A new impenetrable mathematical basis http://www.alansondheim.org/qbasic-27.jpg http://www.alansondheim.org/qbasic-28.jpg Consider a number system to the base e: "The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828" ... (Wikipedia). The first position to the left of the decimal point equals 0 to what? Let's say to 0 to e minus what? Let's say to e - pi/e. The basic concept is to have everything irrational. The next column would be what? Not e^2, but e^e certainly. So we need symbols which are inherently fuzzy, no? A mess, no? The 3rd column would be what? Perhaps e^e^e? Bringing pi into play creates jumps. Where does the e - pi/e come into play? Of course e^e^e begins to grow out of hand. We want everything in this model to be fuzzy, irrational. Of course there is also the issue of positions, 1st, 2nd, 3rd, etc., 1, 2, 3, a, b, c etc. Let's have the positions also irrational. So the first would be e, the second would be e^e etc. So there's no second position, only e, e^e, e^e^e, etc. Now it's getting tangled and I'm way off base, literally. If we permit integers, of course it's easier: the first position would go to e-1, the second to e^2-1, and so forth. So integers appear through the back door. We've got to keep the integers out. Too few of them! And this is wildly out of sync with the concept. So let's say the positions themselves are irrational, the columns are irrational, and the integers simply have no place in this. Something to lose sleep over. I've hardly had any (sleep) that is, and I'm being irrational. But there are so many more irrationals as you know than the integers! So with all their clumsiness, they infinitely dominate the bases, however unwieldy they appear. Think of them as efflorescences, wild numbers. They buzz infinitely. From their viewpoint, the integers and natural numbers for that matter are anything but natural - perhaps regular anomalies, isolated rarities would be a better way to think of them. It's the other side of the coin of the world. A mathematician far more learned than I am should take over now, and work out the details: remember, a number system within which the integers and zero, positive and negative, appear nowhere at all. (Forget e/e for example; e - e and so forth, a form of cheating which will simply not be tolerated here. --------- images from qbasic fractal walk programs, maybe around 1994. Section 11 of The inadequate, a philosophical testament full text at http://www.alansondheim.org/inadequate.txt _______________________________________________ NetBehaviour mailing list NetBehaviour@lists.netbehaviour.org https://lists.netbehaviour.org/mailman/listinfo/netbehaviour
