tag:blogger.com,1999:blog-3722233.post2131195086239732300..comments2024-03-28T18:17:00.135-05:00Comments on Computational Complexity: Should we learn from the Masters or from the Pupils?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-3722233.post-25809917987527272052012-09-15T07:15:18.412-05:002012-09-15T07:15:18.412-05:00Another example comes from the Wikipedia article o...Another example comes from the Wikipedia article on Peano's arithmetic:<br /><br />"Peano's original formulation of the axioms used 1 instead of 0 as the "first" natural number. This choice is arbitrary, as axiom 1 does not endow the constant 0 with any additional properties. However, because 0 is the additive identity in arithmetic, most modern formulations of the Peano axioms start from 0."<br /><br />Peano's original idea may have been more interesting. Zero has at least one additional property - you can't use it as the denominator of a fraction. Jim Blairnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-31824327772775581762012-09-09T04:52:34.337-05:002012-09-09T04:52:34.337-05:00My high school notion of Euclidean Geometry was th...My high school notion of Euclidean Geometry was that it was based on a set of axioms. Recently, I read a translation from the original Greek and was somewhat surprised to find it is based on a set of definitions. Jim Blairnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-12319751177077272272012-09-08T11:07:41.842-05:002012-09-08T11:07:41.842-05:00BECAUSE you made the comment I fixed it!
THANKS!BECAUSE you made the comment I fixed it!<br />THANKS!GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-69945765876987854332012-09-08T10:06:20.999-05:002012-09-08T10:06:20.999-05:00As a novice your Ramsey writeup was made more conf...As a novice your Ramsey writeup was made more confusing by an unfortunate typo in the very first Definition, in which clique and independent set are defined identically. I believe it actually meant to clarify the difference by stating that the latter shares NO edges between pairs of vertices.meliornoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-22369514763868547552012-09-07T01:03:50.640-05:002012-09-07T01:03:50.640-05:00You mentioned recursion theory in the 60s because ...You mentioned recursion theory in the 60s because of injury arguments... hell, you don't need to invoke injury arguments! Back when people weren't as confident about liberally using Church's Thesis, every paper was an absolute god-awful mess full of gruesome coding that not even a mother could love!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-38287354446419619142012-09-06T07:04:34.389-05:002012-09-06T07:04:34.389-05:00Anon 4:03- my question isn't really a YES/NO w...Anon 4:03- my question isn't really a YES/NO which is better<br />Pupil/Student- my question is an invitation for my readers to share their experiences reading original sources vs reading later versions.<br /><br />Anon 9:47- Yes I was being sarcastic.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84792537661522207032012-09-05T21:47:14.896-05:002012-09-05T21:47:14.896-05:00I sense sarcasm. Rand was known for preaching self...I sense sarcasm. Rand was known for preaching selfishness as an economic motivator, not altruism!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-76155111861914983922012-09-05T16:03:47.497-05:002012-09-05T16:03:47.497-05:00Masters are pupils with an new idea. Pupils are ma...Masters are pupils with an new idea. Pupils are masters who refined and completed the old man's thoughts. This is a silly question because masters presume a timeless point in space where some true came into existence. <br />If you are studying the life and thoughts of Goedel, then study his writings. If you are studying his ideas, look to the smart people who picked up his idea, and completed it. <br />If you are looking to impress freshmen, then appeal to the fallacy that the oldest source is the most credible. I'd suggest something like, "You know, in my day we only had four elements, and that was all we needed..."Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-74455775888562974152012-09-05T12:17:59.553-05:002012-09-05T12:17:59.553-05:00The first one to get an idea may illuminate what i...The first one to get an idea may illuminate what it took to get there and what contravention had to be dealt with. Help one in future to do new work. The student may have a plethora of questions regarding what is "obvious" to the master, and these may help the new student to figure out his own understanding. Would have helped me a lot to know more about why SRT was a good solid explanation rather than a cute and disconnected theory. Every student should understand why the twin paradox is not.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-78930367864072535332012-09-05T08:42:36.330-05:002012-09-05T08:42:36.330-05:00At first sight, from the title the most immediate ...At first sight, from the title the most immediate answer is "From both!" It may sound even naive, but as we all know pupils get mastery in their fields whenever they practise enough, always with all the advantages of being wiser but disadvantage of getting less flexible in their thought. As we all get.<br />And I cannot agree with your main example, the second one. Dijsktra (search EWD696 link: http://www.cs.utexas.edu/~EWD/ewd06xx/EWD696.PDF), talks about the issues of learning by example.<br />Your statement "If he had just proven a simple case then it would be obvious how to proceed to his abstract case." is what makes uncomfortable. In a single case or example you get an idea which is more an approximation to it than the idea itself. We tend to add our own constraints on this approach.Fernando Castillo Mhttps://www.blogger.com/profile/04580690872224664072noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70918574363269871192012-09-04T11:36:43.581-05:002012-09-04T11:36:43.581-05:00Perhaps no one rule applies:
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"I won...<b><a href="http://books.google.com/books?id=5wv3-WxzWJ4C&pg=PA13&lpg=PA13" rel="nofollow">Perhaps no one rule applies:</a></b><br /><br />--------<br />"I won't say Onsager was the world's worst lecturer, but he was certainly in contention."<br />--------<br /><br />Onsager's writings are not models of clarity either.John Sidleshttps://www.blogger.com/profile/16286860374431298556noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50965756593930305262012-09-04T11:22:39.085-05:002012-09-04T11:22:39.085-05:00"Another point could be that the process of f..."Another point could be that the process of finding the desired proof really appears in a first paper but not in the subsequent surveys."<br /><br />Counterexample:<br />http://gowers.files.wordpress.com/2009/05/razborov2.pdfAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-46004165549415108572012-09-04T10:04:31.576-05:002012-09-04T10:04:31.576-05:00The fact that the masters are sometimes hard to re...The fact that the masters are sometimes hard to read may be an explanation of why it can be useful to read them. Since one has some pain to decipher their work, one is forced to really think to the subject and thus to understand everything. Another point could be that the process of finding the desired proof really appears in a first paper but not in the subsequent surveys. Anonymousnoreply@blogger.com