Here is a Master Strategy to Create or expand a Successful Business - Ergodic theory

Build your business through the use of Ergodic theory. Ergodic theory relates to the experience where there is a variation in one dimension (such as one pound of yeasted flour dough) to variation in another dimension (such as another one pound batch of yeasted flour dough made from the same batch).

More simply stated Ergodic theory relates to a process in which every sequence or sizable sample is equally representative of the whole. It is important because it involves or relates to the probability that any state will recur given certain factors.

Ergodic theory is fundamental to pattern language and statistical mechanics in business and problem-solving, and offers a mathematical means to study and even predict the long-term average behavior of complex systems; such as the behavior of molecules in a gas, the interactions of vibrating atoms in a crystal, the proper mixing of dough by a baker, or the behavior of water coming into a beach.

Let’s approach this with a classic example of a basic ergodic theoretic problem the mixing of bread dough.  

Let’s begin…

Suppose you have a baker kneading dough. You look at it from a certain angle and make a mental note about its size and shape.

First, the baker stretches out the dough; then, he folds it and cuts it equally; finally, he stacks the two pieces on top of each other. Ostensibly, the baker does this is to make sure that the dough is properly mixed.

How might one prove that this process does in fact mix? For that matter, what does 'mixing' even mean, in a rigorous sense? That is the essence of ergodic theory: you are given a space with some change or transformation on it, and the question is whether, as you apply this transformation again and again and again, will the space will begin to 'homogenize' in some precisely defined sense.

Another way to explain ergodic theory is how we estimate what we see when we stand on a beach and look back and forth and the water. If you look up and down the beach at a point in time, you will see the water reaches higher in some places than others. If you sit at one point on the beach you will see the water come up and down over time—from individual waves, tides, and other flows.

If water height were ergodic, you could look up and down the beach at one point in time, place your beach towel above the farthest point the water reaches at any location, and go to sleep secure that you would not get wet. When the incoming tide rudely wakes you, you’ll realize that the ocean is not ergodic, at least in this one respect.

On the other hand, suppose your dog comes out of the ocean soaking wet and shakes to dry herself off. If you stand beyond the furthest water droplets at a point in time, you will probably remain dry over time—as long as your dog doesn’t move or start shaking harder. Your dog is ergodic in this respect.

So a practical application to ergodic theory concerns how a person can keep their feet dry when walking along a shoreline without having to constantly turn one's head to anticipate incoming waves.

In any systematically designed environment, knowing that the likelihood of change is small or nonexistent (Ergodic) enables a strategist to make accurate predictions for the future.

Here is another example. Suppose you want to buy a pair of shoes. Imagine that a shoe shop exists inside your house. Now you can follow two strategies. One you can visit the shop inside your house everyday and eventually you find the best pair of shoes. Another possibility is you take your car and spend a whole day searching every possible shop in your city and immediately buy the best pair. If the result is the same for the two processes then you can say that this system is ergodic.

This is because ergodicity involves taking into account the past and future, to get an appreciation of the distributive functions of a system. Here is another example.

Let's say a Japanese man by the name Masa Yakamoto is a grandmaster practitioner of the art of making udon noodles. His ancestors who go 10 generations back, started the practice and made udon for the Emperor. This skill has been passed successively down the generations. Masa san, the Udon Master has been making udon since he was 3 years.

Now, every single time Masa-san makes udon, will the udon exactly similar? No, not necessarily. If you were to put every strand of udon noodle made by Masa-san in his entire life (let’s say he’s made udon 1, 777,777times) they will differ.

Ergodicity treats Masa-san as a system and the theory attempts to shed light on the system’s specific properties. Let’s say early in his career when he was 17, Abe-san (who’s 97 years now) received a visit from a food critic. He vowed to make the greatest bowl of udon the critic had ever tasted. Whilst in midway making the perfect udon and overwhelming the critic wit the quality of his udon, Masa-san receives news that his favorite Goldfish had died. Emotionally distraught by this news, Masa-san is suddenly unable to make udon to his usual standards. They are certainly good, actually mediocre but not that great.

But would this batch of mediocre udon noodles be an accurate and robust description of Masa-san’s udon making ability? No.

That’s a good (though not great) example of ergodicity.

Not clear yet? Here is a better example!

Suppose you are concerned with determining what the most visited parks in a city are. One idea is to take a momentary snapshot: to see how many people are at this moment in park A, how many are in park B, and so on. Another idea is to look at one individual (or few of them) and to follow him for a certain period of time, e.g. a year. Then, you observe how often the individual is going to park A, how often he is going to park B, and so on.

Thus, you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people.

Ergodicity is usually described in terms of the objective properties of an ensemble of objects (or factors in a business).

The importance of ergodicity becomes manifest when you think about how we all infer and induce various things, how we draw some conclusion about something while having information about something else.

For example, one goes once to a restaurant and likes the fish, and next time he goes to the same restaurant and orders chicken, confident that the chicken will be good because the fish was good. Why is he confident? Or one observes that a newspaper has printed some inaccurate information at one point in time and infers that the newspaper is going to publish inaccurate information in the future. Why are these inferences ok, while others such as those based on cognitive bias-based profiling are not OK? Because cognitive bias-based profiling is sloppy uncritical thinking and is not a reflection of Ergodicity! 

Articles in a newspaper that reflect some assumptions about people of a certain race, religion, or nationality are not at all ergodic while an ensemble of articles published in a newspaper is more or less ergodic.

Here is an even clearer example: In an election, each party gets some percentage of votes, party A gets a%, party B gets b%, and so on. However, this does not mean that over the course of their lives each individual votes with party A in a% of elections, with B in b% of elections,and so on.

A similar problem is faced by scientists in general when they are trying to infer some general statement from various specific experiments. When is a generalization correct and when it isn't? The answer concerns ergodicity. If the generalization is done towards an ergodic ensemble then it has a good chance of being correct.

Now, let’s say, after reading all of these examples you still can’t make sense of this concept of Ergodic theory and how Ergodic systems work? Be patient, you'll eventually get it.

Here is an approach I once tried with a five-year-old concerning how Ergodic systems work and they understood it. Maybe you’ll understand it too.

1. I asked a child to play a little game with me. This can be done with a coin/dice/ pack of cards.

2. Using a coin I then asked them to toss the coin and asked them to write down the state of the coin after it was tossed (heads or tails).

• With dice it would be the number, when rolled, of the two dice combined,
• With a pack of cards it would be the specific card randomly chosen from the deck.

3. I then asked the child to continue doing this 50–100 times and write down the tabulation.

4. Now, asked the child to repeat this but with two coins, (or two dice, or two cards at a time) and stop at half the amount. I would have them continue this until they got bored or 100 coins/dice one time.

Now you would notice that when repeated many times the heads or tales, the # on the dice, and the type of card (let's say a King) is almost the same in all cases. This is the ergodic hypothesis.

This ergodic rule is important for scientists who want to know how many times 2 does come up when tossing dice 10,000 times and are very busy. This is easier than having 10,000 grad students throw dice a single time (which would work as well). This is how you solve problems in physics using the ergodic hypothesis.

Of course just as there are Ergodic systems there are also Non-ergodic systems. When does this happen?

Suppose you have an old somewhat fragile coin, then by the time you toss it 100 times, it gets extremely chipped and then on only a seemingly random number of times comes up however many times you repeat it then on. Here one person tossing it 10,000 times and 10,000 people tossing it one time would give different answers; these are examples of non-ergodic systems. So, in a non-ergodic system, the individual, over time, does not get the average outcome of the group.

The Takeaway

To review, ergodicity is a statement about how averages in one domain relates to another domain. This is an essential concept for creating a successful business. Consider a simple case of one thousand dice (i.e., 2 dice). If we roll one thousand dice once time do we get the same answer as rolling a single dice one thousand times? The answer is that the statistics are the same if the dice are all fair and independent. True but quite worthless, right? Ergodic theory gets interesting in more complicated scenarios: Suppose the dice rolls are correlated in time for each dice but the thousand dice are independent. Then what can we say? And what is the rate that the individual dice statistics converge to that of the ensemble of 1000 dice. This is a big deal in engineering biology, physics, and in solving business problems.

The Author: Hello, My name is Lewis Harrison and I created a game theory based Business Strategies Playbook and Mentoring Method. I use this system to move individuals and organizations to the next level. Applied game theory (which has won numerous Nobel Prizes) has been the basis of all my great successes in life (best-selling author, NPR Host, a great marriage, financial success, great friendships, etc.).

Please reach out to me. I want to help you transcend your challenges by helping you to get clear on your intention, and your desired outcome by increasing effectiveness, efficiency, precision, productivity, accuracy, and self-awareness. Check out my Linkedin profile, contact me and let’s start a conversation…