checking your sums

20 07 2010

At the algebraic level, you can check your answer by substituting in your numerical answer for the unknown, and then finding out whether the left and the right side are equal, as initially proposed.

There are other, simpler examples of this process. Times tables. 4 x 8 is 32. How can you tell? Well:

1. it sounds right :)

2. 4 x 10 is 40, so two fours less than this is 32

3. count up in eights: 8, 16, 24, 32… the fourth item is 32

4. count up in fours: 4, 8, 12, 16, 20, 24, 28, 32… the eighth item is 32

Two different ways of getting the same answer suggests you’ve got the right answer. Like the general rule of thumb that if you find a fact in two “independent” sources, they greatly increase the chance of them being right.

This should be provable simply with Bayes’ Theorem.

One instance, me thinking there is another side to maths, simply makes it peculiar or unique. Two instances, and we have some validity, and so on. The jump from one to two is huge. This goes for a lot things. 2020worldpeace springs to mind…


time’s arrow

9 06 2010

Consider these things: time, arrows, questions.

I have already covered how questions induce a dynamic in the mind. Normally, the mind chases after the answer like a dog after a stick. Buddhism asks us to consider from where does the question come.

If one thinks of this in terms of time, a question tends to project into the future. It tends to accelerate us. Buddhism asks us to settle on the mind.

In terms of a simple diagram, an arrow, there is the head of the arrow and the base. Buddhism is interested in the base of the arrow.

So, these combine pretty simply. Normal physics, or any application of maths to the objective world, is located at the head-end of the arrow. It’s about the object of thought, it is about things out there. This demands a certain kind of methodology. When scientists attempt to poke around the mind as the object of thought, via psychology etc, they again use the same arrow-head methodology. It can be quite painful being treated as an object. Any patient will tell you that.

Buddhism, as a subjective science, is concerned with the internal processing of the mind as it is experienced by the mind itself. That is, from where does the question come from? It is not about the object of thought, but the conditions which give rise to it. This also demands a certain kind of methodology. One does not go presuming what it in another’s mind, with an arrow-head mentality. One invites others to consider their own mind. Without respect, there is no progress. It is not about fighting one another with arrow-heads, but to be as accurate as possible with one’s own experience so that a confrontation is one of subjectively evaluated truths. It is the examination of the creation of truth. It is dictated by sensitivity.

XQ is merely an exploration of maths in the arrow-base side of how our minds work. As opposed to the arrow-head side of applied mathematics.

So, where are you on the continuum? Where is the balance point? How often is your dynamic predicated on arrow-head mentality? How often on arrow-base?

breathing cycle

31 05 2010

I’ve had a few observations of breathing while conducting meditation. Whether one attends to breathing in, breathing out, or the turning point between them. The texts (eg Foundation of Mindfulness Sutra) generally emphasise the process of breathing in and breathing out, rather than the turning points.

I relate this to cyclic systems such as classic central heating, with boiler and pipes and radiators and thermostats. In the cycle of regulation, which do we emphasise? We can think that the thermostat is the deciding point, but it is merely responding to the temperature change brought about through the heating of the air via the metal of the radiators. Or the chicken and egg, which came first, or in terms of the individual or social when considering change dynamic.

It all depends on where one puts one’s mind in the process. Let’s relate this to counting.

Had a very interesting chat with Esther, and when exploring XQ’s side to counting as a thought experiment, Esther took ten or fifteen minutes to finally recognise that the answer was the first thing that popped into her head — but she dismissed it because it was so obvious. (I love that:)

If counting is something to do with our internal processes (not the sheep counted, but the processing in our head), as Phil outlined, there are two aspects: temporal and distinction. That is, time and mind. So, when we count, we count the difference between one and two and three, differentiated through time. Beat, rhythm, etc, the basis for music… the pattern in time. Hence the relationship of maths to music.

So, when it comes to counting breaths, do we count at the turning point of in-breath to out-breath, or out-breath to in-breath. In the cycle, which do we place the point of distinction from another round of the cycle?

This goes for breathing, as if goes for a lot of things. Consider any cycle, and consider the point which you hook the mind so that one unique cycle can be distinguished from any other. There’s a lot of space between the labels of the events, all of which are necessary and causal in the cycle. (Including cycles that are oppositional, from p to not-p. If we reinforce the not-p, we are conspiring a negative state, whereas if we reinforce the p, we are conspiring a positive state. When really, we need to do both. At least, that’s what the buddhist approach suggests.)

This may sound academic, but it isn’t. When people talk about reading from the same page, we’re talking about being in synch. XQ is in a completely opposite phase to standard application of maths. There’s no point trying to communicate XQ to someone who wants to remain in the phase of normal maths… it just won’t make sense. I wonder if Brian Rotman is going to make sense of this? I think I am approaching the time when a review of his book might be useful.

The simple take-away here is, breathing cycles and counting, and how mind distinguishes difference in time.

can it be simpler?

23 11 2009

I watched a TED video. The chap looked a bit geeky, and didn’t seem too accustomed to people listening to him. Krank-like, I guess. However, his name is David Deutsch and he’s highly respected in the multi-universe physics world. Anyway, he offered a solution to why science has worked since the 16th century (namely because there is low variation), and this definitely rings true. (In my language: not surprising, really, since science is rooted in objective reality, independent of our minds, so there is less variation in terms of interpretation as we hone in on a explanation that matches actuality.) Of course, his concern is with the multiple interpretations of quantuum physics within science itself, as well as the plethora of new-age assigned interpretations…

So, what about XQ and the subjective side of maths? Reasonable amount of intuitive guessing going on here: notions of negative and the mind’s filitering, or addition and category systems. These are speculative. Clearly.

My only answer to this, as I think about it now, is that the amount of variation increases the more complex the maths we deal with. It is like smoke from a stick of incense. Especially when we consider iterative equations, or Riemann Spheres. Seems to me, then, that the simplest thing is where we might meet with more subjective alignment. That is, as close the burning ember as possible. And in maths, that’s counting, isn’t it?

When we count, what exactly are we counting? It looks like we are counting things, however, if the things are fabrications of our mind, how we cloth actuality, then is this a self-referential exercise? We are counting things that are fabrications of our mind, and if mind is process, then at some level we are counting processes, we are counting in time. The real abstraction, our side of maths, is that we are counting in time, and not any thing out there. This is demonstrated in the way we learn our multiplication tables, through repetition of counting steps. (Extract from One Two Many, from the XQ booklets.)

So, is this something which strikes you as true? Or, are there other interpretations, apart from the obvious that we are counting things. And this is the root to our understanding why music holds its endless fascination for us…

Somehow the mind compiles a soundscape of the environment in terms of events. Subjectively speaking, we are particularly attuned to patterns of sound in time, from simple rhythms and melodies in music to the near chaotic jumble of words. Music elicits movement from our bodies, from the tapping of feet, the nodding of head, or the gyration of our hips. Certain melodies grab our passions, others lift us to sublime heights. It is as if we are the instrument, we resonate to the frequencies. We can also invest music with our memories, with rich associations, with specific events. We may link the music to the performance, the violent extraction of sound from the instrument or its gentle teasing, or it may be completely divorced from production. Our primary attention can be led to follow a particular continuity of sound, focussing on the melody for example, enabling us to predict what it to happen. Complex interactions within the soundscape can be simultaneously appreciated, thus deriving our deep affinity to music. (Extract from Haphazard Sensory Observations, from XQ Conditional).

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