Oct 20, 2020 10:28 PM
Dissolving the Fermi Paradox
https://arxiv.org/abs/1806.02404
ABSTRACT: The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be teeming with intelligent life is linked to models like the Drake equation, which suggest that even if the probability of intelligent life developing at a given site is small, the sheer multitude of possible sites should nonetheless yield a large number of potentially observable civilizations.
We show that this conflict arises from the use of Drake-like equations, which implicitly assume certainty regarding highly uncertain parameters. We examine these parameters, incorporating models of chemical and genetic transitions on paths to the origin of life, and show that extant scientific knowledge corresponds to uncertainties that span multiple orders of magnitude. This makes a stark difference.
When the model is recast to represent realistic distributions of uncertainty, we find a substantial {\em ex ante} probability of there being no other intelligent life in our observable universe, and thus that there should be little surprise when we fail to detect any signs of it. This result dissolves the Fermi paradox, and in doing so removes any need to invoke speculative mechanisms by which civilizations would inevitably fail to have observable effects upon the universe. (Paper download site)
An infinite universe of number systems
https://www.quantamagazine.org/how-the-t...-20201019/
INTRO: The rational numbers are the most familiar numbers: 1, -5, ½, and every other value that can be written as a ratio of positive or negative whole numbers. But they can still be hard to work with. The problem is they contain holes. If you zoom in on a sequence of rational numbers, you might approach a number that itself is not rational. This short-circuits a lot of basic mathematical tools, like most of calculus.
Mathematicians usually solve this problem by arranging the rationals in a line and filling the gaps with irrational numbers to create a complete number system that we call the real numbers. But there are other ways of organizing the rationals and filling the gaps: the p-adic numbers. They are an infinite collection of alternative number systems, each associated with a unique prime number: the 2-adics, 3-adics, 5-adics and so on.
The p-adics can seem deeply alien. In the 3-adics, for instance, 82 is much closer to 1 than to 81. But the strangeness is largely superficial: At a structural level, the p-adics follow all the rules mathematicians want in a well-behaved number system. Developed over a century ago, p-adic numbers have become an essential setting in which to investigate questions about rational numbers that go back millennia... (MORE)
https://arxiv.org/abs/1806.02404
ABSTRACT: The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be teeming with intelligent life is linked to models like the Drake equation, which suggest that even if the probability of intelligent life developing at a given site is small, the sheer multitude of possible sites should nonetheless yield a large number of potentially observable civilizations.
We show that this conflict arises from the use of Drake-like equations, which implicitly assume certainty regarding highly uncertain parameters. We examine these parameters, incorporating models of chemical and genetic transitions on paths to the origin of life, and show that extant scientific knowledge corresponds to uncertainties that span multiple orders of magnitude. This makes a stark difference.
When the model is recast to represent realistic distributions of uncertainty, we find a substantial {\em ex ante} probability of there being no other intelligent life in our observable universe, and thus that there should be little surprise when we fail to detect any signs of it. This result dissolves the Fermi paradox, and in doing so removes any need to invoke speculative mechanisms by which civilizations would inevitably fail to have observable effects upon the universe. (Paper download site)
An infinite universe of number systems
https://www.quantamagazine.org/how-the-t...-20201019/
INTRO: The rational numbers are the most familiar numbers: 1, -5, ½, and every other value that can be written as a ratio of positive or negative whole numbers. But they can still be hard to work with. The problem is they contain holes. If you zoom in on a sequence of rational numbers, you might approach a number that itself is not rational. This short-circuits a lot of basic mathematical tools, like most of calculus.
Mathematicians usually solve this problem by arranging the rationals in a line and filling the gaps with irrational numbers to create a complete number system that we call the real numbers. But there are other ways of organizing the rationals and filling the gaps: the p-adic numbers. They are an infinite collection of alternative number systems, each associated with a unique prime number: the 2-adics, 3-adics, 5-adics and so on.
The p-adics can seem deeply alien. In the 3-adics, for instance, 82 is much closer to 1 than to 81. But the strangeness is largely superficial: At a structural level, the p-adics follow all the rules mathematicians want in a well-behaved number system. Developed over a century ago, p-adic numbers have become an essential setting in which to investigate questions about rational numbers that go back millennia... (MORE)
