Gravitational Ramblings
I was never really interested in physics, preferring instead the more pure branches of mathematics. Given that, much of what I'll say in this little discussion is probably already out there or just total nonsense, still just in case it isn't, I figured I just write it down. You never know, it's a strange world.
I was watching a newly published lecture series with the eminent Richard Feynman. He said a couple of things that I had already learned about gravity, but I found fascinating anyways. The first was that Copernicus found that the planets traveled in a ellipse, with the sun being in the focal point. Quite well, known, but the relevance of the sun's position never really dawned on me before. Another thing he talked about was the measurements for a system far away, but the star's position wasn't at the focal point in the ellipse, he pointed out that this was because we were viewing the system from an angle. The final bit that I found interesting was that the earth and moon as a system pivot about a point slightly off center to the earth. The position is accounted for by the masses of both objects being proportionally closer to each other.
My understanding of gravity comes from the commercialization of Albert Einstein's theory of relativity. As scientists tried to explain it to the rest of us, they fell back on easily graspable perspectives. Watching enough of this stuff on TV, I tend to see gravity as being the displacement of space-time by a object of significant mass, much like a bowling ball would form an indentation in the sheets on a queen sized bed. The presence of the ball pushing into the mattress deforms the sheets. For space, if we could see our 3D world as a projection onto the sheet, much like a we can be cast as shadows on a wall, then mass tends toward bending that plane around it.
Somewhere else, I was told that objects in space keep moving in one direction forever. Once force has been applied, momentum cares the object along in a straight-line. Well, not really straight, in the 3D sense, but rather straight in the gravitational sense. In a simple system, with one large object in the center, and a smaller one caught in it's outskirts, the smaller object travels around and around the larger one at the same depth in the gravitation well. If it gets started circling the larger object at a specific gravitational force, the shortest and straightest path is to stay at that same level of force, and circle forever.
And so it was, that I could see in a simple system of two bodies, one body perpetually circling the other body at the same distance. Well, almost. Somewhere in the back of my head I did know that one small object doesn't not really "circle" the other one. That's what Feynman reminded me of, while watching the lecture.
Way back in school, we learned about conics. If you take a cone in 3D and slice through it at a 90 degree angle, the slice should be a perfect circle. If however you start tipping the slice, then it becomes an ellipse. If you tip it far enough, then it becomes a hyperbola. All three of these geometrical objects are related in that they can be generated by a plane intersecting a cone. It's kind of a neat result, in an odd way, and has always stuck with me because of that.
If we have a small object, called A, and a much larger one called B, then the AB system consist of the smaller object orbiting the larger one. In my little universe, this orbit is a perfect circle. If, in this universe, we add in another much much larger object called C, then gravity well caused by this new object should have some type of affect on the original AB system. If the AB system is trapped in the well of C, then it is rotating about C in a perfect circle. That sort of makes sense in this model. More interesting though, is what has happened to the AB system itself. It started as a perfect circle, with A orbiting B. Now however, this system itself sits at an inclined position in the well around C. It sits on a slope in space-time. If the effect of that slop is similar in nature to a plane intersecting with a cone, then the orbit of A around B will no longer be a perfect circle. It will be an ellipse, depending on the gradient of the slope from C. And if there is another even more massive object called D, then the effect of D on ABC will be to for the AB system to orbit C in an ellipse as well, and to change the specifics of the ellipse of A. In other words the effects are accumulative, and seen at every level in every system.
Gravity, like light, seems like it is inversely proportional. Some radicalizing increasing curve of some type. It doesn't really matter, other than it is not linear. From this, we can assume that there is some gravitational horizon in which the affects of an object in space-time exists, and beyond which they do not.
What I though interesting about this perspective is that the interaction between any two bodies is driven by their masses and the accumulative gravitational incline for any gravitation horizon that they sit in. The earlier point about the center of system of the earth and moon not actually belong the center of the earth was interesting. One would expect that two objects of the same size would form an interesting gravity well, much like a sombrero. The deepest regions of gravity would be on the lines of orbit from each other. The center of the system would have less of a gravitational effect.
We would expect, if any of the above were true, that in the many variations of the theme that exist in our universe, we'd see all sorts of different types of smaller solar systems, sitting at all sorts of different inclinations. We'd probably even see a few where the slope is so inclined that any other object is on a hyperbola, and kicked right out of the system.
As I was bouncing these ideas around, I also started thinking that one could view gravity in a number of different ways. One way was as a set of 4 parallel dimensions, the affect of which alters the movement through the other 4. After a bit, I though a nicer version would just be a straight-up 5D universe. Then all points would be (x,y,z,t,g), and we could refactor the laws of motion to always conserve momentum at the same depth of g. Thus (x1,y1,z1,t1,g1) -> (x2,y2,z2,t2,g2) requires no extra force, if g1 == g2. Although I'm not sure if that is equivalent to creating perpetual motion (would the other points on G bind in some ways to the other forces, like electromagnetic, or weak nuke?).
If we knew the slope at any point G, then we could calculate how that would affect a local system, also we could probably model the decomposition of G into various parameters caused by bodies such as the galaxy and the milky way. With each horizon having an affect, the local inclination is bound to change as the objects dance with each other.
Yes, I know, it's probably too simple of a model, but it just seems to tie together a bunch of loosely correlated bits. Worth writing about, even if it's totally wrong.
Sunday, July 19, 2009
Saturday, July 11, 2009
Human-Oriented Dynamics
To model our larger behavior as organizations, we need some irrationally motivated, inconsistent system, that in it's lack of completeness manages to predictably move around the same territory that we do. A system completely opposite in nature to a mathematically formal system, yet one sufficiently expressive enough to be able to draw conclusions from its changes in different states. People are neither logical nor rational, and when they operate in larger and larger groups, these inconsistencies manifest into larger patterns within the over-all interactions. The rules make no sense, yet they shouldn't make sense.
These are a few basic principles (of an infinite number of them):
The Opposition Principle: For anything that someone can do, someone else will attempt to do the opposite.
The Path Principle: To force something along a prescribed path, there must be at least two balancing forces at work.
The Ease Principle: People will always take the easiest path, although that choice is relative to the individual.
The Common Principle: Any organizational attribute will eventually find its way to the lowest common denominator.
The Misinformation Principle: People will always have a significant amount of misinformation, that they are using to make decisions.
The Empathy Principle: People with less empathy will always go higher, and get there faster in any organization.
Wednesday, May 27, 2009
Third-world democracies are often driven by large populations of un-educated voters, resulting in poorly chosen elected officials and mass amounts of corruption. A large stable middle-class tends to stabilize the voting, which indirectly stabilizes the country.
Restricting the voters to something elite like 'land owners' defeats the fairness principles enshrined in democracies. A better approach is for the government to restrict voters based on education. To vote, one needs to pass a basic education. To make it fair, the government needs to offer that specific level (it need not be that high) to everyone, guaranteed, for free (and in night courses too). A better educated set of voters will make more balanced choices.
Monday, May 25, 2009
Simple answers to complex problems always make the problems worse.
You cannot solve a complex problem with anything other than a complex solution; partially solving a problem is just adding to it. The solution must fully cover the problem, or the ignored attributes will cause major side-effects.
A simple answer will work fine for a simple problem, but likely somebody has probably already solved that (since it's simple, and your unlikely to be first).
Tuesday, February 24, 2009
Blowing up a house, to get rid of an infestation of cockroaches is not a real solution to the problem. Too many people on this planet don't seem to understand why it's such a bad thing. That's probably why there are more problems getting created than there are getting solved.
Read more...Countries should be forced to always live by their own rules. They should not be allowed to do to someone else's civilians what they cannot do to their own.
Any technique that a country uses to get its way, should be one that is used equally internally and externally. All they need to to comply with this, is to be honest and document what they've done, and what they are planning to do. Just paperwork, how hard can that be?
Mankind iterates its knowledge. Somewhere, in some dark and dank corner of the web sits the answers to most of our problems. It's just that with all the noise out there, it's unlikely that we'll be able to recognize them in time.
Read more...Monday, February 23, 2009
The world is over-populated. Nearly 6.5 billion is a staggering number of people. Why then are we focusing on curing cancer or saving starving children from dying in regions of the world that clearly can't support them. What we really need is not more old or young, it's a model for how we could possibly live a sustainable life-style. Until we understand how to manage our limited resources, our hubris will just keep making monkeys out of us. A space-ship might help too.
Read more...Monday, February 16, 2009
Competitism -- a form of government based around the idea that competition is good. In general, the goal is to promote competition wherever possible, and intervene when it has become unbalanced for some reason.
In all circumstances, those who are winning bear the greater share of the burden. That is, if you are rich you pay more taxes, if you are better known you carry more public duties. That levels the playing field somewhat, as those trying to pull away from the rest, must go way beyond their abilities. The opposite is also true, if you are poor, you pay no tax, you get lots of help. The systems seeks to keep the gaming going as long as possible, and to balance it as needed.
In any case where competition is no long viable, whether because there are not enough players or collusion has occurred, the government must step in to regulate the circumstance. They must in some way restore competition, at least to the remaining players.
And finally, "caveat emptor" is no longer valid. The buyers are not on the hook to be smart, as cheating them is a way of cheating the game itself. Anyone finding a way around the rules by abusing their customers for example, must carry an extra weight as a consequence. Competition to be valuable has to be fair and honest competition, otherwise it degenerates into something ugly (a principle we hold to in forums like the Olympics).
We need people to accept that there is no "personal" god. That is, one that you can call upon to fix the things in your life, or one that routinely enters into conversations with lots of people.
The problem is that it is too easy for people to claim conversations and divine guidance. The sick or untruthful benefit from this. In that way, they can direct others to do things that are inappropriate. They can claim an authority above and beyond their own; one that they do not have.
Often people just need a reason, so it best not to make it easier for them to get one.
Friday, February 13, 2009
Laws should not restrict us from doing things, unless other people are impacted. People should be allowed the maximum freedom; a government should never play the role of parent. If it's bad for you, it's your problem.
In those cases where society really wants to stop some behavior because it is expense or unpopular, they need only restrict half of the transaction. For instance, it might be illegal to sell weed, but there shouldn't be a law restricting someone from smoking it.
People shouldn't be forced to wear a helmet on a bicycle, but parents can be held responsible for making sure their children do (since it effects their child, who is not able to make their own rational choice). Easy eh?
Sunday, February 8, 2009
We need something better than capitalism. While the competition aspect may work wonders, the system degenerates into a lot of slimy people producing a lot of crap. And the worst part is that it's not sustainable in any way. We need something similar, but where the winners can't pull quite as far ahead of the others, as they do now.
A nicer life, sure. More stuff, OK. Hundreds of people ripped off and pissed, no thanks.
Wednesday, February 4, 2009
Frequent-customer plans should be regulated. If you're going to jack up the price to cover some optional annoying plan that is based around everybody carrying yet another stupid card in their wallet, the least you can do is not be allowed to just arbitrarily enforce some expiry date.
Many people think these things are just 'free gifts', but in reality we pay for them, is it just another excuse to raise the underlying prices. It's easy money.
If they're allowed to 'tax' me to reward frequent customers, at very least I expect them to honor their commitments for as long the customers are willing to continue engaging with the company. Yes, it's expensive to maintain these stupid schemes for years and years, so hopefully it convinces a lot of businesses to stop with these crappy programs, since they are just alternatives to actually providing value at a fair price.
Justice should be swift and decisive. If there is no evidence, or it's circumstantial, the waiting just compounds the problems. If there is evidence, then waiting is a waste. Either way, the accused has a right to get the proceedings over with 'as fast as possible'.
Trial by jury should only be applicable when there is some underlying possibility of doubt. If you have enough solid witnesses, footage, or other irrefutable evidence, the proceedings should go straight to a resolution. People are innocent until proven guilty, sure, but they are proven guilty not always in a court, but when the evidence itself leaves no possibility of reasonable doubt. Give the system a fast-track, and it will improve. Save the long-drawn out proceedings for the really difficult cases.
Wednesday, January 28, 2009
We need quality. Capitalism tends towards producing inferior goods for low prices. We're surrounding our selves with crappy disposable goods, at the same time as we are getting increasingly concerned about recycling. Disposable cloths, computers and gadgets cost more in the long run, and waste more overall.
Read more...Thursday, January 22, 2009
Ban hand-guns. Only military and police should be allowed to own and use them. For the rest of the world, there is no legitimate reason for ownership. Owning a shot-gun or a rifle is should be sufficient for those that like the destructive power of a gun.
Read more...Wednesday, January 21, 2009
New laws don't make things better. Rules must exist, but should be well-thought out and minimized.
Read more...We need a new model for our lives. With the old ones overturned, so many people have been cast adrift in a complex world. How can you make sense of the world around you, if you're not aware of your place in it?
Read more...