... still wrong
Recently I wrote a blog entry called “Einstein v the Church v Galileo?” Without reproducing the whole thing, here’s basically what I said: There was once a view that empty space contains stuff – “ether,” a view that there was an absolute backdrop to space against which all motion in the universe could be measured.
Then making one of my central claims, I noted that the dispute highlighted in the notorious Galileo affair – whether the earth moves around the sun or the sun moves around the earth, really only makes sense when we presuppose this “fixed backdrop” view of motion in space.
Next, I drew support for this claim from Albert Einstein. As has been summarised, “Prior to the generation of Einstein’s theory of special relativity, physicists had understood motion to occur against a backdrop of absolute rest (the “ether”), with this backdrop acting as a reference point for all motion. In dismissing the concept of this backdrop, Einstein called for a reconsideration of all motion. According to his theory, all motion is relative and every concept that incorporates space and time must be considered in relative terms. This means that there is no constant point of reference against which to measure motion. Measurement of motion is never absolute, but relative to a given position in space and time.”
I then applied this summary to Galileo’s claim about the earth and the sun. His view had been it was an objective fact that the earth travelled around the sun, and that it was objectively false (i.e. false from all observational perspectives) that the sun moves around the earth. The above summary of Einstein’s theory (or part thereof) means rejecting this pair of claims. It also means rejecting the reverse claims (that it’s objectively true that the sun moves around the earth, and objectively false that it does not). What it does is that it relativises both positions, thus denying that either position is objectively correct. From the earth’s perspective, the sun is correctly observed to move around the earth. From the sun’s perspective, the earth is correctly observed to move around the sun.
The upshot of this is that in making his claim, which he meant to be an objective claim while rejecting another view as objectively false, Galileo was wrong. Although I was challenged by a visitor who claimed that the above is not connected to Einstein’s theory of special relativity, and that Einstein’s theory, as far as he was aware, was never applied to the question of the earth moving around the sun or vice versa, the fact is, as I found more and more to be true the further I looked, is that the above description of motion in space really is associated with Einstein’s theory by scientists, and it really is appealed to in discussions about the earth and the sun.
The reality, of course, is that it really wouldn’t matter if this perspective on Galileo can be connected to Einstein or not (even though it looks like plenty of people do make this connection). This perspective on Galileo is the subject, and it can be analysed and discussed irrespective of how it connects to other theories.
So in short, my claim was as follows: What would be observed if the earth moved around the sun is actually “observationally identical” to what would be observed if the sun moved around the earth. The facts that we actually see in the universe can be correctly described either way.
In future, rather than repeat this, I will just refer to this position as “my claim.” My claim refers to two ideas: that of the earth moving around the sun, which I will call view a), and that of the sun moving around the earth, which I will call b).
You can think of either a) or b) as a model, but the evidence does not favour one over the other. Yes of course it would favour a) over some specific varieties of b) (e.g. the claim that everything else in the universe follows a perfect circular/eliptical orbit, where the earth is at the centre of that circle/elipse, but obviously that view isn’t required in order for one to hold to some form of view b).
Notice also a couple of terms that I deliberately never used in my blog post (and which do not affect my blog post – since I never mentioned them), but which are still relevant: Geocentrism is the ancient view that the earth is the centre of the universe. It wasn’t the view that the earth is the centre of the solar system, since the idea of a solar system exists within a model that is not geocentric. In geocentrism, the moon, the sun, the other planets and the stars all revolve around the earth. Ancient graphical depictions of geocentrism show all the heavenly bodies moving in a perfect circle with the earth at the centre of that circle, like so:
Heliocentrism is the view that the sun, rather than the earth, is at the centre of the universe and that all the heavenly bodies move around the sun.
As you can see from my summary of what my blog post was about, the issue wasn’t so much geocentrism or heliocentrism, but which travels around which: the earth around the sun, or the sun around the earth. That being said, what I am saying can be extended to say that from an observational point of view, the claim that not just the sun but all the heavenly bodies move around the earth is no better or worse supported than its denial.
Although the number of people taking issue with this blog post was tiny (and coincidentally all people who visit the blog of one person in particular), the comments from one visitor (the owner of said blog) were pretty boisterous. First, a whole string of false claims were made about my views. It was claimed that I excused the church (even though I said nothing about the conduct of the church, and also that the church was just as wrong as Galileo). It was claimed that I had said that Einstein accepted geocentricity (the view that it’s an objective fact that the sun orbits the earth). Things, sadly, did not improve, and when I had the audacity to complain about such misrepresentations, and I committed the sin of not changing my mind to agree with my rather outspoken guest, I was told that the issue, really, is that I have anger issues. Yep, the blog just became a therapy session.
However, there were other guests, and there was decent discussion had. One of the things that I explained is that the mere fact that view a) isn’t objectively true does not mean that it has no advantages. In particular, I explained that it has the advantage of simplicity as a model. We know, for example, that some stars and planets are much closer to the earth at some times than others – much further than could be explained by the claim that they orbit the earth (i.e. in a nice elliptical path with the earth at the centre). What we would have to posit, therefore is a whole range of paths that form shapes where the earth is not in the exact centre, and some pretty curly lines to boot! A geocentric model, to be sure, is more complicated – so much so that plenty of people might regard it as absurd on that basis. But this, of course, is not the same as saying that it is objectively false, or that view a) is objectively true (I made these points in comment 51 and 58 of the earlier blog on this subject).
Still, there was a lingering comment by my rather outspoken guest. Absolutely no reputable scholars would ever support this claim that I was making, I was told. Actually the claim changed over time. First of all I was told that this person had never seen Einstein drawn on in this issue, but as the subject was further introduced to my visitor, that claimed vanished. Clearly people were indeed drawing on Einstein. But nobody, nobody worth reading anyway, I was told, would make these claims about view a). Anybody who dared to consider agreeing with me would be “lining up with Glenn against everyone else – including all astronomers.” All!
However, another visitor then reproduced a quote from the late Sir Fred Hoyle, the eminent British astronomer – someone who surely counted as a “reputable” scholar in the field. That quote, from Hoyle’s work, Nicholas Copernicus: An Essay on his Life and Work, read:
The relation of the two pictures [geocentricity and heliocentricity] is reduced to a mere coordinate transformation and it is the main tenet of the Einstein theory that any two ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view. (p. 78)
My vocal critic who had claimed that absolutely no reputable scholar would support my claim, and that “all astronomers” would surely reject it, reacted immediately. He admitted to never having read Hoyle’s work, but he expressed absolute confidence that Bob was misunderstanding Hoyle.
There was obviously only one way to settle this – actually read Hoyle (what a radical idea – check the source!). Obviously if an argument is plausible, then it doesn’t need Hoyle’s defence, but being able to appeal to someone like Hoyle for support will at very least silence those who say that nobody else supports this view.
Having now actually read the entire chapter in Hoyle’s book from which that quote was taken, I am prompted to add this new blog entry. Call it gratuitous spotlighting of my own vindication, call it what you will. But in fact, Hoyle was endorsing exactly the view that I presented in my previous blog entry: What would be observed if the earth moved around the sun is actually “observationally identical” to what would be observed if the sun moved around the earth. What we actually see in the universe can be correctly described either way. Not only that, but he is not alone among scientists. So first, let’s take a look at what Hoyle said.
The book consists of four chapters and then an epilogue. The chapters are, as one would expect from a work with this title, historical and biographical in nature, and they also detail some of the astronomy/physics/mathematics issues that Galileo dealt with. But then comes the epilogue: “Epilogue from the Twentieth Century,” beginning on page 74. Here is where Hoyle takes advantage of the benefit of the centuries that had passed between Galileo’s time and his own (the book was published in 1973). He throws Einstein into the mix, and turns his attention to the question of whether we can really say that view a) or view b) is really objectively true. The coincidence in subjects between this epilogue and my argument are perfect – he intentionally set out a chapter on exactly the same subject that I was writing about in my earlier blog post. So the first hurdle has been passed: We are on the same page, subject-wise.
Amongst his comments, Hoyle does use the words “geocentric” and “heliocentric,” and he uses the name of Ptolemny in reference tot he former. However, that is because geocentrism is a species of view b), and heliocentrism is a species of view a). He makes it absolutely clear that by including those terms as well, he is not limiting himself only to geocentrism and heliocentrism as defined above. Of this there can be no doubt, as we see thus: In contrasting the two views which, on the whole, he is comparing, (I will continue to use my terms, the a) view and the b) view), he talks about the dominant view as the view “that the Earth really goes around the Sun, not the Sun around the Earth” (p. 75). This is a general position that includes full blown heliocentrism but is not limited to it. OK. We (Hoyle and I) are talking about the question of whether the earth moves around the sun or vice versa, asking whether or not either view can be thought of as objectively correct. The prospects are good that what we find in this chapter and apply to this question, therefore, will not be a case of quote mining and taking statements out of context. Let’s proceed.
Part of the difficulty in conveying Hoyle’s epilogue is that virtually every part of it reads like a deliberate statement of agreement with my position, and I’m not going to quote all of it. Moreover, my guest was so intent on making sure that Hoyle could never be understood by him to agree with me, that he went as far as to say that I would simply put words into Hoyle’s mouth, thereby ensuring that he did agree with me. While this may be a suspicion my guest has come to have based on his usual partners in dialogue, it is not something I do, so I have taken a different approach, as outlined below.
Recall my earlier statement that the reason one might prefer to use theory a) over theory b) is simplicity. Theory b) is difficult to work with, and is, well less useful. It has less utility as a model, hasn’t been as handy at predicting things. It involves all the same physical facts, but changes the way that we look at them in a way that will appear less neat, but this does not make it untrue, nor does it make theory a) true. Now observe Hoyle’s epilogue, reproduced here in full on the grounds that this is an out of print book that is sufficiently hard for some people to locate that this may be the only way you will get to read this chapter in full.
HERE is the chapter in pdf format. Read it, then read on.
You might disagree with Hoyle. That is fine. But if, after reading Hoyle, you maintain that he does not support my view then you either did not understand it, you have not understood me, or, unfortunately, you are not telling the truth. Hoyle explicitly and clearly affirmed that we can treat either the sun or the earth as the centre of rotation of the other, and that neither observational model is more objectively right in any meaningful physical sense. He also noted, as I noted prior to discovering this book, that view b) is less convenient to handle, and that much progress has been made using model a). He even adds that it is Einstein’s theory that lends further support to the b) view, further vindicating that claim on my part.
OK, so we’ve passed a hurdle. There does (did) exist at least one eminent astronomer who supports my thesis (and therefore supports the thesis that Galileo’s claim, which was meant to be taken as objectively true, was wrong). Are there others, perhaps? In fact there are.
The internationally renown astrophysicist George Ellis makes the following comments when discussing the big bang model. He makes the point that there are a range of models in cosmology that could well be correct and which are fully compatible with the evidence. Guess which example he picks?
“People need to be aware that there is a range of models that could explain the observations,” Ellis argues. “For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations.” Ellis has published a paper on this. “You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.”
W. Wayt Gibbs, “Profile: George F. R. Ellis,” Scientific American, October 1995, Vol. 273, No.4, p. 55.
Albert Einstein and L. Infeld, from The Evolution of Physics (New-York: Simon and Schuster (1938), 212.
Can we formulate physical laws so that they are valid for all CS [coordinate systems], not only those moving uniformly, but also those moving quite arbitrarily, relative to each other? […] The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS could be used with equal justification. The two sentences:
“the sun is at rest and the earth moves”
or
“the sun moves and the earth is at rest”
would simply mean two different conventions concerning two different CS.
Note the example they chose to use: the movement of the sun around the earth, or vice versa. The dispute between the two positions is rendered meaningless, say Einstein and Infeld, since either can be expressed with equal justification.
This quote is used in the article by Galina granek of Haifa University in “Einstein’s Ether: E. Annual Motion of the Earth,” Apeiron, 8:3, July 2001. See it online here.
I wish I could locate the source of this quote from Ernst Bloch, where he makes the following comment about the impact of Einstein and relativity on the issue of the earth moving around the sun:
From the moment that…movement is no longer produced towards something, but there’s only a relative movement of bodies among themselves, and therefore the measurement of that [movement] depends to a great extent on the choice of a body to serve as a point of reference, in this case is it not merely the complexity of calculations that renders the [geocentric] hypothesis impractical?
Enough quotes, the concept has been communicated clearly enough already. The quotes were just to dmonstrate that I am far from being the only person to say this.
This page is quite helpful for those still struggling with the idea. It shows an animation showing how we can simply change the centre of our diagram, depict the earth as not moving (as we now do with the sun), and then just let the other objects resume their normal movements as before. They are all moving around the earth, and no observations would be any different from before.
Prompted by Hoyle, then, I have gone looking to see if in fact any reputable scholars would support the point that I have made. In fact they do. Granted, given that I am talking about something that is observationally identical with what believers in view a) already believe, there’s not likely to be a lot of motivation to re-describe the motion of the planets. I have no problem with that, especially given the fact that I do not deny the fact that the earth moves around the sun. As long as people are willing to be clear and say “but that’s not a more objectively true model than a model with the earth at the middle,” because in fact it really is all relative, then astronomers can keep going about their business.
But insofar as Galileo made his claim into an objective knock down to the alternative, he was still wrong. Sorry Ken. 😉
ropata
I feel a strange desire to quote The Wizard of New Zealand:
The problem of reconciling Maxwell’s equations with the absolute space and time of Newton’s cosmology led Einstein to propose the theory of special relativity. Einstein founded his theory upon a new absolute, the “Speed of Light”. The speed of light is postulated to be invariant for all observers. However this axiom is an assumption which simply cannot be explained in terms of the theory. It is both an act of faith and a singularity.
The actual value of the speed of light is not assumed by the theory but, more importantly, what is assumed is its invariance under Lorentz transformations. In just the same way Newton had assumed the existence of absolute space and time which were invariant under Galilean transformations.
It now seems likely that all of the laws of physics can be made into a conformally invariant form. In other words the laws would remain the same when the coordinate system used to describe the whole universe or world system are subjected to a simple conformal transformation. In this conformal transformation, known as inversion geometry, the defined measuring unit for distance is able to change in a regular way from one point to another but angle measurements remain unchanged.
A frame of reference is first selected. The one chosen here being the geocentric model with the frame of reference placed with its centre at the centre of the earth. This is an acceptable model within the terms of reference of general relativity. Inversion geometry is then applied to this frame of reference. As a result we obtain a universe which is totally inverted or turned “inside out.”
🙂
Ken
Some points of clarification, Glenn. (I have not chased down your references at this stage).
Yesterday you gave as your stance:
“My position was, and is: Heliocentrism (your term in post 1 for the view that the earth, as an objective fact, moves around the sun and not vice versa) and geocentrism (the view that the sun, as an objective fact, moves around the earth and not vice versa are both wrong. Galileo, I have said (and nobody has corrected me), advocated the former view, and for that reason, he was wrong.” (Although that may have been altered – I will check to see if I have an original).
Today you say your stance is:
“What would be observed if the earth moved around the sun is actually “observationally identical” to what would be observed if the sun moved around the earth. The facts that we actually see in the universe can be correctly described either way.”
Now, I think Galileo showed both stances are (were) wrong. However, my current point is that they are not the same. Yesterday you were talking about objective facts (which is what scientists all work to achieve and what the Church then claimed could only be got through scripture).
Today you are talking only about observations. Of course this was part of the problem before Galileo in that an instrumental model based on either could explain the observations. (“observationally identical”). Of course Galileo made extra observations which showed the former Ptolemaic model could not explain things like Jupiter’s moons and the phases of Venus. This helped to move support away from the Ptolemaic model.
Anyway, I wonder if there is anything significant in your move away from the concept of objective facts? I wonder if you are promoting a specific epistemological approach here?
I nbelkieve in objecvtive reality and I also believe thast scientific epistemology enables us to get an imperfect (but improving) picture of reality. Currently our picture of the solar system and the universe is that planets do orbit their suns and we are confident that accords with objective reality. We know, though, that there will be details of that, and certainly of many other things in our knowledge which we can’t be so confident of. But just as Galileo’s concept of the solar system gave a closer picture of reality than the Ptolemaic, or even the Copernican, systems did, our current picture is also more accurate than wither of the three.
I am sure I will have further comments on your interpretations of the pieces you quote (after I have read them). But for now – can you please clarify exactly what position your are arguing for? Observational consistency or objective fact?
Glenn
No Ken, there is absolutely no difference of any kind at all between my position in this post and the last. It is identical.
Your quote from my previous blog entry fully confirms this. It says that I am rejecting the view that a) is objectively true and that b) is objevtively false.
Are you absolutely sure, Ken, that you know what “objectively” means? it means that while the descriptions in each case might not be wrong, they have no claim on being the one, only proper way of describing things. Numerous times throughout my previous blog I made reference to the issue of observation. My point was from the beginning and still is, and has continually been expressed as, the view that the physical facts do not commit to one view at the expense of the other. To say that they do is a mistake (which has always been the clear reason for my saying that Galileo was wrong). I reject any suggestion that I have changed anything here. Could it be that maybe you were simply much too hasty last time, didn’t read as carefully as you should have, and just failed to follow what was being said, and now, finally, the penny has dropped?
That may sound uncharitable, but that is certainly how it appeared to my throughout all your comments lest time, Ken. Could it be correct? Do you recall, for example, how you appealed to Hoyle’s view of the physical facts, and I said that this is “not the point”? Do you recall how that confused you at the time?
There is no distinction to be drawn between objective fact and the issue of observation, because the whole reason for using the term “objective” has been to draw attention to the question of whether the observations commit to one view as true or not. I have said throughout, and always consistently, that they do not. This is what I told you my position was last time, and it is still what I say now. The physical facts are not the issue. They never were. The physical facts are exactly the same in view a) and view b). This is why neither has the right to be called the objectively true view.
Two other readers of the earlier blog realised what I meant, as have a couple of other people who did not comment on the blog (because of you and what they saw as a hostility on your part, as it turns out).
If you’re actually now going to tell me that you agree with what I have called “my claim,” please let me know.
Bob
Good stuff Glenn!
We’ve seen animation of sun and the planets all the time. But I wonder now, have we actually sent satellite far enough to photograph our own solar system from afar?
Glenn
Thanks Bob. 🙂
However, even if we did that with a satellite, what we saw would tell us nothing about whether geocrenticism is the right way to describe things or not.
Ken
Just a comment on style at this stage, Glenn.
It does nothing for your case to be childishly personal. If anything, it brings home to me the different experiences I have had in scientific disputes (generally polite but passionate) and religious ones (generally judgmental and condemning).
Your style reminds me of a time when I, as a young child, was terrorised by an old religious lady. I was only collecting the paper money, was ordered inside and then exposed to a lecture about me being a sinner. I see that as psychological child abuse. Talk about diverting attention away from the issue of the overdue paper money.
Well, I am a lot older now. I recognise attempted emotional manipulation and this use of anger and derogatory statements.
It doesn’t effect me, water of a ducks back.
Now, I will be impressed by a calm attitude, simple response to questions of clarification, and sober listening on your part. Currently, that is not happening, and you are missing a lot of information as a result.
You know, if you are right, you don’t need to behave like this.
If you are wrong, then a man can accept mistakes. We all make mistakes.
But continuing in this style discredits you and what you stand for.
Glenn
Ken, behave like what? Are you offended that I suggested that you might have been too hasty last time and didn’t fully understand what was said?
Are you offended that I have now told you that a couple of people chose not to post because they thought you were being hostile?
I think these observations are totally fair (as opposed to, say, comments about people having an ego issue, or being in over their head and unable to admit it, or making up claims about “anger issues”). I see no reason to keep them to myself if I think that they are relevant to the discussion, nor do I think that they are childish.
If we’re going to talk about what discredits a person, I think your attempt to gain a false superiority by playing parent or therapist will do it for you. But I don’t see any childishness in my above comments. I suspect that you are claiming this kind of fault because there’s no identifiable sicentific of logical fault to pick at, so you’ve got to choose something else instead. But if that’s what’s going on, then the complaint of childishness is more than a little ironic.
Honestly Ken, wouldn’t it be better not to even bring up personal jabs like this, and just play the ball, rather than the man? What I’d like, rather than this sort of distraction and ad hominem attack about what you think of my personality, is to see if you’re prepared to reconsider the substance of what has been said here on the subject of this blog post.
Glenn
Ropata – I didn’t even know the Wizard had a website!
Ken
I suspect from your intractability to evidence, that you may be taking a philosophically anti-realist position here. Particularly with your reaction to Bob’s question.
So I propose to proceed by asking you questions.
1: are you arguing there is absolutely no way of detecting if planets orbit the sun or the sum orbits the other bodies in the solar system (or the universe)?
2: if your answer is no, specifically what test would you propose to differentiate between the models, or falsify a specific model?
Obviously your answers to these 2 questions will detine my future ones?
Glenn
Ken, there is definitely no anti-realism lurking in my position, of that you may be certain. What’s more, I believe I have made it clear that the view I have offered is one that is fully open to evidence, and says that the available evidence can be thought of in different ways.
Here’s how I answer your two question.
1) No, I don’t say that there is a fact of the matter about which rotates which, but we can’t tell what the fact is. That’s not the view I have expressed, nor would I word it that way. I say that there’s actually no objective fact concerning what rotates what.
2) In light of my answer to 1), this second question has no answer.
Ken
Sounds pretty close to anti-realism to me. But I think questions may be getting us somewhere. So:
1: do you believe that the sun and the planets have objective existence?
2: if yes, do you think they influence each other, there us an imterconnection? Rotation or otherwise?
3: if yes, do you think it is possible for us tobdetect these bodies and determine the effect of their interaction?
4: if yes, how should this be done?
Bob
Hi Ken,
May be you should comment about the quotes in the post instead? Since you said that for example, Hoyle didn’t mean what he said in the quote.
The quotes in this post strongly support Glenn’s previous post. But may be attacking Glenn is easier and safer than trying to debate the people who are really expert in the field?
Personal attacks are so boring. How about addressing the actual post? More importantly the quotes from those highly regarded people
ropata
Bob said:
But I wonder now, have we actually sent satellite far enough to photograph our own solar system from afar?
Yes. The ‘pale blue dot,’ perhaps the most stunning of space images, was a parting gift from Voyager 1 as it left the Solar System.
Excellent clip narrated by Carl Sagan:
http://www.youtube.com/watch?v=2pfwY2TNehw
Glenn
No Ken, it really has virtually nothing in common with anti-realism. I don’t deny the reality of the existence of scientific laws, of objects, and I certainly have no time for logical positivism (I’m not nearly enough of a verificationist for that – quite the opposite!).
To your questions:
1) Yes, they exist objectively
2) This question asks if, among other things, they interact by rotating. This has been the subject of these two blogs. I have said that what rotates what is a relative question. They certainly move relative to each other. Relative tot he earth, everything goes around us. Relative to the sun, same deal.
3 and 4: Yes, it’s possible to detect such movement/interaction. It can be done by simple observation – literally looking at the objects in question (using whatever devices may be required). Seeing that something is, relative to another object, moving around it, is not complex.
If you mean the exact process of measurement one should use in order to observe whether or not one object is, relative to another, moving around it, then I’m not the best person to ask.
Ken
OK, a step back towards realism.
1: having accepted the possibility of dtecting relative movement/interaction do you accepted that we can study that relative movement/interaction and draw inferences about the nature of that interaction?
2: if so do you accept we will find some if these relative movements arise from the interaction of the specific bodies investigated while other relative movements may have nothing or very little to do with any direct interaction of the specific bodies investigated?
Glenn
Ken, I don’t really know what you mean in that last comment. We can detect relative motion. Other than knowing what that relative motion is, which extra inferences do you have in mind? Could you give a few examples?
Ken
We can detect relative motion of the earth, the moon, a comet, an asteroid and the star Sirius. There will be interactions between some of these but no or neglible interactions between others. The relative motions will on dome cases be determined or influenced by interactions, in other cases they won’t.
Glenn
OK, I think you mean that there will be relative motion between some things that don’t interact in any other obvious way.
If that’s what you meant, then sure, I think we can “study that relative movement/interaction and draw inferences about the nature of that interaction.” Of course, as in all areas of science the inferences we draw will in part depend on our prior assumptions and how much of the relevant information we have (and of course, we can be wrong about how much of it we have), but that’s nothing new to your or to the scientific community.
As far as the second question goes: I’m not sure. Possibly the best thing to say is that there will be some pairs of objects for which we can say that we have detected that their relative movement towards/from/around each other is closely related to some other relationship that they have, and there will be some pairs of objects for which we are not in a position to say this.
While I’m answering these, Ken, I wonder if you’ve had a chance to read that chapter from Hoyle yet. Any thoughts on it?
Ken
Bob – I thought it was obvious that our current discussion is aimed at elucidating exactly what Glenn’s current position is and what he understands from Hoyle’s quote and chapter. I think the approach is working well – for me at least. I think I am getting a clearer picture of Glenn’s position – and you must admit there is far less hostility.
However, a question for you. I have dealt with the quote you gave me from Hoyle. Now I also gave you a couple of quotes from him for your consideration. These were from Evolution of Life: A Cosmic Perspective N. Chandra Wickramasinghe and Fred Hoyle where the authors refer to “(see resulting ejecta [from mars] orbited the sun until 13,000 years ago when it plunged into the Antarctic and remained buried there in ice until its discovery.” And “Carbonaceous chondrites can thus be thought of as fragments of biological comets that have been progressively stripped of volatiles, and within which sedimentation and compaction of microorganisms may have occurred over hundreds of orbits around the Sun.”
Now I suspect you take a religious approach, treating expert’s books like the bible – to be cherry-picked for something that supports your own position. However, to be respectful about this we should see Hoyle in his complete ideas. These quotes show that he, like all modern astronomers, accepts that other bodies in the solar system orbit the sun (to a first approximation). I think these quotes are quite consistent with the one you offered. But I don’t think they are consistent with your interpretation of Hoyle’s other quote.
So, Bob, tell me why you don’t accept this position of Hoyle.
Please.
Glenn
Ken, Glenn’s “current” view? It’s the same as before. 🙂
Feel free to pose any further questions for now, but just be aware that I will intentionally be making myself scare from commenting for the next…. 5-7 days perhaps. I have exams in the coming week plus a few other things, and I’ll be writing a couple of posts that I have planned, as well as finishing off my next podcast episode.
Bob
Hi Ken, the quote you mined there from Hoyle is just about the comets.
Can you find better quote?
Ken
Bob, there’s plenty to quote from any number of astronomers if that’s what you want. Just specify your requirements. However my point is that Hoyle cleat sees bodies in the solar system as orbiting the sun. Comets, planets, asteroids, etc.
Hoyle didn’t publish in opensource journals, unfortunately, but this should be adequate for you.
If you have any doubts let me know and I will find quotes from other astronomers. Or you could look at a few astronomy books yourself.
Ken
Glenn. I think your wariness when it comes to discovering causal relationships may be significant.
Your reference to prior assumptions – to me is rather loaded. We, of course don’t ignore existing scientific knowledge when we make iferences. But we do exactly the same when we make measurements of relative motion. Those measurements will utilize scientific knowledge about electromagnetic forces. Our inferences may utilize scientific knowledge about laws of motion, acceleration and gravity, etc.
There is no different level of utilization of existing knowledge (or what you call assumptions).
So I wonder, given this hesitancy:
1: do you think that description of the motion of say Venus in relation to the earth is equally valid as describing the motion of over 400 recently discovered exoplanets only in relation to the earth?
2: do you accept that describing the motion of Venus relative to the sun is more meaningful?
3: do you not accept that describing the motions of the exoplanets in relation to their own stars ( ie as orbitin those stars) is more meaningful.
4: in desribing the falling of an apple to the ground or the falling of a small meteor towards the earth, maybe actually surviving and crashing to the ground is just S meaninfully described as the earth galling to the apple or the meteor?
5: do you describe the Soyuz and Orbiter craft as orbiting the earth, or the earth as orbiting them? Do you think one can tell the difference?
6: when these craft return to earth are they landing on Terra firma or is the earth landing on them? Can you tell the difference?
Glenn
Ken thanks for your questions.
In my last comment, I answered your questions, and ended with a question for you, so I was hoping you would answer that before asking me more questions (it just seems polite). So when I get back (as I said, I won’t be commenting much, if at all, for about 5-6 days), I’d really like to see your asnwer to that, and then after we’ve discussed that I’ll turn to your new questions.
Until then.
Bob
Hi Ken,
That’s strange how you offered me quotes from other astronomers.
Since you claimed that I misunderstood Hoyle when quoting him, may you can provide me with one or few quotes from Hoyle where we will see that I have indeed misunderstood Hoyle.
Nick
Ok, I have finally had a a chance to read the chapter from Hoyle. Sorry, no direct quotes, as I can’t copy/paste from the PDF. Probably better that way anyhow, as I have to then try explain it in my own words. A bit of a reading comprehension test eh. Lets see if I can score better than Glenn in that respect 😉
As far as my non subject matter expert eye can see, the thrust of this chapter is actually about the reference point and rotational invariance of general relativity.
He highlights this by describing the limitations of Newton’s force and inverse square laws when calculating the orbits of the planets.
In particular, he makes references to what point you take to be the centre of mass of the solar system when making these calculations. He specifically states that the inverse square law does not work at all if you take the Earth as the centre. He then goes on to state, that the law only works when you take the Sun as the centre of mass of the solar system. This however, turned out to only be an approximation, as when the gravitational effects of the planets on each other are more accurately calculated, which did not occur until (after?)the 19th century, then the centre of mass of the solar system is actually a little bit offset from the Sun.
The other point, is that these calculations with respect to the movements the stars, only agree with observations, from certain fixed directions. In other words, these laws are not rotationally invariant. I found it a bit hard to visualize this point, though, so I might be wrong there.
He then goes on to explain, that under Einstein (general relativity I would assume), these problems do not exist, and that you can accurately calculate the motion of the planets regardless of the reference frame or direction used. In other words, the formulas are reference frame and rotation invariant. To add my own point here, this is important as it is indicating the more fundamental nature of general relativity over Newtonian gravity.
Then comes the heavily quote mined bit. The conflation of the Copernican and Ptolemaic models. It seems like this is his way of stressing the invariant nature of general relativity, maybe thrown in to make the reader sit up a bit. In any case, it seems to be a bit sloppily written, as he refers to the Ptolemaic system as an accurate model of the movement of the objects in the solar system, just with the earth as the centre of rest. That is incorrect to my understanding (phases of venus etc…). Of course you can provide an accurate model with earth at the centre of rest, no doubt, but Ptolemy was not it. Perhaps, though he describes what he regards as the Ptolemaic system earlier in the book, and maybe this is the Tychonic model, which apparently is geometrically equivalent to the Copernican. Can’t say, I don’t have the book.
Directly after this however, in a piece of text that doesn’t seem to make it into the quotes. He defuses the point that he had just loaded up, by stating that we never would have achieved an Einsteinian view without discarding the Ptolemaic system in favor of the Copernican system.
My interpretation of this point, is that it is just another way of saying that: Science makes progress. It delivers approximate models of reality that are then superseded by more accurate approximations of reality.
In this case, taking a heliocentric view of the centre of mass in the the solar system, explains the movement of the planets to quite a reasonable degree of accuracy (quite good if the sun is 98% of the total mass of the solar system), good enough to take us to, and past Newton. When better calculations were made in (after?) the 19th century, these indicated that this produced inaccurate results. Luckily , Einstein comes along and provides a much more fundamental understanding that also is easy to calculate from any reference frame or rotation. I think however, that most people find it accurate enough to state that “the planets orbit around the sun”, rather than to spit out the equations of general relativity. So in this sense, we are still using the copernican model.
Business as normal people, nothing to see here. As I have previously stated, only somebody who doesn’t accept that the scientific method gains knowledge, and that all knowledge is provisional (even Einstein’s general relativity), would be going on about how Galileo was wrong.
And again, I would ask why somebody would be doing that? The only reason I can see is to attempt to confuse people about the way science works and the value it has. I think we could now refer to Bob’s comments in the previous thread as evidence that this attack actually works (science should not be taught as fact in schools, and observations from far away satellites might show different orbits of the planets). This is why I agree with Ken, that it is important to challenge these types of statements as clearly as possible.
Glenn
Nick, if I just read you right, you conceded the point and then shot the messenger.
Nick
Looks like your reading comprehension is failing you again there Glenn.
But on another point. Perhaps I was being a bit unkind to Bob in the last post.
So I will try to answer one of Bob’s questions.
Why is science taught as fact?
Well, you might have a point there. I am a long way out of the education system, and don’t have a university education, so you will have to take my comments on the education system with a grain of salt, but:
I think the teaching of science could be massively improved. From my memory, science education did seem to jump right into specifics and calculations without necessarily explaining why those things are important, and what the big picture is.
Perhaps an understanding of these sorts of more philosophical issues would be good to teach very early on. Perhaps a dedicated history of/philosophy of science class would be good.
On the other hand, people might say that these things are a bit too subtle or complex to try and teach to young kids. I don’t know, they don’t seem that complex to me, especially compared to some things. On yet another hand however, if even somebody with a phd in Philosophy has trouble accepting these points, then perhaps it might be a bit tricky for the kids.
I mean, look at how many creationists try saying things like “evolution is just a theory”. This type of thinking seems quite widespread already in some circles. I have just discovered a hotbed of geocentrists in the last couple of days. 😉
Bob
Thanks Nick, I find your comments very concise and useful, really enjoying reading them.
Now could you please find the part in Glenn’s post for anything that contradict your finding from Hoyle’s book?
Nick
Thanks Bob, I will try, but the problem is is that I don’t really understand what point Glenn is trying to make. This is why I keep asking him to clarify this.
I don’t really think its a valuable use of my time to go back through Glenn’s posts with a green pen marking out all the bits I think are wrong, inaccurate or misleading. Although I think there are many inaccuracies there in Glenn’s comments, I think you could probably find some inaccuracies in mine also, (if a professional astronomer ever looked at this thread, I imagine there would be a lot of cringing going on), that is not the point, neither of us are presenting our doctorate theses here for consideration. I am trying to understand what point he is trying to make. (Actually I think that he is trying to have an effect, more than make a point, but that is just my suspicion).
So lets stick to something simple, like perhaps the title of this thread. “Galileo part 2. Yes folks, he was wrong”. Now then, I am not trying to argue that Galileo was right about everything he said. Ken has already pointed out the issue of the tides. No question, he was wrong about some things (I mean he was religious after all ;-), sorry, low blow). But it is just not true to say that he was wrong to support the Copernican model. If Glenn had said something like, “General relativity provides a better explanation than the Copernican model for the movement of the objects in our solar system”, then I would have no problems with that. Or even “The Copernican model does not explain 100% of the movement of the planets in the solar system”, no problems.
However, Glenn is not doing this. Instead, he is stating the Galileo was wrong to support the Copernican model over the Ptolemaic. Further than this, he is trying to say that the Copernican model and the geocentric model supported by the church at the time (Ptolemaic or Tychonic, I am not really sure) are both wrong. The subtext here is that Galileo had no grounds to go against the church on this point.
I am saying that it is invalid to equate a heliocentric model with a geocentric model, essentially because a heliocentric model provides a much more accurate approximation of the motion of the planets in the solar system that a geocentric model. The reason for this is that the Sun comprises over 98% of the entire mass of the solar system. The earth obviously is not the big player in this model. You might find this link interesting regarding relative masses of the Sun and Planets http://www.applet-magic.com/centermass.htm I don’t know how accurate it is though 🙂
Lets try a different approach to demonstrate my point. I will try and construct a scenario in which I would consider that Galileo was wrong to support the Copernican model….. and in which Galileo’s and the churches positions were both wrong. Bear with me:
Imagine that at the time of Galileo, there was a very dense neutron star, or perhaps more plausibly a black hole (the important thing is that is not visible to the telescopes of the time) positioned somewhere, say 800 million miles from the Sun. In this scenario, of course the dynamics of the solar system would be completely different, and the orbits would be completely different. The point is, if the Sun was contributing say, only 30% of the mass of solar system, I imagine you could say that Galileo was incorrect to support a heliocentric Copernican system. In this configuration, though, I imagine that the observations would not be pointing towards a sun centric model, so Galileo would not be supporting that in any case.
As far as I know, Galileo supported the Copernican model as this supplied the best fit with the observations made at the time. Trying to hold him to a higher standard than this is just not realistic. Even if a contemporary of his had come up with general relativity, I suspect that there would have been no observations/evidence at that time to prefer general relativity over a simplistic Copernican model, so it might have been rejected due to complexity. If however, it made some predictions that differed from the Copernican model, which it does, and at some future time, more accurate observations were made that swung the weight of evidence in it’s favor, then general relativity would rightly supersede the Copernican model.
But guess what, if anything, general relativity is actually confirming the Copernican model by providing a more fundamental model of why the Sun appears to be the centre of the solar system.
A final point. Actually some (hopeful) thought provoking questions, to leave you with. What is mass? How does mass attract? Will the Higgs bosun be found? What is dark matter? What is dark energy? Will there ever be a more complete or fundamental model of the movement of the visible objects in the universe than general relativity?
Ken
Yes, Glenn, I had read that chapter. I had thought my questions were obviously related to it.
I am trying to find out how you interpret the chapter, because clearly your interpretation is different to mine. This may arise from philosophical differences, different understanding of scientific epistemology, or different information about the history of the change from geocentric to heliocentric and then to modern pictures of the solar system and astronomy.
Otherwise – my thoughts. Basically the book is on the history of the Copernican system and that chapter should be read in reference to that time – and the information available. That is what Hoyle has necessarily concentrated on. I have no problem with the chapter but one must go far more widely to understand our modern picture. Hoyle does not develop the history from that time to the present.
Actuality the forward from Einstein I quoted in my recent post (Einstein on Galileo’s contribution) did bring out Galileo’s place in the history of science, it covers the subject more widely and adequately than Hoyle did. I like it because it does bring out the significance of Galileo for modern science and society.
However, your interpretation, as I have so far gathered, makes it clear that your are concentrating on the arguments – as the relate to observed motion during that period.
So, yes I have read the chapter. I have no problem with it. It is really only relevant to the period – obviously. I can appreciate some aspects of your current argument. However, i think this form of discussion has proven fruitful. You have been bale to make your viewpoint clearer and I have been able to get a better appreciation of it.
I am still trying to find out the real basis of your claim sthat “Galileo was wrong” and, more recently, “I say that there’s actually no objective fact concerning what rotates what.”
I clearly disagree with you on these – and think all modern astronomers would as well.
But I am trying to find out the basic underlying reasons for the claims.
So hopefully, you will humour me and reply to my questions. They do prove I am listening.
Ken
Bob – please don’t avoid the issue. Of course all astronomers are relevant. I have already given you quotes from Hoyle which make clear that he sees bodies in the solar system orbiting the suns. Do you really think he didn’t believe planets orbit the sun?? If so – where is the evidence.
(Hoyle did have some crazy ideas which creationists love him for but this wasn’t one of them).
Now – you were arguing for Glenn’s position that one could not know if planets orbit the sun. Clearly Hoyle does “know” that comets, planets, asteroids, etc., in t6his solar system do orbit the sun. (OK we can get into philosophy – but if that is your argument – make it clear).
So, Bob, why don’t you accept the position held by all astronomers, including Hoyle, that planets orbit the sun? Why do you insist Galileo was wrong?
Ken
Nick – like your comments.
I think there is a lot of concern about how science is taught. I am aware of some US scientists who lament that science is taught as a collection of facts. They advocate that in the early years science should be taught as critical thinking. The facts can come later.
Mind you, the way society works it might be hard to encourage students to think more critically and creatively. My experience at the university level is that there is a very instrumental approach to knowledge. Students are motivated to learn things so they can be regurgitated in exams. They, after all, are after a meal ticket.
I believe that some women, returning to university after their families have grown, can experience a more creative approach to learning. If they have the financial support of a partner the “meal ticket” pressure is less strong. They can really enjoy learning.
It is strange. I found for example in learning about quantum mechanics in my undergraduate courses it was never a mystery. That’s surprising because it is so counter-intuitive. But students didn’t want to argue out the craziness of the ideas or the philosophy. Just how to use it to get the right answers.
It wasn’t until I had to teach quantum mechanics that I developed a more intuitive understanding of it and could incorporate some philosophical ideas into that understanding. Teaching is probably a very good way to learn. And I think if we didn’t have pressure of exams and “meal tickets” we could actually developing a better understanding of subjects, and the felling of exhilaration that comes with that.
Your comments about the nature of scientific theory never being absolutely correct and always being refined and changed with new information is also very relevant. It’s interesting to see this in respect to changes in the heliocentric and geocentric models and later.
While we say Galileo was right – his model obviously was not absolutely correct they never are). The model underwent continuous tweaking. From circular orbits, to elliptical ones, etc. And from incorporation of Newton laws of motion to general relativity (Mercury’s orbit).
A feature of the tweaking of Galileo’s model, though, was that it was evidence-based, logical and used scientific knowledge, especially new knowledge.
Looking at the heliocentric model – it also underwent tweaking. An early example is the one that Glenn shows in his
amination/a>. This is not the essential heliocentric model – it has been tweaked by adding extra unexplained epicyclical motions of the planets. This was required because the heliocentric model couldn’t explain the observations.
The unsatisfactory feature is that although addition of epicycles gave temporary relief, the only reason for introducing them was to do that. To make the model fit observations. There was no evidence-based information or scientific knowledge from which epicyclical motion could be derived. Quite different to the tweaking of Galileo’s model.
We always suspect we are on the wrong track when we have to introduce features which have no objective reasons just to make the model fit observations.
A bit like postulating negative mass for phlogiston.
What I really like about current interest in the Higg’s field/particle is the attitude of the particle physicists doing the work. Although its existence is a prediction of the very successful Standard Model, and you would think they therefore hope they find it. They are actually saying that the best outcome might be not to find it. that will force them back to the drawing boards and into development of a new model which corresponds better to reality.
There’s something nice about attitudes which can see success in failures like this.
Ken
Bugger – stuffed up the link.
By the way Nick. It’s hardly a hotbed of geocentrists. Only Glenn and Bob. No one else has weighed in to support them (on geocentricism/heliocentricims) although there are a few other blogs currently trying to blame Galileo, and excuse the church, for what happened to him.
Glenn
Ken, two quick questions in passing:
First, you just called me a geocentrist. Why?
Second, you said that there are “other” blogs trying to “blame” Galileo for what happened to him, and which “excuse” the church.”
It’s not the first time you’ve raised comments like that, so I must yet again point out that I have not and will not excuse the church, nor am I blaming Galileo for anything.
I know you don’t like me complaining about misrepresentation, but do you see that – even if if was done for subconscious/involuntary reasons, and not intentionally at all – comments and claims like those two actually do misrepresent me? Is there are reason you do it, or is it just the result of your assumptions about religious people, so it just happens naturally?
Ken
Geocentrist was the term Nick used that I was referring to.
My point about excusing the church is that at a time when humanity is celebrating Galileo’s approach and contribution to science and humanity, his turning of the telescope to the heavens, we are having to face up to a number of nay-sayers espousing sour grapes. Such as Galileo was wrong, Galileo was mistaken, the church was only following scientific consensus, Galileo was playing politics, Galileo didn’t prove it, etc., etc.
This is equivalent to blaming the victim – Vavilov was trying to undermine Lysenko, Sohlshenitsun was arrogant and anti-Russian, Sakharov was provocative, etc., etc. while letting Stalin and the CPU of the time off the hook. Being silent and their about them and their crimes.
Any objective analysis of Galileo’s role and of the Galileo affair would primarily deal with the church’s mistakes and crimes, the terrorism of the inquisition, the death and imprisonment of the victims.
Instead we get people blaming the victims, for anything they can think of. And, significantly, it is coming from apologetics sources. Not only are they out of step, they are wrong and this behaviour is not an accident.
Now, no way do I think this of all religious people – only a minority.
Glenn
Well I know Nick used the term geocentrist first, but your reply indicated that it didn’t apply to a “hotbed” of people, just me and Bob. otherwise you wouldn’t have mentioned me and Bob at all. The fact is, I am not a geocentrist, and my stated position makes it impossible for me to be one.
As for the rest, it’s false to say that a claim that Galileo was wrong (and that the church was also wrong) is tantamount to blaming him for being punished by the church. Astoundingly, I blame the clerics for the poor treatment they gave Galileo (who’d have thought?). I don’t blame Galileo for this.
Since I’ve popped in, I may as well address your questions now.
1) Yes.
2) I don’t think the term “meaningful” is a useful way of putting it, so unless you object, I will change it to “useful.” And yes, it is in most contexts. As I have said, some models have more utility (and simplicity, the combined effect of which is that some declare other models absurd), but this says nothing about a model being the one, objetively correct way of looking at relative motion. As a way of describing movement (and not of sdecribing something else), the sun moves around venus and venus moves around the sun, depending on the observational standpoint.
3) See my answer to 2).
4) It would be very strange to think of the earth “falling” towards an apple or meteor. To get this right you’d talk about “moving.” There’s a typo in the question, but I think you’re asking if it’s just as useful to talk about the earth moving, rather than the apple. I don’t think it is as useful, unless you’re a worm in the apple who might scream “the ground is hurtling towrds us! We’re all going to die!”
Questions 5 and 6 introduce something interesting: Yes, the satellites are definitely moving around the earth (and will land on terra firma), and this has more than the same relative status as any other description. Why? Because there’s a privileged perspective. People put the staellites there so that they would move with the earth as their reference point and (I think, not toally sure on this one) so that they would point in a certain direction with respect to the earth. You ask “can you tell the difference?” And I say yes, just ask someone who knows why they are there.
Now at this point there might be echoes of the video The Privileged Planet here, and you might suspect me of concealing some sort of creationist view that earth really is the privileged observer platform, because God made it and put the privileged observes on it and intended creation to be something they observe. Just in case you leap there, know that this is not lurking behind this at all (after all, I’ve already renounced geocentrism). Who knows, after all, where mankind might one day live in the cosmos?
Ken
I feel that your responses to the questions were not completely consistent in that there seems to be a tendency to favour an earth centric view but accept small bodies like the ISS as orbiting. Similarly Bob seemed unhappy to consider a comet-based perspective.
However, perhaps I can summarise my attitude towards your claims:
“What would be observed if the earth moved around the sun is actually “observationally identical” to what would be observed if the sun moved around the earth. The facts that we actually see in the universe can be correctly described either way.”
and:
“the physical facts do not commit to one view at the expense of the other.”
1: I had always believed that at the time (before Galileo’s discoveries) both the geocentric and heliocentric models could adequately describe observations made – at the time. The heliocentric model was becoming untenable, not because it was any more difficult mathematically (it wasn’t), but because it required more and more adjustments (such as the one your animation showed) for which there was no independent evidence or logical explanation. (Always a bad sign with a scientific theory).
2: I also accepted the possibility of inclusion of exoplanets in a geocentric model – although the mathematics would probably be outrageous and the unwarranted assumptions even more extreme. (As with planetary epicycles such assumptions and adjustments could also have provided independent confirmation of a geocentric model if they could actually be found – they haven’t).
3: I agreed with Hoyle on this. However, closer examination probably show that all such assumptions are not really completely warranted (that’s been my experience over the years, anyway). There had never been any reason why I should look into it more closely. But this student paper suggests that I was wrong, and so was Hoyle with that assumption. That in fact mathematical analysis shows that a heliocentric model could not explain observations completely. In particular they do not give the correct size of orbits.
I have no interest in looking into that more deeply (it’s only of historical interest) but intuitively it sounds correct.
4: Anyway, the limited acceptability of the two models when observational data was limited couldn’t last as more evidence became available, and Galileo played a key role in providing this. It’s an important reason why we celebrate him this year.
5: Even Copernicus had produced predictions from his model which he suggested could be tested. With Galileo’s new application of the telescope some of these predictions could be checked. In other words we no longer had to rely on just the mathematics of the two models.
6: Galileo observed the phases of Venus – one of Copernicus’s predictions, and the orbiting Jovian moons. He also showed that the available observational resolution was insufficient to detect the predicted parallax of distant stars. (That observation came later).
7: It is sometimes forgotten that Galileo was also doing experimental work on motion and acceleration. This helped produced laws of motion which helped in the understanding of the movement of the planets.
So we have gone from Einstein’s Special Relativity to the ability of both models to explain the limited observation of the times for your justification of your claim that Galileo was wrong. I think both arguments have been shown to be misapplied and don’t justify your conclusion.
In the process I have learned two things.
1:That some people are using Einstein to unjustly find Galileo wrong. As I said, that was news to me.
2: My acceptance of the idea that both models explained the limited observations of the time may well have been unwarranted (as suggested by Lu and Aslaksen).
Apart form you dogmatic declarations about Galileo (and I ahve discussed where I think that’s coming from) my main concern with your position (after checking if it was non-realist) is probably embedded in you statement:
“The physical facts are exactly the same in view a) and view b). This is why neither has the right to be called the objectively true view.”
This seems to suggest that the pre-Galilean position, which persisted because of the lack of evidence) should be accepted now. Implicit in this seems to be an attitude that we can’t, in the end, discover the truth of reality by the normal scientific approach.
Glenn
Ken, I don’t think there’s anything in your summary that needs to be addressed by me but which hasn’t yet. So I’m happy to leave your comment as the last say.
Ken
Fine, Glenn. i think it’s all there.
Bob, what about you. There are a few outstanding questions/issues?
ZenTiger
Now I suspect you take a religious approach, treating expert’s books like the bible –
Ken, grow up.
Try reading Aquinas or something for a “religious approach” to logic.