My intention is to register here miscellaneous comments without an elaboration and/or without creating an opinion page for each of them (at least at the current time). The page was started in May 2006, but most of the short texts re-iterate opinions that I have expressed decades ago...
.... very little do we have and inclose which we can call our own in the deep sense of the word. We all have to accept and learn, either from our predecessors or from our contemporaries. Even the greatest genius would not have achieved much if he had wished to extract everything from inside himself. But there are many good people, who do not understand this, and spend half their lives wondering in darkness with their dreams of originality. I have known artists who were proud of not having followed any teacher and of owing everything only to their own genius. Such fools!
See further discussion in my article on our duties as scientists.
It is unclear why it became legitimate not to answer emails, whereas it is considered impolite not to answer phone messages etc. My theory is that it has to do with the media (i.e., the fact that it is never evident that the message was rec'ed, which is actually a good reason to insist that email be always answered). This does not mean that one has to stop whatever one is doing in order to cope with an incoming email; just answering that the email was received but requires some consideration that cannot be undertaken momentarily is perfectly OK. It is also nice to add an estimate as to when one can expect an answer (or before when one should not expect an answer...). Anything of that type is way better than not answering.
In general, in my opinion, it is perfectly legitimate for any of us to hold his/her priorities and to attend to requests accordingly. What is not legitimate, in my opinion, is not to answer requests.
The celebrated essay On proofs and Progress in Mathematics (by William Thurston) starts by rejecting the vulgar view by which Mathematics is about proving theorems, and explains that Mathematics is about advancing the *understanding* of mathematics (where the circular nature of this definition is intentional). It then explores what understanding means, emphasizing the social dimensions that carry the entire project, and drawing conclusion from this observation. There are nice sections about the problem of communicating ideas and about the different roles of formalism and intuitions. I wish to highlight Section 5, which deals with the sociology of the Mathematics community and the relation between its "point scorers" and the rest. [Nov 2010]
When we state conjectures like P is different from NP, some ask at what input length do asymptotically hard problems become hard in practice. While this question is of paramount importance to practice, it is rather secondary from a theoretical point of view. That is, when dealing with fundamental issues, the primary question is what is the typical (or regular) behavior, whereas the question of when do the irregularities disappear is really secondary.
Originally, the idea of an art (or science) festival seems nice. The idea is to collect and stage a large number of works so as to attract the attention of the wider community and/or to facilitate enjoying as many of these works as possible. (The TCS conferences are indeed a typical example; see my comments on STOC/FOCS.) Things get of the track when the framework of the festival starts to dominate the individual works, when people care more about the festival than of the individual works, and when the festival is perceived as more important than the works presented in it. At this point the festival stops serving the works, and the works start serving it. And at this point the festival is to be abandoned, and has to be replaced by a new framework that serves the individual works. [July 2011]
These three issues are briefly mentioned in the first part of Max Weber's famous lecture/essay Science as a Vocation (1918/19). Since Weber's opinions on these issues are, in my opinion, right on the point, let me present them next.
In contrast to the common practice, the primary role of citations is to be informative (i.e., provide the reader with useful information), whereas fulfilling the scholarly duty is only a secondary concern. This means that if you want to refer the reader to a result (or definition) that appears in some text T, then (unless the text is short or the said result is easy to find in it) you should provide more specific information than [T]. For example, [Thm X, T] or [Sec X, T] or [P. X, T] would make the life of the reader much easiler.
Yes, errors should not exist, but they do. Let me quote my father, Isidor Goldreich (1906--1995), who was a civil engineer: There is no 100% guarantee in the world; whoever wants 100% guarantee should not build anything. So if you discovered an error in your (published) work, just fix it (in public). And if you discovered an error in the work of others, just let them know. And let us hope that there will be less errors in the future. [May 2012]
Errors often emerge whenever one handwaves the details rather than actually work them out them rigorous. I have a quote of my father on this too: Wherever the engineer neglects to pay attention, nature pays attention and cracks. So indeed, phrases like ``it is easy to see that X'' are a good place to double-check when going over an argument.
Another suspect phenomenon is a detailed argument that lacks an overview that refers to its main underlying ideas. A sound proof is typically modular: It has underlying ideas and a structure that can be presented at different levels of detail. Providing a modular exposition is not merely crucial for the benefits of readers, but is a good debugging tool (which may leads both to the detection of errors and to simplifications). [June 2012]
While some people believe that there is a benefit in listing publications in their CV in reverse chronological order, in my opinion this belief is wrong (i.e., there is no real benefit in doing so). More importantly, this practice has a cost: It makes the life of recommendation letter writers harder, because when they wish to update their letters, they may need to revise all referemnces to the liist of publications. I believe that it is fair to require candidates to attempt to reduce the workload of their recommenders, by taking this consideration into account. [Dec 2013]
Talking of order reminds me of our good fortune in belonging to a community in which alphabetic order of co-authors to a publication is the norm. (I find the opposite convention of ordering co-authors according to the importance of their contribution to the work quite ridiculus.) I strongly recommend to all members of our community to adherse to the norm of alphabetic order, and warn of the situation in which one has some publications in which the order is alphabetic and some in which it is not so. [Dec 2013]
Although I believe that exercises do not advance my own understanding, I am willing to take the word of others who claim that exercises do help them to advance their understanding. Still, they must also realize that exercises are merely means towards something else; that is, one should never forget that the aim is understanding. This means that one should never allow oneself to get entangled and waste time on an exercise; instead, one should invest the time in gaining understanding of the key conceptual and techincal issues. And here too, the details are means towards understanding the issues. [Dec 2013]
I view arguing as being positioned between thinking and acting, but in this case I disapprove of taking a "middle ground"; that is, I see no point in arguing, and suggest that one should choose between thinking and acting. (This view is stated in response to numerous times in which articulated opinions are answered by rhetoric that picks on some details and is intended to avoid candid consideration of the opinion (by undermining it or its presenter).)
When faced with an articulated opinion of interest, one should first listen to it and try to learn from it, rather than jump to criticizing it or arguing with it. Listening and learning do not necessarily mean adopting, but they refer to an attempt to understand the contents of the opinion and the ideas underlying it. Indeed, once this stage is completed (i.e., once one understands the contents of the new ideas), one may want to consider how to incorporate the new ideas into one's world-view, and a confrontation between ideas may arise. The result may be vary between a full adoption of the new ideas to their full rejection, but a partial integration that leads to a synthesis of ideas is also likely (when the both sets of ideas have their merits). Each result may be couple with deeper understanding of the various ideas, and an articulated reaction to the new ideas may also result and be communicated (or even published). Still the process should start with thinking, not with arguing.
The above refers to opinions that are expressed for the purpose of mutual education, but not every expression is aimed at that. Words can be used as a call for action, and in this case they are instrument of action. If one objects to the proposed action, one better act rather than argue (unless the argument is viewed as an action).
[Aug 2013, rev Mar 2016]
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