We are trying to prove ourselves wrong as quickly as possible, because that's only in that way can we find progress. Richard Feynman.
Intuition can be seriously wrong. When Galileo argued that the Earth spun on its axis, people knew intuitively he was wrong. Intuition is important but without someway of checking the accuracy of what it tells you, it's about as dangerous as it is useful. As often as not, scientific discoveries contradict our intuition.
Talented scientists and mathematicians depend heavily on their intuition in their work. They start with a hunch. But that's just the start. The idea must then be developed to the point where it can be tested against the facts and most 'great ideas' fail at this point. We hear all about Einstein's flashes of brilliant insight. What is usually passed over is the many years of study and disciplined rigorous training that it took to develop this kind of intuition and then, more importantly, the years of meticulous work and calculations it took to convert his ideas into a testable scientific hypothesis. We rarely hear about the vast number great insights that didn't pan out.
People often mistake a feeling of certainty for knowledge. "I just know it's so" is a response I have heard too often. In fact you don't know. If you can't justify your belief, it's not knowledge. It's just a belief. The Scientific Method is essentially an epistemology - a standard for deciding what can be accepted as knowledge. It is the only rational, useful method
ever devised for checking our ideas about the world we live in. It is one of the most important developments in human thought and it came very late in our intellectual history. Galileo in the 16th century was the first known practitoner of the Scientific Method in Western culture. Before him there were no scientists in the modern sense of the word. ( Avicena, an Arab living in the 10th century, described the SM but it was not taken up by the culture of that time.) With a few, childishly simple experiments, Galileo demolished Aristotle's theories on Mechanics which had dominated Western thought for 2000 yrs.
Some important ideas in the SM are:
1. "I don't know" is a perfectly acceptable answer. (Most of the time it's the only good answer)
2. The facts trump any theory. (Every scientific theory is constantly at risk of being shown false by the next experiment)
3. If there is no way an idea could be shown to be false it's useless.
4. It's not enough to explain what is already known, a theory must predict new information.
5. While it is possible to prove with certainty that an idea is wrong, it is never possible to prove with the same certainty that it is the truth.
This is a very loose description and not meant to be a rigorous or complete description of the Philosophy of Science.
An interesting consequence of #2 is that in the scientific sense, there can be no such thing as a supernatural event. No observation can ever be counted as a 'Violation of the Laws of Nature'. Nature is the law and whatever she does is right. If we see something that contradicts what we thought we knew about nature, we get to rethink our ideas. In the meantime, the answer must be 'We don't know'.
(Just in case anyone raises this old saw: Einstein did not fail math. He was a very strong mathematician. If you read his papers you will find them deeply mathematical as is all of physics since the 19th century. He had formidable mathematical skills, he just wasn't an Einstein in math.)
