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Suppose there is an infinitely long ladder in front of me. I do not know that this ladder is infinitely long, only that it is either a very long (but ...
August 19, 2010
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What is the difference between music and an aesthetically interesting grouping of sounds? I ask because I was listening to the opening of Alfred Hitchcock's The Birds and I while ...
September 2, 2010
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Why is it that, in music, major chords, by themselves, isolated and without any musical context, sound bright and happy, while minor chords are dark and sad? How can arbitrary ...
August 31, 2010
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I'm going to be a senior in high school and I've found philosophy podcasts to be a great way to sample the thoughts of famous philosophers without having to drudge ...
September 2, 2010
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I have two questions about hunting and fishing: First, is it is ethical to use powerful machinery and high-technology to find and harvest fish and game? Second, is "professional" fishing ...
August 31, 2010
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Has there ever been shown to be an effect without a cause? Is it even possible for there to be an effect without a cause? If this is not possible, ...
August 31, 2010
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We're told that all matter in the universe is "expanding", presumably due to residual energy release created by the "big bang". But what (or perhaps more importantly "where") is the ...
September 2, 2010
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When I was a child, I wanted to know what forever was. I would sit and concentrate -- think and think and THINK -- until finally I felt what may ...
August 24, 2010
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Duty, engagement, rules, living a life "conditioned" vs. one free, maybe unconventional, following our own inspiration even if it doesn't seem supported by what we call "common sense". Many of ...
August 26, 2010
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Is there a correlation between intelligence and morality? I can imagine an intelligent person giving a sophisticated analysis to a complex moral question before acting as warranted by his/her analysis. ...
August 31, 2010
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In a finite lifetime, you won't be able fully to inspect an object with parts that are infinitely far from you, at least if we assume that you are limited by the speed of light. But there's other evidence. For example, you may be able to measure the gravitational pull of the ladder. If this pull turns out to be exactly what our theory would predict for a ladder that's like the piece of it we have before us (same material, thickness, density, etc.) and infinitely long, then this would be evidence for infinite length. (Note here that the gravitational pull exerted by any one inch of ladder declines with the square of its distance from you. So no matter how long the ladder its, its gravitational pull will not be infinite.) It's also possible that the ladder is expanding (as our universe is), or perhaps contracting. In that case you get a nice Doppler effect: a transformation of light reaching you from distant parts of the ladder -- the farther the light has traveled, the more strongly transformed it arrives. So evidence can provide reasonable assurance. And we have such reasonable assurance now that the universe is in fact finite.
But it's worth noting, as you suggest, that such evidence depends on "reasonable" assumptions. We assume that the laws of nature we've found to hold true around our space-time location also hold millions of light years away and millions of years in the past. Do we have reasonable evidence for this assumption? Well, yes, sort of, if with this assumption we can fit all our observations into one coherent account. Physics hasn't quite achieved this yet. But once physics delivers such a comprehensive theory, then it'll strike us as unreasonable -- bizarre -- to defend an infinite size of the universe by appeal to diverse laws of nature holding at different regions of space-time. But you should ask: the fact that some hypothesis strikes us as bizarre, how much reassurance is this that it's actually false?
In relation to my earlier answer, the following article from the Economist may be of interest. It's advertised as follows: "Can the laws of physics change? Curious results from the outer reaches of the universe." The link is
www.economist.com/node/16941123?story_id=16941123&fsrc=nlw|hig|09-02-2010|editors_highlights
This is not exactly what I had in mind, but relevant nonetheless.
BTW, this question is probably best classified under "physics" rather than "mathematics."