Math is a game

Math is a game, an arbitrary set of symbols and rules. The weird part, the part that always surprises me, is that it's relevant to the real world.

Here's an example: we'll start with just two symbols, Yin and Yang. (Replace those with black and white, circle and square, X and Y… whichever two symbols you prefer.) What can we do with them?

Well, the simplest thing we can do is transform one into the other:

Yin → Yang; Yang → Yin

We'll call this transformation "mirroring" and denote it with the letter "M".

What about combining two symbols? We have a number of possibilities:

A) Yin, Yang → Yin; Yang, Yin → Yin; Yin, Yin → Yin; Yang, Yang → Yin

This is rather boring… no matter what we start with, we obtain an Yin symbol. Nevertheless, let's continue.

B) The opposite of A: Yin, Yang → Yang; Yang, Yin → Yang; Yin, Yin → Yang; Yang, Yang → Yang. Still boring.

C) Yin, Yang → Yin; Yang, Yin → Yin; Yin, Yin → Yin; Yang, Yang → Yang

Ok, so this is a bit more interesting: this combination still overwhelmingly favors the Yin symbol, but at least once in a while we get back an Yang. For completion, we'll also write down its opposite:

D) Yin, Yang → Yang; Yang, Yin → Yang; Yin, Yin → Yang; Yang, Yang → Yin

The last two combinations give us an equal distribution of the results:

E) Yin, Yang → Yin; Yang, Yin → Yin; Yin, Yin → Yang; Yang, Yang → Yang

F) Yin, Yang → Yang; Yang, Yin → Yang; Yin, Yin → Yin; Yang, Yang → Yin

I'll summarize the A..F combinations in a table:

1st 2nd A B C D E F
Yin Yang Yin Yang Yin Yang Yin Yang
Yang Yin Yin Yang Yin Yang Yin Yang
Yin Yin Yin Yang Yin Yang Yang Yin
Yang Yang Yin Yang Yang Yin Yang Yin

So, what was the point of all this? In itself, nothing much. We can imagine that two kids might alternate playing this game, where one of them writes symbols and the other one combines them to obtain the result, and the one with the most correct results wins. It doesn't really matter: the interesting part is that we just re-invented Boolean logic. The Yin and Yang symbols are 0 and 1 (or true and false) and the transformations are the well-known Boolean operators: and, or, xor, equ and finally not for what we called "mirroring" (I've ignored the "boring" A and B). Given that Boolean logic is used by all computers, this is quite amazing - what looked like rather pointless playing with two symbols picked at random proved to be hugely important.

Comments

Post a Comment

Popular posts from this blog

Posting dynamic Master / Detail forms with Knockout

Image
I have the following dynamic form in my GitHub Inventory project : I created the form with KnockoutJS , using some ideas from this article . The detail view looks like this: <table id="acquisition_items" class="jtable"> <thead> <tr> <th>Product Name</th> <th>Quantity</th> <th>Price</th> <th>Value</th> <th><button data-bind="click: addItem">[+]</button></th> </tr> </thead> <tbody data-bind="foreach: items"> <tr> <td> <input data-bind="value: ProductName" type="text" value="" /> </td> <td> <input data-bind="value: Quantity" type="text" value="" /> </td> <td>
Read more

Comparing Excel files, take two

Image
I already wrote this project once, on GitHub , but I can't say that I like the result. I wrote that code without TDD, mostly to see if I can still work in the "normal" fashion. I can, but I had a bug that took me a while to even discover and then was difficult to write tests for. I also hate the temporal dependency in that design (if you don't call the SortBy method first, the ExcludeRecords method will return incorrect results). Anyway; here's attempt number two, writing that code using TDD. Structure I start by creating my usual structure for projects of this type - a library for the logic, a console application for the main program and a test project for tests. I also use the Enable NuGet Package Restore option (right-click on the solution node) to add the three NuGet files that will allow someone to automatically download all the packages I'm referencing without wasting space in the source code repository. (Right now I've only added the Moq pa
Read more

EF Code First: seeding with foreign keys

This is just a quick tip, more for future reference for myself than anything else. When using Entity Framework Code First, one of the things you might want to do while developing the application is to seed your database with some test data. This can be something as easy as: protected override void Seed(InventoryDB context) { context.Products.AddOrUpdate( p => p.Name, new Product { Name = "Hammer", SalePrice = 11.99m, }, new Product { Name = "Nail Pack x100", SalePrice = 0.05m, }, new Product { Name = "Saw", SalePrice = 19.99m, }, new Product { Name = "Toolkit", SalePrice = 39.99m, } ); //... } (I am using the AddOrUpdate method so the code detects whether those products already exist and doesn't add them again if they do.) The Product class is quite simple and – most importantly – doesn't depend on any other: public class Product { public int Id { g
Read more