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.
Until they did.
Duration is duration, regardless of the clock. Distance is distance regardless of the ruler.
We acknowledge this when we talk about the accuracy or precision of an instrument.
Caring about accuracy is a psychological phenomenon, or a requirement for a task.
Accuracy is definitional, but treat it as unimportant, and it bites.
Again, I’m going to ask: are miles and nautical miles incommensurable because some people don’t care about accuracy?
The last chapter of my Carl Schmitt musings is now out–with diversions into The Day the Earth Stood Still and M.T. Anderson’s Landscape with Invisible Hand.
Is it “the last word on deep democratic theory”? Unlikely, but, in any case, it’s probably about as deep as I can get without getting dizzy. https://luckorcunning.blogspot.com/2023/09/carl-schmitt-iii-for-authentic-democrat.html
My guess is, the most workable method that’s close enough for the purpose.
Flint,
I am having trouble connecting the response you just gave to the question that petrushka asked. He is asking about your criteria for incommensurability, but your answer doesn’t address that.
I posed a similar question to which you still have not responded:
I’m trying to summarize this issue in a way that’s acceptable to many, if not everyone.
We started out with the claim that miles an (original definition) nautical miles are incommensurable because:
1. They are different concepts. Miles is distance, and nautical miles is an arc, measured in degrees.
2. They are incommensurable because the earth is not a perfect sphere, and arcs produce different measured distances depending on location and direction.
Okay so far?
My response:
1. On a perfect sphere, miles can be expressed as an arc, and arc can be converted to a distance. On a perfect sphere, they are commensurate.
2. On an imperfect sphere, arc and distance conversion is problematic. With perfect information, they are convertible, but the math is difficult. At least for humans. GPS works, so it would appear that tireless silicon calculators can handle both location and distance, simultaneously.
So it boils down to: What were they thinking? The people who invented the nautical mile.
Was distance important?
I concede that for a navigator, latitude and longitude are all you need to set a course. The course would be independent of size of the earth and distance.
But I’m back to the fact that the unit in question is called a nautical mile, not a nautical coordinate set. I assert that any sane person, crossing a trackless ocean for months, wants to know, how far.
I’d like to turn the who cares argument on its head. I think the early sailors thought the earth was a sphere, and that arcs and miles were commensurate, because discrepancies were too small to be important. If navigators thought distance was unimportant, it was because they took it for granted.
When accuracy became important, the arc definition was abandoned.
When accuracy became critical, with GPS, a whole can of worms opened up. The imperfect shape of the earth, lumps in density, relativity. Now we have phones that tell us our coordinates and how far it is to our destination.
I understood his question to ask, why would people put up with two measures that produced different results. That’s the question I answered.
I assume they didn’t notice the discrepancy because their instruments were too crude. When instruments improved, they started caring.
Or conversely, when they started caring, instruments improved.
My point would be, if they didn’t care about discrepancies, they didn’t notice incommensurability.
I’m with you so far. My reading, which may be wrong, is that the nautical mile wasn’t quite accurate (due to the shape of the planet), but it was much easier to determine with the available tools and the inaccuracy was well within an acceptable margin of error.
I certainly don’t think distance was irrelevant. I’ve tried to argue that given the vagaries of wind, weather, currents etc. total distance traveled between points A and B could vary a great deal from one trip to the next, depending on conditions. So location (“where are we now?”) was the more important factor, the deciding factor in actually reaching point B. If the easiest or most reliable way to determine location produces distances in nautical miles, that’s what to use.
I’d say, not just crude instruments but a crude mode of travel. If the time and distance for a given trip might vary by a factor of 2 (or more) between trips, the difference between statute mile and nautical mile is lost in the noise.
petrushka:
Flint:
The difference between the statute mile and the nautical mile wasn’t the issue. That difference still exists, and it should exist, because the nautical mile was never intended to be equal to the statute mile.
The nautical mile was defined the way it was for convenience. “1 arcminute corresponds to 1 nautical mile” is easier to deal with than “1 arcminute corresponds to 1.1508 statute miles”.
The discrepancy we’re actually talking about is caused by the earth’s non-sphericity, and it’s far less than the 15% difference between nautical and statute miles.
petrushka:
There wasn’t any incommensurability to notice, because there has never been any incommensurability. The SAM and the location-adjusted SAM both produce results in nautical miles, and the nautical mile is and always has been a unit of length. As a unit of length, the nautical mile is commensurable with all other units of length: light-years, parsecs, AUs, statute miles, meters, yards, feet, inches, centimeters, etc.
The discrepancy due to non-sphericity is part of the measurement error, not an indicator of incommensurability.
To elaborate, the non-sphericity of the earth contributes to the measurement error of the SAM in the same way that thermal expansion contributes to the measurement error of the YSM, or variations in air density contribute to the measurement error of the laser rangefinder method.
All of these methods measure length (or equivalently, distance). The SAM produces more error than the location-adjusted SAM, but they both measure length. The YSM produces more error than the environmentally-adjusted YSM, but they both measure length. The rangefinder method produces more error than the density-adjusted rangefinder method, but they both measure length.
All six methods measure length, and length is commensurable with length, so the results of all six methods are commensurable.
Measurement error does not indicate incommensurability.
To Keiths: if you are converting from one unit to another, and your ruler for one of the units is untrue in unknown ways, the conversion fails. Whether the degree of failure is critical depends on context.
My point is, the use of a bad ruler was not deliberate, and convertibility was always desirable. All travel on the surface of the earth occurs on arcs; miles and nautical miles are conceptually convertible. And, given the means, everyone wants to know how far.
I have an old mantel clock. It runs fast or slow depending on how tightly the spring is wound.
I want to time the baking of a cake, but I don’t know the state of the clock spring.
A. Who cares? The discrepancy isn’t great enough to matter.
B. Who cares? Time doesn’t matter. You use a toothpick to test for doneness.
Let’s connect all of this back to the original question, which is whether there is such a thing as length (or equivalently, distance).
Neil argued:
Neil’s argument fails right out of the gate because the two methods are not incommensurable, as I’ve explained above. However, I thought perhaps Neil might be using an idiosyncratic definition of ‘incommensurable’, as is his wont.
He subsequently explained his criterion:
The problem is that unequal results do not imply incommensurability, as I explained above, since both methods produce results denominated in units of distance. Distance is commensurable with distance. Even worse, if unequal results implied incommensurability, then results produced by the SAM would be incommensurable with other results produced by the SAM, and results produced by the YSM would be incommensurable with other results produced by the YSM. After all, there is always measurement error, and measurement error varies from measurement to measurement even when using the same method. For SAM results to be incommensurable with other SAM results is nonsensical, so Neil’s criterion doesn’t work.
Flint took a stab at justifying Neil’s claim of incommensurability:
Except that a yardstick can do that.Temperature and humidity will vary from location to location, and that will affect the results of the YSM since it can change the length of the yardstick. The situation is the same for both the SAM and the YSM: results can vary depending on location.
All this means is that the measurement error can vary from location to location. The YSM still measures distance, wherever it is used. The SAM still measures distance, wherever it is used. And the rangefinder method still measures distance wherever it is used, despite the fact that air density varies from location to location (and across time as well), causing the results to vary.
The SAM and the YSM differ in the nature of their errors, but they both measure distance, so their results are commensurable.
Since Neil’s criterion fails, I have (repeatedly) asked him and Flint whether they have some other idiosyncratic definition of ‘incommensurable’ that they can use to support Neil’s argument. They have resolutely avoided my question.
With the current idiosyncratic definition, Neil’s argument fails. Without a revised definition, we cannot judge whether the argument can be salvaged.
If N&F can come up with a revised definition of ‘incommensurable’ that supports Neil’s argument, they should present it. We can then see how well it works. If they can’t come up with a revised definition, they should acknowledge that.
Or they can continue to obstruct the discussion by refusing to answer my question. I hope they won’t choose that option.
petrushka:
You can always successfully convert from one unit of distance to another; that’s the very definition of commensurability. Nautical miles have always been commensurable with all of the other units of distance.
The problem with the (non-location-adjusted) SAM isn’t that its results are incommensurable with those produced by the YSM. The problem is that the SAM is subject to an error caused by the non-sphericity of the earth. Take a given arc and move it around on the surface of the earth, and the SAM will give you different lengths depending on the location. The error is location-dependent, but the result is always in units of length and is therefore always commensurable with the YSM, which also produces results denominated in units of length.
Yes, and not just conceptually. They are convertible, and that’s because they are both units of distance. Distance is commensurable with distance, and commensurability means that unit conversions are possible.
Right, and I think Flint and Jock agree with that. They just want to downplay the importance of distance and emphasize the importance of location. As far as I can tell, that issue is tangential to the incommensurability dispute. It just came up during your discussion with Jock because he thought you were claiming that the discrepancy due to non-sphericity was an issue for early mariners, and that this was the factor that motivated the redefinition of the nautical mile.
As you correctly pointed out, the discrepancy did eventually become problematic, and this did prompt the redefinition. However, Jock and Flint are correct to maintain that this wasn’t a problem during the old days when other sources of error swamped the discrepancy.
I’ve been trying to adjust my understanding to fit the insights provided by the discussion.
I have read Longitude (and seen the miniseries), and I do understand that distance does not directly affect setting a course at sea. Provided you have the coordinates of your current position, and those of your destination.
petrushka:
Oh, cool! I didn’t realize there was a miniseries. Turns out you can watch it for free online.
Right, but as you pointed out earlier in the thread, if you know the coordinates of your current position and those of your destination, you know the distance (meaning that you can calculate it). It all fits together.
This careful misrepresentation of what I wrote implies that it’s deliberate. Yes, a yardstick can change length depending on temperature and humidity. But the change in yardstick is not systemic, that is, it is not location dependent in the same way. As has been noted, GPS can always compensate for locations on the surface of the earth. There is no way GPS can compensate for changes in the yardstick based on temperature and humidity.
Another way of putting it is, the conversion from statute to nautical miles in a given location will always be the same at that location, while yardstick variation depends on factors not unique to a location.
Another way of putting it is, these are different and trying to force them to be equivalent through threadbare special pleading is (or should be) beneath you.
Flint:
Sure it is. The effect that those things have on length can be, and has been, quantified. For example, my yardstick is steel, and the coefficient of thermal expansion of steel(s) is known. Temperature variation will introduce a systematic error in measurements I make using my yardstick.
What, specifically, is so special about that particular kind of location dependence? Location is just another source of measurement error. The error of the YSM is temperature- and humidity-dependent (and thus location-dependent, despite your protests), and the error of the laser rangefinder is density-dependent. They all measure length, and they are all susceptible to different systematic errors, just like the SAM.
The YSM can be improved to compensate for variations in temperature and humidity, and the laser rangefinder method can be improved so that it compensates for variations in air density. We have ways to detect and correct systematic errors. The error due to the sphericity assumption can be corrected for, and it doesn’t depend on GPS. You just need to know the local geometry of the earth’s surface.
So? There’s no way the mercury thermometer can compensate for the absorption of infrared radiation by the CO2 that lies between the object and the infrared thermometer, but both thermometers are still measuring temperature. There’s no way the standard rangefinder can compensate for density variation, but that doesn’t mean it’s measuring something different from the density-adjusted rangefinder. The fact that systematic errors can differ between two measurement methods does not mean that they aren’t measuring the same thing.
Again, what is so special about location? A mercury thermometer and infrared thermometer can give different answers depending on things like the manufacture of the mercury tube and the accuracy of the IR thermometer’s built-in voltmeter. (There’s even a location dependence, since the object’s proximity to IR sources can skew the result.) The SAM and YSM will give different answers depending (partly) on location, and partly on other factors. In general, the measurement of the quantity X using method M can produce a different error Y depending on external factor Z. Why isn’t Z allowed to be “location” in that statement?
And if the SAM and the YSM aren’t both measuring arc length, what exactly is each of them measuring?
Lol. I feel so ashamed.
Take a spherical globe. Stick a pin in Johannesburg, South Africa. Stick another pin in Halifax, Nova Scotia. Stretch a string between the two pins, forming a great circle route. Drag a pencil alongside the string, drawing an arc on the globe.
That is an arc. It has a length. That length corresponds to the distance between the two cities. Can it be measured using the SAM? Yes. Can it be measured using the YSM? Yes. The exact same thing — the arc we have drawn on the globe — can be measured using both methods.
How could it be any more obvious that we are measuring the same thing in both cases? We are literally measuring the length of the arc we have drawn on the globe.
What kind of result does the SAM give us? A length, denominated in units of length. What kind of result does the YSM give us? A length, denominated in units of length. Both methods measure the arc length, and both yield results denominated in units of length. They are 100% commensurable.
But what if the globe isn’t perfectly spherical? That will increase the error for the SAM method. That might be a problem for applications that are sensitive to error. Does it compromise commensurability? Not at all. Both methods are still measuring the same thing — the length of the arc we drew on the globe — and both are still producing results denominated in units of length. The SAM error is bigger, but commensurability hasn’t been compromised one whit.
To measure a specific quantity X — say, the length of an arc on the surface of the globe — involves using a particular method to come up with an approximation of the actual value of X. Some methods will produce better approximations than others. They will all involve measurement errors, but the nature and magnitude of the errors will be different. Does that mean we are measuring different things? No. We are still measuring X.
The very fact that we are deliberately applying both methods to the arc we have drawn on the globe guarantees that we are measuring the same thing. What else could we possibly be measuring, if not the length of the arc we have drawn?
For any latecomers who are interested in the history of the discussion, it starts here, in mid-August, with Flint resurrecting a topic that (incredibly) ran for more than six weeks starting in late January.
Flint,
I’m curious to hear your response to this:
Regarding those of us who believe in an external reality, you’ve written:
Where, by the lights of your non-crippled mind, did the non-sphericity come from if not from reality?
😉
Where did ANY shape come from? We perceive earth to be slightly flattened at the poles. The question is whether our perceptions ARE reality. I have been saying they are perceptions. For you, as far as I can tell, we are (perhaps imperfectly) perceiving a genuine, external, objective “reality”. For me, we are constructing predictive and descriptive models, and that our perceptions are not reality itself, if there even is one.
Every argument you present requires me to accept YOUR view as a given, and you appear baffled as to how anyone could possibly think otherwise. You see science as asymptotically approaching “real” reality, and I see science as working toward the best possible models. You may well be correct in your view. How could I know?
keiths:
Flint:
From reality, of course. Reality is what tells us that the earth is non-spherical. Our model didn’t tell us that; in our model, the earth was spherical. The predictions of our model clashed with our observations of reality, so we updated the model to better match the behavior of reality.
We constantly update our models in response to input from reality, and this happens both within science and without. When I walk through my pitch-black kitchen at night, I have in my head a model of the kitchen layout and of my position and orientation within it. Suppose someone has failed to push in one of the chairs and I stub my toe on it. I instantly know that there is something wrong with my model. My model predicts that my path is free of obstacles, but I get unmistakable feedback from reality informing me that my model is incorrect. Based on that input from reality, I modify my model, and I’m able to get to the refrigerator without stubbing my toe again.
The information came from outside the model. What is outside the model? Reality.
If there is no such thing as external reality, then why did I stub my toe? After all, my model said my path was clear. What happened? It isn’t a mystery: in reality, someone neglected to push a chair in. I stubbed my toe on a chair that occupied a different position in reality than it did in my model.
Perceptions are perceptions; they aren’t reality. That’s why I disagreed with you when you argued that we live in our models. I wrote:
In other words, we live in reality, but we navigate it via our perceptions — our perceptual model.
Flint:
And to my knowledge, no one has disagreed with that.
We’re doing both, and there’s no contradiction in saying that. Perceptions are only perceptions, but they are not independent of reality. When I stub my toe and painfully perceive that there is something in my path, my perception is just a perception. However, that perception tells me something about reality. If there were no reality out there, and my model was all there was, then I wouldn’t have stubbed my toe. I learned something about reality when I stubbed my toe, even though my perception was just a perception.
Quite the contrary. I am comparing our views, and I am pointing out that your view has a serious flaw compared to mine. I keep asking questions that get at that flaw, and you keep avoiding those questions. Please stop dodging. Engage my actual arguments. Answer the questions I pose. I am engaging your arguments and answering your questions. Why not return the favor?
Models of what? If there’s nothing out there, then what are we modeling?
I stub my toe on the chair. Why did that happen if “reality isn’t real” (to borrow your wording)? Why did I have to update my model if there was nothing outside of it, nothing that I was modeling?
I pick up a scrap of wood and measure its length. Then I measure it again and again. The results are very close. Why? I say it’s because reality determines the result of the measurements. When I repeat the procedure, I am measuring the same thing in reality, so it makes perfect sense that I get consistent results. How do you explain the consistency, if “reality isn’t real”?
I pick up one scrap and repeatedly measure a length of around 5.2 inches. I pick up another scrap of wood and repeatedly measure a length of around 14.9 inches. Neither of those scraps is present in my model until I pick them up and measure them. Where did those measured lengths come from, and why are they consistent? I say they came from outside the model. They came from reality.
I have an explanation for the fact that the measurement procedure produces different results for the two scraps. I also have an explanation of why the results are consistent when we repeat our measurements. You don’t, or if you do, you haven’t presented it.
Please answer the above questions.
Flint,
Here’s what I think is throwing you off. You note, correctly, that we don’t sense reality directly. Our models and our perceptions stand between us and whatever is out there. While that’s true, it doesn’t mean that our models are opaque. To reiterate my metaphor, we can only see reality through the distorting lens of our model(s), but we’re still seeing something. We’re gaining information about what’s out there.
We do in fact get feedback from reality. I stubbed my toe, right? And I stubbed it on something that I wasn’t modeling correctly. I was trying to model the reality of my kitchen’s current configuration, and my model was wrong. It mismatched reality. Reality informed me of my error. If “reality isn’t real”, then where did that feedback come from?
Ditto for the non-spherical earth. Our model was incorrect. It mismatched reality, so we updated it. Where did the feedback come from, if not from reality?
The fact that our models aren’t perfect, and might never be perfectible, does not mean that we can learn nothing about reality, or that reality might not even exist.
Flint,
Here’s how I explained it earlier. You wrote:
I responded:
That example shows that it is possible to learn things about reality even though we can’t perceive it directly. Are you able to see that?
And does this make the case that nautical mile and statute mile are incommensurable? You still have not looked up what incommensurability means, have you? Neil wrongly used a word that happens to be an established term and you stick to it with him.
Here’s what it is: “Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measurement; e.g., metres and feet, grams and pounds, seconds and years.” https://en.wikipedia.org/wiki/Dimensional_analysis
Now, you may wrongly assume with Neil that “directly compared to each other” means that the units compared must directly map to each other and must be convertible without any hassle. This is wrong.
Notice that one of the examples in the definition is seconds and years. These do not directly convert into each other. A calendar year is of different length in different times. But there’s no such thing as “calendar second” derived from calendar year. Rather, the second is the more basic unit. (What should be considered as the more basic unit is also the subject of dimensional analysis, along with the considerations which units are commensurable or not.)
Now back to the measurement of length or distance. Let’s consider whether nautical mile and statute mile are commensurable or not. Do they have the same dimension? Yes, they do. They are unidimensional measurements of length or distance. Arc and surface are not different dimensions. A circumference or radius etc. of an arc or a circle can be measured in statute miles just fine. As I pointed out pages ago, when you measure a real-life road and the real-life road happens to be very crooked and hilly etc. as they often are, you still use the same units to measure its length. Therefore, crooked like an arc makes no difference in this discussion. So checkmark on this one.
How about arc length, such that every circle, big or small, is considered the same length? We are still operating with the same dimension and we are using of a physical quantity of the same kind. Even though arc length and (proper) length are not easily convertible, they are commensurable.
The test for commensurability is this: Can you put the units in a math formula with either unit on either side of the equal sign? To convert arc length into (proper) length you will need to know the circumference or radius of the circle, but with that information you can do the conversion. Same with calendar year versus a second: You will need to know whether it is a leap year or not, and you can do the conversion. It does not matter how complicated the formula is. It only matters that the equal sign is true.
From the physical point of view, length and arc length are the same physical quantity. Also time is the same physical quantity, so our standard time measurement and Japanese traditional time are commensurable, even though not at all easy to convert.
All discussion attempting to assert Neil-world commensurability as something worth considering is a sad mistake.
Uh-huh.
Jock,
You rather unhelpfully linked to the Wikipedia disambiguation page for ‘commensurability’, but you didn’t tell us which definition you think Neil was using. I’ll quote Neil’s argument and then ask you some questions.
Neil wrote:
1) Do you think, as Neil does, that the results of the SAM are incommensurable with those of the YSM?
2) What are your criteria for commensurability?
3) Assuming that you agree with Neil about the incommensurability of SAM results with YSM results, do you also agree that this incommensurability “argues against the idea that distance comes from nature”? If so, why?
4) You’ve indicated that the SAM and YSM measure different things, in your opinion. What does the SAM measure? What does the YSM measure? I think that both are ways of measuring the distance between two points on the earth’s surface. How about you?
5) If the SAM and the YSM measure different things, as you claim, then why do they produce results that are so close in value?
I used the word correctly.
With that test, I used the word correctly.
Neil:
The SAM and the YSM both produce results denominated in units of length, and length is commensurable with length, so you used the word incorrectly. SAM results are not incommensurable with YSM results.
Which brings us back to this exchange:
keiths:
Neil:
keiths:
Please answer the question this time.
One of those measures in units of angular distance, which is incommensurable with linear distance.
And here you are, requiring that I take your notion of reality as a given. You concede that we can’t perceive reality directly, but you can’t let go of the conviction that it must exist, because you THINK it exists.
Tell me, have you stopped beating your wife? Do you understand the difficulty of answering a question that requires you to accept something you don’t agree with? I keep telling you, but there it is again and again.
So the answer is no.
False.
If angular distance were incommensurable with linear distance, it would not be possible to measure the distance of a crooked road by linear statute miles. Unfortunately, this is over your head. You use the concept of commensurability as one should use convertibility. Back to primary school for you.
Neil:
The SAM does not produce results in units of angular distance. The units are those of plain ol’ distance. Just like for the YSM.
The units of angular distance are degrees, minutes, seconds, radians, grads, etc. The units of plain ol’ distance are light-years, parsecs, nautical miles, miles, yards, inches, etc. The SAM produces the latter, not the former. It produces distances, and distances are denominated in units of distance, not of angle.
The SAM measures a subtended angle (which is an angular distance) along the way, but it doesn’t stop there. It proceeds to convert that angle into a distance — a plain ol’ distance, denominated in units of distance, which are the same units that the YSM uses. If I ask you how far it is from Johannesburg to Halifax, I am not looking for an answer in degrees, minutes, and seconds; I’m looking for an answer in miles, or nautical miles, or kilometers. Both the SAM and the YSM are capable of producing the desired answer, denominated in units of length. They’re commensurable.
Suppose I’m flying from Johannesburg to Halifax and then on to Reykjavik. I use the SAM to determine that the distance from Johannesburg to Halifax is 6,535 nautical miles. I use the YSM to determine that the distance from Halifax to Reyjavik is 1,785 nautical miles. What’s the total flight distance? Well, just add 6,535 to 1,785 and you’ll get a total distance of 8,320 nautical miles.
Wait — what just happened? I added the result of a SAM measurement — a distance — to the result of a YSM measurement — a distance — and I got a distance as my final answer. Weird, isn’t it? It’s almost as if the two results were commensurable, or something.
And whaddaya know, they are commensurable, for the shocking reason that length is commensurable with length. The SAM and YSM produce commensurable results, and your argument, which depends on their incommensurability, therefore fails.
Flint,
Um, no. You are free to take your own notion as a given, and in fact I encourage you to do so, provided that you then answer my questions instead of running away from them.
Let’s start with this one:
And this one:
Flint:
I think it exists because I infer its existence based on reason and evidence.
If reality doesn’t exist, what did I stub my toe on?
If reality doesn’t exist, why do repeated measurements of this wood scrap give answers that are all close to 14.9 inches, while repeated measurements of this other scrap give answers that are all close to 5.2 inches? Those numbers aren’t built into my model. Where do they come from, if not from reality?
If reality doesn’t exist, why do we have to update our models in light of new discoveries? Why doesn’t every observation match what is already predicted by our models?
When I run an experiment, what am I interacting with, if not reality?
If reality doesn’t exist, what exactly are we modeling? If there’s nothing to model, how can we speak of improving our models?
None of these questions require you to take my notion of reality as a given. Answer them based on your own views. But please answer them instead of avoiding them.
Come on, Flint. You know perfectly well that I’m not asking wife-beater questions.
My questions require no such thing. I am asking you to answer them from your own perspective.
In a moment of clarity, keiths wrote:
Yup. This is in fact the first example I have of an semi-accurate read-back by keiths. Positively a red-letter day! Although, sadly, the comment went south thereafter. We also believe that they aren’t measuring the same thing because they are not, err, measuring the same thing.
Today we get
This is a pretty good distillation of his mistake. Per keiths, because you can convert, with some math, some assumptions, and appropriate conditions, a SAM into a YSM, that means that they are measuring the same thing.
Never mind that the angle is a ratio (thus dimensionless, and lacking in units, so apparently exact, heh), whilst the YSM is measured in {rulers wot I have here}, which confused the poor kid previously.
Next thing he’ll be telling us that a pitot-static tube measures velocity. (Hint: right up to the moment when it doesn’t)
Next up, voltmeters.
Jock writes, “Per keiths, because you can convert, with some math, some assumptions, and appropriate conditions, a SAM into a YSM, that means that they are measuring the same thing.”
Not sure what is wrong with that. I used to do a very common lab in trig where we built a simple angle measurement tool from a protractor and a paper clip, measured back from a telephone pole 100 ft along level ground, which we assumed because we were on the football field, and using the subtended angle and the tangent function computed the height of a telephone pole. We could have measured the height of the telephone pole, in theory, by climbing it and measured down it with a 100ft tape. The “subtended angle method” used some math, made a number of assumptions, and was admittedly not very accurate, but surely it was measuring the same thing the climbing the pole method was: the height of the pole.
No it was not.
You measured something else, and then used some math and some assumptions to get an estimate of the value you were interested in. Simply put, the methodology you use matters, as you yourself admitted. Almost all science these days involves indirect measurement. But the precise method used matters, because sometimes one of those assumptions might be wrong, and it is essential that your audience is able to audit your process.
Jock, to aleta:
Your choice of words betrays you. You just acknowledged that the method aleta described does in fact measure the height of the pole. It’s just that it’s indirect.
Indirect methods are commonplace. Recall what I wrote about thermometers:
Thermometers may not measure temperature on Planet Jock, but here on earth they do.
You can pick nits all you want, but land miles are measured on the surface of the same sphere as nautical miles. There are some highways in the American west that are long enough and straight enough that you use them to perform the earth circumference measurement.
Let’s ask NOAA:
https://oceanservice.noaa.gov/facts/nautical-mile-knot.html
There’s a technical term for people who refuse to acknowledge that words can have multiple meanings.
I can find an equally esteemed source that says:
https://www.marineinsight.com/guidelines/nautical-mile-knot-units-used-sea/
petrushka, quoting NOAA:
The word ‘mile’ in ‘nautical mile’ ought to be a clue to Jock et al that we are talking about distance. That was true even when the nautical mile was first defined, despite the fact that it depended on a subtended angle.
ROFL
“Your choice of words betrays you”
You are really bad at this.
Jock:
Jock, you just got through telling us that aleta’s method indirectly measures the height of the pole. Guess what? It infers the height of the pole from the angle and the distance along the ground. Inference and measurement aren’t antithetical — not even by your own standards. Oops.
Haha.
Jock:
No, that’s not what I’m saying at all.
First, the SAM is a distance-measuring method. Conversion is unnecessary because the result is already a distance.
Second, even if you did have to convert the result, you wouldn’t be turning the SAM into a YSM. The ‘M’ stands for ‘method’, and the methods are different. The fact that you end up with a distance in both cases doesn’t mean that the methods are the same, obviously.
Third, they’re clearly measuring the same thing. Earlier, I wrote:
Jock:
You’re confusing ‘dimensionless’ with ‘unitless’. They aren’t the same. Angles are dimensionless, but degrees, arcminutes, arcseconds, radians, and grads are all units. If you need convincing, here’s Wikipedia on radians:
Note the last sentence. If someone talks about an angle of π/2 without specifying the units, the units are generally understood to be radians. The other units — degrees, arcminutes, arcseconds, and grads — are generally stated explicitly.
Jock:
Lol at my purported confusion. That conversation didn’t turn out too well for you, Jock.
Not velocity. Airspeed. See the label on the gauge below? That isn’t a lie. The designers weren’t idiots. The system truly does measure airspeed.
Measurement methods fail if the conditions aren’t right. That’s just as true of the yardstick method as it is of any other. Try using your wooden yardstick to measure distances inside an operating blast furnace and let us know how it goes. Or try using your laser rangefinder in a smoke-filled building.
Should be fun.
Ok, Karen