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# The Basics of Logic

Let’s jump right in at the only place we can: the very begining, diving into the perfectly obvious and terribly argumentative 'rules of logic'.

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Let’s jump right in at the only place we can: the very begining. The programs we write every day are based on orchestrated algorithms and data structures that all have their roots in a single thing: LOGIC. Let’s quickly explore some basic logical rules as we’re going to build on them later on.

## Logic… What Exactly Is It?

The first, most obvious is question is how are we defining the term “logic”. There are a few different definitions so let’s start with the first, offered by Aristotle. In trying to come up with a framework for thinking, Aristotle described what are known today as The Laws of Thought. Let’s take a look at each one using JavaScript!

The first is The Law of Identity, which simply states that a bit of logic is whole unto itself - it’s either true, or false, and it will always be equal to itself.

Here we’re describing this as `x === x`, which… yes… I know seems perfectly obvious but stay with me.

The next law is called The Law of Contradiction, which states that a logical statement cannot be both true and false at the same time. Put another way - a true statement is never false, and a false statement is never true.

Again - this is perfectly reasonable and seems obvious. Let’s keep going with the third law: Excluded Middle.

This one’s a bit more fun as it states that something can either be true or false - there is no in-between. Using JavaScript we can demonstrate this by setting `x` and `y` to true and false and playing around with different operations - the only thing that is returned, based on those operations, is `true` or `false` - that’s Excluded Middle in action.

And right about now some of you might be bristling at this.

## Ternary Logic

As I’ve been writing the statements above we’ve been seeing JavaScript evaluate the result of each, which has been `undefined`. The idea here is that there’s a third state, that’s neither true nor false - which is undefined. You can also think of this as `null` for now even though, yes, null and undefined are two different things. We’ll lump them together for the sake of defining what’s known as “ternary logic” - or “three state logic” which kicks Excluded Middle right in the teeth.

## Problems

Aristotle had a problem with his logical system - it only deals with things that are known. The only things we can know for sure are things that have happened already and that we have witnessed somehow… even then there’s a question of whether we truly know them. Let’s sidestep that rabbit hole.

When asked to apply his Laws of Thought to future events - such as “will Greece be invaded this year” Aristotle replied that logic cannot apply to future events as they are unknowable. An easy out, and also a lovely transition to Ternary Logic.

## Determininism

Let’s bring this back to programming. You and I can muse all day about whether Aristotle’s brand of logic - which we can call “binary” for now - is more applicable or whether the world can be better understood with the more flexible ternary logic. But I don’t want to do that because I’m here to talk about computer programming and for that there’s only one system that we can think about - a deterministic system.

If you read the first Imposter’s Handbook you’ll likely remember the chapter on determinism (and non-determinism). If not - a simple explanation is that a deterministic system means that every cause has an effect and there is no unknown.

Programs are deterministic because computers are deterministic. Every instruction that a computer is given is in the form of groups of 1s and 0s… there are no undefined middle points. This is important to understand as we move forward - the math that we’re about to get into and the very advent of computer science is predicated on these ideas. I know what you’re thinking though…

## What About Null, None, Nil or Undefined?

Programming languages define much more than simply true or false - they also include the ability to have something be neither in the forms of null, nil, none or undefined. So let me ask you a question… is that logical?

Let’s take a look.

By default, JavaScript (and many other languages) will default a variable to an unknown value such as null or, as you see here, undefined. If I ask JavaScript if something undefined is equal to itself, the answer is true. If it’s not equal to itself the answer is false - so good so far.

What about being equal to not-not itself? Well that’s false as well which makes a bit of distorted sense because `!y` is false so `!!y` returns true… I guess. But if something is `!undefined` … what is it? To JavaScript… it’s simply `true`.

## The Billion Dollar Blunder

The creator of ALGOL, Tony Hoare, is credited with creating the concept of `null` in a programming language:

I call it my billion-dollar mistake…At that time, I was designing the first comprehensive type system for references in an object-oriented language. My goal was to ensure that all use of references should be absolutely safe, with checking performed automatically by the compiler. But I couldn’t resist the temptation to put in a null reference, simply because it was so easy to implement. This has led to innumerable errors, vulnerabilities, and system crashes, which have probably caused a billion dollars of pain and damage in the last forty years.

Have you ever battled null problems in your code or tried to coerce an undefined value into some kind of truthy statement? We all do that every day.

Computers aren’t capable of understanding this. Programming languages are, apparently and at some point the two need to reconcile what `null` and `undefined` means. What makes this worse is that different languages behave differently.

### Ruby

Ruby defines `null` as `nil` and has a formalized class, called `NilClass` for dealing with this unknowable value. If you try to involve `nil` in a logical statement, such as greater or less than 10, Ruby will throw an exception. This makes a kind of sense, I suppose, as comparing something unknown can be … anything really.

But what about coercion? As you can see here, `nil` will be evaluated to false and asking nil if it’s indeed nil will return true. But you can also convert nil to an array or an integer… which seems weird… and if you inspect nil you get a string back that says “nil”. We’ll just leave off there.

### JavaScript

JavaScript is kind of a mess when it comes to handling `null` operations as it will try to do it’s best to give you some kind of answer without throwing an exception. `10 _ null` is 0, for instance… I dunno…

It’s the last two statements that will bend your brain, however, because `10 <= null` is somehow false… but `10 >= 0` is true. I know JavaScript fans out there will readily have an answer… good for them I’m sure there’s a way to explain this but honestly it’s not sensical to begin with because, as I’ve mentioned, `null` and `undefined` are abstractions on top of purely logical systems. Each language gets to invent it’s own rules.

If you ask JavaScript what type `null` is you’ll get `object` back - which isn’t true, as MDN states:

In the first implementation of JavaScript, JavaScript values were represented as a type tag and a value. The type tag for objects was 0. null was represented as the NULL pointer (0x00 in most platforms). Consequently, null had 0 as type tag, hence the bogus typeof return value.

### C#

Let’s take a look at a more “structured” language - C#. You would think that a language like this would be a bit more strict about what you can do with Null… but it’s not! OK it DOES throw when you try to compare null to !!null - that’s a good thing, but when you try to do numeric comparisons… hmmm

And null + 10 is null? I dunno about that.

## The Point

So, what’s my point with this small dive into the world of logic and null? It is simply that null is an abstraction defined by programming languages. It (as well as undefined) has no place in the theory we’re about to dive into. We’re about to jump into the land of pure logic and mathematics, electronic switches that become digital… encoding… encryption and a bunch more - none of which have the idea of null or undefined.

It’s exciting stuff - let’s go!

## The Code

Code for this video (and for the entire series) can be found in the production GitHub repo.

• ### The Basics of Logic

Let’s jump right in at the only place we can: the very begining, diving into the perfectly obvious and terribly argumentative 'rules of logic'.

• ### Boolean Algebra

You're George Boole, a self-taught mathematician and somewhat of a genius. You want to know what God's thinking so you decide to take Aristotle's ideas of logic and go 'above and beyond' to include mathematical proofs.

• ### Binary Mathematics

This is a famous interview question: 'write a routine that adds two positive integers and do it without using mathematic operators'. Turns out you can do this using binary!

• ### Bitwise Operators

Up until now we've been representing binary values as strings so we could see what's going on. It's time now to change that and get into some real binary operations.

• ### Logical Negation

We've covered how to add binary numbers together, but how do you subtract them? For that, you need a system for recognizing a number as negative and a few extra rules. Those rules are one's and two's complement.

• ### Entropy and Quantifying Information

Now that we know how to use binary to create switches and digitally represent information we need to ask the obvious question: 'is this worthwhile'? Are we improving things and if so, how much?

• ### Encoding and Lossless Compression

Claude Shannon showed us how to change the way we encode things in order to increase efficiency and speed up information trasmission. We see how in this video.

• ### Correcting Errors in a Digital Transmission, Part 1

There are *always* errors during the transmission of information, digital or otherwise. Whether it's written (typos, illegible writing), spoken (mumbling, environment noise) or digital (flipped bits), we have to account for and fix these problems.

• ### Correcting Errors in a Digital Transmission, Part 2

In the previous video we saw how we could correct errors using parity bits. In this video we'll orchestrate those bits using some math along with a divide and conquer algorithm to correct single-bit errors in transmissions of any size.

• ### Encryption Basics

In this video we play around with cryptography and learn how to encrypt things in a very simple, basic way. We then ramp up our efforts quickliy, creating our own one-time pad and Diffie-Hellman secure key transmitter.

• ### Hashing and Asymmetric Encryption

In this video we dive into hashing algorithms, how they're used and what they're good (and not so good) for. We'll also dig into RSA, one of the most important pieces of software ever created.

• ### Functional Programming

Functional programming builds on the concepts developed by Church when he created Lambda Calculus. We'll be using Elixir for this one, which is a wonderful language to use when discovering functional programming for the first time

• ### Lambda Calculus

Before their were computers or programming languages, Alonzo Church came up with a set of rules for working with functions, what he termed lambdas. These rules allow you to compute anything that can be computed.

• ### Database Normalization

How does a spreadsheet become a highly-tuned set of tables in a relational system? There are rules for this - the rules of normalization - which is an essential skill for any developer working with data

• ### Big O Notation

No video with this one - just a post with lots of code for quick review. Understanding Big O has many real world benefits, aside from passing a technical interview. In this post I'll provide a cheat sheet and some real world examples.

• ### Arrays and Linked Lists

The building block data structures from which so many others are built. Arrays are incredibly simple - but how much do you know about them? Can you build a linked list from scratch?

• ### Stacks, Queues and Hash Tables

You can build all kinds of things using the flexibility of a linked list. In this video we'll get to know a few of the more common data structures that you use every day.

• ### Trees, Binary Trees and Graphs

The bread and butter of technical interview questions. If you're going for a job at Google, Microsoft, Amazon or Facebook - you can be almost guaranteed to be asked a question that used a binary tree of some kind.

• ### Basic Sorting Algorithms

You will likely *never* need to implement a sorting algorithm - but understanding how they work could come in handy at some point. Interviews and workarounds for framework problems come to mind.

• ### DFS, BFS and Binary Tree Search

You now know all about trees and graphs - but how do you use them? With search and traversal algorithms of course! This is the next part you'll need to know when you're asked a traversal question in an interview. And you will be.

• ### Dynamic Programming and Fibonnaci

Dynamic programming gives us a way to elegantly create algorithms for various problems and can greatly improve the way you solve problems in your daily work. It can also help you ace an interview.

• ### Calculating Prime Numbers

The use of prime numbers is everywhere in computer science... in fact you're using them right now to connect to this website, read your email and send text messages.

• ### Graph Traversal: Bellman Ford

How can you traverse a graph ensuring you take the route with the lowest cost? The Bellman-Ford algorithm will answer this question.

• ### Graph Traversal: Djikstra

Bellman-Ford works well but it takes too long and your graph can't have cycles. Djikstra solved this problem with an elegant solution.

• ### Design Patterns: Creational

Tried and true design patterns for creating objects in an object-oriented language.

• ### Design Patterns: Structural

As your application grows in size you need to have a plan to handle the increase in complexity. The Gang of Four have some ideas that could work for you.

• ### Design Patterns: Behavioral

Mediators, Decorators and Facades - this is the deep end of object-oriented programming and something you'll come face to face with as your application grows.

• ### Principles of Software Design

You've heard the terms before: YAGNI, SOLID, Tell Don't ASK, DRY... what are they and what do they mean?

• ### Testing Your Code: TDD and BDD

Testing code has moved beyond the realm of QA and into the realm of design, asking you to think about what you do before you do it. Let's have a look at some strategies.

• ### Shell Script Basics

It's a Unix world. You should have a functional knowledge of how to get around a Unix machine using the command line, as well as how to complete basic tasks using shell scripts and Make files.

• ### Hands On: Creating a Useful Shell Script

I use the static site generator Jekyll to write my blog. I store the site at Github, who then translates and hosts it all for me for free. Jekyll is simple to use and I like it a lot. There's only one problem: it's a bit manual.

• ### Deciphering a Complex Bash Script

I use the static site generator Jekyll to write my blog. I store the site at Github, who then translates and hosts it all for me for free. Jekyll is simple to use and I like it a lot. There's only one problem: it's a bit manual.

• ### Making Your Life Easier with Make

Make is a build utility that works with a file called a Makefile and basic shell scripts. It can be used to orchestrate the output of any project that requires a build phase. It's part of Linux and it's easy to use.

• ### Using Make to Improve Your Test Suite

No video with this one - just a post with lots of code. Make has been around forever and is often overlooked in favor of tools that recreate precisely what it does, but in crappier ways. Let's see how you can use Make to help your testing process.

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