basics:energy_and_ecology:about_growth
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basics:energy_and_ecology:about_growth [2024/10/31 10:52] – [(3) Some math: The sum of the infinite geometric series converges!] yaling.hsiao@passiv.de | basics:energy_and_ecology:about_growth [2024/10/31 11:14] (current) – yaling.hsiao@passiv.de | ||
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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: | 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: | ||
- | ((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.)) The historical analysis: Even past growth has not been exponential at all over extended periods.\\ | + | (1) The historical analysis: Even past growth has not been exponential at all over extended periods.\\ |
- | ((Of course only if we do not fall victim to a hyper-hype of exaggerated, | + | (2) The role of efficiency factors (such as product lifespans)\\ |
- | ((it doesn' | + | (3) Some elementary mathematics: |
- | ((because it doesn' | + | (4) Is it all just theory? A few concrete implementation approaches; Viewed in light: There' |
- | ==== (1) The historical analysis: Even in the past growth has not been exponential over extended periods ==== | + | ==== The historical analysis: Even in the past growth has not been exponential over extended periods ==== |
- | [{{ : | + | [{{ : |
+ | Percentages are usually communicated regarding economic growth. That's easy to understand - and there' | ||
+ | - Yes, there has been **steady and sustained growth** - except for a few (well-known) short-term dips. | ||
+ | - But that was by no means exponential, | ||
- | Percentages are usually communicated regarding economic | + | This could not be transformed into exponential |
- | - Yes, there has been **steady and sustained growth** | + | Conclusion: Excessive growth expectations are an illusion. But also: There is no acute danger that ' |
- | - But that was by no means exponential, | + | If the whole thing continues to take place in an orderly (linear) manner, then there is time left to solve the problems((Not to be misunderstood: |
- | ====(2) The role of efficiency factors ==== | + | |
+ | |||
+ | ==== 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. [[https:// | 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. [[https:// | ||
- | How good is “good enough”? \\ | + | //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 $p$((factor $(1+p)$ in the service quantity; e.g. $p=.5% , then +p= .025)) , 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 " | 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 $p$((factor $(1+p)$ in the service quantity; e.g. $p=.5% , then +p= .025)) , 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 " | ||
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- | ====(3) Some math: The sum of the infinite geometric series converges! ==== | + | ==== 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!\\ \\ | 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 ' | First the facts: Let $q$ be a factor with an absolute value smaller than 1. Then the ' | ||
$1+q+q^2+q^3+...$ \\ \\ | $1+q+q^2+q^3+...$ \\ \\ | ||
+ | |||
a **finite value**. If you find the following box with the formulas too challenging, | a **finite value**. If you find the following box with the formulas too challenging, | ||
- | {{ :grundlagen:energiewirtschaft_und_oekologie: | + | {{ :picopen:geometric_row_04.png?350|}} |
For this the notation with the sum sign $\sum$ has become common in mathematics: | For this the notation with the sum sign $\sum$ has become common in mathematics: | ||
$\; | $\; | ||
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 " | 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 " | ||
Here, of course, " | Here, of course, " | ||
+ | |||
+ | <WRAP box> In short: $q<1$ or **increase in efficiency greater than increase in demand** actually solves the growth problem.\\ \\ To put it another way, provocatively: | ||
<WRAP lo> Of course it is clear to me that this does not suit any of the two " | <WRAP lo> Of course it is clear to me that this does not suit any of the two " | ||
- | 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 ' | + | 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 ' |
- | ==== (4) Is it all just theory? ==== | + | ==== Is it all just theory? ==== |
- | No! This is already in many applications common practice today((The problem is, it's not been followed consequently.)) . There is already a lot available on Passipedia: namely, concrete descriptions of the measures that go down to the " | + | No! This is already in many applications common practice today((The problem is, it's not been followed consequently.)) . There is already a lot available on Passipedia: namely, concrete descriptions of the measures that go down to the " |
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basics/energy_and_ecology/about_growth.1730368326.txt.gz · Last modified: by yaling.hsiao@passiv.de