n-Body progress

I am reposting this video at the top of the blog because I think it is significant enough. If it isn't a complete solution, it is a very fine tool anyway. It took almost all day programming to get the framework established. I am looking forward to finishing this and integrating a few bells and whistles to have vector pointers on objects to show velocity, force and 'field' strength in 3D. The sheer number of vector transforms is mind boggling.

This works so well it is scary. I have some bounding conditions set for display and it interferes here, but ths will deal with any number of objects simultaneously and I am using only one at this time to get all the things tuned in, but it looks really good now that I removed some of my software glitches. If you program you understand how easy it is to miss a decimal point or just type the wrong variable. When you add equations as complex as this it just gets worse.

If you program you will know this feeling, I have been at this for 20 hours straight and before I got it all together, I was looking a the code for 15 minutes saying "This can't happen!" and yet you are looking at it, and that stupid thing is happening. This is all I can do today so I am going to sleep.

ADDED: Though this is useful in the analysis of interaction of multiple objects in space, the general principle can be used to solve any number of recursive simultaneous equations. I can think of several places where this is applicable. It really opens up a whole new area of possible methods that I can apply to system analysis. I need to rebuild my antfarmgl code to integrate this and get rid of some trash code that comes from experimenting with new methods. This should be applicable in 5 dimensions with thousands of objects. The strange thing is that this scales at O(n²) and when I first started working with it I assumed it had to scale at O(n!) which is worse than bad. I can accept n² complexity for this , but I am now wanting a Beowulf cluster of them. I need to integrate all the detail of the algo and it is just a proof of concept model now and so if I incorporate Maxwell's equations it should give me some interesting solutions to some things like complex systems of particles acting under electrical, momentum, magnetic, and gravitational force. There is a lot of work to be done to integrate all these into the process and I will probably post a new video on Monday with the results.

ADDED: I noticed the title was progresss and that is what happens when you don't get proper sleeeeeeeeep because you have to finish something.

Many bodies problem conjecture

I was trying to find an equation that resolves to the other equations like wave motion and stress, strain, deformation and such. By an odd coincidence I was studying several different methods at once to keep from being bored. Eigenvalues, Eigenvectors, unsigned circular motion, etcetera. I think I have a solution to the three+ body problem and much like many solutions, I wonder why I didn't think of that before. I will do a video of the solution, but this is not much of a question as I am creating programs that perform the actions and this serves as a proof as far as I am concerned. If it models the real world given a set of starting values like the position, masses and velocity of planets.

It seems this is something that is wanted, but it don't see where it has fantastic consequences. I see where it is useful for me to determine some properties of fluids or even the nucleus and complex atoms. Maybe it will lead to some other solutions when applied.

I think this could be a solve for space junk. That would be useful. It would seem the equations would be worth a couple Euros. That is correct, now I see that the way in which it is computed now, even a simple single collision between a small piece of space junk and the ISS is impossible for others to solve. I had a clue to this several years ago and pounded my head against it and failed to solve it. I remember that well, as it hurts to spend a week trying solutions and then failing with nothing to show. I didn't have all the pieces then, new understanding gets new solutions.

ADDED: So I am adding the function for this to my program and it seems fairly straight forward, but I will see if it does what I think it will. I will add the video here when I am done.

After some openGL issues and a lot of vector resolution and handedness issues, it seems that it is working and though it is too early to tell for sure, it is looking exactly as I expected it would. I have been working to add field gradients and direction so I can see if is doing what I think it is. I intend to add spheres for the planets, just to be realistic and then make a panel to set the initial velocity and masses. I thought it wasn't working at first, but realized that without an initial angular velocity it just fall down go boom, big batta boom. The video is a real mess as I just added stuff on top of the Fourier junk I was doing because I was in a hurry to see whether it was worth wasting the time to complete.

I will put the next video in a new post when it is clear that all things are working , as far as I can tell it is doing exactly as I thought it would do and I need to establish some valid initial conditions, distances, masses and vectors before I can be absolutely sure, if it doesn't completely work out it is a great spatial interaction tools anyway, as it is fast and can handle dozens of elements easily. It isn't really possible to ever be sure of anything until it is all polished and in the box ready to ship. Just ask Duke Nukem Forever.

Infinity on a stick

The adoption of terminology to describe the universe is troublesome when it implies more than it is represents. If I look at the universe as a whole, there is no negative sign to be seen. I would guess that my way of looking at things is confusing to some people. Less than nothing. What exactly does that imply? In the case of vectors it is left and right , up and down, fore and back, future and past. There is no real negative there except by convention. Left is negative or positive and the rotation of vectors changes positive to negative, left to right.

I have an equation which works for dimensional space as a transform of these axis conventions and I do not think that it can be done any other way and be intelligible or useful. It is quite a bit easier to describe and demonstrate principles with programs, as the type of complex relationships are inherent.

find -L ~/ -maxdepth 4 -type f -size 0 -print0 | xargs -0 -r ls -la | grep antfarm | grep x

This is an example of command line programming that involves sets and characteristics of objects and methods(functions) applied to sets. It is my opinion that a competent programmer has intuitive knowledge of mathematical relationships beyond the bounds of institutional math. I could do f(z=f(y=f(x))) as a normal , everyday thing. I would write it with more clarity in the naming conventions ( one would hope), but in the end it describes the interaction of multiple variables.

I can get out my oiler[sic] or more properly Euler or Naperian to lubricate the process, but in the end there is only XUL.

In order to remove the imaginary and increase the clarity of the product, it is necessary to introduce properties of numbers in a dimensional system that have relationships defined by functions ( methods) in the same way that + - / * are defined for quantity. In vector math and matrices, these are already inherent and it is merely the terminology applied that suffers. The root relationships , literally , have additional properties that must be expressed to exclude the ambiguous. A process does require interpretation as to its context unless context is excluded in the process of its analysis. In dimensional space, the relationship in space of 1, 2, 3, 4, or 5 objects has unique combinatorial significance.

An example of what I am implying is as follows:
state_of_bouncing_ball=(sin(t))/(t^2) // where t is time from 1 to n
// a decaying oscillation.
t can be negative here and it could be said that it describes something in the past, but honestly there is no sense in applying some mystical significance to my choice of axis center about t. In this particular case it is wrong to conclude that -t describe a past state of the system. It mirrors on t ( -1 to -n). If it were predicting the past of such a function, it would be the inverse in logic, or sin(-t)*t^2 and in this case the -t becomes a direction vector of CCW or CW ( Meaning Clockwise or Counterclockwise). And even that is ambiguous without defining a plane surface normal (N). Thus it would better be written as sin((N)CW*t)*f(t) or sin((N)CCW*t)*f(t).

It seems that defining a function which is the infinite extension of the concept of slope (1/n), automatically makes it infinitely differentiable and integrable. It is like Hilbert's Hotel with a Schroedinger's cat in every other room. An infinite series shifted left or right is still a recursive to infinity and equal when all the terms are continuous products.

I could be off base here, but this seems less mystical a relationship and more of a circular definition ( no pun intended ) , all hail Leibniz and Euler. Another thing is bothering me, When I have two equations describing a line like:
2x + 5y = 0
and
58x + 145y = 0
145*2=290 and 58*5=290 because they are the same line and to call that some super special method is being way to serious about the elegant complexity of that relationship. I won't bore people with the detail,, but if the slope of A and slope of B are the same then inverting one and multiplying is hardly more than junior high level geometry foo. I could be wrong, but I could also be right. The next videos will be the inclusion of various periodic functions in factorial combination. Fibonacci and fractals with sines and exponential loops should be something interesting to see in 3D.