Considerations of Human Population Ranges
Assumptions
Earth Based: The consideration of human population sizes is for people on Earth only, and does not attempt to consider population impacts and sizes in the event of colonization of areas beyond Earth (such as Mars, K2-18b, or passing asteroids). While such colonization would impact overall population level considerations, the general considerations for Earth would likely still be generally valid.
Surface Based: Humans depend on air, water, light, and nutrients, all of which are found predominantly in a relatively thin area around the surface of the Earth. In addition, efficiently countering gravitational forces allows development only in certain modes. For these reasons, it will be assumed that the human population on Earth will live in a relatively narrow band along the surface of the Earth (no flying or air suspended cities nor any deep sea or subterranean cities).
Surface Area: The following are used for surface areas and densities based off general reference sources.
Earth’s total surface area: 510,000,000 square kilometers (5.1 * 10^8 km² or 1.97 * 10^8 mi²)
Usable land space: ~64,000,000 square kilometers (~6.4 * 10^7 km²) [crudely using an eighth of the Earth’s surface are]
Population density Manilla: 41,500 people per square kilometer (4.15 * 10^4 people / km²) [Manilla as a proxy for current densest living conditions]
Average Solar Radiation: [~5 kWh/m² per day] [this is the amount usable light that reaches the surface of the Earth; need to improve accuracy of this amount]
Notes on Ranges
The question of ideal population sizes (if such a question and concept is in itself valid) most likely cannot be thought of a certain number, but most likely a probabilistic range based on certain inputs (such as consumption needs, technological capacity, desired types of living, human population use, and so on).
There are likely many considerations to population size. At a basic level, the population size needs to be large enough to sustain itself, maintain its current capabilities, and likely to increase its capabilities as well. It likely cannot be so large that each additional person decreases the prospects for the survival and capacities of all. There are also major religious and cultural questions as well, such as what is the purpose of a human life and what sort of life should we want to live that also need to be considered.
There likely is no answer to this question, only opinions and actions which by aggregated thought and action will determine the path we chart as humanity. Below are proposed some on options for Earth’s population levels for consideration and as a thought experiment. While the sections below seemingly focus simply on human dwelling area, it is recognized that the greatest land (and ocean) use requirements are for crop and minerals production, and that simply having space for people to exist is but the most basic element of the question (some general allowances have been made for obtaining energy on per person basis assuming that light energy is the predominant energy source of the future, as it is now, and that mineral extraction and processing would not be the limiting constraint, but rather energy [the sections below are intended to be preliminary and to be followed up with more detailed analysis and revision later concerning energy, mineral, water, air, and systems processing limitations]). It would seem that somewhere between one million and one trillion people can viably be accommodated on Earth, but this like all population considerations is undoubtedly so ignorant of the future as to be proved wrong within a lifetime, and is such a broad range with so many impacts to lifestyle as to perhaps be almost meaningless. Nonetheless, the considerations seem valid based on the information available (please see the comparative options below).
In the Realm of Science Fiction
One (10^0)
This supposes asexual reproduction of one individual in perpetuity, a being of such omniscience and omnipotence that it can perfectly replicate and survive by itself. This is obviously of such different nature as to no longer be considered human, and would also present the risk of extinction due to lack of redundancy (single system failure risk).
Quintillion (10^18)
At this level of human population, there would be about 2,000 people per square meter over the entire surface of the Earth (including oceans), such that people would be stacked standing (shelved) approximately 400 people or more on top of each other across the entire Earth. Each person’s allocation of light energy would be so little that the human body would need to be adapted to account for this, and massive infrastructure required to support this type of living. Mobility and lifestyle traditional to human life would by necessity be quite different, resulting in something that had only vague resemblance to the traditional version of human life.
Perhaps Feasible but Unlikely Given Current Capabilities
Thousand (10^3)
This level of population would require a high degree of caution, perseverance, capacity, and motivation of each individual, as the loss of any individual would be a substantial overall loss. It would require highly improved knowledge, skills, and tools transfer amongst the generations, and would have high risk of extinction of regression.
Quadrillion (10^15)
At this level of population, there would be about 2 people per square meter spread across the entire surface of the earth (including the oceans), which even though using all land and oceans would be about 47 times more densely populated than the most densely populated cities currently. Light energy allocation would be limited by this surface allotment, and substantial infrastructure would be required to support this type of life.
Within the Realm of Possibility
Million (10^6)
This level of population might find itself as a few hundred small cities or villages across the globe with some level of scattered population as well. Some level of communication and transport would have to be considered to allow for circulation of knowledge and resources amongst all.
Trillion (10^12)
At this level of population, there would be over 15,000 people per square kilometer of usable land, or if consolidated into areas akin to current high population density cities, human habitation areas would occupy about 38% of the usable land area of the Earth (leaving the remainder, as well as the less usable land, for crops, mineral resources, parks and rural areas, and preserves.
Billion (10^9)
Something akin to our current population level (about an order of magnitude below). People could choose to increase population density into urban areas, or decrease it by increased rural expansion.