But this seems wound up with division by zero and how communicate it in hypertext. Want to buy calligraphy and guide programs. ...Undivision is the horizontal energy in concert with vertical energy.
Division is the horizontal energy. When not divided, in concert with vertical energy. That's the difference between the horizontal line, y=0 slope is defined but the line x=0 slope is undefined is not divided.
(Written while taking notes on math books--page 57 of intermediate math book.). What we try to do is something like 0^2 is a point. Then divide by the point and redefine point operations with great similarity to i. That way maybe our notation could be a dot after the number when there are typesetting problems. And after we have done what we do, we must rigorously test it in every way possible to determine if any of the reasons for the commandment (not to divide by zero) have been violated. So in the course of creating our /0, if we don't succeed, at least we will have learned a lot about the reason for the commandment. But if we can't find any reason not to do what we propose doing, we still much contend with the religious aspect of the commandment. Art we just rationalizing a transgression? Zen may come to our aid. We cannot stop the mind from thoughts, but we can become detached from them. Maybe from the point of view of detachment...which is not really a point of view. Being non-attached, perhaps we can allow the validity and usefulness of the thoughts to manifest.
Why do we want to do it? For Art's sake. Having an MFA, the artist is probably my biggest protagonist. I thought she was dead when the technologist manifested. But becoming the tech writer already compromised my position. I guess the artist's problem was that there didn't seem to be any art that had not been done for art's sake. Or there didn't seem to be anything worth doing for art's sake. But finding a way around the commandment, n/0 seems a worthwhile blend of the artist and the techie. Do it for the sake of technology (still unanswered why we need it). Do it for art's sake. The Zen of dividing by zero has been very well maintained, hasn't it? This needs thought and maybe more references. Relate to ri (ref?) 10. Keep quality undefined is the secret. Q is closed for all division that is defined..
Notes while looking at the calculus book (Ref #4), page 365 when discussing "determinate forms": How do the terms "undefined, indeterminant, and meaningless" relate? 0/0 qualifies for all three. Does it make sense to add infinities when you can't divide zeros? 0-0 is OK though.
With respect to page 527: A good note for another study on the implications of hyperbolic orbits. Maybe the solution is the curved space. "If the line y=k+(b/a)(x-h) is to be an asymptote to the hyperbola, then the difference of the y-values of a point on the hyperbola and a point on the asymptote must approach zero as x becomes infinite."
In general: Approaching zero is very important in calculus. The result that has been divided by zero will be approaching even closer, but it will be different from zero in a different way...not an imaginary way, not a real way, simply a conceptual or metaphysical way. When
Page 37 of the Zen scripture is a good quote of /0 state from zen experience. We can count it, or be aware of it.
Z/0. Need to name a new set of numbers that includes /0. I have thought about this before but can't remember if I found a name . point numbers. eie numbers. holonumbers. hypernumbers. the hyperset the hyperNumbers. and the hyperplane. no, we can draw the plane, yes but if hypernumbers are 0 dimensional (real are 1 dimension on number line, complex are 2 in plane) then they can't be drawn on a plane.
Working on trig book notes. It might be said that the one fact that zero is undefined causes an extremely strict and time-consuming necessity to define every occurrence of that possibility, thus resulting in a great deal of secondary definition. This should be one of my main theses: by defining /0, what would it do to math? At first thought, we would think that we need to say not to do it and emphasize not doing it because it is so important in our teaching. Estimate % of time teaching and problem work is absorbed with nondivision necessities.
The hypernumbers are the set that includes the null numbers and complex numbers. Null numbers are defined as follows. a/0=circle a. O o how do the complex numbers relate? What about the case when b/0 and i/0? This must be addressed.
Look into that Hacker font that looked like it had circles around each number . otherwise do have to circle whole expressions? What is the alternative? To circle each individual number of an expression? And furthermore, can an expression consist of /0 mixed with complex...no, because there are no operations possible with /0 numbers. So what happens when /0 comes up? Go through math notes and show how each case will now be taught, explained, shown, proved, and demonstrated.
Working on z/0 notes from math books. It looks like keeping 0 undefined is doing secret service in rigorously defining all of our math and algebra. It is an enormous crutch. I'm not going to get away with disposing of it easily.
Making a Venn diagram showing how the null number set fits into all numbers and relates to the other sets.
A terrific problem has just surfaced. Here I have numbers to 10, nicely circled. But if I wanted (120)/0, Romanagen, o great math poet, can you help me? (I just saw a 1 hour Nova TV program about this math genius who died so young.) I have the feeling that the point can be factored out of anything divided by zero, so it can go free. But I know there can be no operations...so how can we work it out. Do like they do for limits. Play tricks. So what is harder..to encircle whole huge expressions which happen to get undivided--or to work on tricks to avoid the situation and divide something easy to represent by zero, such as numbers 0-9 or the point, by zero? On the other hand, the true representation is the whole thing and any other representation would be false. And as far as the assymtote, it won't appear any differently. So, maybe we can invent another notation, just as one lie breeds another. Anything more than 10 can be...no, simpler, just a graphic solution, we could bubble terms or grey them.
z/0. Is there some point to be made? That it is our right hand that is associated with words, division etc. (left hand politics, sinister, female) whereas it is the right brain associated with intuition, art etc. and the left brain that is male, structure etc. The cross-over, the twist. Somehow this is related. If only by the corpus callosum of integration. Some research into brain research may yield clues.
Now z/0, I'm working on the number line. Problems come up-- when 0/0 at the first moment it looks like circle 0, then it looks like circle point. This is a very interesting area of investigation.
--When do it as coordinates, 0 and circle point are vied for the origin position.
--Then on the plane, numbers divisible by one are mixed with indivisible numbers. Such as -1-circle1. Even having a -circle 1 looks like you are starting to do operations on it. Like factoring out the -1. Just have to realize can't operate on it. So I may just keep it as a null number line which never can be plotted on a plane.
z/0. Going into pre-calculus algebra book I came upon an important point: definition of /0 allows practical interpretation of assymtotes. See page 225 of Ref #9. When the assymptote is reached defines the practical limit of this equation in the real world as we know it today.
However, preservation of the equation allows it to be applied to other worlds, or other times when for some reason this practical limit is extended. For this use, we would have to have a record of the smallest amount existing before zero was reached. So along with the circled amount, the last value is recorded. I guess this is impure mathematics. This is applied mathematics. We need to make the numbers infintely powerful, so as never to limit our potential or the universes.
But this illumines the nature of zen too. How zen insists on no definition, yet is emminently practical. Is this a duality? A paradox? Is it strange that something should be ultimately lofty and ultimately practical at once? So it is only when we find that ex. 13 on p 225 is defining numbers of something, such as x=apples and y=number of worms. That the size of the worm would be the determining factor...no this isn't true. The equation doesn't speak of size, except maybe in the constants. With number of worms, the limits (are they limits) would be number of worms fitting in any apple. This could be estimated and would be dependent on size estimate of largest size worm and largest size apple. So we would write circle((2x-3)/((x^2)-9)), (this would be the value(s) of x where the worms wouldn't fit). Should the equation be located by date and place as well? Everything in math seems to lead to the ridiculous.
Conclusion of the morning is that assymptotes are very interesting, but tangential to our topic. Assymtotes just exist, but it seems they exist for more reasons than /0 not being defined.
Later: found on p55 of Calculus book that three different functions can have the same graph with the exception of x=3 (in one case is undefined, another is not equal to the point on the line, another x does equal 3 and limit is 3) in the first case, we could say circle (f(x)=(x^3-1)/(x-1)),x=3 Also need to restudy limits. Because do they have anything to do with the discussion above of practical applied reasons. ?? I may put this item in "Show", subject to assertaining its usefulness.
When talk about definition, in integration, use these notes which were written 3/1/88 when taking notes on math books. In Ref # 3 page 30 "...we assume that x>=0 because otherwise sq.rt.(x) (also sq.rt.(x^5))is not defined". On page 129 imaginary numbers get defined. So a mathematics writer is able to say the sq.rt. of -1 is undefined, while in another part of the book, does defining it. This inspires an important thought. ./0 can stay undefined. Yet we can define it conceptually for the set of conceptual numbers. Another thought: /0 might just be part of the imaginary numbers.
/0 decision. Is inf/inf same as 0/0 = point? It may still be meaningless because infinities can be larger or smaller with respect to each other, but still indeterminantly so. However this method is used to figure asymptotes.
Working on /0. Trying to find the last letter of the Hebrew alphabet. Found in my journal 4/21/80 in reading the Keys of Enoch by Jim Hurtak, near page 189 alpha and omega in Hebrew is aleph and Tav. It is drawn but can't relate to my fonts. See key 306 key of resurrection, an omega minus function. Need this book as a reference.
Hypercard and z/0: one journal entry, from 5/28/82. I can't understand. I will repeat it here, but I'm leaving it out of the book. I have this obligation to guidance to do the best I can to transmit the raw stuff for others. But this doesn't fit with anything true. There must be something missing. What is
is the diff betw a # and zero. If something = 0 the whole thing can be sphere wholed.( x^2 + 2y +4 = 0) all circled arrow circle 0. another formula is circle (x^2 + y)(arrow circle 2) = 0. Can write x^2 + y = 0 as circle 0 = 2. Sorry, I'm as Eliz says...clueless. As I say, in Gaza.
One fantastic inconsistency I think is that 0! =1 whereas 0^(any nonzero number) is 0. I believe the first subject of integration will be an assemblage of the troublesome oddities of zero as a number. Get these together with my zero point and my consciousness symbol (sphere whole symbol) somehow. God it looks hard today!
The practical test for whether need operations and to be able to come back from being divided, can be determined by going through list of undefinitions using the definition and see how the need comes up.
Math thoughts. I struggle with infinities. There seem to be two ways of getting small. One is going towards zero, or nothing, between one and zero is one way of diminishing, where you can never get there. We do not define a totally nothingness number other than zero and we can always make up a tiny decimal. The other way of diminishing is towards negative infinity. These also are smaller and smaller numbers which I can always make a smaller one and never get to the infinitely smallest. But the negative numbers are very tricky. In terms of wavelengths they form a continuous scale of getting smaller. In terms of dBm signal also.
But in terms of debt, having to pay back $2 is greater than paying back $1. In this sense I was going to take the symmetrical sense of numbers to make zero an end point. This is a very interesting field right here. I have identified two categories of negative numbers. One is where the negative number is continuously smaller than zero. The other where the numbers fold about zero and the numbers get larger as they recede from zero in either direction.
The second category could be visualized as the positive number line. Each number has two faces, itself and its opposite. To the right these pairs of numbers extend to infinity--the infinitely large. To the left these pairs of numbers extend toward zero, which is the lack of magnitude. This is very consonant with Fuller's synergy. A vector is equal to a number, the opposite vector is no less a vector., Also he finds an inherent twoness in primary manifestation.
There is a word for a sound chamber, I have seen at Watkins-Johnson, like anechoic. Also, in the folding of the number line there is a beauty of the reconciling of opposites, here is where zen comes in. And simply the corpus callosum and the getting together of the two sides of our brain. Male and female union. It is when opposites are seen as parts of one whole, union. This is symbolic of our political struggles. Them and us. East and west. US and Russia.
It may be appropriate to designate two infinities, one outward and the other inwards towards zero. The thought comes, however...heh heh. with Einstein's curved space. In reality, there may be no infinities. Inward, we experience the absolute, state of being undivided. To define is to be able to move another step towards an infinite. To leave undefined is...wishy washy. To posit an absolute nothing is theoretical head trip also. Nothing can be verified (listen to the double entendres of that).
It is my belief that there is an undivided state. It can be isolated here and there. A dot on a graph, an asymptote. If large numbers eventually curve back to small and small numbers eventually become undivided. There are no infinities, actually.
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