Paradox and Pandora’s Box; Some Things Just Have to be Opened.

 

pandora

My last blog examined the world of natural language, formal theories, and computer linguistics.  Now we will explore computer language and mathematical theories.

I know, I know!  I wanted to skip to another topic myself, but once I delved into the assignment, I found it fascinating.  Hang around and we’ll explore it together.

In school students are taught that math never lies; it’s either right or wrong.  While that’s true in a general sense, math, like spoken language, can have its share of quirks. Both computer and natural languages have complex components that don’t fall into neatly defined categories.  A great many theories have been put forth in order to work with these anomalies.

Bertrand Russell,  a British philosopher and logician, is best known for his work in mathematical logic and analytic philosophy. In the Early 1900s, he began work on what would become known as Russell’s Paradox.

bertrandrussellphoto

This mathematical puzzle involves the formal study of set theory. No yawning; it gets better.

The paradox arises in connection with the set of all sets that are not members of themselves.  Sound confusing?

Watch this YouTube video for a great explanation of the paradox.

The paradox’s circular argument, referencing back to something that cannot logically be referenced, disturbed the foundation of set theory. If this sounds familiar, think back to the donkey pronoun that Discourse Representation Therapy struggled with. (See my previous blog)

In response to the paradox, Russell began work on creating Type Theory; a formal system of hierarchy that serves as an alternative to set theory. A type system is a collection of rules that assign a property, called a type, to variables, expressions, functions or modules. 

Type theory’s main purpose is to reduce bugs in computer programs and then check that the parts are connected in a consistent way. These systems are the backbone of thousands of computer languages.  Constructive Type Theory has been a topic of interest to computer scientists, mathematicians, logicians and philosophers for a number of years.

alex wright

In Type Theory Comes of Age, Alex Wright said of Russell,

He could hardly imagine that his solution to a simple logic paradox, defining the set of all sets not in themselves, would one day shape the trajectory of 21st century computer science.

According to the article, scientists are currently creating hybrid systems from two important set theories. Intrigued, I explored through the arguments on static and dynamic systems. This led me to a computer language I use everyday.
Let me introduce you to HTML, that is, hypertext markup language.                                                                                                                 
HTML forms the building blocks of all websites.  This language provides a means to create documents by denoting structural semantics for text such as headings, paragraphs, lists, links, quotes and other items.  In other words; it lays out everything on the website in an organized manner.  As I write this blog, HTML  automatically sets up the format necessary to put words and pictures out on the web.
By learning  HTML, a writer can manipulate the way words and images appear on a web page.                                                                                           
I was curious if I could make changes myself. Like a cadet on the Starship Enterprise, I was off to the academy…the Code Academy. This site gives interactive tutorials for the basics of HTML.  Within minutes I was creating a mini web page. I learned standard commands are put into bracketed sets. For example,  <title> is the start of a title and </title> will denote the end of it. Header hierarchy is H1 (most important) through H6 (least important).

HTML

I went into my blog page and found that I could change headings, the title, and paragraph layouts.  Awesomeness! This knowledge gives me an important tool for creating changes in my page whenever I want.

The physical layout of a page is a crucial part of keeping a visitor’s interest. Simply having great content doesn’t ensure someone will stay on a site.  A seamless visual flow allows the reader’s eyes to effortlessly move through the story and enjoy the journey the author so carefully planned.

Our journey today certainly covered some deep topics. I hope a few sparks of interest have been ignited in hearty adventurers everywhere!  Now if I could just write code for starting the theme song to Star Wars along with some light saber sounds. For now, we’ll carefully close the lid on Pandora’s box and place it back on the shelf…until next time!

Darth Vader (l) and Luke Skywalker (r) in scene from film ''Star Wars V: The Empire Strikes Back'' at Star Wars exhibition, Powerhouse Museum 20 Nov 2008. Source: AdelaideNow
Powerhouse Museum 20 Nov 2008. Source: AdelaideNow
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