science and technology is a serious disconnect and perhaps a danger.
As it happens a beautifully cultivated ignorance and questions is more fundamental to the forward motion of science. I suspect applying some of the techniques may be very important to other fields where "out of the box" creative thinking is required and I sometimes rely on it in my consulting practice. The recent post on ignorance brought some email reaction, so it makes sense to wade in a bit deeper..
The general notion of what a scientist does is to collect data (information is a better term) by observing and manipulating bits of the natural world by doing something called experiment. There is a methodology - the scientific method - which is based on observation, hypothesis, manipulation, further observation , a new hypothesis and so on... There is a sense of order, but that turns out to be far from the truth. You experiment to learn something - ideally to discover something.
Discover, dis - cover, is the act of revealing. What is revealed can be very beautiful and it often becomes a "fact" in text books and teaching, but what many consider the end product of science are known to be unreliable to the scientist. Nothing is safe - nothing is above question. Not even something like the absolute speed limit of the speed of light.1 Scientists don't know things absolutely, but rather report how well it is known. Newtonian mechanics turn out to be incorrect - but at the scale where humans live and observe everyday things it is more than accurate enough that we still routinely use it as a "good enough" descriptive model. We know where it begins to fall apart and have made other discoveries to more accurately describe those areas - special and general relativity for example.
In the 19th century it was believed the universe was permeated with with a luminiferous ether to allow a substance through which light could propagate. It was the wrong path and, in 1907, Albert Michelson became the first American physicist to be splashed with the Swedish holy water for failing to observe the ether in his extremely clever measurements of the speed of light.
Think about it for awhile - Michelson got the Nobel Prize for an experiment that didn't work.
Some would later describe the ether as the black cat physicists had been theorizing about, experimenting and trying to measure in a pitch black room for decade. Literally hundreds of approaches and many many scientist years of effort. Michelson somehow found the light switch and it became clear the ether didn't exist to a rather high degree of accuracy. The confusion that resulted led to an entirely new line of questioning - several doors to new rooms, all pitch black with their own black cats, appeared with the light provided by Michelson. A patent clerk who went by the name of Albert was pushed to a line of novel questions that gave us a fundamentally new understanding of the universe. And even better he opened the way for many rich new questions - questions that were beyond our imagination until we saw a bit of the nature of his black cat.
Sure we had learned something, but it gave us a new appreciation for how much more ignorant of the universe we really were.
We keep discovering and adding to this area we call knowledge and people often make practical use of these discoveries, but the meaningful product of science is not facts or knowledge, but rather the expansion of an informed and cultivated ignorance.2
One of my mathematical heroes is Kurt Gödel. Mathematicians had a sense that everything - at least everything in mathematics - was comprehensible and could be explained with math itself. Gottfried Leibniz, one of the inventors of the calculus, tried to construct an alphabet of human thoughts that would allow you to take combinations of thoughts and form any idea just as letters can make words and words can make sentences. A few hundred years later David Hilbert made an attempt to similarly code knowledge.
The impressive achievement of Gödel was to show that all of this was impossible. Gödel was a shy and quirky person - hardly anyone's candidate for a revolutionary - but he is incompleteness theorems rocked mathematics and physics. I can't give a rich general level discussion of what he did, but at its core he showed an consistent system in math (like the whole numbers and the operations - like addition, multiplication and so on) can't be complete and consistent.3 This may seem to be a depressing notion - finding a fundamental limit in mathematics, but rather it opened an incredibly rich source of new questions to Gödel and others. It is fair to say that unknowability and incompleteness led to questions, reasoning and discoveries that have impressively benefited computer science - and to think that computer science is fundamentally based on absolute and complete logic:-)
This ignorance - the recognition that we really don't know something as deeply as we thought we did - is a fundamental driver of science. The problem of the unknoweable isn't a real obstacle, but is really just a serious of paths to deeper understanding. Also, to a scientist, the explosion of information isn't terribly important either - at least not at a fundamental level. The rich sources of discovery are more dependent on new questions that arise from cultivated ignorance. Questions are the goal of science - it just happens to generate results (with attached confidence levels!) that have historically advanced civilization and cultivated ignorance is a necessary component of making the process move.
It is ignorance rather than data that moves science along.
A very import and somewhat subtle point of doing science is that scientists use ignorance to work and the management of this ignorance is incredibly important. Sometimes it is called the taste in picking and progressing with problems. It is often chaotic with communication and collaboration often being extremely important. At the leading edge it is often cross disciplinary. I have a tendency to not be able to describe exactly what I do. This is really common among scientists and the area they are currently working in is often shifting dynamically. It is messy and may even seem inefficient, but it is a proven path to real discovery.
1 Which is why the recent neutrino experiment got so much attention. People have been testing the limit for over a century and so far all of the results that suggest it can be violated, including the most recent, have turned out to be so flawed as to be invalid. A good deal of pseudo-science is based on experimental "results" that are incorrect - they are often trivial, but sold to non-scientists as something absolute.
2 The time gap between discovery and practical use can be very long. Faraday thought his early work with electricity and magnetism would have no practical use. A practical use for general relativity seemed a crazy notion for fifty years, but it turns out to be a critical component of making the global positioning system work as accurately as it does.
3 Consistency is the characteristic that a system's rules will not result in self contradictory statements. Think of science fiction as a rich source of counter examples - when Captain Kirk defeats machine logic with simple logic puzzles. Take a card and write "the other side of this card is true" on one side and "the statement on the other side of this card is false" and think about it for awhile:-)
At least two readers of this blog are mathematicians and my appologizes for the very rough high-level treatment of something that is very rich and deep. If you are a student just study the work! If you aren't technical I strongly recommend Rebecca Goldstein's book on the subject.
Maple pecan pie - really good with vanilla ice cream or gelato!
° 1 unbaked pie shell
° 215 grams/2 cups pecans (coarsely chopped)
° 55 grams/¼ cup dark brown sugar
° 25 grams/¼ cup tapioca starch
° 4.5 grams/ ¾ teaspoon kosher salt
° 240 grams/1 cup grade B maple syrup. Grade A or "fancy" may not be strong enough
° 60 grams/¼ cup heavy cream
° 4 grams/1 teaspoon vanilla
° 2 large eggs
° Preheat the oven to 425°F
° Place the chopped pecans in the unbaked pie shell. Whisk together the sugar, tapioca starch and salt in a medium sized bowl. Whisk in the maple syrup, cream and vanilla. Whisk in the eggs. Pour over the pecans.
° Bake for 20 minutes and then turn the heat down to 350°F without opening the oven. Bake for an additional 30 minutes. Let pie cool at room temperature for at least 30 minutes before serving.