Nuggets of knowledge which will outlast everything else you know about our world
This page will contain various math/logic/computer science/game theory related musings as I have the time to come up with them, this is basically a summary of some of the most interesting stuff I've run across.
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Introduction
Math has the advantage of being irrefutable. Everything you know about pop culture may be passe in a year and extinct in a decade. Any fact you may collect may be proven wrong or turned useless by a broadened understanding of the world. Any opinion you may have is up for debate, and the odds are you have a counterpart somewhere who thinks the exact opposite that you do. You can debate any topic in the world except for math. There, the rules and definitions have been whittled down so precisely that there is no room for doubt or ambiguity. There is simply truth, and there is error.
Mathematics is a metaphor. It is an internally cohesive system of thought and propositions which can be used to describe some abstract domain with absolute certainty. With it we can reason about the behavior of stars and solar systems, monopolies and markets, and describe everything from musical sonatas to nuclear explosions. There are just a few problems with it. We can't perfectly measure and quantify the world, and the world doesn't always like being reduced to a set of numbers and formulae.
That said, there's a lot we can rely on. If I give you five apples and take away three, you'll always have two left. The basic formulas of mathematics have stood from Pythagoras and Euclid until today. Math just gives us a more precise and logical way of describing things which happen to be precise and logical. Such as most of what you'll be able to read on the rest of these pages.
On Language and Possibilities
Every day of your life, you say something that has never been said before. Take that sentence I just uttered. Do a search for it in quotes on Google and you'll find out that no one else in the history of the internet has ever composed a phrase exactly like that. Click here to read the rest
Games and Levels of Complexity
Consider the following list of single-player games:
- Minesweeper
- Tetris
- Mastermind (once a combination has been chosen, it's essentially single-player)
- Freecell
- Sliding Tile Puzzles(finding the fastest solution, specifically)
- Sudoku
- Liar/Truthteller Logic Puzzles
- Picross
These games have three things in common. First of all, they're all equivalent. If you find an extremely efficient method of tackling one of them you have a method which can solve all of them. Secondly, they're all known to be extremely hard. There is no known way to solve any one of these problems which is any better than brute force, or simply considering every possibility. And thirdly, if you can come up with an efficient way to perfectly play any of these games, or even prove there is no efficient method, you'll be a millionaire overnight. Click here to read the rest
Game Theory
The Nature of Intelligence
Coming Soon
Liar's Dice
Get to know your inner swashbuckler
Orders of Magnitude
Numerical Value |
Magnitude Represented (loose estimates) |
29,200 |
The number of days you will probably live |
200,000 |
The number of English words in active use |
2,000,000,000 |
The number of operations your computer can perform in a second |
10^11 |
The number of possible seven character lower-case passwords, |
10^16 |
The number of planets in the universe |
4.247 * 10^17 |
The current estimated age of the universe in seconds |
3.1 * 10^20 |
The number of seconds before every star in the universe dies |
10^22 |
The number of stars in the universe |
10^43 |
The number of seconds before every proton in the universe decays |
10^50 |
The number of possible positions in a game of chess |
10^80 |
The number of atoms in the entire universe |
118^(10^80) |
The number of possible universes down to the atomic level |
Updates
7/20/06: Found an interesting proof of concept game, kkrieger, a detailed first person shooter written in 96k. Download. Updated my essay on adventure gaming
7/12/06: Continued editing the magnitude page, added a page talking about a dice game: Liar's Dice from Pirates of the Carribean. May want to break these pages down by regular essays and stuff relating to riddles/games
6/27/06: Wrote the page on orders of magnitude, and found another cool online game for the spatially inclined
6/5/06: Added a table with some general orders of magnitude. Open to ideas on other entries or general presentation.
5/16/06: Yeah, so no updates in a long while, this page has slowed to a crawl, but in my defense I never expected to release much to the world anyway. So here's the latest things I've been working on:
Liar/Truthteller Logic Puzzles
I'm blessed with more ideas than I can get out of my head, let me know if anyone still actually reads this.
4/10/06: An interesting visual puzzle, related to graph theory: planarity
May fill this page with some mathematical musings related to a few classic computer science problems, poker, and liar and truth teller logic puzzles. So much to say and so little time.
Copyright Mark Newheiser, 2007.