Cognitive Capital

In this episode I jump into abstract algebra.I discuss the following topics:1. Binary Operators2. Closure Property3. Commutativity4. Associativity5. Identity Elements6. 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.

What is a Proposition?A statement that can be true of false.Examples: sqrt(2) is irrational. 1+1=5 The tiger will become extinct before the Gorilla on the planet Earth. Socrates was left handed.Main Points: Difficulty of establishing the actual (realworld) truth value is unimportant 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: Can you please pass me the Ketchup? x^2 = 49 This sentence is false.Main Points: Interrogative statements are neither T nor F. #2 may be T or F depending on the value assigned to x. 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.

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

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.