contemplating zero

16 09 2011

Reading Douglas Harding’s The Science of the 1st Person, has certainly been reaffirming, and challenging. He definitely plays around with zero, nothing, the no-thing that is the person. He interprets this as “no head” or “headless”. Quite amusing. He alternates this appreciation with two-way looking, at the object out there and the no-object in here. This seems to reflect the notion of a cambium layer, the event horizon of self.

Simply, he is absolutely affirmative that there is nothing inside. This is rather nice. It echoes the experience I had when I was high for three years, that state that was self-sustaining. It is all about engagement with the world, and the engagement is the world. And so the individual is freed from the prison-interpretation that the I is trapped inside the body, and the world is out there, and all I can do is respond to sensations, electrical impulses and the like that the body generates. Nope, not at all, says Harding. The world is engagement, the world is the head, not a meaty thing. Nice. Definitely recommend the book.

Right, to math! He talks about the science of the 1st person, appreciation of no-thing inside, works perfectly or not at all, says Harding. The (non)experience of no-thing is the same for everyone, and hence the science of the subjective first person is actually the only objective thing that can be determined. But consider bananas: their DNA might be identical, but each banana is still quite distinct. So, is this not the case with us? I also have the notion of zero, the end of the psycho-social continuum ending in each of us, and yet because of its similar quality, fathoming one’s own nothing is tantamount to fathoming anyone else’s.

It comes down to how we use zero. 0 as in “no beans on the counter”, 0 as “no millions, no thousands, no hundreds, perhaps even no units. That is, zero as a marker for “none” in terms of place value.

Contrast this with, 0 as in “the absence of any number” or even, “the absence of anything and everything”. That is, the void.

As we know, in actuality, there is no such thing as nothing. Or at least, what we thought of as empty space, isn’t. I am not sure what is going on in an atom, the “space” between electrons”, but I suspect we are injecting our sense of “nothing” into these “spaces”.

So, this causes me to reflect on whether we actually use “zero” in anything other than the first way, as a marker for place value. We never come close to the actual (actual?) meaning of void. And here we encounter the buddhist sense of void, and indeed, I have suggested that mind is effectively the absence of matter, the stuff of mind is “negative”. Indeed, we thought of negative numbers as being purely mental, and that -7 meant “not 7” rather than the additional concept of “opposite” to positive.

That is, if we are going to conduct appliedXQ, which is to say, if we are to consider XQ seriously with application to our lives, then comprehension of zero is essential. Not just in the guess we have made about infinitesimals as buddhist perform a kind of calculus on their subjective experience, as time tends to zero, but in terms of performing mathematical calculations with the deep appreciation of zero as void.

One of the attempts by mathematicians to rationalise maths was to ground counting in set theory. They do this funny thing, which I can’t quite get my head around. They talk about the empty set, then the empty set as a thing — that’s one. Then the empty set and one — that’s two. Now the empty set, one and two — that’s three, and so on. It’s a bit weird.

But as far as I can understand it, 0, or the empty set, is not a number. 1 is a number, and 2 is a number, they are the same sort of thing. The 2 in 201 is similar to the 1. Two apples are suggesting the apples are the same, ignoring the fact that they are different, slightly different flavours etc; we are just drawing attention to their distinctness, their unique thingness. Just like the 0 in 201, that there are no apples. Not that there is no anything, just no apples. So, 0 can be considered a number, when it is used like a digit like other numbers. But when is it ever used as the absence of everything? Ie, a non-number?

What does it mean when we add the absence of anything? Or we multiply by the absence of anything? Or we multiply to the power of the absense of everything? This gives some sense, ironically, not to the absence, but to the function. With addition, the absence of everything doesn’t change a thing. With multiplication, the absence of everything nullifies whatever value it touches. Multiplication is like the black hole function when associated with the absence of everything. And with indices, the answer is 1, always one, a number, the only number, the whole, perhaps even “everything”.

Does this give us an insight into what multiplication means subjectively speaking? Like when we multiply -6 by -1 we get +6, a state change, something we have suggested earlier is involved in our mental processes: if we master the “multiplication by -1” it doesn’t matter what value of negative we encounter, we can convert it immediately with the same function, to its positive. That is, we can turn any apparently disadvantageous situation into an advantageous one.

So, what does multiplication by 0 mean? Neutralising whatever is good or bad? Meditation? But meditation we have surmised is calculus, as time tends to zero. Hmmm, when we look at how Newton invented his calculus, he used multiplication by a fluxion, or a number which tended to zero. This was ironed out of the explanation later, and we adopted Leibnitz’s interpretation I think, because Newton’s fluxion was eventually used to divide things, and as we know, we can’t divide by zero. That’s interesting, now… we can’t divide by zero…

Ok, let’s say that the inner state of being is the zero state. We can multiply concepts, insights, beliefs, visions, whatever consists of the substance of the mind by zero. We can perform this function of multiplication, we can apply the zero state to our substance of mind. And by doing so… we realise the empty state of mind? That everything we thing and so, is actually empty, void? That makes some kind of sense. Can this turn out to be “therapeutic”? Can we apply this function, when we are actually performing maths, and it has an equivalent resonance at other levels of our thinking? 7 x 0 is… 37 x 0 is… 6,431,407 x 0 is… Meditate on this. Or rather contemplate this, in your mind, as you sit and have objects of thought. Imagine seven apples, and applying the function of multiplication as an application of the void that is self. Or, the obverse, from these considerations, the effect of multiplication by zero, come to an appreciation of the empty state of self, of zero itself.

Following closely, contemplate an object of thought, a feeling, a sensation, and apply the function of division, of separation, of analysis, of parts to it. Into no parts, into the absence of any parts. Well, clearly, we can’t. We can’t divide a thing into no parts. Well, if we did, it should be just the one part, itself… one? Or, if we apply mind as void to it… what does this mean? What light does this cast on the mental process of division? That is, can not be done? What can not be done in the mind? An object of the mind can not be divided by the empty state of mind. To divide, requires something. Requires discernment, requires categories. And hence the mind that is empty, the core of the being that is void, can not be used to divide, to analyse, to consider the parts of any mental object, or perception, or sense? Does this make sense?

And what might be the practical, appliedXQ, exercise here? It is like a koan. 7/0. 37/0. x/0. Observing the mind’s… neutrality, or stillness.

Another way of thinking about divide is to share. So we share 8 sweets between two people and they get 4 each. We share 7 things between absolutely no people… hmmm, no… There are other ways of thinking about division, and one of them means that numbers divided by zero become infinite. Divide a chocolate block with 8 knobs into two parts; each part will have 4 knobs. Divide it into four parts and each will have 2 knobs. The less number of parts you divide it into, the more knobs. Dividing by a fraction, produces more. The chocolate bar divided into 1/2 knobs can be shared by 16 people.

There is a massive difference between a number, however small it might be, and zero, in this sense of absolute nothing, absence, void.

What this may mean for powers, I don’t know. It is another country! Mandelbrot land, me thinks.

When we apply the state of void to numbers in an “addition” or “subtraction” way, we get no change. When we apply the state of void to numbers in a “multiplication” way, we get the void. And when we apply the state of void to numbers in a “division” way, we can’t… or I have a vgue recollection that if you do, we get infinity.

Definitely related to the reimann sphere.

Briefly, repetition of a function, multiplication by constant, will make a value get bigger or smaller, stretch towards infinity, or approach zero. But they never reach “infinity” whatever that means, and they never reach “zero” as the absence of everything. The numbers will be finitely large, and finitely small. The leap to “infinite” or “zero” is a step change. They are not numbers. However, when we multiply by zero, bang, we have the step change. And if we divide, by symmetry, bang, we have the step change of infinity, whatever that is.

Oh look, no-state — bang we have 1, a thing separate from void, number. Then we can see we have no-state, and 1, the thing separate, that’s 2 — and like an unzipping we get 3 (no-state, 1 and 2). All because of the mistake of thinking of zero a number. If it is not a number, we can settle on being aware of no-state. 1 and 0. Something being aware of nothing, without it incrementing.

Which really brings out the comparison of addition and multiplication. What are the mental versions of this? Repeated addition is multiplication. 2+2+2+2 is 2×4 = 8. 2 added to itself x times, 2x or for some reason i’d like to write x2, would be infinite too. And x3 would be a larger number than x2. Counting up in tens, x10, normally written n10 (or 10n) as n increases.

2 added to itself 4 times is 2×4 = 8. 2 added to itself no times is 2×0 = 0. 2 added to itself once is 2×1 = 2. Or shouldn’t that be, 2 added to itself once is 2+2 = 4. This is a language mistake. 2 added to itself 4 times is 2 +2+2+2+2 = 10. That is, we have the original 2 to count in. So, multiplication doesn’t count its original. It changes it. Adding 2 doesn’t change the original value. Multiplying does. Or we could say that multiplication implicitly contains a zero to start with in terms of addition. My that’s ugly. But all that means is 2×4 means 0 +2+2+2+2 = 8.

And of course, multiplication means perform the same addition function. Just like when we count two apples, we are saying they are the same. So, we are saying +2 is the same. When of course, we know that 2+2 is quite different than 100+2.

So, continuing the ante-previous paragraph, the reason why multiplication by 0 end up with zero is because that is what is assumed we start with. The function 2×4 is more correctly (+2) done four times. It is not the number 2 that is manipulated, but the function of +2, add 2. That’s pretty smart. So if we multiply a function of +x by zero, if we perform the +x function no times, then clearly, we have nothing.

But we already knew this, of course…. the trick is applying… reflecting on what the processes that are going on in our heads, not so much in the maths…

Multipling by -1 means performing a function of +x negative one times. Or better, performing a function of -x (ie a “bad” thing) negative one times. Performing a function of a bad thing precisely not once. Performing a “bad thought” precisely “not once”. Performing “bad thinking” precisely “not once”. Performing “a thought that is going in the wrong direction” precisely in the “opposite direction”.

Multiplying by negative one is precisely the operation of the mind’s capacity to be oppositional. So, if the direction of a thought is going towards zero, ie has negative alignment, ie is aiming to self, multiplying by -1 means be oppositional, and turn the negative alignment into a positive one, ie aiming out to the world. hmm, not that it should be battered back like a tennis ball, at the zelf, zero, that is the other person. No, one doesn’t aim. One reverses, into the world. It would take the other person to see this as something which is directed at them, negatively. Hmmm, is this why buddhist wisdom is knife-edged? It can be taken “negatively”. Or why, when encountering a person who is “nothing”, all you can see is what is “reflected” back at you.

Hmmm, this is a lot… we veered too much off our course. Making a little progress towards the subjective appreciation of addition as contrasting multiplication. Oh, and counting is just the simple case of multiplication on the +1 function. Or rather, just repeated +1 function. Addition is wider ranging phenomena, eg +5+7 = +12. When we are adding things that are not similar. And another thing: we can count holes, but these are like counting discrete items, eg not7 and not5 is not12. This is quite different that void, the absense of all things.

Wait a mo. The void of things, that’s like the interpretion of negative numbers as not. The void of self is zero.

Interpreting multiplication as repeated addition, repeated function +x or -x, zero times, ie by not repeating it. Leave the flower to do its flower thing. No need to think about it. Name it. Colour it. Event appreciate it. Because, the body does that anyway. No need for mind to re-present, or repeat. No need to count. Multiplication by zero negates addition or subtraction. Nullifies.

That’s pretty simple. That’s rather neat. The judicial application of “not”.

Applying repetition oppositionally in mind, is to create a version of a thing in mind. Seeing 7 and thinking -7. Or Seeing a thing, and thinking the bad version of it. Or thinking the opposite of it. Not so good. Misapplication of x-1. The correct application of mind, of x-1, to repeat once in opposition, or precisely not once, is on the mind itself, turning a -7 into a 7. Seeing a bad thing, and thinking the better version of it.

I really need to get in touch with this zero, subjectively speaking, for me to be able to apply it as zero repetitions, or the extreme form of apply precisely never. To eg itch, so that it is nullified, no action follows. I have been using the force of my mind. And after a few days of negating itch, I eventually break, and I end up scratching terribly. The trick is not negation, but nullifying. In this case. And this is effortless if it is “employing” the absolute zero.





2 responses

16 09 2011

I followed that! It was great. This is how we should all think about maths…

20 09 2011

i can’t believe it :) really, it is like a still white water ride

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