Sometimes very active discussions about peripheral issues overwhelm a thread, so this is a permanent home for those conversations.
I’ve opened a new “Sandbox” thread as a post as the new “ignore commenter” plug-in only works on threads started as posts.
Jock:
Impressive rejoinder. You just might qualify for the Planet Jock debate team.
petrushka:
The subsequent sentence is key:
The nautical mile is, and always was, a unit of distance. Its adoption was a matter of convenience, not necessity. As the sentence indicates, the use of nautical miles makes it easier to determine the distance between two points given their latitude and longitude, and vice-versa. “1 arcminute corresponds to 1 nautical mile” is a lot easier to work with than “1 arcminute corresponds to 1.1508 statute miles”.
Jock,
It would help clarify your position if you would respond to the questions I posed to you earlier:
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?
Hmmm. It seems to me most measurement is “indirect” if by that you mean there are some intermediaries. Yes, I can measure distance using a ruler. But what about weighing something on a scale, where the weight is transferred through a spring to a dial. Or measuring distance with an odometer which ultimately goes back to the rotation of the tires, or measuring time with a grandfather clock, with all its gears?
In fact, what are some other examples of direct measurement other than laying a ruler on a length? Are most measurements indirect in some way or another?
In fact, Jock wrote,
“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.”
That is all true. But if “almost all science these days involves indirect measurement” what is the argument here about? I guess I really don’t know what the issue is, so I should probably just stay away, as I have been doing.
Gawking at train wrecks is hard to resist.
Yes
The one “most commonly used” per the page that I “unhelpfully linked to”.
No opinion.
SAM measures a ratio. Dimensionless, yet a measurement. Weird, huh.
YSM measures in {rulers wot I have here}.
Cross-calibration.
You still have not even tried to explain how your Smoot error differs from Karen’s error.
“SAM measures a ratio. Dimensionless, yet a measurement. Weird, huh.”
Not quite sure what is weird here. Any use of trig to calculate a distance is using a dimensionless ratio to help calculate a distance which is otherwise not measured directly. Like any measurement, all sorts of things have to be taken into consideration to get as much accuracy as possible, with the understanding that there will be some range of uncertainty about the end result.
So what? What is weird here?
keiths:
Jock:
You’re referring to this page, where mathematical commensurability is cited as the most commonly used.
That’s unfortunate, because it indicates that you don’t understand mathematical commensurability. Here’s Wikipedia’s definition:
It’s trivial to show that your incommensurability claim fails, even by this alternative definition. Suppose I pick two points on the earth’s surface and want to measure the distance between them. The subtended angle is 9°, and the internet tells me that the earth’s circumference is about 24,900 miles. The SAM therefore yields a distance of (9/360) * 24,900 miles = 622.5 miles. That’s a rational number. Now suppose I measure the distance using the YSM and obtain a result of 619.3 miles. That’s also a rational number. The ratio of two rational numbers is always a rational number, and so the results are mathematically commensurable, contradicting your claim.
You guys are barking up the wrong tree with this incommensurability business. The SAM and the YSM are commensurable by both of the definitions you have tried to invoke.
keiths:
Jock:
The SAM measures a distance. It does so by measuring an angle, computing a ratio, and multiplying by a circumference in order to produce a distance as the final measurement result. See my example above. The ratio is only an intermediate stage, not the final result.
The SAM and the YSM both measure distance — specifically, the distance between two points on the surface of the earth. They are commensurable.
keiths:
Jock:
How do you cross-calibrate if the two methods aren’t measuring the same thing?
The “smoot error” was yours, not mine.
I’ve wondered about what is meant by incommensurable in these discussion. In math, rational and irrational numbers are incommensurable because you can’t divide a rational number into pieces a number of which will completely cover the irrational number. I don’t that is what is being meant here.
The other definition on the linked page is implies that two things are incommensurable if they are not measurable or comparable by a common standard. That’s pretty general.
Can you explain more, Jock, and what definition you are using and how it applies.
Also, keith writes, “The SAM measures a distance. It does so by measuring an angle, computing a ratio, and multiplying by a circumference in order to produce a distance as the final measurement result. See my example above. The ratio is only an intermediate stage, not the final result.”
Yes, a subtended angle only helps to compute an estimate of a distance if the radius of the arc is known. The moon and the sun subtend, approximately, the same angle, but absent any other facts that only tells us that the ratio of s/r is the same for both. It can’t give us an actual number for either the distance or the diameter of the body.
aleta,
I’m using “incommensurable” is the way that Thomas Kuhn used it in his “The Structure of Scientific Revolutions”.
Neil:
Could you elaborate? To my knowledge, Kuhn’s notion of incommensurability applied to successive theories or paradigms, not to measurement methods within a single paradigm. The SAM and YSM fit nicely within a single paradigm and so do not qualify as incommensurable in that sense.
Are you aware of some other meaning of ‘incommensurable’ in Kuhn’s writing that applies to the SAM and YSM?
aleta:
At this point I think these guys would be happy if they could find any definition of incommensurability under which the SAM and YSM could be said to produce incommensurable results.
To prop up Neil’s argument, however, they need incommensurability of a kind that supports his claim:
This should clear things up:
https://www.oxfordbibliographies.com/display/document/obo-9780195396577/obo-9780195396577-0022.xml
https://plato.stanford.edu/entries/incommensurability/
This is from an article on Kuhn.
It would be fitting to think this whole argument is about irrationality.
Bottom line: NOAA is correct. Nautical mile is distance. Always has been.
The reason it was defined as an arc is not because sailors were uninterested in distance, but because arc was the only ruler available at sea.
I’m old enough to remember printed road maps. Most of them had an index of cities, and the index included coordinates (J-6, for example) to help locate the city.
Nautical mile is not a location. The dimension of an arc is not a location. The dimension of an arc is not even a direction. It is the spherical trig analog of the side of a triangle. It has a length.
And, it is just as valid on land as at sea. I learned the concept as a child. As the crow flies.
Neil says, “I’m using “incommensurable” is the way that Thomas Kuhn used it in his “The Structure of Scientific Revolutions”.”
In respect to philosophy of science and Kuhn, Wikipedia says, “On the other hand, theories are incommensurable if they are embedded in starkly contrasting conceptual frameworks whose languages do not overlap sufficiently to permit scientists to directly compare the theories or to cite empirical evidence favoring one theory over the other.”
Is this how you are using the term, Neil?
petrushka,
That paragraph is a description of the concept of mathematical incommensurability, which Kuhn borrowed from, but not a.description of the way Kuhn applied it in his own work.
Here’s how Kuhn used it:
That clearly doesn’t apply to the SAM and the YSM, so my question for Neil is whether he’s aware of some other way that Kuhn used incommensurability that does apply.
ETA: Ninja’d by aleta!
Suppose it is 1564, and you are sailing from France to Fort Caroline. (The deed to my house traces ownership back to this event. Kind of cool and disturbing at the same time.)
Describe the procedure you would follow to establish your position at sea during the voyage.
The only concept of commensurability that applies in this discussion is the way it is used in dimensional analysis of measures, which is a field of physics. I have referenced it and explained it. I knew what to look for because, incidentally, this is the way I was taught in primary school.
Neil has now acknowledged that he pulled the word from a different context, from an inapplicable one. In other words, he never knew what he was talking about to begin with. I have noticed this with him often enough.
ETA. Perhaps most to the point: In Kuhn’s sense, nautical mile and statute mile are perfectly commensurable, since both were devised under the same scientific paradigm. It is ludicrous to assert that arc length is incommensurable with “linear” length in Kuhn’s sense. In fact these lengths are commensurable in every other sense too. A road can be circular and still be measured in “linear” length units. Linear units are not as rigidly linear as Neil thinks they are.
Erik writes, “he only concept of commensurability that applies in this discussion is the way it is used in dimensional analysis of measures, which is a field of physics. I have referenced it and explained it. ”
I haven’t beem keeping up with this. Could you reference and explain again, or point back to the dates of previous posts?
Thanks,
aleta,
I think this Kuhn business is just Neil’s attempt at bluffing his way out of a bind. In fact, he keeps changing his tune, and Kuhn is his third attempt at justifying his incommensurability claim.
At first the supposed incommensurability was due to the location dependence of the SAM. Then it was because the results of the SAM are angular distances while the results of the YSM and “linear distances”. Now he claims to be using ‘incommensurable’ in the Kuhnian sense.
None of that works.
Here’s his location dependence argument:
And:
None of that has anything to do with Kuhn or the incommensurability of theories. Neil is just arguing that since the SAM produces results that are location-dependent, that makes it incommensurable with the YSM. Flint has repeated that error.
Their mistake is in not realizing that the location-dependence of the SAM is just one more source of measurement error. There’s nothing special about it. And the existence of measurement error obviously doesn’t indicate incommensurability, because if it did, every distance-measuring method would be incommensurable with all of the others. Even worse, any given method would be incommensurable with itself, because repeated measurements differ in the magnitude of the error.
Here’s his angular distance vs linear distance argument:
Jock has repeated that error. Their mistake is in failing to recognize that the SAM produces results that are denominated in units of distance, not of angle. That should be obvious, since the SAM has always been capable of producing results denominated in nautical miles. The word ‘mile’ is a dead giveaway that we are talking about distances, not angles. Both the SAM and the YSM produce distances, so they are commensurable.
Having failed with those two arguments for incommensurability, Neil is now trying to invoke Kuhn. That doesn’t work, because Kuhn was talking about incommensurability between theories or paradigms, not between measurement methods.
Will he make a fourth attempt, or will he finally realize that this incommensurability business isn’t going to fly?
If N&F&J are right that the SAM and the YSM measure different things, then they face the problem of explaining why the two methods produce results that are so close. Each of them has attempted unsuccessfully to explain this fact.
Here’s Neil’s explanation:
That isn’t an explanation; it’s just a restatement of what needs to be explained. Why are the results so close?
Here’s Flint’s attempt:
That explains why the SAM and the location-adjusted SAM produce results that are close, but it doesn’t explain why the SAM and the YSM do so.
Here’s Jock’s attempt:
The problem is that you can’t cross-calibrate if you aren’t dealing with commensurable results, so Jock’s argument undermines his claim regarding incommensurability.
My explanation is the obvious one: The results of the SAM and the YSM are close because the two methods are measuring the same thing: the distance between two points along the surface of the earth.
It gets worse for Flint, because he maintains that external reality might not exist at all. His argument that “the earth is very nearly spherical” depends on there being such a thing as the earth. If external reality doesn’t exist, then neither does the earth.
If he tries to argue that the non-spherical earth exists solely in our models, but not outside in (the nonexistent) external reality, then he’s got an additional problem. The earth was originally spherical in our models. Why did it change? Flint hasn’t offered an answer.
My own explanation? It’s because our interactions with the world outside of our models — our interactions with external reality — showed us that the earth was in fact non-spherical.
Meanwhile, Jock has gotten himself into trouble in a few different ways.
He has claimed that since we first measure an angle when using the SAM and then use that angle along with the earth’s circumference to infer the distance, the SAM really measures angles, not distances. That puts him in the awkward position of claiming that any indirect method doesn’t really measure the thing it’s intended to measure. He affirms that here:
That means, for instance, that mercury thermometers and infrared thermometers don’t measure temperature, that odometers don’t measure distance traveled, and that airspeed indicators don’t indicate airspeed. That’s just dumb.
He also contradicts himself by inadvertently admitting that indirect measurement methods do in fact measure what they are intended to measure:
Also, to claim that the SAM measures angles but not distances undermines his cross-calibration explanation for the similarity of SAM results to YSM results, as I described above.
Last, he is now claiming that when he talks about incommensurability between the SAM and the YSM, he’s talking about mathematical incommensurability:
I replied:
In that same comment, I explain why the SAM and the YSM aren’t mathematically incommensurable.
To borrow an appropriate metaphor, these guys are really lost at sea when it comes to incommensurability.
I’m trying to find out what the issue about incommensurability is. Erik offers this definition, which seems pretty clear (although I’m not quite clear what point “can be directly compared to each other” is making.
““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.”
Also, I think I gather that part of the discussion right now is about measuring the length of an arc on the earth’s surface using two different methods.
Given Erik’s definition, it seems to me that the distance measured directly by measuring the length of the arc “with a yardstick” (maybe better, a very long seamstress’s tape) and the distance measured indirectly with a subtended arc and other adjustments based on circumstances are commensurable, despite the differing methods for finding the result.
Who thinks this is true, and if someone thinks it is not true, why? Or is some other definition of incommensurable being used, and if so, what. (And obviously not the definition that separates rational from irrational numbers.)
Can anyone give a concise summary?
aleta:
He’s just saying that distances expressed in statute miles can be compared to distances expressed in yards, for instance, since it’s possible to convert from miles to yards and vice-versa. You can’t do that with, say, pounds and degrees Fahrenheit. Distance is commensurable with distance, but weight is incommensurable with temperature.
Right, and those two methods are the SAM and the YSM.
I think it’s true, and I think that that is the appropriate sense of “commensurable” to use in this context.
These are the various explanations I’ve seen in this thread for why the SAM and the YSM supposedly produce incommensurable results:
1. They are incommensurable because they produce unequal results, since the SAM is location-dependent.
2. They are incommensurable because the SAM measures angular distance while the YSM measures “linear distance”.
3. They are mathematically incommensurable, meaning that the ratio of a SAM result to a YSM result is an irrational number.
4. They are incommensurable according to Kuhn’s standard.
None of those work. N&F&J are throwing everything at the wall to see what sticks. And merely getting something to stick isn’t enough. A successful definition would also need to support Neil’s claim that the incommensurability
False. I never made any such claim. At least try to keep up. You measure an angle, assume a radius, and derive an arc length.
See? You got there eventually. AVO meters don’t measure voltage or resistance. They do measure current, although somewhat indirectly.
Maybe to you, Karen, but not to people who actually measure stuff.
DNA writes, “You measure an angle, assume a radius, and derive an arc length.”
I think you do more than assume a radius, as that is another distance that you have some reason to believe is accurate, to some degree.
But other than that, is there any problem with measuring and angle and then figuring out an additional distance? As I think we have said (do you agree?) almost all measurements are indirect in some way or another, such as this one would be.
Good point. You assume a radius, and recognize that there is an error distribution around your assumption. This affects the error distribution in your result.
No problem at all. As you note, the process is rather ubiquitous. But, for the umpteenth time, each step introduces the possibility of differing errors, so the process and method used matters. Static-pitot tubes measure a difference in pressure and then infer an airspeed (given an assumption about air density, and a square-root calculation, so it’s not even linear…)
Jock writes, ” But, for the umpteenth time, each step introduces the possibility of differing errors, so the process and method used matters. ”
Does anyone think this is not true?
But, I’d like to go back to this point: I don’t think “assume” is the best word to use. I don’t just assume the radius of the earth is 4000 miles (or whatever number I use): I use a number based on evidence. A quick search shows this: “Assume: Assume is mainly considered supposing to be the case, without proof, or taking on power or responsibility.” or “to accept something to be true without question or proof.” We may use intermediary numbers to move from measured numbers to a calculated final result for a measurement, but we don’t just “assume” those intermediary results.
(Note: we might assume an intermediary number, calculate a result, and then go find the result in a different was to test our assumption, but that’s a different process.)
keiths:
Jock:
Haha. Here’s a pro tip, Jock. C = 2πr. I swear it’s true. See if you can figure out how that applies here.
keiths:
Jock:
I like how Jock will defend even the stupidest positions to the bitter end rather than admit his mistakes.
Your assignment for the next year: scour the internet looking for sites that (correctly) describe AVO meters as measuring A (current), V (voltage), and O (resistance). Insist that they “correct” their statements. Observe as they tell you to get lost.
After you’ve finished that assignment, start visiting the airports near your home and inform every pilot you can find that airspeed indicators don’t indicate airspeed. Observe as they dial the folks at airport security to report a crazy person roaming the ramp.
keiths:
Jock:
OK. Third assignment: Roam the halls at the National Weather Service, informing every meteorologist you encounter that they’ve been doing it all wrong, trying to measure temperature with their silly thermometers.
Let us know how it goes.
Jock, to aleta:
As aleta keeps reminding you, you don’t merely assume a radius. You use a known value.
Right. As with all measurement methods, there are errors associated with the SAM. Uncertainty in the angle is one source of measurement error, and uncertainty in the figure you use for the radius (or circumference, lol) is another.
Those sources of error don’t apply to the YSM, which has its own. That hardly means that the SAM and YSM don’t measure the same thing. They do, and what they measure is the distance between two points on the earth’s surface.
keith writes, “That hardly means that the SAM and YSM don’t measure the same thing. ”
to Jock (and anyone else): I am trying to understand the actual issues here, and who believes what. So here’s a question.
We have a large hollow glass hemisphere with points A and B on the surface and center O available to us inside the hemisphere. Joe (outside the sphere) stretches a string taut from A to B (thus being along a great circle), and then takes the string and measures it with a linear measuring device on a plane, this measuring what he thinks is the length of arc AB. Bill stands at the center and measures both the distance AO and the subtended angle AOB, and then calculates what he thinks is the length of the arc AB.
Understanding that each has different considerations about the accuracy of their result, did they measure the same thing?
aleta,
Are you asking how long is a piece of string? 😱
aleta,
I asked a similar question several days ago, but unsurprisingly, N&F&J all avoided answering it. Let’s hope they summon the courage to answer yours.
I wrote:
keiths,
What is “the same thing” of which you speak?
My goodness, the discussion is getting cute.
I’m so old I can remember when voltmeters were rated as to ohms per volt.
Anyone else remember that, or what it means, or why it matters?
Are we really going to equivocate measurement to death?
If you are navigating, the questions you want answered are, what course to set, and how long will it take? Depending on your level of knowledge and the instruments available, the procedures and accuracy will vary considerably.
I find it useful to read most of you while hearing the voice of John Cleese.
I disagree. You seem to be loading the word with some negative connotations that it does not have in my line of work. An assumption is a received value — ‘taken’ originally. It may be warranted, or it may be unwarranted. It may be highly accurate, or not. Most importantly, it may be fit-for-purpose, or not.
No they did not. Thanks to your careful use of verbs, that is quite clear.
Thanks, Jock, and can you be more specific, because it is not “quite clear” to me what distinction you see. Possibly you mean this:
The second method does not actually measure the length of the arc because it calculates it from things that are measured. The two methods both find a number for the length of the arc, but the second method is not itself actually a measurement.
2. However, if the two methods are finding numbers for two things that are really different, can you describe what those two things are. I think they are both finding the length of the arc, so I don’t understand what two different things you might be thinking of.
To be clear, perhaps you can complete these sentences:
Method 1 (the string method) is finding _________________-, and
method 2 (the arc and radius method) is finding _____________________-.
Thanks.
I have a question for those involved. Are we looking at one distance which is the length of the arc, and another distance which is the distance from point A to point B? In other words, if our arc is 180 degrees, then does method A produce a distance which is 1/2 of the circumference and method B produce the diameter of the sphere?
I have seen rather far-fetched proposals of drilling a tunnel from coast to coast which is absolutely straight. (The train would be going downhill for half the trip, and uphill for the other half). Assuming friction can be overcome, this is the most efficient way to go cross country, because the distance would be the shortest!
Flint,
It works for Switzerland.
petrushka:
TSZ’s entertainment value comes in part from observing the lengths (heh) to which some will go in order to deny their mistakes, even when the denials force them into ever more ridiculous positions. I’d bet a hundred bucks that before this discussion, Jock wouldn’t have blinked an eye at someone who asserted that airspeed indicators indicate airspeed or that thermometers measure temperature. He’s only doing so now because previous statements of his force him to, given that he’d sooner make ridiculous claims than admit earlier mistakes.
Here’s how Jock backed himself into this particular corner. He started out simply wanting to defend N&F’s claim that the SAM and the YSM measure different things. He went looking for a distinguishing feature of the SAM that could justify that claim, and he latched onto the fact that the SAM proceeds indirectly by first measuring an angle and then inferring an arc length from that angle and the radius of the earth (but not the circumference, mind you! lol). The SAM really only measures angles, he said, while the YSM measures arc length. They measure different things, so the results are incommensurable.
After committing to the position that the SAM is indirect and therefore doesn’t measure arc lengths, he was shown that the same logic leads to absurd conclusions such as the following:
– mercury thermometers and infrared thermometers don’t measure temperature
– odometers don’t measure distance traveled
– laser rangefinders and tape measures don’t measure the same thing
– few measurement methods actually measure what they are claimed to measure
Like the rest of us, Jock knows that those conclusions are ridiculous. Yet instead of acknowledging his error and rejecting the premise that leads to those absurd conclusions, he has doubled down, insisting that airspeed indicators don’t indicate airspeed and that AVO meters don’t measure voltage and resistance (more on AVO meters later).
Even funnier, he claims that “people who actually measure stuff” agree with him and not me. It’s reminiscent of his similarly ridiculous claim that “the mathematicians” agree with him and not me regarding the infinite precision of the real numbers.
Another amusing thing is that he keeps contradicting himself by admitting that indirect methods actually can measure what they are claimed to measure. Here, for instance:
And here:
His own statements betray him. He knows he’s wrong, but he can’t bring himself to admit it. Debates like this often end up being more about psychology than about the issues they superficially seem to address.
I doubt that anyone involved in or reading this discussion, including Jock, thinks that thermometers don’t measure temperature. So why the denials? If he isn’t fooling anyone, what’s the point? My best guess is that the act of admitting error is simply too painful, in and of itself, even if what he would be admitting is something that everybody already knows.
Length of the arc on the surface of the sphere.
Flint:
Both methods measure the distance from A to B along the surface of the sphere, as aleta notes, and so both methods will produce a result that is half the circumference.
The SAM gets from angle to distance via the following formula…
d = (θ/360) * C
…where d is the distance, θ is the subtended angle in degrees, and C is the circumference.
For Jock’s benefit (lol), this can also be expressed as
d = (θ/360) * 2πr
where r is the radius.
In your example, θ is 180°, so we get
d = (180/360) * C = C/2
which is the same answer you get using the YSM.
On the topic of AVO meters:
Jock’s position is that indirect measurements don’t really measure what they are purported to measure. That puts him in an difficult spot, because the things that AVO meters (which are just analog multimeters) measure — A (current), V (voltage), and O (resistance) — are all measured indirectly. Conclusion: If Jock is right, then AVO meters don’t measure A, they don’t measure V, and they don’t measure O.
Awkward.
To soften this, Jock writes:
By admitting that they indirectly measure current, Jock is contradicting himself. And if indirect measurements of current count as measurements, then why not indirect measurements of voltage and resistance?
A quick comment, about which I more complete thoughts.
Linear distances can be measured directly with a representative of the abstract number line such as a ruler. Theoretically one could measure area and volume by filling a space with unit squares or cubes, but nobody does that.
All other quantities (weight, temperature, and time for instance) are measured indirectly with various mechanisms.
Since so many quantities can only be measured indirectly, it doesn’t make much sense to distinguish between direct and indirect measurement. Rather we should concentrate on the various levels of possible inaccuracies of whatever method one uses, which is what people in the real world do.
Well, that generally happens. Here, we have other priorities.
Yes, but what are they? That’s what I’m trying to figure out. What issues are people interested in? Why does Jock think that two different methods of measuring an arc length are measuring (or doing something) with two different things?
For folks who are unfamiliar, I should probably offer a description of how analog multimeters work. This will be a simplified description, but it will accurately portray the principles involved.
The meter is built around a coil. When you pass a current through the coil, a magnetic field is induced.* The meter contains a permanent magnet. The induced magnetic field from the coil interacts with the magnetic field of the permanent magnet, producing a force. That force is applied to a spring-loaded needle, deflecting it. The magnitude of the deflection corresponds to the amount of current flowing through the coil. The dial of the meter is marked so that the user can read the measured value by observing where the needle is pointing. As you can see, the current measurement is indirect, as even Jock acknowledges.
So what about voltage and resistance?
When measuring a voltage, the meter applies the voltage to a known resistance inside the meter. By Ohm’s Law,** this will produce a current that is proportional to the voltage. That current is passed through the aforementioned coil, causing the needle to deflect, and the user notes where the needle is pointing and reads the voltage off the dial.
When measuring resistance, the meter internally generates a known voltage and applies it to the resistance that is being measured. By Ohm’s Law, this will produce a current that is inversely*** proportional to the resistance. That current is passed through the coil, deflecting the needle, and the user reads the resistance off the dial.
Those are all indirect methods, so by Jock’s logic, the AVO meter doesn’t measure A, doesn’t measure V, and doesn’t measure O. Which is ridiculous.
On Planet Jock, the only thing an AVO meter actually measures is the deflection of the needle.
* Actually, a current passing through any conductor will generate a magnetic field. A coil simply magnifies the effect, and that’s what we need in an AVO meter.
** Ohm’s Law states that V = IR, where V is voltage, I is current, and R is resistance.
*** That’s why, if you look at the way the dial below is labeled, the indicated voltage and current increase with increasing deflection while the indicated resistance actually decreases with increasing deflection.
In a previous post, I wrote, “Linear distances can be measured directly with a representative of the abstract number line such as a ruler. …All other quantities (weight, temperature, and time for instance) are measured indirectly with various mechanisms.”
Keith has given an example. In general, we don’t measure most quantities directly. We measure the effect they have on some mechanism which is then linked to some scale.
I think Jock agrees that most measurements are indirect. He wrote back on September 20,”Almost all science these days involves indirect measurement.”
So, at least for me, this matter is settled. The question I have for Jock, using my example about an arc length, is why if you measure an arc two different ways, such as directly with a string or indirectly with a calculation, are you measuring two different things?
Please see my post from 4:46 pm today.
It’s right there in the verbs that you carefully used: Joe measures the length of his string, whereas Bill “calculates what he thinks is the length of the arc AB.”
Pretty much. The second method measures an angle and calculates an arc length.
“finding” seems to be a wholly useless verb, reminiscent of what we refer to at work as “numeroproctology”. I suggest we stick with measuring, assuming, and calculating.