Explore every episode of the podcast Cognitive Capital

In this short excursion I discuss the definition of Kolmogorov Complexity and work through a few examples.

In this episode I jump into abstract algebra.

I discuss the following topics:

1. Binary Operators

2. Closure Property

3. Commutativity

4. Associativity

5. Identity Elements

6. Inverse Elements

In this episode, I ramble on a bit about some of the parts of neural network mathematics, particularly activation functions and bias.

1. Activation Functions: https://en.wikipedia.org/wiki/Activation_function

I also talk about a book by Jeff Heaton, Introduction to the Math of Neural Networks. It's very short and simple but a nice fast read for a quick introduction to the topic. Check it out if you're interested: https://www.amazon.de/-/en/Jeff-Heaton-ebook/dp/B00845UQL6

In this episode we discuss the conditional proposition or the conditional sentence

Topics:

1. What is If P, then Q. (conditional)

2. If P, then Q (definition, antecedent, consequent)

3. Truth Table for if P, then Q.

4. Thinking about and conceptualizing the conditional in terms of promises.

5. True & False Examples

6. The Converse

7. The Contrapositive

8. The Equivalence of if P, then Q <=> ~Q, then ~P.

In this episode I talk about

1. Logical Connectives: Conjunction, Disjunction, Negation.

2. Truth Tables

3. Examples of True and False well-formed formulas using conjunction, disjunction and negation.

4. Propositional forms.

What is a Proposition?

A statement that can be true of false.

Examples:

1. sqrt(2) is irrational.
2. 1+1=5
3. The tiger will become extinct before the Gorilla on the planet Earth.
4. Socrates was left handed.

Main Points:

1. Difficulty of establishing the actual (realworld) truth value is unimportant
2. Some values can be immediately computed as T or F #1 or #2, others may take many years #3 or we may never know #4.

Non-Proposition Examples:

1. Can you please pass me the Ketchup?
2. x^2 = 49
3. This sentence is false.

Main Points:

1. Interrogative statements are neither T nor F.
2. #2 may be T or F depending on the value assigned to x.
3. Neither T nor F - a paradox.

Atomic Propositions - do not contain any other propositions - ex: It is raining. 

Compound Propositions - are formed by combining logical connectives with atomic (simple) propositions - ex: I am drinking coffee and its raining outside.