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The section at the end of the page in my description of an imaginary computer architecture that describes Subdivided Medium floating-point operation has received a substantive change which modifies how this form of addressing operands of unusual length works.

A page in the section on the slide rule has been updated with a brief description of the Hemmi 200 and 201 slide rules, with extra-long split scales to allow more accurate multiplication. The Unique Ten-Twenty is also mentioned. Also, the discussion of a complex number cylindrical slide rule has been expanded, with a mention of the Faber-Castell 989 Complex Slide Rule Calculator.

The page on Dice of Other Shapes (than cubical) has been updated to include an idea of mine for using the idea behind Koplow Double Dice to make a heterogenous die of that type - a d20 inside a transparent d6 - to make a universal die. As well, some information on the history of polyhedral dice has been updated, and more information on the current availability of some new unusual types of dice has been added.

The page on computer arithmetic, as it contained a list of alternate versions of hexadecimal notation used on early computers, now has had duodecimal characters, and some early character sets with characters for pence in sterling currency, added; one of those character sets, used on the Elliott 503 computers, is Cluff-Foster-Idelson code, which anticipated ASCII. On both that page, and the page about punched card codes, I've also added a reference to the GOST 10859 code from the former Soviet Union.

The former of those two pages now also exhibits the character coding for the STRETCH (IBM 7030) computer, as that code, like GOST 10859, has many of the special characters originally used for ALGOL. The IBM 7030 code had the unusual characteristic of putting the upper-case and lower-case letters of the alphabet in the sequence aAbBcC... in the vain hope of simplifying collation; and so I've also included in the diagram for it an image of the ARMSCII code, which placed the letters of the Armenian alphabet in AaBbCc... style order.

As well, I've made some changes to the diagrams on this page, about modifying ASCII, and a diagram of FIELDATA has finally been added to this page.

An attempt has been made to unravel the mystery of the tone generator used for the chorus feature of the model BC, D, and E Hammond organs on this page. RECENTLY UPDATED, thanks to my having been able to see a photo of part of a chorus tone generator.

The page about building blocks and the Pythagorean triangle has been updated showing two ways in which additional directions of walls could be added with alternate block types.

Several updates have recently been made to the section on Chess, among them:

A page describes a number of the systems for recording the moves of a Chess game, including several quite obscure ones.

The description of Korean Chess has been corrected and extended.

Most recently, yet another variant form of Chess has been added, placing the King and Queen off center to better preserve Castling on an enlarged board, and proposing an interesting use for a second King.

A new page has been added discussing memory interleaving techniques.

The apparently contradictory conditions for the efficient use of data elements the lengths of which are not in a simple power-of-two relationship have now been reconciled. On this page I explain how, after dividing a 256-bit memory word into five or seven parts (for 51-bit intermediate-precision and 36-bit single-precision floating-point numbers), I can then, at the cost of a small amount of additional wastage of storage space, calculate physical addresses efficiently without resorting to division by five or seven.

As well, several portions of the section on A Computer Architecture have been modified, both to incorporate this added feature, and to incorporate the feature of selectively saving or updating condition codes to allow speculative execution to be avoided.

Also, a 12-bit oriented example architecture, fleshed out in more detail than the previous 12-bit example in that section, has been added to the section on dealing with nonstandard lengths of data.

The section on basic HTML has been extended with a page about the use of Cascading Style Sheets for formatting.

Two early computers from the People's Republic of China are now mentioned on this site: a description of the instruction format of the 757 vector computer has been added to the section on 32-bit computers, and a description of the instruction format of the DJS-21 computer has been added to the next page.

The section describing the Fast Long Single and Fast Intermediate modes of operation has been moved to its own page, and has been revised and extended.

The description of "The Immortal Game" (or "Die Unsterbliche Partie") between Adolph Andersson and Lionel Kieseritzky has been modified.

Previously, the sequence of moves found in most anthologizations of the game in the English language was presented; now, having seen the original sources myself, I have corrected it to the actual move order played, to which some recent researchers have called attention.

In addition, I have added competent annotations of the moves, from such noted Chess players as Wilhelm Steinitz, Ernst Falkbeer, and Lionel Kieseritzky himself, as the sources in which these are found have entered the public domain, and it seemed only fair to provide those who make the effort to visit this web page with some commentary on the moves which is an improvement on my own puerile commentary. (Of course, though, my comments had a purpose as well, to teach the basics of Chess with this game as an example.)

As well, I have added a description of yet another new variant of Chess, which I call Chess 2016. This serves the same purpose as Random Variant Chess, but it has been improved in two areas. Castling is restored to the same level of usefulness as in normal Chess, and the random selection of a variant can be carried out by rolling ordinary dice instead of using special equipment (i.e., drawing from a customized set of lots).

Also, a page has been added describing a few of the popular openings for Chess games, and another page has been added describing a number of systems of Chess notation.

In addition, in the section on Chess, further modifications have been made to the description of another variant of my invention at the bottom of this page, and on this page I have added a radical proposal to eliminate White's advantage from having the first move, with an even more radical proposal to avoid draws from insufficient material which I felt made it necessary to reduce White's advantage as well.

A page about stars and how they produce energy has been added.

The page about Backgammon has been extended to include a discussion of games such as Pachisi and Ludo, with a colorful illustration added.

The page about Geomancy has had an illustration of the dice used in India for the form of Geomancy known as Ramala there.

Two further changes have been made to the section on A Computer Architecture: the first is that more opcode space has been allocated to the three-address supplementary instructions in both normal mode and scratchpad mode, and this allowed instructions for operations on alternate data types to be used with that instruction format, as well as a new addition: instructions, inspired by those recently added by IBM with the z196, to use the high half of the supplementary registers.

The second change is that the interaction between the fast long single and fast intermediate feature and data memory width control has been clarified, with the primary description of that feature now moved to the same page as that for data memory width control.

In a truly shameless bid to attract more traffic to my site, I have now added a page describing several systems of astrological house division, and another page describing a novel system of astrological geomancy, perhaps the first since Gerard of Cremona.

My pages on chess now include a page on Jetan, the form of chess played on Barsoom (Mars) according to Edgar Rice Burroughs. Also, in the page on various national variants of chess,, I've included an illustration of the alternative form of Burmese chess described in some old English-language books.

A new page with a brief account of how the positions of the planets and the Moon can be calculated to a first approximation.

A further change has been made to the section on A Computer Architecture: in Local Mode and Hybrid Mode, the form of indexed addressing which involved pre-indexed indirect addressing had its address field shortened, which still allows a large number of large arrays to be handled, so that conventional indexed addressing could also be made available in those modes. It has also been added to the normal mode of operation, along with the three-address instructions for the supplementary registers. As well, since the addition of 32-bit RISC-like three-address instructions using the supplementary registers to Scratchpad Mode left some unused opcode space, a set of three-address floating-point instructions with one memory reference, also 32 bits in length, was added to that mode.

On the end of my page with ordinary chess variants, a new one has been added on a 12 by 8 board.

Three changes have been made to the section on A Computer Architecture: a correction has been made to the page on Long Vector Instructions to correctly identify the instruction modes in which they are available, and Fast Long Single and Fast Intermediate modes, which are described on the page about the Program Status Block, have been modified to better facilitate the addressing of data in the left-over portions of the 256-bit memory word. This latter change reflects an additional note previously added to the description of the general technique involved in the section on A Perfect Computer, and the Scratchpad Mode has been modified, through the replacement of one group of instructions by a group of three-address register-to-register instructions, so that a subset of the instructions available in that mode exists which more closely approximates the instruction set of a RISC computer; as well, indexed memory reference instructions were modified in a manner that was later extended to Local Mode and Hybrid Mode, as described above.

The page on A Peculiar Deck of Cards has been updated to include an illustration of the symbols from the Archéometre Saint-Yves - and, as well, contains the exciting discovery that Papus, in his Le Tarot Divinatoire, switched the correspondences of the symbols from Joseph-Alexandre Saint-Yves d'Alveydre's primitive alphabet, as given in the Archéometre, which were assigned to Shin and Than in the Hebrew alphabet. Other minor corrections were also made to the page.

The page on The Mayan Calendar has been updated with information about the related Aztec calendar, as part of a blatant attempt to cash in on the 2012 hysteria.

A page has been added to the section on Chess, describing a proposal for a revision of the Elo rating system.

In the section on unit conversions, I've now added information on the gold content of the British sovereign in addition to pre-1933 American coinage.

I have even sunk so low as to include a page describing a way of calculating lucky numbers to put in dream and number books!

A major revision has been made to the section on A Computer Architecture. This architecture began with several alternate modes of operation, distinguished by differences in the available addressing modes. The number of these modes of operation had increased over time, from about 16 to about 128.

Some time ago, with the introduction of a mode that conserved opcode space using a technique introduced on the SEL 32 computer, operating only on aligned operands in memory, and placing values in the unused least significant bits of address displacements to distinguish between data types, a number of these alternate modes, which were introduced in attempts to allocate opcode space preferentially to various types of instructions as might be most useful in different given types of programs, were obsoleted, and removed, as the result of this introduction.

A further refinement has now been achieved, which has made it appropriate to eliminate the feature of having alternate modes of operation with respect to the decoding of instructions. The addressing modes have been organized in a manner which, in addition to allowing nearly all types of instructions of reasonable frequency to be as short as possible, also organizes the different addressing formats such that determining the length of an instruction, and hence the space it occupies and the beginning of the next instruction, is considerably simplified as to do so no longer requires decoding the instruction completely.

Since this was done, a further relatively minor change has been made. A way was found to reduce the opcode space required for the shift instructions by half using a similar principle, and this has allowed replacing a set of 16-bit instructions for use of the scratchpad registers with a set of 16-bit memory-reference instructions.

While the scheme is not as simple as the original one of the IBM 360 computer (00: 16 bits, 01 or 10: 32 bits, 11: 48 bits) or that of the IBM 1401 computer (where a single bit in each character was used as a marker to indicate where instructions began), the simpification is considerable, and should be sufficient to allow the length of an instruction to be determined in a single cycle even under circumstances of extreme pipelining.

The page on the instruction formats of 16-bit and 32-bit computers now includes an updated chart of the instruction formats of the IBM 360 and its successors, up to and including z/Architecture.

The page about Color Charts now includes a comparison of several different color wheels, including the possibly obscure one of Hilare Hiler.

A page has been added to the section about a perfect computer, noting one way in which it might be practical to design one which would work with standard current memory parts. Also, a modification made has been made to the description of a proposed format for 48-bit floating-point numbers shown on the page about a perfect computer, along with a brief explanation of the rationale behind the precise choice of the length of the exponent field.

The page about the punched card has been extensively modified, with information on a number of older styles of punched cards added.

A new page has been added providing a simple explanation of Einstein's strange theory of Special Relativity.

The page Making Wargames More Complicated now includes one possible way to build a dungeon with random tiles representing sections that allows one basic card type to be used while avoiding dead ends except those intentionally placed on the cards, yet allowing a dungeon with a limited number of entrances. Also recently added is a new image of a grid in which a grid of octagons with small squares in the corners between them alternates with a hexagonal grid; the result is chequered using a somewhat complicated color scheme. As well, a page has been added to the section which it starts specifically addressing how to use three ordinary dice as a substitute for a 20-sided die.

The section on Unit Conversions now includes a page discussing the difficulties in specifying the sizes for the keys on a piano keyboard of standard size and shape, due to an apparent mathematical flaw in its conventional layout. It has also had a proposal for a metric inch of 2.52 centimeters and a metric pound of 453.6 grams, based on the idea that they would allow divisions into thirds (and, fortuitously, sevenths!) in even metric units, much as the day can still be divided into 27 parts which contain an integral number of seconds, the metric unit of time, added to it. Also, a discussion of the standard tournament sizes for boards for a number of different games has been added, as well as a note on the length measures of Barsoom.

The section on the musical scale now includes a mention of the Valotti and Kellner temperaments, as well as a temperament found by the research of Dr. Bradley Lehman.

A brief explanation of the system of vowel points used with Hebrew is given on this page.

I have now had the audacity to begin a page which describes how ASCII could be turned upside down to make the handling of Armenian and certain other languages somewhat more convenient.

The section of featured images now includes a brief mention of the format of player piano rolls.

The section on Aspect Ratios has had a note about and a diagram of the Super 16 and Ultra 16 film formats added.

The page about Keeping the Earth Solar Month in the discussion of a Martian Calendar has been updated with an illustration of a simplified calendar that maintains an approximate correspondence with both the month and the week on Earth.

A description of Rotating Spaceship Chess has been added to the bottom of this page.

A correction has been made to the unit widths for Times Roman on this page; as well, several recent additions have been made to the chart of unit widths: the widths for the Mid-Century face on the IBM Executive typewriter, those for Diablo 630 proportional-spacing printwheels, and the unit widths for several special forms of type made for easier setting of tabular matter by American Type Founders: Self-Spacing Type, Quick-Set Roman, and Typotabular Gothic No. 4.

On this page, I describe a board game which meets a number of desiderata for a board game that I had not previously seen how to fulfill all at once.

I have finally found the moves of the infamous repeated game of the 1863 world championship checkers match between Wyllie and Martins, and have illustrated that game move by move on this page.

A page on the game of Rithmomachy has been added to the site, this topic being a natural for this site, it being a complicated board game of a mathematical bent.

A page to remind people that before both Auction Bridge and Contract Bridge were invented, there really was another game that was called just plain Bridge (the one that is now called Russian Whist to avoid confusion). As well, most noticeably inspired by the Russian game of Vint, on a following page I describe what seems to me to be the next step in the evolution of Bridge, given the pattern of what has gone before: Siberian Semi-Contract Whist (or Bridge). And now I have added a simplified version of Bridge that requires six players.

A new chess variant, Antimatter Universe Chess, is now described wherein conventional chessmen may be used in a game which allows one to drop captured pieces on the board as in Shogi by having players control forces of opposing colors on the secondary board formed by the interior points of the chessboard. As well, a second additional chess variant is described here on this page, and a number of additional combinations have been added to Random Variant Chess.

Major additions have been made to the page about using the roll of three identical ordinary six-siced dice for a greater number of purposes in such applications as role-playing games.

On the page about the games of Chivalry and Camelot, descriptions of the game of King's Court (also known as Supercheckers) and of the Strand War Game have been added. As well, a page about Backgammon has been added.