Welcome to episode #2 of the series, if you missed episode #1, check it out here: https://qubit-and-neuron.beehiiv.com/p/can-computers-do-pull-ups

If you were hoping for an answer to the question at the end of Episode #1, I’m afraid you’ll have to wait a little longer. It takes several episodes to lay enough groundwork before we can get there. So, for now, let’s step back and dig a little deeper.

The story begins in a crowded classroom in 19th century England. A young teacher named George Boole sat with a stack of schoolbooks and a head full of questions. People around him argued about numbers and planets and steam engines. Philosophers argued about the rules of reasoning. Boole looked at both conversations and wondered a simple, strange thing. What if thinking could be handled like calculation?

His first insight was stark. Any clear logical statement ends in one of two outcomes: true or false. Boole chose 1 for true and 0 for false. Suddenly every statement could be represented by a single number. “Milk is white” becomes 1. “Water contains gold” becomes 0. It may seem trivial, but this was the first time in history that a logical statement had been expressed mathematically.Then came the deeper question: can composite statements also be expressed mathematically? Everyday speech is full of conditions like “I will take an umbrella to office if it is cloudy.“ If you closely observe there are two statements in it:

A. I will take the umbrella to office

B. It is cloudy

What ties them together is not a new kind of truth, but a connection between truths. Boole’s great labor was to find the smallest set of connections that could express any compound statement. He proved that only three are needed: Inclusion, Choice and Exclusion: AND, OR, and NOT. With these, every logical structure — from the simplest condition to the most elaborate argument — can be built and manipulated like algebra.

The basic rule is simple:

– AND is true only when both statements are true.
– OR is true when at least one of the statements is true.
– NOT reverses a statement: if the statement is true its negation is false, and if it’s false its negation is true.

The symbols for these three are:

Returning to the umbrella example, the statement “I will take an umbrella to the office if it is cloudy” becomes:

A+B’ = 1

Let’s decode it:

So the expression says: “Either it is not cloudy, or I take an umbrella.”
That is exactly how the original sentence behaves when you put it into Boole’s symbolic calculus.

The entire maze of conditions in everyday life reduces to combinations of these three operations. That’s the heart of Boole’s discovery: the whole complexity of reasoning sits on a tiny, elegant base. With those moves he turned sentences into symbols and reasoning into calculation. This branch of mathematics is now called Boolean algebra, in his honour.

Interesting. Isn’t it? Let’s try a trickier, real-life rule.

I go through the intersection when it's green, but I stop if there's heavy traffic ahead even with a green light, unless I'm already in the intersection when the light changes.

We have to first identify all the statements and give a symbol to each of them:

Each of these can be 1 or 0 — think of 1 as “Go” and 0 as “Stop.”

Now we combine them with Boole’s three connectors. This sentence actually hides four separate statements, and all their possible combinations determine whether you go or stop. The neat way to see this is to lay everything out in a truth table: list every possible pattern of green light, heavy traffic, and being in the intersection, then compute the outcome for G using the rules of AND, OR, and NOT. It’s like a recipe — each row of the table is one set of ingredients, and the last column tells you the dish you get (“Go” or “Stop”).

You can build the expression yourself or just follow the table below. Either way, you’ll see how even a complicated instruction in natural language becomes a clean Boolean rule once you break it into its pieces.

So don’t forget that when you decide whether to cross the street, book a flight, or choose what to eat, you’re quietly evaluating a Boolean expression! Yes, you are doing math all the time!

And then another curious mind posed an even bolder question: if logic can be turned into mathematics, could mathematics itself be turned into something a machine can do?That, however, is a story for another episode — stay tuned.