That is where our interpretations diverge. I say that his idea was not the only possibility, and he never gave any reason why it should be.

I will not repeat my arguments, it would be a waste of time for all of us.

Let us then agree to disagree. Unless you prefer insults and name calling.

That is where our interpretations diverge. I say that his idea was not the only possibility, and he never gave any reason why it should be. — Hachem

You haven't given a an alternative interpretation of Roemer's results. ...at least not one with a decipherable meaning.

I didn't call you names. I just said that maybe you should reconsider whether you're right and all the astronomers and physicists are wrong.

If you're done, at least that's an improvement.

It would have been easier to just ignore you. But I didn't want to insult you in that manner. I wanted to be polite enough to take you seriously, enough to answer you, to try to explain the subject to you.

It turns out that you didn't deserve that politeness, respect or effort.

So yes, let's agree to disagree on whether you're right and all the astronomers and physicists are wrong.

Michael Ossipoff

So yes, let's agree to disagree on whether you're right and all the astronomers and physicists are wrong. — Michael Ossipoff

I am really disappointed in your analytic insight. The discussion is not about the speed of light, nor about astronomy. It is about the historical validity of Rømer's argumentation.

Trying to fault my logic through facts is really irrelevant, and I am sure you already know that.

I am not judging facts, I am judging an argumentation.

I am really disappointed in your analytic insight. The discussion is not about the speed of light, nor about astronomy. It is about the historical validity of Rømer's argumentation. — Hachem

Oh, the discussion is most definitely about the validity of Roemmer's method for determinig the speed of light. That's what Roemer's "argumentation" was about. :D

You've rambled at great length, but haven't told of anything wrong with Roemer's "argumentation" I told you what Roemer's "argumetation" was. You said he'd circularly pre-assumed his conclusion. I pointed out that his measurement and determination neither implied nor needed any such presumption.

So then you retreated to your vague statement that Roemer's "argumentation" was wrong. ...in ways that you haven't coherently, intelligibly disclosed :D

Trying to fault my logic through facts is really irrelevant

:D

Forgive me for bothering you with mere facts

When you've made up your mind, what do facts matter?

I am not judging facts, I am judging an argumentation.

[/quote]

Judge away.

You haven't decipherably told what was wrong with Roemer's "argumentation".

...except that several times you tried to, and your objections were answered. So you're continuing to evasively dance around your failure to support your claim that you're right and everyone else, including all the astronomers and physicists, are wrong..

Anyway, as I said, I've devoted more than enough time to be polite enough to not ignore you, and to try to explain this subject to you. Discussion concluded.

Over and out.

Michael Ossipoff

You have not understood what he did.

I am curious what you will make out of this

Why?

if you need to ask you don't need to answer.

It looks like you are trying to avoid the issue of this thread by pointing to another.

the discussion with both of you on this thread has come to an end. Why prolong it unnecessarily? We all know where each of us stands.

We all know where each of us stands. — Hachem

Well, no. Your argument remains obscure.

Wait, I think I might know what Hachem's objection is.

If I'm right, the Hachem was saying something that was true, though he wasn't right about Roemer getting it wrong. Roemer didn't get it wrong. Roemer's method was valid. But there was more to it than we were talking about.

Hachem said that Roemer was assuming a value for the speed of light, in order to find the speed of light.. That's true. Roemer's determination required an initial assumption of what the answer might be.

But no, that doesn't mean that Roemer used circular reasoning.

I was talking about, the fact that, as measured and calculated by Roemer, the speed of light is determinable from the duration between moon-eclipse beginnings when the Earth is moving toward Jupiter, and when the Earth is moving away from Jupiter. I wasn't getting into details of the actual mathematical technique, which involved more than I spoke of.

In algebra courses, and in the mathematical problems that people are most used to, the answer is in the form of a formula, or a completed calculation. Even when it's necessary to solve a system of linear equations, and a lengthy procedure needed, it's still a completed calculation. Disregarding any lack of precision of your calculator, the answer is exact, and is completely arrived at after a relatively short finite calculation.

That's referred to as an answer "in closed form". in terms of numbers and elementary functions (like the sine, cosine, log, etc. on a scientific calculator).

But that isn't possible for all mathematical problems.

In fact, for most problems with any complexity the situation is that there's an answer, but it isn't in closed form in terms of numbers and elementary functions. It isn't completely arrived at by a finite amount of calculation, as is the case with simpler problems.

Such problems require some sort of step-by-step numerical solution, a step-by-step iterative solution.

Because such problems are so common in physics, engineering and mathematics, those numerical solutions are a much-studied and discussed topic in mathematics.

What are some examples of both kinds of problems?--

Well, for the area of a circle, a formula can be derived, pi * R squared. And then, you can solve that formula for any of its variables in terms of the others.

An example of a relatively simple physics calculation is Force = Mass * Acceleration. If you know all but one of those quantities but one, then you can solve for the one that you don't know.

Likewise for Galileo's formulas for accelerated motion--formulas that relate acceleration, initial position, initial speed, and the object's speed and position at any subsequent time. If there's just one of those quantities whose value you don't know, then you can solve for it in terms of the other values.

An example of a problem solvable only iteratively, is a planet's position in its orbit at any time. If I remember correctly, when you solve the differential equations for a planetary orbit, as a two-body problem (no perturbations), you can get an exact solution, in closed form with regard to numbers and elementary functions, for the time at which the planet will reach a particular place in its orbit. But if you want to know where the planet will be at a particular time, the formula doesn't have a closed-form solution for that. You can only get an iterative numerical solution for where the planet will be at a certain time.

There are lots of map projections for which, if you know a latitude-longitude position you can calculate where that point will be on the map. You can transform from Lat/Lon to X/Y. And you can also transform from X/Y to Lat/Lon. ...and get an answer in closed form.

But there also a lot of map projections for which a closed-form solution is avalable only for [/i]one[/i] of those transformations, in one direction. If you want to transform in the other direction, you need to solve an equation by a step-by-step iterative method, based on an initial assumption.

And that's just talking about solving equations. Step-by-step methods are also needed for most complicated integrals and differential equations too.

When solving such an equation, you start with a first guess about the answer, and, from that, an iterative method gives you a better approximate answer. Repeating the iteration, you can get as close as you want to the correct solution.

As I said, there are well-known efficient methods for such problems. Several of those methods were well-known before Roemer's time.

So, given the duration between eclipse-beginnings, when the Earth is moving toward Jupiter,and when the Earth is moving away from Jupiter, it's possible to get an accurate answer for the speed of light. ...an answer as accurate as you want, by an iterative method that must start with an estimate of the answer.

So yes, Roemer had to start with an estimate of the answer that he sought. But the subsequent iterative procedure brought him as close as desired to the correct answer. (...with the understanding that he knew that his accuracy was limited by his clock's accuracy.)

And I'll just repeat that, not only did Roemer's llght-speed determination method need an iterative solution, but even the calculations of the positions of Earth and Jupiter any some particular time (something needed in Roemer's determination) needed an iterative solution too.

So a lot of iteration was needed. No one said that it was an easy solution, especially in those pre-computer days.

But Roemer's principle was valid, and his answer would have been completely accurate if his instruments were completely accurate.

(disregarding the round-off error that happens in big iterative calclulations)

Michael Ossipoff

I wish I could agree with you because it makes a lot of sense.

I am afraid that my interpretation is quite different.

You are still trying to justify the accuracy of the method in calculating the speed of light, while I consider it a secondary, technical problem. Which by the way you describe beautifully.

There are, or at least were, two possible solutions, or more, to the question as to why the moon appeared later when the distance was larger, and sooner when the distance was shorter.

The first alternative, the one chosen by Rømer, and since then, by everybody, is that light needs time to reach us. Once you assume that this is the right solution, the rest is simple math.

The second alternative, the one I presented, even if it is not necessarily the right solution, could not be excluded. According to that alternative, our perception of two distinct objects as distinct from each other depends on the distance between us and those objects. The farther the objects are the longer it takes for moving objects to appear distinct to us. The closer they are, the easier it is.

There may be other logically possible solutions, but that is the only one I could think of.

The discussion should not focus on which of those alternatives is now considered as the right one, but on the fact that Rømer in his time had no justification in choosing one and discarding the other.

If you want to prove me wrong, and I am not saying I cannot be, you should concentrate on this alternative solution and exclude it from consideration, whether Rømer did it or not.

In other words, if you can prove that distance in no way could affect the perception of the moon as a distinct object from Jupiter, then you will have proven this alternative wrong, and by extension my whole argumentation.

There may be a very simple argument to prove me wrong. It would go like this:

Two dots appear as two distinct dots from a distance smaller than or equal to x. If the distance is larger the two dots will appear as one.

To see them as two distinct dots from a larger distance, those two dots will have to be farther from each other than they were. The extra distance between them takes more time of course.

Now all you have to prove is that the distance between the moon and Jupiter was the same at all Earth positions on the orbit path. But I wonder if that is possible. More importantly whether it were possible in Rømer's time.

An extra problem is that it really sounds like begging the question: how can you determine that the distance between the two dots has (not) changed?

Anyway, good luck to you.

Romer didn't initially know or assume that light takes time to reach us. That was his conclusion when he found that the duration between successive eclipse-beginnings was different when the Earth is moving toward, instead of away from, Jupiter.

After he noticed that, then yes, he interpreted it as meaning that light propagates at a finite speed and takes time to reach us. Then, by a very laborious but valid process, he calculated the light-speed that is consistent with his observations.

So yes, as you said, he assumed the finite propagation-speed as the explanation for the differing observed duration between successive eclipse-beginnings.

Your point is that there could be a different physical theory to explain the observation. Sure, of course there can always be a different physical theory.

So, (at least) two theories that could be consistent with the observations:

1, Light propagates at a finite speed.

2 Light propagates at infinite speed, and our perception of two distinct objects as distinct from each other depends on the distance between us and those objects. The farther the objects are the longer it takes for moving objects to appear distinct to us. The closer they are, the easier it is.

But William of Ockham, in the lale 1200s or early 1300s, pointed out that, when there are two rival theories to explain an observation, the simpler one is preferable, and maybe even more likely to be the correct one.

Your alternative theory says that the distinct appearance of two objects as distinct is something that propagates at finite speed, and that the propagation of that observed-distinctness is some separate phenomenon, separate from light's propagation-rate. ...and that that happens in addition to light's propagation at an infinite speed.

It was already known that light propagates (at finite or infinite speed), and you're adding an additional phenomenon that also propagates--the ability of objects to appear distinct to us.

Your theory is more complicated than Roemer's, and requires an additional assumption, an additional physical property or fact that propagates. You're assuming something ,else to be going on, more than the propagation of light.

So Roemer's explanation is the simpler one.

Whether light was regarded as a wave or a particle, no waves or objects were known to move at infinite speed, and so it wouldn't have been surprising to Roemer when he got observational results consistent a finite light-speed.

But yes, all physical theories are just theories, and eventually one is better confirmed and supported than its rivals. So yes, Roemer couldn't have known for sure that some more complicated theory didn't obtain.

That has often been the case in physics. Newton had no way of knowing that the more complicated theories of relativity or quantum mechanics obtained. But it turned out that there were more ultimate and more complicated laws of motion, mechanics kinematics and dynamics that were different from what Newton proposed.

So the simple theory isn't always the one that's right. But often it is, and in Roemer's case, that happened to be so.

Michael Ossipoff

I think we can now safely close the discussion.