Math

On or and its various incarnations

Well, starting from “Or” considered harmful. we noticed that the distinction of andor, xor and ewok is certainly a useful concept, however, the naming scheme leaves room for improvement. Andor is certainly too long for practical usage and ewok always raises associations to small furry creatures.

On the quest for appropriate names we thought that or certainly suffices for andor, just like (mathematical) logic tells us. Xor is short and pronounceable enough for everyday use and the meaning is clear with the usual knowledge of geeks. This leaves ewok. sh suggested eor, which may be interpreted as ewok-or. It does not sound too stupid, is short enough and thus quite usable.

The only challenge now is to switch my writing and talking habits over to those new words :-)

Nullity

Anyone ever heard of Nullity? A great new (well, about 10 years old, by now) mathematical concept (not to be confused with the other mathematical concept that goes by this name) invented by James Anderson that enables us to divide zero by itself. Along with this special "number" comes the so-called "Transreal arithmetic". So, basically Nullity is a special non-real number and defined as the result of 0 ÷ 0. It has been shown that it is also equal to 00 and 0 ⋅ ∞. The only real difference to existing concepts as NaN is that Nullity (Φ) is equal to itself, while NaN is not in standard IEEE floating point arithmetic. Apparently he even convinced a school to teach that concept and is building computers that use it. As for me, I have yet to encounter a final solution of 0 ÷ 0 and thus Φ to a problem. When dealing with limits, l'Hôspital usually takes care of that. And since most computations have their roots in maths I never encountered something that yielded NaN. Positive and negative infinity—sure, but no NaN. Furthermore, replacing NaN by Φ won't gain us anything, except for calling d.IsNullity() instead of d.IsNaN(). Just my two cents on this issue. Wikinews has a little more opinions on this.

Postscript 2D Vector Library

A while ago I tried writing a postscript function that draws flux lines for electric current or magnetic fields. While this still hasn't happened I wrote essentially all vector operations in 2D I could think of and those are collected in the attached file. Nothing too fance but as optimized as I could. All functions are bound, thus will be precompiled and use only stack operations, no dictionaries.

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