Sometimes very active discussions about peripheral issues overwhelm a thread, so this is a permanent home for those conversations.
I’ve opened a new “Sandbox” thread as a post as the new “ignore commenter” plug-in only works on threads started as posts.
Jock, to petrushka:
The circumference of the earth is a distance.
Circumference, arc length, and subtended angle form a triad. If you know two of them, you can determine the third. That means you can take a known arc length (which is a distance), together with the subtended angle, to calculate the circumference (which is also a distance). That’s what Eratosthenes did. Or you can take the known circumference (which is a distance), together with the subtended angle, to calculate the arc length (which is also a distance).
In both cases the concept is being used to calculate a distance. So when petrushka wrote
…he was correct.
Jock:
Why the ‘ffs’? What petrushka said is correct.
First, longitude is emphatically not a position, ffs (heh). It’s a meridian.
Now invoke the triad. The clock enables you to determine longitude, so you take the longitude at both ends of your east-west arc. The difference in longitude gives you a subtended angle. That subtended angle, together with the circumference of the earth at that latitude, gives you the length of the arc, which is the distance you’ve traveled, ffs. (lol)
How do you find the relevant circumference? You use your trusty sextant to measure your latitude, and then combine that information with the known circumference of the earth, coming up with the circumference at that particular latitude.
You have used your clock and sextant, together with the known circumference of the earth, to determine the distance you’ve traveled along the east-west arc. Ffs.
That’s a distance, not a position, ffs.
I’m not sure I understand this dispute. Yes, you can use latitude and longitude to determine where you are on the surface of the earth. Knowing the earth’s circumference (a great circle intersecting two positions), you can determine the distance between any two points. So OK, what is it you want to know?
1) Where am I?
2) How can I get from point A to point B? For this, you use the direction.
3) How far away is point B? For this, you calculate the distance.
4) How long will it take? Use distance and speed to determine this.
Seems to me, knowing where you are is the starting point. Knowing where some other location is relative to where you are is important if you are traveling. Knowing how far to travel might be useful as well. So?
(I understand that if you know the location of your destination, you can get the distance. If you only know the distance, that’s not a lot of help.)
Flint:
As far as I can tell, it’s just been petrushka making a series of reasonable statements and Jock looking for reasons to disagree with them.
More on this shortly.
I won’t assert I’m correct. But I could post links to my sources.
I will grant that in the 15th through 18th centuries, an error of one percent could not be detected. Probably.
https://en.wikipedia.org/wiki/History_of_geodesy
From a quick review, I think these are the points of disagreement between petrushka and Jock:
1. Petrushka correctly pointed out that the original definition of the nautical mile was “wonky” due to the fact that the earth isn’t a perfect sphere, and that the definition was modified for that very reason. Jock responded
…which is incorrect. If the original definition had been fine, there would have been no reason to modify it. What Jock seems to have meant, based on other things he has written, is that the error was small enough not to matter to early mariners. That’s true, but it doesn’t contradict anything that petrushka has said, as far as I can see, and it doesn’t mean that the original definition “was just fine.” It was good enough for early mariners, but it was flawed.
2. Jock asserts that distance wasn’t important to mariners, but location was. In fact, both were important, and Jock ironically made this point himself by bringing up Christopher Columbus. Petrushka asked:
Jock replied:
Again, I’m not aware of petrushka saying that the small error was consequential to early mariners. However, distance certainly was (and is), as he pointed out:
Petrushka is correct that sailors cared about distance, and that they used the SAM to calculate arc lengths. And not just sailors.
3. Jock made a big deal over the following:
The radius of the earth is known; you don’t have to assume it. And the conversion of subtended angle to arc length is part of the SAM, and the SAM yields a distance measurement and uses distance units, not angular units. The measurement of the angle is just an intermediate step, and as I commented earlier with regard to infrared thermometers, it is common for measurement methods to work indirectly via intermediate results.
4. Jock asserted that petrushka “had it backwards” in saying that
Jock wrote:
As I pointed out here, the circumference of the earth is a distance, and the use of the SAM to calculate the circumference of the earth from a known arc length and an angle is just the flip side of calculating an arc length from the known circumference of the earth and an angle.
petrushka:
As far as I can see, you never asserted that early mariners were thrown off by this small error and that this motivated the change in definition. If you had made that assertion, then Jock would have been correct to point out that this wasn’t the reason that the definition was changed.
Knowing your position and knowing the distance from your origin are complementary.
Knowing the distance is essential for commerce.
petrushka:
Right, and for exploration too. You need to know the distance in order to provision properly.
I don’t think this is quite the issue here. Nobody will question that if you intend to go somewhere, it’s important to know both the location where you’re going, and the distance to get there. From there, you can factor in your mode of travel, an estimate of speed using that mode (the wind isn’t always reliable), and get a probable travel time, and from that figure out what provisions you’ll probably need. I think this is all pretty obvious.
But let’s say you only know the location of your destination. Well, you can use SAM (actually, GPS) to derive an estimate of the distance. Alternatively, let’s say you only know the distance. Then your destination falls somewhere on a circle with that distance as the radius.
Not too helpful. I don’t have any links, but I recall that sailors looking to reach Pitcairn Island had a location, from which they could estimate a distance, but traveling that distance was problematic – they had to deal with storms, currents, breakdowns, provision stops (not too many of them in the mid-Pacific), becalming, etc. So they really couldn’t make a good estimate of just how far they would end up traveling through the water.
But the solution was fairly straightforward: On a regular basis, take sightings to get your current location. Get a new direction. Head in that direction. When your location and Pitcairn Island’s location match, you’re there. Your starting distance was likely not very helpful, because of the necessity of side trips, and because you might very well get blown off course in a storm, and because you wanted to avoid getting stuck in the doldrums. Best to pack for a MUCH longer trip than the initial distance calculation suggested (and be equipped to do a lot of fishing).
Today, I think this issue is largely moot, because our means of travel are so much more reliable. Say your yacht cruises at 14 knots. So you fire up the engine, aim at your destination, and hold your course. Today’s ships aren’t so concerned with location (except to get a direction), it’s basically all distance and speed. So they cross the Pacific and arrive at their destination within an hour of the estimated time, though they’re at sea a week.
“Sextant: A Young Man’s Daring Sea Voyage and the Men Who Mapped the World’s Oceans,” by David Barrie, is a good book about the longitude/chronometer issue.
Longitude, by Dava Sobel, is another good one.
ETA: She also wrote Galileo’s Daughter, which I really liked.
keiths:
Flint:
Tell that to Jock. When petrushka asked this…
The correct answer would have been “Oh, no. They were very interested in distance.” Instead, Jock cited Columbus’s massive planning error and pointed out that the SAM error was insignificant in comparison to it. That’s true, but it doesn’t follow at all that sailors and mapmakers were uninterested in distance. Jock was wrong to disagree with petrushka on this.
Which is why petrushka was correct to assert that distance, as well as position, was (and is) important to mariners (and mapmakers, and folks figuring out distances to Mecca, etc.).
That doesn’t mean that distance was unimportant — far from it. It just means that they also had to factor that other stuff into their planning. Distance was a crucial part of the planning.
The initial distance calculation was crucial, because it set the floor upon which all of the other adjustments could be added.
Which still requires you to make that initial distance calculation. There are plenty of adjustments to make on top of that, but you have to start somewhere. And it’s not like you can just go completely overboard (so to speak) on provisioning. Your vessel’s capacity is limited, after all. There are also financial considerations. It costs money to purchase provisions. And if you were involved in the spice trade, for example, carrying excess provisions would mean carrying less lucrative cargo. For safety, it was necessary to add margins to your provisions, but you didn’t want to overdo it and sacrifice profits unnecessarily.
That’s a recipe for disaster. First, you need to account for the fact that you won’t be able to maintain a precise heading. In flight school, I learned the handy “1 in 60” rule, which says that if your heading is off by 1° and you travel 60 nautical miles, you’ll be roughly 1 nautical mile off course. That adds up quickly, and it doesn’t even account for the fact that the winds will vary along the way and may be quite different from what the forecast called for. You can’t afford to simply point the nose in what you think is the right direction and expect to arrive at your destination.
It’s much the same for marine navigation. Imagine you’re sailing from New Zealand to Pitcairn Island. That’s about 3500 miles, which is roughly equal to 60 x 58. Applying the 1 in 60 rule means if your heading is off by a mere 1°, you’ll be off by 58 nautical miles by the time you get to Pitcairn, and that’s neglecting the effect of winds and ocean currents. Pitcairn is 2 miles long and 1 mile wide, so being 58 miles off course is a big deal. There’s no substitute for being aware of location and distance.
Yes, I think Longitude might be the better book.
Flint,
So that we can proceed with the discussion, which of your two stated opinions do you now hold?
Are you sure about the existence of an external reality, as you write here?
Or do you think people who believe in an external reality are cognitive cripples, as you write here?
Hint: External reality exists, and it explains the consistency of our measurements.
Neil:
Which brings us back to your odd assertions. You claim that both my conception of truth and my belief in a human-independent objective reality imply theism. What is your reasoning? I don’t see any connection, so I’d like to understand how you reached that conclusion.
Sigh. You are being excessively literal-minded. I have done a lot of sailing, I had a great compass, and I’m aware that “holding your course” is kind of like driving down a straight road – you can’t lock the wheel in one place, you have to make constant adjustments.
And nobody is arguing that distance is completely irrelevant. The question is, given the mode of travel, what is its relative importance. I tried to make the case that location was more relevant than distance in the days of the old sailing ships, and that distance is more relevant than location with today’s ships. I provided a good number of factors that made this true. But neither location nor distance has ever been irrelevant.
Neil, Flint,
You still haven’t answered the following questions, though they are central to the discussion. I’m reproducing them here for your convenience.
Questions for N&F:
1. You claim that the subtended-angle method (SAM) and the yardstick method (YSM) don’t measure the same thing. What, precisely, are the two different things that they do measure?
2. The SAM and the YSM both yield results denominated in units of length. To me (and Erik, and petrushka) and the world at large, that means that the results are commensurable. Which is no surprise at all, because both methods measure length and yield lengths. Why do you consider them incommensurable? What are the criteria for commensurability, in your view?
Neil initially said that what makes them incommensurable is that they yield different results, but that can’t be right. By that criterion, both methods are incommensurable with themselves, since repeated measurements can differ, and that’s nonsensical.
What criteria have you applied in order to decide that they are incommensurable?
3. If they aren’t measuring the same thing and aren’t commensurable, what accounts for the fact that they yield results that are very close to each other?
You just said it here yourself. You speak of a “belief in a human-independent objective reality.”
OK, keiths. You are completely correct. The reason you can’t understand any different viewpoint is because there are no other viewpoints that are valid. Forgive us, for we are wrong.
Flint:
Lol.
keiths:
Flint:
You and Neil crack me up. You complain that I’m not trying to understand you, yet when I ask questions about your views, you either bristle at them or ignore them altogether.
Why are you here, Flint, if you’re not willing to discuss and defend your views? The questions I am posing here are in response to your claims.
You claim that the SAM and YSM don’t measure the same thing. What do they measure, then? You claim that the results are incommensurable. By what criteria? If they aren’t measuring the same thing and the results aren’t commensurable, then why do they match so closely?
Flint:
If you’ve changed your mind on any of your claims, why not simply say so? And if you haven’t changed your mind, why not defend them? Why lash out at someone for asking questions on a site that is dedicated to discussion and debate?
Neil, Flint,
I should note that both of you attempted to answer #3:
Neil said:
But that’s just restating the question. “They are correlated” is just a restatement of “the results are very close to each other”. What are those different things, and why are they correlated?
Flint said:
That explains why the SAM and the location-adjusted SAM give similar results, but it doesn’t explain why the SAM and the YSM do so.
For me, the answers are simple: Both methods measure length (distance), the results are commensurable, and the reason the results are similar is precisely because they are measuring the same thing.
Flint:
I also believe that the sun rises in the east. Your point?
Belief doesn’t imply doubt. It’s quite possible to believe things that you are confident about.
ETA: I’ll add that the most common philosophical definition of ‘knowledge’ is ‘justified true belief’. If we know something, we believe it.
Flint:
Flint, I have nothing to go on other than your words. I’ve never met you, we don’t speak over the phone, I can’t observe your body language, I don’t overhear your conversations, I’m not telepathic, and I haven’t consulted your friends and family to learn about your views on navigation or whether you have relevant experience. All I have is your words, and when you contrast the old days with today, writing:
…I have to take you at your word. I’ve got nothing else to go on.
And that’s the point. You are making adjustments, and if the average heading is off, your course will be off. Also, it isn’t just a question of steering — you have to take magnetic variation and compass deviation into account as well. Then there are variable winds and currents.
It isn’t “fire up the engine and aim at your destination”.
The thing about Pitcairn (and the reason I mentioned it originally), was that it had been charted incorrectly as being at 133°21′W, when in fact it lies at 130°06′W, an error of over 200 miles. When Fletcher Christian did find Pitcairn (after some difficulty…) he knew that anybody looking for them there would be 200 miles off, and there was a good chance that (like Captain Cook) they would give up without finding Pitcairn.
The crew members who stayed on (accurately charted) Tahiti were promptly captured by HMS Pandora and shipped off to England in a box for court martial. It would be another 18 years before Pitcairn was (re)discovered, by which time only one mutineer was still alive.
The distance from Pitcairn to anywhere else was not critical – remember that the original discussion here was whether the 1% variation in the nautical mile mattered: I viewed the mile as fit-for-purpose, whilst petrushka viewed it as wonky and unworkable. Mariners knew that dead reckoning could never approach that level of accuracy: they would expect a 2 to 5 degree error in course made good, and a 5 to 20% error in distance made good. As for how much provisions to carry, time taken to cover any specified distance could vary three to five-fold, so a 1% error seems irrelevant. By way of example, the Bounty had covered 5,000 miles and had only 5,000 to go when Bligh decided to go East instead – tripling his distance to go. Because of the wind direction…
What did matter was location. Hence all the faffing around measuring lunars and building better clocks. Ironically, using the moons of Jupiter to calibrate your clock was only practical on land, so it was something that explorers such as Cook could only do occasionally.
Jock:
Petrushka called it ‘wonky’, which is correct, but in reviewing his comments, I never saw him claim that it was unworkable or that it created problems for early mariners.
He wrote:
His point being that the discrepancy was not because they were measuring different things, but merely because the “ruler” didn’t behave as intended:
I don’t see anything objectionable in either of those statements, and he didn’t claim that the nautical mile was unworkable or that it created a problem for early mariners.
Those two statements are not contradictory, unless you are using a creationist level of literalism.
I don’t think I have ever used “imply” in comments related to this.
And that definition is obviously wrong, if you are calling it “ordinary language philosophy.” I tend to treat that as a definition of technical terminology, rather than ordinary language.
I know the story of “Little Red Riding Hood,” but I do not believe it.
Jock,
Also, petrushka noted that distance was important to mariners and mapmakers, which strikes me as an uncontroversial claim, but you objected.
In response to this question of petrushka’s…
You talked about Columbus’s massive planning error and pointed out that the nautical mile discrepancy pales in comparison. That’s true, but it doesn’t in any way support the notion that distance was unimportant to sailors and mapmakers.
So again, I can’t see anything objectionable about petrushka’s claim.
Well, he wrote:
and
to which I replied
and, in case you missed the point about Loran, even SA GPS was more accurate than Loran, but it was less reproducible, which is what you need to find that lobster pot in fog.
keiths,
It was petrushka who brought up Columbus’s self-serving calculation, I was merely highlighting how bad an example it was. Frankly, the idea that I need “an authoritative reference” for my claim that position was more important than distance accurate to 1% (notice I did not say they were uninterested, just that they were satisfied with a ball-park estimate.) struck me as ridiculous.
Ask any sailor.
Jock:
Fair enough. He did use the word ‘unworkable’. And it is unworkable when you are dealing with applications that can’t tolerate that much of an error. But he didn’t claim that early mariners found it unworkable, or that the definition was changed because of that.
He wrote:
If the original definition of the nautical mile had been completely unworkable, then no one would have used it in the first place. They did use it, but as petrushka notes, it was later modified and then abandoned.
I can’t see anything objectionable in what he wrote.
The nautical mile standardization was made in the 20th century. When a small error became significant.
Will none of you admit that location has more than two parameters, and that longitude and latitude are applicable to spheres of any size?
Tell me how I am wrongly interpreting your argument.
What I’m hearing or reading is: nautical mile is incommensurable with landlubber mile because it’s only about longitude and latitude. Distance is not important.
I think that’s fantasy.
I think it’s closer to the truth to say that educated people in the age of sail knew the size of the earth accurately enough to quickly calculate distance from coordinates. They did this because they believed arcs and distance were convertible.
This was accurate enough to find their destination, with a bit of dithering.
But needs change over time, and the Harrison chronometer was a response to the need for precision. There were ships lost due to errors of a few miles.
So gradually the deviation from spherical became important.
My point is, there was never a time when navigators thought that arc was not convertible to distance. Instead, there was a gradual realization that their ruler was not true.
Jock:
Petrushka was responding to this exact claim of yours:
He was right to disagree. They cared a great deal about distance. Among other things, you needed to know the distance when planning and provisioning a long voyage, and you needed to know the distance when deciding whether you ought to divert en route in order to resupply.
When petrushka asked this:
…why didn’t you just say something like “Oh, they were definitely interested in distance, but the error in distance due to a non-spherical earth was unimportant to them”?
petrushka:
Exactly, and that’s why I keep asking Neil and Flint why they think the SAD and YSM produce results that are incommensurable. Arc length is arc length whether it’s measured using the SAM or the YSM. The results are denominated in the same units. Nautical miles are commensurable with nautical miles, yards with yards, millimeters with millimeters. Distance is commensurable with distance.
This was Neil’s argument:
In that quote Neil seems to be suggesting, with a straight face, that before the redefinition, nautical miles were incommensurable with statute miles, meters, etc. But why? They weren’t incommensurable. Arc length is arc length, so Neil’s argument fails.
It became important as technology provided the means to detect it.
People put up with all kinds of unpleasantness when they see no alternative.
Imaging an airline pilot having to search visually for the airport after an overseas flight. I’m pretty sure that was done.
keiths, to Flint:
Neil:
Lol. The only way I can see of reconciling them is if you assume that Flint has been calling himself a cognitive cripple this entire time. “I’m sure that external reality exists” is incompatible with “only crippled minds believe in an external reality” unless Flint regards himself as a cognitive cripple.
keiths:
Neil:
Come on, Neil. Word choice isn’t going to get you off the hook. You’ve written:
And:
And:
Whether or not you used the word ‘imply’ isn’t the issue. Those quotes are pretty blatant. How do you justify them? What is the connection between my conception of truth, on the one hand, and theism, on the other? Or between my belief in a human-independent objective reality, on the one hand, and theism, on the other? I’d like to understand your reasoning because I see no connection whatsoever.
If you no longer stand behind those claims, just say so.
keiths:
Neil:
If someone asks you “Do you believe that Chicago is in the United States?”, will you say “no”? Oh, wait — scratch that. Let me try again. If I ask a normal Chicagoan “Do you believe that Chicago is in the United States?”, do you think they’ll say “no”? I don’t. I think they’ll say “yes, of course”, and that’s because they know that Chicago is in the US.
keiths:
Neil:
Oh, please. “I know the story”, “I know Steve”, “I know that voice”, and “I know downtown Chicago” aren’t using “know” in the same sense as “I know that Chicago is in Illinois” or “I know that three is less than five”. Other languages even use different words for these two kinds of knowing. Are you unfamiliar with ‘conocer’ vs ‘saber’ in Spanish, or ‘connaître’ vs ‘savoir’ in French?
When I wrote “If we know something, we believe it,” I was clearly talking about the second kind of knowing. As you know (in the second sense) perfectly well.
Cue Neil: “You can’t use different meanings! That’s Calvinball!”
I think there’s a lot of equivocation going on.
Words like approximate, length, and distance, take on hyper-technical meanings without any value added.
Looks like obfuscation rather than clarification.
Depends on how your faith is applied. I tried to say that I found the hypothesis of an objective reality plausible but unreachable. For any and all practical purposes, what we prefer to think is an underlying reality is sufficient. I notice here that you carefully omitted half of my sentence, and omitted a key word in what you quoted. Why? Any particular reason, other than you had to distort what I said to construct a dishonest claim?
I think it’s like the difference between disputing whether there is something spiritual about the world beyond our ken, and disputing whether Jesus had acne. My version of objective reality means nothing more than that I believe that our understanding of our universe can continuously improve – that we can build ever more predictive models. There is no need to believe reality is real, fixed, and objective when we can never know this. The need to believe it anyway, I regard is a crutch.
Flint,
My characterization below is correct, based on what you yourself have written:
Interested readers can find the details here.
Flint:
OK, so it sounds like you’ve reverted to your earlier position. You are not sure that an external reality exists, and you would disagree with your statement here:
To question whether “reality is real”, as you did just now, is to question its existence. If you’re questioning its existence, you are not sure it is there.
For the benefit of readers who may wonder how we arrived at this point, here is a short description of the arc (heh) of the discussion:
Way back in January, Flint wrote this:
I pointed out that 1 and 1.00000… truly are the same number, and we were off to the races. Ever since then, I have been explaining to Flint and Jock why those truly are the same number and why the additional zeros don’t change that.
There were many twists and turns, and lots of strange assertions were made along the way, but the two biggest disagreements IMO have been these:
1) whether “12” and “12.0”, for example, represent the same number (they do); and
2) whether it is possible and proper to use exact real numbers (infinitely precise, having only one value, like all real numbers do) to express inexact measurements (it is, and we all do it). “5.2 inches” is an inexact measurement, 5.2 is an exact number, and there is nothing problematic, misleading, or dishonest about saying this.
Amongst many side discussions, I made some simple arguments in favor of the two points above. Flint and Jock have avoided addressing them, literally for months.
Regarding #2, they insisted that in order to express inexact measurements, it is necessary to employ inexact numbers. While the intuition behind that is easy to see and seems persuasive at first glance, it is incorrect, and my simple argument shows why.
We dubbed these inexact numbers “the flintjock numbers”, which Jock later rechristened “the measurement-derived real numbers”, or “MDRs”. Despite the name, the measurement-derived reals aren’t real numbers at all, because real numbers are exact and MDRs are not. The MDRs are distributions (or ranges, depending on who you ask and the time of day). Nevertheless, F&J have refused to rename them, insisting that they truly are real numbers.
I’ve spent a lot of time describing why the MDRs are completely unnecessary and badly broken, but to no avail.
My main argument for why it’s perfectly fine to express inexact measurements using exact numbers (presented most recently here and here) uses the phrase “true length”. Neil objected to that phrase because he believes that length does not actually exist.
That led to the current discussion of whether the SAM (the subtended-angle method) and the YSM (the yardstick method) measure lengths (distances), whether the results are commensurable, and whether their supposed incommensurability suggests that distance does not “come from nature.”
I’m left wondering how we got here from a discussion of whether nautical miles can be converted to miles.
I’d like to see an authoritative reference asserting that the people who used the original definition thought of them as incommensurable.
petrushka:
They (Neil, Flint, Jock) won’t be able to point to one, because the people who came up with the original definition obviously thought that miles and nautical miles were both units of distance and therefore commensurable.
I mean, they even chose a name for the new unit that had the word ‘mile’ in it, ffs! (Hi, Jock!)
The only reason they invented a new unit at all is because they wanted a clean correspondence between the subtended angle and the distance unit. “1 arcminute corresponds to 1 nautical mile” is a lot cleaner than “1 arcminute corresponds to 1.1508 miles”.
Another deeply strange request. I’m with keiths on this one: of course they thought that there was a constant ratio between the two. Of course they were wrong about that. But here’s the bit you are missing: they did not care.
It was only when people started writing specs for dreadnoughts that the fuzzy nature of “twenty knots” became an issue.
What the Longitude story teaches is that knowing location requires knowing what time it is. Another can of worms, because the earth — in addition to being an imperfect sphere — is an imperfect clock. Does anybody really know?
I find it fascinating that we can define units of measurement, and over time, discover that our rulers are imperfect. Then find better rulers.
I can grok that units and definitions are fiction. Inventions. But something about them hurts when we kick them.
petrushka:
When we kick the units, our toes hit reality.
Flint is fine with saying that the earth isn’t a perfect sphere and that the original nautical mile definition had to be changed because of that. But he also questions whether “reality is real”. Well, this non-spherical earth is part of reality, and if reality isn’t real, then neither is the earth.
If the non-spherical earth isn’t real, then why did the nautical mile definition have to be changed? After all, the earth was spherical inside the model. It should have just worked. What went wrong?
The answer is blindingly obvious: the inconvenient non-sphericity didn’t come from inside the model. It came from outside. It came from reality.
N&F&J all appear to be thrown off by the fact that the SAM is quite different from the YSM, and that the errors produced by the SAM differ in nature from the errors produced by the YSM. They take this to mean that the two aren’t measuring the same thing. I commented on this earlier:
Jock responded:
So Jock, like Neil and Flint, is convinced that they don’t measure the same thing. My challenge to him, and to Neil and Flint, is to look at the eight methods I mentioned in my comment and answer these questions:
1) Is each of those eight methods measuring something that is different from all the others? Or do they all measure distance, as I (and presumably petrushka) maintain?
2) If each of the eight is not measuring something different from the others, then please organize them into groups. For each group, tell us what the methods within that group are measuring.
3) What are the criteria you applied in answering the questions above?
If history is any indication, they will avoid these questions. Their goal seems to be to obstruct the discussion when it’s going in a direction that’s difficult for them and for their stated positions.
Hopefully they’ll surprise me. Neil, Flint, Jock, how would you answer the above questions?