Sandbox (4)

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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.

5,932 thoughts on “Sandbox (4)”

  1. keiths: Do you at least agree with the obvious fact that it does cease to be shorter? That change has occurred?

    We would normally describe that as a change occuring. But we cannot pinpoint an actual instance of change.

  2. Neil:

    We would normally describe that as a change occuring.

    You can say that again.

    But we cannot pinpoint an actual instance of change.

    We don’t have to pinpoint the instant of change. We know that it exists, and that’s enough.

    As I put it earlier:

    If length is a continuous quantity, then the antenna will cease to be shorter at the moment when the lengths are equal. In order for the lengths to be equal, they need to have definite, identical values. I would say that those values indicate the true lengths of the antenna and the ruler at that moment.

    Now suppose that length is a discrete quantity, not a continuous one. In other words, suppose that length can only take on certain values and that intermediate lengths are not possible. It might even be that the lengths that are possible for the antenna differ from the lengths that are possible for the ruler.

    Under these assumptions, there still must be a point at which the antenna ceases to be shorter than the ruler. Since the lengths are discrete and the possible lengths of the antenna might differ from the possible lengths of the ruler, there might be no point in time at which the two are equal. In that case, the antenna would go from being shorter than the ruler at one instant to being longer than the ruler in the next instant. If this is possible, then it still seems to me that there must be such a thing as true length. The true length of the antenna is less than the true length of the ruler at one instant, and in the next instant the true length of the antenna is greater than the true length of the ruler.

  3. Alan:

    I didn’t. My first concern was economy. Rolled high carbon steel strip is sold in various cross sections but (in the stockholder I use) always in 6 metre lengths. So I chose a length of railing that would create least waste. Pragmatism.

    I’m not talking about your your purchasing decision. I’m talking about your method for cutting sections to the proper length:

    I had to scrap my first attempt as I was not attentive enough to cutting the railing length precisely enough for it to not look a bit amateur when welded up.

    ETA One error was to forget to use the same cut railing as a template for cutting the others.

    As I said:

    You didn’t just try a bunch of stuff randomly, stumbling upon the fact that lining up objects next to each other and then cutting them tends to make your projects work in the long run. You chose the lining-up technique based on your concept of length and of the idea that if two objects are the same length, they can be placed next to each other in such a way that their ends will coincide.

    We don’t arrive at our measurement techniques by sheer trial and error. We design our measurement techniques to quantify properties that we see in the real world. There can be some trial and error involved in perfecting a technique or an instrument, but we don’t just arrive at the basic idea randomly, by sheer trial and error.

    It wasn’t just blind pragmatism. Your method was based on your understanding of length as a feature of objects in the real world, the objects in this case being sections of railing.

  4. keiths: I’m not talking about your your purchasing decision.

    It wasn’t a purchasing decision. It was a pragmatic decision made after buying 6 metre lengths as how to cut them with least waste. A pragmatic decision.

  6. keiths: Your method was based on your understanding of length as a feature of objects in the real world, the objects in this case being sections of railing.

    Method? My first attempt at making railings for our elevated terrace? You flatter me. 😊

  7. Alan,

    You’re dodging the point, which is that your cutting method treated length as an objective property of the railing sections, thus belying your assertion that

    Claiming length is an objective property is not useful or informative, however.

  8. @keiths

    I’m sorry (English idiom) for not taking you seriously on this. But it does seem I find your use of “objective” in this context unconvincing. Anyway, there’s no resolution since Plato and Aristotle.

  9. Alan,

    It’s simple. Railing sections are real objects in the real world. Length is a real property of those real objects, and you have to get the lengths right if you want to fit those real objects together so that your terrace doesn’t look like crap. You took advantage of your knowledge concerning length — a real property of real objects — in order to come up with the idea of using a previously-cut rail section as a template for cutting the others.

    This wasn’t “try a bunch of stuff and use whatever happens to work”. You (correctly) treated length as a real, objective property of those railing sections, and you deliberately designed your technique based on your knowledge of this objective property.

  10. Flint, Jock,

    Your motivation for inventing the “measurement-derived reals” (aka “MDRs”) was that you wanted numbers that would carry error distributions around with them. You thought that such numbers were needed in order to express inexact measurements properly. I’ve already explained why you don’t need inexact numbers for that purpose, but there’s a point I want to stress.

    We all agree that you can express a measurement in this format…

    4.958 ± 0.0005 inches

    …in which case the error window is explicit, or you can express it this way…

    4.958 inches

    …in which case the error window is implicit.

    Jock agrees that the 4.958 in the first expression is an exact number (an “IPR”, not an MDR), but maintains that the 4.958 in the second expression is inexact (an MDR). In other words, he believes that when you remove the “± 0.0005”, the error information is effectively absorbed into the IPR 4.958, turning it into an MDR. I think Flint would go along with that.

    Here’s an old exchange between Jock and me regarding what happens when you rewrite the measurement “4.5 ± 0.1 inches” as “4.5 inches”:

    keiths:

    In reality, the “± 0.1” hasn’t been absorbed. It’s simply been omitted, and the recipient will know that. There’s still a range, but it hasn’t been explicitly expressed.

    Jock:

    The first sentence is wrong. The second two are what we have been trying to explain to you for weeks. I am still puzzled how you can simultaneously hold to the first and last sentences here. They are OBVIOUSLY contradictory.

    keiths:

    No, they aren’t contradictory. Omission does not imply absorption. Take the name “Robert Stevenson”. If I omit his surname, I get “Robert”. Has “Stevenson” been absorbed into “Robert”? No. Someone reading the name “Robert” can reasonably assume that Robert has a surname, but no amount of staring at “Robert” will reveal what that surname is. It’s the same with error ranges. If I omit the “± 0.1” from the measurement “4.5 ± 0.1 inches”, I’m left with “4.5 inches”. People know that there is an error window, but it has been omitted. The “± 0.1” hasn’t been absorbed into the number 4.5, it’s been omitted.

    Remember when I asked you to give me the range for the flintjock number “8.29” [“flintjock number” being the original name for an MDR] and you couldn’t do it? The error term hadn’t been absorbed into the “8.29”, and that is why you couldn’t produce it. You — one of the “architects” of the flintjock numbers — couldn’t get them to do what they were intended to do. That’s a pretty spectacular failure.

    There’s an error associated with every measurement, but the information does not get absorbed into the number when you decline to state the error window explicitly. The error information is omitted, not absorbed.

  11. keiths,

    Not disputing reality. You, who once claimed we can’t be certain of anything, now seem to be certain of your “objectivity”.

  12. keiths: …you have to get the lengths right…

    No. Just good enough. The variation was unacceptable aesthetically, not “objectively”.

  13. I’m imagining the Monty Python German vs Greek philosopher construction competition.

  15. Alan:

    The variation was unacceptable aesthetically, not “objectively”.

    The aesthetics were subjective, of course, but the lengths were objective. Yes, Alan, objects really do have lengths. As you seemed to acknowledge at one point [Hi, Neil!] in time:

    I had to scrap my first attempt as I was not attentive enough to cutting the railing length precisely enough for it to not look a bit amateur when welded up.

    Or were you trying to get the subjective length precisely right?

  16. keiths: Or were you trying to get the subjective length precisely right?

    No, because my first effort looked aesthetically unappealing, I was more careful on my second effort. Trial and error. Pragmatics. But the decision was subjective. My wife said it looked fine to her but she is a very kind person.

  17. petrushka:
    I’m imagining the Monty Python German vs Greek philosopher construction competition.

    I’ve had this going through my head for some time now. Still waiting for keiths to explain how Karen’s error differs from what he did here.

  18. Jock:

    Still waiting for keiths to explain how Karen’s error differs from what he did here.

    And I’m still waiting for Jock to acknowledge that I’ve long since answered his question.

    Also waiting for Jock to get around to addressing the arguments of mine that he’s been avoiding for months.

  19. keiths: As I put it earlier

    And still wrong.

    You are making the same mistake as that of Zeno’s paradox. And that’s probably what Petrushka meant when he called it “Zeno’s antenna.”

  21. Neil:

    You are making the same mistake as that of Zeno’s paradox. And that’s probably what Petrushka meant when he called it “Zeno’s antenna.”

    He was joking, Neil. Do you seriously think he believes that the expanding antenna never becomes longer than the ruler?

    But since you apparently think Zeno’s paradox is relevant here, could you explain why?

  22. keiths: And I’m still waiting for Jock to acknowledge that I’ve long since answered his question.

    Well, if you have, it should be easy enough for you to link the your statement, of the form “what I did on Jan 23 differs from what Karen did in this way:…”
    You’ve rabbited on endlessly about all the terrible mistakes that you think I have made, but never addressed your stupidity. There’s a pattern, Karen.

  24. Neil,

    Are you actually saying that if the antenna was shorter than the ruler at t1, but longer than the ruler at a later time t2, there was only “theoretically” a change in between?

  25. Jock:

    Well, if you have, it should be easy enough for you to link the your statement, of the form “what I did on Jan 23 differs from what Karen did in this way:…”

    Haha. This is another of your “unless you use the words I’ve scripted for you, you haven’t answered my question” deals.

    Get over yourself, Jock. I already summarized the situation here:

    To summarize:
    Karen’s only error was to treat a measurement of 20 yards as exact. That was her mistake. Using π instead of 22/7 was not a mistake.

    Alice’s error was to use 22/7 as an approximation of π when she could have borrowed Karen’s calculator and used the π key.

    Your error was in failing to treat a unit conversion as exact. You reflexively and aggressively rounded the result, which meant that in effect, you changed the inches-per-smoot conversion factor from 67 to 67.5. It was an unforced error.

    I avoided all three of the above errors. Which, frankly, was not very difficult.

    Karen was right to multiply by π and refrain from rounding. I was right to do an exact unit conversion and refrain from rounding. Alice was wrong to use 22/7 instead of π. You were wrong to round aggressively after a unit conversion which should have remained exact.

    I explained your mistake (again) in detail here. Pay particular attention to the toy example in which I do a unit conversion from inches to ‘zorgbats’.

    Do you understand your error now?

  26. keiths: Are you actually saying that if the antenna was shorter than the ruler at t1, but longer than the ruler at a later time t2, there was only “theoretically” a change in between?

    My objection was not to “change”. Rather, my objection was to the existence of a point at which change occurred.

    However, now that you bring it up, “change” is itself a theoretical idea.

  27. Neil:

    My objection was not to “change”. Rather, my objection was to the existence of a point at which change occurred.

    OK, so change occurred, but there was no point in time at which change occurred.

    Which brings me back to my earlier question:

    So in Neil World, there are no such things as points in time? ‘Now’ doesn’t exist? (Don’t bother invoking relativity. We’re talking about a single frame of reference here.)

  29. keiths: So in Neil World, there are no such things as points in time? ‘Now’ doesn’t exist?

    In ordinary usage, “now” refers to a range of times (usually a somewhat vague range). That does not require the existence of points in time.

  30. keiths: Karen’s only error was to treat a measurement of 20 yards as exact.

    And your error in treating a measurement of 9 feet as exact differed in what way, precisely, from Karen’s error?
    Errors that you claim I made, or Alice made, are off-topic.

  31. Neil Rickert: In ordinary usage, “now” refers to a range of times (usually a somewhat vague range).That does not require the existence of points in time.

    While I don’t claim to understand general relativity in any detail, the concept of “now” is pretty meaningless – everywhere in the universe has a different “now”, what with time working differently depending on mass and velocity. Relativistic effects play interesting games with “now”. And along these lines, distances in an expanding universe are measured with a rubber ruler. Points in time or space are constructs dreamed up for convenience (and they are very convenient). But there is no “theoretical underlying reality” for either of them.

  32. Jock:

    And your error in treating a measurement of 9 feet as exact differed in what way, precisely, from Karen’s error?

    Lol. Tendentious phrasing, much? I didn’t treat my measurement as exact. Karen treated hers as exact, according to your vignette. That’s the difference.

    You claim that I did treat it as exact. Back up your claim, please. What did I do, specifically, that amounted to treating the measurement as exact?

    Errors that you claim I made, or Alice made, are off-topic.

    They’re absolutely germane, because Alice’s error is the flip side of Karen’s correct decision, and your error is the flip side of my correct decision.

    Alice chose to use 22/7 instead of π; Karen declined to make that mistake.
    You aggressively rounded after a unit conversion; I declined to make that mistake.

  33. Flint, to Neil:

    While I don’t claim to understand general relativity in any detail, the concept of “now” is pretty meaningless…

    I addressed that here:

    So in Neil World, there are no such things as points in time? ‘Now’ doesn’t exist? (Don’t bother invoking relativity. We’re talking about a single frame of reference here.)

    Within a single frame of reference, ‘now’ is meaningful.

  34. Neil:

    In ordinary usage, “now” refers to a range of times (usually a somewhat vague range). That does not require the existence of points in time.

    There’s some wiggle room in ‘now’, but I don’t see any wiggle room in ‘at this exact moment’ or ‘at that exact moment’. Or substitute ‘instant’ for ‘moment’ if that feels sharper to you. Are those verboten in Neil World?

    Also, we can skirt the linguistic issues altogether by using more of a mathematical argument. I’ll wait to see how you respond to the ‘exact moment’/’exact instant’ modification, though.

  35. keiths: What did I do, specifically, that amounted to treating the measurement as exact?

    This:
    keiths

    9 feet converted to smoots is actually 1.6119…, and you are rounding that down to 1.6. That’s an additional error of 0.0119… smoots

    as compared with

    “No! You are wrong! 20 is an exact number”
    20 π x [Karen is using an old HP30]
    “See! Twenty times pi is 62.83185… exactly!
    When you rounded to 63 you introduced an additional error of, err,
    [     63 – ]
    0.16815 yards!”
    Bob explains that Karen cannot make that claim, as the original measurement was only accurate to 1%. Everyone agrees.

    The problem here is that Karen “exactified” the MDR “20.” and treated it as if it were the IPR “20,” she forgot where it came from, performed her 15-digit-precision calculation, and thought that her result was accurate to 5SF or more. She’s wrong.
    Now, you might argue that the problem lies, not with using an exact number to represent a measurement, but rather with Karen’s forgetting what kind of number she was dealing with. But that IS the risk of treating MDRs as if they were IPRs.
    You One might argue that nobody would be that silly, but one would be wrong.

    [strikethrough for humorous effect in original]
    It’s the inappropriate precision of your claim about the “additional error”, silly..

  36. keiths: Or substitute ‘instant’ for ‘moment’ if that feels sharper to you. Are those verboten in Neil World?

    Yes, just imagine. A child is told to “tidy up your room this instant”, and the child replies “Oops, the instant has already passed. It’s too late, so no need for me to tidy anything.”

    Somehow, I don’t think that would work. In ordinary usage “this instant” refers to a range of times.

  37. Neil:

    Somehow, I don’t think that would work. In ordinary usage “this instant” refers to a range of times.

    For your argument to work, it would have to be the case that “this instant” never refers to an actual instant. But of course it does, as in the very conversation we are having right now.

  38. t

    keiths:
    Within a single frame of reference, ‘now’ is meaningful.

    Sigh. I agree that “now” is meaningful by convention. In Neil’s sense, the word is used to describe a period of time that varies with context. I’m amazed you think any two locations can share a “single frame of reference.” I suppose that, for the sake of communication, we can think of “now” as a moving dimensionless instant (time being a dimension), that travels along an imaginary timeline at a rate that is essentially the same for everyone everywhere. But it remains a convention, and I’m not convinced that the convention rests on any theoretical underlying reality.

  39. keiths:
    Neil:

    For your argument to work, it would have to be the case that “this instant” never refers to an actual instant. But of course it does, as in the very conversation we are having right now.

    For your argument to work, the word “actual” must mean something. You believe it does, I don’t. I think that’s about as far as we can take this. Your notion of an “exact” number requires agreement on an underlying theoretical reality. So does your notion of “now”. I simply doubt that our concept of reality is actually perfect in either case. Instead, we have models of numbers, of distance, of time. This is easy to forget. As you illustrate, it’s not hard to fall into the error of thinking the map IS the territory.

  40. Jock:

    It’s the inappropriate precision of your claim about the “additional error”, silly…

    I’ve already shown you, in detail, why my claim is correct and not overly precise in the slightest. I look forward to hearing your substantive response to my reasoning.

  41. Flint:

    I’m amazed you think any two locations can share a “single frame of reference.”

    You are? You think it’s unreasonable to assert, for example, that two adjacent atoms in my calculator — the calculator that understands that 12 is equal to 12.0 — share a single frame of reference?

  42. Neil, Flint,

    Allow me to present another argument that may help us set the linguistic issues aside, or at least minimize them.

    In my antenna example, Neil has already agreed with the following: There is a time t1 at which the antenna is shorter than the ruler, and a later time t2 at which the antenna is longer than the ruler.

    Flint, are you in agreement with us?

  43. keiths: In my antenna example, Neil has already agreed with the following: There is a time t1 at which the antenna is shorter than the ruler, and a later time t2 at which the antenna is longer than the ruler.

    I don’t think I ever agreed to that specific wording.

  44. Flint:

    Your notion of an “exact” number requires agreement on an underlying theoretical reality… Instead, we have models of numbers, of distance, of time.

    The real numbers are exact by definition. This isn’t a question that is subject to empirical observation or experimentation. We can’t go out in the field, lasso a bunch of numbers, and then bring back to the lab to be dissected and inspected for exactness. The real numbers are exact by definition.

    You and Jock have agreed that exact numbers exist. The dispute hasn’t been over existence, it’s been over the proper use of those numbers. In particular, it’s been over the question of whether exact numbers can legitimately be used to express inexact measurements. I’ve shown that they can, and I’m waiting for either of you to screw up enough courage to address my argument.

    ETA: The argument also spills over into this comment.

  45. Neil:

    I don’t think I ever agreed to that specific wording.

    What about now? Do you agree? If not, why?

  47. Neil:

    I’m dubious about the existence of t1 and t2.

    So the very concept of a specific time is verboten in Neil World? You’d be uncomfortable saying “The antenna was shorter than the ruler at 8:00 AM, but by 8:05 AM it was longer”?

    What could you possibly object to in that?

  48. keiths: You’d be uncomfortable saying “The antenna was shorter than the ruler at 8:00 AM, but by 8:05 AM it was longer”?

    That’s not the same thing at all. We usually understand “at 8:00 am” as referring to a range of time, so it is not asserting the existence of a t1.

  49. OK, so you think that ranges of time exist, but not specific times. How small can those ranges get?

  50. Flint: Instead, we have models of numbers, of distance, of time. This is easy to forget. As you illustrate, it’s not hard to fall into the error of thinking the map IS the territory.

    Indeed.👍

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