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.
flint writes, “And this also repeats what I wrote above, that there is an agreed mutual intersubjective agreement about the concepts we use, the measurement techniques we use, the model of an objective reality we agree on whether it can be said to “exist” or not. And we accept this agreement because it works, until we run into a situation where it doesn’t work, and we have to re-conceptualize.”
I think I agree with this. There are lots of “agreed mutual intersubjective agreement about the concepts we use” because we are all human beings with approximately the same sensory experiences. However, as our concepts become more generalized and abstract we become less in agreement.
I thought the strength of science was in discovering or inventing techniques that could be employed by anyone and yield the same result.
Yes, in principle. Which is why papers in science specify their methodology in exhaustive detail, so that replication studies can do everything precisely the same way. In practice, not many studies are replicated in this way, and not many that are replicated produce the same results. There is actually a joke “journal of irreproducible results”, but the journal Nature tells us that “There is growing alarm about results that cannot be reproduced.”
Flint:
That’s a methodological issue, not an indication that external reality doesn’t exist!
Flint:
At the risk of forking off another topic, I’ll bite. Why not?
I think most utilitarians would agree that it’s impossible to tell when the utility function has been maximized, but I suspect they’d argue that while we can’t reach that ideal, we can still aim for it, and that coarser measures of utility can get us a long way toward that goal. (For the record, I lean consequentialist, but not utilitarian.)
That’s almost certainly true in practice, but I’ll point out that it isn’t inherent in the concept of utilitarianism itself. It is at least conceivable that a state of affairs could maximize the overall utility function while simultaneously maximizing the utility enjoyed by one or more individuals.
Also, there is such a thing as “good enough”. The mere fact that individuals’ goods are not maximized does not guarantee that civil unrest will follow.
Dictatorships do get overthrown, and they are not always replaced by new dictatorships. There can be instability in dictatorships as well as in democracies. Think of South America. Chile, Brazil, Argentina, and Uruguay all immediately come to mind as democracies that were formerly dictatorships.
That’s really stretching it. I doubt that you’ll find many people who agree that the US is an authoritarian state (except perhaps among deluded MAGAites who think the deep state is after them and that Biden is orchestrating it). The danger certainly lurks if Trump or a future Trumpoid rises to power, but in its current form, no, the US isn’t authoritarian.
Flint:
I’m not going to assume that Neil agrees with you, point by point. That would be silly. He can indicate where he agrees with you and where he doesn’t. Anyway, since you and I are the discussants, let’s make our own views the topic. Neil can jump back in if and when he summons the courage.
Nor did I. I simply took him at his word. As I keep telling him, he’s free to revise his statement, and if he doesn’t stand behind it any more, I would encourage him to do that.
Ignore the rules and say what you mean. I can take it. If the mods try to censor you, I’ll object. They’ve usually refrained from acting in cases where the “offended” party asks them not to, and hopefully that will continue.
Here’s what I’m saying. Yes, distance is part of our model. Yes, distance may not appear in external reality in the same way it appears within our model. You could even argue that it might not exist “out there” in a form that would be recognizable to us as ‘distance’. However — and this is crucial — there is something “out there” that maps to what we call ‘distance’, and that is the reason we get consistent results when we measure distances or lengths.
As I put it with regard to temperature:
Maybe the question I pose at the end of the following will help us progress:
Flint:
As hard as it might be to believe, my position doesn’t change instantly when you guys say “it simply ain’t so”. The onus is on you to provide a persuasive argument.
Could you explain exactly what you mean when you say there is no one-to-one mapping?
I’ve asked myself that question, but the answer keeps coming back “conversion is possible”. Or more accurately, “conversion is not needed”, because 500 yards is 500 yards, whether you measure it with one method or another.
keiths:
Flint:
What, specifically, are those two concepts of distance?
Performing a measurement perfectly does not mean that there can be no measurement error. I explained earlier how and why a perfectly functioning infrared thermometer can give an incorrect reading, and it’s no different for subtended-angle measurements.
Measurement error is the difference between a measured value and the true value. In past comments, you have insisted vehemently that I consider measurement error (which is odd, since I have always done that). You now seem to be denying that there is anything we can call the ‘true value’. If so, how do you define measurement error?
The yardstick method is also location dependent. The yardstick length can be affected by local temperature (think thermal expansion) and local humidity (if the yardstick is wooden). There are also geometric considerations, which I can talk about if necessary.
Infrared thermometer measurements are also location-dependent, since differences in reflectivity and the proximity of IR sources can throw them off. Location dependence doesn’t mean that IR thermometers don’t measure the same thing as mercury thermometers, and it doesn’t mean that the subtended-angle method doesn’t measure the same thing as the yardstick method.
I feel your pain. It must be excruciating for a man of your brilliance to interact with a stubborn dullard like me.
And those are?
We can’t experience it directly, but we can infer its existence by the fact that repeated measurements are consistent despite our models not specifying the values. The way I think of it is that we can “see” external reality, but only as it is refracted through the lens of our model.
How do you account for the consistency of the measurements, and the agreement between different methods of measurement, if not by appeal to external reality?
The original definition of nautical mile was modified, then abandoned, because it was insanely complex and unworkable. Every direction of travel would require a different yardstick. So option two is the one eventually adopted.
The original nautical mile was based on a spherical earth, and objective reality intervened.
GPS is affected by the shape of the earth, and the calculations are insanely complex.
But calculations are easy for computers. They get neither tired nor bored.
The assertion that nautical miles are incommensurable with yardstick miles is wrong. The problem is the original — and abandoned — definition of nautical mile was based on a bad model of the earth.
Science evolves. It is invented, and its models do not describe reality.
But its models are shaped and constrained by reality, just as living populations are constrained by necessity.
Now, leopards and slime mold are both alive, and both constrained by selection.
So it is fair to ask if there leopard models of reality, and slime mold models, both alive and both valid.
No doubt.
But look under the hood, and they are not that different. They are cousins. They are constrained by the same reality.
There is no essential difference between nautical mile and ordinary statute/imperial mile (or whatever it’s called). They are commensurable just fine. The only difference is that nautical mile as defined originally was an arc measurement. Guess what, arc has length, so nautical miles always worked the same way as all other units of length.
If somebody still insists that nautical mile and other units of length are incommensurable, then they must also insist that it is impossible to measure the length of a crooked road by imperial miles or kilometres – because the road is crooked, not straight! Let such people step forward and make their position known.
The same way as Neil’s earlier position about true values has no standing in science, also Neil’s position about incommensurability has no standing. It is helpful to everyone not to get stuck in Neil World definitions. Helpful even to Neil himself.
What this means is, there is no simple formula to convert one length to the other. To do such a conversion, you must also include a location (which means, a variable depending on earth’s curvature at that location). As I told keiths, one measure always produces the same result, while the other produces a RANGE of results depending on location. If you don’t know where the measurement was taken, you can’t do the conversion. Note that the difference would be even greater on Saturn, the least spherical of the planets. One measurement would map to a much wider range than on earth, while the other would remain unchanged.
Compare temperature, where there is a simple formula to convert Celsius to Fahrenheit, no additional variables involved. And Neil also said that these two measures of temperature are NOT incommensurable.
Flint,
I know what you are saying. And you are wrong. There is no simple way to convert between the two, but both are still measures of length, so both are measuring the same thing, and therefore there is, despite obstinate objections and other difficulties, a way to convert between the two. You gather more data points and you can do the conversion. What’s the big deal? Moreover, the issue at the heart of Neil’s argument is that, based on his peculiar dogmatism, length does not exist, and this is of course blatantly wrong.
Take traditional Japanese time. Japanese hours (more like “times of day” à la morning, afternoon etc. altogether six for the time sun is up and six for nighttime) are very different from European hours. Depending on different times of the year, the Japanese hours are of different length. They are not easy at all to convert, yet you can build the same measuring device, namely a clock, to measure them and therefore it won’t wash to state that they are incommensurable. And it makes no sense to state that time does not exist, if you are a mathematician or physicist.
Flint,
Much of your confusion is related to measurement error.
First, you seem to have forgotten that measurement error is defined as the difference between a measured value and the true value. If there is no true length, as you and Neil claim, then there is no measurement error. That’s ridiculous, of course. Your premise has led to an absurd conclusion. Toss it.
I brought this up over a week ago, when Neil first floated the idea that true lengths don’t exist:
Second, there’s this. You wrote:
Both methods produce a range of results, because there is an error associated with every measurement. The ‘yardstick method’ isn’t somehow magically immune from error. It isn’t immune from location dependence, either, because there are local factors such as temperature and humidity that can influence the results.
Third, you haven’t grasped that when the subtended-angle method produces different results depending on location due to deviations from perfect sphericity, that is just one more example of measurement error. Instead, you put the differences into a separate category, for some reason:
But of course they’re producing measurement error, just like any other measurement method, and deviations from sphericity contribute to that error.
Perhaps this will help. Suppose I set about measuring a very long rope. By measuring it, I am trying to determine the length of that rope. I apply the yardstick method, and then I apply the subtended-angle method. I know that there is an error in both cases; neither method yields the exact length of the rope.
When I look at what is contributing to the errors, I notice that the factors that contribute to error in the yardstick method are different from those that contribute to error in the subtended-angle method. The yardstick method is susceptible to variations in temperature and humidity, but the subtended-angle method is not. The subtended-angle method is susceptible to deviations from perfect sphericity, while the yardstick method is not.
Does that mean that what I’m measuring with one method isn’t the same as what I’m measuring with the other? No, of course not. In both cases I am measuring the length of the rope, and there is an error. It’s just that the sources of the error differ between the two methods.
What I’m measuring is the same. The difference is in the errors.
Erik, to Flint:
Actually, there’s an extremely simple way to convert between the two: don’t change anything. (It triggers Flint when I say that. Prepare for some entertainment.)
Both methods produce approximate results. A result of ‘500 yards’ via the subtended-angle method is an approximation, and a result of ‘500 yards’ via the ‘yardstick method’ is also an approximation. No conversion is needed in order to change ‘approximately 500 yards’ into ‘approximately 500 yards’. And since the ‘approximately’ is a given, we can say that no conversion is needed in order to change ‘500 yards’ into ‘500 yards’.
Now, we could take location into account to produce better approximations of the true distance, but in doing so we would be changing the method. It would no longer be “the subtended-angle method”. Perhaps we could call it “the location-adjusted subtended-angle method”. The error would be smaller, but the new method would still be measuring the distance.
The same holds true for the yardstick method. We could take temperature and humidity into consideration to produce better approximations of the true distance, but in doing so we would be changing the method. It would no longer be “the yardstick method”. Perhaps we could call it “the environmentally-adjusted yardstick method”. The error would be smaller, but the new method would still be measuring the distance.
All four methods would be measuring distance, and if you want to convert a distance measurement to a distance measurement, you change nothing.
‘500 yards’ will be associated with different error distributions depending on the method used to obtain it, but that doesn’t affect the ‘500 yards’ itself.
But while one method produces a distance of 500 yards, the other produces a distance of N arc-seconds at this latitude. Change the latitude, and N arc-seconds is a different distance. These aren’t different “measurement errors”, these are qualitatively different approaches to measuring distance.
I see Eric has as much difficulty grasping this as you do. You start out by defining 500 yards as the “true distance” and seem cognitively incapable of wondering if there is such a thing in the first place.
None so blind as he who WILL not see.
Yes, you can convert between the two. But to do so, you need to know where on earth the measurement was taken, and you need to need to know the curvature of the earth at that location. Early sailors couldn’t know the first with any precision (they didn’t have clocks accurate to the second), and didn’t know the curvature of the earth where they were at all. So they didn’t measure yards, they took a sextant and measured angles. Latitude mattered.
So they have commensurability. Read up on Wikipedia, if you do not know what commensurability means.
Neil does not know and never wants to know. You do not have to be like him. Actually, according to Neil it’s all convention anyway, so we should be able to agree on any terms and definitions on the fly and move on to the actual point, but instead… Well, whatever.
Flint:
They both produce measurements in yards. To insist that the SAM (subtended-angle method) only measures arc-seconds is to overlook the fact that the inference of distance from angle is part of the method.
It’s no different in principle from an infrared thermometer. The infrared thermometer doesn’t directly measure temperature. After all, temperature is defined in terms of the average kinetic energy of the molecules that make up an object, and the thermometer can’t directly measure that, especially since it isn’t even in contact with the object. It measures radiation intensity instead and infers the temperature from that.
The inference is part of the measurement method both for the SAM and for the infrared thermometer.
Infrared thermometers and mercury thermometers are qualitatively different approaches to measuring temperature. Please tell me that you accept that both types measure temperature. The fact that the SAM and the yardstick method are “qualitatively different” doesn’t mean they aren’t measuring the same thing.
Here’s another example. There are two poles in a field, and I measure the distance between them, first with a tape measure, and then with a laser rangefinder. Those are qualitatively different methods, but would you seriously argue that I’m not measuring the same distance in both cases?
Regarding the SAM, you don’t have to take latitude into account in order to measure a distance. Taking latitude into account is an optional step that you can employ if you want to reduce the error.
1. You can use the spherically-based SAM, but
2. you can enhance it by taking latitude into account, and
3. you can enhance it even further by taking tidal effects into account, and
4. you can enhance it further still by taking into account the uneven distribution of mass within the earth,
and so on.
Those four methods are not measuring different things. They’re all measuring distance, but they vary in the magnitude of the measurement error.
It’s the same with the yardstick method. You can use the plain old YSM, or you can use the environmentally-adjusted YSM, but in both cases you’re measuring distance. It’s just that the second method will reduce the measurement error.
Ditto for the rangefinder method. You can use a plain old rangefinder, or you can use one that adjusts based on air density, since light travels more slowly through denser air. The second method will reduce the measurement error, but both methods are measuring the same distance.
Flint:
No, 500 yards is the measured distance, not the true distance.
That’s a classic Flintism. The fact that I don’t agree with you doesn’t mean that I haven’t asked myself the question. I have asked it, and I’ve concluded that yes, there is such a thing.
Meanwhile, you still haven’t answered my question. You say that true distance doesn’t exist, yet we both know that measurement error is defined as the difference between a measured value and the corresponding true value. If true distance doesn’t exist, then the difference doesn’t exist, and thus measurement error doesn’t exist. That seems, um, problematic.
You have a problem, Flint. How do you resolve it?
Amen.
I’ll just say that I agree with this. We are talking of two measuring systems that are measuring different things.
This is nonsense.
It seems that keiths has a religious commitment.
In the beginning, God created heaven and earth.
And God said “Let the be true length”. And there was true length. And the evening and the morning were the first day.
Although keiths is a declared atheist, he has a very rigid “god’s eye view” conception of truth. And it doesn’t work.
For measurement, we normally judge the error of a measurement based on the defining standards for that system of measurement. Measuring in nautical miles had its own set of standards that were not derived from those for yardstick measurement.
The standards themselves are human constructs. We do not have any standards other than those constructed by humans.
Neil:
We’ve had this conversation before, more than once. In Neil World, anyone who accepts the existence of objective reality is a theist, whether or not they believe in God.
There sure are a lot of us theistic atheists in the world.
For fun, I googled ‘measurement error’ and scanned the results. I was unable to find a single case where measurement error was defined as anything other than the difference between a measured value and the “true value” or “actual value”. It’s a standard term with a consensus definition.
Let’s be clear: Since you deny the existence of true lengths, you are denying the existence of measurement error. There is no such thing in Neil World.
That’s pretty embarrassing, so you are trying to slap the label “measurement error” on something else entirely, because you want to be able to say “See? I do believe in measurement error.” But to borrow one of Flint’s favorite metaphors, you can call a tail a leg, but it’s still a tail and not a leg.
So let’s be honest. Measurement error doesn’t exist in Neil World, but you are proposing something else that you hope will fill a similar role. Let’s refer to your concept as “Neilian error”.
Regarding Neilian error, you wrote:
Suppose someone designs a new rangefinder based on, say, ultrasound. Using the principles of Neilian error, how would you go about determining the accuracy of the new system?
Okay, I have gotten into the habit of writing comments but not posting them. It’s Frank Fontaine and Jerry Lewis – related.
Here’s my response to Neil’s “in the beginning” comment.
In case the analogy wooshed, keiths, you would calibrate your ultrasound device against a (totally arbitrary) TRVTH standard.
If length is a fiction, then “measurement error” is a fiction too. Both useful fictions, mind you. Although you never really got your brain around the difference between accuracy and precision.
Now, I disagree with Neil about underlying reality, but your “arguments” against his fictionalist position fail. Abysmally. Your reductio‘s are hilarious.
Neil,
Another question for you and Flint:
If the subtended-angle method and the yardstick method are measuring different things, why do they yield measurement values that are so close, time after time after time? Is it coincidence? I say it’s because they’re both measuring length, so naturally they produce similar results.
If you measure the length of object A using two distinct, reasonably accurate measurement techniques, you’ll get similar answers. If you measure the length of object B using those same two techniques, you’ll also get similar answers. Repeat that on as many objects as you like, and you’ll get similar answers.
That’s easy for me to explain, because I know that each method does the same thing: it comes up with an approximation of the object’s actual length. How do you explain this amazing congruence, since there is no actual length for the techniques to approximate?
Neil, you noted earlier that even though you don’t think objects have true lengths, you’d be willing to say that an object A is longer than an object B based on measurements. Suppose I measure two objects using Method #1 and get a length for object A that is much greater than that for object B. I do the same thing with Method #2 and find the opposite: object B’s measured length is much greater than object A’s.
Which of the following is true?
1. Object A is longer than object B.
2. Object B is longer than object A.
3. Neither object is longer than the other.
4. Each object is longer than the other.
Describe your reasoning.
Jock:
Probably safer that way.
Oh, good! The standard is totally arbitrary. In that case, let’s pick this one:
Construct a pole that spans the distance. Place that pole on a scale. Now measure the distance using the ultrasound device, and calibrate it so that the readout matches the weight indicated by the scale. How well do you think that arbitrary TRVTH standard will work out?
Or consider the photo below. For our arbitrary standard, we pick a device that indicates that object B is far longer than object A. Have we made the right choice? I mean, the TRVTH standard is arbitrary, so it shouldn’t make any difference, right?
Over here in Normal World, we would reject both of those “arbitrary” standards. That’s because a) we understand that objects do have actual lengths, and b) we are not idiots.
The thing about nautical miles is the people who devised the definition assumed it would provide a reliable unit of length. There is no philosophical difference between length measured by a surveyor’s chain, and length measured by a segment of the surface of the earth. (They share the attribute of measuring a curved surface.)
When it was discovered that the original definition did not produce reliable results, the definition was changed.
It was changed because sailors have the same concept of distance as surveyors.
They don’t. At the equator, one arc second is about 100 feet. At the 45th parallel (roughly at Minneapolis, halfway to the pole), one arc second is about 75 feet. So if you are reckoning your speed and distance with a sextant, and you have traveled west one hundred arc seconds, how far have you traveled? Don’t forget that this is the ONLY measure of distance available to you.
So far, you have measured your longitudinal movement (in arc seconds).What this means is, you also need to know your latitude. You can also get this with a sextant, so then you have a point on the surface of the earth, expressed in degrees. Now if we also measure our speed through the water (and this was not difficult), and if you water-speed has been constant, your sight reductions tell you that if you are traveling due west, your distance per arc second is constant. If you are traveling due north, your distance per arc second is decreasing even though your speed through the water is constant. And that’s because each arc second maps to a smaller distance than the last one.
GPS eliminates all this messy calculating and estimating, and gives you yardstick distance – that is, it does all the calculations for you. Which is why navigators think the GPS is a wonderful development.
You are reading what you want this to mean, rather than what it was intended to mean, at least as I interpret it. Nobody is saying that an agreed on standard produces arbitrary results, they’re saying that the chosen (agreed on) standard is arbitrary – it can be yards, or arc seconds, or cubits, or how far someone just threw a rock. All that’s necessary is that the arbitrary measure of distance (1) is used consistently by all concerned, and (2) that it works, that it doesn’t produce results unsuitable for the intended purpose.
I’m not sure what you mean by a philosophical difference here. There would have been no actual difference if the earth were a perfect sphere. So maybe no philosophical difference, but an actual difference in practice.
I don’t think so. I think it was changed because the measures are inconsistent because of the earth being flattened at the poles, so not all great circles are the same length. This made calculations messy, so the definition was simplified.
Flint:
You’re misunderstanding what the subtended angle is. It isn’t equal to the change in longitude.
Gotta run. More later.
Just to be clear here, I do agree that there is an underlying reality. It’s just that there are no true statements we can make about it. I’m inclined to agree with Kant’s view, that we cannot know the world in itself. All we can know comes from our experience interacting with reality.
When I say “there isn’t a way that reality is”, I am not denying that there’s a reality.
Just to be clear, that is not my position at all. I agree that there’s an objective reality. However, we probably disagree on the meaning of “objective”. In particular, “objective” cannot mean “human-independent.”
That’s because there is a strong correlation between those different things.
Neil writes, “Just to be clear here, I do agree that there is an underlying reality. It’s just that there are no true statements we can make about it. I’m inclined to agree with Kant’s view, that we cannot know the world in itself. All we can know comes from our experience interacting with reality.”
I agree with Neil on this.
Neil also writes, “However, we probably disagree on the meaning of “objective”. In particular, “objective” cannot mean “human-independent.””
I’m not sure what Neil means here, but I wrote above someplace, ”
However, back a page I wrote, “Given all that we have learned about how the world is different than how it appears, all the way down to the world of quantum events, I think this position (that IF there is an objective underlying reality, we cannot know it.) is probably true. I think, even more so, that we can’t know whether what underlies the world we can and do know can be properly described as objective or reality.”
Seems reasonable to me.
keiths:
Neil:
This is another case of trying to call a tail a leg. When people speak of objective reality, they do mean that it’s human-independent. A sampling of definitions:
– having reality independent of the mind
– existing outside of the mind : existing in the real world
– being, or regarded as being, independent of the mind; real; actual.
So it is your position that I, and anyone else who believes in an objective reality, is a theist. Which is ridiculous.
If your thinking causes you to take someone who doesn’t believe in God and classify them as a theist, then your thinking is broken.
From past discussions, I’ve concluded that your confusion is based on this: you note that objective reality could be observed from a God’s-eye viewpoint, which is correct, but then you leap to the conclusion that if objective reality exists, there must be a God viewing it, which is false. It doesn’t follow.
I remember pointing out that we can speak of a bird’s-eye view of something even when there are no birds around to do the viewing. Why, then, can’t we speak of a God’s-eye view when there is no God to do the viewing? The availability of a perspective does not require that there be someone or something who is taking that perspective.
keiths:
Neil:
You’re merely restating what needs to be explained. Why are they strongly correlated?
I say they’re the same thing, and therefore the correlation makes perfect sense. What is your explanation of the correlation?
Flint:
Agreed.
Arcseconds are an angular unit, not a length unit, so they don’t belong in your list. You can derive a length from an angle by using the SAM, but it’s a length and will therefore use length units, not arcseconds.
Everything else in your list is a unit of length, and lengths are commensurable. If all you were claiming was that any given length can be expressed using different units, then of course no one would disagree. You and Neil are saying something far more radical — namely, that a length produced by the SAM is incommensurable with lengths produced by other methods, because the SAM is measuring something different. That’s wrong, as I’ve explained.
Likewise, Jock isn’t merely claiming that the choice of units is arbitrary. He’s saying that the standard of truth is totally arbitrary, which is quite radical:
I showed how the use of totally arbitrary truth standards can completely screw things up. Workable standards aren’t arbitrary; they’re constrained. Constrained by what? Reality.
Flint,
What you described in this comment isn’t the subtended-angle method (SAM) of length measurement. You’re talking about a distinct method wherein you’re taking the change in longitude, along with knowledge of the latitude and of the dimensions of the earth, and using that to determine the length of a path along that particular line of latitude. A clue that this isn’t the same as the SAM is that for a given change in longitude, the path length can vary all the way down to zero depending on the latitude. That amount of variation is way more than what we’re talking about with the SAM. Also note that the problem you describe (of needing to know the latitude) would be there even if the earth were perfectly spherical. That’s another clue that you’re dealing with something other than the SAM.
Here’s how the SAM works. First we’ll assume that the earth is perfectly spherical, and then we’ll take deviations into account.
Take any two points on the earth’s surface. From each point, draw a line straight down to the center of the earth. The angle between those two lines is the subtended angle, and the value of that angle, together with the radius of the earth, allows you to infer the distance between the two points along the surface. In effect, you’re just using the angle to “cut” an arc out of the great circle that passes through the two points. As long as the earth is perfectly spherical — that is, as long as the radius is everywhere constant — a given angle, say 12° for example, will always cut out an arc of the same length on the surface. It’s simple geometry. The angle determines the arc length exactly.
Now consider what happens if the earth isn’t perfectly spherical. In that case the radius isn’t everywhere constant, and great circles aren’t really circles anymore, so the 12° angle won’t always cut out an arc of the same length anymore. The arc length will depend on where the two points are located on the surface of the earth.
How much of an error does this introduce? Very little in reality. The maximum deviation of the earth’s radius is only around a third of a percent, so the length error is correspondingly small.
That means that my question still applies:
I can explain it easily. How do you explain it?
The word “true” is being used equivocally.
Science is utilitarian, and truth is lowercase and provisional.
By utilitarian, I do not mean it creates digital watches. I mean it creates theories and hypotheses that are predictive.
The original nautical mile was based on a hypothesis that the earth was spherical. This produced inconsistent predictions.
The problem was not that the measurements were incommensurable. The problem was that one method was wrong. The earth is not a true (lowercase) ruler.
The problem was not different visions of length, it was a wonky ruler.
Surveyors face an equivalent problem. A surveyor’s chain differs in length depending on temperature and on the tension applied to hold it off the ground. There is no problem with the idea of length. There is a problem with instrumentation.
Clock pendulums are another example.
Whatever happened to the concept of operational definitions?
When you say objects don’t really exist, or numbers don’t really exist, this looks like equivocation.
Numbers exist not as platonic objects, but as definitions and operations. Calling them fiction adds nothing. Distance exists not as a platonic object, but as operations.
An octopus is a predator. It must deal with distance to capture things to eat. We do not need to speculate about how as octopus experiences distance. We can observe that it behaves in a way that is equivalent to the way humans reach for objects.
“Really existing” is just to precious. [ behaving in a very formal and unnatural way by giving too much attention to details that are not important]
If we did not have coherent operational definitions of distance and length, we would not be able to talk about relativity, and the effects of acceleration.
The earth is very nearly spherical.
Thanks for the explanation of SAM.
Well, I’m with Neil and aleta and Jock, in saying that there probably is an underlying reality, but we can only grasp it as we relate to it. I don’t think there IS a god’s eye view, and any underlying reality isn’t really knowable. But hey, you go to your church and I’ll go to mine. I’d say we have devised a view of reality that works for us.
Flint writes, ” I don’t think there IS a god’s eye view, and any underlying reality isn’t really knowable.”
I like this way of putting it.
P.S. However, if there is no God’s eye view (a nice phrase) and whatever underlies the world we can know through experience is unknowable, then perhaps “reality” is not a word we should use to refer to whatever that underlyingment is. (I invented a word to make my point.)
Flint:
I agree. We experience reality only indirectly, via our senses. We can’t grasp it directly.
Yet one sentence ago you were saying that we could “grasp it as we relate to it”. What is that “grasping”, if not knowing? It’s incomplete knowing, for sure, and it isn’t direct, but you still learn things about reality when you interact with it. If you learn things about it, then you are gaining knowledge, which means that reality is in fact knowable, albeit with limits.
Uh-oh. A second person trying to force religion on me. Well, at least you aren’t accusing me of being a theist, unlike Neil.
The existence of objective reality isn’t a faith question, Flint. It’s based on observation.
aleta:
I would argue that if something exists, it’s part of reality. When you refer to “whatever underlies the world”, you are referring to something that exists, and “reality” is an appropriate word for it.
keiths:
Flint:
First, note that by acknowledging that the measurement values are close, you are acknowledging that the two things are commensurable. That’s progress!
Regarding near-perfect sphericity, that doesn’t explain why the SAM gives results that are close to those produced by the yardstick method. That’s the fact I am asking about.
My explanation is that both methods are being used to measure the same thing: the distance along the surface between two given points. If you use two accurate methods to measure the same thing, you should get results that are close, and that’s what we see.
According to you, we aren’t measuring the same thing with both methods, which is why the closeness of the results demands an explanation.
The near-perfect sphericity is an explanation for why the length given by the SAM is close to the length given by the location-adjusted SAM, but not for why the SAM and the yardstick method give results that are close.
No, they don’t.
My objective reality contains highways, football fields, golf courses. None of those is human independent.
What distinguishes a golf course from a grassy field, is mostly the way that people use it. Truth is a social phenomenon. There us no purely physicalist account of truth.
It’s well past time for you to stop being concerned about my confusion, and to start looking into your own confusion.
When I accuse you of having a “God’s eye view” conception of truth, I am really saying that you have a “keiths’ eye view” of truth. You make strong truth claims. And when people disagree, you go to great length and many tedious posts to try to demonstrate that they are wrong. Maybe you should try spending some of that effort in trying to understand why they disagree with you.
That’s pure bullshit.
You should stop trying to tell me what I believe.
However, numbers are not definitions and they are not operations.
Taking a step back (or assuming a God’s-eye view, as it were*), this entire sub-discussion started because Neil looked at my argument regarding exact numbers and inexact measurements (the one that Flint and Jock have been avoiding for months) and objected that “true length” isn’t a thing.
Yesterday I noted that when you google “measurement error”, you get result after result after result defining it as the difference between the measured value and the “true value”, or “actual value”. Besides Neil, is there anyone among you who contests the existence of “true length” or “true distance”?
If you accept the existence of measurement error — and I think all of you do, including Neil — then you implicitly accept the existence of true length and true distance. (Unless, like Neil, you execute a call-a-tail-a-leg maneuver and redefine “measurement error” idiosyncratically.)
*That’s a joke, in case anyone is tempted to jump on it.