EPILOGUE 28;
ties. As I mentioned earlier, it is impossible to prove all the true statements in arithmetic within the postulates of arithmetic. Arithmetic is
incomplete. There will always be true statements in arithmetic that
can be proven only if one moves to a much larger system that includes
arithmetic as a subset.
Although some things in mathematics are impossible, it is always
dangerous to declare that something is absolutely impossible in the
physical sciences. Let me remind you of a speech given by Nobel laureate Albert A. Michelson in 1894 at the dedication of the Ryerson Physical
Lab at the University of Chicago, in which he declared that it was impossible to discover any new physics: "The more important fundamental
laws and facts of physical science have all been discovered, and these are
now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote... Our
future discoveries must be looked for in the sixth place of decimals."
His remarks were uttered on the eve of some of the greatest upheavals in scientific history, the quantum revolution of 1900, and the
relativity revolution of 1905. The point is that things that are impossible today violate the known laws of physics, but the laws of physics, as
we know them, can change.
In 1825 the great French philosopher Auguste Comte, writing in
Cours de Philosophie, declared that it was impossible for science to determine what the stars were made of. This seemed like a safe bet at the
time, since nothing was known about the nature of stars. They were so
distant that it was impossible to visit them. Yet just a few years after he
made this claim, physicists (using spectroscopy) declared that the sun
was made of hydrogen. In fact, we now know that by analyzing the
spectral lines from stars emitted billions of years ago it is possible to
determine the chemical nature of most of the universe.
Comte challenged the world of science by making a list of other
"impossibilities":
• He claimed that the "ultimate structure of bodies must always transcend our knowledge." In other words, it was impossible to know
the true nature of matter.
ties. As I mentioned earlier, it is impossible to prove all the true statements in arithmetic within the postulates of arithmetic. Arithmetic is
incomplete. There will always be true statements in arithmetic that
can be proven only if one moves to a much larger system that includes
arithmetic as a subset.
Although some things in mathematics are impossible, it is always
dangerous to declare that something is absolutely impossible in the
physical sciences. Let me remind you of a speech given by Nobel laureate Albert A. Michelson in 1894 at the dedication of the Ryerson Physical
Lab at the University of Chicago, in which he declared that it was impossible to discover any new physics: "The more important fundamental
laws and facts of physical science have all been discovered, and these are
now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote... Our
future discoveries must be looked for in the sixth place of decimals."
His remarks were uttered on the eve of some of the greatest upheavals in scientific history, the quantum revolution of 1900, and the
relativity revolution of 1905. The point is that things that are impossible today violate the known laws of physics, but the laws of physics, as
we know them, can change.
In 1825 the great French philosopher Auguste Comte, writing in
Cours de Philosophie, declared that it was impossible for science to determine what the stars were made of. This seemed like a safe bet at the
time, since nothing was known about the nature of stars. They were so
distant that it was impossible to visit them. Yet just a few years after he
made this claim, physicists (using spectroscopy) declared that the sun
was made of hydrogen. In fact, we now know that by analyzing the
spectral lines from stars emitted billions of years ago it is possible to
determine the chemical nature of most of the universe.
Comte challenged the world of science by making a list of other
"impossibilities":
• He claimed that the "ultimate structure of bodies must always transcend our knowledge." In other words, it was impossible to know
the true nature of matter.