Why Understanding Ergodicity Is Critical To Your Long Term Survival

How Not To Be Fooled By Randomness

Why Understanding Ergodicity Is So Important To Your Long Term Success. Picture of Joker playing card.

Introducing Ergodicity

Ergodicity is an ugly word from the world of mathematics.  It is an umbrella term for two sets of conditions of probability and outcome.

These two conditions form the basis of a lie that you have been sold by governments, economists and investment "advisors" for the past 150 years.

Ergodicity matters, and is a major factor in your long term health, wealth and peace of mind.

What may seem to be a dry and boring exercise in semantics and mathematical fancy footwork very rapidly morphs into:

  1. A potent expose of how we have been misled and ripped off by the so called experts, and then offers
  2. An explanation of how to side step these lies and fallacies and position yourself for survival and success.

This is about:

  • Randomness
  • Probability
  • Time
  • Sequence
  • Outcomes

    The two conditions of ergodicity are:

    [1] Ergodic systems and processes  - where there is a consistency of outcome.

    [2] Non-ergodic systems and processes - where there is a certainty of extreme variation.

    We all want to be enjoying the certainty offered by the first condition, but in reality are flying blind on the roller coaster ghost train of the second.

The failure of the "experts" to understand the core characteristics of what is required to achieve a consistent outcome and to disregard the certainty of extreme variation means that your long term health, wealth and peace of mind are at risk.

You think I exaggerate? Reflect on these realities at time of writing in 2022:

  • Why do you think the peoples of Europe are facing catastrophic price rises in the costs of their energy?
  • When I say catastrophic price rises I am talking about increases of 20 to 50 times [yes twenty to fifty!] in the price of the Liquid Natural Gas [LNG] which at time of writing they are so desperately trying to import?
  • How the German government has found itself so desperately exposed after decades of single source reliance on Russia?
  • The arrogance  of the UK Government's energy policy which has only been superceded by its ignorance in the light of recent events: "The Government is relying on a policy of ‘gas by default’ which assumes there will always be a secure and affordable supply of natural gas to meet demand. This is guaranteed by sufficient physical infrastructure, diversity of supply and a reliance on market forces." [But then this shouldn't be a surprise as the Government minister heading this at the time was the now discredited Kwasi Karteng who recently tanked the UK public finances with his recent mini-budget of unfunded tax cuts.]
  • Why do you think that here in the UK, in the winter of 2020/21 we had no secure longterm contracts for the supply of LNG and that the Prime Minister of the day had to go cap in hand to the ruler of Qatar to secure 4 ships of LNG?
  • Consider the febrile and totally inadequate global response to the recent pandemic and the devastating second order consequences on employment and business failures as a direct result of the lock-downs that were imposed upon us.
  • Reflect on how the rapidly rising rates of inflation and the attendant interest rate rises are going to devastate the finances of countless millions of people in the first world and cause countless deaths in third world countries.
  • Consider the many financial scandals in recent decades that have destroyed wealth  - ordinary peoples' savings as well as the rich - exemplified in 2008 by the unfettered greed and unregulated stupidly of major US banks and financial institutions that came within days of wiping out the world's financial systems and that would have reduced us to the stone age in about 10 days.
  • Here in the UK at time of writing, and beyond the recognition or comprehension of most people, is the looming collapse of major pension funds as a result of their over-exposure to risky financial instruments aptly named Liability Driven Investments [that's an oxymoron if ever I heard one!]. The effect of this will be to wipe out the long term savings and retirement incomes of large numbers of the population.
  • And here's the big one - reflect on how it is that at time of writing the world is closer to a nuclear war than it has been since the Cuban missile crisis in 1962? Don't just default to the easy answer of blaming Vladimir Putin [and of course he is culpable for engaging in the Russian invasion of Ukraine] but consider the policies and actions of the US and NATO governments over the past 15 years, and the assumptions that were made, that have led to this situation.

    How can we achieve a consistency of outcomes against the certainty of extreme variations?

Explaining Ergodicity

At the end of this article I have included a bibliography of some of the sources I have used in research into ergodocity. As you will see most, if not all, of the material on this subject is written for the investment community and the terminology used and the illustrations given reflect that.

The result of this is that much of this material is impenetrable to the lay reader.

This is unfortunate because these concepts are - at root - fairly straight forward, and have universal application.

Having said all that,  I am reasonably bright and it took me about three working days of study and reflection to get to a position of being able to reframe these ideas in a way that makes them easy for the lay reader to understand and apply.

We are going to look at

  • Each condition of ergodicity in more detail and attempt to define clearly what it means and how to apply it.
  • The contraints on achieving a consistency of outcome and how best to work within those constraints to get as close as possible to the desired consistency.
  • How to protect ourselves against extreme downside risk.
  • How to position ourselves to identfy and exploit the extreme upside opportunities which always accompany downside risks and what are often referred to as Black Swan events.
  • How to leverage these protections and positionings to achieve a greater level of consistency in the outcomes we experience.

So here goes:

[1] Ergodic systems and processes - where there is a consistency of outcome

Consistency Is Key.Graphic.


    A system or process is ergodic if:

    1. The outcome for the individual is the same as for the group, AND IF
    2. The outcome for the individual and the group remains the same over time. i.e. the outcome is universally the same.

    An ergodic system or process always has these qualities, it:

    1. Is not path-dependent i.e. what has gone before has no bearing on what happens in future.
    2. Has no dependencies or variables i.e. there is nothing that can affect the outcome.
    3. Is independent of conditions i.e. the outcome will be the same regardless of the circumstances.

Unless a system or a process can demonstrably meet all of these criteria then there can be no certainty of a consistent outcome.

Every article I have read on ergodicity tries to illustrate the conditions with thought experiments based on russian roulette and games of chance, and they focus on the probability of different outcomes.

But, in common with many readers, I do not gamble so I find these illustrations hard to relate to.

The only area in life which does fully conform to these criteria is in the application of the laws of Newtonian Physics and Classical Mechanics namely: gravity, motion, space, time, mass, force, momentum, torque, and angular momentum.


    A simple and ridiculous example of an ergodic process involving the law of gravity

    Example of ergodic process with 100% consistency of outcome. Picture of a sky diver.

    If an individual jumps out of a plane without a parachute, he/she will not survive.

    Example of an ergodic process involving the law of gravity. Picture of group sky diving.

    If a group jumps out of a plane without parachutes, they will will not survive.

    If another individual and group are stupid enough to repeat this at multiple points in the future they too will will not survive.

    There are no dependencies, variables or conditions.

    There is a 100% consistency in the outcome, for the individual, for the group, and at all points in time.

    This is an ergodic process.


    Average rates of return - are wrongly presented as an ergodic process offering consistency of return to the individual investor

    Example of a non-ergodic process with zero consistency of outcome. Picture showing an average rate of return.

    Why is it that the world of investment and financial services invariably cites an average rate of return over a fixed period of time as a criteria and metric for making an investment decision?

    Suppose that the cited average rate of return is 8% per year over the past 20 years.

    Let's apply the tests.

    1. Does every individual achieve an 8% annnual rate of return the same as the whole group of investors does?
    2. Does the individual achieve this 8% return every year for 20 years?
    3. Does the group achieve this 8% return every year for 20 years?

    The answer in each case is "No!".

    Why? Because the stated annual rate of return is an average and thus includes an incredibly wide range of outcomes for all individuals [i.e. extreme variations of individual outcomes within the group]  and the sequence and timing of those individual outcomes is unknown.

    An average group rate of return is meaningless and irrelevant to the expectations and experience of any individual investor and therefore should not be offered or taken as basis for making an investment decision....and yet it is.... it is not only wrong but it is also misleading!

    There is zero consistency of outcome for the individual investor.

    This is not an ergodic process.


    The fallacy of averages

    The fallacy of averages. Graphic showing Median vs Average.

    The average of a range of numbers is the total of those numbers added together divided by the count of items in that range. In the example above the average is $498,000.

    The median of a set of numbers is that figure where half of the numbers are lower, and half of the numbers are higher. In the example above the median is $105,000.

    The wider the range of numbers the greater will be the disparity between the average and the median.

    For example, the average income in the US in 2019 was $69k the median income was $36k.

    The range of extreme variation was from below $15k [bottom 10%] to $600k+ [top 1%]

    The median is a better indicator of the likely outcome for the majority, BUT the outcome for the individual is subject to the probability of extreme variation.


    Normal Distribution vs Power-Law Distribution

    This describes how the certainty of extreme variations is ignored by those who rule us because their basic assumptions are wrong - they are using the wrong model!

    Normal Distribution vs Power-Law Distribution. Graphic of bell curve vs fat tail.

    In a normal distribution -  commonly known as a bell curve - the outcome for the vast majority of the group clusters at or around the mid-point or average.

    There will be outcomes experienced by small number of individuals at both ends of the outcome spectrum that will be much higher or lower than the average.

    This normal distribution/bell curve is the model most frequently [and wrongly] assumed in the modelling of governments, economists, businesses and investment advisors.

    They assume a consistency of outcome and traditionally regard the possibility of extreme outcomes - technically "tail risk" - as irrational i.e. it is ignored.

    A Power-Law - commonly known as the Fat Tail -  describes a relationship between two things in which a change in one thing can lead to a large change in the other, regardless of the initial quantities.

    Statistically it describes a range of variations from the mean that can be very large.

    It also describes a rate of growth that is exponential i.e. the speed of the change is as important as the growth - it gets bigger faster!

    This is a non-ergodic process where there is certainty of an extreme variation.

    The obvious question that arises is what causes or triggers these extreme events to occur and to take place so unexpectedly and so quickly?  

    Often we may never know what fully causes these things to happen but the process of what happens can be described as an inflection point.

    Inflection points occur when there is build up of forces, a critical mass, that lead to a spontaneous and often irreversible change of direction and an unstoppable effect or change takes place.

    Example of inflection points are:

    • In business the point at which an issue, an idea, a concept, a product, crosses a certain threshold and achieves significant momentum that is triggered by some small factor or change.
    • In medicine, and taking the covid-19 pandemic as a good example, the point at which a minor development precipitates a crisis, such as every infected person brings us closer to the tipping point, when the outbreak becomes an epidemic.
    • In physics, the point at which an object is no longer balanced, and the addition of a small amount of weight causes it to topple.
    • In relationships, the point at which the accumulation of a number of negative behaviours and factors reaches a point of no return and one party terminates the relationship.

    These tipping points can lead to a negative event that is rare, unpredictable and has devastating consequences that can destroy wealth, health and peace of mind... and lives.

    The pandemic, the Russian-Ukraine war, the 2008 banking crisis, the impending major financial correction/disaster and potential collapse of fiat currency, and the eventual and probable devastating war with China over natural resources that has yet to happen, could all fall into this category in so far that few foresaw these events.

    The reason why our leaders and rulers make this fundamental mistake and use the wrong model is because they only focus on what they can see and what they can measure - and ignore the rest.

    In the interconnected world we live in it is these hidden - and ignored - factors that will contribute to these extreme outcomes.

    They are hidden because they are intangible and not easily measurable.

    They are hidden because the time spans and sequencing of these outcomes are random.

    The risks they are carrying are dismissed as "irrational".

    This fundamental error by our rulers and leaders is what Nassim Taleb refers to as being:


[2] Non-ergodic systems and processes - where there is a certainty of extreme variations

Non-ergodic systems and processes  - where there is a certainty of extreme variations. Image of "The Deer Hunter" film russian roulette scene.


    A system or process is non-ergodic where:

    1. There is a possibility of extreme variation of outcome which can lead to a total wipe-out and ruin, or a massive gain, AND
    2. Over time this becomes a probability, AND
    3. Over the passage of more time it becomes an occurrence.

    A non-ergodic system or process always has these qualities:

    1. It is path-dependent i.e. history matters, the longer it continues the higher the probability of extreme variation.
    2. Past probabilities do not apply to future outcomes.
    3. At some unknown and indeterminate point in the future there is a stop in the system or process which results in ruin or massive gain.

    The ruin is inevitable but its mitigation or transmutation into massive gain is entirely dependent on preparation.

How can we achieve a consistency of outcomes against the certainty of extreme variations?

How can we achieve a consistency of outcomes against the certainty of extreme variations? Picture of a coffin.

As we have already established above, once we move away from newtonian physics and classical mechanics it is impossible to achieve a 100% consistency of outcome in any area of life.

So the blunt and scary reality is that we face extreme variation in most, if not all, areas of life together with the consequences.

The most obvious example of extreme variation is your mortality. You are going to die. The only unknowns are how and when.

Fortunately, there are a wide range of practical steps that you can take to mitigate the risk of these extreme variations and to position yourself to make massive gains - whenever possible - when they do occur.

In the example of your mortality, whilst you can't avoid it you can take steps to mitigate the effects of this extreme outcome and ensure that your loved ones and dependents are financially protected by having adequate life insurance in place.

Here are two guiding principles drawn from the work of Nassim Taleb [whose work is featured on this site and which I commend to you]:

[1] Learn to perceive the world as it really is - and not to delude yourself into seeing it in the manner that makes you feel most comfortable.

Black Swan events. Picture of a black swan.

  • We like to think of the world in simple and predictable models. While this works much of the time, there are rare and seemingly unexpected fat tail events, known as black swans.
  • Black Swans are events that are impossible to predict, rare and with devastating consequences.
  • Because our standard models don’t take black swans into account, hidden risk looms behind seemingly safe and predictable events.
  • It is extremely foolish to just ignore the potential for black swans to occur.
  • To take the view that because we cannot predict them we will pretend they don't occur is setting yourself up for trouble  - which of course is exactly how most individuals, companies and governments operate.

[2] Make decisions that focus on the consequences - which you can know - and not on the probability of an event - which you cannot know.

Antifragile. Graphic.

  • Your survival depends on the ability to weather black swans.
  • The best way to be prepared for black swans is to understand and develop the qualities of antifragility.
  • Antifragility is the quality of something that gets better, or thrives, in the presence of disorder.
  • It is more than resilience it is the ability to become stronger in the midst of chaos and unpredictability.
  • Learning how to live a life of antifragility allows you to deal with the unknown, to do things without understanding them - and do them well.
  • It enables you to "think round corners", think and live creatively and learn how to identify and exploit the unseen margins and position yourself for massive gains when these extreme events occur.


    How to mitigate the effects of extreme variation. Picture of nuclear explosion.

    [1] Insurance

    This is so obvious that it shouldn't need explaining.

    However, it does amaze me how many people I know who are not insured or under-insured for major life-changing extreme variations on the basis that "it won't happen to me" or "I can't afford it"....

    [2] Contra-Investment

    I know a man who has investments in the hospitality industry and he owns a number of bars and restaurants, and to mitigate his risks he has invested in self-catering accommodation and the take-away/take-out sector and he has also recently launched a consultancy service and has developed an online business for home-cooking.

    He is well positioned to succeed in one or more of those businesses regardless of economic circumstances.

    I call this contra-investment - rather than diversification - because you invest your time, energy and resources in activities that are the 180 degree opposite of your core activity, business or main job.

    [3] Balanced Diversification

    In this scenario you focus 70-80% of your time, energy and resources on your core activity, business or main job, but you invest 20-30% of your time, energy and resources into several quite different areas of activity or projects, that interest you.

    [4] Live A Life Of Antifragility

    This starts with an attitude to life that embraces uncertainty and understands Antifragile - How To Benefit From Disorder and practices living an antifragile life.

    This is all about creating options and slack in your life and having Plans B, C & D and being flexible. Please checkout the links above and the extensive resources on those pages.


    How to position yourself for major opportunity arising from extreme variation. Graphic.

    An example of an ergodic approach that failed and non-ergoic approach that brought massive opportunity and gain

    I run a company based in Singapore that specialises in commoditities, and I have a colleague who focused on the semi-refined gold [dore] market with producers in Africa and buyers in the Middle East. 

    His approach was 100% ergodic. It was all about the numbers and chasing the deals - the things that were visible and easily measurable, and where he [wrongly] assumed that with the right amount of effort he would get good results.

    Over a period of several years I suggested that he build up his knowledge of the sector and focused on a small number of high quality key relationships with producers.

    I tried, unsuccessfully, to persuade him to focus on the intangibles and thus build up a reputation as an expert and so attract business. But he wouldn't listen. He used to say to me:

    "It's all about the deal Stephen...the deal..."

    Fast forward a couple of years and post the pandemic and he now has no business and no money.

    In contrast, I have another colleague who works in the fuel sector and he took a totally different and non-ergodic approach.

    He focused on deep learning of the business, he sought hidden value in the intangibles of the business and treated every opportunity and countless failures all as learning experiences to build reputation and a knowledge base.

    He built deep and strong relationship with producers and narrowed his focus to crude oil and liquid natural gas [LNG] figuring that at some point in the business cycle there would be huge demand for these products.

    Of course with recent events in Ukraine and the embargo on Russian fuel this has proved to be a good move as the extreme variations that have hit the fuel market have created massive and extremely lucrative opportunities for him and he is making a lot of money.

    The way to position yourself for major opportunity arising from extreme variation is to identify and exploit the unseen margins

    How to exploit the unseen margins. Graphic.

    I recently wrote an article on this subject, which I commend to you. Here is an indexed key point summary:

    How To Benefit From The Unseen Margins - Defining Our Terms

    1. Margin - Types: Tangible & Intangible
    2. Metrics - Primary and Secondary Currency
    3. Visibility - Margin Type + Currency

    How To Benefit From The Unseen Margins In An Environment Of Complexity

    1. Gaps Between The Map And The Territory
    2. Top-Down Over-Simplification
    3. Cause And Effect in The Passage Of Time
    4. Human Laziness, Need and Greed

    5 Key Tips On How To Benefit From The Unseen Margins

    1. How Can I add Value To This Person Or This Situation?
    2. How Can I Leverage This Situation For Future Advantage?
    3. Who Is This Affecting And How Is It Affecting Them?
    4. What Are They Measuring, Where Are The Gaps And What Are They Missing?
    5. What Is The Bigger Picture Here - Who Stands To Gain/Lose And Why?

    Guiding Principles On How To Benefit From The Unseen Margins

    1. Understand Your Currencies And The Relationship Between Them
    2. Prepare For The Unexpected
    3. Work With Probability
    4. Play The Long Game [And Be prepared To Pay The Price]

    Life is non-linear, which makes the rewards of continued effort disproportionately big, but because progress on the extra mile isn’t clearly visible, most people give up too early.


Further Reading:

The Fat Tail Fractal Factor

How Positive Asymmetry Can Transform Your Life

How To Benefit From The Unseen Margins

Finding Signal In The Noise

Next Article: Dealing With Imposter Syndrome

Return from "Ergodicity" to: Walking The Talk

Or to: Mental Models

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