Thoughts on math and physics
John asks, "Do you feel that Renee over-reacted after proving mathematics to be inconsistent? Couldn't the system of mathematics used to that point, even if it were proved to be technically inconsistent, continue to be used for everyday purposes?"
Yes, it certainly could. But practicality isn't everything.
When I was in college, I had a conversation with a philosophy professor about whether it was important if something were true or not, if there were no practical situation in which it would make a difference. She offered the following example: suppose a person you loved was in terrible pain all the time, but was forced by some supernatural power to act as if nothing was wrong. Suppose there was no test or experiment that could reveal this person's suffering to you; as far as you could tell, the person is just fine. Does this person's pain matter? If so, why?
I don't know how many real mathematicians would react the way Renee reacts in the story. But I think many people have an enormous emotional investment in knowing what is true and what is not, even if it has no practical relevance.
John also asks if traveling faster than the speed of light is the same as traveling back in time. This is true according to current scientific thinking, but the explanation is fairly complex. Read the following page if you want details:
http://www.theculture.org/rich/sharpblue/archives/000089.html
A somewhat less complex method of traveling back in time is described in the last chapter of Kip Thorne's book Black Holes and Time Warps. This would require technology far beyond our current capabilities, but it wouldn't break any known physical laws.
So if you can travel back in time, does that mean you can change the past? No. The physicists who've analyzed this believe that you'd be able to interact with the past, but your interactions would always lead to the history you already knew. This means there can never be a paradox (like Marty McFly keeping his parents from marrying and thus preventing his own birth, in Back to the Future).
Of course, most physicists believe a greater understanding of physical laws will show that traveling back in time is impossible. So why don't they just say it's impossible right now? To some extent, it's because of their faith in mathematics.
The equations for Einstein's relativity have turned out to be correct in every test we've ever been able to devise. This gives physicists enormous confidence in those equations. It's possible that there's an experiment no one has yet thought of, one in which the equations will turn out to be wrong. But until they find that experiment, physicists feel comfortable relying on Einstein's equations.
Time travel is a very weird notion, but if it's not strictly forbidden by relativity, many physicists aren't going to definitively say it's impossible. They rely on the mathematics to tell them what's impossible and what's not.
Yes, it certainly could. But practicality isn't everything.
When I was in college, I had a conversation with a philosophy professor about whether it was important if something were true or not, if there were no practical situation in which it would make a difference. She offered the following example: suppose a person you loved was in terrible pain all the time, but was forced by some supernatural power to act as if nothing was wrong. Suppose there was no test or experiment that could reveal this person's suffering to you; as far as you could tell, the person is just fine. Does this person's pain matter? If so, why?
I don't know how many real mathematicians would react the way Renee reacts in the story. But I think many people have an enormous emotional investment in knowing what is true and what is not, even if it has no practical relevance.
John also asks if traveling faster than the speed of light is the same as traveling back in time. This is true according to current scientific thinking, but the explanation is fairly complex. Read the following page if you want details:
http://www.theculture.org/rich/sharpblue/archives/000089.html
A somewhat less complex method of traveling back in time is described in the last chapter of Kip Thorne's book Black Holes and Time Warps. This would require technology far beyond our current capabilities, but it wouldn't break any known physical laws.
So if you can travel back in time, does that mean you can change the past? No. The physicists who've analyzed this believe that you'd be able to interact with the past, but your interactions would always lead to the history you already knew. This means there can never be a paradox (like Marty McFly keeping his parents from marrying and thus preventing his own birth, in Back to the Future).
Of course, most physicists believe a greater understanding of physical laws will show that traveling back in time is impossible. So why don't they just say it's impossible right now? To some extent, it's because of their faith in mathematics.
The equations for Einstein's relativity have turned out to be correct in every test we've ever been able to devise. This gives physicists enormous confidence in those equations. It's possible that there's an experiment no one has yet thought of, one in which the equations will turn out to be wrong. But until they find that experiment, physicists feel comfortable relying on Einstein's equations.
Time travel is a very weird notion, but if it's not strictly forbidden by relativity, many physicists aren't going to definitively say it's impossible. They rely on the mathematics to tell them what's impossible and what's not.
posted by Ted at 11:40 AM
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