Latest New Additions

I have reinvented a scheme to allow the orientations of spaceships in a three-dimensional space battle game to be kept track of, while allowing only relatively simple orientations to keep the complexity of the resulting board game almost within reason. This is the latest addition to the section on making games more complicated, which has been split into several pages, and which now includes a rather elaborate scheme for a more realistic kind of stock market game. Also, if games are going to have a world-wide scope, shouldn't they acknowledge that the world is round? An illustration suggests one way to do this.

A page has been added to the site describing the Parker Brothers game which was the personal favorite of George S. Parker, and which had received glowing testimonials from experts in Chess, Checkers, and Bridge, including one from José Raoul Capablanca. Also, a very brief page with a few facts about alternate forms of Go has been added, and it has been joined by a page about Checkers which has just recently been updated to include a description of the eleven-man ballot in addition to full descriptions of the two-move restriction and the three-move restriction, and another page which deals with Ming Mang, Alea Evangelii, and Gess.

The brief description of the DEC Alpha instruction formats has been moved to this page after the Motorola 88000 was added to this section.

The page on computer front panels was been expanded and divided into several pages some time ago. Most recently, two pages (of which this is the first) have been added for the front panels of several computers from DEC, a minicomputer company that produced machines with particularly stylish and friendly front panels. New Addition: that page has been rounded out with the front panel of the KI-10 chassis of the PDP-10. Earlier, three pages were added to deal with the IBM System/360 alone, one of which deals with the least well-known front panel within the IBM System/360 series, the front panel of the IBM System/360 Model 85 computer, as part of a series of pages covering the front panels of all the System/360 models. (New Addition: these pages are rounded out with diagrams of the front panels of the Model 20 and Model 25, and alternate front panels for the Model 44 and the Model 50.)

My second attempt at a tall building design is now present on this site on this page, and some additional material has been added to this page about building blocks and the Pythagorean Triangle as well.

A page within the section on unit conversions has now had added to it a suggestion for slightly changing the length of the inch in order for it to serve a very useful purpose in complementing the metric system; this same page also recently had a bit more information added to it about the old definition of the metre in terms of the red line of Cadmium; this is partly due to a mystery concerning the definition of the Potrzebie by Donald E. Knuth.

A new page in the section on Chess concerns Dynamic Scoring, a proposal inspired by the successful adoption of komidashi in the game of Go, for adjusting the way Chess games are scored in such a way as to motivate both players to play less defensively and more aggressively. Why this proposal might have a chance of being effective, if suitably adjusted, is illustrated with a graph and with a discussion based on game theory.

Also, the page on Random Variant Chess has been updated by the addition of a revision which maintains the normal secured position of the castled King, in line with the nature of most historical enlarged chess variants.

Also, a two-page section about Hexagonal Chess has been added to this web site, and a page about using more of the regular Chessboard for a new game has also been added as well as another page about a modification of the board for three-player chess. Previously, a page had been added to the section on chess describing a few of the traditional forms of chess, and a further page deals with Tsiu Shogi, Timur's Chess, Courier Chess, and Hiashatar. For Qiguo Xiangqi, however, you need to go here.

A section illustrating, briefly, the advantages of a 36-bit word for a computer with presumed ideal sizes for floating-point numbers is added. Afterwards, exploring other possible ways of providing floating-point numbers of those sizes, I mentioned the possibility of using a 45-bit word on that page, but on the next page, I went into more detail about a possible computer architecture that manages to fit into 12-bit and 24-bit instructions the same type of operations that I had used 16-bit and 32-bit instructions for elsewhere. The principle used there was applied to Mixed Operation Mode in the main illustrative computer srchitecture as well. (New Addition: Flexible Register Mode has been added to the modes of operation described, and also Short Memory Reference Mode. More recently, also building on the same principle, I have added Full Opcode Short Memory Reference Short Shift Mode.)

In how many ways can the numbers from 1 through 9 be arranged, each number occurring only once, in a 3x3 square, so that whenever a number is above or to the left of another number, it is also less than that other number?

The answer to this question is one you may already know. This question is important because, as it happens, there is a connection between the series of the numbers of NxN Young's tableaux and the moments of the Riemann zeta function. And the Riemann zeta function is very important in mathematics, because it is a link between number theory and analysis. Could that make this question important enough to actually be...

the great question of life, the Universe, and everything?

(Yes, that's the answer!)

Is this: The Mandelbrot Function a major (or minor) mathematical discovery, or did someone already think of this particular view of the Mandelbrot set?

The page on the assignment statement in my description of an unimplemented computer programming language now includes a feature taken from Python, an assignment of components of the value of an expression to multiple separate individual items on the left-hand side of the assignment. And here, I go after Python's crown jewel, the dictionary type; but in a form suitable to a statically-allocated language like old-style FORTRAN.

The section on color filter array designs includes some possibilities based on hexagonal grids.

In the section on calendars, a page has been added on the Mayan calendar; as well, corrections have been made to the perpetual calendars for its Tzolkin component on the perpetual calendar page, and the correspondence between the Haab calendar and the vague year of ancient Egypt has been corrected on the page about the Julian Day. Also, they said it couldn't be done! A luni-solar calendar that is as uniform as the World Calendar! Well, almost. You have one 14-month calendar that you always use...but you need a table to tell you whether you're currently using the whole calendar, or just the first nine months, whether this year has 13 months or 12, and, consequently, also which month is which.

The page about eyepieces has a chart of eyepiece fields of view added, and has also received a few minor updates; correct glass type colors are now present for the six-element Erfle, and a diagram of the Type 2 Nagler is added.

A series of pages has been added on the dialects of FORTRAN over the years, but these pages are not yet complete.

My page on signal flags has had a minor addition: flags used in automobile racing have been added to one illustration.

A page illustrating the Equation of Time has now been added to the site!

My pages on keyboards have recently been changed: the page on large keyboards has added a diagram of the so-called Space Cadet keyboard, as well as one of the keyboard from Symbolics that succeeded it; and on a later page, I include this image:

of one famous keyboard from another major computer manufacturer. (New Addition: images of two Japanese keyboard arrangements.)

My pages on pentagonal tilings have finally been updated with a drawing of the tiling found on the Darb-e-Imam mosque referred to in the paper by Peter J. Lu in Science recently.

In addition, the page on heptagonal tilings now finally includes a substitution tiling, based on rhombs, that closely resembles quasicrystalline rhomb tilings made based on the grid method (also known as dualization).

The page on decimal representations, which had included a description of IBM's Densely Packed Decimal number format, has now been split into three pages; both Chen-Ho encoding and Densely Packed Decimal are described on the next page, and, in addition, a description on the decimal floating-point format added to the new z9 mainframes from IBM which uses the Densely Packed Decimal encoding is now present on another added page. Instructions that follow the "ideal exponent" rules used with this type, but with one of the existing types in the architecture have been added on this page, and on that page as well, a correction to the description of unnormalized multiply and divide instructions has been made, so that they will not cause unnecessary loss of significance in their results. Instructions to handle this new format itself are now added on this page. One of the uses to which this format has been put is to carry out targeted arithmetic, a capability inspired by the instruction set of the Naval Ordnance Research Computer built by IBM for the U.S. Navy.

The preceding page on floating-point formats adds the floating-point formats of the Stanford S-1 computer and the Univac 418 computer, and also now includes a brief note on the various names for the two fields of a floating point number most often called the "exponent" and "mantissa" that have been used over time (principally because the term "mantissa", although very familiar, is, for reasons noted on that page, something of a misnomer). (New Addition: the original floating-point format of the HP 3000 computer.)

Featured Images

A conformal map of the world, in two hemispheres, using a conic conformal projection for each hemisphere instead of the Stereographic, is illustrated below:

Being conformal, so that small sections of a detailed world map can serve as maps of the localities within it, and keeping the distortion of areas fairly low, this seems to me to be a map projection eminently suitable for use in wall maps and in atlases.

The number of interruptions is also limited; the world is divided into two hemispheres, and each hemisphere is cut along one line since each one is projected using a conical projection instead of an azimuthal projection.

Other new items now added to the section on map projections are: the section on the Mercator projection has had the illustration of an oblique Mercator for use in depicting the Americas improved; the section on the Mollweide projection now also includes an illustration of the Wagner IV projection; the section on the Globular projection now includes Nell's Globular projection as well as Nicolosi's, the section on the Lagrange Conformal projection illustrates how the central part of that projection might be used for maps of small areas somewhat larger in one direction than the other, the section on the Hammer-Aitoff projection now also includes an illustration of the Wagner VII projection, as well as an illustration of how the principle behind the Oxford projection can be applied to projections such as the Aitoff Equal-Area projection, and how the central part of the Hammer-Aitoff projection might be used for maps of small areas somewhat larger in one direction than the other, and the section on the Winkel Tripel projection includes that projection in its original form, rather than merely illustrating Bartholemew's variant of it.

Further additions now include a modified form of the van der Grinten projection, and the Fahey projection. And now, I have added an interrupted form of the Van der Grinten IV projection! (New Addition: minor changes and additions to the pages on the van der Grinten, Mercator, and Lagrange Conformal projections.)

Copyright (c) 2008 John J. G. Savard