Power of Exponential

The power of exponential surrounds us and is within us. It is key to success in life, to the way we grow, and how we learn. It is key to the spread of anything be that a new idea, kindness, fire or an infectious disease. When it is understood we can use it to create leverage; the tiny change that changes the whole world. We can use it to improve our lives and connect with others. We can be successful and empowered. When we don’t understand it, we become insignificant victims and we pay the price.

# So, what is this thing called exponential?

Graph of Linear, Quadratic and Exponential growth. source

Exponential is a mathematical term for a form of compound non-linear growth or decline over time. In this chart, the horizontal X axis is time and the vertical Y axis is an accumulation. The graph illustrates how exponential growth (green) eventually surpasses both linear (red) and cubic (blue) growth. However, at first this is not apparent.

# Exponential means that the rate of change is itself changing

In the early stages, growth can masquerade as insignificant linear change or no change at all. Our minds extrapolate this and we believe the rate of change is so slow that nothing is really happening (or at least, very little). If the “accumulation” is the escalation of a problem, we are fooled into believing there is nothing to be concerned about. It takes us by surprise when, “suddenly”, huge changes manifest.

A lack of understanding of the underlying causes can lead us to some poor choices. Maybe we have been trying to develop an initiative, and because we don’t get the immediate returns we are hoping for (the red linear growth line above), we stop the initiative which was about to blossom.

# Example 1: Paper Folding

Imagine that I could fold a sheet of A4 paper in half 39 times.How tall would the paper tower be?

The surprising answer is that it would reach the moon!

Jule Verne made the calculations. source

How can that be? Well, the moon is 252,088 miles from Earth and a piece of paper of (0.1 cm) thick folded 39 times exponentially would be 54,975,581,389 cm thick, which equals to 341,602 miles, which would not only reach the moon but well beyond it!

But pause for a moment as the more amazing fact is that on the 38th fold it would only be 68% of the way there and on the 37th fold only 34%! Pretty incredible, isn't it? But that's the power of an exponential, that it lets you turn small things into huge things by simply compounding what you have, over and over, again.

And incredibly, it only takes 39 folds of a paper to get from the Earth to the Moon, and only about 94 folds of a paper to make something the size of the entire visible Universe! And how surprised are you that the answer is so small a number? This is exponential power!

# Example 2: Origin of Chess

People that understand exponential have an advantage over others that don’t.

Chess. source

There's a famous legend about the origin of chess that goes like this. When the inventor of the game showed it to the emperor of India, the emperor was so impressed by the new game, that he said to the man "Name your reward!" The man responded:

"Oh emperor, my wishes are simple. I only wish for this. Give me one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before."

The emperor agreed, amazed that the man had asked for such a small reward - or so he thought. After a week, his treasurer came back and informed him that the reward would add up to an astronomical sum, far greater than all the rice that could conceivably be produced in many, many, centuries! The moral of the story? Chess players understand exponential! (At least, entrepreneurial inventors often do!)

In both these examples, if we want to influence results we need to understand parts and relationships. Fortunately, there is a analytical approach called Systems Thinking which gives us the tools and techniques to do this.

# Systems Thinking

A system is a set of parts which inter-relate to function as a whole.

So, you are a system, and so am I. We form more systems through our inter-relationships with others and the world. Ultimately, the biggest system of all is the Universe. Technically, this is THE SYSTEM. All other systems are sub-systems of this one Whole.

We all want the systems we are a part of to be strong systems: We want ourselves, our families, our friends, our businesses, our communities, to be strong and resilient. To achieve this, we tend to focus on improving the parts of the system, but what makes a system strong is the connections.

Optimising the parts will not necessarily optimise the whole. Imagine an aircraft, built of optimal parts but held together with string: Would you want to fly in it?

Systems Thinking is the study of feedback in systems.Feedback is a circle of cause and effect relationships where a change in an element causes a further change to that element in future. There are only two kinds of feedback: Reinforcing feedback which we know in life as virtuous or vicious cycles, and balancing feedback, which limit growth or decline and tend to goal seek. Exponential behavior patterns emerge from reinforcing feedback.

Chicken and egg problem. source

The answer is that the two are a system. They are mutually interdependent. Inseparable.

Let’s explore the language of systems thinking using this example. The language is a very simple shorthand language using arrows and symbols.

# CHICKEN OR THE EGG? So, how do chickens and eggs inter-relate? Well I believe that if there are more chickens there will be more eggs. In the language of systems thinking we would capture this as follows:

A Supporting Relationship. source

This is shorthand for “the number of chickens affects (arrow) the number of eggs in the same (S) direction all other things being held equal”.

Similarly, if there are more eggs, there will be more chickens.

A Supporting Relationship with a Delay. source

These are both “S”, for “Supporting” or “Same” direction, relationships. Note that this will involve a time delay (which is the time for the chick to become an adult chicken). This is represented by the “II” sign on the arrow.

And, again, if there are more chickens there will be more eggs. Note also that if there are less chickens, there will be less eggs, and therefore, in future, less chickens than there would otherwise have been. And so less eggs, and so on. The two are connected in an endless cycle, a feedback loop driving growth or decline. This is depicted as follows:

A Reinforcing Loop. source

Reinforcing (R) loops like these cause vicious and virtuous cycles, that is exponential growth and decline, from the same underlying structure.

This basic “chicken and egg” structure underpins a variety of seemingly disconnected things.

So, the growth of human population; the spread of an infection (like a cold virus); the spread of a rumour or a new fashion; the spread of lilies on a pond; the spread of kind deeds or smiles, are all outcomes of reinforcing feedback.

This means that if we want something to “go viral”, we need only stimulate the right reinforcing loop and the system will do the rest of the work for us! For example, at school, more effort yields better results, which improves motivation, and stimulates more effort.

The feedback we have considered here is simple feedback between a small number of variables over a relatively short time period. Feedback in real systems can be much more complex, involving much longer chains of interactions with a multitude of variables over years, decades or much longer time frames.

# Example 3: Our body temperature

Reinforcing exponential feedback is rarely seen alone. This is because the system would not be viable. It couldn’t survive; it would either explode or disappear! For this reason, viable systems also incorporate another form of feedback called balancing loops. Balancing loops control reinforcing loops. They limit their growth or decline. They generate goal seeking behavior. Let’s consider an example.

Your body temperature needs to be close to 37 degrees C. If you get too hot your body will start to sweat. This is a balancing loop to correct (reduce) temperature. The relationship is an “O” for “Opposite”, relationship. So, if sweating goes up, then temperature will go down. If, on the other hand, you get too cold, your body will start to shiver. So, if shivering goes up, then temperature will go up. This is a balancing loop to increase temperature. Note that these responses are not within our control. Our body is designed like this. There are things we can do voluntarily to help including putting on, or taking off, layers of clothing or increasing/ reducing movement.

Multiple Balancing Loops driving Body Temperature. source

If we are in a building, we could also regulate the room temperature through heating/cooling. And, in turn, room temperature is affected by the temperature outside. Which brings us nicely to the big systems driving global warming and the part we play.

# Example 4: Climate Change

Temperature has been increasing since the start of the 20th century, as has the carbon dioxide (CO2) parts per million (ppm) in the atmosphere. The problem is that we have some pretty, powerful feedback happening with significant delays. Our problem is our inability to understand exponential accumulation.

It is the accumulation of CO2 in the atmosphere which affects temperature, NOT the flow of emissions. Reducing emissions can be one important factor. But, even if we reduced emissions to zero today, the accumulation in the atmosphere would persist unless there was a flow out! Then there is the question of the optimal ppm; like our body temperature of 37 degrees, what is the ideal level of CO2? Some scientists have postulated that it is the blanket of CO2 wrapped around the Earth that is protecting us from an ice age! These differing perspectives on the same system can be exposed and explored using systems thinking to build the commitment to action we need.

So, how do we control the flow out (drawdown) of carbon from the atmosphere safely? Well, nature’s key to this is plants and photosynthesis. Plants are brilliant. They take in CO2, give us oxygen to breathe, and store the carbon in their body.

As parts break away (eg leaves in autumn), they decompose and create stable soil carbon. Over time, layers build up pressure, compressing carbon and creating fossil fuels: Nature’s safe storage for carbon…and note, renewable, over long time-frames. The issue is that we have been digging them up, and burning them, and releasing the carbon into the atmosphere.

Another pre-requisite for photosynthesis is water. Plants can’t grow without it. If the soil isn’t absorbent, the rain runs off, and raises water levels in rivers and oceans. Our modern industrial farming methods compound this problem by cultivating the soil, burning stubble and clearing and leaving fallow: All practices which lead to deterioration of the soil’s ability to absorb water and so less photosynthesis.

Run off is only one aspect of rising sea levels. As temperatures rise, ice melts and increases water surfaces. This means less reflection of heat (albedo) and increased temperatures.

Greta Thunberg. source

The big question is why do we not change?

If we do not understand the systems around us, we only have one option and that is to react. Sometimes our reactions only serve to compound the problem we’re already reacting to: We see ourselves as victims of something or someone we cannot influence.

If the same problem persists or repeats we may start to notice a pattern and we adapt our behavior to protect ourselves from the phenomenon. We still see the problem as outside ourselves and outside our influence.

If instead, we start to think about the system of cause and effect relationships and the feedback creating the problem, we start to understand our relationship to the problem and our power to fix it. This can be a profound and truly life changing experience.

Why does this not happen? Well, at least not very often. Several reasons I think. Maybe because we see ourselves as separate from the world outside, rather than a part of it. Maybe because we’ve been taught to see the world in this way, as lots of random separate objects: Language creates this separation and school reinforces this by emphasizing separate subjects and examining us individually. We are not routinely taught how to “see” systems as children. We are rewarded for remembering and not sharing. For believing that someone else knows what is best for me, usually someone called “an expert” (be it a teacher, a doctor or a fireman).

If I follow the experts I don’t have to think, my choices are all made for me. But where do they lead?

# Grenfell Tower

Let me tell you a salutary tale about this. In June 2017 a fire in Grenfell Tower in London killed 72 people and injured many more. The fire broke out on the 4th floor caused by a faulty fridge-freezer. The policy in tower block fires is to compartmentalize the fire: That is to say, confine it to one apartment. A “stay put” policy ensures that residents are not blocking the stairs and other access routes, so ensuring the fire brigade can control the fire. This didn’t work, and an ongoing inquiry is seeking to identify what caused the fire to spread and who is culpable for the losses.

Grenfell Tower Fire 14 June 2017. source

For me there is a more profound question. Why did some people die and others survive? Data shows that the majority of the deaths occurred higher up the building. Only two people died on floors one to thirteen. Data also shows that the majority who escaped did so whilst the stay put moratorium was still in force.

A systems analysis revealed one key variable driving human behavior: the expected time for the danger to reach me. Those higher up the tower believed the experts and waited to be saved. They paid the ultimate price.

One resident, a woman on floor 11, decided to take a look for herself. She saw the rate of advance of the fire and knew she had to get out. She put the plugs in her sinks and bath and turned on all the taps. She shut up her flat and encouraged others on her floor to do the same. She saved her own and many other lives. She is a systems thinker. We need more of them. A lot more.

I think we are all sitting on the top floor of Grenfell Tower, staying put, when we could be making life saving choices. The only difference between Grenfell Tower and Earth is scale and time-frame. See Grenfell tower.

# The way forward

It’s incredible that only two types of relationships and feedback, combined in different ways, create every behavior pattern we see on Earth! This means that understanding systems is the key to making better choices in life. And systems thinking is the way to understand systems.

Systems Thinking enables us to harness the power of exponential, not become a victim of it. I hope this has convinced you to find out more!