1,371 thoughts on “ChatGPT narrates TSZ”

1. The last word on measurement:

   https://www.jpost.com/science/article-733651

2. petrushka,

   🥴! What is the height of one standard dromedary?

3. One standard dromedary is 17.2193877551 bananas.
   That’s a unit conversion, so it’s exact.

4. Alan Fox:
   petrushka,

   !What is the height of one standard dromedary?

   It’s at the link. And very exact.

5. [Jock and keiths are discussing measurements.]

   keiths:
   There are exactly 12 inches in a foot, 8 ounces in a cup, and 67 inches in a smoot.

   Jock:
   Give me a break. You’re telling me there are exactly 12 inches in a foot? Plus or minus zero? Exactly 67 inches in a smoot? That’s impossible.

   keiths:
   I swear it’s true. You can look it up. Unit conversions are exact.

   Jock ignores what keiths has told him, and this happens:

   23) Jock saw the “1.61194…” and rounded it to “1.6 smoots”, resulting in an error of a full 0.8 inches.
   By rounding, he introduced an error of (1.61194… – 1.6) smoots, or 0.01194… smoots. That’s a full 0.8 inches, meaning that he shifted the window by that amount. In real life, the window would be pretty small (remember that we only chose ± 0.5 feet to make the explanation easier to understand). A realistic window would be ± 0.25 inches. In that case, Jock’s new window would not even overlap the old one, and in fact there would be 0.3 inches of space between them. A disaster.

6. Jock,

   Remember how impatient you were to see the final “chunk” of my explanation of your error?

   Now, can I have my fourth and final chunk, so that we can get on to the question of how Karen’s error differs from what you did.

   I gave it to you five and a half days ago, with nary a peep in response. What’s up with that?

7. keiths: Jock,

   Remember how impatient you were to see the final “chunk” of my explanation of your error?

   Now, can I have my fourth and final chunk, so that we can get on to the question of how Karen’s error differs from what you did.

   I gave it to you five and a half days ago, with nary a peep in response. What’s up with that?

   Well, I was deeply disappointed in how content-free your “reveal” was. That was your “prestige”? A fictional narrative? And I was enjoying your claims regarding the forces imparted by pre-Newtonian angels on celestial bodies. There’s an issue with conceptual thought, it seems.
   Your 25th and final chunk didn’t warrant a response because it depended on 1, 4, 5, and 20, and it continued the fictitious narrative of 23 and 24, as noted previously.
   For those of you following at home, #4 claimed

   The systematic error is a predictable error that occurs on each measurement. It is always the same value.*

   which keiths did admit was false. There really is not anything to respond to.
   On the other hand, it’s been 11 days since you promised

   You’ll have to wait until later today for a detailed explanation
   [emphasis added for s&g]

   regarding how Karen’s error differs from what you did here.
   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, or more than 3/4 inch. Not good.

   versus Karen:

   See! Twenty times pi is 62.83185… exactly!
   When you rounded to 63 you introduced an additional error of, err, 0.16815 yards!

   It’s the identical mistake!
   You offered up your explanation of why you think Karen is a moron, but never explained how what you did was not equally moronic.
   What’s up with that?

8. Jock,

   You’re as bad at spinning as you are at bluffing.

   The reason you stalled for 5 1/2 days is because you can’t find a flaw in my reasoning. If you’d found a flaw, you would have jumped on it immediately. Instead you remained silent, hoping this would blow over. Only when I called you on it did you finally respond.

   I’ve shown in detail what your mistake was, why the error you introduced was so large, and why your efforts to downplay it are based on faulty logic. Like it or not, it’s all right there.

9. Jock:

   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, or more than 3/4 inch. Not good.

   versus Karen:

   See! Twenty times pi is 62.83185… exactly!
   When you rounded to 63 you introduced an additional error of, err, 0.16815 yards!

   It’s the identical mistake!
   You offered up your explanation of why you think Karen is a moron, but never explained how what you did was not equally moronic.

   Ah, now I think I can see where the confusion is coming from. Your scenario is poorly worded.

   I took you to be saying that because Karen regarded the number 20 as exact, she also took the measurement “20 yards” to be exact and computed the amount of paint based on the assumption that there was no measurement error. That was reinforced by the fact that only Alice and Bob mentioned measurement error. It’s why I wrote this:

   Karen’s mistake, amusingly, was the same one you and Flint have been making for five entire weeks: she assumed that if the exact number 20 were used in the measurement “20 yards”, the implication was that the measurement was also exact. Big mistake. The exactness of the number 20 neither indicates nor implies the exactness of the measurement “20 yards”.

   If I’ve unraveled this correctly, you were actually trying to say that by using 22/7 as an approximation for π, Alice and Bob didn’t introduce any additional error, because the difference was somehow too small to matter given the possible sizes of the measurement error. That’s wrong, and it’s analogous to the mistake you made by rounding the pole length down to 1.6 smoots. 22/7 isn’t equal to π, and the difference adds to the overall measurement error in the same way that your mistake added to the overall measurement error in the case of the pole. The window is shifted in both cases, which is exactly what we don’t want.

   Alice and Bob’s mistake is less severe than yours, because the percentage difference between 22/7 and π is only 0.04%. Nevertheless, it’s still an additional error that would have been avoided if they had used π instead of 22/7.

   It boils down to this:
   If you shift the window, you’ve introduced a systematic error.

   We are trying to avoid error, not increase it.

10. keiths: If I’ve unraveled this correctly,

    you haven’t.
    The point is that keiths made the identical mistake that Karen made.
    EVERYBODY agrees that Karen made this mistake, treating an approximate measurement as exact. The whole point is keiths makes the same mistake.

11. keiths: You’re as bad at spinning as you are at bluffing.

    Wrong, as ever.
    I’ve been sitting on my response to give you opportunity to dig yourself deeper, whether it’s about Karen or the limitations of angelic impulses.
    Here goes:

    When you communicate a number to someone, you are in fact communicating two things.
    A value, and an estimate of the precision of that number. Context will be needed to ascertain the accuracy of the value (such as the measurement standard and methods used). As a generality, the implied precision that a simple number carries is that the rightmost digit has a better than 50 – 70% chance of being correct – better than 10% chance if you are being sloppy. If your measurement is 2.7111, with a sd of 0.05, then reporting out 2.7 conveys appropriate precision. If you reported out 2.7111, you are using excess precision, false precision, inappropriate precision, misleading precision, call it what you will.
    If you want your audience to have access to that overly precise value, then you can report it out with an explicit description of the imprecision, e,g, “2.7111 ± 0.05” so long as you also note how you came up with the error term: is it the S.E.M., or something else? It is often better to provide a 95% confidence interval, as one does for Hazard Ratios (which interestingly, are dimensionless measurements, utterly lacking in units)
    “Males 0.39 (0.26 – 0.58), Females 0.75 (0.46 – 1.21)” [Reck et al. N Engl J Med 2016;375:1823-33.]
    Note that the intervals are decidedly asymmetric. Also, 100% confidence ‘windows’ don’t exist.

    As noted previously,

    it is standard practice to use excess precision to perform all intermediate calculations, but to report out the appropriately rounded value, in order to avoid misleading your audience.

    The flintjock thesis is that all measurement-derived reals (MDRs) arrive in your inbox with an implicit error term attached. These are the numbers that everybody uses. It is important NOT to imbue these values with an exactitude that they do not possess, but rather to keep track of the distributions, whether informally or formally. If you do this, you will notice the potential danger when one of the following happens: you subtract one MDR from another and get a result that is much smaller than the input MDRs, or you divide a value by a very small MDR. Calculations such as (A – B)/(C – D) are high risk.
    Frame keiths argument.

    1) Imagine we measure many different poles, all close to 9ft, and we are just considering the occasions when the measurement turns out to be exactly 9ft
    [safer to imagine we measure one pole; we could measure it many times, but this reading, today, happened to be 9ft]
    2) Measurement error = result – actual value
    [I think result = {actual value} + {measurement error} is a much safer way of thinking about it, but the equations are equivalent]
    3) Measurement error has a sign
    4) {measurement error} = {systematic error} + {random error}
    “The systematic error is a predictable error that occurs on each measurement. It is always the same value.* For example, a scale might consistently read low due to systematic error”
    keiths goes off the rails here, and it is symptomatic of his larger problem.
    As he notes with his asterisk, systematic errors can vary [correct] as long as they are predictable [nope]. He claims [in error] that this complication makes no difference to the current discussion.
    5) Systematic error and random error are both signed, so they may reinforce or cancel
    [he uses an example where the systematic error is known and invariant. His error in 4) has propagated.]
    6) I write a specification of 9,0 ± 0,5 ft and declare that the pole’s actual length must be within this range. [we have covered why this is false previously. Keiths recognizes this, as he also stipulates “No Mars Climate Orbiter type scenarios, either.” Where the competent professionals he puts so much stock in fucked up royally. 100% confidence intervals do not exist.]
    7) Units are arbitrary
    8) 9,0 ± 0,5 ft = 108,0 ± 6,0 inches
    9) The range is unchanged
    10) 108,0 ± 6,0 inches = 9,0 ± 0,5 ft
    11) Unit conversions are infinitely precise
    12) Unit conversions are exact
    13) And reversible (as shown in 8 thru 11)
    14) Whatever the units
    15) See?
    16) Even with [finite] decimal expansions [not so easy with 32-digit recurring decimal expansions, but anyhoo…]
    17) But don’t truncate
    18) If we truncate
    19) Then the unit conversion is not reversible
    20) It’s fine to report out false precision values, with an error term [so long as you also report the error term]
    21) Converting to and from Smoots using fractions
    22) Now using decimals
    23) By rounding Jock introduced an error of 0.01194… Smoots [I understand keiths’s ellipsis here to denote 0.0(119402985074626865671641791044776)recurring Smoots. Hey at least he’s owning this one…]
    24) Jock converted to Smoots and rounded. He’s a bad boy.
    25) An error window that was formerly located at 108 ± ε inches has been shifted to 107.2 ± ε inches. Jock is embarrassed, then excited, but prematurely. [those epsilons are distributions, not values, and they are not the same as each other]

    To dispose of this ‘argument’ first: like Yossarian tending to Snowden, keiths has been treating the wrong wound.
    I’ve never been motivated to reduce or minimize the size of the rounding adjustment I made: I had a choice between quoting the result to 2SF “1.6 Smoots” or quoting to 3SF “1.61 Smoots”.
    In inches, that is 107.2 ± 3.35 or 107.87 ± 0.335
    Given keiths description of his ruler-aligning technique, I suspected errors up to an inch or so were possible over the eight alignments required. However, there was also the question of just how far away from “exactly 9” would the pole need to be before keiths would admit that it was not simply the count nine, and start using the markings on the ruler… His actual reported result was “9”, which he explicitly claimed was a count, so the next nearest values would be 8 and 10.
    His implied error window is thus 108 ± 6, so my version 107.2 ± 3.35 is actually claiming higher precision. Not that it matters at all.
    My point, all along, has been that your claim that “By rounding, he introduced an error of (1.61194… – 1.6) smoots, or 0.01194… smoots.” Contains an implicit claim that your measuring technique is accurate to 5SF.
    I have explained this to you a couple of times, but it evidently did not sink in.
    Here goes one more time.
    There is one pole. It has a unique, exact, unknown length.
    When we measure the pole, we are sampling from the distribution of possible results we might get.
    The nature of this distribution depends on the technique we use. The technique will be imprecise (there will be random variation in the results) and the technique will be inaccurate (there will be non-random ‘systematic’ variation away from the true value.) For any given measurement, the contributions of random and systemic variation are unknowable, since there is variation in the systematic error.
    You can improve precision, but not accuracy, by taking multiple independent readings and averaging them, but each ten-fold improvement in precision comes at a 100-fold increase in time and effort…
    Two orders of magnitude improvement requires 10,000 replicates. By that point, other sources of error will dominate, in most cases.

    {measured value} = {true value} + {measurement error}
    {measurement error} = {mean systematic error} + {variation in systematic error} + {random error}
    {reported value} = {measurement value} + {rounding adjustment}
    Total error = {measurement error} + {rounding adjustment}
    If, and only if, these latter two values have the same sign, then the additional error due to rounding is precisely equal to the rounding adjustment. You cannot know whether that is true or not. All you can say is that the rounding has introduced an additional error of EITHER ({rounding adjustment} – 2 x {measurement error}) OR {rounding adjustment}. You claimed that rounding introduced an additional error of 11.9 milliSmoots (so between 11.85 and 11.95 milliSmoots), thus 2 x {measurement error} < 0.1 milliSmoots, that’s 3.35 thou.
    In this way the accuracy and precision of your measurement acts as a limit on the precision with which you can state the additional error introduced due to rounding. Any claim that “rounding introduced an additional error of X” contains within it an implicit claim that the accuracy and precision of the measurement is better than the quoted precision of X. This was Karen’s error. You agreed that Karen erred.
    Valid claims that could be made would include “rounding introduced a potential error of X” or “rounding introduced an additional error of up to X”
    The tale of Karen entertains me. Karen was almost called Kevin, or Kenneth…
    Keiths asked the question:

    1) What goes wrong if real numbers, which are exact, are used to express measurements, which are inexact? Please describe a scenario in which this creates a problem.

    I responded, in part

    DNA_Jock: Her mother Karen, however, knows that you can use exact numbers to represent inexact measurements. Reviewing Alice’s notes she upbraids her thus “No! You are wrong! 20 is an exact number”
    20 <enter> 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,
    [ <enter> 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.
    YouOne might argue that nobody would be that silly, but one would be wrong.

    When I wrote that story, I fully expected keiths to spot the parallel (I mean striking out “You” was intended as a big flashing neon sign “YOU DID THIS VERY THING”), and therefore maintain that Karen was actually correct. My goal here was, as ever, to induce keiths to write palpably ridiculous things.
    Did not go as I expected. Went much better.

    Much to my surprise, keiths, sided with Alice, writing

    Knowing that the measurement was approximate, she would have gone along with Alice and Bob and taken measurement error into account

    That’s right!
    You are going to need to explain, very carefully and without digression, how Karen’s error differs from what you did here
    You promised to do so a 11 days ago, and you still have not.
    e2fix blockquote

12. Will this marathon of a chess game ever end up with an exact number of moves?

    DNA_Jock: In inches, that is 107.2 ± 3.35 or 107.87 ± 0.335

    Here’s what I think:
    107.2 inches is a measurement which is relative, always approximate and never exact.
    107.87 inches is a measurement which is relative, always approximate and never exact.
    3.35 inches is a measurement which is relative, always approximate and never exact.
    0.335 inches is a measurement which is relative, always approximate and never exact.
    These four are approximately relational to something external to themselves, and can be used to measure something. (they are never exact).

    ***

    107.2 is a real number which is absolute, singular, non-physical, abstract and exact.
    107.87 is a real number which is absolute, singular, non-physical, abstract and exact.
    3.35 is a real number which is absolute, singular, non-physical, abstract and exact.
    0.335 is a real number which is absolute, singular, non-physical, abstract and exact.
    These four are exactly sufficient within themselves, and can never be used to measure anything. (they are never approximate).

13. CharlieM,

    Hence the introduction of ratios…
    The Hazard Ratios reported out in Reck et al 2016 — 0.39 and 0.75 — are numbers with no units attached. But they are measurement-derived.
    So, according to your division, which category do they fall in?
    They appear to be real numbers that are never exact.

14. DNA_Jock:
    CharlieM,

    Hence the introduction of ratios…
    The Hazard Ratios reported out in Reck et al 2016 —0.39 and 0.75 — are numbers with no units attached. But they are measurement-derived.
    So, according to your division, which category do they fall in?
    They appear to be real numbers that are never exact.

    Correct me if I’m wrong, but as I see it the Hazard Ratios are a comparison between a predicted outcome or event and some sort of control outcome or event. This means that these numbers are estimates and so they are relative, always approximate and never exact. But without the ‘Hazard Ratio’ appendage, they are absolute, singular, non-physical, abstract and exact.

    0.75 is to 0.75 Hazard Ratio as 0.335 is to 0.335 inches.

15. Jock,

    Methinks thou dost protest too much. That was a lot of words to spend trying to cover up your mistakes. Your 5 1/2 day silence tells the real story.

    It’s pretty much a given that you’ll never own up to your mistakes, but that doesn’t obligate me to explain them over and over. I’ve already done so in great detail.

    Here’s the bottom line:
    You shifted the window from 108 inches to 107.2 inches. That’s a full 0.8 inches of systematic error, and it was totally unnecessary.

16. CharlieM,
    No, the Hazard Ratio is a dimensionless number, just like any other real number. It is the result of exponentiating a parameter that has been estimated from the survival data.
    HR = e^β
    It is meaningless to try to attach the units “Hazard Ratio” to it as an appendage. It is a number, a measurement-derived real (MDR). You appear to be arguing that a number suddenly becomes exact when you forget where it came from.
    This is keiths’s position, so you would have company of a sort.

17. DNA_Jock:
    CharlieM,
    No, the Hazard Ratio is a dimensionless number, just like any other real number. It is the result of exponentiating a parameter that has been estimated from the survival data.
    HR = e^β
    It is meaningless to try to attach the units “Hazard Ratio” to it as an appendage. It is a number, a measurement-derived real (MDR). You appear to be arguing that a number suddenly becomes exact when you forget where it came from.
    This is keiths’s position, so you would have company of a sort.

    Surely it’s an estimated percentage. So I have to ask, 75 percent of what? It is a number which is applied to a physical situation, to a norm. 0.75 is a real number, no more, no less. As an applied measure it will have a margin of error, but as a pure number it is exact.

18. Vividbleau (a commenter at Uncommon Descent) posted a link to this article which mentions “context” a few times. The author also uses “woke” quite a bit, so perhaps caution is needed. I’ve not heard of James Lindsay before.

19. keiths: Jock,

    Methinks thou dost protest too much. That was a lot of words to spend trying to cover up your mistakes. Your 5 1/2 day silence tells the real story.

    Awww.
    My “dost protest too much” is a mere 60% of your chunk-a-thon, kid.
    But I understand your silence.
    On February 25th, you promised to explain, later that day, how Karen’s error differs from what you did here.
    The closest you got was to offer your description of Karen’s error. Not really on point: we all agree Karen made a stupid error, but you are going to need to explain, very carefully and without digression, how Karen’s error differs from what you did.

    It’s been three weeks now; what are we to conclude from your continued silence?

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