OptimisticCynic

That means you are repeating what you heard from other people. Unless you did investigate in person. Let's go further back. The Palestinians moved back from Egypt. They fought some other tribes and took over the land. They were later called Israelites. The history of that part of the world shows so many different peoples conquering and losing the area that it's a lie for any group to claim it as "our" land. Plus the times when all tribes had to abandon the area because of years of drought. I agree. It doesn't have to be binary. The people currently calling themselves "Palestinians" have no more ancestral claim to the territory than the Egyptians or the British. Winners of wars make rules and losers whine. When it comes to nations, "Might makes Right," is definitely a thing. World war 2 changed a lot of countries. The Israelis would have been wiser to refuse to build up the Gaza strip at all. They made it nice so Arafat decided to steal it. If Israel had left it undeveloped and stopped feeding them, the "Palestinians" would have moved away long ago.

When did you personally go investigate Israel's secrets? Are you going by what people say about Israel? Was it Hamas leaders who said that they wanted to nuke Israel and the USA? You're showing off how pathetic your points are by ignoring my points in favor of changing the subject. Are you admitting now that you support killing Jews and Americans along with uninvolved civilian bystanders in every country around the world? Hamas has a good chance to buy nukes from Iran or Russian thieves. Hamas would immediately use nukes. It's a lucky thing for civilization that tyrants and terrorists tend to be incompetent blusterers. Have you decided to stop supporting every government that goes to war yet? Or are you going to keep propagandizing for your favorite liars?

An optimistic cynic is someone who believes it is possible for things to be better, but it's practically guaranteed things won't get better. Don't you hate it when you play with an old, unsolved science question and solve it quickly? It's true, your solution is probably wrong, but now you have to dig into it seriously. This was supposed to be for fun! When your solution looks more solid, predictive and useful every time you try to prove it wrong, you have to work on it more. Then you have to improve your understanding enough to explain it to others. If they think it might be useful, you have to write a paper, find a publisher, and defend your thesis. Don't you hate it when a lazy entertainment turns into a serious and important job?

I'm not taking your word for any of that. The only thing you can be sure of is that someone told you what you think you know. You should NOT take my word. I'm a total stranger. Nor should you accept what someone tells you just because you know that person. Check against other sources. Deliberately search for evidence to prove your beliefs wrong. Finding support for your beliefs is usually very easy. Reality is not balanced. Reality is rarely one sided. Act like a scientist, do your research and test your hypotheses. While we're at it, we should Free Palestine From Hamas ! Why is it? The words and actions of Hamas match, but you won't admit they might really mean what they say? As I said before, I'm supporting the side that is not threatening to kill me and everyone I know.

Sound waves are not just longitudinal. They move out spherically from the source. Plus, when you have multiple sound sources, they get really mixed up in three dimensions. In the simplest mechanism, a circular diaphragm has a needle mounted at its center. This center mounting on a diaphragm fixed around the circumference constrains the needle to move (almost, some very limited material flexing) only perpendicular to the plane of the diaphragm. For a gramophone, the precursor to the spinning disc record player you're probably familiar with, the diaphragm was mounted edge vertical. The needle had a bend so the tip, bouncing transverse to the spin, would touch the disc. Edison's original phonograph made indentations of varying depth in a foil. Many different configurations of mounting the diaphragm, bending the needle, and moving the recording surface are possible. The gramophone design was more practical. The same song could be recorded simultaneously on multiple configurations and at multiple speeds. As long as the direction and speed were repeated correctly for each, the playback would be effectively identical. If you didn't already know the correct direction and speed to play the record, is there a way to calculate it from examining the track?

In a mechanical memory system, such as a tape recorder or gramophone, the input movements of sound waves are constrained by the mechanism to motions back and forth along a single line. A separate mechanism(s) adds motion along a different line to stretch the needle marks far enough that they don't overlap at frequencies within the design range. The question is, how can the speed and direction of the added movement(s) be calculated from the recording needle track? With a needle bouncing perpendicular to the length of a recording tape, if the tape moves in a straight line past the moving needle there are only two directions to choose from. Can we tell if the tape speed changes at some point? With a gramophone, the needle bounces perpendicular to the arm it is mounted on. The spin of the disc and the slide of the needle toward or away from the disc center combine to make a spiral track. Can the length of the arm which slides the needle along an arc be determined from the track on the disc? How can the speed of the spin be determined? Near the outer edge of the disc, the speed of the needle relative to the disc surface is faster. What is a method for mathematical transformation of the recorded sound pattern at the faster speed to the same sound pattern at the slower speed near the disc center? When the needle mount is moved in a straight line at an angle not perpendicular to the bouncing, how would you calculate the difference in shapes of the sound waves vs that recorded on a perpendicular? This puzzle is presented for the entertainment of better educated mathematicians than me.

Okay, which pile of dead bodies do you want to count first? The dead residents of the Gaza strip, men, women and children that were directly killed by Hamas members since they seized power? The Gaza residents who died from lack of resources because Hamas seized the resources for themselves? The residents who died from Israeli fire because Hamas forced them to stay put in the line of fire or be killed by Hamas immediately? The Israel residents who were killed by Hamas on October 7? The Israeli soldiers killed by Hamas? The Hamas fighters who were killed by IDF attacks? The Israelites killed by Hamas launched rockets over the last thirty years? Pick one and we can start counting.

I deduce or infer (I'm not sure which is correct usage here), from your addressing only one side in your reply, that you either believe that Hamas is lying or you support world wide killing of Jews and Americans. Which is it?

In chronological order: Hamas said, "We will eliminate all Jews from the planet. Then we will destroy the U.S.A.." Israel said, "We will eliminate Hamas from Gaza." Which side is lying? If they are both telling the truth as they see it, do you support world wide killing of Jews and Americans, or do you support killing Hamas members in Gaza? I believe both sides fully intend to do exactly what they say. I support the side that plans to leave me alive.

I was replying to jeff einstein. The original post author.

You are wrong. What you missed is the shapes of the masses and the initial and changing angles of the forces. From the start, your masses m1, m2, and E are all pulling towards each other's center of mass in straight lines. From center to center to center the lines form a triangle. As m1 moves towards m2, the direction of the pull of E changes. The angle between the two lines of force from the center of E to m1 and m2 reduces. The linear distance from m1 to center of E, and from m2 to center of E remains equal as they accelerate. The line from m1 to m2 remains tangential to sphere E throughout. Watching the triangle, on the plane of the triangle, as the masses move, the triangle tilts and grows narrower while remaining isosceles. Both m1 and m2 are always the same distance from the center of E at every moment of falling no matter how disproportionately they accelerate towards each other. Their paths on the plane will be different in length, but as long as m1 and m2 are equal diameter spheres, they will always reach a spherical E simultaneously. If E was flat, they would reach the surface at different times. Are you living on a flat Earth? 🤔

We, consciousnesses, cannot understand our own thinking in real time. You could figure out all of the details producing a single thought that you had. It would take a very long time to do. For a starting point, take the millions of inputs from your sensory nerve endings just before and during the length of the thought. Your mind has to reduce that amount of input through multiple iterations of reducing processes. Then every memory accessed to add to the immediate inputs, plus any loops involved. It's all just TMI. (Too Much Information) Eventually the brain which evolved to reduce from TMI to decision points saves the condensed meanings to memory. After it is saved you can become consciously aware of having had that thought. To watch the change patterns of a thought while they are happening requires an outside observer. That outside observer might be thinking other thoughts while observing yours. This explanation comes from my personal theory of how minds work. Working title: TMI Theory. It's fun to play with.

"the microwave wavelength"

I am not presuming classical physics when dealing with QM. I am pointing out a factor common to the measurement of oscillating systems. I am using your example of the electron spin-flip and my pendulum example as extremes. To illustrate how, in both systems, there comes a point where something, which is described mathematically as an approach to a limit, becomes an actual change. This flip from "approaching" to "moving away from" is precisely the point where classical physics gives way to quantum mechanics. Where "many" particles reduces to "one" particle. from Wikipedia --Introduction to quantum mechanics"In this sense, the word quantum means the minimum amount of any physical entity involved in an interaction. Certain characteristics of matter can take only discrete values." The electronic oscillator measures the microwave wavelength. from Wikipedia --"The actual time-reference of an atomic clock consists of an electronic oscillator operating at microwave frequency. The oscillator is arranged so that its frequency-determining components include an element that can be controlled by a feedback signal. The feedback signal keeps the oscillator tuned in resonance with the frequency of the electronic transition of caesium or rubidium."

Thanks for the forum use tip. Given the electron as a point particle, I see your valid point. (all puns intended) As a counter argument; from my point of view, something moves within the mechanism of that clock as a result of the spin-flip. Thus, distance is measured. To show that we are both right, I'll use a pendulum clock for an example. When the pendulum reaches the top of its arc, it has no motion. Then its vector flips and it is in motion again. There is nothing moving at the peak of a pendulum's arc or an electron's spin-flip. The same combination of motion and change without motion could be said to exist in most oscillating systems. Which is being measured can be spun either way -ask any politician-.