Quartile

What I meant by the sentence you quoted is that the notion of Hilbert space is a mathematical tool which opens many doors for all types of analysis. It is a cornerstone of modern physics, which is the study of matter. I know my understanding of Hilbert space may be somewhat weak compared to yours. Is the sentence that came after the one you quoted correct?

Hilbert space is a tool used to mathematically identify properties of matter that are hidden to other types of analysis. In my understanding it is similar to a regular euclid space that includes all limits of all functions within its boundaries. I can understand why an orthonormal basis is applicable to the notion of a Hilbert space, but I have a question. How can the relative position of two separate objects be determined, if the Hilbert space does not extend beyond the boundaries of the two objects themselves? That is, in a Hilbert space containing two separate objects, is the space between them required to accept an orthonormal basis as well? Thanks!

Back on topic.. (sorry man, you aren't helping) Given the large mass and small number of objects in the solar system I digress back to my initial presumption that nth derivatives of motion can be used to describe existing physical phenomena. How is gravitational force related to motion? I am somewhat familiar with Kepler's laws and the two and three body problem as well as the big question mark that comes in when describing the exact mechanisms of "planetary accretion." Perhaps when the masses involved in a system are in ratio similar to sun:planet the force is so large as to cause high derivative motion, accounting for the shape of the solar system? Kyrisch: Would the space-time description work when describing something that is at rest in all reference frames? Thanks!

"You" would be c in the case of person A and person B wouldn't you? But you don't have a ball, you have two eyes and a brain. The paradox still exists in a very broad sense because there are initial conditions that change almost instantaneously from our frame of reference, so probability is the best tool for studying what is probably the behavior of what are probably electrons. Doesn't sound like physics to me, either.

IIRC the fourth fifth and sixth derivatives are called snap crackle and pop I am having trouble understanding why these derivatives don't show up in solutions to special types of motion. Surely they have some physical significance?

What is the difference between acceleration and jerk? Jerk and the fourth derivative? What happens as n approaches infinity? How does the energy of something change as it experiences jerk or 4th derivative motion in a certain direction? It seems like higher derivatives of motion could describe vibration or other frequencies.

A path to the unknown! Yar! Try to see if you can make what you're saying into mathematical sense by assigning values to things and formulating a working equation that describes the phenomena as applying generally to spacetime. If you can and it can be verified in experiment then you will have successfully expanded science.

I posted this topic because I recently came across stellar evolution. The fact that things in space are involved in such long-durations of change is, to me, groundbreaking physical evidence that there is an underlying process at play in the universe. A white dwarf is not massive enough to have a hydrogen burning stage either, will you debate with me whether or not a white dwarf could have once been involved in hydrogen fusion? What is the process by which a star grows and decays? Do human beings really know, or have we fudged the math this way and that in order to get an answer that stops people from questioning?

I apologize for posting here. My mind is too open and my ideas make more philosophical sense than they do physical sense. Whoever thickened the line between the two was a moron and an asshole.

Ignite? Explain our molten iron core in a way that excludes the possibility that Earth is a star, still involved in fusion. Our inability to observe processes that last millions of times longer than we do allows room for the philosophical proposition that since stars and planets are made of the same thing, they are the same thing. I think this philosophical proposition may have physical credence. Will someone with a good understanding of fission/fusion tell me why this isn't possible?

The earth wasn't a star at some point in time and has coalesced (as stars do) through its stages of stardom all the way to its current state. In other words, what happens to dwarfs after they "die"?

What is the sound it would make and how would it be measured? Scientific answers to these questions exist today, but thousands of years ago when philosophical ideas like "would it make a sound?" were being developed and communicated for the first time they were no doubt understood mostly as descriptions of the concept of relativity, the relationship between observer and observed. Science would not be where it is today unless these questions were asked when they were. The knowledge base at the fingertips of modern man is absolutely massive - there have been many generations of people contributing to it throughout time. The answer science gives is something along the lines of: sounds are compression waves that travel through matter and vary in frequency based on the elastic modulus and the.. BS BS etc.. but at its heart, what is sound? Kinetic energy (mostly, I think) transferred between objects of various mass. Living creatures obtain the ability to perceive/interpret sounds through evolution. Perhaps the scientific answers to these philosophical type questions are philosophical answers as well. Maybe the existence of energy-transfer phenomena is what allows for evolution to occur and for life to exist at all. The long-term plasticity of various elements/compounds comes to mind. I was mentioning that Zeno's paradox is true if you consider only the object in motion while excluding all outside forces. Its motion would never end and its stopping point would be infinitely indeterminable. This is the problem with Zeno's paradox, again as people have pointed out: objects do not come to rest on their own. There always seem to be outside forces.

I don't know if its just me, but I see the paradox being heavily grounded in the nature of the observer (namely, the amount of things the observer observes/considers simultaneously). I know this sounds weird. When Zeno developed this paradox he somehow came to the conclusion that an object's position when it comes to rest is impossible to observe. How could this be possible, unless you were to consider that an object in motion will stay in motion until it is acted upon by an outside force? Could it be that Zeno was considering only the mathematically instantaneous reference frames that are accumulated as an object moves, instead of also including its position when it comes to rest? As some posters here have mentioned, if Zeno had opened his eyes he would have seen that an object always finds its destination because it goes where it goes to stop where it stops. In more physical terms, its position when it comes to rest is used to describe its motion in the time directly previous to stopping. But are we doing Zeno an injustice by assuming that he didn't see this obvious blunder? Upon consideration of Zeno's paradox in relation to Netwon's laws of motion, it becomes apparent that Zeno's reason didn't provide him with the realization that more than one object does exist. That is, the object being scrutinized is not the only object worth considering. However, as Zeno pointed out, if we focus the reasoning power of mathematics on only one moving object (excluding even gravitational effects from other objects), we see that its position when it comes to rest cannot be described by calculus. When you pretend that the object in question is the only object in existence, Newton's first law allows for Zeno's paradox to become scientifically rational. Perhaps Zeno was actually highlighting the relativistic nature of observation by pointing out this paradox. I added paragraphs in a desperate attempt to help this make sense lol. Please feel free to re-read it? If anyone thinks I'm making even the slightest philosophical or pseudo-scientific sense please give me a hoo-rah.

So, in short, the flow of charge follows the path of least resistance.

What causes the shape of a Lichtenberg figure? http://en.wikipedia.org/wiki/Lichtenberg_figure

Could zero-point energy provide what is necessary to produce a vertical wave at the Planck scale?

Thanks for your post Mike! Although I would never trust myself to produce any of the math underlying some of the things you have addressed I do feel that I have a working understanding of many of the concepts. I find it interesting that a truly square wave cannot be produced using a finite number of Fourier transforms. It would seem that in this way there is an "asymptote" governing absolute vertical motion in any wave. I use the word asymptote in quotes to point out that I understand this is an incorrect usage of the term, but it does serve to illustrate the point. There is also asymptotic behavior governing absolute horizontal motion in any wave; "flat waves" do not exist. I found this after typing the above. Can anyone tell me if its true? If this is the reason for no vertical waves, then a horizontal wave represents one that carries zero energy, which is, by definition, no longer a wave.

[$.02] A few things that have always seemed strange to me about the Big Bang are the first questions that come to everyone's mind, which are also the questions that have yet to have a definitive answer: What is exploding, where did the explosive energy come from, and why did it explode? I understand that the math behind the Big Bang scenario fits quite well. Could it be possible that the math is not describing an event that occurred at the "birth" of the universe but rather an event that is occurring all the time at relatively smaller energies? [/$.02]

So it is possible to formulate different shapes of waves artificially using equipment and whatnot, but is it possible for these shapes to be formed in nature by "accident"?

More specifically then, is it possible for physical waves (other than sound) of the same type (electric, magnetic, transverse, or otherwise) to combine together as Fourier components to form different wave shapes like square, triangle, saw, etc?

I am not referring to sound as I do understand how different wave shapes are produced in music. I am referring specifically to other physical phenomena. If everything can be expressed as a wave function then it certainly has a wave form? Maybe I'm missing something.

What is the shape of physical waves? I would assume they are usually sin waves, but is it possible to have a shaped wave like square or triangle occur naturally? How would the shape of a wave be determined?

I have not lost track of anything nor have I oversimplified things in a way that would subtract from the point I am making. If what a woman wants is a quality mate, then what the woman wants is the quality mate. I am simply highlighting the most extreme of the extremes in the points you are making in order to paint the picture of a man who would take everything on earth for himself to see that his insanely demanding wife's "needs" are met. Of course few people have been able to live so lavishly, but if I follow you correctly then it was the same desire driving Henry VIII's family to lead their lifestyle as it is driving a middle-class man and woman to lead theirs. And when we consider that the many different degrees of resource gathering perpetrated by men all over the world are all happening at once, what difference do the parts of the whole impact make? The blame is to be placed on the general acceptance of the mentality that has grown in us that each individual one of us has something special that no one else has. If the population stops growing there might be a chance that we won't rape the entire planet of its resources in the name of ourselves, but at this rate it doesn't seem like that will be the case. Regardless, my point is that individual happiness is a more important goal to any individual than is reproductive success. Many people would say that they would like to have a child in order to be happy, not be happy in order to have a child. Is there not a middle place where everyone can ground themselves, regardless of the experiences that teach them "how"? If parents dropping their children off at daycare believe they are doing their best to raise their children then how can you appeal to a woman's desire for reproductive success as part of the family raising process? If daycare providers are included in the child rearing process, then how can you say that it is a woman's ultimate goal to find the correct man (who will provide for the family) when it could instead be the woman's goal to find the correct social services? As you have implied, reproductive success being the figurative "goal of goals" doesn't work so well in modern society. "Being happy" means simply that. It applies at all times unconditionally. How many of these happy people would remain happy after being fired from a good paying job? Shit happens and the response of your significant other should be nothing but supportive, but how often is it that we would feel the need to hide something like this in fear of being berated for it? Why is it that to tell your significant other that some thing has gone wrong feels so similar to telling your parents that you crashed their car? In this way I strongly believe that happiness is not something to be found by setting and satisfying goals. As human beings we still haven't answered the question of questions, do we know enough to set our own goals? Yes I don't doubt that this exists and I understand its place in each person as a tool of evolution. I only disagree with the way it has manifested: meeting the status quo of being someone who cares about others means that you wave to your neighbor on your way into the garage, it means that you say please and thank you, and it means that you turn the other way when people have personal problems. Wanted to add something aside from those gigantic walls of text that I built in here.. Is reproductive success the target of the goals that we make or is it survival? You can't reproduce unless you're surviving. And my original point was just that it is easy to complicate survival in modern times; perhaps happiness is only as difficult as we make it.

By living in the moment instead of living one's life as a slave to desire. It is as easy as making a choice when you are able to see it for what it is, but actually becoming that choice is a difficult process. It requires lots of effort, willingness, and change. People, whether male or female, have an innate desire for happiness and well-being. At what point should a woman make an exception to her desire for the alpha-male so that she might go on living her own life? At what point should a man stop fighting towards the top of the pyramid so that he might go on living his? If the desire for successful reproduction was many times stronger than the desire for personal happiness and well-being, we would see that women would settle for nothing but the best and men would battle constantly for the resources necessary to be seen as the best. This is what is happening in the world today in some places, but there are at least several billion people that choose not to fight the fight. They simply enjoy whatever life gives them instead of treating themselves like the most important human being alive. So my question is: what is so important about money, a nice house, and a comfortable living? Is it so a woman can reconcile her deep-seeded "I am a queen and I will select whomever will treat me as such" self image with the realization that she is nobody? Is it so a man can reconcile his deep-seeded "I am a king and I will be selected and reign supreme" self image with the realization that he is nobody? So goal-seeking is done solely for the advantage of the family unit? What about when a couple drops their child off at daycare (school) every day before they both go to work and they don't see their son/daughter again until they come home at 6 pm? Is this just an example of misplaced priorities? Then the question is why are these priorities being misplaced? Perhaps they might think the fruit of their goals isn't ripe enough to settle for yet. Is life just a game? If men stopped shooting baskets and women stopped keeping score would we cease to exist?