# Algorithm | Echo

Clear and distinct ideas. Chronicle of Luc de Brabandere.

I know, **the word is a little ugly**. It could be the name of a particularly difficult musical instrument designed for the best pianists, or a sea salt-based medicine designed to stabilize heart rate. But this is not so.

In the spirit of this column (“algorithm” is the fiftieth word analyzed), let’s begin by offering a definition.

Algorithm a** a method of achieving a goal with a finite number of distinct steps**. Consciously or not, this is what we do all day. Whether it’s mowing the lawn, finding maple syrup in a supermarket, or choosing a vacation spot, we have work to do. Algorithm a **formalized and available “instructions for use”** it avoids having to start from scratch when any problem or desire arises. It can be individual, cultural or universal.

The one who says “method” says “odos”, that is, the way. It’s not random because it’s using an algorithm **follow the marked route **and progress in leaps and bounds. It is a codified, structured, memorized form of knowledge and therefore reusable or transferable. The** tiramisu recipe** it’s an algorithm like a sequence of instructions that descales a coffee machine.

## If then…

These two examples from the culinary world show the simplest case, the “straight line” algorithm, which we faithfully follow one after the other. The path is the same for everyone and you reach your goal without asking too many questions. But this situation is ultimately rare because **Often, as soon as you want to achieve a goal, many questions arise**.

Determining the best way to reach the top of Mont Blanc from Luxor depends on your time and budget, your environmental beliefs, your health and political conditions, your temperament and physical condition, the people who might be traveling with you, and more. it will depend. **The initial question will generate dozens of other questions, often of the “If, then” type.**

An algorithm is a method that achieves a goal through a certain number of different steps. Consciously or not, this is what we do all day.

Most algorithms are full of such forks, which involve multiple options. **We see it when he fills out his tax form**: “If you have no property income, then go to box 17” and so on.

But **There are surprises in the logic of “and” and “or”.**. All you have to do to convince yourself of this is to compare the following two lines of reasoning… and look for the error.

If I’m 18, I can vote.

If I’m 18, I can drive.

So if I’m 18, I can vote and drive.

If I have 4 euros, I can buy a newspaper.

If I have 4 euros, I can buy a sandwich.

So, if I have 4 euros, I can buy a newspaper and a coffee.

## Convergence

Algorithms are like any method, some are more efficient than others.

Even in the simplest case, when “if, then” questions do not arise, **some algorithms are faster than others**. Mathematicians say they “converge” faster towards their desired goal.

In 1674, Leibniz developed an extremely simple formula for calculating pi.

Pi = 4(1 – 1/3 + 1/5 – 1/7 + …)

**The method is correct, but the convergence is very slow**, enough to get 300 terms… to two decimal places, the famous 3.14! We understand that the method was not very successful at a time when the calculating machine was practically non-existent. **The science of algorithms is, among other things, the science of their efficiency. **The progress achieved in the calculation of pi is a great example of the creativity of mathematicians in the design of algorithms.

In more complex cases of “bifurcation” algorithms, the issue of convergence emerges more sharply.

In “if-then” fork algorithms, the number of possibilities becomes large very quickly, then combinatorial explosion.

for** Alphabetize five hundred business cards**, one method might be to take them one by one and classify them in the correct place each time from first to last. But it will go faster by starting with first sorting by the first letter, then sorting each of the packets individually before putting them in alphabetical order one by one.

## Combinator explosion

In “if-then” fork algorithms, **the number of possibilities is increasing rapidly**, then a combinator talks about explosion. If in Scrabble an algorithm can still confirm with certainty what the best move to play is, in chess it is no longer possible. If I move that pawn, he will move his rook, and I will move my queen… But if I don’t move my pawn, he…** “If, then” quickly becomes “if, then, then, then…” and the algorithm goes crazy.**.

This brings us to a third distinction, this time between algorithms that can achieve a particular goal and others that can only approximate it. **The goal is no longer to optimize, but to find the most satisfactory solution possible.** This is the case with the Compostela pilgrim who chooses what he puts in his backpack, or the bookseller who wants to make his display as attractive as possible. They will never be able to know for sure whether they made the best choice.

As you can see, I am coming to the end of this column devoted to algorithms,** without using the words “computer” or “Internet”.**. This is clearly not a coincidence.

**Luc de BrabandereBusiness philosopher and founder of CartoonBase agency**

*All Écho columns from 2017 to “Clear and Dissent” are available at www.lucdebrabandere.com.*.