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.
This is wrong.
Yes, “true length” exists in our theoretical models. But it doesn’t exist in real life.
We often refer to things from our models as if we are talking about whatever it is that they model. And that usually works well enough. But you cannot do that if the discussion is about how well the theoretical model fits what it is trying to model.
Carrying my point about true lengths a bit further, I would claim that in the pic below, object A is longer than object B, and this is because the true length of A is greater than the true length of B.
Is there anyone here who contests that?
That sounds like an operational definition.
I can think of several ways of relating.
For the amnesiac, everything is new, every time. For most people things are either routine or extraordinary. For the scientist, reality is a puzzle that can be partially solved.
By solving I do not intend to say that science gets to Truth. Just that science develops increasingly detailed predictions about what will be observed under what circumstances.
keiths:
Neil:
If you accept the use of “true length” in cases where we aren’t talking about the fit of our model to reality, then why did you object when I used “true length” in my argument regarding exact numbers and inexact measurements? I wasn’t talking about the fit of model to reality there.
Likewise, why did you feel compelled to redefine “measurement error” so that it didn’t refer to “true value”? Measurement error is part of our model, so why balk at defining it in terms of “true value”, which is also part of our model?
keiths:
Neil:
Yes, they do. Remember, I quoted some actual definitions for your benefit:
Note the phrase “independent of the mind”.
Neil:
If humans poofed out of existence five seconds from now, those things would still exist. They are human-independent. The fact that humans created those things, or have assigned names to them, doesn’t mean that their existence depends on us. If we are poofed out of existence in five seconds, there is no reason to believe that the rest of reality will be poofed along with us.
Yes, of course you were. You were arguing about exact vs. approximate.
No, I’m not. Note that by putting your words into other people’s mouths and your conclusions into other people’s views, you are distorting their positions just as Jock pointed out and making no attempt to understand why others might disagree with you, just as Neil pointed out. If Neil wishes to continue correcting this practice, that’s up to him. As for me,
OK keiths.
keiths:
Neil:
Measured lengths are as much a part of our model as true lengths. I was comparing measured lengths within our model to true lengths within our model. I wasn’t talking about the fit of our model to reality.
Flint,
I thought this one was good, too. I suspect he did not understand what a truth standard is. I mean, I was talking about calibration, ffs!
Rehearse, filter, advise. Lather, rinse, repeat.
Well, fit-for-purpose. In the Golden Age of Sail, there really was not much use for accuracy when talking of distances at sea. What mattered was location. The nautical mile was a convenient way of ball-parking the distance between two locations.
Mariners were focused on being able to get back to a recorded location, whether it was Pitcairn using celestial nav, or (before they got rid of the dithering of GPS) a lobster pot using Loran.
keiths:
Flint:
You’re right. I shouldn’t have said that you acknowledge that they’re commensurable. Sorry about that.
Let me rephrase. You’re able to judge that they are close only because they are commensurable, even if you don’t realize that that is the reason.
Lengths are commensurable with other lengths. The SAM produces lengths, and so does the yardstick method. Thus the results of the SAM are commensurable with the results of the YSM.
To judge that the result of a SAM measurement is close to the result of a YSM measurement, they need to be commensurable. Suppose the SAM produces a measurement of 500.0 yards, while the YSM yields 500.1 yards. Those are close, and I am only able to say that because they are commensurable.
Suppose instead that the measurements are 500.0 kilograms and 500.1 yards. Are those measurements close to each other? No. They aren’t commensurable, so they aren’t close to each other even though the numbers themselves are close.
Note that lengths are commensurable even if the units used to express them differ. 1 foot is close to 12.1 inches. The numbers are different, the units are different, yet those lengths are close. How do I know? They’re commensurable, meaning that I can convert one into the other via a unit conversion, and when I do the conversion, the resulting numbers are close in value.
If we take two points on earth and measure the distance between them using the SAM, and then measure the distance between them using the YSM, we are measuring the same thing in both cases, and the resulting measurements are commensurable.
You claim that we aren’t measuring the same thing in each of those cases and that the results aren’t commensurable. In light of the above, how do you justify those claims?
I suspect we’re not using the same understanding of what “commensurable” means. The dictionary definition is, “divisible without remainder by a common unit.” The opposite verges on “incompatible”. The example given on one site is of people growing up in places with entirely different legal systems and customs, and unable to understand how they did anything wrong when visiting a different culture.
There are many possible ways of determining distance, so I suppose you could argue that using surveying tools, and guessing, are “commensurable” if the two distances are fairly close.
Flint:
In the context of measurements, the definition I’ve always seen is the one I employed above. Here’s Wiktionary:
Flint:
It’s the other way around. Commensurability doesn’t mean that they’re close, but closeness does mean that they’re commensurable. 3 millimeters and 1.2 parsec are commensurable, but not close at all.
Anyway, what I’m really interested in is not so much your terminology, but rather the thinking behind your claim that I’m not measuring the same thing when I use the SAM as when I use the YSM. Could you elaborate?
Jock:
You were talking about calibration, and so was I. You wrote:
I pointed out that the “TRVTH standard” can’t be totally arbitrary, and gave a couple of counterexamples:
We can’t calibrate to “totally arbitrary” standards. Not if we want our system to work.
Neil.
You objected to my use of “true length” in my argument regarding exact numbers and inexact measurements. For a measurement to be inexact means that there is a measurement error, or equivalently that the measured value differs from the true value.
All of that is contained within our model, and you’ve indicated that “true length” does in fact exist in our model. Yet for some reason you objected to its use in my argument. Why? And if “true length” is to be avoided for some reason, then how specifically do you suggest we quantify the measurement error?
Then there’s the meter, “ … originally defined as 1⁄10,000,000 of the length of the meridian arc from the North pole to the equator…”
My point is, these units were not intended to be imprecise or wonky, and as better technology has become available, the units have been redefined.
I see nothing helpful in pointing out that early efforts to define units of measure were less successful than later efforts.
The thing is, there’s an underlying concept of length that governs the definitions, and motivates improvements in technology.
If humans poofed out of existence, the golf courses would become grassy fields. With nobody playing golf on them and nobody manicuring their greens, they would no longer be golf courses.
If I understand the golfing history correctly, at the beginning there were no manicured fairways or greens, the clubs used had strange names, and golf courses wouldn’t be recognizable to today’s golfers. But they were still golf courses because those playing there SAID they were golf courses. If people all vanished at once, today’s golf courses wouldn’t be golf courses because there would be nothing to recognize them as such.
Yes, no question about it. The concept of length is exactly that – a concept. I think a strong case can be made that even if there is no underlying reality of length, the closer we can operationalize our concepts, the better things work. So there might as well be an underlying reality. Even if our preference that reality “exists” is a conceptual error, pretending that it exists works really well.
Well, we can do what aleta’s class did – take all apparently appropriate instruments and measure what we’d consider a length a great many times, by a great number of people, perhaps even using multiple different kinds of techniques. This exercise, as aleta’s did, produces a solid (that is, well defined) curve with mean, median, skewness, kurtosis, standard deviation. With such a curve, we can do a decent job of narrowing what we could consider the “true” length. Deviation from this length could be deemed measurement error. It could even be quantified to a degree of precision relative to and depending on the number of measurements used to derive the curve. Enough measurements, we can get our kurtosis quite small. Which is to say, increase our confidence in our measurements to more significant digits of precision.
Neil:
First, reality doesn’t care about the names we apply to it or its parts. If humans were poofed out of existence, Stonehenge would still exist even if there were no one around to call it ‘Stonehenge’. It’s human-independent.
Second, a golf course wouldn’t instantly go to seed. An hour after the poofing, its condition would be essentially unchanged, and it would still merit the label ‘golf course’ even if there were no one around to call it that.
It would be existing independently of humans, it would continue to merit the label ‘golf course’, and it would be part of objective reality, like Stonehenge.
Flint,
The procedure you described would in fact approximate the true length. It would converge to one value, say 5.7 inches, and not to 45.3 inches. What would cause it to converge to the first value and not the second? External reality. Our model doesn’t dictate the true length of every object in the universe. We have to interrogate external reality in order to obtain that information, and we’ll get different answers for different objects.
Regarding my photo, it really is correct to say that object A is longer than object B, meaning that the true length of A is greater than the true length of B. (You can tell this by sight, without even needing to take any measurements.) Indeed, if you were to apply the procedure you described to both objects, you would find that you converged on a longer length for object A than for object B. Why? Because the true length of A is greater than the true length of B, and your procedure approximates the true lengths of objects.
ETA: And since you agree that it can be appropriate to refer to a length as “true”, do you see any legitimate reason why Neil should object to my use of the term “true length” in my argument?
Flint:
The question you and Neil still haven’t answered is this: If external reality doesn’t exist, why are we able to get consistent measurements? What is responsible for the fact that your procedure converges on 5.7 inches, if not external reality?
There’s nothing about the procedure itself that dictates that the result will be 5.7 inches. For another object, it will be different. There’s nothing about our model that dictates the 5.7 inch result either. What, besides external reality, could be responsible for the consistency?
Yes, I do. Neil and you disagree as to whether an “objective reality” actually exists, even though for practical purposes it’s useful to pretend this. So you and Neil are using the same phrase “true length” but Neil regards this as an empirical quantity, while you regard it as an absolute gods-eye-view quantity. You are using the same phrase using different referents.
Is it even ever necessary to believe in any external reality? We have something that produces consistent results, to the needed precision. I think that’s entirely sufficient, without asking “why”, like a small child. As far as I’m concerned, the faith in an external “objective” reality is a cognitive crutch not needed by a mind that isn’t crippled.
I’m confused, I guess, about the difference between an external reality, and “as close as human perception and instrumentation can come to converging on some consistent model.” I’m OK with the idea that there is a stonehenge, and that any person happening on it would observe what any other person would. Whether this mutually agreed perception matches or fails to match some hypothetical “real” stonehenge is like counting angels on pinheads.
To repeat myself, I do believe that an external reality exists.
We are able to get consistent results because of pragmatism. We prefer ways of interacting with reality that give consistent results. But our knowledge is limited to knowledge derived from our interactions. “Length” is one of the terms we use to describe those interactions.
Maybe that’s a better way of expressing it. We live in an empirical reality. I see no utility in hypothesizing some “absolute” reality.
Flint,
We are aiso up against the limit of human cognition that only advances on an evolutionary scale.
And the unconceived alternative, of course.
Flint writes, “We live in an empirical reality. I see no utility in hypothesizing some “absolute” reality.”
I agree, pretty much. We might hypothesize some absolute reality that is beyond and other than our empirical reality, but we can’t know anything about it, so that doesn’t really do anything for us.
In my view, reality is that “empirical reality” that is available to our senses, directly or indirectly through instruments that we have invented to extend our senses, including those internal experiences we have that are only accessible to ourselves.
What reality “really is”, how it got here, and why it is, are different kinds of questions than asking about the details of what is real and how does reality works.
Indeed. I’d suggest people who are interested in separating the topics into more manageable chunks could open a post. It needn’t be more than a sentence or two with a title that is more informative than “Sandbox”.
I’m toying with one on unconceived alternatives. 🤔
keiths:
Flint:
I find that very hard to believe. There’s nothing unusual about my usage of “true length” in that argument. I simply say that what makes a measurement inexact is that the measured value differs from the true value, and that the measurement error is equal to the difference between the two. I said exactly that for weeks on end with nary a peep from you, so why object now?
Remember all those definitions that came up when I googled “measurement error”, that defined it as the difference between the measured value and the “true value” or “actual value”? Do you think that all of those people screwed up? My usage was no different from theirs. Are we all wrong?
Neil says he’s OK with using “true length” in the context of a model, and that’s exactly what I did in that argument, so for him to object is inconsistent. The fact that we may differ on what lies beyond the model forms no basis for his objection, because what I did — using the phrase “true length” in the context of my model — is something that Neil says is fine.
Flint:
Wow, Flint. Asking “why” is the lifeblood of science, one of the best traits of humans, and essential to our survival and flourishing. My own curiosity has been one of the greatest sources of joy in my life. It astounds me to hear you disparage the asking of “why” questions.
Why is the sky blue? Why do I feel sick this morning? Why does Katherine look so happy today? Why is gravity so much weaker than the other fundamental forces? Why do the markets sometimes react negatively to what seems like good economic news? Why is my engine check light on?
“That’s just the way it is” is not the appropriate answer to those questions, so why give that answer when the questions are about the reality underlying our experiences of the world?
Here’s an analogy: At one point human perception was limited to what our unaided senses could reveal to us. People could have, and probably did, say things like “we’ll never know what goes on at the tiniest of scales in nature. Our sight isn’t acute enough. What we know from our macroscopic observations is all we’ll ever know. That’s just the way it is.” Other people weren’t satisfied with that. They tried to infer what was going on at smaller scales. They experimented and came up with instruments that could augment our senses, such as microscopes. By doing all of this, they ended up discovering a whole world that was previously inaccessible to us.
The point isn’t that such efforts always succeed. Rather, it’s that such efforts are worthwhile because if you don’t try, you won’t succeed.
Trying to push the boundaries of what we know about reality is absolutely the right thing to do. Shrugging and saying “that’s just the way it is” is for lazy and incurious people.
TSZ old-timers may recall discussions in which I defended Cartesian skepticism, which is basically the idea that we can’t be certain that we aren’t being massively deceived by someone or something that is controlling all of our sensory input. We might be brains in vats, or caught up in the Matrix, or part of a computer simulation, so that reality is quite different from how we perceive it. (It’s really just a more extreme version of what we’ve been talking about in this thread, the only difference being that the disconnect between our models and reality might actually be something that is deliberately being imposed on us.)
There’s no way to tell — at least not in general. But what about specific cases? People have come up with some candidates for subtle but telltale signs that we might be able to observe if we live in a simulation is being run on an otherworldly digital computer of some kind. Imagine how wild it would be if we actually had good reason to believe that we’re living in a simulation!
Is this approach going to pan out, and will anything come of it? I certainly wouldn’t bet on it, but the people asking these questions are absolutely doing the right thing instead of throwing up their hands and saying “It is what it is; we’ll never know”.
Flint:
You’re such a Flint, Flint.
First, it isn’t faith. Second, how is it a crutch? Third, given that you rely on the crutch of the “measurement-derived reals” that you and Jock invented, despite the fact that they are completely unnecessary, perhaps you should be a little more circumspect about criticizing the supposed “crutches” of others.
The difference is that reality is by definition what actually exists, while our model is just a model of what actually exists. We’d like the behavior of our model to match the “behavior” of reality, so we interact with reality, pay attention to how reality responds, and modify our model as necessary to improve the match.
If angels actually existed and occupied space, I would want to know how many of them could fit on a pinhead. I’d have all kinds of questions about angels that I’d want to ask, even if the answers had no practical applications whatsoever. I guess what a lot of this boils down to is curiosity. Some people are more curious, some people less so. Judging by what you’ve been saying here, you seem to be one of the less curious ones. That’s your choice, but I think you’re missing out if you keep saying “Things are the way they are, and that’s just how it is. No need to ask why.”
You’re at your least attractive in judgmental mode.
Alan:
…says Alan, judgmentally.
Lol.
You’re the best, Alan. Good night.
PS It crushes me to hear you say that, given that my whole purpose here is to be attractive to you.
I refute it thus…
Pragmatism motivates us to seek increasingly detailed and reliable knowledge.
Knowledge defined as assertions that action X will have result Y, whether the action be kicking a stone, measuring a distance.
If I have a disagreement with anybody, it is in the notion that two systems of measurement have different and incompatible underlying concepts.
The original nautical mile definition was wonky because it uses a bad ruler. Bad in the sense that the ruler did not conform to expectations.
Just following your lead in offering unsolicited advice.
I’m not sure what you think you are refuting. I’m not seeing any actual refutation there.
I’m not sure what that is about. From my point of view, concepts are subjective. And if anything, I’m inclined to see our systems of measurement as underlying our concepts, rather than the other way around.
One more try. You and Neil use the phrase “true value” to mean two different things. For me, perhaps for Neil, “measurement error” is the difference between what our measurement produces, and the best empirical value people are capable of determining. For you, it’s the difference between a measurement and a hypothetical “absolute reality” value. I take the position that even if “absolute reality” exists, we can never know what it is. The best we can do is a process aleta and I described – reducing the kurtosis of our measurement curve as much as possible. If you wish to believe that in the process, we are honing in on an underlying “real” value, fine. If that helps you, I won’t argue.
But just out of curiosity, when you measure something, how do you determine the difference between your measurement and the “true” value? How did you determine the “true” value?
petrushka:
Which brings us back to Neil and Flint’s claim that the two methods are measuring different things, and that we know this because the results are incommensurable.
Questions for N&F:
1. You claim that the subtended-angle method (SAM) and the yardstick method (YSM) don’t measure the same thing. What, precisely, are the two different things that they do measure?
2. The SAM and the YSM both yield results denominated in units of length. To me (and Erik, and petrushka) and the world at large, that means that the results are commensurable. Which is no surprise at all, because both methods measure length and yield lengths. Why do you consider them incommensurable? What are the criteria for commensurability, in your view?
Neil initially said that what makes them incommensurable is that they yield different results, but that can’t be right. By that criterion, both methods are incommensurable with themselves, since repeated measurements can differ, and that’s nonsensical.
What criteria have you applied in order to decide that they are incommensurable?
3. If they aren’t measuring the same thing and aren’t commensurable, what accounts for the fact that they yield results that are very close to each other?
Flint:
I don’t determine the true value. If I knew the true value, I’d write that down instead of the measurement!
When we measure something, we know that there’s an error — that is, we know that the measured value doesn’t equal the true value — but we don’t know the magnitude of the error. The entire point of an error distribution is to indicate the possible magnitudes and their associated probabilities.
Flint:
What makes a particular value the best one, in your opinion? For me, the best value is simply the actual true value. If I want a round peg to fit snugly in a particular round hole, the true diameter of the hole needs to be ever so slightly greater than the true diameter of the peg. Diameter is an actual thing, and in reality, a peg won’t fit into a hole unless the true diameter of the former is less than the true diameter of the latter.
Suppose I try to fit a larger peg into a smaller hole. Reality responds, informing me that this won’t work. I line the peg up with the hole and push, and nothing happens. Have I learned something about reality? Yes, of course. I have learned that the true diameter of the peg, in reality, is greater than the true diameter of the hole, in reality. The peg and the hole both exist in reality, and in reality, you can’t fit larger pegs into smaller holes. (I am of course assuming perfect circularity for the purposes of this illustration.)
Now, it’s quite possible that ‘diameter’ in my model corresponds to some aspect of reality that would appear quite different if I were able to perceive it directly. For example, suppose we are living in a computer simulation, which is a possibility I mentioned above. In that case, ‘diameter’ might just be an attribute of objects of the class RoundThings, represented by values stored in the otherworldly computer’s memory. When I try and fail to push the peg into the hole, I have learned that the diameter of the former is greater than the latter, which might just mean that in reality,
peg.diameter > hole.diameter
in the computer’s memory. I don’t know what’s “out there”, but I have learned something about it by trying and failing to fit the peg into the hole.
There really is something out there that corresponds to diameter, and it has a true value.
Time to repose this question to N&F:
I claim that in the pic below, object A is longer than object B, and that this is because the true length of A is greater than the true length of B.
Do you contest this?
Note that you can determine that object A is longer than object B simply by looking. You don’t need to measure them. It isn’t just an intellectual concept. We perceive length, and that’s no surprise, because our perceptual apparatus was shaped by evolution, and evolution in turn favored an apparatus that is capable of seeing that A is longer than B in reality.
A is longer than B, meaning that the true length of A is greater than the true length of B, and we can perceive that simply by looking. No surprise, because there really is something “out there” that corresponds to what we perceive as length in our model.
aleta’s process lets us narrow down the best value quite effectively. Note that her process isn’t simply for a single ball bearing, it also helps us assign reliability (that is, accuracy and precision) limits to different measuring techniques. If by trial and error we learn that a yardstick produces consistent readings, both between one reading and the next, and between yardsticks and other tools, this is transferable to other measurements with high confidence.
Which you just admitted you do not know and can not know. We haven’t even agreed on whether there IS a “true value”. Do we need to go around this circle again?
So you said (1) the best value is the actual true value, and (2) we don’t know the magnitude of the error! But we don’t know the magnitude of the error because we do not know the “true value”!!! Which is the value you just said was what you’d use. Calvinball at its finest.
Flint,
Suppose you try to put a larger peg into a smaller hole and find that it doesn’t fit. Then you put a smaller peg into a larger hole and find that it does fit.
Earlier, you wrote…
External reality isn’t a crutch; it’s an explanation. Based on your earlier comments, I think you would say that when larger pegs don’t fit into smaller holes, but smaller pegs do fit into larger holes, that there’s no reason for this. It’s a brute fact. It’s just the way things are.
I say that it’s because pegs and holes really exist, that they have diameters, and that reality dictates which pegs fit into which holes, based on those diameters. My model doesn’t dictate that. It’s dictated by something outside of my model, and that thing is what is known as ‘external reality’.
I have an explanation; you just shrug and say “No reason. That’s just the way it is”. I think it’s pretty clear which approach is better.
* Side note to Alan. You criticized me as judgmental merely for saying that Flint was missing out by not being more curious, yet you said nothing when Flint called me a “crippled” mind that uses the notion of external reality as a “cognitive crutch”.
Just to be clear, I have no problem whatsoever with Flint calling me a crutch-leaning cognitive cripple. That’s part of the fun of debating him. He cracks me up, and his fulminations are probably entertaining to the readers also.
I’m just pointing out your blatant double standard. You are so transparent.
keith writes, “his fulminations are probably entertaining to the readers also.”
For the record, I’ll note that I don’t really find any of the fulminations entertaining.
aleta:
Fair enough. To each his own.
keiths:
Flint:
That doesn’t answer the question. I’m not asking how you obtain the best value. I’m asking about what makes it the best value.
keiths:
Flint:
Where did I say that I’d use the true value? I can’t use it, because I don’t know it. But the fact that I don’t know it doesn’t mean that it doesn’t exist.
Consider the change jar in my bedroom. I have no idea how many pennies are in it, but there is a definite number of pennies. The number exists, but I don’t know its value. If I count the pennies, I’ll probably get the wrong answer (it’s a big jar). I won’t know the true count; I’ll just have my result. The (unknown) error will be the difference between my count and the true, unknown count.
Likewise with measurements. This pen has an actual length. That number exists, but I don’t know it. The best I can do is to measure the pen and accept that the result is an approximation of the true length. The (unknown) measurement error is equal to the difference between the measured length and the true length.
The true count of pennies and the true length of the pen both exist, but I don’t know their values, and therefore I don’t know the magnitude of the errors.
You need to read what you wrote. You said you’d use the best value, and you said the best value is the true value. If that doesn’t mean you’d use the “true value”, you have a logic problem.
Flint:
I didn’t say I’d use the best value. I said that for me, the best value is the true value.
It’s the value we shoot for in our measurements, but one that we can’t pin down precisely since our measurements are inexact. We aim for the true value, which would be the best value if we could obtain it, but we have to settle for an approximation since measurements aren’t perfect. We can’t have the best, so we settle for “good enough”.
Measurement error is a way of quantifying the shortfall.