Tensegrity is a special kind of structure made of push and pull.
This page is not for the faint of heart, since it will probably come across as somewhere between very speculative and quite insane. On the other hand, this kind of extreme challenge to the imagination might lead to a very new and interesting insights into the nature of pretenst structure.
There’s something about building a virtual model which is very educational, since the software builder is challenged to make the model behave in plausible and natural-seeming ways, while knowing that behind the scenes there are only numbers to represent everything.
The pretenst model is one in which time sweeps across the software objects in a very specific stepwise manner. This is so that no parts of the tensegrity get any kind of priority over others. From the model’s point of view, everything happens simultaneously to all elements.
The force that each interval applies to the two joints at either of its ends depends on the difference between the length that the interval “wants” to have (the length it would have if it were completely alone) and the length that it currently has (the pythagorean distance between its two joints at the moment).
The word “interval” was chosen to describe the relationships between two joints specifically to widen the scope of what we might consider it to be. It’s intentionally ambiguous, because it could be an interval in space or and interval in time. Now that we’re going to imagine relativistic tensegrity, we should start to imagine an interval more as an interval in time.
As we have known for more than a century now, there is an inherent speed in the universe which we call the speed of light. That means when we think in terms of this speed, we can always talk about distance using units of time. For example a nanosecond is equal to almost exactly 30 centimeters.
Here things start to get very strange and uncomfortable. As mentioned above, intervals express themselves as the difference between the length they want to be, or maybe we can say the length that they think they are, as compared to the length that they are forced to be due to the circumstances of being caught inside of a tensegrity structure under pretension.
What would that mean in terms of time? To grasp this idea we have to imagine a kind of light-signal being sent from one end to the other of an interval. If the interval is 30cm long, for example, the signal has a nanosecond to get across. Suppose that the frequency of the light is 1 gigahertz, because that would result in a wavelength of this very same 30cm.
What we then might imagine is a standing wave of light that has frequency 1Ghz which somehow creates an interval of 30cm. Let’s say that the frequency of the interval is 1Ghz because it wants to be 30cm long.
Now let’s take this same idea and add the idea of pretension. Starting with a compression interval, we have a situation where the interval actually experiences its ends to be too close to each other relative to what it wants. That would mean that a signal sent from one end to the other of a compression interval would arrive a bit too early.
Now pretenst structures must involve the interplay between tension and compression, so looking at the case of a tension interval we have to conclude that a signal sent from one end to the other will arrive slightly later than expected.
Now joints are the places where the intervals come together, and every step of the way as the model iterates, their job is to try and keep in balance. If the sum of forces add up to a vector pointing in some direction, they try to redress the balance by moving to a position where the forces would add up to zero. Indeed, when the pretenst structure comes to rest, all of the forces impinging upon all of the joints each sum up to zero.
We’ve taken the plunge here to introduce lightspeed and go from talking about distance to talking about time. That means we can start to imagine joints to be events, or rather collections of events. There is always one single compression interval at a joint, and it connects with four or more tension intervals. Say we have 5 tension intervals.
Imagine the signals coming in. The signal coming through the compression interval is arriving a bit early, and the signals coming through the tension intervals are all arriving a little bit late. That’s why we might think of a joint to be a collection of events, and since a joint is a place where everything is striving for balance, the signals should somehow average out so that we can talk about a joint as a single event consisting of a somewhat predictable series of sub-events. We know that the compression signal comes early and the tension signals come in late.
Picture game of throw and catch happening inside every interval. Since we’ve seen that compression events come in early, if we imagine being a joint, we will have to somehow keep expressing the fact that the compression event should ideally (according to the interval) be coming in a bit later. If our joint’s function is like a catch player, we will have to catch the ball, hold it briefly, and then send it back a little bit later.
The corresponding game of catch in the tension interval is a little bit stranger, because we can’t hold the ball for a negative amount of time and send it back before we caught it. This is no ordinary game of catch! It’s more like a juggler with multiple balls going back and forth.
For the jugglers in the tension intervals to be able to express themselves properly, they will have to hold on to the previous ball and throw it back after a time which corresponds to the length that they want to be.
We now know how long the joints have to hold on to the balls of the game of catch going on in each interval? But we still don’t know exactly when to throw the balls. Since balls will be arriving early and late, we can’t just send a ball back at a moment a certain length of time after that ball arrived, because that would all just happen at light speed and we could no longer properly express the desire of each interval.
The amount of time that an interval end has to hold the ball will be relative to the aggregate “event” that can be registered at a joint based on all the intervals that meet there. So let’s imagine one cycle of this game.
The compression ball arrives early, followed by a number of tension balls, and we take the average of these to decide on the “moment” that we mark as this particular move in the game. Every ball is held for a time corresponding to this moment plus the desired length of the interval that it is within.
This page is a disturbing collection of ideas and metaphors, but something about this way of thinking seems to intuitively have merit. Perhaps a future version will make a whole lot more sense, time will tell. (No psychedelic drugs were used in the writing of this page, and no animals were harmed)