## Blog entry by Alan Chapman

Anyone in the world

The word 'exponential' is one of the most meaningful in the modern age. This article briefly explains why.

The main point is: exponential means 'more and more rapid'.

Exponential has several deeper complex mathematical meanings, but basically in modern usage, exponential means 'more and more rapid'.

When we understand this in our world now - especially climate, economics, technology, and human development - we begin to appreciate the true nature of:

• change (happening in our world more and more rapidly and >
• the implications >of this increasingly rapid change. for humanity and other life on earth.

In more detail...

First, the origins of the word, because this offers insights for meanings and implications: origins are from history, and history gives lessons for the present and future.

Origins of the word 'exponential'
In mathematics, the root word is exponent, and the root definition is 'symbol indicating what power of a factor is taken'. This is already unnecessarily and too complicated to be very helpful in understanding exponential in its modern wider usage,
but I offer it for those who'll value it.

Incidentally, this somewhat challenging technical mathematical definition separately offers an example of how language and accessibility are major obstacles to conveying the biggest things we might learn personally and societally, and how
teachers might convey and cascade the most important teachings for everyone interested to learn, which is basically everyone really, (e.g., subjects such as  philosophy/meaning of life; systemic bias; economics; personality theory; religion;
ethnicity; human evolution; maths; physics; and specific genius concepts such as Einstein's Theory of Relativity; etc.) I plan to cover language and accessibility in other articles.

Anyway, on with 'exponential'...

Interestingly 'exponent' also refers to a person or thing that 'sets forth or interprets', which equates to someone or something - a modifying factor - that advocates/determines the use or behaviour of something else.

Returning to mathematics, the exponent is a determining factor, the implication of which is that unless there is an intervention, change will continue at the rate determined, until a collapse of some sort, because nothing lasts forever, except numbers,
in theory (such as an infinite series).

Meaning of the word exponential, in common usage, referring to change or projections
The interesting aspect of exponential change when applied to practical real-world issues, is that resources and capacity are very definitely limited to much more confined and absolute limitations than a theoretical series of numbers (as in maths).

In other words, theoretical mathematical exponential trends can go on infinitely, but life on earth, and how it is maintained (e.g., economics and climate and ecosystem) definitely cannot.

Commonly exponential change is represented by a graph showing a long gradual trend that becomes increasing steep (up or down) and suddenly almost vertical (continuing up or down), which is typically a point of collapse or disintegration or disaster, ending
whatever is being graphed.

Look at some of the graphs for global warming, for example: https://en.wikipedia.org/wiki/Global_warming
Exponential change is particularly meaningful to us all in the context of:

• Climate
• Ecosystem
• Environment
• Economics and technology
• Society
Exponential is often used to describe situations that have a 'tipping point' at which a slow trend turns into an increasingly rapid acceleration that is difficult or impossible to stop.

This can be for:

• a growth (for example global warming temperature increase of Earth, or the adoption of a new technology) or
• a reduction (for example melting of Polar/sea ice, or the collapse of a species)
Exponential also relates to 'the law of diminishing returns', where for example we try to keep optimising something indefinitely, so that the effort to achieve a constant or improving efficiency will eventually be defeated by reducing returns and necessarily increasing inputs. We can apply this to economics, or technology, or feeding and meeting the lifestyle/health demands of an ever-growing global population with ever-increasing demands of quality, wastefulness, consumption, and life expectancy. In the end, diminishing returns and exponential factors guarantee that there is a collapse, because infinite growth is impossible, and so systemic belief and action based in this is fundamentally unsustainable.

We cannot continue to optimise anything forever.

Implications of exponential change in our world
Growth, especially exponential growth, is self-definingly - obviously - fundamentally unsustainable.

Trying to make it so, has created the exponential collapse of climate change and environmental effects combined with unsustainable economics, now underway.

When we consider the nature of 'more and more rapid' obviously the size of the intervention required increases exponentially too.

We see this in all types of life and decay; i.e., early interventions can successfully stop a trend before the trend (of growth or decline) reaches a tipping point and the end-stages of the exponential 'graph'; whereas after a tipping point, even huge
interventions might fail, and if left too late are simply impossible.

A metaphor would be a plant that's not been watered. In the final stages of what becomes an existential collapse (i.e., how it dies and its eventual death), no amount of water will save it.

This is rather like planet Earth now or very very soon, in terms of its ability to sustain human life.

For many millions, it's too late to water the plant.

Exponential collapse began decades ago, actually with the industrial revolution, but most seriously since globalisation and the computer age (from the mid-1900s), when authenticity and ancient wisdom were mostly forgotten and forsaken in pursuit of the free
market 'wealth creation' infinite growth economy that is still sold to us all by deluded self-serving corporate leaders and investors and their political allies.

Consider 'exponential' - more and more rapid.

Many millions of people, for whom its too late to water the plant, will become all life on earth, unless we intervene very radically now.
This is 'exponential' when we consider it properly in our world today.

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[ Modified: Wednesday, 11 September 2019, 5:42 PM ]