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The Simple Ergodicities

Here’s a question for you to take your mind off COVID-19: Who is your favourite bear?

Is it Paddington? Or maybe it’s Rupert. For many it is Yogi, who is, after all, smarter than the average. Personally, I always had a soft spot for Boo-Boo. But if my life depended upon it, I think I would have to choose Baloo, if only for his wise counsel that we should all “Look for the bare necessities.”

Wise words indeed. But wiser still would have been the bear that entreaties we look for the ergodicities. Yes, the simple ergodicities of life will come to you. But only if you plan for them. Sadly, that bear of my dreams has yet to be born, and so the majority of us, unable to rest at ease without the ergodicities, continue to live out our decidedly non-ergodic lives with nothing but the precautionary principle to console us. Allow me to explain.

Me Explaining

Under the somewhat misleading heading of ‘Informal Discussion’, Wikipedia explains the simple ergodicities as follows:

“For a discrete dynamical system (X,T), where the space X is endowed with the additional structure of a probability measure space which is invariant under the transformation T, ergodicity means that there is no way to measurably isolate a nontrivial part of X which is invariant under T.”

Need I say more?

Okay, so let me put it this way. If you took 100 dice and threw them simultaneously, do you think (allowing for statistical fluctuation) that the total score would be the same as if you took just a single die and totalled the score after 100 throws? If the answer is yes, then you are dealing with an ergodic system.

Why does this matter? It matters because so much of risk assessment implicitly assumes ergodicity, since it seeks to predict the average performance over time using a probability density function that assumes ‘invariance under T’. In effect, the throwing of a die 100 times is treated as statistically equivalent to 100 dice thrown at the same time, thereby enabling the probabilistic calculations required for economic evaluations such as cost benefits analysis. In oh so many cases this is a perfectly safe assumption, but in oh so many more, it is not. Very often a throw of the die has a huge bearing on what follows, in which case there is no equivalent to the scenario of 100 simultaneous throws. Take, for example, a game in which throwing snake eyes means ‘game over’. With such, so-called ‘ruin’, scenarios the old economic game of calculating ‘equivalent values’ and performing costs benefits analyses doesn’t make much sense. Instead, the game is non-ergodic and we need a game play that takes into account the fact that, in order to attain the 100 die readings required to determine a total, one will need an extraordinary run of good luck. What we need instead is a precautionary approach.

As an example of this principle in action, take the case of house insurance. Every day of our lives we cast the die. We win when our house and contents are safe at the end of the day, but we lose when they are not. Furthermore, we are out of the game, because most of us cannot afford to replace everything in the event of catastrophe. The probability of that happening on any given day is low, but the probabilities stack up. So we take out insurance. With insurance we lose every day (by paying out a pro-rata daily insurance fee) but the losses are predictable and never enough to remove us from the game. A non-ergodic setup has been turned into an ergodic one. Of course, from the perspective of the insurance company the situation has always been ergodic. They are throwing dice simultaneously and paying out for housing disasters every day, but the premiums have been set up so that even on a statistically bad day, they can always take it on the chin and stay in business.

And so, in our daily lives, the successful management of risk depends critically upon identifying the ergodic and non-ergodic situations and acting appropriately. In the non-ergodic situation, it’s all about minimizing the maximum loss in order to keep oneself in the game so that one can reap the compensatory benefits of any upside further down the road. Ideally, one would always wish to transform the non-ergodic into the essentially ergodic, usually by means of a judicious risk transfer such as taking out insurance. Unfortunately, however, this is not always possible, and so other strategies are often required, normally involving the precautionary principle.

And then Along Comes Global Warming

Global warming is often cited as the classic ruin scenario leading to a non-ergodic game. Worse still, the human race cannot transfer the risk in order to contrive ergodicity because there is no one out there listening (apologies to all the religious readers). It should come as no surprise therefore that the precautionary approach is advocated. No one wants to talk about cost benefits analysis anymore because no one is deceiving themselves that ergodicity applies. In fact, no one even wants to talk about probabilities anymore. All that is required to invoke non-ergodicity, and the lurking precautionary principle, is to conceive a plausible worst case that takes us all out of the game. Now any cost can be justified to manage the risk – and I do mean any cost.

I might be going along with all of this if it were not for one thing: Even when probability is deemed immaterial, uncertainty still has a role in the game. It isn’t risk aversion anymore, because one needs to assess probabilities in order to assess levels of risk. But it is still ambiguity aversion because we are basing our decision-making upon the notion of plausibility – a concept heavily invested in epistemic uncertainty. This is a crucial point since, as soon as a plausible worst case scenario has been agreed, it forms the basis for a deterministic approach in which one proceeds on the premise that the worst case will happen. This is all very well but there is now an awful lot at stake based upon the somewhat problematic notion of plausibility. Nor is it simply a case of replacing a non-ergodic game with an ergodic one. Can we really be confident that we will stay in the game, considering the economic shock entailed when following Extinction Rebellion style ‘climate emergency’ management?

Hold on a minute! I’ve just remembered that my favourite bear is Sooty. He’s a rebellious little sod, so forget everything I’ve just said. What’s that Sooty? You’ve got a magic wand?

38 thoughts on “The Simple Ergodicities

  1. XR are simply replacing one non-ergodic scenario with another non-ergodic scenario, via the sleight of hand that this translation is a ‘normal’ response, albeit scaled-up, i.e. a kind of insurance type approach (and hence seemingly ergodic). And in practice, it’s even worse than that. Because while we can’t know the probable outcomes for either, as indeed we can’t attach probabilities, as you point out the plausibility of losing the game due to the imposition of crash net-zero, is at least one that is both nearer and clearer.

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  2. I suppose I have no one but myself to blame, but I can’t help but think that the bear debate has captured the imagination more than has my exposition of the relationship between egodicity and deterministic risk analysis.

    For what it is worth, I stand by Baloo. Once a Baloomer, always a Baloomer.

    Liked by 2 people

  3. Shock news. Chinese influence penetrates deep into Cliscep hierarchy. Winnie the Poo banned as potential “favourite bear” on Madam Jamie’s orders. It’s a honey grab (or trap). The world waits for a response from Cliscep Towers.

    Meanwhile confusion reins about “ergodicites” as people succumb to smoking tobacco laced with ergot in the mistaken belief it will solve their climate change worries.

    Liked by 2 people

  4. Cogito ergodic sum. I think therefore the probability that I am is invariant under t.

    That’s without any ergot! Just some ethyl alcohol distilled from red-skinned grapes.

    Liked by 2 people

  5. John. You have my sympathies. You will have spent much effort and thought when writing and refining this post and it has (currently) resulted in only one relevant response. Yet you hit a comedic nerve and that’s no mean achievement. Elsewhere we are griping on about coronavirus and the liberties our government is taking with our freedoms and our opposition to climate change absurdities is temporarily in abeyance. But for a short, short time we considered lighter things, what was our favourite bear and the comedic possibilities of a strange new word. Thank you.

    Liked by 1 person

  6. But Alan, you don’t see it, do you? Global warming has taken a back seat of late and some of us are now ‘griping’ about the new non-Ergodic ruination pseudo-scientific theory which is doing the rounds and laying waste to our society and freedoms in a fraction of the time which the Greenies could ever have hoped for. Even the XR nutters realised that 2025 was the earliest they could wish for to demand the full imposition of their nihilistic agenda.

    John says:

    “Global warming is often cited as the classic ruin scenario leading to a non-ergodic game. Worse still, the human race cannot transfer the risk in order to contrive ergodicity because there is no one out there listening (apologies to all the religious readers). It should come as no surprise therefore that the precautionary approach is advocated. No one wants to talk about cost benefits analysis anymore because no one is deceiving themselves that ergodicity applies. In fact, no one even wants to talk about probabilities anymore. All that is required to invoke non-ergodicity, and the lurking precautionary principle, is to conceive a plausible worst case that takes us all out of the game. Now any cost can be justified to manage the risk – and I do mean any cost.”

    We now have the catastrophe modelers AGAIN telling us that in a ‘worst case scenario’ (i.e. without a government lockdown), 120,000 people will die this winter and we have Chairman Johnson telling us that the government will be “getting on with its agenda” and doing “everything in its power” to prevent an imaginary “second spike” in infections this winter. They’re re-running the March Ferguson Imperial fiasco. John’s words are prophetic: “Now any cost can be justified to manage the risk – and I do mean any cost.” The government does not want to talk about probabilities – it just wants to press ahead with its agenda. That will include massively ramping up ‘flu vaccinations this winter for anyone aged over 50 or deemed ‘at risk’. Big Pharma is going to make a killing this winter – as are those government ministers with their noses in the trough. Meanwhile, we can maybe look forward to a thoroughly miserable Christmas under mass house arrest.

    Liked by 1 person

  7. Alan,

    If I had used the ruin scenario of a second wave as my example, and used it to discuss the pros and cons of mask wearing, I might have encountered more interest. However, my intention had been to deliberately shun that particular limelight. I am happy with my article and I am egotistical enough to be satisfied with that.

    Liked by 1 person

  8. It would seem that I can’t even compliment an author of a post without being beset by insults that “I don’t see it”. Perhaps I’ll retire for a spell and leave you good folks for a spell.
    TTFN.

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  9. Alan,

    I very much appreciated the compliment and I do not doubt for a moment that you ‘see it’.

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  10. I’ll be taking a long break too. I was personally attacked for calling the government “staggeringly incompetent” and using such dreadful language as “bloody”. Just one person on this site defended me on this. I’ve been accused of caring more about the economy than human life and lacking humility and compassion, now I’m “griping” about loss of liberty re. being forced to wear a mask in supermarkets and being accused of “insulting” commenters. Even when I realistically compared the doomsday climate scenarios with the doomsday Covid scenarios I was criticised. So please feel free to continue making comments Alan. I’m not getting involved anymore because it’s all getting just a little too personal and heated and my direct, somewhat confrontational style is becoming less appreciated on this urbane platform it would seem. Best wishes to you all.

    Liked by 1 person

  11. To b or not to b, that is the question:
    Weather ’tis nobler in the mind to suffer
    The slings and errors of ergodic fortune,
    Of to take arms against, etc, etcetera…
    Must give us paws. – For who would bear
    The whips and scorns of time, etcetra,
    (Etc) makes us rather bear the ills we have,
    Than fly to others that we know not of…
    Etcera. etceterah …

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  12. Jaime @ 8.41a.m. I so-o j’aime yr comment…Can’t do the ”like’ button, my comutah says no-o.

    Alan, what was the WW2 code calling planes back to base, ‘whisky, tango- something?
    Come in Allan!

    Liked by 1 person

  13. Jaime,

    Before you go, I should acknowledge that you are quite right to recognize that the article would have applied just as much had I chosen the COVID-19 second wave as the ruin scenario. This is one of the many ways in which climate change and COVID are two sides of the same coin.

    One of the implications of the non-ergodic game is that a deterministic approach is then taken to risk management, and I think this creates a dividing line between the alarmed and the sceptical (a false dichotomy, perhaps). It seems very odd to some people that a possible calamity should result in actions that only apply once calamity has been assumed. However, in safety critical applications this is quite the norm. For example, a nuclear power plant is built to withstand the severest possible earthquake because there would be no point in doing otherwise. This approach, however, inevitably means that plausibility becomes the battleground. In the nuclear power plant example, there is historical data to call upon to scientifically determine the limits of plausibility. In other examples I could mention, the scientific basis is much more controversial. Your comment already points them out, and so I will not.

    Don’t stay away too long. Cliscep needs passion, whether it likes it or not.

    Liked by 2 people

  14. May I make a plea for the early return of both Jaime and Alan?

    It’s all too easy to allow comments to become personal, and for strongly-held views to be expressed with such force that others take unintended offence.

    So long as we can all remain friends and keep it polite, I think the force and variety of views are very important. I’m firmly in the camp of defending free speech, not of supporting the taking of offence and closing down debate.

    I for one value and appreciate most contributions on this site, and would regard anything other than a short break by Jaime and Alan to be a great loss to us all.

    Liked by 3 people

  15. Lots of going off in a huff here. Is it isolation that’s making everyone so touchy? Ever considered the possibility that the main purpose of the Deep State in imposing their dastardly lockdown was to cause rifts in the ranks of sceptics?

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  16. Thanks Mark and John. It’s not just a case of me stomping off in a huff. I’m now exhausted emotionally with this virus nonsense and I feel I’ve just said about as much I can on the subject now and it’s not our core subject here anyway but naturally, we’ve all become a little fixated on it because it has affected us all in so many ways, Alan directly. I have tried on an earlier post to get right back on topic with the Antarctic, but it didn’t generate a great deal of interest if the viewing figures and comments are anything to go by. We all seem to be stuck in a bit of a Covid/lockdown rut at the moment and it’s getting quite depressing and dispiriting, so I’m going to take a break until something new and exciting happens, which may be rather a long time, I fear. Take care all.

    Liked by 1 person

  17. ” I’m not getting involved anymore because it’s all getting just a little too personal and heated and my direct, somewhat confrontational style is becoming less appreciated on this urbane platform it would seem. Best wishes to you all.”

    irony.

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  18. Mosher, probably one of our most confrontational of commenters from the ‘other side’, who clearly has made his objections quite personal at times waits until I sign off for a while to come back with a snide comment. Irony.

    So please forgive this brief off-topic comeback John.

    How’s that “dumb shit theory” going Mosh? Any explanations as to why it appears to be pretty mainstream now, even to the point of quite probably stopping people dying now in London, New York and Stockholm?

    We lost our way here guys. Covid-19 cast us adrift. Even Paul hasn’t been here to steady the tiller. We’ve still got a sticky from March 14th on causation by John! Nothing really new is happening. Sure, we have had some articles since March which have attempted to focus on climate alarmism and we’ve had some good contributions from new authors Mike Dombroski and Tony Thomas, but the near constant drum-beat has been Covid alarmism, woke politics, media and government corruption. The media has largely abandoned climate alarmism for now to concentrate almost exclusively on Covid alarmism. I used the same approach to that hype as I have used for climate hype, but whereas we all mostly agree on climate hype, we definitely do not all agree on the Covid-19 issue. I’ve been accused of racism, lacking compassion, attacking our wonderful government without merit or sufficient domain knowledge, calling them incompetent, using nasty bloody swear words and even of putting the economy before lives. I’m concerned that a few of my comments may have disappeared, though it might just be me unable to find them. This absurd world-wide over-reaction to a ‘flu like illness which has killed the elderly and those with existing serious illness, not the young, middle aged, working age or the healthy has irreparably damaged our cosy little world here at Cliscep as it has done the world outside. I preferred the old normal, where the Greens and climate alarmists were telling us we must transition to the New Green Deal Normal in 12 years or die horribly – but we were still free. I don’t like the New Normal where globalist control structures have been wheeled into place to prevent people dying horribly, whilst making it more likely that people will die horribly.

    Liked by 1 person

  19. I was intending to write a post somewhat similar to Jamie’s, but I get tired in the evenings and find it difficult to concentrate sufficiently to write coherently. So I set this task aside until this morning,. Wherein I found Mosher’s unnecessary contribution awaiting. Then came Jamie’s repost and a most interesting contribution upon the influence of Covid 19 upon the makeup of Cliscep in recent months. After a short spell of reflection not only do I completely agree with her perceptive analysis, but realised that it applied more widely. JoNova has been almost completely subsumed by discussions of the virus, as has large chunks of WUWT.
    What is required here I believe is a liberal dose of Brad to drive us to the dictionary and to mop up a multitude of coffee drenched keyboards.
    I doubt if Jamie or I can agree on Covid 19. We view it from different peaks and the battleground has been bloody and personal. So we have both retired injured to lick wounds but will be back, hopefully with peace treaties. This is an early attempt.

    Liked by 2 people

  20. The accusation of irony or hypocrisy is the baseline for confrontational rhetoric. It is meant to hit home like Thor’s hammer, accompanied by the thunder of the gods. In reality, it is weak chest thumping accompanied by flatulence that is best ignored. And guess what — we all fart.

    Now, if we can get back to the actual purpose of this article: Who is your favourite bear Steven?

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  21. JAIME

    The media has largely abandoned climate alarmism for now to concentrate almost exclusively on Covid alarmism. I used the same approach to that hype as I have used for climate hype, but whereas we all mostly agree on climate hype, we definitely do not all agree on the Covid-19 issue.

    This is normal. I don’t even agree with myself most of the time. Covid is a fast developing situation with new data coming in all the time. What we’ve seen with the various propaganda efforts, fake science etc. is like Climategate speeded up a hundred times. And, as you point out, the fake science and propaganda is having an immediate effect on our lives right now, instead of being a vague threat to ruin the economy sometime in the near future.

    Mosher coming over ironical is funny, and very revealing. He’s obviously never been in a debate where people cared about finding out the truth and get upset when they feel their efforts are being obstructed.

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  22. I think everyone of us, deep down, knows exactly who our favourite bear was (or still is). It’s our childhood teddybear. Or in my case it was my sisters teddy that I lusted after. To my undying later shame I had a gollywog, but he was extremely handsome.

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  23. Alan,

    I received my first teddy bear before I was potty trained. It became known as Turdy Bear, for reasons that I will leave to the imagination.

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  24. I never had a teddy bear. We wos poor. And young people today won’t believe you when you tell them…..

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  25. In the 1980s in California you could buy very expensive teddy bears dressed up to become famous personages of the past. So my wife recieved presents of William Shakesbear, Amelia Bearnheart, Scarlett O’beara and the like.

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  26. I meself have always been into dogs, https://virulentwordofmouse.files.wordpress.com/2012/06/thurber-dog-reading.jpg Jaime you and I would be able to share many true and amazing canine tales.

    I also, in Grade 3, had several horses, black, white, grey, chestnut,…Beauty, a black stallion was my particular favourite, I would often stand astride two horses as we galloped across the plains, we practised many tricks in the back yard. …Their stables were drawn in chalk upon the back fence. 🙂

    Liked by 2 people

  27. How could a serf-let on a turnip farm afford the upkeep of a menagerie of horses? What with hay and feed, costs of shoeing for so many animals would have been so prohibitive. Even chalk stables would need refurbishment. A third-grader must have had great dedication and concentration but would have been rewarded by many adventures.😊

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  28. Flaming galahs Beth what caused shifting turnip field boundaries? – strong winds produced by unstoppable and ergodic climate change?

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  29. “” I’m not getting involved anymore because it’s all getting just a little too personal and heated and my direct, somewhat confrontational style is becoming less appreciated on this urbane platform it would seem. Best wishes to you all.”

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  30. When Mosher writes five stupid posts in a row does that have the same impact as a single stupid post for five successive days? Let’s not find out.

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