wow ... i am saving this.
again - it is useful information form music.
repeat: for me p is a beautiful number.
H G Lundahl wrote: I have sometimes seen two men together or three or four - but never pi men or e men. Same goes for animals or plants. And actually for minerals too, since even if you divide them, you do not get fractions of them, but the divided parts count as new wholes. What IS it that can be numbered by pi? Measures? Certainly they can be related by pi, but measure is not concerned with number, rather with sizes in unitary things. Pi does not answer the question "how many?" but rather the question "how much more than?" in a proportional matter. It is and remains a size relation, not a number.
Hans Georg Lundahl
I begin to understand...
I wish I did...;(
H G Lundahl wrote: "Omnia disposuisti numero pondere et mensura."
The Psalmist praises God for having disposed everything in number weight and measure. If modern mathematics were right in saying weight and measure are simply numbers, it would go "in number, number and number" - which is ridiculous. A half isn't a number, it's a size relation if you mean half as big, a weight relation if you mean half as heavy (and that's the most likely place for half a loaf, though it would be half as big as well) and a number relation if you mean half as many: which may mean any number, as long as you are comparing it to the number twice itself. Whatever can be counted for the sake of counting, and not just as an alternative to weighing or measuring, is counted as wholes and therefore in whole numbers - and that's what the Greeks and any sensible man first and foremost means by number, and that's why pi cannot count as a number. But I've never denied it's beautiful.
Hans Georg Lundahl
Thank you Hans.I do not understand all of the math involved, but the Greeks were reasonable were they not?And the psalmist was right to praise God as well...
H G Lundahl wrote: The psalmist certainly was right, as he was inspired by the Holy Ghost.
And the Greeks were reasonable - like reasonable enough to know that size and number are two different kinds of quantity, that some relations can be taken over from number relations to size relations, but some size relations obviously cannot be reduced to number relations. The number relation 3 10/70 (22:7) they knew to be greater than pi, the number relation 3 10/71 to be smaller than pi. They didn't bother about standardising fractions to decimal fractions, but if you work it out you will see that both are just a little above 3.14 but way low below 3.15.
- 3.140845=3 10/71 ancient lower limit approx
- 3.14159.pi, modern five decimal accurate approximation
- 3.142856=3 10/70 anc. higher limit approx
Whatever fraction you use, it will be higher or lower.
Hans Georg Lundahl
If the Greeks were so reasonable so long ago, in their understanding of things, what do you supposed has happened to propigate so much ignorance, or rather, semantics, in the generations after them?
Enlightenment? (so called)
My answer - so far:
According to a source cited in writings of Lyndon La Rouche, he seems to have been an occultist. CSL noted, although he didn't go as far as calling the first modern scientists magicians, that science (in the modern sense) and magic were born in the same area and time, more or less. Bacon of Verulam ("scientist", though he made no discoveries) and Pico della Mirandola (definitely magician, whether in practise or only in theory) shared the same goals. Only the methods differred. If the source "Discovering Newton" is correct, Newton went from one method to another.
Newton made mathematics - irrespective of whether he meant arithmetic or geometry - the new foundation of science and he remodelled the definitions of mathematics (if Voice Of Principle is correct) changing even the definition of number, it seems. Perhaps he was tainted by magic experience of numerology? Perhaps he thought equations done with algebraic fictions wouldn't work unless he called the fictions facts? As a matter of fact they do. There is no need whatsoever to call zero, negatives, irrational size relations numbers to understand them or deal with them. But in magic (remember the Pythagoreans were reputedly magicians) it is thought vital to touch the essence of the matter, and essence is thought to reside in, amongst other things, number. So, if science was to reach the goal of changing human conditions, of making its practitioners the high and mighty benefactors of mankind, it might have been thought vital to call as many things as possible number and as few things as possible - ideally none - fictions. That's when one starts calling pi a number rather than a size relation and 0 a number rather than a fiction and -3 a "number lower than zero" rather than a relation between numbers, showing by how many (3) one number is lower than another (-).
Hans Georg Lundahl
pi, e, the square roots of all numbers, decimals, fractions, the square roots of negative numbers ... just to name a few are included in my mathematics as numbers. ...
Were you just calling e a number? Make a coordinate system. Plot a curve getting above horizon in x=1, which everywhere has the direction coordinates 1:x and therefore in this point the angle 45 dgr, but which changes angle at every point getting flatter and flatter. Now where y=1, x=e. Add the y for x=3 (where direction coordinate is 1:3) to the y for x=4, you will get the y for x=12. That is what natural logarithms are. Are we agreed so far? Good. We were using the words coordinate system, curve, angle - are these arithmetic things or geometric? Are these numbers or figures, dimensions? In my mathematics they are figures (curve) and dimensions (y=height, x=length). Is e:1 a number proportion or a size proportion? In my mathematics it is obviously a size proportion.
Was I saying earlier on that e is no number? Yes. Was I saying it was no size or size relation either? No. Was I saying that a logarithm, having no arithmetic existence nevertheless has a geometric existence? Yes. Was I right on all these points? Yes, thank you.
one could argue that pi is what it is because God wanted us to think and not make it easy.
Pi is no difficult: it is the size relation between perimetre (circumference) and diametre of a circle. It is greater than a 3:1 relation, and than a relation of 223:71, but smaller than a 22:7 relation, greater than 31,415:10,000, smaller than 31,416:10,000. And so on. It is greater or smaller than any given ratio, any given number to number relation. It is irrational and a size relation without any real correspondence in arithmetic.
at one level all things in the universe are illusion and what we perceive as reality is based on ideas we have not on hard evidence - is the reality of a cup that you just put down still a cup or the image of a cup?
Your believing that is one of the bad things that come with believing all sizes to be numbers, all size relations to be numeric relations or even all relations of whatever quantity to be numbers.
If believing all is illusion gives your mind quiet, it is not the soundest mind. True peace has nothing to do with illusion or believing truth to be such.