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Penrose diagram of an infinite Minkowski universe, horizontal axis u, vertical axis v. In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity.
A logarithmic timeline is a timeline laid out according to a logarithmic scale. This necessarily implies a zero point and an infinity point, neither of which can be displayed. The most natural zero point is the Big Bang, looking forward, but the most common is the ever-changing present, looking backward. (Also possible is a zero point in the ...
There is also a distinct projectively extended real line where + and are not distinguished, i.e., there is a single actual infinity for both infinitely increasing sequences and infinitely decreasing sequences that is denoted as just or as .
A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other. This composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. (For example, if we have a chart of Europe and a chart of ...
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, [ 1 ] after the lemniscate curves of a similar shape studied in algebraic geometry , [ 2 ] or "lazy eight", in the terminology of livestock branding .
The twist can be in one of two directions and opposite twists can cancel out by deformation. The total number of twists after cancellation is an integer, called the degree of the mapping. As in the case mappings from the circle to the circle, this degree identifies the homotopy group with the group of integers, Z. [citation needed]
One version of intelligence explosion is where computing power approaches infinity in a finite amount of time. In this version, once AIs are performing the research to improve themselves, speed doubles e.g. after 2 years, then 1 year, then 6 months, then 3 months, then 1.5 months, etc., where the infinite sum of the doubling periods is 4 years.
Specifically, future null infinity consists of all points where = and < <, and past null infinity consists of all points where = and < <. [ 2 ] From the coordinate restrictions, null infinity is a three dimensional null surface, with a cylindrical topology R × S 2 {\displaystyle \mathbb {R} \times S^{2}} .