The level of technological development of any civilization can be gaged in large part by the amount of energy they produce for their use, but also encompasses that civilization’s stewardship of their home world. Following the Kardashev definition, a Type I civilization is able to store and use all the energy available on its planet. In this study, we develop a model based on Carl Sagan’s K formula and use this model to analyze the consumption and energy supply of the three most important energy sources: fossil fuels (e.g., coal, oil, natural gas, crude, NGL and feedstocks), nuclear energy and renewable energy. We also consider environmental limitations suggested by United Nations Framework Convention on Climate Change, the International Energy Agency, and those specific to our calculations to predict when humanity will reach the level of a Kardashev scale Type I civilization.
Humanity’s path to avoiding extinction is a daunting and inevitable challenge which proves difficult to solve, partially due to the lack of data and evidence surrounding the concept. We aim to address this confusion by addressing the most dangerous threats to humanity, in hopes of providing a direction to approach this problem. Using a probabilistic mode, we observed the effects of nuclear war, climate change, asteroid impacts, artificial intelligence and pandemics, which are the most harmful disasters in terms of their extent of destruction on the length of human survival. We consider the starting point of the predicted average number of survival years as the present calendar year. Nuclear war, when sampling from an artificial normal distribution, results in an average human survival time of 60 years into the future starting from the present, before a civilization-ending disaster. While climate change results in an average human survival time of 193 years, the simulation based on impact from asteroids results in an average of 1754 years. Since the risks from asteroid impacts could be considered in the far future, it can be concluded that nuclear war, climate change, and pandemics are presently the most prominent threats to humanity. Additionally, the danger from superiority of artificial intelligence over humans, although abstract in its sense, is a factor of careful study and could also have wide ranging implications, impeding man’s advancements towards becoming a more advanced civilization.
In Mathematics, we see a large number of functions, each having its own properties. Some of these are very interesting and contribute greatly to the intensive research in the field of Mathematics. This paper deals with one such function (which we have termed as the phi function) which emerges from a chain of inequalities, established from the basic concepts of differential calculus. This paper establishes several inequalities which relate to functions and their integrals. Another important expression (from the point of view of notations) links a class of divergent infinite series to the phi function. Finally, we will dive into a brief overview of the phi-form of plane trigonometric functions and derive the trigonometric identity sin2(θ) + cos2(θ) = 1, thus marking their importance. Throughout the paper, we will be analyzing functions in R+ such that the functions are always greater than 0. We will also consider that the functions are continuous and differentiable in the intervals under consideration.
The level of technological development of any civilization can be gauged in large part by the amount of energy it produces for its use, but also encompasses that civilization’s stewardship of its home world. Following the Kardashev definition, a Type I civilization is able to store and use all the energy available on its planet. In this study, we develop a model based on Carl Sagan’s K formula, and use this model to analyze the consumption and energy supply of the three most important energy sources: fossil fuels (e.g., coal, oil, natural gas, crude, NGL, and feedstocks), nuclear energy, and renewable energy. We also consider environmental limitations suggested by the United Nations Framework Convention on Climate Change, the International Energy Agency, and those specific to our calculations, to predict when humanity will reach the level of a Kardashev Scale Type I civilization. Our findings suggest that the best estimate for our civilization to attain Type I status is within the common calendar year range of 2333 to 2404.
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