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.
Neil:
No, you’re saying this:
You’re suggesting that my atheism is somehow incompatible with my claim that objective reality exists. It’s a silly claim that you have never supported. I invite you to do so now.
Here’s another example from earlier in the thread:
The irony is that it is you who are making a theological claim here, not me. Why does the idea that something is “out there” imply the existence of God?
I agree with keith here. Speculating that something exists beyond our observable world, and possibly explains things about its causation or functioning, is a very far cry from implying that that something is a personal, conscious deity, aka a god.
I agree with that.
My comments to keiths were not about his realism. They were about his conception of truth.
Neil:
You disagree with both my realism and my conception of truth.
I believe in an external, objective, human-independent reality with definite characteristics. You reject that. You pay lip service to “objective reality”, but your call-a-tail-a-leg definition of “objective” bizarrely excludes anything that is human-independent:
In other words, you do reject what I and the rest of the world call “objective reality”, and that is why you wrote:
You claim that both my conception of truth and my belief in a human-independent objective reality imply theism, but that seems obviously false to me. How do you justify your claims?
Neil, Flint,
I’m still interested in your response to the following questions, taken from an earlier comment:
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?
As usual, this is a misrepresentation of what was said. I think Neil and I (and probably aleta) think that whether or not an “external, objective, human-independent reality” exists, it’s practical to regard it as existing and use as a very functional and useful working hypothesis.
But I’m saying I believe that even if it exists, it is necessarily filtered through human perception and conceptions and models and instrumentation. The result is that, in practice, “external reality” can’t be more than what we say it is. Nobody is making the argument that if a tree falls in the forest and there’s nobody there to hear it, that it didn’t make a sound. We’re saying that even if a hundred people were there and heard it, the sound is what they heard or recorded or detected in some other way. Which might or might not be the “actual” sound that was made, whatever that means, but who cares?
Flint:
It’s right there in his own words, Flint:
I affirm the existence of a human-independent objective reality. He denies it explicitly, because his (idiosyncratic) definition of “objective” excludes anything that is human-independent. That may not be your view, but it’s his stated view.
He disagrees with me regarding my position on objective reality, and he also disagrees with my conception of truth. He oddly suggests that both of those imply the truth of theism. I’m interested in hearing his explanation of the link, because I can’t see one. There is no conflict between my atheism and my views on truth and reality.
Flint:
Sure. That’s what I’ve been saying, too. Here, for example:
Flint:
You’re confusing the map with the territory, which is ironic considering how often you warn against exactly that. Anything we model can be more than what the model says it is, and indeed, that’s true for the vast majority of our models. Models are almost always simplifications, and thus incomplete. Reality is more than what our models say it is. That should be obvious, given that we are constantly discovering new phenomena that require us to extend our models.
If I a tree falls in the forest, the actual sound is much more than what I myself hear, for an obvious reason. As a human, my hearing is limited to a particular range of frequencies. The spectrum produced by the treefall extends beyond that range.
Curious people care. You’ve established your lack of curiosity on these questions, but don’t project that onto others. There were people — curious people — who weren’t satisfied with the range of human hearing and devised equipment capable of hearing infrasound and ultrasound. They uncovered lots of interesting stuff, including the fact that bats navigate via ultrasound. Curious people aren’t satisfied with our existing knowledge of reality; they want to extend it. That’s what science is about.
He does no such thing. He argues that any human independent reality is not precisely knowable to humans. Humans have NO CHOICE but to live in the reality they observe and experience. Which is by definition human dependent. This does NOT mean “objective reality” would be any different at all if humans were to all vanish (except it wouldn’t have any humans). It would remain squirrel-dependent to squirrels, cat-dependent to cats.
To go back to the analogy you also abuse: What humans have is a MAP, it’s a very detailed, highly researched and examined map, but is still a map. It cannot avoid being a map, because it is the human perception of reality, not necessarily the “real thing” if in fact it makes sense to talk about the real thing.
Another misrepresentation, as usual. I have as much curiosity as anyone, and I’m as enthusiastic about making every possible improvement to our maps as you are. I applaud every scientific advance, and I think the pursuit of science is perhaps the highest calling people have ever devised.
But we are improving the MAP. I hope we never stop doing so. If you prefer to believe that the map is forever converging on a perfect description of “reality”, fine. Not a necessary conceit, but not a problem. Deciding that the map has become “close enough”, now, that IS a problem.
Flint:
Please carefully note the words “on these questions”:
Your curiosity abruptly ceases at points where my curiosity, and that of other curious people, does not. You wrote:
Curious people care, which is why the question was asked in the first place.
That’s not quite right.
I disagree with your realism, but such disagreement is not uncommon.
I am utterly appalled by your absurd conception of truth, which you use as a bully.
I generally like thoughtful discussions, and I expect disagreement. But the way you use your absurd conception of truth as a weapon turns me off. It is why I often don’t respond to your posts.
They both yield results denominated in units. Whether those are units of length is what is in dispute.
keiths:
Flint:
You can stamp your feet and insist that he hold the same view as you, but his words say what they say:
Neil believes in the existence of external reality, and has stated as much elsewhere, but here he is unambiguously denying the existence of a human-independent objective reality. I don’t see how he could be any clearer about that.
If you’re wondering about this external reality that he says is not objective, well, join the club. He’s written about it in the past, and as far as I can tell, he regards it as some kind of undifferentiated entity. IIRC, he’s said that external reality has no “seams”.
Flint:
You’re still confusing map and territory. Humans do not live in the map (the model); they they live in the territory (reality), and they use the map to navigate the territory (the real world). This is true of literal roadmaps, and it’s true of our perceptual and conceptual models of reality. We live in reality; we don’t live in the models.
Flint:
The model is becoming a better and better model of reality, because bit by bit, we are eliminating discrepancies between what the model predicts and how reality actually behaves.
The model is clearly converging, and the convergence is not being imposed from within the model. It’s coming from outside, in the form of responses from reality that fail to match the predictions of the model. How do you explain the convergence, if it isn’t being caused by external reality?
keiths:
Neil:
You say it’s not right, but then you go on and immediately confirm it! You disagree with my realism, and you call my conception of truth “absurd” and “appalling”:
That sure makes it sound like you disagree with both.
How does my conception of truth act as a weapon? I’m not seeing that at all. It’s just a conception of truth. You may disagree with what I regard as true, but my assertion of those things is to be expected, and my denial of things I regard as false is also to be expected. This is TSZ, a site intended for discussion and debate. Don’t we all have conceptions of what truth is, and don’t we all argue for what we think is true and against what we think is false?
Back to the topic: You’ve suggested that both my realism and my conception of truth imply theism. Why?
Neil:
What are they units of, then?
I think it would be helpful if you would answer all three of the questions I posed. Here they are again:
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?
This is simply wrong. I’m as curious as anyone. I tried to point out that we produce as consistent and accurate a map as we can, we fight to minimize our limitations, and whether our descriptions of reality are less than a perfect match for “real” reality is a meaningless concern. We keep improving, making progress, increasing our understanding. We don’t stop, and I hope we never do.
You yourself wrote that you couldn’t possibly measure the “true length” because you can never know what it is. Now, if I thought the way you do, I’d accuse you of claiming measurement itself was a waste of time, and that you didn’t think accuracy mattered. But that’s not what you meant. You want your measurements to be as accurate as necessary, the more accurate the better. Whether what you are measuring is “length” in some absolute sense is a philosophical question.
What an odd question. They are units of measurement, according to whatever units your technique uses.
OK, this is a clear philosophical difference. I would say that people live ONLY in the map, which is the best people can ever do. Some people’s maps are pretty damn inaccurate, and some people (Fox News, looking at you) make every effort to distort the maps their audience relies on. Scientists in general try to keep distortion to a minimum, and in an increasingly granular manner. I applaud this. Like you, I can dream of a “perfect” map, but I am constrained by the concepts, the data, the knowledge that I have.
Yes, I’d say it’s most useful to think that our model is converging on an increasingly accurate picture of external reality. This is a Good Thing. Earlier, I spoke of decreasing the kurtosis of observational error. If that kurtosis ever becomes a single vertical line, we can usefully say we’ve reached external reality. You seem to have faith that such a condition is possible; I don’t.
But that doesn’t mean I completely swallow Kuhn’s view that scientific “progress” consists of endless changes in consensus, as older scientists die off and younger ones with a different philosophy are ascendant. That probably happens, but it’s not the whole story.
Length is what measurement does.
Length is also the concept that causes us to judge a system of measurement to be reliable. It is also what causes us to think about what happens to measurement when the standard ruler is uneven, or when relativistic effects become noticeable.
keiths:
Flint:
Look, I’m not accusing you of a crime. It isn’t a sin to be less curious than someone else. I’m just pointing out that your curiosity does in fact end where mine (and that of many other people) continues.
Here are some examples from this thread. You wrote:
I’m curious about what the “real” Stonehenge is like. We don’t get answers to all the questions we ask, but if we fail to ask the questions, we’re guaranteed not to get the answers (unless they fall into our laps unbidden). I think it’s worth asking the questions, but you apparently don’t.
Likewise with the angels. I don’t believe that angels exist, but I’d be very curious about them if they did, including wanting to know how many of them could fit on the head of a pin. In fact, I’m curious about them even now despite the fact that I think they don’t exist. You can still ask questions about them based on their hypothetical characteristics, or examine whether they are logically consistent. Any conception of angels that is logically inconsistent can be ruled out even without any evidence from reality for or against their existence.
In other words, there are certain things that we can learn about reality simply by thinking about them. But we have to ask the questions first.
Another example. You wrote:
I care, and a lot of people care, including the person who first asked the classic question. You may not care, but not everyone shares your lack of curiosity on this issue.
And this one:
Not only does your curiosity cease at that point, but you even denigrate the asking of “why?” as if it were a childish thing. Trust me, there are plenty of fully mature, curious adults who continue to ask “why?” at points like that even if you don’t.
So no, you’re not just as curious as everyone else.
Like I said, it isn’t a sin to be less curious than someone else. I’m just pointing out that there is a downside. If you stop asking questions, you’ll stop getting answers.
Right, but that’s not for lack of curiosity, or for lack of trying. I want to know the true length. I’m curious about it, and it could be useful to have it. I don’t fault anyone for wanting to know it or for working to get answers that are closer to it.
keiths:
Flint:
There’s an easy way to see that we don’t live in the map or model. If we did live in the model, then nothing could ever happen that wasn’t already compatible with or produced by the model. But we do experience things that are incompatible with our model, and that’s why we update it. That stuff comes from reality, not from the model.
We see things in terms of our model, but that doesn’t mean that we live in it. In terms of my lens analogy, we live in reality, but we view it through the distorting lens of our model.
Of course. We all are, but the fact that we are constrained in those ways doesn’t mean that reality is. And indeed, reality surprises us, and we have to modify our models in response.
Neil:
keiths:
Flint:
Those techniques use units of length, of course, as I’ve repeatedly pointed out. It’s obvious:
The SAM can yield results in nautical miles, statute miles, kilometers, meters, yards, feet, inches, millimeters, and so on.
The YSM can yield results in nautical miles, statute miles, kilometers, meters, yards, feet, inches, millimeters, and so on.
Those are units of length. Therefore, the SAM and YSM both yield results in units of length.
Neil disputes that. Do you?
You and Neil say that the results of the SAM are incommensurable with the results of the YSM. That means you are claiming that a SAM measurement denominated in yards is incommensurable with a YSM measurement denominated in yards.
To those of us who know what ‘incommensurable’ means, that claim is bizarre. But Neil is fond of idiosyncratic definitions, and perhaps you are too. Hence question #2 in my list:
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?
Flint:
Why don’t you think our model truly is becoming a more and more accurate picture of external reality? After all, its predictions line up better and better with the actual behavior of reality as time goes on.
What do you think it’s converging on, and why is it converging on that and not on something else? For me the answer is obvious: reality causes the convergence, and that’s why as time goes on the model becomes a more and more accurate model of reality, not of something else.
I have never claimed that we will eventually achieve a perfect model. I doubt that we will. But to leap from that fact to the conclusion that reality isn’t driving the convergence, or that external reality might not even exist, isn’t justified. It doesn’t follow.
Length is what measurement does.
Length is also the concept that causes us to judge a system of measurement
I find it amusing that we keep coming up with better and better ways of measuring fictional attributes. Using fictional numbers.
I am less curious about what is really real, and more curious why there is so little effort to converge on terms and concepts.
From where I stand, engineering is motivating the search for better definitions of length, by requiring more consistency and more precision in manufacturing.
I could easily be wrong, but the most precise measurements of tangible objects I am aware of are for the shape of telescope mirrors.
We seem to be constantly searching for ways to approach Platonic ideals in manufactured objects, and for better ways to test actual objects for conformity to ideals.
I do not think of “Platonic” as limited to the short list of solids. I think of it as any shape defined by a mathematical expression.
petrushka:
You can hear some weird shit at TSZ, and this months-long discussion has been especially productive in that regard. I’ve kept notes on some of the weirdest things that have been asserted since this discussion began in late January. Here’s a sampling:
– no two numbers can be approximately equal, because there are always infinitely many numbers between them
– if I buy 3 pies with the intention of dividing them between two people, I have bought 3.0 pies, not 3 pies
– it is infinitely unlikely that 3.0 is equal to 3.0
– 3 and 3.0 are not the same number
– the measurement “9 feet” is “horrendous”
– mathematicians disagree that the real numbers are exact
– humans must perform a “type conversion” on the number 3 in order to operate on it using real arithmetic
– integers are exact, but non-integers are approximate
– rulers might change length when they are rotated 180°
– something that isn’t measurement-derived, isn’t real, and isn’t a number can be classified as a “measurement-derived real number”
– every point on the number line is occupied by infinitely many numbers
– nobody uses infinite-precision numbers
– we shouldn’t tell people that exact numbers can be used to express inexact measurements, despite the fact that it’s true, because telling them the truth might confuse them
– 1 divided by 2 is equal to 2
– division is not permitted in integer arithmetic
and recently
– yards, feet, inches, etc., are not units of length
– a measurement denominated in yards can be incommensurable with a measurement denominated in yards
You’d expect a discussion of measurement to be pretty dry — and much of it has been dry — but the weird claims have been interesting and entertaining.
I’m as sure that there is an “absolute underlying realty” as I am sure that we can never know precisely what it is. My belief is that we are using approximations any time we measure anything, with the goal of getting as close as possible to our concept of whatever we’re measuring. One inch is a measured attribute, not a fiction. One precisely perfect inch to an infinite number of significant digits is an ideal, a conceptual model. Same with numbers – they are intended as representations of some underlying ideal perfection, which I regard as a concept, not a “thing”. When we use numbers and measurements, in practice we are striving toward an unattainable ideal. This doesn’t mean the ideal doesn’t exist, it means it’s an ideal.
I see keiths has gone to the trouble to extract quotes taken entirely out of context, from people trying to distinguish between ideal perfection and practical “as close as necessary” in some cases, and “as close as possible” in others. The fact that language has such words as “accuracy” and “precision” and “error” is a semantic acknowledgement that our efforts may be asymtotic to “reality”, but never achieving perfection.
Flint:
Those are actual assertions made by people in this thread, you among them. Context doesn’t change their meaning. They truly are as ridiculous as they seem.
Flint:
This is progress! Recently you have been questioning whether external reality even exists. For example:
And:
And:
It’s good that you’ve overcome your doubts and are now adamant that it exists!
karen,
Rehearse. Filter. Advise.
Lather. Rinse. Repeat.
I have evidently failed to communicate my point.
The original nautical mile definition was just fine.
The “subtended angle method” measures the subtended angle (as dear keiths would put it “it’s even in the name!”). What are measured are angles, which tell you (quite reproducibly) where you are on a theoretical sphere. If you want to, you could think of the angle between any two measured positions as being the ratio of the radius to the arc length. If you want to quote that as a distance, then the units would be “radii”.
If you are willing to make an assumption about the radius, then you could convert the angle to an arc length.
I’m going to type that again.
If you are willing to make an assumption about the radius, then you could convert the angle to an arc length.
The mariners using the celestial nav really did not care very much about distance, but they cared a LOT about position.
Civil servants writing specs for Dreadnoughts were the people with an interest in having a definition of mile that did not vary with latitude. It was easy enough for the French, since an average nautical mile is exactly 10 000 000 / 5 400 metres, thanks to the original definition of the metre. (So converting 1791 metres to 1906 French Nautical miles was an exact unit conversion, until they rounded it up to the nearest metre…)
The Brits and the Yanks had to go their own way, choosing 6080 ft and 6080.2 feet respectively.
I can only imagine the sailors’ reaction to being told that their nautical mile was not fit-for-purpose because the ruler was wonky.
“Your nautical mile is wonky, because one minute of latitude corresponds to a greater distance at the equator than near the poles”
“How big is the difference”
“Nearly one percent”
“Why on earth would I care about that? Get back to working on a better chronometer, ffs! Do you even know how we measure speed? It involves a bit of wood, a knotted rope and a 28-second hour-glass. Then there’s leeway and tides to estimate. Sheesh.”
They’re actual quotes? Blimey, I thought they were keithsummaries. Why no links, I wondered? To avoid the context, perhaps.
Alan Fox,
Some are quotes, stripped of all context. Some are keiths paraphrases, none of which are accurate.
I found it quite revealing that when I noted that I could not recall a single instance of keiths providing accurate read-back of an argument with which he disagreed, keiths response was disbelief. And to clarify: I believe that keiths believes he is striving to understand us. He’s wrong, of course.
This is a common creationist tactic. Yet keiths is puzzled that I sometimes liken him to a theist.
You can assume that, but you would be wrong in a couple of ways.
Columbus argued that the east coast of the Americas was only three thousand miles from Japan. Distance is location. The size of the earth was known by Europeans by 1500. Approximately, if you’ll allow the word. Columbus argued for the smallest size estimate, possibly to make it easier to get financing.
And the Arabs had developed spherical trigonometry much earlier, to calculate the distance (if you’ll allow the word) from various places to Mecca. Arc is distance to them. 500 years before Columbus.
Do you have an authoritative reference for the claim that sailors and map makers were uninterested in distance?
Which is of course very different from what I said. In fact, it’s very nearly the opposite of what I said. He even quotes me that it’s not knowable, that we can usefully pretend that it exists, and that our pretension is an article of faith. I wonder if he even tries to read what he quotes, or just assumes we either see things his way or we’re wrong.
Well, for starters, that Columbus chappie. He calculated the longitude he would need to cover (wrong) and then converted that to a distance (using the wrong units). He was denied funding because his estimates were obviously wrong. He was off four-fold, but you are telling me that a 1% error in the nautical mile was problematic. You really are missing the point.
I’ve read a fair amount about the history of nautical navigation, and I’ve done a fair amount too (although I have no practical experience of celestial navigation). On my first offshore trip, the distance covered over the ground was twice our distance through the water (a lot of cross-track error, thanks to the tides). After just 48 hours, we really had no clue about how far we had traveled, and did not care, but we desperately needed to know where we were.
When you write stuff like “Distance is location.”, I am at a loss as what you are trying to convey; to me, it’s obviously gobbledygook. You are correct about the Arabs (and Egyptians) determining the size of the earth by reconciling subtended angles with (terrestrial) distances.
For the last time: mariners could measure the former, but not the latter.
Help me understand why Columbus had funding problems due to errors in estimating size and distance, but sailors were not interested in distance.
Also, it seems that the people who invented the mathematics behind nautical miles were interested in distance. And may or may not have been sailors. Their motivation was religious.
But they used arcs to calculate distance.
keiths:
Flint:
Lol. Let’s see about that. You wrote:
OK, you’re telling us that you’re as sure of the former as you are of the latter. We know you’re sure of the latter, since you keep reminding us. Therefore you’re sure of the former. Pretty straightforward, isn’t it?
Yet until now you’ve been telling us that you’re not sure, as I demonstrated with these three quotes:
And:
And:
Here’s another one, which I think is by far the best:
According to you, someone who believes in an external reality is a mental “cripple” leaning on a “cognitive crutch”. And now you say that you believe that very thing, and that you’re sure of it:
The direct implication of your own statements is that you are a mental cripple leaning on a cognitive crutch. That’s a spectacular own goal. You’re embarrassed by it; who wouldn’t be? But why make things worse by lying about what you wrote?
How stupid — how colossally moronic — do you think the readers are? Do you really think they can’t read and comprehend the words that you yourself have written?
You are acting just like Vivek Ramaswamy. Say something unambiguously and then deny that you said it, even when confronted with an exact quote.
What would have been so horrible about simply admitting that you’ve changed your mind, and that you’re now sure that there is an external reality? You’ve made progress, so why not celebrate that? Instead you’re denying it in a way that is spectacularly counterproductive. Why?
Jock:
LMAO at “none of which are accurate.”
Why would I bother making these things up when you guys deliver them to me on a silver platter? Just yesterday Neil delivered this one:
keiths:
Neil:
He is actually questioning whether two methods, one of which we appropriately call “the yardstick method”, yield results denominated in units of length. Two methods that return results in units of nautical miles, statute miles, kilometers, meters, yards, feet, inches, millimeters, and so on, and Neil is disputing that those are units of length.
I couldn’t make this stuff up if I tried.
Just to forestall a potential objection, Neil does agree that we can measure lengths and say on that basis that, for example, one object is longer than another. So we can measure lengths and get results that are denominated in units of nautical miles, statute miles, kilometers, meters, yards, etc., and we can use the results to judge that object A is longer than object B, but Neil disputes that those are units of length:
TSZ is wild.
I don’t find a map particularly useful if I don’t know where I am. Many aircraft crashes in the Andes in the past were caused by failures in dead reckoning due to unpredicted air currents (wind) at high altitude.
That is a mystery.
petrushka, to Jock:
If nothing else, you’d think that the term ‘nautical mile’ would be a clue to these guys that we’re talking about distance. The fact that the SAM infers distance indirectly from the subtended angle and the radius of the earth doesn’t mean that it isn’t inferring distance.
Mercury thermometers infer temperature indirectly from the thermal expansion of mercury. Infrared thermometers are even more indirect: the temperature of an object causes it to emit infrared radiation of a certain intensity; that radiation is focused onto a thermopile, heating it; the heated thermopile produces a voltage; the voltage is measured, and the object’s temperature is inferred from the measured voltage. It’s highly indirect. Nevertheless, infrared thermometers do measure temperature, obviously.
The SAM measures distance, just like the YSM.
Are you actually arguing that knowing where you are doesn’t involve distance?
I’m not arguing at all. I made two observations. Firstly one of personal experience that taking a hike in state forest land with only the local IGN map as a guide depended on being able to reliably match where you thought you were to the map model. Easy to mistake one forest track for another. GPS and walking apps have made things much easier.
Secondly, dead reckoning as a sole means of navigation when flying in poor visibility at altitude in mountainous terrain is a risky business.
Though I have to say the phrase “knowing where you are doesn’t involve distance” doesn’t convey enough information to me to decide whether it does or doesn’t make sense.
The main take I have from this interminable thread is that language is an imperfect means of communication.
I have provided the missing piece, and no one has addressed it.
It is not a complex idea.
The people who invented the math, did so to calculate distance. They were mostly not at sea. The first use of the concept behind nautical miles was to calculate distance.
But there’s more.
You can’t know the size of the arc you’ve traversed without a clock. At least going east/west, which accounts for much of sea commerce.
Certainly the revolution in marine navigation needed John Harrison’s chronometer.
You seem to have this backwards. They already KNEW the distance from Syene to Alexandria thanks to the annual work of the bematists.
They also knew that the elevation of the noonday Sun varied as you moved North-South, thanks to the Phoenicians who circumnavigated Africa. By sea.
The difference in angles, combined with their prior knowledge of the distance, allowed them to estimate the circumference of the earth.
What weird wording. You can ‘know’ the distance you have covered by throwing a log off the boat, counting to 28, and seeing how much line payed out. Do that every half hour, and you ‘know’ how far you have traveled through the water, give or take 10 – 15%.
If you want to know your longitude (that’s a position, not a distance), then you’ll be needing a clock. Hence the reference to Pitcairn, ffs.