Paying It Forward : Infinite Nothingness

Posted by leo in April 28th, 2008

A person of my acquaintance has shown the unfortunate habit of demonstrating ignorance, both in the sense of not knowing something and in the one of (apparently) intentionally ignoring it.
flaming dog penis In particular, the willful ignorance of the definitions of both infinity and nothingness. He believes, as many of you do, that those two things are numbers and are also inverses of one another.

I tell you - and you will be able to understand (I hope) - that neither of those two defining statements is true.

Zero is not a number. It is a concept.

Infinity is not a number. It is a concept.

Numbers are used for counting things, and for putting them in order. Any other use may be convenient, but it does not have to do with the idea of “number” as such.

We grow up in the society of today, as we have for a couple to three or four hundred years, with the idea that “fractions” are numbers. We learn in our schools to talk about and think about - and even calculate about - such things as “half” of something, or “three quarters” of something else, and - worse, by far - “fifteen percent” or “0.15″ of yet another thing. Those of us whose education leads into more intensive arithmetic may learn to deal with other ideas that are clearly conceptual even though we learn to treat them as numbers - concepts such as “pi”.

None of these things is a number.

A “fraction”, as we are taught to call it, such as “one half” - or 1/2 as it is written when we look to its use in calculations - is not a number. It is in fact, and quite obviously at that, two numbers and a symbol, namely the numbers “1″ and “2″, and the symbol “/”. If we care to treat it as a single entity, we can call it a “ratio” - although in our modern usage, should we actually run into the idea of the ratio, we usually see the “/” symbol replaced with the “:” symbol, as in 1:2 - and it is specifically the ratio of one to two. If we’re dealing with calculation - which is the near-universal use of the thing, the idea of “half” rears its ugly head, and in the modern era of calculators and spreadsheet programs, it quickly transforms itself into the far worse “0.5″, which rather than being called “one half”, is far more generally called “point five” (less often, “zero point five”, and still less often, “five tenths”).

flaming dog penis Even worse, this whole idea of “fractionation”, once it has taken root as some sort of arithmetical operation, degenerates into the assertion that any “fraction” in which the second number is twice as large as the first one is “numerically” equivalent to “1/2″… for example “3/6″. This is, on its very face, completely absurd - no one can possibly believe that an apple divided into two pieces, each identified as “half an apple” and are ridiculously asserted to be identical, which they assuredly are not, are furthermore identically the same as any three pieces of another apple which has been divided into six “equal” pieces… let alone any 50 pieces of an apple divided into a hundred… and so on.

So, to return to that point: one (or 1) is a number; two (or 2) is a number. 1/2 is not a number - it is two numbers and a symbol denoting either comparison or fractionation (dividing).

And while multiple divisions of something may be “equivalent” - that is, the same in some ways - they are not and cannot be “identical” - at least, not insofar as we deal with reality. One half of an apple divided into two pieces is - in reality - obviously and clearly not identical to three sixths of another apple, even if the two apples are indistinguishably identical.

The very “operation” of division of something into parts - which is indicated by the two numbers and the symbol - leads directly to a very important conclusion regarding nothingness and infinity.

First of all, you cannot divide “nothing”, so it is obvious that the first number cannot be “zero” - another way of looking at this is to consider (as do the alleged mathematicians who write the text used in almost all “courses” of maths) that zero (”0″) divided by any number is mathematically identical to zero divided by any other number, and that value is zero; that is to say, regardless of how many pieces you attempt to fractionate zero into, you still have nothing… if you start with nothing, you end with nothing. This should be more or less intuitively obvious, since, if the primary use, or property, of a “number” is to count things or to put them in order, and since you can’t count or order “nothing”, why, nothing (zero, 0) cannot possibly be a number.

More later - I have errands to do.

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Jeff Said in April 29th, 2008 @7:52 am

This is very interesting, i recently ordered a book on the history of 0 but i am afraid it shipped to the wrong address. However, I was very fascinated by mention of the development of the concept of zero happening in different ways within different cultures. My primary interest in the concept is ontological and almost frighteningly binary. I am interested in the relationship between Being and Nothingness. 0 and 1.

What about the mathematical use of 0. It is typically used as a place holder, i.e .0009. I suppose this could be better referred to as a qualifier but none the less, how can something which represents nothing hold place or qualify? I may be babbling… looking forward to the next post.

leo Said in April 30th, 2008 @5:45 am

I’d be willing to bet the book is by the same person who wrote a history of “i” - the square root of -1… at least the users of this concept have the good grace to call it “imaginary”.

The relationship between Being and Nothingness (it’s been a loooong time since I read Sartre - and anyone who does so risks lack of “true understanding” unless he also inspects the circumstances of Sartre’s personal Being, i.e. massive manipulation of society in terms of War, Boom, Bust, More War, More Bust… it’s easy to see where living through such times would make anyone cynically bipolar) is - and this is my personal view, not Sartre’s - very simply the relationship between Self and Universe - which is One and which is Zero depends of course on which side of the sack of seawater is the viewpoint.

The ultimate dichotomy - Me and Everythingelse - turns out to be the Trinity once the Me discovers that Twoness automagically creates Threeness for the simple reason that differentiation between the One and the Other requires the existence of the mechanism of distinction, that is, in the specific case of Self and Universe that “edge”, which most take as being the outside layer of skin containing the seawater (although others recognize a field extending beyond the skinsack, and still others a series of fields).

In fact, once One removes the distinction from consideration, Everything becomes apparent, and (perhaps worse, or at least even more maddening) without distinction it turns out that Everything and Nothing are identical.

Well, enough of that… what about the “placeholderness” of Zero?

It is exactly that: a placeholder… NOT a “number”! It is used for the purpose of directing the operation of assemblage and disassemblage of things being counted or ordered. It is, in that sense, an operational instruction (don’t multiply, don’t divide) rather than a number.

This usage comes not from “number” itself, but from the representation of number in various forms. “Ten” is a good example, perhaps… in the Roman system of representation with which most of us are at least passingly familiar, “ten” is represented by the letter “X”; in the currently standardly used Decimal system (based on the number ten itself) using those symbols which we are pleased to call “Arabic” numerals, it is represented as “10″ - the instructions being “multiply one by ten, and no ones”. Using those same symbols, but in different systems of enumeration, “ten” in binary (based on two) is represented as “1010″ - “multiply one by two by two by two, don’t multiply two by two, multiply one by two, don’t multiply one by one; total these” - in Octal (base eight), as “12″ - multiply one by eight, multiply two by one; total these), and (perhaps worse) in Hexadecimal (base sixteen) simply as the letter “A” - “multiply ten by one”.

So, in representing the same Number (the word “Ten” itself is of course, again, a representation only) the symbol “0″ appears in two of the five (six if you count the “word” - and let’s not even talk about “zehn” or “dix” and the other several hundred words) and is used as an instruction to NOT take any multiples of a particular place’s numerical value.

Jeff Said in April 30th, 2008 @7:25 am

Ya, this 0 stuff makes sense and is interesting to read since it is not the typical path of my own thoughts.

You make an acute observation about the very fact that otherness implies a trinity. My own undereducated opinion of Sartre is that he grasped some incredibly important concepts and allowed them to become convoluted in his own elaboration. I do maintain a great appreciation for him however and in reference to the trinity, i agree from the perspective of a contemporary of Sartres, Merleau-Ponty, that existence implies a plurality. I am fascinated by the magick you mention, perhaps we will be able to discuss it a little at the next trivia night.