Time

This page is a sub-page of our page on Mathematical Concepts.

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The sub-pages of this page are:

Laurent Expansion of Time

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Related KMR-pages:

Oscar Reutersvärd
M.C. Escher

Disambiguation
Entropy
Function
Homology and Cohomology
Homotopy
Space
Products
Quotients
Topos
Duality
Topology
Uncertainty
Dimension

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Other relevant sources of information:

Modular arithmetic
Gregorian calendar

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How big is your clock?

How many ticks does it take
to take it back
to where it started?

Different types of clocks: \, 7 \, , \{ 12, 2 \} \, , 24 \, , { \{ 28, 29, 30, 31 \} }^{12} \, , {\{ 365, 366 \}}^{ \, n \; ≥ \; 1583 } \,


hours, days, weeks, months, years, decades, centuries, millennia, …

Expanding the duration of each tick:

\, N_{days} \, = \, 7 \times N_{weeks} \,

\, N_{hours} \, = \, 24 \times N_{days} \,

\, N_{years} \, = \, 10 \times N_{decades} \,

\, N_{decades} \, = \, 10 \times N_{centuries} \,

\, N_{centuries} \, = \, 10 \times N_{millennia} \,

Modular arithmetic: \;\; x \, + \, n \times a \, \equiv \, x \pmod n \, \equiv \, x \pmod a \, , \forall \, x, n, a \in \mathrm Z.

What this formula means (in plain English) is that the integers \, x \, and \, x + n \times a \,
have the same remainder when you divide them by either the integer \, a \, or the integer \, n .

• Arithmetical crossfire

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Weekday calendar:

\, N_{days} \, = \, 7 \times N_{weeks} \,

\, \mathbb{Z} \, / \, 7\mathbb{Z} \, = \, {\mathbb{Z}}_7 \,

Question: What is the weekday a million days from now?

\, {10}^6 \pmod 7 \, \equiv \, 1 \, \in \, {\mathbb{Z}}_7 .

Answer: The same weekday as tomorrow.

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The shifting sequence of moments:

The shifting sequence of moments

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