BANGED OUT QUICK -- MIGHT BE MISTAKES

Programmers daily work with 32 and 64 bit quantities so it's sometimes easy to loose sight of scale.  Additionally humans are better at thinking in terms of linear changes and have difficult with fast growing functions.  Likewise once number get bigger/smaller beyond some point, any additional bigger/smaller has less and less meaning to to point where changes become somewhat meaningless.

Distances (in meters) greater than 10⁶ are officially termed "Astronomical", which is ~2²³.

The following table list some powers-of-two along with the bounding factorials and some quantities of that scale:

12!	232	13!	Diameter of the sun is ~230m. Number of people alive today.
20!	264	21!	Number of people whom have ever lived: ~237 Thickness of the Milky Way's gaseous disk ~255Km Distance from the sun to Proxima Centauri is ~255m Age of the universe is ~259 seconds.
34!	2128	35!	Observable universe has an estimated radius of 93 billion lightyears which is ~2119 nanometers.
57!	2256	58!	A tight bounding box around a proton occupies ~2199 planck volumes Radius of the observable universe is ~2205 planck lengths
98!	2 512	99!	Number of atoms in the observable universe is ~2266.
170!	21024	171!	Number of planck volumes in the observable universe is ~2614.

Notice to reach a mere 2⁶¹⁴ we are measuring the incomprehensibly large in terms of the incomprehensibly small.

Now consider the value of 2⁶⁴-2³².  Without stopping to think you might be tempted say that this is ~2³², when actually the value is ~2^64-2-32 or ~2^{63.999999999664}.

Since we're programmers it is probably more useful to consider computation. Real world examples below are using FLOPS measurements.

• AMD 7970 system which can perform ~2⁴⁴ computations per second and ~2⁶⁸ per year.
• The Cray Titan which can perform ~2⁵⁴ computations per second and ~2⁷⁹ per year.
• It's estimated super computers will reach ~2⁶⁰ per second by 2018.
• It's estimated super computers will reach ~2⁷⁰ per second around 2030.
• Imagine an atom which is a quantum computer that can perform one computation per Plank's time (5.39106*10^-44s).  Then this atom computer can perform ~2¹⁴⁴ computations per second and ~2¹⁶⁹ per year.
• Imagine a supercomputer made of all the atoms in the observable universe which is ~10⁸⁰, each of which is one of the above, resulting in ~2⁴¹⁰ computations per second and ~2⁴³⁵ per year.

We'll also define a time scale BB which is equal 4.339*10¹⁷s, the amount of time from the big bang until now.

The Titan can perform 2⁶⁴ computations in ~17 minutes and 2¹²⁸ in ~2¹⁶ BB.
The atom computer could perform 2¹²⁸ computations in ~15 milliseconds and 2²⁵⁶ in ~2⁵³ BB.
The universe could perform 2²⁵⁶ computations in less than one Plank time and 2⁵¹² in ~2⁴³ BB.

It would take the Titan ~2⁶⁵ years to perform one second of the atom computer.  The big bang was merely ~2³⁴ years ago. It would take the atom computer ~2²⁴¹ years to perform one second of the "universe" super computer.