Letters to the Editor, Volume 45, Number 1
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letters.qxp 3/11/98 10:56 AM Page 5 Letters to the Editor Electronic Communication who would like to be part of this com- twice in his book, all known manu- Isolates Some Mathematicians munity but simply cannot afford the scripts before the advent of printing I turned recently to the pages of your hardware and software now required. differed from one another, often in Notices in order to seek information In the old days all that was required hundreds of places. A few changed concerning the forthcoming Interna- were a few rupees or pesos for letters are quite enough to destroy tional Congress of Mathematicians in stamps, a post office in the neigh- his “codes” and those of Rips. Berlin. I have previously attended two borhood, and a friendly and recep- In a similar vein, his “prediction” of tive Hardy at the other end. Are those the comet collision with Jupiter was such Congresses, but I now find that days definitely gone? made months after it had been an- because I have not kept up with the nounced by astronomers. Even then he technology, I may never be able to at- Bernardo Recamán Santos got the date in the Jewish calendar tend another. Indeed, as an indepen- Bogotá, Colombia wrong due to not knowing that the dent mathematician, I am not con- Jewish day ends at sunset. (However, nected to the Internet and still rely (Received September 29, 1997) the Hebrew translation of War and mostly on the post to keep in touch. Peace gives the right date.) But, alas, nowhere in the information Editor’s Note: Dr. Recamán’s letter Just as amazing is Drosnin’s claim provided by the Notices is there any refers to the September announce- that I “searched for many past assas- help for those of us not yet connected. ment in the Mathematics Calendar. sinations in many texts” until I “found I do not believe I am the sole back- The first announcement of ICM98, one random pattern.” Drosnin knows ward mathematician in the world yet which appeared in the November No- full well that he chose Moby Dick him- to go electronic, and I am very con- tices (page 1392), tells how to register self and that I found, not one, but cerned that the enormous amount of using paper mail. many assassinations. In fact, I can find emphasis that is being placed on ad- almost any I look for, including that vanced modes of communication, far Reply to Bible Code Author of Rabin. from making it easier for all to have Having recently had the doubtful plea- The bottom line is that the only access to information, is widening the sure of hearing Bible Code author thing Drosnin did that I have not re- gap between those who have and those Michael Drosnin telling a litany of lies peated in Moby Dick is to predict an who have not the means, financial and and half-truths to the media here in assassination before it happened. Even otherwise, to keep up with the tech- Australia, it is rather amusing to read that prediction can be best described nology and hence to keep in touch his accusation (Notices, November) as a guess, as the words Drosnin with the international mathematical that I am the one perpetrating a hoax. claims as “assassin that will assassi- community. I worry in particular for Take for example his claim to have nate” are from a verse about acci- young mathematicians in many parts the “original Hebrew text” of the Bible. dental homicide and can be read in a of the world—budding Ramanujans Contrary to the very explicit lie made variety of ways that include Rabin JANUARY 1998 NOTICES OF THE AMS 5 letters.qxp 3/11/98 10:56 AM Page 6 Letters to the Editor being the killer or the killer being uniform continuity; one variable and Benefits of Electronic Journals killed. one quantifier is thereby removed. Despite the many benefits of elec- On the matter of Ilya Rips, I am But it is not enough to rename and tronic publishing of mathematical re- sure that he sincerely believes in his δ; their significance must be illus- search journals, Steven Krantz’s edi- “codes”, but he has not presented clear trated. Here is a natural way of doing torial (in the September 1997 Notices) evidence that requires a miraculous this. chose to highlight and exaggerate explanation. Until he does so we are A function is a rule or algorithm some potential drawbacks without entitled to withhold belief in his that for each input of a real number discussing the actions that are widely claims. Everyone who alleges scien- x in the domain of the function pro- taken to address them. I wish to help tific proof of a miracle should expect duces a real number y as output. This inform Notices readers about those the same response. concept is more abstract than it actions, so that we can all participate Readers are invited to inspect a hu- sounds, because the input x is an in- to help direct this inevitable change to morous reply to Drosnin and a serious finite decimal; it would take an algo- our profession. reply to Rips at http://cs.anu. rithm an infinite amount of time to Most of the e-journals that cur- edu.au/~bdm/dilugim/torah.html. process it. To achieve finiteness, we rently exist (such as those published observe that at no time are we inter- by the AMS) hold to the same editor- Brendan McKay ial and ethical standards as main- Australian National University ested in the exact value of the output y; we only need to know it within a stream paper journals—a paper is sub- mitted to an editor and then (Received October 3, 1997) certain tolerance, dictated by the use to which it is put. The tolerance varies anonymously refereed by one or two from occasion to occasion; sometimes suitable peers. No big difference there Use Uniform Continuity to we need to know y with 2-digit accu- from paper journals. Why should there Teach Limits racy, sometimes with 6-digit accuracy, be? It is a system that has worked well for a long time. In the May issue of these Notices, but we never need infinitely many dig- However, an enormous difference pp. 559–563, David Mumford argues its. passionately that when teaching cal- Suppose now that our function has between paper and e-journals is the culus to “the millions”, the basic con- the following property: To compute time lag between acceptance of a cepts should be introduced in an in- the output y with 2-digit accuracy, paper and publication. Paper journals tuitive fashion in terms familiar to the we need to know the input x with, say, often have backlogs of two years or uninitiated. In this spirit Mumford ac- only 3-digit accuracy; to compute y more; no e-journal leaves a paper in final form waiting for more than a cepts the Harvard Calculus definition with 6-digit accuracy, we may need couple of months. Another big ad- of continuity of a function: “the closer to know x with, say, 9-digit accuracy. vantage of e-journals is that authors x gets to a, the closer f (x) gets to In general, in order to compute the and readers can subsequently append f (a).” In the September Notices, p. 893, output with k-digit accuracy, we need (edited and refereed) notes to the Saunders Mac Lane objects to this de- to know only a finite number, say n, paper so that future readers can fol- finition, because it seems to imply digits of x. This property of a func- low later developments in the sub- that f (x) approaches f (a) monotoni- tion is called uniform continuity. ject. cally and also because it fails to say Since a continuous function on a Krantz voices the popular fear that that f(x) gets arbitrarily close to f (a). closed interval is uniformly continu- “deans” will not “count” papers in ref- Therefore, he holds out for the (,δ) ous, our students encounter mostly definition of continuity, although he ereed, respected e-journals for pro- uniformly continuous functions. allows the substitution of Latin let- motion and tenure decisions. Why There are other reasons for prefer- ters for Greek ones. shouldn’t they? Why would a poorly ring uniform to pointwise continuity: In my opinion neither Mumford nor edited paper journal be worth more to it trains the mind to think of a func- Mac Lane nor Leonard Gillman in a a dean? On the contrary, most uni- tion, not as the conglomeration of its note in the September Notices, versity administrators are keen to en- values, but as a thing in itself. This is pp. 932–934, has come up with a de- courage electronic journals, since they finition that is congenial to “the mil- of great help even at the introductory appreciate the potential financial ben- lions”. As Gillman points out, the dif- calculus level—for instance, in grasp- efits. ficulty that students have with the ing the idea of the definite integral, in Krantz worries about the archiv- notion of continuity is the number of discussing uniformly converging se- ing of mathematical material; he be- quantifiers and their subtle placement quences of functions, and in many lieves that as new media for storing in the definition: “For any a and for other contexts. data emerge, the technical world will any > 0, there is a δ depending on not be willing to find a way to move a and such that when x differs from Peter D.