The Hotel Inference Challenge-From the discoverer of the Sleeping Beauty problem

Sdílet
Vložit
  • čas přidán 19. 05. 2024
  • I am an elderly man who developed from his teens a radical view of what we are that has startling implications for our self-interest and our death. Also startling is how firmly we can establish the truth of the radical view. 'The Hotel Inference Challenge' will show you this.
    A shorter 'Finding Myself' video has been appended to the ‘Hotel Inference Challenge’ video.
    The brilliant visuals you will see have been added by the brilliant Mark Berezov ('Hotel Inference Challenge') and the brilliant Jason Resch ('Finding Myself').
  • Věda a technologie

Komentáře • 25

  • @jemandoondame2581
    @jemandoondame2581 Před 11 dny +2

    I wish I had more time in life.. to make this view more popular. The importance of universalism, makes the everyday things (that I see many people do).. seem mundane. At the same time, when someone is spreading the knowledge of universalism, one isn't taken serious at all..

    • @ArnoldZuboff
      @ArnoldZuboff  Před 11 dny +1

      It is always great to hear from you! My book Finding Myself is going to be published, which should help. I wrote a reply to BluetonicUK28, who had called this Hotel Inference video ‘hard going’. I thought my reply was an effective brief presentation of the argument, and I have been trying to improve it. Perhaps it can be a script for a short video. It might be helpful to you in explaining why universalism has to be true. I’ll paste in the latest version in a reply to this reply.

    • @ArnoldZuboff
      @ArnoldZuboff  Před 11 dny

      Imagine that you wake up and learn that that awakening was the result of one of two alternative ‘awakening games’ having been played.
      In the ‘hard game’ you would have been awakened only if a fair coin that was flipped a thousand times happened to have matched precisely in its pattern of heads and tails a list of one thousand words-each being either ‘heads’ or ‘tails’-that had been assigned to you as a kind of security code. Even one flip not corresponding to your list and you would have stayed sleeping forever.
      In the alternative ‘easy game’, although the same coin was flipped, there was no list assigned to you and you were simply sure to be awakened without the coin’s pattern of heads and tails mattering at all.
      You must infer that it is enormously more probable that your awakening had not depended on the absurdly improbable matching that was required by the hard game.
      In the area of thinking about personal identity, there is also a hard game and an easy game.
      The hard game-the usual view of personal identity-requires for your existence that, in your begetting and the begetting of each of your ancestors, just the one sperm cell crucial for your eventual emergence (out of something like two hundred million sperm cells competing in each begetting) was the one that got to the egg first each and every time. Even one of these sperm cells not making it and you would be excluded forever from existing in the usual view.
      The only easy game regarding personal identity is universalism, in which you would have existed no matter which sperm cells hit which eggs for the sole reason that an experience being yours only ever requires that the style of the experience be first-person, like the style of the experience that you know to be yours right now. So, since all consciousness is first-person in style, all consciousness is equally yours; but in each conscious thing it naturally misleadingly feels as though only this one thing’s experience is yours-as though the cut-off experience of the other conscious things is not also yours. (Universalism says it feels like this merely because the experience in each conscious thing is cut off from the others. But the ordinary view adds to this already sufficient explanation of feeling cut off from the others the unneeded, unthinking and unwarranted assertion that you also only are one conscious thing-a thing that to exist would have had to have won a series of sperm cell lotteries.)
      And in your reasoning regarding personal identity you must apply the exact same logic as you would in the earlier imaginary awakening game. It is enormously more probable that your existence-your awakening to consciousness-had not depended on an absurdly improbable matching of actual winning sperm cells to the sperm cells that were required for you to emerge in a game as hard as the usual view of personal identity.
      This means that you don’t disappear with the death of any single conscious thing and that your real self-interest must extend to all conscious things. Retribution is a mistake because both victim and perpetrator are you.
      And here is my challenge: Either reject the inference in the imaginary case or show a relevant difference between that and the inference to universalism. I think that nobody can do either. And, so, nobody can avoid universalism.
      Now, you may feel less than confident about the basic principles of probability inferences. And inferences can be invented that are fishy or plainly absurd. If, however, a coin has landed only heads in a random sequence of one thousand consecutive flips, nobody can think other than that the coin is overwhelmingly more probable to be loaded or double-headed than it is to be fair. And the overwhelmingly greater probability of the easy game in each of the inferences I have described has that same indubitable character. So, universalism is unavoidable.

    • @jemandoondame2581
      @jemandoondame2581 Před 4 dny

      @@ArnoldZuboff Which publisher is it going to be? That message will also be helpful! I will translate it into German.

    • @ArnoldZuboff
      @ArnoldZuboff  Před 4 dny

      @@jemandoondame2581 Thank you! The book will be published by The Philosophy Documentation Center.
      Here is a more developed version of that reply. (I am now thinking of putting this at the beginning in the book):
      Imagine that you wake up and learn that this awakening was the result of one of two alternative ‘awakening games’ having been played.
      In the ‘hard game’ you would have been awakened only if a fair coin that was flipped a thousand times happened to have matched precisely in its pattern of heads and tails a list of one thousand words-each being either ‘heads’ or ‘tails’-that had been assigned to you as a kind of security code. Even one flip not corresponding to your list and you would have stayed sleeping forever.
      In the alternative ‘easy game’, although the same coin was flipped, there was no list assigned to you and you were simply sure to be awakened without the coin’s pattern of heads and tails mattering at all.
      You must infer that it is enormously more probable that your awakening had not depended on the absurdly improbable matching that was required by the hard game.
      In the area of thinking about personal identity, there is also a hard game and an easy game.
      The hard game-the usual view of personal identity-requires for your existence that, in your begetting and the begetting of each of your ancestors, just the one sperm cell crucial for your eventual emergence (out of something like two hundred million sperm cells competing in each begetting) was the one that got to the egg first each and every time. Even one of these sperm cells not making it and you would be excluded forever from existing in the usual view.
      The only easy game regarding personal identity is universalism, in which you would have existed no matter which sperm cells hit which eggs for the sole reason that an experience being yours only ever requires that the style of the experience be first-person, like the style of the experience that you know to be yours right now. So, since all consciousness is first-person in style, all consciousness is equally yours; but in each conscious thing it naturally misleadingly feels as though only this one thing’s experience is yours-as though the cut-off experience of the other conscious things is not also yours. (Universalism says it feels like this merely because the experience in each conscious thing is cut off from the others. But the ordinary view adds to this already sufficient explanation of feeling cut off from the others the unneeded, unthinking and unwarranted assertion that you also only are one conscious thing-a thing that to exist would have had to have won a series of sperm cell lotteries.)
      And in your reasoning regarding personal identity you must apply the exact same logic as you would in the earlier imaginary awakening game. It is enormously more probable that your existence-your awakening to consciousness-had not depended on an absurdly improbable matching of actual winning sperm cells to the sperm cells that were required for you to emerge in a game as hard as the usual view of personal identity.
      This means that you don’t disappear with the death of any single conscious thing and that your real self-interest must extend to all conscious things. Retribution is a mistake because both victim and perpetrator are you.
      And here is my challenge: Either reject the inference in the imaginary case or show a relevant difference between that and the inference to universalism. I think that nobody can do either. And, so, nobody can avoid universalism.
      Now, you may feel less than confident about the basic principles of probability inferences. And inferences can be invented that are fishy or plainly absurd. If, however, a coin has landed only heads in a random sequence of one thousand consecutive flips, and either a fair coin or a loaded coin was used, nobody can think other than that it is overwhelmingly more probable that the loaded coin was used. And the overwhelmingly greater probability of the easy game in each of the inferences I have described has that same indubitable character. So, universalism is unavoidable.

    • @maximumrobocop4935
      @maximumrobocop4935 Před dnem

      @@ArnoldZuboff I am looking forward to this book!

  • @nickk882
    @nickk882 Před 18 dny +2

    As you described, I think the outcome I observe as a conscious being is one of a 1000 fair coins that landed in a specific 1 sequence of a large probability space. The biological mating process is the analogous hypothesis to a fair coin being flipped. Just as predicting any one sequence of 1000 coins is just as likely to occur as the all heads case, it's unlikely that I specifically would have occurred if there was knowledge of my being before I came to exist. The main issue I take with your argument is that any awakener would be "me", thus I am always an awakener - is the conscious mind not the result of initial conditions and proceeding experiences and probabilities? How would my consciousness differ if a different sperm had won? I believe it impossible to model such a multivariate process at this time. This would suggest that "I" am not the awakener, but that some awakening occurred, which has a much higher probability than any one awakening, and that I am the resulting development of that outcome. By this I don't refute the small probability of my exact outcome, but I reframe the hypothesis with which you predict my being.
    I also challenge your use of numbers beyond the limits of human comprehension for statistical analysis. It's very clear that these numbers are immense, but how do these numbers compare with some of the other probabilities in the same scale? How likely is it that the specific electrons in my phone are where they are in their distribution space at this instant to allow me to type this comment? I believe the chances of this specific arrangement of subatomic particles will belittle the rarity of my specific existence.

    • @ArnoldZuboff
      @ArnoldZuboff  Před 18 dny

      Thank you so much for your comment!
      But I do think you have somehow overlooked some crucial points made in the video.
      You admit at the end of your first paragraph that what you say there doesn’t ’refute the small probability of my exact outcome’. So far, then, I guess that you basically agree with me. (I’m not clear what you mean by also saying there that you ‘reframe the hypothesis’.)
      Then you go on in the second paragraph to make your point against my argument, which is that improbable things are happening anyway-like the specific arrangement of particles in your phone.
      In the video, I argue that there is no improbability for you in anything like the arrangement of particles in your phone but, within the usual hypothesis of personal identity, there is a perspectival improbability for you (but not for others) in the particular results of all the sperm cell lotteries that were required for your existence having-immensely luckily for you-resulted in your existence. (And if what had been required for your existence in some weird hypothesis had been instead that exact arrangement of particles that obtains in your phone, then that arrangement occurring would indeed have been an absurdly lucky coincidence for you.)
      The guiding theme of the video is that you would have to favour the easy awakening game in the hotel inference and that already amounts to you having to favour universalism as the easy game in personal identity. So, let’s see if your phone particle arrangement point can make a dent on the hotel inference.
      You wake up in the hotel and understand that either the hard game (where a thousand random flips of a fair coin would have had to have matched a list of a thousand heads or tails assigned to you for you to be awakened) or the easy game (where the flips are disregarded and everyone is awakened) had been played. You are about to infer the far greater probability of the easy game accounting for your awakening and then your eye falls on a mobile phone sitting on the bedside table. You think, ‘It’s so improbable that the phone particles have whatever precise arrangement they have that I won’t make the inference to the easy game accounting for my awakening after all’. That makes sense to you? You won’t infer that it is more probable everyone was awakened than that you were awakened by a thousand coin tosses matching your pre-assigned list of heads and tails because you think the arrangement of particles in your phone is improbable? If a coin was tossed a thousand times and had landed all heads and you knew there were two coins available-a fair coin and a coin loaded to land heads-you would not infer the far greater probability that it was the loaded coin that was tossed because you think the arrangement of particles in your phone is improbable?
      PLEASE ALLOW ME, IN THE COMMENT BELOW, TO EXCERPT SOME POSSIBLY HELPFUL PASSAGES FROM THE SCRIPT OF THE VIDEO:

    • @ArnoldZuboff
      @ArnoldZuboff  Před 18 dny

      ‘But couldn’t I just have been lucky?’
      Well, it is not an impossible contradiction that the usual view be true and that your coming into existence was therefore the most incredible luck imaginable.
      But you must, insofar as you are rational, regard it as overwhelmingly improbable that you were that lucky. It is on this improbability that I am insisting in this argument.
      A variation on that question: ‘Someone would have existed on the usual view; couldn’t that just have been me?’
      Again, yes-that wouldn’t have been impossible.
      But-also again-you must regard it as overwhelmingly improbable that that lucky someone was you.
      ‘Even if there is no coincidence for me in my existing, given the truth of universalism, isn’t it still going to be somehow equally improbable that a particular body or a particular mind has emerged from a long line of begettings?’
      No. Once you adopt universalism there is no longer anything coincidental for you in any such mere details of specific bodies or minds. If your awakening depended on a pre-specified pattern of heads and tails having been realised in one thousand tosses of a fair coin, then that pattern’s realisation would have been a great, lucky coincidence for you. But if you would be awakened no matter which pattern came up, there is no coincidence for you in the pattern that did come up. Something’s being improbable from your perspective would require such a coincidence.
      There is a temptation for some to think that there is always an improbable result when a fair coin is tossed one thousand times, because each possible pattern has only a one in two to the thousandth power chance of occurring. But what this really means is that each possible pattern of heads and tails designated independently of simply being the one that occurred has only that slight chance of occurring in one randomly observed sequence of a thousand tossings. If we are merely reading off an actual result there is no coincidence and no improbability.
      Recall that universalism and the usual view can agree on the conditions of body and mind that obtain in the world. They disagree only on where to draw the line between the essential and the incidental conditions for your existence. The usual view makes certain complex conditions of bodily or psychological identity essential requirements for your existence, while admitting that others, like the colours of your clothing, are incidental. Universalism puts all the conditions-other than that lone requirement of possessing a capacity for experience had with immediacy-on the incidental side of the line, along with the colours of what you are wearing. And if such demanding conditions as bodily identity are not required for you to exist, their realisation represents no coincidence or improbability for you at all-no more than do those colours of your clothing.
      The inference to universalism is, like all probability inferences, perspectival. And in this case you could not be using what the usual view would regard as the existence of others as the basis of your inference. For from the single perspective you are supposed to occupy within that usual view, the production of others would not have been improbable, since, once you existed (which is the hard part), you would be in the position of simply seeing any winners there might be in the begettings of others. This would be a guaranteed observation for you of them but a random and therefore incredibly improbable observation of your own existence for you, but not for them.
      Universalism, however, puts you into the guaranteed observation position regarding all conscious organisms bar none. (There is no hard part.) For universalism, of course, makes it irrelevant to whether you and this experience exist what sperm cells hit what eggs. All experiencers would be you merely on account of the immediacy, the internality, the first-person character of their experience. So, you are always an awakener, and seeing yourself as an awakener, no matter what.
      (What I just said about the existence of others within the usual view not involving improbability for you-and vice versa-is not strictly true. If you are an identical twin almost all your improbability of coming into existence would be shared by your twin. And to the extent you share ancestry with others-and at some very distant point in the past you share ancestry with everyone-you share also that much of your improbability and therefore that much of your basis for the inference to universalism.)
      Even if the usual view, with its absurdly improbable requirements for one’s existence, were true, it must have been wholly irrational for any conscious being existing to believe it. It would be like the one lucky winner in the hotel’s hard awakening game rightly inferring the enormously greater probability that the easy game is being played. It would be, from an awakener’s perspective, immensely improbable to be awake to be misled if the hard game is being played. And all conscious beings thinking straight about this must judge to be immensely improbable that they existed to be misled if the usual view of what they were was right instead of universalism.
      AND LATER:
      There’s a way of bringing the hotel inference closer to the analogy of inferring that a coin landing heads a thousand times consecutively is not a fair coin, another inference that everyone accepts. When I first published the hotel inference it had that wrinkle in it.
      A fair coin landing heads a thousand times consecutively is indeed improbable. Yet it would be just as improbable if a thousand random fair coin flips had happened to match a single random list of heads and tails that had been written out before the flips. In my original hotel case, each of the countless sleepers had a different such list assigned to him or her.
      Then a fair coin was to be flipped a thousand times.
      In the hard game the sleeper was to be awakened only if those coin flips had matched his or her personally assigned list (much like all the series of begettings having to go just right for you to come to consciousness in the usual view of personal identity). In the easy game everyone would be awakened no matter how the coin flips turned out.
      Imagine you were awakened in one of the hotel rooms and it was explained to you that your awakening had resulted from one of those two games.
      If I awakened and had that explained I would virtually know I was awakened in an easy game because it would have been ridiculously improbable for me that I had been awakened if that event required the fair coin producing by chance the strict pattern assigned to me.
      Since there are countless sleepers in this story, there will be countless awakeners in a hard game too. Just much much much rarer. But each will be obliged to reason perspectivally, as I did, that the game was immensely more probable for him or her to have been the easy one. I technically could have been awakened in a hard game. It wouldn't have been an impossible contradiction. But it would necessarily have been immensely improbable for me that I would be awake in a hard game to be misled by this proper probability reasoning if such an improbable matching had been the requirement for that to happen.

    • @ArnoldZuboff
      @ArnoldZuboff  Před 17 dny +1

      For the flipping of a coin substitute a momentary arrangement of particles in a phone. In the hard game, for you to have been awakened that pattern would have had to match an independently designated possible pattern of particles that had been assigned to you. In the easy game you were to have been awakened no matter what the arrangement of particles happened to be. You know you are awake. You must infer that it was absurdly improbable this awakening had depended on a momentary arrangement of particles in a phone happening to match an independently designated pattern.

  • @BluetonicUK28
    @BluetonicUK28 Před 21 dnem +2

    Hard going this

    • @ArnoldZuboff
      @ArnoldZuboff  Před 14 dny +1

      Let me try to help by giving you a pared-down representation of what I am saying:
      Imagine that you wake up and learn that this awakening was the result of one of two alternative ‘awakening games’ having been played.
      In the ‘hard game’ you would have been awakened only if a fair coin that was flipped a thousand times happened to have matched precisely in its pattern of heads and tails a list of one thousand ‘h’s and ‘t’s that had been assigned to you as a kind of security code. Even one flip not corresponding to your list and you would have stayed sleeping forever.
      In the alternative ‘easy game’, although the same coin was flipped, there was no list assigned to you and you were simply sure to be awakened without the coin’s pattern of heads and tails mattering at all.
      You must infer that it is enormously more probable that your awakening had not depended on the absurdly improbable matching that was required by the hard game.
      In the area of thinking about personal identity, there is also a hard game and an easy game.
      The hard game-the usual view of personal identity-required for your existence that, in your begetting and the begetting of each of your ancestors, just the one sperm cell crucial for your eventual emergence (out of something like two hundred million sperm cells competing in each begetting) was the one that got to the egg first each and every time. Even one of these sperm cells not making it and you would be excluded forever from existing in the usual view.
      The only easy game regarding personal identity is universalism, in which you would have existed no matter which sperm cells hit which eggs for the sole reason that an experience being yours only ever requires that the style of the experience be first-person, like the style of the experience that you know to be yours right now. So, since all consciousness is first-person in style, all consciousness is equally yours; but in each conscious thing it naturally misleadingly feels as though only this one thing’s experience is yours-as though the cut-off experience of the other conscious things is not also yours. (Universalism says it feels like this merely because the experience in each conscious thing is cut off from the others. But the ordinary view adds to this already sufficient explanation of feeling cut off from the others the unneeded, unthinking and unwarranted assertion that you also only are one conscious thing-a thing that to exist would have had to have won a series of sperm cell lotteries.)
      And in your reasoning regarding personal identity you must apply the exact same logic as you would in the first imaginary awakening game. It is enormously more probable that your existence-your awakening to consciousness-had not depended on an absurdly improbable matching of actual winning sperm cells to the sperm cells that were required for you to emerge in a game as hard as the usual view of personal identity.
      This means that you don’t disappear with the death of any single conscious thing and that your real self-interest must extend to all conscious things.

  • @maximumrobocop4935
    @maximumrobocop4935 Před 3 dny

    This is a really good explanation and I feel I've grasped the force of the hotel argument now after listening to this latest presentation, more better than I had previously.
    I wonder, though, if some might find a way around the argument, by claiming that the proper analogy to the Hard Game is not, in fact, the ordinary view of personal identity, but rather, the view that I am the only person _who exists_. Ie, that the argument works merely as an argument against solipsism, and not as an argument for universalism.
    I'm not sure how to work through this thought. I intuitively believe the truth of universalism (and have done for a long time). I also feel that the ordinary view, and solipsism, are one and the same on some deep level--perhaps it's just that they are both equally irrational!

    • @ArnoldZuboff
      @ArnoldZuboff  Před 3 dny +1

      Thank you so much for your comment. Before I directly address what you are saying, let me paste in a much shorter version of what I am saying in the video:
      --------------------------------------------------------------------------------------------
      Imagine that you wake up and learn that this awakening was the result of one of two alternative ‘awakening games’ having been played.
      In the ‘hard game’ you would have been awakened only if a fair coin that was flipped a thousand times happened to have matched precisely in its pattern of heads and tails a list of one thousand words-each being either ‘heads’ or ‘tails’-that had been assigned to you as a kind of security code. Even one flip not corresponding to your list and you would have stayed sleeping forever.
      In the alternative ‘easy game’, although the same coin was flipped, there was no list assigned to you and you were simply sure to be awakened without the coin’s pattern of heads and tails mattering at all.
      You must infer that it is enormously more probable that your awakening had not depended on the absurdly improbable matching that was required by the hard game.
      In the area of thinking about personal identity, there is also a hard game and an easy game.
      The hard game-the usual view of personal identity-requires for your existence that, in your begetting and the begetting of each of your ancestors, just the one sperm cell crucial for your eventual emergence (out of something like two hundred million sperm cells competing in each begetting) was the one that got to the egg first each and every time. Even one of these sperm cells not making it and you would be excluded forever from existing in the usual view.
      The only easy game regarding personal identity is universalism, in which you would have existed no matter which sperm cells hit which eggs for the sole reason that an experience being yours only ever requires that the style of the experience be first-person, like the style of the experience that you know to be yours right now. So, since all consciousness is first-person in style, all consciousness is equally yours; but in each conscious thing it naturally misleadingly feels as though only this one thing’s experience is yours-as though the cut-off experience of the other conscious things is not also yours. (Universalism says it feels like this merely because the experience in each conscious thing is cut off from the others. But the ordinary view adds to this already sufficient explanation of feeling cut off from the others the unneeded, unthinking and unwarranted assertion that you also only are one conscious thing-a thing that to exist would have had to have won a series of sperm cell lotteries.)
      And in your reasoning regarding personal identity you must apply the exact same logic as you would in the earlier imaginary awakening game. It is enormously more probable that your existence-your awakening to consciousness-had not depended on an absurdly improbable matching of actual winning sperm cells to the sperm cells that were required for you to emerge in a game as hard as the usual view of personal identity.
      This means that you don’t disappear with the death of any single conscious thing and that your real self-interest must extend to all conscious things. Retribution is a mistake because both victim and perpetrator are you.
      And here is my challenge: Either reject the inference in the imaginary case or show a relevant difference between that and the inference to universalism. I think that nobody can do either. And, so, nobody can avoid universalism.
      Now, you may feel less than confident about the basic principles of probability inferences. And inferences can be invented that are fishy or plainly absurd. If, however, a coin has landed only heads in a random sequence of one thousand consecutive flips, and either a fair coin or a loaded coin was used, nobody can think other than that it is overwhelmingly more probable that the loaded coin was used. And the overwhelmingly greater probability of the easy game in each of the inferences I have described has that same indubitable character. So, universalism is unavoidable.
      --------------------------------------------------------------------------------------------
      I don't see how anyone could say that the usual view is not a hard game. So, whatever you are saying about solipsism, this argument does succeed in getting rid of the usual view.
      What do you mean by 'solipsism'? This argument gets rid of solipsism if you mean by 'solipsism' a view in which only one conscious thing among countless potential conscious things ever really comes into existence. That would be even worse than the usual view because at least the usual view allows a large number of these potential persons to exist. If by 'solipsism' you mean a view that anyone existing has to be you because all experience must equally have the first-person immediacy that makes it yours-then what you are calling 'solipsism' is universalism. If solipsism is supposed to be a view that downgrades the experience of what the usual view regards as others so that it somehow does not possess immediacy within it, then I agree with you that that is like an aspect of the ordinary view. The ordinary view both grants and does not grant the same being 'mine' that is in your experience to be in the experience of others.

    • @maximumrobocop4935
      @maximumrobocop4935 Před dnem

      @@ArnoldZuboff Thank you for your reply --- what you say makes total sense.

    • @ArnoldZuboff
      @ArnoldZuboff  Před dnem

      @@maximumrobocop4935 Thank you!

  • @Xander081987
    @Xander081987 Před 21 dnem +1

    2 Comments, both blocked. Thank you for your work sir.

    • @festerbutt
      @festerbutt Před 20 dny

      CZcams is a censored platform😂😂

    • @ArnoldZuboff
      @ArnoldZuboff  Před 14 dny

      I’ve never blocked any comments.

    • @festerbutt
      @festerbutt Před 14 dny

      @@ArnoldZuboff It's automatic by youtube.

    • @Xander081987
      @Xander081987 Před 13 dny

      @@ArnoldZuboff Oh I wasn't thinking that you were at all sir. It just happens to be what this platform does with certain folks. I appreciate your work. Thank you so much.

    • @ArnoldZuboff
      @ArnoldZuboff  Před 13 dny +1

      @@Xander081987I’m so sorry to have got you wrong about that! Thank you! At first I wasn’t sure, but then defensiveness got the better of me. By the way, I’ve recently replied to the viewer who found the video to be ‘hard going’. I tried to get the main point across briefly but clearly. Please have a look and see if you like what I’ve said there.