Am I a crank?
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From: Nathan on 28 Aug 2006 23:31 david petry wrote: > It could be argued that since the mathematics community does expend a > great deal of energy in the search for formal proofs of conjectures > having ridiculously high probabilities of being true, and often turns a > blind eye to the probabilistic arguments, the mathematics community > itself engages in crank-like behavior. I have read many heuristic arguments advanced by mathematicians to suggest what *might* be true, especially in number theory. I disagree that the community "often turns a blind eye" to such. It's just that these still leave the actual question unanswered.
From: david petry on 28 Aug 2006 23:42 Nathan wrote: > david petry wrote: > > > It could be argued that since the mathematics community does expend a > > great deal of energy in the search for formal proofs of conjectures > > having ridiculously high probabilities of being true, and often turns a > > blind eye to the probabilistic arguments, the mathematics community > > itself engages in crank-like behavior. > > I have read many heuristic arguments advanced by mathematicians to > suggest what *might* be true, especially in number theory. I disagree > that the community "often turns a blind eye" to such. It's just that > these still leave the actual question unanswered. It all depends on what the "actual" question is. If mathematics is thought of as a science having the purpose of explaining why we observe the phenomena that we do observe, then the heuristic argument really does answer the "actual" question. There's absolutely no reason to believe that we can do better than a heuristic argument in many cases.
From: Robert Israel on 29 Aug 2006 00:12 In article <1156822962.655075.212160(a)i3g2000cwc.googlegroups.com>, david petry <david_lawrence_petry(a)yahoo.com> wrote: > >Nathan wrote: >> david petry wrote: >> >> > It could be argued that since the mathematics community does expend a >> > great deal of energy in the search for formal proofs of conjectures >> > having ridiculously high probabilities of being true, and often turns a >> > blind eye to the probabilistic arguments, the mathematics community >> > itself engages in crank-like behavior. >> >> I have read many heuristic arguments advanced by mathematicians to >> suggest what *might* be true, especially in number theory. I disagree >> that the community "often turns a blind eye" to such. It's just that >> these still leave the actual question unanswered. > >It all depends on what the "actual" question is. If mathematics is >thought of as a science having the purpose of explaining why we observe >the phenomena that we do observe, then the heuristic argument really >does answer the "actual" question. There's absolutely no reason to >believe that we can do better than a heuristic argument in many cases. Except that 1) in many cases we _can_ do better. 2) many perfectly plausible statements, supported by all kinds of heuristics, turn out to be wrong. Robert Israel israel(a)math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
From: John Schutkeker on 29 Aug 2006 11:03 "skialps10(a)yahoo.com" <skialps10(a)yahoo.com> wrote in news:1156726253.271394.246990(a)m73g2000cwd.googlegroups.com: > I like to think I came up with a fairly unique way of modeling the > Goldbach Conjecture and was thinking of programming it up to see if I > could find any patterns. This sounds like an honest-to-god research project in numerical experimentation. You should write your codes, crank out your plots and submit the results to a journal, the same way a regular scientist does. Science only rarely produces large breakthroughs, and the work is more often methodical and incremental. This sounds like an incremental step along the way to a solution of Goldbach, an your ideas about looking for patterns may inspire pure theorists to look in the same places. You may not be able to solve it, but a theorist may be able to use your work the same way Kepler used Brahe's data to develop Kepler's Law. If you remain as humble as you seem right now, you're probably safe from becoming a crank. And if you can recommend a good freeware contour plotter, preferrable an add-on to Excel, I'd be thrilled.
From: Jeremy Boden on 29 Aug 2006 11:35
On Tue, 2006-08-29 at 15:03 +0000, John Schutkeker wrote: > "skialps10(a)yahoo.com" <skialps10(a)yahoo.com> wrote in > news:1156726253.271394.246990(a)m73g2000cwd.googlegroups.com: > > > I like to think I came up with a fairly unique way of modeling the > > Goldbach Conjecture and was thinking of programming it up to see if I > > could find any patterns. > > This sounds like an honest-to-god research project in numerical > experimentation. You should write your codes, crank out your plots and > submit the results to a journal, the same way a regular scientist does. > Science only rarely produces large breakthroughs, and the work is more > often methodical and incremental. This sounds like an incremental step > along the way to a solution of Goldbach, an your ideas about looking for > patterns may inspire pure theorists to look in the same places. You may > not be able to solve it, but a theorist may be able to use your work the > same way Kepler used Brahe's data to develop Kepler's Law. Unfortunately mathematics is not an experimental science. I predict that you will notice that even really big even numbers can be written as the sum of two primes. .... > > If you remain as humble as you seem right now, you're probably safe from > becoming a crank. And if you can recommend a good freeware contour > plotter, preferrable an add-on to Excel, I'd be thrilled. That's a bit of a non-sequitur! -- Jeremy Boden |