let’s talk about time, baby :) pt1 :s

21 09 2010

Just watched Caroll’s video on his arrow of time. A lot of thoughts popped up, and plenty of them are rather… abrasive. Sorry. Put it down to polemics and my defensive condition as I recuperate here in Madeira.

Before launching into them, one self-observation. Talking about time is like just about anyone talking about education — and boy, did I get miffed listening to every man and his dog expound their theories about education without checking out valuing my experience. after all, going into school as an adult is different. Anyway, I am sure caroll’ gets all manner of kooks coming up theories, and he’d be right in saying we are mostly crackpots… the one thing he has that we don’t is the hard reality of the equations. Because he has made a job of it, his interpretations are based on them. We don’t have to worry about correspondence with the math. The interesting balance point, of course, just like in education, is that the institution isn’t working as well as it should. that is, the equations only work so far… Hence, Caroll is guessing… and only once some one of these physics egg-heads guesses right, or some computer ai chap more likely IMHO, and gets a remarkable, undeniable result, that the world will change. It’s not going to come out of a blog, neither in the writing or reading, however excited we monkeys get with our objects of thought. Given this apology, this monkey can’t help but chase the rabbit a bit.

He contends that physical reality has boundary, eg table – not table. This is actually a boundary we impose with mind. There is continuity from table to air, you know, how atoms substitute into embedded molecules at the boundary of their materials…? In exchange, the idea of boundaries in time… perhaps more like limits, maybe like the outer boundary bubble distending in so ace of our first radio signals on this planet… I think they are somewhere past the solar system, but who knows how far… the next solar system? Anyhow, boundaries in time… interesting kernel of thought to be explored sometime.

Clock, the bit in a cycle which is marked, eg the “klok” sound when a bell is struck.

“Biorhythms are not very good clocks.” What a clueless comment, as if an objective timer is the way to measure time! A human scaled timer at that! We are inside the biological clock — this will influence the perception of it, clearly. Parallel this to Einstein talking about being in a rocket and his relativity theories. We must start with the obvious, that we are in a clock as we are inside our bodies. After all, we are in actuality, rather than this rather absurd academic position of being “objective”.

“Time has a direction.” After poo-pooing biology, he then sets up past and future (delightfully omitting present), which clearly involves us, as the cutting point in time.

His arrows point in a rather strange way. He presents young Elvis on the left, an arrow pointing to the right, and an old Elvis. So, Elvis was moving left to right, as he got older? When, intuitively for us westerners, we tend to think of old people as being from the past, somehow. Hmmm… something interesting going on here in terms of diagrammatic representation… and you would have thought this would be covered in the talk — I know Brian would be interested in this (as a passing comment, no doubt). It’s to do with whether we think we are moving or time is passing us; definitely something about relativity again.

Here’s the big one: entropy. I have several problems with this concept. First, an insight: life appears to go in the opposite direction if entropy… is that wrong thinking on my part? It complexities, it traps energy into forms, the whole planet is creating molecules and structures and altering matter due to the off-shed heat from the sun. Perhaps it doesn’t go opposite, it just reduces the rate of entropy… is that more correct? You see, I don’t like the concept.

He applies it to life and death! And memory! And cause and effect — this one I will grant him, but only for simple billiard ball like situations. Hasn’t chaos theory penetrated physics yet?

(How does entropy as second law of thermodynamics compare to laws of subjective reality, like the dreaded law of attraction? I equated attraction to gravity initially, but it may be better opposed to entropy since gravity is also dissipative. I know that involves a few twists, but I can’t be bothered entangling myself in the pop-culture…)

Wrt the planet, we absorb one photon and emit 20, which means there is a dissipative effect. (This makes no sense to me as I review my notes.) We are far from equilibrium. That’s what a boundary sets up, a differential. He states that equilibrium means no change. Browniam motion? He is not talking about zero Kelvin, so, given a stable energy mix, there’s no… movement?

My main problem is that entropy sounds a bit too much like flogiston. I know that entropy is better embedded in maths and concepts, but… I remain skeptical, and here’s why. Maybe it is just a word thing. A glass of mixed coffee and milk is high entropy, whereas the separated materials glass is low entropy… which seems to go against something in my head about high boundary, or potential for change, like electricity. Ie, far from equilibrium indicates a high value. Whereas, entropy seems to be describing a state as it approaches zero.

But finally, an explanation. Blotzmann’s definition, about the potential for translation/transivity/movement at a lower level of scale. Scale?! (I think we are getting our first glimmer of emergent levels here…) It is also dependent on a zero-sum game: in a closed system, like a glass, the milk and coffee will mix. (Hmmm… to complicate things, isn’t a cell an attempt to create a kind of closed system? And of course, it is not.)

So, Carrol posits that entropy was lower yesterday, and so on. (Reads so strangely for me: low entropy, when it means it was more bounded/separated/had more potential.) He goes all the way to the big bang. (Typical linear thinking again. Finite and closed system.)

But this bit is good: time’s arrow is the aftermath of an influential event. That is almost clear! It was when I heard it first, but when I write about it now, I can’t think but it is another typically western revamping of old ideas, to justify a book sale, to justify a life in academia. I mean, they have to come up with something to justify their jobs… (Cynical I know, but always in the back of my head is that remark that medieval academics used to argue about how many angels could fit on the head of a pin. I think we are living during such times, and especially in the field of physics with its ancient and venerated history.)

Here’s my most interesting interpretation of his material which still holds for his statement, the aftermath of an event. He is talking about birth. And not just in the life-time blood and pain sense, but in the Buddhist sense of origination-dissolution occurring presently. Forget about all these words here, they are more for me to make notes, to externalise and in so doing I remember — check out his explanation and try mapping it to your understanding of consciousness. It does seem to hold some water, and this isn’t even a third of the way through — it gets better!

10^-8 ergs per cubic cm. 73% of the universe. In “empty space”. (Sooooo linear… and I don’t mean in terms of maths, I mean in terms of thinking. I am always skeptical of such claims about the universe. Science always consists of people being certain, only to find they were wrong, or at least completely inaccurate. Happens big time in physics with newton-Einstein, and innumerable times in biology, eg evolution. Surely we should be sophisticated enough to stop making ludicrous claims about the universe when we can’t even determine scientifically that we are pissing our own backyard and f**king the environment?)

He also mentions that black holes evaporate. Yup.

Notice his pointing out where we are in terms of big bang to dissipated high entropy end of universe model. Looks rather like the Mind-drop solution, with the higher and lower boundaries of ego. I thought this was funny. What do others make of this, if they are trying to map their understanding of consciousness to this talk? 41-43 mins happens to be a fine explanation of consciousness emerging and disappearing (my notes are vague: does this refer to present conditioning consciousness or the bubbling of adult self-reflection through adolescence?).

Man… this goes on… I will deal with the rest in a second part if I can be bothered. I am not sure how useful this post is. It has some pointers, but is mostly a commentary on a lecture, and I don’t go into enough detail to explain. As I mentioned before, it is more for me. Apologies to readers.

lakoff and nunez’s 4 G’s

15 09 2010

Very interesting reading, this Where Mathematics Comes From, but there is a whiff of smoke and mirrors, as I shall draw attention to towards the end. But first, what are their 4 G’s. They are the metaphoric mappings they have constructed to explain arithmetic, namely:

  • object collection – how piles of things behave
  • object construction – how things are composed of parts
  • measuring stick – a comparative standard
  • motion along a path – how things, including ourselves, move in space
  • Brilliant, I have to say. Very useful I would have thought in terms of teaching. Simple explanations as to how to make sense of the magic that is numbers and arithmetic.

    I have six/seven observations about the first section which takes up the first quarter of the book, and mostly regarding the all important third chapter.

    First, the language of “grounding metaphors”. There is some confusion as to the “direction” of this metaphor. It sounds like the abstract arithmetic is grounded metaphorically in physical systems. But this is clarified on page 101: the physical experience is the basis from which the metaphor projects into arithmetic. That is, from “sensory-motor” they call it to abstraction of number system. This may appear pedantic, but it reveals something about the active intent of lakoff and Nunez; think Reflexive Imposition here: their thinking is influencing the thing they are thinking about, rather forcefully.

    Second, for us to be playing around with piles and measuring sticks and the rest of it, there must be a mind to make sense of it. L&N don’t examine this, for this is the direction of Buddhism. They present mind’s rather splendid ability to shift piles and manipulate wholes and parts a priori, and use this to explain the jump to maths. Nowhere in this is an understanding, or even an explanation as to how we do these things in the first place. Academically, at least, this is an interesting if not peculiar position — not that their exercise is thus invalidated, for actually, I think this represents the self-referential and self-enclosed nature of explanation that this realm entails. Indeed, I think it supports the methodology I have set out with XQ.

    Third, as an explanation of arithmetic, including the metaphoric interpretations to 0 and 1, it fulfills the operational standard of science: it explains the mysteries of the mind with our understanding of things. Definitely a lot less crude than slapping electrical nodes onto the skulls of buddhists to attempt to divine the effects of meditation, but nevertheless, still a little clumsy in attempting to push our objective thinking into the subtleties of our conscious condition. Neat as it is, and useful to, it is the same as the instructions you’d find on a tin of paint.

    (This is coming across as being more scathing than when first these thoughts came to me. I suspect it is to do with the medium of writing, and the association of exaggeration that written polemic induces. I think L&N are brilliant in their exposition. I need to show the limitations of their western methodology. And the more convincing it appears, and indeed useful it is, the more we must be vigilant that we do not get seduced by this way of thinking; after all, as westerners steeped in scientific methodology, we are the most susceptible to it.)

    Fourth, L&N talk of the grounding domain as “forming collections”, “putting objects together”, “using measuring sticks” and “moving through space”. These are all processes. Again, requiring mind to perform them. It sounded like it was grounded in things, in motor-sensory experience, but really, it is all process. Thus, the metaphoric mapping they are producing is rather sophisticated, equivalent IMHO to the complex mapping of functions that is calculus.

    Which leads me to the fifth observation: their list of simple cognitive capacities on page 51 equate to arithmetic, but their additional cognitive capacities on page 52 equate to algebra; that is, the ability to use symbols or representations, that is, words. It would be wise for us to be aware that L&N may appear to start simple and then go into more complex fields, as is the want of a standard scientific text book, but they have actually begun at rather sophisticated levels to start with. After all, these are not high school teachers, but university academics at the bleeding edge of cognitive psychology.

    Which leads further to my sixth observation — what do you think of their final sentence to their first section on page 103?

  • We are now in a position to move from basic arithmetic to more sophisticated mathematics.
  • XQ may start with arithmetic too, but the direction of greater… subtlety… is towards counting. That is, it is not about creating a foundation of understanding, as L&N put forth so enticingly, but rather to intuit interpretations of internal processing in one’s own mind. And the simpler it is, the deeper it’s operation in mind, and the calmer the mind of the subjectivity needs to be. The direction of genuine inquiry in this direction, in terms of examining the mental processes involved in mathematics, is characterized by simplicity and sensitivity.

    It all makes for interesting reading, for sure. And I suspect that their explanations will appear in my mind while I continue with my XQ exploration. Indeed, they can’t fail to because they are now in my mind because I’ve their their book! Nevertheless, there is a striking validity to their contributions; I’d just like to approach them from the inside, as it were.

    Finally, almost like their commentary on the metaphors for 0 and 1, a few small points:

  • motion on a path refers to time — a topic blaringly omitted from a serious academic text that purports to examine the processing of mind, tut
  • the measuring stick is the minimal artificial mechanism, actually probably after the tally sticks; the first virtualizations of our ability to notice patterns in space-time
  • object construction is related to wholeness, to completeness, something which is central to a way of thnking that comes naturally to us human beings, thus giving rise to part and fractions
  • object collection relates to our granular way of comprehending actuality, as sums of wholes likes apples, say
  • Thus, the 4G’s are not like the three laws of subjective reality, something which we can depend upon no matter what thoughts and ideas we navigate in our intellectual endeavours, but more a useful constellation of terms and concepts to help us explain, or even describe, how to do arithmetic well. After all, all kids have these experiences, and what better way than make the shift of abstraction to number and arithmetic than through their direct experience?

    The book is shaping up to show more about how Lakoff and Nunez think about the world, or rather reveal about their thinking processes, than it might about mind, consciousness and mathematics. Interesting not only for L&N, but as an indicator of current scientific progress in this realm.

    Pi as a period of time

    1 09 2010

    This is a bit of a revelation. And I read this revelation from a book. I have started to real Lakoff and Nunez book, Where Mathematics Comes From. It was given to me by Leon for my trip to Maderia; I intend to spend the rest of my thinking life exploring XQ and this is a good start.

    I was reading with a certain trepidation: what if these guys have explored the space already, more rigourously and comprehensively than my meandering and intuitive forays? That would make XQ an incidental eccentricity destined for obscurity… But it is also relieving to know that hard-core academics are exploring the space.

    I read the preface and the introduction with interest. Some big claims, the abstract universality of mathematics as purely embodied in the human experience. I also benefited from reading Leon’s written commentary, such as his exploration as to mapping his notion of stance to a mathematical framework. What caught my attention was their new interpretation of Euler’s remarkable equation, e^Pi*i = -1. So I turned to that section of the book, the final section.

    Very interesting. It made clear how their use of metaphor works. I remember noting that mathematics used metaphor, and exemplified it with pointing out that a graph was a metaphor. They use it rather more precisely, stating that an angle is metaphorically described by a number. That is, as far as I can tell, they use metaphor to describe a mapping of anything to number. That is measure is a metaphor.

    Anyhow… in their explanation of what they call the Unit Circle Blend, they combine simple circle in Euclidean space with Cartesian co-ordinates, with enumerated angle, with Pythagoras theory. It is simple and beautiful. They then follow this with The Trigonometry Metaphor, and thereby map length of side a to the function of cos theta, and length of side b to the function of sine theta. And on page 397 state:

    Where Pi was previously only the ratio of the circumference of a circle to it’s diameter, 2Pi now becomes a measure of periodicity for recurrent phenomena, with Pi as the measure of half a period. This is a new idea: a new meaning for Pi.

    Actually, it is a new meaning for me! Not only does this give my query as to the significance of special numbers such as Pi new material to think about, it might even shed some significant light on Euler’s equation and the “shape” of consciousness!

    That is, if some young genius studying AI were to come across these guys and combine it with the jump I have made with XQ… and maybe another piece out there…

    Honestly, Pi as a period of time. Wow. That’s huge. At least in my mind. Thanks Lakoff and Nunez :)

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