1518 === Subject: hp48gx Can a average joe fix the input/output pins on a 48? If so are there steo by step directions anywhere on the web? I can solder ok, just need directions and a possible source for parts. BV === Subject: Re: hp48gx > Can a average joe fix the input/output pins on a 48? ÊIf so are there > steo by step directions anywhere on the web? ÊI can solder ok, just > need directions and a possible source for parts. > BV BV: The I/O Connector (I'm assuming you are referring to the Serial connector at the top of the calculator) is a custom surface mount connector. The plastic body of this connector is heat-staked to the main pcb. Cleanly removing these heat stakes should require removing the main pcb from the calculator. The connector is not commonly available - the only possibility is from another HP48G/GX. Of course, you must have disassembled the calculator which can be done by a number of methods. Given that you can solder, this disassembly/ reassembly is the most difficult and tedious part of the repair. TomCee === Subject: Re: A bug and a related mini-challenge re LSQ > First, some terminology. The AUR uses the word solution > in places where it should add an adjective in front to be precise. > I'll use the terms exact solution, approximate solution, > minimum norm solution and minimum residual solution. > By exact solution, I mean a solution x (a vector) > that gives a residual norm, NORM(A*x-b), of exactly zero. > By approximate solution, I mean a solution x that gives a non-zero > residual. There are almost always many approximate solutions, > even if there is also an exact solution (he said tautologically). > By minimum residual solution, I mean a solution which gives a minimum > residual norm. Typically this term will be used when there are many > approximate solutions and no exact solution, but over the set of > approximate solutions, only one has the smallest residual norm; > this would be the common overdetermined least squares solution. > By minimum norm solution, I mean a solution vector which has the > smallest Euclidean length (norm) compared to all other solutions. In some > underdetermined systems, there an infinite number of exact solutions, > but only one solution vector is of minimum length. So then, is a minimum norm solution, among all minimum residual solutions what LSQ does for under-determined systems? It sounded simpler (and more general) where the AUR sums it up in one sentence, though, if you completely drop the word solution from it, as someone said, but all equivalent things are equal (he said, confusedly :) > In the early days of linear algebra (Gauss' time), elimination methods > were used to solve linear systems. Such methods have a hard time with > systems whose A matrix is singular, but such systems can often be solved > approximately with modern methods, giving a relatively small residual > (we hope). Sometimes systems with a singular A matrix > even have an exact solution. Even in approximate mode? [just a rhetorical, humoretical interjection :] > Modern methods of solution using orthogonal decompositions > are able to provide solutions for almost any system. > The AUR doesn't mention it, but a third party book I have mentions > that LSQ uses QR and LQ decompositions to obtain solutions. Sounds good, and you and Werner seem to have found the bug, so congratulations! === Subject: how to display and copy long formula from HP50 Stack? Hello out there, I am looking for a solution for the following problem: when having having performed a symbolic calculation there often results a long expression on the stack, which is too long for the HP50 display. Especially when using the EMU emulator, I would like to dispay the whole expression and copy it by CTRL+C into the windows memory, for example to put it into a word document by CTRL+V. Have you any suggestions to solve this problem? Peter === Subject: Re: how to display and copy long formula from HP50 Stack? > I am looking for a solution for the following problem: > when having having performed a symbolic calculation there often > results > a long expression on the stack, which is too long for the HP50 > display. > Especially when using the EMU emulator, I would like to dispay the > whole > expression and copy it by CTRL+C into the windows memory, for example > to put it into a word document by CTRL+V. Have you any suggestions to solve this problem? Peter The emulator's Edit menu Copy command is what you are looking for. It copies the contents of stack level 1 to the Windows clipboard. It works with real numbers, integers, and strings. If you have some other type, such as a symbolic, use the ->STR command to convert it to a string, then copy it to the Windows clipboard. You have to use the Edit menu instead of CTRL+C since that key combination would be interpreted as the calculator's RightShift+F3. -wes === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=9rwnLQoAAAC_FoizTwvxTD73niS5ww5R Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) >[...] It > works with real numbers, integers, and strings. If you have some > other type, such as a symbolic, use the ->STR command to convert it to > a string, then copy it to the Windows clipboard. Wes, great hint. I had not figured out that the Copy Stack command of Emu48 only worked with strings (by the way, that's why many times I got screwed up when trying Copy&Paste :-/ ). Learning never ends (fortunately) :-) Giancarlo === Subject: Re: how to display and copy long formula from HP50 Stack? Wes: > If you have some other type, such as a symbolic, > use the ->STR command to convert it to a string, > then copy it to the Windows clipboard. Whenever 8-bit characters are involved (e.g. summation, integral and derivative symbols, pi, infinity, less or equal symbol, program delimiters, Greek letters, etc.) the possibility arises of different displays or interpretations, whenever transporting these strings between the (emulated) calculator, whose character set is similar to ISO-8859-1 (more info below), and the far larger and more varied world of numerous character sets used in computer applications, which have only the ascii subset in common. So the HP48/49/50 all have a built-in system, capable of translating any string to pure ascii, and vice-versa. The original software for calculator <-> computer transfer (including the calculator's internal version of Kermit) can perform these translations automatically, but the emulator's Copy/Paste string functions do not, and neither does copying text to or from an SD card, so that's where you might consider replacing ->STR and STR-> by small calculator programs which include the same translations, in a way that's compatible with all computer programs, editors, displays, printers, email, web pages, newsgroup postings, etc. The following post starts off with very simple versions, and also includes fancier optional versions to process a header, which the calculator can also use to indicate its own mode settings: Ascii Import/Export for SD card and Emulator [for all HP48/49/50] There are also computer programs or scripts to do the same, but why bother when any real or emulated calculator is involved, which can do this by itself? Treatises on character sets: http://htmlhelp.com/reference/charset/ ISO-8859-1 explicitly does not define displayable characters for positions 0-31 and 127-159, and the HTML standard does not allow those to be used for displayable characters. The only characters in this range that are used are 9, 10 and 13, which are tab, newline and carriage return respectively. If you attempt to display these invalid characters on your own system, you may find some characters displayed there, but please do not assume that other users will see the same thing (or even anything at all) on their systems. ISO alphabet soup http://www.unicodecharacter.com/charsets/iso8859.html http://aspell.net/charsets/iso8859.html [same] http://www.cs.tut.fi/~jkorpela/latin9.html [-1 vs. -15] http://en.wikipedia.org/wiki/ISO_8859 http://turnbull.sk.tsukuba.ac.jp/Tools/I18N/LJ-I18N.html [Japan] Meanwhile, back in Emu48/49: Giancarlo: > the Copy Stack command of Emu48 only works with strings Originally so, when called Copy string, but since being called Copy stack, it also works with numbers (real and integer), producing what STD mode would display (even if current number display mode isn't STD). Paste string originally could be relied upon to paste only a string, but paste stack now also _interprets_ anything resembling a number, sometimes inadvertently converting an integer string to a real number object, or even converting a hex string, e.g. 4162080000210 to either a large integer or real number, whereas it actually represents the integer object 12, if only it could be left as a string when pasted, so that H-> could then properly be applied to it (similarly with S->H and H->S, or strings of digits meant to remain as nothing but strings of digits). No confusion was introduced into Emu48 by generalizing Copy stack to include more objects, but generalizing Paste stack to assume that all numeric-like strings should be immediately interpreted as numbers can be mistaken, because a string of digits, for example, might need to be left as exactly that, for other uses. === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=9rwnLQoAAAC_FoizTwvxTD73niS5ww5R Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Wes: If you have some other type, such as a symbolic, > use the ->STR command to convert it to a string, > then copy it to the Windows clipboard. Whenever 8-bit characters are involved > (e.g. summation, integral and derivative symbols, pi, infinity, > less or equal symbol, program delimiters, Greek letters, etc.) > the possibility arises of different displays or interpretations, > whenever transporting these strings > between the (emulated) calculator, whose character set > is similar to ISO-8859-1 (more info below), > and the far larger and more varied world of > numerous character sets used in computer applications, > which have only the ascii subset in common. So the HP48/49/50 all have a built-in system, > capable of translating any string to pure ascii, > and vice-versa. The original software for calculator <-> computer transfer > (including the calculator's internal version of Kermit) > can perform these translations automatically, > but the emulator's Copy/Paste string functions do not, > and neither does copying text to or from an SD card, > so that's where you might consider replacing ->STR and STR- by small calculator programs which include the same translations, > in a way that's compatible with all computer programs, editors, > displays, printers, email, web pages, newsgroup postings, etc. The following post starts off with very simple versions, > and also includes fancier optional versions to process a header, > which the calculator can also use to indicate its own mode settings: > There are also computer programs or scripts to do the same, > but why bother when any real or emulated calculator is involved, > which can do this by itself? Treatises on character sets: http://htmlhelp.com/reference/charset/ ISO-8859-1 explicitly does not define displayable characters > for positions 0-31 and 127-159, and the HTML standard > does not allow those to be used for displayable characters. > The only characters in this range that are used are 9, 10 and 13, > which are tab, newline and carriage return respectively. > If you attempt to display these invalid characters on your own system, > you may find some characters displayed there, > but please do not assume that other users will see the same thing > (or even anything at all) on their systems. > Meanwhile, back in Emu48/49: Giancarlo: the Copy Stack command of Emu48 only works with strings Originally so, when called Copy string, > but since being called Copy stack, > it also works with numbers (real and integer), > producing what STD mode would display > (even if current number display mode isn't STD). Paste string originally could be relied upon > to paste only a string, but paste stack now > also _interprets_ anything resembling a number, > sometimes inadvertently converting an integer string > to a real number object, or even converting a hex string, > e.g. 4162080000210 to either a large integer or real number, > whereas it actually represents the integer object 12, > if only it could be left as a string when pasted, > so that H-> could then properly be applied to it > (similarly with S->H and H->S, or strings of digits > meant to remain as nothing but strings of digits). No confusion was introduced into Emu48 by generalizing Copy stack > to include more objects, but generalizing Paste stack > to assume that all numeric-like strings > should be immediately interpreted as numbers > can be mistaken, because a string of digits, for example, > might need to be left as exactly that, for other uses. John, thank you for your - as usually :-) - highly informative reply. Giancarlo === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=itRlSAoAAADIJvOzSGM8mjsK7gvlk1wg Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) I am additionally interested in copying a pretty print expression into the windows clipboard. My very complicated solution works like this: create the expression on HP50G, transform it into a grob by expression 0 ->GROB store it into a variable and store this variable into a file by means of the connectivity kit. Then read the file with XNVIEW and store it into the windows clipboard. So finally you have a pretty expression in a word document. Has anybody got a simpler solution for this, perhaps using EMU? Peter === Subject: Re: how to display and copy long formula from HP50 Stack? > My very complicated solution works like this: > create the expression on HP50G, > transform it into a grob by expression 0 ->GROB store it into a variable and store this variable into a file > by means of the connectivity kit. > Has anybody got a simpler solution for this, perhaps using EMU? I thought it was about Emu48 to begin with, but in Emu48 you can Save object (e.g. any grob) directly from the stack to a file, and in real HP50 (or 49G+) you can also store/copy to SD card, whose files can in turn be directly read by computer. > Then read the file with XNVIEW XnView 1.93.4 does not seem to understand a grob at all, and grobs do not seem to be listed in its built-in Info | Supported formats (nor in its built-in Help) even though it is shown on http://pagesperso-orange.fr/pierre.g/xnview/enformats.html Has XnView stopped supporting HP grobs? Meanwhile, NConvert (v4.92) still does: http://pagesperso-orange.fr/pierre.g/xnview/en nconvert.html A tested example of use: nconvert -out jpeg -o xxx.jpg xxx.gro Or Grob2Tiff? http://www.hpcalc.org/search.php?query=grob2tif However, this program does NOT convert binary objects! (read the doc; I can't even get it to convert the result of ->STR on a grob, after saving as text; is it because of being one 2188-character long line?) How about this one? http://www.hpcalc.org/details.php?id=3851 (you try, I've had enough for one day :) Here declared shareware (for $30) http://www.orbitals.com/gv/ for Windows95 and Windows 3.1 (page last updated on 27 July 2001) Any more? http://www.hpcalc.org/hp48/pc/misc/ http://www.hpcalc.org/hp49/pc/misc/ === Subject: Re: how to display and copy long formula from HP50 Stack? > XnView 1.93.4 does not seem to understand a grob at all, > and grobs do not seem to be listed > in its built-in Info | Supported formats > (nor in its built-in Help) even though it is shown on > http://pagesperso-orange.fr/pierre.g/xnview/enformats.html Has XnView stopped supporting HP grobs? It turns out that this was just my newbie oversight; the next tip of the day to appear, as if reading my own mind (or politely indicating that I should have rtfm) said: By default only the most common formats are available for loading/saving. If you want to have special formats, also, please visit the options, category General > Startup where lo, there is a check-box for: [x] Display all image file types and even reads HP49/50 OpenFire! XnView and NConvert (updated frequently) http://www.xnview.com/ === Subject: Re: how to display and copy long formula from HP50 Stack? thank you for your suggestions to my problem. My idea is to make a little manual, how to solve symbolic problems with a HP50. To do this, one has to save the results of many steps in a word document. - from HP50 via SD card, from EMU via SAVE OBJECT - then converting into *.bmp by NCONVERT, which can do this for many grob files in one step Peter === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=57eBeAkAAABkNMhsZnDBzGQsstJRmvKD Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) just use the EQW from the 50G in emu48. Then use 'Copy Screen' inside the 'Edit' Menu from emu48. If your equation is larger than the screen shift it and connect the pictures with an image program like Photoshop, for example. HTH Andreas === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=itRlSAoAAADIJvOzSGM8mjsK7gvlk1wg Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) On 30 Apr., 00:18, Andreas M.9aller pictures with an image program like Photoshop, for example. ok, the solution of Andreas works. On the other hand, I did not really find a good solution for long expressions. Of course you could do this in a software like Photoshop, but this is also not really simple. More suggestions? Peter === Subject: Re: how to display and copy long formula from HP50 Stack? posting-account=zYTuBQoAAAC_bXzGjGVT5rxv8bOnpefP Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > On 30 Apr., 00:18, Andreas M.9aller If your equation is larger than the screen shift it and connect the > pictures with an image program like Photoshop, for example. ok, the solution of Andreas works. On the other hand, I did not really > find a good solution for long expressions. Of course you could do this > in a software like Photoshop, but this is also not really simple. More suggestions? Peter Install com0com. Then setup a virtual null modem cable and connect EMU48 to the Connectivity Kit. This way it will work just like your 50g for getting GROBs. OR Do like many of us. Install some math fonts (I use MathType) and create proper mathematical expressions in Word. === Subject: Re: how to display and copy long formula from HP50 Stack? CLR 1.1.4322),gzip(gfe),gzip(gfe) > Especially when using the EMU emulator, ÊI would like to dispay the > whole > expression and copy it by CTRL+C into the windows memory, for example > to put it into a word document by CTRL+V. To copy a stack level into the calculator's clipboard: press the up arrow (for the Interactive Stack), cursor to the desired level and press Copy (RS-VAR). Press ON to return to the normal stack. I don't have the emulator at hand, but there are Copy Stack and Paste Stack commands available in the menu at the top of the emulator. Bill === Subject: selecting number of stack digits for RPN program posting-account=WQAFhQoAAADVIZyoCZq2pp0WHDCa2Uyk 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I want to create a short routine to convert degrees minutes seconds and decimals of a second (in the input format DDD.MMSSssssss) to Degrees Minutes and decimals of a minute in the format DDD.MMmmmmmm. I was planning on doing this by - In the input data on the stack, I basically need to select eveything to the left of the seconds (DD.MM) and put it to one side. Then select all of the seconds (SSssssss), divide them by sixty then 100 and then add that to the previously put to one side DD.MM data. How do I select the SSssssss data? Basically I need to seperate the input data two decimal places to the right of the input data decimal point and work on each part seperately. How is this done? Dene === Subject: Re: selecting number of stack digits for RPN program > I want to create a short routine to convert degrees minutes seconds > and decimals of a second (in the input format DDD.MMSSssssss) to > Degrees Minutes and decimals of a minute in the format DDD.MMmmmmmm. I was planning on doing this by - In the input data on the stack, I > basically need to select eveything to the left of the seconds (DD.MM) > and put it to one side. Then select all of the seconds (SSssssss), > divide them by sixty then 100 and then add that to the previously put > to one side DD.MM data. How do I select the SSssssss data? Basically I need to seperate the > input data two decimal places to the right of the input data decimal > point and work on each part seperately. How is this done? > Dene Multiplying first by 100 allows you split off the integer and fractional parts (using DUP IP SWAP FP) of DDDMM.SSssssss into DDDMM. and 0.SSssssss. Then convert 0.SSssssss to 0.mmmmmmmm, by dividing by 0.6, add to DDDMM. and divide out the 100 you multiplied by to start with. === Subject: Re: selecting number of stack digits for RPN program > I want to create a short routine to convert degrees minutes seconds > and decimals of a second (in the input format DDD.MMSSssssss) to > Degrees Minutes and decimals of a minute in the format DDD.MMmmmmmm << HMS-> DUP FP .4 * - >> === Subject: Re: selecting number of stack digits for RPN program > I want to create a short routine to convert degrees minutes seconds > and decimals of a second (in the input format DDD.MMSSssssss) to > Degrees Minutes and decimals of a minute in the format DDD.MMmmmmmm Already posted: D.MMSS to D.MM << HMS-> DUP FP .4 * - >> To convert the opposite way: D.MM to D.MMSS << DUP FP 1.5 / + ->HMS >> Which comes from: The latter looks into where things can (and do) go wrong, as is always something to watch out for, in what seems like the simplest of straightforward calculations. Something similar, for FT <-> FT.INSS (feet, inches, sixteenths) I dimly recall that Joe Horn may have posted some general scheme for working out other conversions along these lines, but can't seem to conceive how to search for it. === Subject: Re: 10 years ago: Unofficial Emu48 Update of the superb Emu48 (and PocketPC version), which turn out to have actually replaced my calculators :) and for all the enhancements (plus personal help) which you have generously provided. The one thing the emulator still doesn't fix, however, is the bad keyboard (because my computer keyboard is also branded HP, and is equally bad :) Best wishes. . === Subject: Re: 10 years ago: Unofficial Emu48 Update John H Meyers schrieb im Newsbeitrag > The one thing the emulator still doesn't fix, however, is the bad keyboard > (because my computer keyboard is also branded HP, and is equally bad :) I don't know what you mean, I would call this a perfect emulation. ;-) Christoph === Subject: Re: 10 years ago: Unofficial Emu48 Update Le 21 avril 2008, Christoph Giesselink a .8ecrit : > It's now 10 years ago, on April 21th, 1998 I published my first update for > Sebastien Carlier's Emu48 emulator. Emu48 has been so useful for debugging purposes, from SysRPL and Saturn ASM programs (by me... and by others) to RPL programs. can't remember what kind precisely. It used the STR-> command. I could have written a Perl script, or I could have used the Unix tools or whatever, but I choosed to use the decompiler of HP48's STR->, because it was more concise and more elegant. So, I loaded the data into Emu48, I ran my RPL program, and I saved the result to a file. The work was done! (Well, the data wasn't bigger than a few dozens Kb...) Emu48 has also been useful to me for testing purposes. Once you have writtena new library, you can test it against any user flags configuration, or against any randomly generated input data. It just takes the benefits of fast computers and avoid memory crumbling due to unwanted crashes. Briefly, lots of thing would be different without such great an emulator. Keep your good work and thank you very much! === Subject: Re: 10 years ago: Unofficial Emu48 Update posting-account=9rwnLQoAAAC_FoizTwvxTD73niS5ww5R Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Christoph, user :-) and *please* keep up the good work for all the HP users' communiyt. All the best. Giancarlo === Subject: Re: 10 years ago: Unofficial Emu48 Update posting-account=57eBeAkAAABkNMhsZnDBzGQsstJRmvKD Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Let me add my two cents that with the seamless integration of EMU48 and debug4x it makes developing software for this machine so much easier. Hopefully we will see an emulator in the future that supports the ARM chip and the SD-card interface so that more useful software for it can be easily developed. Happy anniversary, Andreas === Subject: Re: 10 years ago: Unofficial Emu48 Update Christoph Giesselink schrieb im Newsbeitrag > It's now 10 years ago, on April 21th, 1998 I published my first update > for > Sebastien Carlier's Emu48 emulator. What can I say. Amazing Emu48. Loving it while working on my PC or PPC. Playing arround without risk to harm my real HP. Having the benefit of using the PC-power, because emulating 4 MHz on a 3 GHz CPU gave some speed benefit e.g. compared to HP 49G... Congratulations Christoph! Heiko === Subject: Re: 10 years ago: Unofficial Emu48 Update On 2008-04-22 03:37:13 +1000, Christoph Giesselink said: > It's now 10 years ago, on April 21th, 1998 I published my first update for > Sebastien Carlier's Emu48 emulator. The publishing address Impressive. Happy anniversary and thank you for this great tool. -- They who would give up an essential liberty for temporary security, deserve neither liberty or security (Benjamin Franklin) === Subject: Programmatically displaying (numeric) solver menu What's the magic command to programmatically display the numeric solver menu? Either the old school one (where the variables appear across the bottom line of the display with the regular stack left intact) or the new one (where the variables and equation itself occupy the upper part of the screen) would be fine. I remember finding the answer to this question something like, um, 10 years ago on an HP-48, and I believe it was a SYSEVAL? ---Joel Koltner === Subject: Re: Programmatically displaying (numeric) solver menu Numeric solver menu: 'expression' or { list } STEQ 30 MENU [an optional list element can be used to format the menu] Numeric solver form: #B4001h LIBEVAL Multiple Equation Solver: { list } STEQ MINIT MSOLVR [MITM can be used to arrange the menu] TVM solver: TVM (or 80 MENU) === Subject: Re: Programmatically displaying (numeric) solver menu === Subject: Emporio Armani Ladies watches AR5695 - 2 - Cheapest Watch posting-account=aeAjGwoAAABV8Fha8oDGTE7lMn6FnETI 5.1),gzip(gfe),gzip(gfe) Emporio Armani Ladies watches AR5695 - 2 - Cheapest Watch Emporio Armani Ladies watches AR5695 - 2 Link : http://www.watchesprice.net/Emporio-Armani-Ladies-watches-AR5695-2-7858.html Cheap Watches Home : http://www.watchesprice.net/ Lower Price Emporio Armani Brands : http://www.watchesprice.net/Emporio-Armani-Watches.html Emporio Armani Ladies watches AR5695 - 2 --- one of best selling watches, it is crafted in high quality Watches. 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However, adapting my previous programs, just like Navigator and Chat HP, I was wondering : want to use to communicate ? Since now, you have IrDA, USB and serial... Before, with the HP48GX, you had the serial RS232C and the IR. With the HP49G, you only had wire RS232C... The hp49g+ was coming back to the IR, with the IrDA specifications, plus the USB. But the hp50g has that particulatiry to have 3 communication ports, which may be more complicated to select in Saturn assembly language Can anyone help ? Yoann Desir. === Subject: A rusty math student calculates constructible polygons by trial. Cc: mcdonewt@yahoo.co.nz posting-account=TV2szgkAAACrA1vyuh8IN_0zzgzcwogw 5.1),gzip(gfe),gzip(gfe) A rusty math student calculates constructible polygons by trial. By Donald S. McDonald, 63/3 Hutchison Rd, WELLINGTON 6021. Ph +644 389-6820. e-mail :: MCDO//newt@yahoo.co.nz 8/2/2008. 1/ Constructible, adj. able to be constructed in finitely many steps with ruler and compass. Dictionary of Mathematics, Collins Reference EJ BOROWSKI & JM BORWEIN, 1989. A celebrated result of Gauss's is that the only constructible regular polygons are those with 2^m.p1.p2...pn sides, with each pk a distinct Fermat prime,... 2^(2^n) +1. ^ raised to the power of. e.g. 3 4 5 6 8 10 12 15,... 510, 512, 514, n-gons... are 'constructible.' 2/ The central angle of a regular pentagon is 2*pi/ 5 = 72 degrees. Let cis 36.bc = (cos 36 + isin 36), i= sqrt (-1) = V-1, pi = 3.141... Then, according to de Moivre's theorem: generally, (cos x + isin x) ^ n = cos nx + isin nx. (cis x)^n. = cis nx. In particular, cis 180 .bc = -1 = (cis 36 .bc) ^ 5, cos^2 + sin^2 ==1. Hence, the RHS [right-hand side] can be multiplied out and, equating the real and imaginary parts to -1 and 0 respectively, leads to solving for cos 36 and sin 36 as quadratic surds. The steps for constructing the regular 5-gon and regular 10-gon follows. 3/ Continued fractions for tan 75 .bc and cos 72 .bc. 4/ For many years I proposed an absolutely simple 1-1 mapping of the rationals (continued fractions) onto the natural numbers (binary surreals.) !! 5/ Continued fraction, a number that is an integer plus... a fraction, whose denominator is itself an integer plus a fraction, and so on. (Dictionary of mathematics, above.) F = a + 1/ ( b+ 1/ (c + 1/( d+1/... It is usually assumed that the sequence of [divisors] [a; b, c, d, .. ] be [positive integers.] 5a/ I happily propose that a continued fraction can also be expressed with rational (signed) or decimal divisors, perhaps to considerable advantage . 6/ Casio schools fx-82 MS scientific calculator, shows Tan 75 .bc = 3.732 05 0808. Try ( ANS - 4.00) ^-1 = - 3.732... = - ANS. The coincidence compelling even this rusty mathematician to enquire ... SOLVE quadratic equation x = 4 - 1/ x. X*x - 4*x +1 =0. X = ( 4 +/- sqrt (16-4)) /2 = 2 +- V3. 7/ Try t = 2- V3. (ALSO very RUSTY, double angle formula?) Sin 2A = 2t / ( 1+ t^2) = ( 4- 2V3 ) / (1+4+3 - 4 V3) = 0.5 == sin 30 .bc. Hence, t = tan (30/2) = tan 15 .bc = 2 - sqrt 3. Tan 75 .bc = 2 + sqrt 3. 8/ Prove 1/ cos 72 deg = 3.236 067 978 = 3.25 - 1/( 72-1/(4.5 -1/(72-1/(4.5 - ...))..) = sqrt (5) +1. e.g. Casio fx-82, rational arithmetic, fraction key, (backwards L) = a b/c. steps 4=, iterate.. 4+ 1 L ANS = = = 4 L 17 L 72 Equation x = 4 + 1/ x. -2 = 2 L 17 L 72 X^2 = 5 L 1 L 5184 = 5/1/5184.. 9/ Solve X = 72 - 1/( 4.5- 1/x ). X^2 - 72x +16=0 x = 36 + root 1280 = 4*(9+4 sqrt 5) cos 72 * ( 3/ 1/ 4 - (9 - 4 sqrt 5)/ 4 ) = cos 72 * (1+ rt 5) = = 1. 10/ Construct angle 72 .bc = 2 pi/5 = Acos (1/( root 5 +1)) (In north-east quadrant.) Draw x-axis, OX ~ ~ 4 units. MARK O I U at 0,1,2 units. Construct vertical UP, P = (2,1). Construct Secant-Diameter, OSPQ = (root 5 +1), where SUQ is unit semicircle D on centre P. Draw unit circle centre Q, arc PT. Either above or below good, it does not matter very much. Draw tangent, right angle OTQ. THEN angle < OQT equals required angle 72.bc = 2 pi/5. 11/ Ex. Path OIU PQT = 1+1+1 +1+1 = 5 units. (Figure, 'upside down pot.') 12/ Ex. Tan 72.bc * cos (Atan 0.5 -18.bc) = 3.0433 593 93. Rt angle < OQT is just over 3 units to the right of origin (0,0.) = 3+1/ (23+1/ (16- 1/7... ) = 3 L 111 L 2560. 13/ Puzzle... 780 tan 75 deg = 2910.999 63 nearly 2911. Because tan 75 deg == 2 + root (3). EXACTly! the above may be an optimal approximation. 14/ Ex. 1/ cos 72.bc = 1+ V5 = 233/ 72.00. 15/ Ex. (tan 75 .bc)^ 10 = 524,174. 2 ^ 19 = 524,288. ^ raised to the power of. E n d o-o-o-o-o Don S. McDonald ... === Subject: Re: equation of 3D line from 2 Points posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) A 1-dimensional line imbedded in 3-dimensional space can not be specified by a single equation in the sense you want. It can be specified by vectors or it can be specified parametrically, but no function of the form z = f(x,y) will specify a line. Let P1 and P2 be the two points. Consider the vector V = (a,b,c) = P1 - P2. Now look at the *vector* equation P = P1 + q * V for q in R. === Subject: Conductor into Expression of Energy in Fuse Burnout (by Seung B. Kim) posting-account=qttmhgkAAAChICW4cnappYtBT9kM3JuS CLR 1.1.4322),gzip(gfe),gzip(gfe) in energy value. Highest expression of x is therefore in T = r which is energy at T.00000001 and threshold of conversive expenditure of r does not belong in set M where F(M, r) where r does not belong to M so excessive generation into depletion of substance. Conductor into Expression of Energy in Fuse Burnout (by Seung b. Kim) === Subject: math help can you fill in the blank brackets 20 [ ] 2 [ ] (18 [ ] 6 ) =14 === Subject: Re: math help 20 [YES ] 2 [WE ] (18 [CAN ] 6 ) =14 === Subject: Re: math help === Subject: Re: math help reply-type=response yes 20 [ ?] 2 [ ?] (18 [? ] 6 ) =14 Now what? Bob F. === Subject: Re: math help reply-type=response ok, ok, This is a three variable simultaneous equation. Since there are no other givens as to what's in the brackets it can be re-written as: 20x * 2y * (18y* 6 ) =14 or This is a problem of finding operators such as +, -, /, *, sqrt, ^ or Other. Which one? Bob F. === Subject: Re: math help As explained to me by my fifth grader .. it is order of operations (hope that makes sense)? And before you even ask.. I am not smarter than a fifth grader. === Subject: Re: math help posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.34; Windows NT 5.1; SV1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-dtc-tf05.proxy.aol.com[CDBC70A5] (Prism/1.2.1), HTTP/1.1 cache-dtc-ad07.proxy.aol.com[CDBC74C9] (Traffic-Server/6.1.5 [uScM]) So the brackets are operations. Let's see, 14 is smaller than 20 & 18, that's a clue. Oh, we have parens, so look at it first. 18 [ ] 6 18 is a multiple of 6, so a good first guess is the operation is [/] making (3). Now we've got 20 [ ] 2 [ ] (3) = 14 should be obvious from this point. What do you do to 20 to get 14? Subtract 6. Can we make 6 from 2 [ ] (3)? Sure, by multiplying. Answer: 20 [-] 2 [*] (18 [/] 6) = 14 === Subject: Re: math help So the brackets are operations. Let's see, 14 is smaller than 20 & 18, that's a clue. Oh, we have parens, so look at it first. 18 [ ] 6 18 is a multiple of 6, so a good first guess is the operation is [/] making (3). Now we've got 20 [ ] 2 [ ] (3) = 14 should be obvious from this point. What do you do to 20 to get 14? Subtract 6. Can we make 6 from 2 [ ] (3)? Sure, by multiplying. Answer: 20 [-] 2 [*] (18 [/] 6) = 14 ask again! === Subject: Re: math help Ok yes, there's a grade schooler and it appears OP is a parent, perhaps even a married parent, in which case the observation that there are parents is acceptable. Now however, how does acknowledging there are parents, assist in solving the problem? === Subject: Re: math help posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.34; Windows NT 5.1; SV1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-dtc-th01.proxy.aol.com[CDBC70E1] (Prism/1.2.1), HTTP/1.1 cache-dtc-ad07.proxy.aol.com[CDBC74C9] (Traffic-Server/6.1.5 [uScM]) It doesn't. But at least when you're dealing with a parent of a 5th-grader you're likely to get a thank you. If I did a search on William Elliot+thank you would I get many hits? === Subject: Re: math help I was hoping for some answers === Subject: Iron Solution - by Seung B. Kim posting-account=qttmhgkAAAChICW4cnappYtBT9kM3JuS CLR 1.1.4322),gzip(gfe),gzip(gfe) Of that tension where as one the tightened senses pull closer together the muscular form, there too is will by its unity in which spacial knowledge is based on relativity of the unified mass in relationship with itself. Iron filaments can by stress and strain on matter cause stones in the body organs. The aptest solution is to treat it with milky substances and replenish the body chemistry by fiber induced ejaculations of iron filaments. The body to this exterme can be loosened till the contractions are not framed by a stiff structure needed to produce analog motions of the body. Iron filaments hence must be injected with a polarity for homeostasis so the iron seeps into the calcium centre and the skeletal frame becomes enhanced in structural exigence. Iron Solution - by Seung B. Kim === Subject: JSH: Factoring may be stupid simple posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) I was puzzling about the latest failed factoring idea wondering where I went wrong, as I really felt that there was information wrapped up in the intersection of the residues modulo T of two primes. So I pondered some more. Before too long I was writing out things along these lines: (f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = (r_1 + k_1*p_1) and (g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2) And I multiplied out and solved for k_1 and k_2 respectively and again pondered what if you GUESSED using f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2, so you'd know the f's and the g's, and I realized that then you could just solve for the c's by using (f_1 + c_1*p_1) = (g_1 + d_1*p_2) and (f_2 + c_2*p_1) = (g_2 + d_2*p_2) and I realized you could solve for everything and reduce to a solution for d_1. If it were an integer, you'd guessed right. If not, you'd try some more f's and g's, as you only have p_1 - 1 pairs of f's and p_2 - 1 pairs of g's. And that's when I kind of freaked out which was a few minutes ago as that's stupid simple if it works. I mean STUPID simple. If it's that freaking stupid simple then, oh, I don't know. Kind of still freaking out as if it's that stupid simple then it's all just too weird for me. Think I'll go think about something else now for a while. James Harris === Subject: Re: JSH: Factoring may be stupid simple I have several recommendations as to where to go from here. Even though one could argue that it is not strictly necessary, it would be to helpful to program your algorithm: - The coding process would assure that you have worked out all of the details. - The resulting program can be used to automate the testing process. You can quickly confirm that your program works for many integers by running the program on a large number of small examples and checking the output. - The program can be used to time your algorithm. Granted, the timing tests will not prove that your algorithm is faster (a formal proof would be required), but it certainly would be a good sign if your program was faster than the commonly used factoring programs. There are plenty of free programming tools on the internet, so there is no good reason not to code your algorithm. I would recommend doing additional research on current number theory and complexity theory. Before you can surpass the state of the art, you need to know what that state is. Moreover, this research will provide you tools for writing better algorithms and proofs. In your previous threads, you admitted that you needed an expert on the Chinese Remainder Theorem. Why not do some learning so that you could become that expert? Besides, I would imagine that who loves Math as much a you do would actually enjoy this learning process. You should also keep some perspective. Many excellent professional Mathematicians have worked on fast integer factoring. Modular arithmetic is just one of many tools used in attempts to create a faster algorithm. Although it is not impossible for an amateur to finally solve this puzzle, the chances of this happening is exceedingly slim. If you don't succeed this time, don't be hard on yourself. It doesn't mean that you aren't bright or devoted. It just means that you have discovered, like many before you, that this is an exceptionally hard problem. Try to view your goal in this exercise as learning about numbers and algorithms: if this exercise produces a groundbreaking result, great! If this exercise doesn't produce such a breakthrough, however, it was still worthwhile for the mathematics you would have learned from it. Finally, in all future posts, try to maintain the same positive tone that you have in this one. Don't take your anger and frustration out on USENET. You'll just end up playing the part of class clown for your detractors. If you treat other posters with respect, you will find that they will treat you in kind. -- All things extant in this world, Gods of Heaven, gods of Earth, Let everything be as it should be; Thus shall it be! - Magical chant from Magical Shopping Arcade Abenobashi Drizzle, Drazzle, Drozzle, Drome, Time for this one to come home! - Mr. Wizard from Tooter Turtle === Subject: Re: JSH: Factoring may be stupid simple posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) I have proven Fermat's Last Theorem. Mathematicians lied about that proof. Your society lies. However, if I just prove at a moment that I have solved the factoring problem, your society can escape its lies. But if I wait, when, for instance, many physics students know that 4 equations with 4 unknowns means you get a solution, then I can make the point that your society would let people die rather than tell the truth, or lose all their money. Then that means, for instance, if I say you should be fired from your position if you are a mathematician, then the world will probably listen. So the time now is about your job and the jobs of mathematicians around the world and I'm telling you so that you know it is fair. I want you out of your positions as mathematicians. It's that simple. So wait if you want, and if I'm right, you will be out of your position and finding a new way to make a living, if you are a mathematician. That is my promise to you. IF I am right. James Harris === Subject: Re: JSH: Factoring may be stupid simple Well, the kinder, gentler tone did not last very long. Let the record show that I tried to keep the conversation on a civil level. My comments follow the latest James Harris screed. First of all, I have a question for James. Rotwang, Randy Poe, Uncle Al and I all responded to your initial post. IMO my response was the least critical, most supportive of those initial responses. And yet it was that got you more upset than, say, the post from Uncle Al? As been pointed out many, many times, your proof of FLT has errors. I won't try to convince you of this, for there is no reason to believe that I would succeed where scores of other writers have failed. You seem determined to go to your grave believing that your flawed proof is brilliant, that Wiles's proof has some sort of obvious flaw, and that all of this is being covered up by an improbably massive conspiracy. But now we are treated with your latest fantasy. In this fantasy, you have solved the factoring problem. Apparently, the world will be so grateful for this discovery, and so angry at the math community for not discovering it first, that you will be given the power to fire any or all professional mathematicians. You will then rid the math world of all the people who did not give you your just due, and replace them with your apostle. This fantasy is completely unrealistic and just plain childish. Look at the history of breakthroughs made by amateurs. Can you think of one instance where such a breakthrough resulted in the mass firing of a class of professionals? Can you think of an instance where the amateur who made the breakthrough is given the regal power to fire a whole class of professionals? The king of math employment part of the fantasy sound like it came from a six year old. You are too smart to believe such nonsense without the assistance of a severe case of NPD. The most likely outcome of your latest factoring algorithm will turn out far less favorably for you. If you proceed as usual, the following events will surely unfold: - You will only give anything like a complete description of the algorithm through a series of questions from posters. - You will proudly refuse to either write out a test program, or try out your algorithm on a reasonable set of integers. - Because your pride prevents you from actually testing your algorithm, other posters will discover the counterexamples. - Because your pride prevents you from actually coding your algorithm, it will be other posters who will do the coding and timing. - You will display unrelenting hostility towards those who offer you assistance, including those who are doing work that you should be doing. - At some point, you will finally see errors in your method, and will abandon this approach with a casual remark (So I made an error. No biggie.). How do we know this will happen? Because this is precisely what happened with your previous attempts to solve this problem. There is no reason to believe that things will go any differently this time. This forecast of the future is based on what one can observe from the USENET groups. Based upon my readings on Narcissism, I can add two more forecasts: - During the writing of these threads, you will be in a state of euphoria. You will be the heir apparent of your world, ready to assume your rightful place in history as one of the few truly great thinkers. - As soon as errors in your method become apparent, you will be thrown into a deep depression, with nearly intolerable levels of disappointment and self loathing. I would honestly love to be wrong about that last forecast. One would have to be a sadist of the first order to wish the fate that awaits you on anyone. You could avoid this fate if you would deal with your Narcissism. That is why I implore you to seek therapy. You have wasted too much of your life to this malady. Don't waste the rest of it. -- All things extant in this world, Gods of Heaven, gods of Earth, Let everything be as it should be; Thus shall it be! - Magical chant from Magical Shopping Arcade Abenobashi Drizzle, Drazzle, Drozzle, Drome, Time for this one to come home! - Mr. Wizard from Tooter Turtle === Subject: Re: JSH: Factoring may be stupid simple On Sun, 10 Feb 2008 13:47:20 -0500, Frank J. Lhota I agree, your post was perfectly reasonable. Agreed, James is not stupid, he has a good brain, it is just that his perceptions and reactions seem to be distorted by his NPD. Part of James technique seems to be to leave sufficient ambiguity in his description of his various methods that he can always point to an implementation error in any given implementation, hence invalidating in his eyes any results from that implementation. But the excuses he comes up with as to why he does not test his ideas show a lot of creativity. :) James does not need to test his algorithms since all his work is free from errors (until he notices the errors). Helps to pass the time. Been there, done that, got the T-shirt. This is reasonably obvious from James' posts. He starts off modestly - I have a new idea which might solve the Factoring Problem. Within a few days he convinces himself that his new idea is THE ONE and starts going on about how the world will finally recognise his true greatness. When the rest of us fail to agree he goes into his angry phase - as with the post you are responding to. That also has happened many times before. You would think that someone of James' intelligence would be able to recognise this cycle and do something about breaking out of it. Agreed. I would not wish that on anyone. Good advice James. You should take it. rossum === Subject: Re: JSH: Factoring may be stupid simple [snop cap] We will help you, Ode to James Harris Somebody said it couldn't be done, But James with a chuckle replied That maybe it couldn't, but he would be one Who wouldn't say so till he'd tried. So James buckled right in with the trace of a grin On his face. If he worried he hid it. James started to sing and he tackled the thing And James never ing could do it. Somebody scoffed: Oh, you'll never do that; At least no one has ever done it; But James took off his coat and he took off his hat, And the first thing we knew he'd begun it. With a lift of his chin and a bit of a grin, Without any doubting or quiddit, James started to sing and he tackled the thing And James never ing could do it. There are thousands to tell James it cannot be done, There are thousands to prophesy failure; There are thousands to point out to James, one by one, How hopeless that task set before you. But just buckle in with a bit of a grin, James take off your coat and go to it; Just start to sing as you tackle the thing And James, you'll never ing do it. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: JSH: Factoring may be stupid simple posting-account=bSICGQkAAADSbkxAJ5uMxFegr4rp0Qig Even simpler than that. Since your procedure involves lucky guessing, here's an even simpler procedure that involves guessing: Guess an f1 that solves f1*f2 = T And bingo! You've factored T! Holy cow, it's a single step! - Randy === Subject: Re: JSH: Factoring may be stupid simple posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) No, you guess at the residues. So like with T = 119, and p_1 = 5, your f_1 and f_2 would be given by f_1*f_2 = 4 mod 5 so like, f_1 = 1, and f_2= 4, and f_1 = 2 and f_2 = 2, would be solutions for the f's above, as those are RESIDUES, and not the factors. So you pick a second prime and find g_1*g_2 = T mod p, and again you get the g's, and just pick a set of f's to go with a set of g's, and then you can solve out everything and get an answer. If you picked right then (f_1 + c_1*p_1) = (g_1 + d_1*p_2) and (f_2 + c_2*p_1) = (g_2 + d_2*p_2) as those are explicit equations, where remember, the f's and g's are RESIDUES and the p's are your primes, so you get just a bunch of simultaneous equations, and you can, say, solve for d_1, which means you can now just get the factors directly. The secret to figuring this out seems to be guessing. Possibly the concept of guess was what kept anyone from breaking things out explicitly in this way, where you still have all the information, as notice that T = (r_1 + k_1*p_1) means that you have the full target composite, and for a large composite, k_1 would be VERY large, but it's still just a variable in some simultaneous equations. Oh, if you pick wrong then you won't get integer solutions. James Harris === Subject: Re: JSH: Factoring may be stupid simple posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) It has come up as an issue that a step was not shown. Given (f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1 you can multiply out and get f_1*f_2 + c_1*p_1*f_1 + c_2*p_1*f_2 + c_1*c_2*p_1^2 = r_1 + k_1*p_1 reduce to c_1*f_1 + c_2*f_2 + c_1*c_2*p_1 + m_1 = k_1 where m_1 = floor(f_1*f_2)/p_1). So you do have 4 equations and 4 unknowns. The factoring problem is solved, where the important step was to use the integer requirement. The answer was there all along. The issue was finding it. If the mathematical community does not inform the world then I can assure it that the world will find out anyway and replace the current mathematical community. It can replace all of you. If you think it can't then you need to ask yourself, why not? I can force the situation, I guess, but I'd rather not. Still. So you can wait and see what happens. But if 24 hours passes and you do nothing then I will assume that you have decided that if I choose, I can tell the world to replace you all. So I and the world can start fresh with new students of mathematics. James Harris === Subject: Re: JSH: Factoring may be stupid simple posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1),gzip(gfe),gzip(gfe) Delusional narcissist! === Subject: Re: JSH: Factoring may be stupid simple He reminds me of a little French Poodle; alway yapping, but never biting. If they made a movie about this, I wonder what actor they would use in the comedy, to play him. I'm not sure he's an actor, but so far, all I can come up with for the part of an annoying little nerd is Andy Dick. === Subject: Re: JSH: Factoring may be stupid simple posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) The problem is that the four equations you give do not have a unique solution among the rationals, so that you can't simply solve for everything and reduce to a solution for d_1. Note that any three of the equations imply the fourth; for example, if (1), (2) and (3) hold then (4) is automatic. So if f1 != 0 mod p1, then choosing d1 to be *any* integer will yield rational values for d2, c1 and c2 using the first three equations, and these values will then satisfy (4). Of course, if you can find integer solutions to all four equations then you have a factorisation of T, but you have given no indication of how to do this efficiently, and it's not clear that a method to do so exists. For example, suppose we have guessed the f's and g's, and we proceed by trying to find integer solutions to (3): this equation says that f1 - g1 = d1*p2 mod p1. Since the integers mod p1 are a field there always exists a unique d2 mod p1 satisfying this equation, but since we are looking for a factor which could be as high as sqrt(T), it seems as though we need to check each of the natural numbers less than this which are congruent to d2 mod p1 to see whether they give integer solutions for the other variables; there are approximately sqrt(T)/p1 of those, and to be certain of finding a factorisation of T we have to try this many values of d1 for each pair of residues f1 and g1. So approximately p2*sqrt(T) checks - slower than trial division. Do you have a better idea as to how to find integer solutions quickly? === Subject: JSH: Denial is a sad thing posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) I've been wrong before with my math results--lots of times. I know that bad feeling when you just screwed up, which is why I appreciate when the mathematics is correct as I learned to value that more than believing something was true. So now I found some equations that relate to the factoring problem. That is just mathematics. The four equations are: (f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1 (g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2 and (f_1 + c_1*p_1) = (g_1 + d_1*p_2) (f_2 + c_2*p_1) = (g_2 + d_2*p_2) where the second set is only true for all integers if you guess at f_1, f_2 and g_1 and g_2 correctly, where those are residues and f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2 Here and now those of you who think you can be mathematicians make the choices that determine what you really are. Sure, later you can lie and claim to have gone one way even if you go another but make no mistake, eventually I and people like me who will clean up the discipline will find that out, as there is more to this mathematics thing than many of you have guessed. And it is so important to the human race that it will be our duty to find you out, and push you out of the field. Decide here and now what kind of people you are. James Harris === Subject: Re: Denial is a sad thing We are hard working Mathematicians, all with high paying jobs. You are a parasite. * I now pluck out the thinking part of your brain, and replace it with a clam.* There, feel better now? Not so much to worry about? You may make fewer mistakes now, too. === Subject: Re: Denial is a sad thing posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) If a magnetic north pole(X) approaches both a south pole(Y) and another north pole(Z) at the same time the repulsion and the attraction is subtracted. 1 - 1 = 0 After approach work is extracted from both approached magnets(Y and Z). 1 + 1 = 2 Then we progress to move-away the actuator magnet(X): If we do this after extracting minimal work: 1.1 - 0.9 = 0.2 And if we do this after extracting maximal work: 1 - 0 = 1 Never do we get anywhere close to 2. Furthermore we may slide a shield between the actuator(X) and it's targets(Y and Z). The shield will conduct the flux disallowing interaction with the actuator. (Y to Z). http://www.youtube.com/watch?v=I4nDAuob2rQ Have fun hard working mathematician :-) http://magnetmotor.go-here.nl/text === Subject: Re: Denial is a sad thing posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) I was unaware that there was a degree program in physics at Cartoon U. Build a real one. Film it. Post the video. See if you can do better illusions than Chris Rock. Tom Davidson Richmond, VA === Subject: Re: Denial is a sad thing posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) We take an iron bar(X). We induct 2 fields into the bar using 2 magnets(Y and Z). [S-N] [ bar ] [N-S] If the bar has enough volume relative to the strength of the magnets both magnets will attract it. If the volume of the iron bar is not sufficient it will favor one side adopt it's polarization then repel the other magnet. It's hard to change the volume of the bar, but it's easy to increase the amount of flux. [N-S] [S-N] [ bar ] [N-S] The extra magnet(W) now compliments the (Z) flux inducted into the bar by the magnet at the right. The original magnet at the left(Y) is now repelling the bar. http://forum.go-here.nl/viewtopic.php?p=524 flux switching pendulum === Subject: Re: Denial is a sad thing posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Decide. Here's the answer missing from my original post but on my math blog since last night: Given (f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1 you can multiply out and get f_1*f_2 + c_1*p_1*f_1 + c_2*p_1*f_2 + c_1*c_2*p_1^2 = r_1 + k_1*p_1 reduce to c_1*f_1 + c_2*f_2 + c_1*c_2*p_1 + m_1 = k_1 where m_1 = floor(f_1*f_2)/p_1). So you can exploit wanting integers. Problem solving is about wanting the answer. And then it's about finding it. Most of you do not have what it takes to be mathematicians. To be real ones versus the fantasy that has taken over this little world. Being a mathematician is so much more than most of you can even imagine. The knowledge you gain puts you at a level that requires that you be a certain type of person. I want those of you who do not have what it takes to go ahead, and just move on to other things in this life. If this latest answer escaped you, fine. You may have things to learn but you may still have what it takes. But it's gut check time. You need to forget what people TELL you is the answer, and look deep inside and see if you can do what no one else thinks you can do, and if you can stand when everyone stands against you because you have mathematical proof. You have to decide what's inside you and if you can be someone like me who can stand for the truth when the entire world says I'm wrong because I can prove what it is true then you stay in the field--or you get out. Decide. James Harris === Subject: Protein/O2 injection (by Seung B. Kim) posting-account=qttmhgkAAAChICW4cnappYtBT9kM3JuS CLR 1.1.4322),gzip(gfe),gzip(gfe) Cardiovascular rhythm if uneven breaks healthy tissue down since pulsewidth doesn't acquire momentum. If cardiovascular rhythm is even the oxygenation process congeals oxygen with protein compounds in the digestive tract leading to muscular growth and overall body mass. A formula of protein that gains solidic quality after injection composited with oxygen capsules that are released in the bloodstream can if protein is amassed by the lifting of H2O from the mix of protein and liquid where H20 is dispensed in the urinary tract, form healthy body tissue and repair the uneven pulsewidth that would otherwise break down nutrients in an unhealthy manner. The consequence of remaining in low homeostasis of this manner is the atrophy of the cardiovascular system and how it relates to protein build up in the body. Protein/O2 injection (by Seung B. Kim) alt.technology === Subject: Animus in Thought (by Seung B. Kim) posting-account=qttmhgkAAAChICW4cnappYtBT9kM3JuS CLR 1.1.4322),gzip(gfe),gzip(gfe) Of tension produced there is an efferential energy caused by muscular contraction that in effect burns fat to replace it with muscle. Afference receives sensory data from nerve endings and transfers them to the brain where it is processed. In afference of the eyes there is a sponge-like learning process..but efference there results in an animus of thought that is more creative than merely absorbing the sensory input. Trauma causes afferential absorption of sensory data on a more retentive level since it a response to stimuli. Through tension, efferential energy must be exerted before mere response to stimuli even to evaluate the sensory input so it can be made sense of before it is apprehended. Animus must exist in the mindset for conscious review of thought. It is ideal that afferent energy and efferent projection of the energy be simultaneous to produce involvement with the absorbed data which exists in problem solving and engages the individual with active consciousness since otherwise one succumbs to the passive approach and there is more subjectivity to trauma as such. Animus in Thought - Efference as Presence of Mind (by Seung B. Kim) === Subject: Re: Is multidimensional Weyl algebra a simple ring? Originator: bergv@math.uiuc.edu (Maarten Bergvelt) UÀytkownik Mariano Su.87rez-Alvarez napisaÒ: I am interested in algebras of polynomials in which x_n always appear in form of differences (x_n - x_m). -- It should be noted that no ethically-trained software engineer would ever consent to write a DestroyBaghdad procedure. Basic professional ethics would instead require him to write a DestroyCity procedure, to which Baghdad could be given as a parameter. - Nathaniel Borenstein === Subject: Macaulay 2 workshop in June Originator: bergv@math.uiuc.edu (Maarten Bergvelt) With funding from the NSF, we are organizing a Macaulay 2 workshop, for the period Saturday, June 28, 2008 to Thursday, July 3, just after the MRC meetings Snowbird, Utah. Travel days will be the Saturday and the Thursday, and activities will start Saturday evening. (This is not the same event as the Macaulay 2 conference in March.) The purpose of the workshop is to bring the Macaulay 2 developers together with those who would like to share or to develop their skills at writing packages for Macaulay 2 and at developing the corresponding mathematical algorithms. Sample software projects that might be undertaken are visible here: http://www.math.uiuc.edu/Macaulay2/dev/projects/ Attendance is by invitation only, and financial support is available for approximately 15 people. If you would like to attend, please let us know as soon as possible. Everyone interested is encouraged to apply, including graduate students and postdocs. Your application should include 1. information about what algorithms you would like to work on, and what you have done in the past, 2. a good estimate of travel expenses, and whether you would require financial support for housing and meals, 3. your current institution, and if you are a graduate student, your advisor's name. We would like to receive applications by March 1 and to allocate funds to participants by March 15. Our organizer for the workshop is Amelia Taylor, and applications should be directed to her. === Subject: Re: Finiteness theorem in algebraic geometry Originator: bergv@math.uiuc.edu (Maarten Bergvelt) More thought as a question: what if the support of F is proper over Y? === Subject: Twelve papers published by Geometry & Topology Publications Originator: bergv@math.uiuc.edu (Maarten Bergvelt) Seven papers have been published by Algebraic & Geometric Topology (1) Algebraic & Geometric Topology 8 (2008) 1-17 Examples of exotic free 2-complexes and stably free nonfree modules for quaternion groups by F Rudolf Beyl and Nancy Waller URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p001.xhtml DOI: 10.2140/agt.2008.8.1 (2) Algebraic & Geometric Topology 8 (2008) 19-51 On relations and homology of the Dehn quandle by Joel Zablow URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p002.xhtml DOI: 10.2140/agt.2008.8.19 (3) Algebraic & Geometric Topology 8 (2008) 53-79 Knots in lens spaces with the 3-sphere surgery by Toshio Saito URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p003.xhtml DOI: 10.2140/agt.2008.8.53 (4) Algebraic & Geometric Topology 8 (2008) 81-99 Ideal boundary of 7-systolic complexes and groups by Damian Osajda URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p004.xhtml DOI: 10.2140/agt.2008.8.81 (5) Algebraic & Geometric Topology 8 (2008) 101-153 Knot Floer homology and integer surgeries by Peter S Ozsvath and Zoltan Szabo URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p005.xhtml DOI: 10.2140/agt.2008.8.101 (6) Algebraic & Geometric Topology 8 (2008) 155-171 Topology of random linkages by Michael Farber URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p006.xhtml DOI: 10.2140/agt.2008.8.155 (7) Algebraic & Geometric Topology 8 (2008) 173-210 Loop structures in Taylor towers by Gregory Z Arone, William G Dwyer and Kathryn Lesh URL: http://www.msp.warwick.ac.uk/agt/2008/08-01/p007.xhtml DOI: 10.2140/agt.2008.8.173 Five papers have been published by Geometry & Topology (8) Geometry & Topology 12 (2008) 1-95 A desingularization of the main component of the moduli space of genus-one stable maps into P^n by Ravi Vakil and Aleksey Zinger URL: http://www.msp.warwick.ac.uk/gt/2008/12-01/p001.xhtml DOI: 10.2140/gt.2008.12.1 (9) Geometry & Topology 12 (2008) 97-101 Addendum to: Commensurations of the Johnson kernel by Tara E Brendle and Dan Margalit URL: http://www.msp.warwick.ac.uk/gt/2008/12-01/p002.xhtml DOI: 10.2140/gt.2008.12.97 (10) Geometry & Topology 12 (2008) 103-176 Equivariant homotopy theory for pro-spectra by Halvard Fausk URL: http://www.msp.warwick.ac.uk/gt/2008/12-01/p003.xhtml DOI: 10.2140/gt.2008.12.103 (11) Geometry & Topology 12 (2008) 177-197 Teichmuller geodesics that do not have a limit in PMF by Anna Lenzhen URL: http://www.msp.warwick.ac.uk/gt/2008/12-01/p004.xhtml DOI: 10.2140/gt.2008.12.177 (12) Geometry & Topology 12 (2008) 199-232 Homology and derived series of groups II: Dwyer's Theorem by Tim D Cochran and Shelly Harvey URL: http://www.msp.warwick.ac.uk/gt/2008/12-01/p005.xhtml DOI: 10.2140/gt.2008.12.199 Abstracts follow (1) Examples of exotic free 2-complexes and stably free nonfree modules for quaternion groups by F Rudolf Beyl and Nancy Waller This is a continuation of our study [Algebr. Geom. Topol. 5 (2005), 899--910] of a family of projective modules over Q_{4n}, the generalized quaternion (binary dihedral) group of order 4n. Our approach is stably free nonfree modules of rank 1, which are then used to construct exotic algebraic 2-complexes relevant to Wall's D(2)-problem. While there are examples of stably free nonfree modules for many infinite groups G, there are few actual examples for finite groups. This paper offers an infinite collection of finite groups with stably free nonfree modules P, given as ideals in the group ring. We present a method for constructing explicit stabilizing isomorphisms theta: ZG+ZG = P+ZG described by 2 by 2 matrices. This makes the subject accessible to both theoretical and computational investigations, in particular, of Wall's D(2)-problem. (2) On relations and homology of the Dehn quandle by Joel Zablow Isotopy classes of circles on an orientable surface F of genus g form a quandle Q under the operation of Dehn twisting about such circles. We derive certain fundamental relations in the Dehn quandle and then consider a homology theory based on this quandle. We show how certain types of relations in the quandle translate into cycles and homology representatives in this homology theory, and characterize a large family of 2-cycles representing homology elements. Finally we draw connections to Lefschetz fibrations, showing isomorphism classes of such fibrations over a disk correspond to quandle homology classes in dimension 2, and discuss some further structures on the homology. (3) Knots in lens spaces with the 3-sphere surgery by Toshio Saito In this paper, we improve a necessary condition, which we gave in to admit an integral surgery yielding the 3-sphere. As an application, we prove that if the lens space of type (p,q) is obtained by Berge's surgery on a nontrivial nontorus doubly primitive knot in the 3-sphere, with |q|<5 and prove that they are obtained only by torus knots. (4) Ideal boundary of 7-systolic complexes and groups by Damian Osajda We prove that ideal boundary of a 7-systolic group is strongly hereditarily aspherical. For some class of 7-systolic groups we show their boundaries are connected and without local cut points, thus getting some results concerning splittings of those groups. (5) Knot Floer homology and integer surgeries by Peter S Ozsvath and Zoltan Szabo Let Y be a closed three-manifold with trivial first homology, and let K subset Y be a knot. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K. As an illustration of these techniques, we calculate the Heegaard Floer homology groups of non-trivial circle bundles over Riemann surfaces (with coefficients in Z/2Z). (6) Topology of random linkages by Michael Farber Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters -- the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure. The main results of the paper apply to planar linkages as well as for linkages in R^3. We also prove results about higher moments of Betti numbers. (7) Loop structures in Taylor towers by Gregory Z Arone, William G Dwyer and Kathryn Lesh We study spaces of natural transformations between homogeneous functors in Goodwillie's calculus of homotopy functors and in Weiss's orthogonal calculus. We give a description of such spaces of natural transformations in terms of the homotopy fixed point construction. Our main application uses this description in combination with the Segal Conjecture to obtain a delooping theorem for connecting maps in the Goodwillie tower of the identity and in the Weiss tower of BU(V). The interest in such deloopings stems from conjectures made by the first and the third author [Filtered spectra arising from permutative categories, J. Reine Angew. Math. 604 homotopies for certain projective chain complexes of spectra. (8) A desingularization of the main component of the moduli space of genus-one stable maps into P^n by Ravi Vakil and Aleksey Zinger We construct a natural smooth compactification of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth compactification of the space of smooth genus-zero curves, that is, the space of stable genus-zero maps. In fact, our compactification is obtained from the singular space of stable genus-one maps through a natural sequence of blowups along bad subvarieties. While this construction is simple to describe, it requires more work to show that the end result is a smooth space. As a bonus, we obtain desingularizations of certain natural sheaves over the main irreducible component of the genus-one moduli space. A number of applications of these desingularizations in enumerative geometry and Gromov--Witten theory are described in the introduction, including the second author's proof of physicists' predictions for genus-one Gromov--Witten invariants of a quintic threefold. (9) Addendum to: Commensurations of the Johnson kernel by Tara E Brendle and Dan Margalit Let K(S) be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. In our earlier paper, we showed that Comm(K(S)) = Aut(K(S)) = Mod(S) when S is a closed, Farb's conjecture in all cases (the statement is not true for g <= 2). (10) Equivariant homotopy theory for pro-spectra by Halvard Fausk We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is pieced together from the G/U-homotopy theories for suitable quotient groups G/U of G; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce pro-G-spectra and construct various model structures on them. A key property of the model structures is that pro-spectra are weakly equivalent to their Postnikov towers. We discuss two versions of a model structure with underlying weak equivalences. One of the versions only makes sense for pro-spectra. In the end we use the theory to study homotopy fixed points of pro-G-spectra. (11) Teichmuller geodesics that do not have a limit in PMF by Anna Lenzhen We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space. We also show that for this construction the limit set is contained in a one-dimensional simplex in PMF. (12) Homology and derived series of groups II: Dwyer's Theorem by Tim D Cochran and Shelly Harvey We give new information about the relationship between the low-dimensional homology of a space and the derived series of its fundamental group. Applications are given to detecting when a set of elements of a group generates a subgroup large enough to map onto a nonabelian free solvable group, and to concordance and grope cobordism of classical links. We also greatly generalize several key homological results employed in recent work of Cochran-Orr-Teichner in the context of classical knot concordance. In 1963 J,Stallings established a strong relationship between the low-dimensional homology of a group and its lower central series quotients. In 1975 W,Dwyer extended Stallings' theorem by weakening characteristic series, G^(n)_H, associated to the derived series, called the torsion-free derived series. The authors previously established a precise analogue, for the torsion-free derived series, of Stallings' theorem. Here our main result is the analogue of Dwyer's theorem for the torsion-free derived series. We also prove a version of Dwyer's theorem for the rational lower central series. We apply these to give new results on the Cochran-Orr-Teichner filtration of the classical link concordance group. === Subject: Re: A Certain Elementary Function on the Unit Square Originator: bergv@math.uiuc.edu (Maarten Bergvelt) According to the Sobolev imbedding theorem, a function with more than two integrable derivatives will be continuous on the closure of the square. Your function is discontinuous at the origin. === Subject: A Macaulay 2 Conference Originator: bergv@math.uiuc.edu (Maarten Bergvelt) A Macaulay 2 Conference will be held March 16-19, 2008 at Cornell University, in Ithaca NY. The meeting will begin with some surveys of recent work on the Boij- Soederberg conjectures, in which Macaulay2 has already played a major role. Starting the second day there will be talks of various kinds. Some will present more research for which Macaulay 2 was useful or would likely be useful. Others will present useful algorithms or packages written in Macaulay 2, or algorithms that would be useful in a future version of Macaulay 2. Not everyone coming will be a Macaulay 2 expert, so this would also be an opportunity to learn Macaulay 2 or to improve your Macaulay 2 skills. Dan Grayson and Mike Stillman will be staying in Ithaca also on March 20 and March 21, so if your schedule allows it, and you are interested in writing some Macaulay 2 packages, or honing your Macaulay2 skills, please think of staying in Ithaca for these next two days! If you might stay, please email Mike Stillman. Who may attend: Anyone! But please email Mike Stillman to sign up. Funding? There may be some funds available to partially offset participant expenses. Please email Mike Stillman as soon as possible to apply for partial support. The meeting will start at 2 pm, Sunday, March 16, 2008. The meeting will end Wednesday, March 19, 2008, with Thursday as the optimal travel day. A block of rooms at the Holiday Inn in downtown Ithaca has been reserved until February 15. Details on our web site. We hope to see you here! Web site: http://www.math.cornell.edu/~mike/m2conference2008.html Organizers: Mike Stillman (mike@math.cornell.edu), Dan Grayson, David Eisenbud. === Subject: A Macaulay 2 Conference Originator: bergv@math.uiuc.edu (Maarten Bergvelt) A Macaulay 2 Conference will be held March 16-19, 2008 at Cornell University, in Ithaca NY. The meeting will begin with some surveys of recent work on the Boij- Soederberg conjectures, in which Macaulay2 has already played a major role. Starting the second day there will be talks of various kinds. Some will present more research for which Macaulay 2 was useful or would likely be useful. Others will present useful algorithms or packages written in Macaulay 2, or algorithms that would be useful in a future version of Macaulay 2. Not everyone coming will be a Macaulay 2 expert, so this would also be an opportunity to learn Macaulay 2 or to improve your Macaulay 2 skills. Dan Grayson and Mike Stillman will be staying in Ithaca also on March 20 and March 21, so if your schedule allows it, and you are interested in writing some Macaulay 2 packages, or honing your Macaulay2 skills, please think of staying in Ithaca for these next two days! If you might stay, please email Mike Stillman. Who may attend: Anyone! But please email Mike Stillman to sign up. Funding? There may be some funds available to partially offset participant expenses. Please email Mike Stillman as soon as possible to apply for partial support. The meeting will start at 2 pm, Sunday, March 16, 2008. The meeting will end Wednesday, March 19, 2008, with Thursday as the optimal travel day. A block of rooms at the Holiday Inn in downtown Ithaca has been reserved until February 15. Details on our web site. We hope to see you here! Web site: http://www.math.cornell.edu/~mike/m2conference2008.html Organizers: Mike Stillman (mike@math.cornell.edu), Dan Grayson, David Eisenbud. === Subject: Re: Set existence Originator: bergv@math.uiuc.edu (Maarten Bergvelt) I would propose: In addition to the empty set every set exists which contains elements of x and no elements which do not belong to x. Alternatively, though not well defined: Every conceivable subset of x exists. This would bear the problem that we can conceive (or imagine or name or denote) only a countable number of individual objects. On the other hand it would show that Skolem's condition is already satisfied in our mathematical reality. === Subject: Re: Set existence Originator: bergv@math.uiuc.edu (Maarten Bergvelt) suspect, too, that incompleteness has a lot to do whith this matter. I don't understand this argument very well. Relativization and absoluteness seem relevant here. However, I don't see exactly how they're being aplied. === Subject: Re: Set existence Originator: bergv@math.uiuc.edu (Maarten Bergvelt) Torkel's book is available at amazon.com for under $30 and qualifies for free shipping in the USA. Your original issue was that a set should have every possible combination of its elements as a subset. So for your set theory (first order), select a countable model M - this is always possible. There is a countable infinite set in M, say I, which represents the positive integers. Let P be the power set of I and note that P and its elements are in M. Since M is countable to us viewing it from the outside, P must be countable too (to us viewing it from the outside). Of course P is uncountable within M. Since P is in actuality countable it cannot have every possible combination of elements of I as its elements. -- Jeff Barnett === Subject: Re: Set existence Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) Originator: bergv@math.uiuc.edu (Maarten Bergvelt) The difficulty, as David Ullrich has pointed out, is that it's not clear precisely what you're trying to say, let alone how one would express the idea precisely in *any* language, first-order or otherwise. Intuitively, I think you're trying to say something like, given a set, any arbitrary combination of elements from the set is also a set. But what exactly do you mean by an arbitrary combination of elements? Do you just mean any subset? But that can't quite be it, because presumably by definition a subset is a fortiori a *set*, so we would get any arbitrary combination of elements from the set *that itself is a set* is a set, which is tautologous. So to make sense of your statement you need some concept of combination of elements from a set that is not *definitionally* a set. It's not clear how you would do this, or what the point would be. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Set existence Content-Length: 955 Originator: bergv@math.uiuc.edu (Maarten Bergvelt) Maybe he would be happier with... ** Every sub-collection of a set, is a set. ** It's not much more helpful, but at least not so directly tautologous. Though interestingly, it is actually *false* in at least one respectable set theory. In Vopenka's work on semisets, based (I think) within NGB, the intersection of a proper class with a set is called a semiset, and not all semisets need be sets. Bill Taylor === Subject: Re: Discovery: Concurrency problems might be used to create pseudo random number generators or filling patterns. This estimate seems very high. === Subject: Re: Discovery: Concurrency problems might be used to create pseudo random number generators or filling patterns. On Tue, 12 Feb 2008 10:25:11 +1000 Well, again consider that current timer chips have a very high granularity up to microseconds. I don't expect any attacker (without the ability to manipulate the keyboard or OS) to be able to estimate the exact time of a key press any more precisely than to milliseconds. That makes 10 bits pretty reasonable. Maybe I've missed something? What do you think? But even if I did, and even if this method adds only a single bit per key stroke, I'd still consider it a better entropy source, because it's random, while Skybuck's method is highly predictable. Ertugrul S.9aylemez. === Subject: Re: Discovery: Concurrency problems might be used to create pseudo random number generators or filling patterns. So far I have seen no proof that it was predictable. Check out the latest version which has the bug fixes. Bye, Skybuck. === Subject: Re: Discovery: Concurrency problems might be used to create pseudo random number generators or filling patterns. On Tue, 12 Feb 2008 19:47:41 +0100 Yes, because Usenet just isn't an appropriate place for specifications. Unless you write a paper about your method, including analysis, simply nobody is going to be interested seriously. So nobody feels like analyzing your little elaboration any more than telling you that it wouldn't be useful in real-world scenarious anyway, even if it would provide a reasonable amount of entropy. Ertugrul S.9aylemez. === Subject: Re: Discovery: Concurrency problems might be used to create pseudo random number generators or filling patterns. Lol, excuses. Bye, Skybuck. === Subject: Re: Denial is a sad thing We induct 2 fields into the bar using 2 magnets(Y and Z). [S-N] [ bar ] [N-S] If the bar has enough volume relative to the strength of the magnets both magnets will attract it. If the volume of the iron bar is not sufficient it will favor one side adopt it's polarization then repel the other magnet. It's hard to change the volume of the bar, but it's easy to increase the amount of flux. [N-S] [S-N] [ bar ] [N-S] I was unaware that there was a degree program in physics at Cartoon U. Build a real one. Film it. Post the video. === Subject: Re: Denial is a sad thing posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) 2 magnets, each attached to the rim of a wheel. The wheels are positioned in a sandwich formation. The magnets attract another. We slowly spin the magnet 1 toward magnet 2. As soon as the magnet comes within reach wheel 2 spins in reverse direction then the magnets lock in place. When magnet 1 approaches magnet 2 a bit faster the wheel doesn't spin backwards before locking. If we spin magnet 1 even faster it jerks over magnet 2 only dragging it along for a little bit. However, If the primary magnet is spinning within the resonant frequency it may: - first attract the secondary magnet then - accelerate it in opposing direction AND - jerk passed it as a result of the increased interaction speed. If there is a sufficient lack of friction/vibration the speed can then be increased by tuning the air gap. There where there isn't a sufficient lack of friction the interaction may be used to speed up conventional electric motors. resonance-slow.gif (GIF Image, 420x300 pixels) resonance-to-fast.gif (GIF Image, 420x300 pixels) resonance-match.gif (GIF Image, 420x300 pixels) RESONANT MAGNETOMECHANICS ABSTRACT Unleash complimentary reaction forces in resonance there~with. http://magnetmotor.go-here.nl/resonance/text :) Build a real one. Film it. Post the video. :) :) Build a real one. Film it. Post the video. :) http://www.metacafe.com/watch/665396/how_increase_speed_of_electric_motor/ http://www.youtube.com/watch?v=Jc9rbysrv24 http://www.youtube.com/watch?v=jYcjjSfiNNE http://www.youtube.com/watch?v=mCANbMBujjQ http://magnetmotor.go-here.nl/video === Subject: Data redundancy If I have 100 equal size packets of data (set A), is there a way I can transform them into 200 equally sized packets of data (set B), such that with any 100 of the packets from set B it is possible to recreate set A? I believe that is possible, just can't remember the name of the tansformation or find it on the net. The same question in a more general form: If I have (n) packets of data, where each packet is (m) bits (set A), is there a way I can transform them into (p) packets of data, where each packet set B it is possible to recreate set A?