4 comments on “Infinite Series – A Health and Safety Warning

  1. Pingback: An infinite series of blog posts which sums to -1/12 | The Aperiodical

  2. Pingback: White Group A level JC H2 Maths tuition: 107th Carnival of Mathematics

  3. Pingback: Patrik Lindenfors blogg » Desinformation eller matematisk insikt? Vad är summan av alla positiva heltal – del 2

  4. It seems that with such alternating “convergent series,” we can separate all the positive and negative terms into two divergent series leaving us with, you should pardon, infinity – infinity = ?, in short, anything we like. In a sense, this really returns us–past the gymnastics–to the Great Crisis introduced by Weierstrass in 1872.

    Now combine the history of Hilbert’s “On The Infinite,” Godel’s Incompleteness Thm., and finally the birth of algorithmic information theory–and finally add General Relativity and Quantum Mechanics (intuited by Hilbert to an extent in “On the Infinite”), and voila–you can construct a convergent infinite series approximately modeling a finite interrelationship in physical reality.

    That is, this math is the drawing of a finite algorithmic information target bullseye about the intersection of the previously shot arrow and the tree. However, if there is a law of physics–an empirical pattern in our sensory perception (what axioms really are, per Bertram Russell and Kurt Godel) to how arrows tend to hit a tree, such infinite series constructs can be a useful minimal shorthand to describe it.

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