Hi !
Featured games (85)
games approved by the League of Dukes
Games in Showcase (636)
Games in Android Showcase (178)
games submitted by our members
Games in WIP (687)
games currently in development
News: Read the Java Gaming Resources, or peek at the official Java tutorials
    Home     Help   Search   Login   Register   
Pages: [1]
  ignore  |  Print  
  Orders of magnitude  (Read 4203 times)
0 Members and 1 Guest are viewing this topic.
Offline Wiki Duke


« Posted 2012-11-27 13:22:32 »

Note: you are watching revision 0 of this wiki entry. ( view plain diff )

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:
Diameter of the sun is ~230m.
Number of people alive today.
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.
Observable universe has an estimated radius of 93 billion lightyears which is ~2119 nanometers.
A tight bounding box around a proton occupies ~2199 planck volumes
Radius of the observable universe is ~2205 planck lengths
98!2 51299!Number of atoms in the observable universe is ~2266.
170!21024171!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 ~264-2-32 or ~263.999999999664.

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.
This wiki entry has had 2 revisions with contributions from 2 members. (more info)
Pages: [1]
  ignore  |  Print  

Dwinin (72 views)
2015-11-07 13:29:08

Rems19 (81 views)
2015-10-31 01:36:56

Rems19 (74 views)
2015-10-31 01:32:37

williamwoles (107 views)
2015-10-23 10:42:59

williamwoles (93 views)
2015-10-23 10:42:45

Jervac_ (106 views)
2015-10-18 23:29:12

DarkCart (135 views)
2015-10-16 00:58:11

KaiHH (116 views)
2015-10-11 14:10:14

KaiHH (156 views)
2015-10-11 13:26:18

BurntPizza (171 views)
2015-10-08 03:11:46
Rendering resources
by Roquen
2015-11-13 14:37:59

Rendering resources
by Roquen
2015-11-13 14:36:58

Math: Resources
by Roquen
2015-10-22 07:46:10

Networking Resources
by Roquen
2015-10-16 07:12:30

Rendering resources
by Roquen
2015-10-15 07:40:48

Math: Inequality properties
by Roquen
2015-10-01 13:30:46

Math: Inequality properties
by Roquen
2015-09-30 16:06:05

HotSpot Options
by Roquen
2015-08-29 11:33:11 is not responsible for the content posted by its members, including references to external websites, and other references that may or may not have a relation with our primarily gaming and game production oriented community. inquiries and complaints can be sent via email to the info‑account of the company managing the website of java‑
Powered by MySQL Powered by PHP Powered by SMF 1.1.18 | SMF © 2013, Simple Machines | Managed by Enhanced Four Valid XHTML 1.0! Valid CSS!