[math-fun] Re: HTML in math-fun, seqfan posts
I understand the tribulations of picking through MIME and HTML in a nonsupportive mail reader. But., my current version of MS Outlook includes HTML and MIME in outgoing messages by default, these features are preferable for most of my mail; I have to explicitly switch to plaintext mode for math-fun and seqfan postings, and sometimes I forget. I can't select HTML or plaintext per recipient, consequently slips will happen, and I can't be eternally apologetic. If people can't overlook the occasional slip on this account, I can easily go away. At some point, I think math-fun and seqfan will have to acknowledge that technology is moving on. Despite my personal distaste for Microsoft and its applications, the reality is that MS Outlook is now the most commonly-used email application, that it supports HTML and MIME, and that users rely heavily on the associated benefits, such as formatted and colored text, images, backgrounds, links, attachments, etc. I appreciate that math-fun and seqfan like to be accomodating, however, accomodating HTML-disabled users will increasingly disaffect a growing majority of HTML-enabled users, and will deprive math-fun and seqfan of some very useful technologies (when MathML browsers become common, will you not take advantage?). I understand wanting to accomodate HTML-disabled users, and the desire to save on server space; and undercurrents of nostalgia, UNIXphilia, and MSphobia all warm my heart. It may also be that math-fun and seqfan want to discourage a floodgate of membership, considering some recent incidents of inconsiderate new users disrupting our coffeehouse atmosphere. Notwithstanding, my considered opinion is that catering to the technologically lowest common denominator will become increasingly costly to math-fun and seqfan as technology advances.
The point of my last message on this subject: like it or not, my world and a lot of other peoples' worlds are stuffed with HTML and RTF, and as things stand, this will cause occasional problems between math-fun/seqfan and myself, that's life. I stick to the opinion that it would be better if math-fun and seqfan could deal with these formats, however, I accept that there are other opinions on this subject. Various people have given me suggestions on how to deal with recurring problems with HTML in my mail. I will take these suggestions under serious consideration. I also received flames, effectively accusing me of being inflammatory and/or arrogant. I was not intentionally inflammatory or arrogant, I reread my message carefully, and I do not see anything inflammatory or arrogant there either, unless broaching the subject is automatically adjudged to be so. But it is abundantly clear to me now that this subject is closed to level-headed discussion. I will never again take up the subjects of race, religion, politics or HTML in math-fun or seqfan. I will not again post, or answer replies, on this subject. :-)
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote:
...
At some point, I think math-fun and seqfan will have to acknowledge that technology is moving on. MIME and HTML are different issues, and I don't think they're as much issues of technology as issues of design choices and policies related to . MIME has by now gained wide-spread acceptance and support in current mail readers on Unix platforms as well as PC's and Mac's (which are actually now Unix). I had HTML turned on in my mail reader until I caught on that its main benefit seems to be to spammers--- live links are used to give confirmation that email addresses are valid, also to put in obnoxious unwanted content. For formatted stuff, I'd prefer included PDF or the like. Bill Thurston Microsoft and its applications, the reality is that MS Outlook is now the most commonly-used email application, that it supports HTML and MIME, and that users rely heavily on the associated benefits, such as formatted and colored text, images, backgrounds, links, attachments, etc. I appreciate that math-fun and seqfan like to be accomodating, however, accomodating HTML-disabled users will increasingly disaffect a growing majority of HTML-enabled users, and will deprive math-fun and seqfan of some very useful technologies (when MathML browsers become common, will you not take advantage?). I understand wanting to accomodate HTML-disabled users, and the desire to save on server space; and undercurrents of nostalgia, UNIXphilia, and MSphobia all warm my heart. It may also be that math-fun and seqfan want to discourage a floodgate of membership, considering some recent incidents of inconsiderate new users disrupting our coffeehouse atmosphere. Notwithstanding, my considered opinion is that catering to the technologically lowest common denominator will become increasingly costly to math-fun and seqfan as technology advances.
Quoting wpthurston@mac.com:
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote: [something which implied that we are all lesser people if we don't use the latest fads in technology]
Maybe I should give up reading ASCII on our Model 33 teletype which has served us well over the years. Common denominators do have their place, after all. To take an example, this group has frequent postings of intricate identities involving hypergeometric functions, amongst other complex textual material. I am sure those formulas would have looked much prettier had they been typeset in LaTeX, which has now given way to PDF and then to other things. Neverthelesss, it seems to me that people have been interested in the information content, and have been willing to forego elaborate displays which only a few (or maybe, just not everybody) have the fortune to possess, or at least have access to. It is the old problem of whether you can express something in words, even though pictures, dramatic presentations, or other adornments could enhance understanding. A practical solution to this dilemma, which also cuts down on bandwidth, is to post a description of whatever is interesting at the moment and then refer those who are concerned and have the facilities, to a deposit where a more elaborate presentation can be consulted. Whatever happened to that Internet II, which was supposed to have stupendous bandwith and allow the exchange of far fatter mesages? On Internet I, I have the delight of accesssing sites where the commercials load instantly while the text I want to see dawdles along, where I am offered a wonderful selection of things I will never buy, and so on .... I have a certain nostalgia for discussion groups which stick to a topic, where the exchanges are short and concise (with pointers, if need be, to the rest of the world). No doubt better technology will come along, and this group will begin to use it. Or other groups will be formed to take its place. In the meantime I will endure multiple copies of all (well, some) postings in French, English, and German, as well as Microsoft Office, as I merrily skip over the "personality enhancers," credit restorers, online casinos, and the remaining benefits of modern communications. - hvm ------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos
So far I have stayed out of the math-fun politics, but it appears some people like to complain about math-fun. I propose a solution. Someone want to start a new math-fun-politics whereby everyone can complain about every particular of math-fun. The math-fun-politics could then be summarized, and sent out once every couple months to the math-fun list. ----- Original Message ----- From: <mcintosh@servidor.unam.mx> To: <math-fun@mailman.xmission.com> Sent: Tuesday, March 04, 2003 11:22 PM Subject: Re: [math-fun] Re: HTML in math-fun, seqfan posts
Quoting wpthurston@mac.com:
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote: [something which implied that we are all lesser people if we don't use the latest fads in technology]
Maybe I should give up reading ASCII on our Model 33 teletype which has served us well over the years. Common denominators do have their place, after all. To take an example, this group has frequent postings of intricate identities involving hypergeometric functions, amongst other complex textual material. I am sure those formulas would have looked much prettier had they been typeset in LaTeX, which has now given way to PDF and then to other things.
Neverthelesss, it seems to me that people have been interested in the information content, and have been willing to forego elaborate displays which only a few (or maybe, just not everybody) have the fortune to possess, or at least have access to. It is the old problem of whether you can express something in words, even though pictures, dramatic presentations, or other adornments could enhance understanding.
A practical solution to this dilemma, which also cuts down on bandwidth, is to post a description of whatever is interesting at the moment and then refer those who are concerned and have the facilities, to a deposit where a more elaborate presentation can be consulted.
Whatever happened to that Internet II, which was supposed to have stupendous bandwith and allow the exchange of far fatter mesages? On Internet I, I have the delight of accesssing sites where the commercials load instantly while the text I want to see dawdles along, where I am offered a wonderful selection of things I will never buy, and so on .... I have a certain nostalgia for discussion groups which stick to a topic, where the exchanges are short and concise (with pointers, if need be, to the rest of the world).
No doubt better technology will come along, and this group will begin to use it. Or other groups will be formed to take its place. In the meantime I will endure multiple copies of all (well, some) postings in French, English, and German, as well as Microsoft Office, as I merrily skip over the "personality enhancers," credit restorers, online casinos, and the remaining benefits of modern communications.
- hvm
------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
It would be simpler to just rename math-fun to grumpy-math-kvetch. Then all the complaints, which are invariably much longer and more numerous than the original purported offenses, will fit right in. --Shel At 12:53 AM 3/5/2003 -0500, you wrote:
So far I have stayed out of the math-fun politics, but it appears some people like to complain about math-fun. I propose a solution. Someone want to start a new math-fun-politics whereby everyone can complain about every particular of math-fun. The math-fun-politics could then be summarized, and sent out once every couple months to the math-fun list. ----- Original Message ----- From: <mcintosh@servidor.unam.mx> To: <math-fun@mailman.xmission.com> Sent: Tuesday, March 04, 2003 11:22 PM Subject: Re: [math-fun] Re: HTML in math-fun, seqfan posts
Quoting wpthurston@mac.com:
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote: [something which implied that we are all lesser people if we don't use the latest fads in technology]
Maybe I should give up reading ASCII on our Model 33 teletype which has served us well over the years. Common denominators do have their place, after all. To take an example, this group has frequent postings of intricate identities involving hypergeometric functions, amongst other complex textual material. I am sure those formulas would have looked much prettier had they been typeset in LaTeX, which has now given way to PDF and then to other things.
Neverthelesss, it seems to me that people have been interested in the information content, and have been willing to forego elaborate displays which only a few (or maybe, just not everybody) have the fortune to possess, or at least have access to. It is the old problem of whether you can express something in words, even though pictures, dramatic presentations, or other adornments could enhance understanding.
A practical solution to this dilemma, which also cuts down on bandwidth, is to post a description of whatever is interesting at the moment and then refer those who are concerned and have the facilities, to a deposit where a more elaborate presentation can be consulted.
Whatever happened to that Internet II, which was supposed to have stupendous bandwith and allow the exchange of far fatter mesages? On Internet I, I have the delight of accesssing sites where the commercials load instantly while the text I want to see dawdles along, where I am offered a wonderful selection of things I will never buy, and so on .... I have a certain nostalgia for discussion groups which stick to a topic, where the exchanges are short and concise (with pointers, if need be, to the rest of the world).
No doubt better technology will come along, and this group will begin to use it. Or other groups will be formed to take its place. In the meantime I will endure multiple copies of all (well, some) postings in French, English, and German, as well as Microsoft Office, as I merrily skip over the "personality enhancers," credit restorers, online casinos, and the remaining benefits of modern communications.
- hvm
------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hear hear! :-D ----- Original Message ----- From: Gershon Bialer So far I have stayed out of the math-fun politics, but it appears some people like to complain about math-fun. I propose a solution. Someone want to start a new math-fun-politics whereby everyone can complain about every particular of math-fun. The math-fun-politics could then be summarized, and sent out once every couple months to the math-fun list. -- Mike Stay staym@clear.net.nz
On Wed, Mar 05, 2003 at 12:53:52AM -0500, Gershon Bialer wrote:
So far I have stayed out of the math-fun politics, but it appears some people like to complain about math-fun. I propose a solution. Someone want ...
Quoting wpthurston@mac.com:
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote: ... So let it die down!!! Sorry about my post, it was written immediately after David Wilson's, which I thought merited reasonable discussion at the time; unfortunately it arrived a week later because I forgot and sent it from a different email address. ============= I've kept quiet about the discussion of different bases --- there's a whole lot that is known about these kinds of questions. One interesting angle that hasn't been mentioned is that there are interesting alternate choices of digits even for standard integer bases. For instance, digits {-4,-3,-2,-1,0,1,2,3,4,5} for base 10 work in some sense better than the usual choice, since you don't need a sign to describe negative numbers. As another example--- in base 5, the digits {-3, 0, 1, 3, 4} at least uniquely give all positive numbers. ... can you characterize which sets of digits "work" for integer bases?
One motivation is that for complex bases, there is no canonical choice of digits. BTW, a while ago I gave a characterization of those real or complex bases for which there is an almost-always unique representation of any number given by finite-state rules: this can be done if and only if the base is an algebraic integer whose Galois conjugates are not larger (in modulus) than itself. Bill Thurston
The whole idea of weird bases can lead to some interesting things. If you consider the base m/n where (m,n)=1 and m>n, then I believe you can create unique representations with {0,1,2,..m-1) that I believe represent all the integers plus some more stuff. A somewhat related question that seems interesting is what numbers are represented by 2^(a_1)/3^1+..2^(a_k)/3^k for arbitrary k with various sets of a_k. For example, what can represented with a_1<a_2<a_3<a_4<a_5<..<a_k or a_1<=a_2<=...<=a_k? Can this be slightly modified to obtain a basis for all integers? Gershon Bialer ----- Original Message ----- From: "Bill Thurston" <wpt@math.ucdavis.edu> To: <math-fun@mailman.xmission.com> Sent: Wednesday, March 05, 2003 11:22 AM Subject: Re: [math-fun] politics, bases
On Wed, Mar 05, 2003 at 12:53:52AM -0500, Gershon Bialer wrote:
So far I have stayed out of the math-fun politics, but it appears some people like to complain about math-fun. I propose a solution. Someone want ...
Quoting wpthurston@mac.com:
On Thursday, February 27, 2003, at 07:54 AM, David Wilson wrote: ... So let it die down!!! Sorry about my post, it was written immediately after David Wilson's, which I thought merited reasonable discussion at the time; unfortunately it arrived a week later because I forgot and sent it from a different email address. ============= I've kept quiet about the discussion of different bases --- there's a whole lot that is known about these kinds of questions. One interesting angle that hasn't been mentioned is that there are interesting alternate choices of digits even for standard integer bases. For instance, digits {-4,-3,-2,-1,0,1,2,3,4,5} for base 10 work in some sense better than the usual choice, since you don't need a sign to describe negative numbers. As another example--- in base 5, the digits {-3, 0, 1, 3, 4} at least uniquely give all positive numbers. ... can you characterize which sets of digits "work" for integer bases?
One motivation is that for complex bases, there is no canonical choice of digits. BTW, a while ago I gave a characterization of those real or complex bases for which there is an almost-always unique representation of any number given by finite-state rules: this can be done if and only if the base is an algebraic integer whose Galois conjugates are not larger (in modulus) than itself.
Bill Thurston
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Wed, Mar 05, 2003 at 08:22:31AM -0800, Bill Thurston wrote:
I've kept quiet about the discussion of different bases --- there's a whole lot that is known about these kinds of questions.
Do you kow some good references? (Besides Knuth Vol. 1)
.... As another example--- in base 5, the digits {-3, 0, 1, 3, 4} at least uniquely give all positive numbers. ... can you characterize which sets of digits "work" for integer bases?
Before I think about this too much, is this an open research problem, or is the answer known?
One motivation is that for complex bases, there is no canonical choice of digits. BTW, a while ago I gave a characterization of those real or complex bases for which there is an almost-always unique representation of any number given by finite-state rules: this can be done if and only if the base is an algebraic integer whose Galois conjugates are not larger (in modulus) than itself.
Nice! What are the assumptions? Do you assume that the digits are all integers, or is that irrelevant? There's even a more general context, where you allow the "place-shifting" operation to be something more general than multiplication by the base b. One good general context is to pick a set of elements of PSL2R or PSL2C as your "digits". As far as I know, this generalisation has mostly been studied by people interested in real computation, where unique representations are not desirable, since it may require an unbounded amount of computation to produce the next digit. I believe there are many open questions here; in particular, I don't think digits in PSL2C have been studied much at all. Best, Dylan
On Wednesday, March 5, 2003, at 12:00 PM, Dylan Thurston wrote:
On Wed, Mar 05, 2003 at 08:22:31AM -0800, Bill Thurston wrote:
I've kept quiet about the discussion of different bases --- there's a whole lot that is known about these kinds of questions.
Do you kow some good references? (Besides Knuth Vol. 1)
I only wrote up lecture notes for some AMS talks I gave, which aren't in print. I'm not sure what the current best references are, but Rick Kenyon in particular pursued this line of investigation further, and wrote a number of papers. One key-word is self-similar tilings, i.e. tilings of the line or the plane with finitely many tile types where each tile can be subdivided into similar copies, with some given expansion constant \lambda. The various bases correspond to tilings with finitely many tiles up to translation.
.... As another example--- in base 5, the digits {-3, 0, 1, 3, 4} at least uniquely give all positive numbers. ... can you characterize which sets of digits "work" for integer bases?
Before I think about this too much, is this an open research problem, or is the answer known? I don't know the full answer; I'm not sure it's not known, and if it is I don't think I've heard the answer. For any particular set of digits it's a finite check, but I don't know whether or not the answers have a simple characterization.
One motivation is that for complex bases, there is no canonical choice of digits. BTW, a while ago I gave a characterization of those real or complex bases for which there is an almost-always unique representation of any number given by finite-state rules: this can be done if and only if the base is an algebraic integer whose Galois conjugates are not larger (in modulus) than itself.
Nice! What are the assumptions? Do you assume that the digits are all integers, or is that irrelevant?
I guess typically you'd use algebraic integer digits---but that's not necessary as an assumption.
There's even a more general context, where you allow the "place-shifting" operation to be something more general than multiplication by the base b. One good general context is to pick a set of elements of PSL2R or PSL2C as your "digits". As far as I kno this generalisation has mostly been studied by people interested in real computation, where unique representations are not desirable, since it may require an unbounded amount of computation to produce the next digit. I believe there are many open questions here; in particular, I don't think digits in PSL2C have been studied much at all. One theory of this sort is the theory of automatic groups and automatic semigroups, which is actually how I first got interested in the subject. I.e. if the "digits" are generators of a lattice in PSL(2,R) or PSL(2,C) then there are good forms for representations of "numbers" i.e. points on the real or complex projective plane. Cf. "Word-processing on groups" by Epstein et al. <-- that little abbreviation includes me, also cf. Derek Holt's web site maths.warwick.ac.uk/~dfh (I think) for some software; there's also a lot of other literature and software.
Best, Bill
here is a mathematical question. in trying to convince a class where linear differential equations are being solved that it is obvious that the derivative of the determinant of the solution is the trace of the coefficient matrix (the theorem is known; the discussion centers on whether it is obvious) there is a step whereby the derivative of a determinant is a sum of determinants wherein the columns are differentiated, one by one. Since the columns are vectors, their derivative is just a multiple by the coefficient matrix, leaving a sum of determinants in which the columns are multiplied by a matrix factor, one by one. Somehow this asssemblage acquires an invariant of the coefficient matrix as a factor, namely the trace, which is the result. Recalling that the determinant of a product is the product of determinants, this can be rewritten as a determinant of columns in which each column is multiplied by the coefficient, an again an invariant appears as a coevvicient, namely the determinant. These are two extreme cases. Suppose that two columns are multiplied by matrices, then these determinants summed over all pairs of columns. Will this give as a coefficient the second invariant, namely the sum of the diagonal 2x2 minors? Looking in Google, the rule for differentiating a determinant is attributed to Jacobi, although it is not so hard to deduce from the sum-of-products definition of a determinant and this is cast in the form of the formula for the inverse of a matrix using the adjugatge with the determinant sitting there as a factor where it can be differentiated. Is there some lore of determinant theory that we don't know about which contains results such as these, and possibly the answer to the question about invariants? - hvm ------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos
participants (8)
-
Bill Thurston -
David Wilson -
Dylan Thurston -
Gershon Bialer -
M. Stay -
mcintosh＠servidor.unam.mx -
Shel Kaphan -
wpthurston＠mac.com