# Graphical timeline from Big Bang to Heat Death

This is the timeline of the Universe from Big Bang to Heat Death scenario. The different eras of the universe are shown. The heat death will occur in 10100 years, if protons decay.

Usually the logarithmic scale is used for such timelines but it compresses the most interesting Stelliferous Era too much as this example shows. Therefore, a double-logarithmic scale s (s*100 in the graphics) is used instead. The minimum of it is only 1, not 0 as needed, and the negative outputs for inputs smaller than 10 are useless. Therefore, the time from 0.1 to 10 years is collapsed to a single point 0, but that does not matter in this case because nothing special happens in the history of the universe during that time.

${\displaystyle s={\begin{cases}\log _{10}\log _{10}year&{\mbox{if }}year>10{\mbox{ , corresponding to }}year=10^{10^{s}}\\0&{\mbox{if }}0.1\leq year\leq 10\\-\log _{10}(-\log _{10}year)&{\mbox{if }}year<0.1{\mbox{ , corresponding to }}year=10^{-10^{-s}}\end{cases}}}$
Comparison of log10 and log10log10 scales
year log10 year combination of log10log10 year and
-log10(-log10 year)
1010000 10000 4
101000 1000 3
10100 100 2
1010 10 1
102 2 0.30
101 1 0
100 0 undefined but here forced to 0
10−1 -1 0
10−2 -2 -0.30
10−10 -10 -1
10−100 -100 -2

The seconds in the timescale have been converted to years by ${\displaystyle second/31557600}$ using the Julian year.