half a link

Submitted by danmc on Wed, 04/06/2005 - 09:33

In a universe of motion, motion is both continuous (a progression) and discrete. Because the discrete units are units of progression, the progression continues within the units of motion. Aside from the surface contradiction that motion is both continuous and discrete, I've always had a hard time with this notion. I'm hoping someone can shed some light.

Larson likens the situation with a chain.

Quote:
The absence of fractional links in the chain does not prevent us from identifying different parts of a link, or from utilizing fractions of a link for purposes such as measurement. For example, we can identify the midpoint of a link, and measure a distance of 10½ links, even though there are no half links in the chain. The same principles apply to the discrete units of scalar motion.

The situation with the chain is clear enough. We can identify a half a link because we can measure it. A fractional position is always relative to the length of the link. My question is, can we really do the same with a unit of motion? It seems to me that if we do, we are only once again in the position of merely spatializing motion. When we identify the progression as "being" at the midpoint of a unit, we are freezing the motion, halting it at some "spatial position", to make our identification, and violating the continuity of the progression.

We do this with everyday vectorial motion all the time. We say the trajectory of some object is at a specific point at a specific time, but that is an impossibility -- no matter how finely we slice up the instant to get at the object's position. If motion is a continuous whole, then it can never be measured at a precise location. The most we can say about its position at a given instant is that that is the location if would occupy if it came to a halt, or where it would be passing through at some instant. I feel like we have an analogous situation with regards to identifying a portion of a link: we are spatializing the motion and confusing it with some sort of abstract space we overlay it onto.

Forums:

Alluvion's picture

Alluvion

Wed, 04/06/2005 - 23:56

but again with fractions we are dividing a whole into parts of 'one' each - those one's are in a harmonic relationship when they constitute and even measurement to the whole, such as 1/8th or 5 16'ths, within a whole, an equal number of divisions can be made - the proportion of the 'parts' as units of 'one' constiute the 'whole'.

But even if we divide the chain into 5 parts, 4 of which are larger than the last, there measure's differ but they are still 'individual' portions of the link that constiutue the whole. One-ness (as in, unity) means all things as 'whole' unit(y)s. Working with architecture I get into proportional relationships as much as possible though current education doesn't focus nearly enough on it as I think it should. Architecture is itself paradoxial work - dividing space to connect it yet again. As is the statement that motion is continuous and discrete. Of course, frame of refence depends upon how one is going to apply conceptualized linguistic tags to events or experiences.

_A

danmc

Thu, 04/07/2005 - 08:27

great post

WarmSylph wrote:
but again with fractions we are dividing a whole into parts of 'one' each - those one's are in a harmonic relationship when they constitute and even measurement to the whole, such as 1/8th or 5 16'ths, within a whole, an equal number of divisions can be made - the proportion of the 'parts' as units of 'one' constiute the 'whole'.

I think I know what you are saying here, but, number theory aside, take a look at your experience of motion. Take your hand and move it from the left side of your desk to the right side. The first thing that is apparent is that it is all of one motion. No matter where I divide the motion I break it up, and I am no longer dealing with the whole motion any longer, but two or more discrete motions, the original motion is lost. I can divide the space over which I lay the motion, but can I treat the motion the same? Can I legitimately "spatialize" motion in the same way?

Take a musical scale, or a melody, if you'd rather. Each is a unit(ABCEFGA..., Jingle Bells) If i take a piece of it, divide it, stop it, I violate the unit (don't ever do that, it's painful...) -- a half a musical scale is not the scale, neither is half a melody the melody.

Now, I gather from what you're saying above, you would regard the relationships, the proportions of the parts, to be the whole. But then, you haven't done any dividing, you haven't taken merely one-half of the scale, but are regarding the parts in their entirety, their whole relationship.

WarmSylph wrote:
Working with architecture I get into proportional relationships as much as possible though current education doesn't focus nearly enough on it as I think it should. Architecture is itself paradoxial work - dividing space to connect it yet again. As is the statement that motion is continuous and discrete.

Sounds interesting. I'm a big fan of alchemical artworks where these kinds of things are important as well. Maybe we'll spin off a thread. And I agree to an extent, which is why I called it a "surface contradiction"; perhaps only seeming, depending on your reference frame.

Alluvion's picture

Alluvion

Thu, 04/07/2005 - 09:16

danmc wrote:
great post
WarmSylph wrote:
but again with fractions we are dividing a whole into parts of 'one' each - those one's are in a harmonic relationship when they constitute and even measurement to the whole, such as 1/8th or 5 16'ths, within a whole, an equal number of divisions can be made - the proportion of the 'parts' as units of 'one' constiute the 'whole'.

I think I know what you are saying here, but, number theory aside, take a look at your experience of motion. Take your hand and move it from the left side of your desk to the right side. The first thing that is apparent is that it is all of one motion.

>>>but that is your subjective definition of an act. What defines motions within a feild of motion? A change in motion. Stillness and motion are polemics but at some level they are both motion.

No matter where I divide the motion I break it up, and I am no longer dealing with the whole motion any longer, but two or more discrete motions, the original motion is lost.

>>>I completely disagree. Thats like saying by refracting white light and seeing the rainbow that the white light is somehow 'gone' - its not gone at all. Its been redefined or revealed as multidimensional. If motion is 'broken up' into moments what is really happening is that a single continuous act ( the birth of creation to the present moment in its infinite activation) is defined by beings as different in different ways. 'breaking' a duration of experience into moments is quantizing levels of experience but that means that you are only refining your 'eyes' for experience to a certain level. I beleive the fractiling holography of creature is apparent in experience as well - even Buddah was apt to say that year after year his learning would become deeper and deeper, the onion NEVER stops peeling. The question is how 'deep' you are willing to look, name, reconstitute etc.

But in anycase, that origional motion is still not 'lost' - it is redefined.

I can divide the space over which I lay the motion, but can I treat the motion the same?
>>>the only way to notice motion is a change in the motion relative to some other change in the motion. The mind is linguistic and so reads experiences in syntactic and semantic ways. Syntactic meaning is about organization and relationships, semantics is closer to symbology and concept. These are not polemical ideas but equaliy present and necessary ideas. Without syntactic intelligence evolution cannot occur. Without semantic intelligence there is nothing to evolve. I strongly beleive that division is still 'false seperation' - redefinition is simply changing the boundaries of qualities. You cannot divide space, you can 'rezone' it through your apprehension of its qualities and possibilities therein.

Can I legitimately "spatialize" motion in the same way?

>>>changes do have stages, stages and sequencing to me indicate some level of intelligence or awareness. You cannot really willfully do anything without some level of intelligence, so can you redefine and re'zone' your actions and motions? sure!

Take a musical scale, or a melody, if you'd rather. Each is a unit(ABCEFGA..., Jingle Bells) If i take a piece of it, divide it, stop it, I violate the unit (don't ever do that, it's painful...) -- a half a musical scale is not the scale, neither is half a melody the melody.

>>>this is true. But to me this is like the refraction of white light - you see all its constituent parts. And they are there to see, but not everyone sees them the same way - some cultures see only 3 colors and others, like american culture, sees into the infinite gradiations of color between the most prominent bands (which we are socialized to recognize as well). But I digress.

Musical scales are harmonic units, and if you removed the EFG from a an octave you've define a new set of notes but definately do not have a contextual octave. But that action of 'seperation' or revision depends upon the semantics of 'octave' which is a discrete unity of meaning. Other cultures may not define 'octave' in the same way, that is a possiblitity. However most music is standarized in this format and sharing that semantic meaning helps people share in objetive knowledge. Gamelan musicians in Bali however use instruments that create melody from tone and they don't use the same octave system we do, however we could probably investigate and pull out moments which are resonant with the harmonic unity of the 'octave' within their music.

Again I beleive the seat of this is mostly cultural. American's have eyes that look at 'things' and 'material' which to me is absolutely about discrete units. To contrast, the japanese culture has eyes which looks at the space between things, which is more architectural, and so more continuous. The concept of 'blank space' is absolutely false to the japanese but makes sense to most of the western world. So in considering things wholes, but not considering the wholeness of QUALITY or CONDITION, one runs into a semantic and later syntatic 'wall' in which the continuous and the discrete seem mutually exclusive.

Now, I gather from what you're saying above, you would regard the relationships, the proportions of the parts, to be the whole. But then, you haven't done any dividing, you haven't taken merely one-half of the scale, but are regarding the parts in their entirety, their whole relationship.

>>>exactley! even if you cut the link in half and had two seperate 'things' they would still constitute a whole when viewed in terms of that syntatic relationship. Another issue with the using the idea of a musical scale as opposed to a metal link is that a musical scale IS syntactic and doesn't operate at the semantic level. Individual notes 'mean' nothing alone, ever played a piano one note at a time without the tempo or rythm to link notes together? There is no narrative or emotion or evocation. There is just sound and sensation. However, an octave places notes and sets of notes in relationships to eachother and that syntactic construction allows the discrete moments to be viewed along a continuum. As such, a continum of frequencies is organized into discrete units along the scale - vice and versa.

WarmSylph wrote:
Working with architecture I get into proportional relationships as much as possible though current education doesn't focus nearly enough on it as I think it should. Architecture is itself paradoxial work - dividing space to connect it yet again. As is the statement that motion is continuous and discrete.

Sounds interesting. I'm a big fan of alchemical artworks where these kinds of things are important as well. Maybe we'll spin off a thread. And I agree to an extent, which is why I called it a "surface contradiction"; perhaps only seeming, depending on your reference frame.

precisely. How 'deep' are you willing to look and how 'deep' CAN you look? Wide vision suggests a large but shallow scope of vision or knowledge, deep vision suggest a more specific but intensely intimate scope of vision or knowledeg. The real work is to balance quantity (wide) with quality (deep).

_+A

Alluvion's picture

Alluvion

Thu, 04/07/2005 - 09:22

continuous reading of my desktop:

Low, curving cermic and glass holds salty tuna and shiny bent metal casting shadows near elongated plastic which clicks and slides.

discrete reading of my desktop:

a bowl with tuna and a fork near the keyboard.

the first statement is about qualities, sensations and conditions. The second is about objects. Depending on the level of semantic and syntatic 'deepness' one reads with these statment can become either highly polarized in meaning or incredibly similar.

_A

bperet's picture

bperet

Thu, 04/07/2005 - 15:05

Don't forget to consider your "origins" -- and I mean that more than one way. The only way to find the center of a chain link, is to know the exact locations of its boundaries and bisect.

Larson's chain analogy is a reference that the "origin" of measurement, in the natural reference system, is at Unity -- the point where two links touch -- and is the only absolute measurement. Without the boundary, you cannot subdivide at all. Thus the "discrete" nature of motion. The chain moves continuously, but the units are the only measurable boundary.

Perhaps you can look at the chain as a sine wave, Y=sin(X). The points where Y=0 are the discrete unit boundaries, yet I can interpolate any value inbetween, because I have the origin of measurement.

The yang and yin principles work the same way. The yang are the points where links touch; Y=0. The yin are the infinite series of points between; Y0.

Now I can also integrate the sine function and end up with the cosine -- still has zero crossings but now they are where the yin series has reached minimum and maximum values, and what was a fixed, yang function is now part of the infinite yin series.

In its very basic projection, you are looking at the point-plane dichotomy of space-counterspace relationships. Points are fixed yang; planes are infinite yin. They are compliments (inverses) of each other. The essence of duality.

danmc

Fri, 04/08/2005 - 11:49

Quote:
but that is your subjective definition of an act

No, there's nothing intellectual about it, it's a simple perception of a simple act. Obviously, all perception has a subjective component, but I'm not defining anything, I'm simply perceiving the motion. And what arises directly from the perception, and NOT from a theory about the perception, is that it is all of one piece. The idea that it can be taken apart and reconstituted merely stems from a theory or idea we conceive after we move away from the perception. Goethe, the scientist of quality if there ever was one, used to stay, "Stay with the phenomena" for this very reason.

Quote:
Stillness and motion are polemics but at some level they are both motion.

Yes, in a universe of motion, the only kind of stillness that can exist is a simulated one.

Quote:
Musical scales are harmonic units, and if you removed the EFG from a an octave you've define a new set of notes but definitely do not have a contextual octave.

That's the nut of it, right there. You do define a new set of notes, and those notes in isolation are not the octave. Similarly, the whole motion of your hand from A to B is the context, it is the "harmonic unit", the "octave". When we divide that whole motion, that context is lost in that it's not to be found in the isolated divisions. This is not the same thing as saying that it disappears from experience altogether.

In a universe of motion, the motion of that universe and its contents are the same thing, much like the octave and its contents are the same thing. You can't take the contents out of a universe of motion or you have no universe, or whatever it is you have, it not a universe of motion. Similarly, you can't take out the EFG from the octave for the same reasons.

We've covered a lot of ground in a short time, and brought in issues that, though valid and useful, and certainly applicable, have muddied the water somewhat. Let me restate my original concern. Is it legitimate to treat, or transpose motion as length, to "spatialize" it? When we move our attention from the unity of a melody to the notes it contains, we are no longer with the melody. We've stepped away from it. The melody can only be "understood" if we stay in its whole motion from "start to finish".

When we treat motion as length we are saying that it consists in nothing but the positions we identify. This isn't true of a melody or a unit of motion. The positions aren't part of the unit, but only the space, real or imagined, we overlay it onto. Now, it may be that when Larson says half a unit doesn't exist, but that we can identify it for purposes of measurement, we can let it go at that. Close enough for government work. But I think we need to realize at all times that it does not represent reality.

One last comment on this go around. When you say "the seat of this is mostly cultural", the point is not lost on me, but I think it can go too far in the other direction and suffer from the same defect. One culture may indeed see three colors and another a thousand, but the fact that both perceive color at all is lost. I bring this up to point out that certain considerations do cross cultural "boundaries". Obviously, again, the cultural aspects are important, and it would be silly to try to divorce them completely, but how the fact of lifting my arm, or moving my hand across my desk and seeing it a whole thing is tied to my socialization, escapes me. We are moving away from the phenomenon and what arises from our direct perception of it, and into theories about the origins of why I see it that way. To turn the phrase in another direction, sometimes a cigar is just a cigar.

danmc

Fri, 04/08/2005 - 15:31

My problem isn't so much with finding a point inside the unit. I feel there is an error creeping in, if not conceptually, than at least philosophically, when we substitute points for motion, spatialize motion, as I said in other posts. I keep reaching for analogies since it's kind of a subtle point, almost an inversion of the normal view. In a race between runners we only care about the points labelled "start" and "finish". What happens in the interval is irrelevant. A runner may stumble, decide to do the race on his hands, whatever. As far as our interest in who wins the race, the motion is a non-issue, only the two points matter.

We are in some way doing the same when we reduce the continuous motion inside a unit to a series of positions, as if a unit of motion were somehow an immobile container for the motion that takes place within. It assumes the unit of motion can be infinitely divided, yet less then one unit cannot exist. Even if this is going to far, that Larson doesn't contend less than one unit exists, we can't contend that it is possible to "locate" motion in this way, i.e. that the motion is now "here" at the halfway point. I don't see how this could be gauged.