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About Growth

About Growth

Most economists love growth: economic growth. Wealth must increase so that there is more to distribute, because people's desires are insatiable. Because this whole connection is, so to speak, the core belief of the branch.

There aren't that many critics - but they do exist. They have well-founded criticism of the central importance given to growth. In contrast to the growth fans, they usually see growth as such and fundamentally as the decisive reason why there are 'more and more problems'.

Here I will present a few points of view that point to a concrete solution to this dilemma. A solution that can be developed and implemented as a transformation in continuation of a process that is already underway. The analysis has several parts:

(1) The historical analysis: Even past growth has not been exponential at all over extended periods.
(2) The role of efficiency factors (such as product lifespans)
(3) Some elementary mathematics: The sum of the infinite geometric series converges - but what does that have to do with growth?
(4) Is it all just theory? A few concrete implementation approaches; Viewed in light: There's actually quite a lot going on!

(1) The historical analysis: Even in the past growth has not been exponential over extended periods

Growth in the past has not been exponential at all; it was pretty much linear. That takes the edge off quite a bit!

Percentages are usually communicated regarding economic growth. That's easy to understand - and there's nothing wrong with it. However, the fact that the percentage once measured must then be continued year after year at the same level - that of course does not follow from this type of information. This is at the end a question of empirical research: its results exist and are even easily accessible to the general public (given by the statistical offices). An important point must of course be taken into account: for reality, both in terms of prosperity and the required material resources, it is not the nominal gross domestic product (GDP), but rather the inflation-adjusted one that is decisive. The statistical offices are aware of this, which is why the data is available as GDP number series in real values [Statista 2023]. The graphic shows this using Germany as an example for the period after World War II. And there are already two surprises:

Yes, there has been steady and sustained growth - except for a few (well-known) short-term dips.
But that was by no means exponential, but, with a surprisingly convincing correlation, linear!

This could not be transformed into exponential growth so quickly, even with enormous efforts. Even if some politicians like to promise that every now and then. Short-term „fires in the straw“ are certainly possible - but this is usually at the expense of the subsequent time after the fire has flared up excessively. This may disappoint some - and perhaps some 'growth critics' too, because under these circumstances there is ultimately no danger of a huge overshoot⁵⁾. And above all: Under such conditions, the time span for action of the society remains manageable ⁶⁾.

Conclusion: Excessive growth expectations are an illusion. But also: There is no acute danger that 'growth as such' will become a fatal problem for society in the foreseeable future. The entire problem deserves to be approached a bit more calmly. In other words: let's leave the hyper-hype with unlimited exponential growth or a demand for it⁷⁾; and let's also stop staring paralyzed at the „snake of exponential growth“ ⁸⁾.

If the whole thing continues to take place in an orderly (linear) manner, then there is time left to solve the problems⁹⁾. Time for a sensible transformation towards sustainable business. And whether and how much it will grow - that becomes secondary given this background. This becomes clear if we also add (2) and (3).

(2) The role of efficiency factors

Here I am only talking about material and energy efficiency, which is important in this context. The topic of energy efficiency is dealt with in detail on the Passipedia pages, e.g. here. I will therefore take up the topic of material efficiency here. It is often argued that there is “not much to be had” because a certain minimum amount of material for a given task is obvious. Even that is by no means as clear as it seems at first glance. But there is another consideration: namely the length of time that a material once obtained remains in use for this task. It can be very different in length. 'Any' different length? That would be a pretty philosophical discussion: the Voyager space probes, for example, have been on the move since September 1977; and they're still running! I dare to make the bold thesis here: For the practical questions of today, the useful life can be extended 'virtually' arbitrarily, as long as it is not a consumable material. This requires careful consideration - and as a rule the avoidance of any form of „consumption“ that does not rely solely on renewable raw materials. As has been shown again and again using the example of energy: Improve efficiency at least to the point that the rate of renewable raw materials is sufficient to cover the consumptive part of sales ¹⁰⁾.

How good is “good enough”?

Here we are in for the next surprise: This is a purely mathematical question. If a task is currently completed with a system of useful life $t_N$ and the growth is $p$¹¹⁾, then the new lifespan of new systems of this type only now needs to last more than $(1+p)\cdot t_N - t_N = p \cdot t_N$ longer; let's say the new lifetime is $(1+\epsilon)$ times $t_N$, then $(1+\epsilon)$ is a typical efficiency factor. The fact that it can be „multiplied“ every year is undeniable at the beginning - in the long run, of course, worth discussing ¹²⁾¹³⁾. The amount of material required to be eyploited each year then develops according to

$\;\displaystyle q=\frac {1+p}{1+\epsilon} < 1 \;$

with an annual factor $q$ less than 1, i.e. decaying exponentially. This is the crucial point, as is clear from paragraph (3).

(3) Some math: The sum of the infinite geometric series converges!

This is not new, almost everyone has had it at some point in school - of course not discussed with the practical implications that it has; As is often the case with mathematical findings: Many of them are much more relevant than the mostly dry mathematics lessons make it seem; This can be really exciting in many places!

First the facts: Let $q$ be a factor with an absolute value smaller than 1. Then the 'infinite sum' (called: geometric series) is

$1+q+q^2+q^3+...$

a finite value. If you find the following box with the formulas too challenging, you can skip the box for now and find a more elementary illustration in the page linked here.

For this the notation with the sum sign $\sum$ has become common in mathematics:

$\;\displaystyle { \sum_{n=0}^\infty {q^n} = \frac{1}{1-q} } \;$

We have already given the solution for this sum, namely the reciprocal of $1-q$. For example, if $q$ is 90%, then $1-q=$0.1 and the infinite sum becomes 10 times the current production of the material in question; That's enough for „supply“ in „eternity“. The graphic illustrates this sum for the case $q=$0.9 for up to N=73; That's already very close to „10“, but there is still room for an infinite number of constantly decreasing $q^n$ (we'll put the proof in a footnote¹⁴⁾ ).

Here, of course, „eternity“ is just as practically irrelevant as it is in the debate about never-ending material exponential growth: once times have reached a few centuries, solutions can always be found, as long as the need-values are not gigantomanically high - what they cannot be, according to the $q^n$ expansion with a $q<1$. On the contrary: $q^n$ always becomes completely insignificantly small for some $n$, just like the following summands. So small that it is simply insignificant in practice because there are then renewable resources that can easily cover it. It will no longer be valid if we really talk about 'infinite times'¹⁵⁾¹⁶⁾.

In short: $q<1$ or increase in efficiency greater than increase in demand actually solves the growth problem.

To put it another way, provocatively: An increase in prosperity is still permitted: As long as it occurs with a „sense of proportion“, that is „better efficiency and renewable resources have to'finance' that growth“¹⁷⁾.

Of course it is clear to me that this does not suit any of the two „camps“: not the growth apologists, because they see everything below eternal exponential unlimited growth as unsexy; and not the growth critics, because suddenly a moderate further increase in 'prosperity' seems at least conceivable¹⁸⁾.

Let’s approach these questions with an open mind. It would not be the first time that a simple mathematical analysis actually solves a question that has long been considered 'unsolvable' ¹⁹⁾. Yes, technical progress does exist; However, it cannot be forced and we have to use it responsibly. I could always put efficiency gains right back into excessive waste - that's what some people seem to want; It must be clear that this only goes as far as $q<1$ remains valid. But that doesn't mean a „standstill“ ²⁰⁾. We can grow as much as we honestly and sustainably deserve - and then no non-renewable resources have to be exploited beyound limists. This is sensible economics in the generalized sense; and that is honest prosperity that is sustainably earned. But let's not kid ourselves: we are currently still a long way from such an equilibrium economy - the excessive increase in consumption based on substance has been driven forward for too many decades; We are only gradually becoming aware of this. The change will be strenuous, but it can be done - and we use relevant examples to show how.

(4) Is it all just theory?

No! This is already in many applications common practice today²¹⁾. There is already a lot available on Passipedia: namely, concrete descriptions of the measures that go down to the „construction instructions“ that prove to be implementable in practice, at least in the area of the energy system: efficiency measures. The fact that the goals are actually achieved is shown in detail there²²⁾.

Furthermore, there is already empirical experience that we have already highlighted here for two application sectors, namely traffic (German) and Heating (German).

The specific energy requirement of passenger vehicles in Germany from 1990 to 2019 is the measure of the technical in-efficiency of the cars. Until around 2008, efficiency was actually improved by around 1 tenth of a liter per 100 km annually. Since then, practically nothing has happened. This would be a relatively convenient way to solve many problems at the same time. $q=$0.99 < 1 in this case. This is technically possible - a battery-electric car only 'needs' around a quarter of the final energy; If the inefficiency of the still existing share of fossil electricity generation is taken into account, consumption is still reduced by more than 50%; The more renewable energy is expanded, the more this approaches less than 30%. And in the end, this 30% can easily be generated completely renewable.

Before 2010, the thermal protection measures introduced in the German building stock were quite successful, as the green dashed trend line 2000-2010 shows. During this period, we averaged around 5 kWh/(m²a) in reduction each year, which was more than 2.7% (annually!); $q=$0.973 < 1 in this case. This is technically and economically possible in any case: A properly carried out EnerPHit renovation reduces the heating requirement in each individual case to less than 33 kWh/(m²a), which is on average a reduction to one quarter. Even if we spread these improvements over around 30 years, that's enough to achieve the stated quota - and we obviously did it successfully at exactly this pace between 2000 and 2010.

In fact, we have successfully realized $q<1$ in each of these two sectors for over a decade. That would then take around 30 (building) or 100 (car) years „alone“ - but because sustainable energy production is also being ramped up at the same time, the improved curves for „renewable generation“ and „consumption reduced through efficiency“ will meet each other in the meantime; This can be achieved within 25 to 35 years - if we make a concerted effort to achieve it. It worked until the lobbyists successfully persuaded us that none of this was necessary²³⁾. .

So we have already proven that this can be done successfully, even for an entire economy. However, it is also clear that this does not happen completely automatically and by itself, we have to actively initiate it and then actually carry it out. It's possible - we've already done it successfully once.

The rapid expansion of renewable energy is of course part of this: so that the falling demand curve and increasing renewable generation can meet, and not just in 2100²⁴⁾ but around 2050²⁵⁾.

To offer a little more positive perspective: From around 2050 onwards, 'renewable overproduction' of energy will be possible in this way (beyond the need for services). We could then, for example, put them back into „even faster cars“, but I don't think that's the best idea. It is better that we then use this energy surplus to actively remove more CO₂ from the atmosphere; It has long been demonstrated that this is also possible (so-called “direct air capture”, DAC). This will be necessary in order to correct the sins of the past that have already been committed: Today we have already emitted more CO₂ than is good for sustainable development on the planet. If we then make a little more effort, we can still achieve the 1.5°C target by 2100: It would be irresponsible to rely onnly on decisions that won't be made for another 25 years ²⁶⁾. However, this consideration shows one thing: solutions that enable a transition to sustainable development do exist. It's not 'all lost' yet.

To come back to the introductory analysis of the gross domestic product, which in reality only grows linearly (the diagram under (1)): Anyone who has followed and recalculated (2) and (3) will find that both will still hold without the assumption that there is no such thing as long-term exponential growth; Even in (2) a constant percentage growth $p$ was still used. For (2) and (3) it only matters that the percentage efficiency gain $\epsilon$ is greater than this percentage growth $p$. However, the empirical finding that real GDP growth is not exponential but linear is practically relevant: Since the improvement in efficiency (at least for the next 1000 years or so) can correspond to the descending geometric sequence, it always catches up with any linear increase at some point. Real growth in GDP in Germany e.g. is currently on average around 1.25% per year. This is already intercepted with an $\epsilon$ of the same height (1.25%/a); We've already done better than that - and we can/ always do it again: It's just a question of will.

What is important: All efforts to improve energy and material efficiency! This includes, among other things, thermal protection, heat recovery, heat pumps, low-flow shower heads, efficient electronics, electric traction, countercurrent ovens, longer service lives, ability to repair, prevention instead of accepting damage and much more. This means that within just a few decades we will be diving below the limit that must be reached for sustainable economic activity. From then on, further growth in prosperity, if we want it, can follow the increase in renewable generation; Maybe we'll have found so much fun with the efficiency approaches that we'll continue with them and then create even more room for further growth ²⁷⁾. For the next 30 to 50 years, the time that matters, the efficiency potential for around 3% efficiency gain every year has already been proven and demonstrated in practice: We have already built houses whose heating energy consumption is negligibly low - and vehicles that can reach 100 km/h using muscle power alone. And we can always improve with all of this, there is no fundamental “best value limit”; or if, that one is extraordinarily small.

Related: Find an analysis to the so called „Fermi-Paradox“: "Why don't we see highly advanced aliens everywhere around us in the milkyway?".

Sources

[Statista] Statistisches Bundesamt, documented in 'statista', Internet last approached 13.12.2023 Index of GDP up to 2022 (German)

⁵⁾

As is always perceived with exponential growth: from a certain point onwards it looks like an explosion„. Meanwhile, in reality, it has always been exponential - but because the absolute values initially seemed small, no one cared at the beginning.

⁶⁾

Of course only if we do not fall victim to a hyper-hype of exaggerated, ill-considered 'quick-quick' interventions

⁷⁾

it doesn't work anyway

⁸⁾

because it doesn't exist anyway

⁹⁾

Not to be misunderstood: We need to start solving these problems now, there is no time left to wait. But, the time to orderly introduce the measures, which are necessary, to solve the problems, is still available: To change the energy-infrastructure will need some 25 to 35 yrs to complete. That's exactely the time, we have.

¹⁰⁾

just like every year in the fields as much cabbage grows back as we eat

¹¹⁾

factor $(1+p)$ in the service quantity; e.g. $p=$2.5% , then $1+p= $1.025

¹²⁾

On the question about this „duration“: Here Worries about time periods in „200 years“ are now irrelevant; within 200 years were will be even wiser solutions again. Youu can't say this for a period of just 10 years - which is why, for example, 'solutions' with previously unresolved disposal problems are to be banned, as long as the disposal has not been resolved.

¹³⁾

There is certainly an objection here from growth policy: Of course, the longer lifespans reduce the growth measured in GDP (and also the material sales). Nevertheless, the overall growth can be p, there can be more systems sold - the inventory then increases accordingly. This means that it is actually a real increase in value - while the reduced sales as a result of longer lifespans are in reality only a replacement purchase; in an economic sense, too, the shortening of lifespans is actually not real growth: It simply causes occupational therapy in the treadmill to maintain the status quo maintained - just with more effort. Extending lifespans therefore also means an increase in prosperity economically, because the working time gained can be used for more useful issues or, depending on social priorities, can also be additional free time. This is a typical example of how higher self-interest (namely increased sales of an individual company generated by short lifespans) is not identical with higher benefit for everyone, but on the contrary, it can be counterproductive. This does not have to apply to all the cases at the individual level; only: There is no automatism. Therefore, legal requirements regarding warranty periods and repairability do make sense. Growth through shortened lifespans is actually false growth, even loss of value. Creating political incentives for this reduces the overall performance of the affected economy. This example also shows that GDP, as it is currently measured, is the wrong measure of the actual increase in prosperity, even from an economic point of view. When shorter lifespans are pursued for a growth goal, the result is actually quite the opposite.

¹⁴⁾

The geom. series with positive $q< $1 converges because this value keeps increasing, but remains to be limited. We get the value of the infinite sum if we consider the self-similarity of the series: we multiply $S=1+q+q^2+q^3+. ..$ with $q$ itself, then we get $q\cdot S=q+q^2+q^3+...$; that's (almost) the same as the original row, only the leading „$1$“ is missing. If we subtract the shifted row from the original one, then we get $S-q\cdot S=1+q-q+q^2-q^2+q^3-q^3+...=1$ and from that immediately $ S=\frac{1}{1-q}$.

¹⁵⁾

But: what is that? 100 trillion years? Not really, still much, much more

¹⁶⁾

Whether that even makes sense in reality, as long as the universe exists and what it will look like in future, we don't have the slightest idea about any of this at the moment. And I admit that I'm happy to speculate about this for entertainment purposes, but I don't think it's of any relevance right now and we all know, that nobody at this time can claim to have the ultimate answer. It's not even clear that there can be such an ultimate answer - in this time of history that doesn't matter; because, if we ever want to work to solve these questions, mankind needs to survive the 21st century. That's what this is all about: A finite problem in a finite time period.

¹⁷⁾

But only then! Because if we eat away more than we grow, then it will be at the expense of the substance.

¹⁸⁾

What might be quite important if we consider folks on planet Earth, who do still not have access to enough food, clear water and decent education. There is no question that to improve the supply for them will need a growing economy at that site on the planet.

¹⁹⁾

An example is the „squaring of the circle“ by Archimedes. Or quantum mechanics of the atomic shells; or the relativistic formulation of mechanics; … could be continued.

²⁰⁾

It goes without saying that the sellers of consumables (oil, gas but also cement and steel) would rather sell more rather than less - we shouldn't expect anything else. Not that we should grant all the wishes of that lobby unlimited freedom of interpretation on the questions concerned. Of course, these lobbyists would prefer to see efficiency gains eaten away again and again by additional demand: these larger, heavier cars are an example. That's not an inevitable 'rebound' - it is the result of a hard-working lobby and willing politicians.

²¹⁾

The problem is, it's not been followed consequently.

²²⁾

It can also be checked with a short rough calculation: the efficiency of the overall system must increase by around 2% per year. That is around 75% savings for the individual measure given if the complete conversion does not take longer than around 50 years. The most important thing is that the individual measure leads to a truly comprehensive improvement: This is the case, for example, when switching to e-traction in vehicles, the specific electricity consumption is then at around 15 kWh/(100 km) and therefor by more than a factor of 4 below today's average consumption (namely over 60 kWh/(100 km) for petrol or diesel). The situation is similar with the change in heating: heat pumps alone bring at least a factor of 2 (electricity generation in winter already included through backup, therefore not 3 or 3.5), the step by step renovations of the buildings bring at least another factor of 2. And, all of this can be completed within around 25 to 35 years get over. If we want it!

²³⁾

Talking points hat been: „Russian gas is so cheap“ and it is „environmentally friendly“ <taxonomy!>. Both turned out to be wrong.

²⁴⁾

that would be too late

²⁵⁾

it is always better to achieve it even faster. Many other useful measures can contribute to this.

²⁶⁾

Because one thing is also clear: a surplus of renewable energy will only be available from 2050 if the generation is expanded very quickly and if at the same time the efficiency is improved to the extent shown here. DAC will always be a quite small contribution, the main share will have to be increased by efficiency and renewables. This will only work if we start consistently today and then stick with it for three decades. Only then, from 2050 onwards, even the small potential of DAC will then offer us the chance to change the situation to further improvement.

²⁷⁾

Mind: at the moment, increasing efficiency cannot only be channeled into material increases in sales; after all the above, we now have to come down from the excessive exploitation of nature that has occurred. By the way, the danger of a so-called rebound does not exist in reality: We have already had the topic Rebound effect, but I will create a more general version later.