Editing Kardashev scale (section)

=== Human civilization: a model for extrapolation ===
Kardashev poses the following question: "Is it possible to describe the development of a civilization in general terms over large cosmological periods?" Now many of the fundamental parameters that characterize the development of civilization on Earth are [[Exponential growth|growing exponentially]]. In the field of energy, astronomer Don Goldsmith estimated that the Earth receives about one billionth of the Sun's energy, and that humans use about one millionth of it.<ref name="Kaku-2007" /> So we consume about one millionth of a billionth of the Sun's total energy. Since human expansion is exponential, we can determine how long it will take for humanity to go from Type&nbsp;II to Type&nbsp;III according to [[Michio Kaku]].<ref name="Kaku-2007" /> 

Thus, the rate of development of our own world remains the only criterion for [[Extrapolation|extrapolating]] the state of civilizations older than humanity.<ref name="Kardashev-1971" /> The same is true for social values and basic needs according to Ashkenazi.<ref>{{Cite journal |last=Ashkenazi |first=M. |date=1998-05-01 |title=On the applicability of human cultural models to extraterrestrial intelligence civilizations |url=https://www.sciencedirect.com/science/article/pii/S0094576598000344 |journal=Acta Astronautica |volume=42 |issue=10 |pages=739–743 |bibcode=1998AcAau..42..739A |doi=10.1016/S0094-5765(98)00034-4 |issn=0094-5765 |archive-date=2015-09-24 |access-date=2023-08-27 |archive-url=https://web.archive.org/web/20150924161916/http://www.sciencedirect.com/science/article/pii/S0094576598000344 |url-status=live }}</ref> Therefore, the time to double technical knowledge is about ten years, and to double energy output, available reserves, and population is about 25 years. Two scenarios are then possible: spatial expansion or energy stagnation, the latter being possible only for 125 years, according to Kardashev, using the following relationship <math>\alpha = 1.04</math>:

<math display="block">t = \frac{\log \left(P/P_o\right)}{\log \alpha}</math>

where <math>t</math> is the number of years, <math>P</math> is a parameter that increases annually as a function of <math>P_o</math> and of <math>t</math> according to <math>P = P_o \alpha^t</math> and <math>\alpha</math>, a growth rate.

If <math>\alpha = 1.04</math>, then humanity's energy consumption will exceed the incident solar power (1.742 × 10<sup>17</sup> <abbr>W</abbr>) after 240 years, the total power of the [[Sun]] (3.826 × 10<sup>26</sup> <abbr>W</abbr>) after 800 years, and that of the Galaxy (7.29 × 10<sup>36</sup> <abbr>W</abbr>) after 1,500 years.{{NoteTag|1=" If the growth rate a = 1.04 is maintained after the critical period, the human power output will exceed the quantity of incident solar radiation after 240 years, after 800 years the total energy radiated by the Sun will be exceeded, and after 1500 years we will exceed the total radiation output of the entire Galaxy'."}}<ref name="Kardashev-1971" /> Based on this calculation, Zuckerman estimates the number of civilizations that could exist in our [[galaxy]] at 10,000.<ref>{{Cite journal |last=Zuckerman |first=B. |date=1985 |title=Stellar evolution – Motivation for mass interstellar migrations |url=https://ui.adsabs.harvard.edu/abs/1985QJRAS..26...56Z/abstract |journal=Quarterly Journal of the Royal Astronomical Society |volume=26 |pages=56–59 |bibcode=1985QJRAS..26...56Z |issn=0035-8738 |archive-date=2023-08-27 |access-date=2023-08-27 |archive-url=https://web.archive.org/web/20230827100101/https://ui.adsabs.harvard.edu/abs/1985QJRAS..26...56Z/abstract |url-status=live }}</ref> Kardashev concludes that the current exponential growth is a transitional phase in the development of a civilization, and that it is inevitably limited by natural factors. In fact, he believes that the required [[mass]] and [[energy]] will continue to grow exponentially for another 1,000 years.<ref name="Kardashev-1971" /> Civilization is thus defined by an exponential rate of increase. Humanity as a model for thinking about the development of extraterrestrial civilizations has its limitations, which can be truly overcome by a [[Interdisciplinarity|multidisciplinary approach]] according to the work of Kathryn Denning.<ref>{{Cite journal |last=Denning |first=Kathryn |date=2011-02-01 |title=Ten thousand revolutions: conjectures about civilizations |url=https://www.sciencedirect.com/science/article/pii/S0094576509005694 |journal=Acta Astronautica |series=SETI Special Edition |volume=68 |issue=3 |pages=381–388 |doi=10.1016/j.actaastro.2009.11.019 |bibcode=2011AcAau..68..381D |issn=0094-5765}}</ref>