A Chocolate-Sharing Game

Almost everyone is probably familiar with the following game from childhood - or from their own children or grandchildren.

A bar of chocolate is laid out at a party. At first, everyone grabs it - it turns out that the bar is particularly tasty - but there is only one.

It is often the case that the last piece - a rather small, finite amount - is left behind as a „leftover“. Until someone comes up with the idea of dividing this piece in half with a knife. One half is taken and eaten, the other is left lying around.

The party then discusses how long this process can be repeated: Always take only half of the remaining food again. This works for a surprisingly long time: and it usually ends not because it seems difficult to halve the small amount further, but because the game gets boring at some point.

What is it like in 'reality'? Well, there are many aspects to this, a few of which we will briefly touch on:

Mathematically speaking, it is possible to continue such a halving process for longer and longer periods: and so the availability of chocolate can therefore be permanently ensured, even if at some point in the end in microscopic quantities.
Chemically and physically, however, we eventually reach the limit of a continuous division process, where the result of further division would no longer be „chocolate“, but altered molecules (that is around 70 such division steps, whereby the practice of dividing with a normal knife would then become quite difficult). Does this refute the approach? Yes, with regard to the infinite process - but as soon as we realize how many larger mini chunks could still be produced long before this molecular limit from, for example, a quarter of a piece of chocolate (several billion), it becomes clear again that the process does lead to a (finite) solution; it makes a sustainable solution possible because a sustainable supply of chocolate is certainly possible from renewable resources to a certain extend. Where exactly this sustainability point lies must be determined under the given boundary conditions; and, this value could certainly change with technological innovations.
The parable has a certain weakness that does not apply to most of the processes with scarce resources discussed today: because the consumer here is directly the human being, which can no longer really do much with microgram doses of chocolate substance. This experience results in the widespread intuitive rejection of this type of solution: Microscopic quantities of chocolate are simply psychologically indistinguishable from 'no more chocolate'. This is not the case for many technically used materials and their duration of use. Especially in the technical field, such a solution can therefore go quite far, as illustrated, for example, for Energy-Efficiency.

If the quantities under consideration correspond to typical resource and consumption data, the situation is e.g.

A recoverable reserve $R$ of about 100 times the amount of consumption $V$.
Then the following strategy would work: We extract just 1% of the yet existing reserves in each actual phase (e.g. 1 year). Then the initial extraction is $V_0$=1 (=1% of $R$), the following extraction is 1% out of 99% = 0.99, the third 0.99*0.99 etc. With this approach, it is immediately clear that the reserves are not completely exhausted. After 30 years, around 74% of the initial ressource is still available, and even after 100 years around 37%.
A period of well over 100 years is certainly sufficient to find and implement sustainable solutions for the task to be fulfilled; this is made possible by improving efficiency. In general, a reduction in consumption to around 1/5 to 1/3 of the current baseline is in most cases sufficient to dip below the sustainability threshold.
In the economics of resource management, it is generally assumed that significantly higher reserves can ultimately be tapped, but usually only at a higher cost. While this is certainly true for materials such as rare earths or lithium, it is different for the pollution tolerance of the earth's atmosphere, for example - there are no hidden resources that have not yet been tapped. Therefore, civilization must (at some point - and that is still in this century!) switch to a completely sustainable energy supply. In terms of energy as a resource, this is possible - because the amount of new energy radiated to the earth each year via solar radiation, which is also emitted again as heat radiation in the normal steady state, is more than enough to cover all the needs of a highly developed civilization. Of course, only part of this can be „diverted“ by tapping into the natural energy flow. With increasing knowledge of the interrelationships and technical progress, this usable part may even be increased to a certain extent ¹⁾ .

Back to the debate on economic growth.

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The total annual energy flow available in this way is limited, however. The energy demand on earth would then initially have to remain below this limit of annual consumption; however, if it is to be used to create value on a growing scale, this can still be achieved by further improving energy efficiency. The school of further strong growth expectations sees future expansion in the exploitation of extra-planetary resources (e.g. asteroids). Whether this can become a reality in the distant future is still 'in the stars' in the truest sense of the word. Within this century, however, a significant contribution from such extraterrestrial resource utilization can be ruled out due to the enormous costs involved: The experts in these areas see the development of extraterrestrial resources as being primarily for use in space (outside the Earth), because resources from the Moon, for example, are generally far cheaper at the Moon than from the Earth