Introduction

In this post, we’re going to give you an idea as to why numbers and their representations are such a big part of AI. 

Numbers mean precision

If you want to know the quality of your experience at a restaurant, you could say something like “I found it to be pretty good.” Okay. But pretty good compared to what?

Alternately, you could answer the same question by saying “On a scale of 1 to 10, I give the quality a 9.” 9 means it’s better than 8, but worse than 10. So, 9 means the quality wasn’t perfect, but it was very nearly perfect. 

Just by assigning a scale and providing a number on that scale, you were more precise than just pretty good. Thus, numbers = precision. 

The number line representation

The picture above shows a number line. 

Now, the question is why do we put numbers on a line, like that? Well, there’s a lot more information in that line than just the numbers:

  1. There is a middle number, 0. 
  2. There are 1, 2 and 3 on the right of 0.
  3. There are – 1, – 2 and – 3 on the left of 0.
  4. The scale is – 3 to + 3.
  5. 3 is the highest score.
  6. – 3 is the lowest score. 

At this point, you might wonder why can’t 0 be the lowest score? Why the negative numbers? Well, you can think of it this way. Take the restaurant quality example again.

  • 3 = The food was perfect.
  • 2 = The food was nearly perfect.
  • 1 = The food was okay, could have been better.
  • 0 = It’s only a restaurant because people go there to eat. Otherwise, the food is ordinary.
  • – 1 = The food smelled a little.
  • – 2 = The food smelled a little and it made you sick.
  • – 3 = The food smelled a little, it made you sick and you found cockroaches in it. 

Notice here that: 

  • 1, 2 and 3 highlight things that added to the experience. This is why they are positive scores.  
  • – 1, – 2 and – 3 highlight things that took away from the experience. This is why they are negative scores. 
  • 0 is sort of a baseline. Neither positive nor negative. Nothing good to say, and nothing bad to say. Just the baseline. The bare minimum. 

As you can see, a number line is a way to give more meaning to the numbers. The numbers make the scores precise, and the scale (0, negative and positive) lets you compare and contrast. 

The coordinate axes representation

In the previous example, we talked about a number line representation for restaurant quality scores. Those scores only talked about the food. But what about service?  Service is part of restaurant quality too, isn’t it? So how can we represent service scores alongside the food scores? Well, we could use two number lines as shown below:

Notice that we’ve used a different scale for the service.  Not – 3 to + 3, but – 20 to + 20. We’ll explain the service scale. So:

  • 20 = 20 % tip (generous tip, the service was fantastic)
  • 15 = 15 % tip (pretty generous, the service was good)
  • 10 = 10 % tip (the service was not too bad)
  • 5 = 5 % tip (the service was a little sloppy, but they made it work)
  • 0 = No tip (the service didn’t deserve any additional tip)
  • – 5 = Take 5 % off the bill (the waiter put some water on my shirt)
  • – 10 = Take 10 % off the bill (the waiter made a stain on my shirt)
  • – 15 = Take 15 % off the bill (the waiter made a big stain on my shirt)
  • – 20 = Take 20 % off the bill (the waiter spilled it all on my shirt)

Again here:

  • 5 to 20 represent positive regard for the service. 
  • – 5 to – 20 represent negative regard for the service.
  • 0 represents neither positive nor negative regard for the service.

So, we use two number lines now because quality is not just about food, but also about service. But the two number lines don’t tell us whether there is a connection between food and service. 

So, let’s use a coordinate plane, instead of just two number lines, like so:

What do we have here? Well, it looks as though higher food scores = higher service scores. At food score = 1, the service score = 5, and as food score goes up to 3, the service score goes up to 20. So… there is a connection.

Let’s look at the service scale again:

  • 20 = 20 % tip (generous tip, the service was fantastic)
  • 15 = 15 % tip (pretty generous, the service was good)
  • 10 = 10 % tip (the service was not too bad)
  • 5 = 5 % tip (the service was a little sloppy, but they made it work)
  • 0 = No tip (the service didn’t deserve any additional tip)
  • – 5 = Take 5 % off the bill (the waiter put some water on my shirt)
  • – 10 = Take 10 % off the bill (the waiter made a stain on my shirt)
  • – 15 = Take 15 % off the bill (the waiter made a big stain on my shirt)
  • – 20 = Take 20 % off the bill (the waiter spilled it all on my shirt)

According to this scale, the explanations for – 5 to – 20 negative scores are quite specific. They all have to do with the degree of spillage on the customer’s shirt.

On the other hand, the explanations for 5 to 20 positive scores are not very specific.  The positive service scores are simply explained as sloppy or not too bad or good or fantastic. Nothing specific.

But now, we know the specifics. The cross-plot from before told us that higher food scores = higher service scores. So:

  • fantastic service = fantastic food
  • good service = good food
  • not too bad service = not too bad food
  • Sloppy, but made it work service = okay food

In this way, coordinate axes allow us to check for connections between scales. We can’t check such connections by just drawing individual number lines alongside each other.

2D, 3D and Multi-D (D is for dimension)

What we just discussed is a 2D coordinate plane, because there were only 2 dimensions: food and service. 

Similarly, there could be 3 dimensions, say, food, service and ambience. In that case, we’d need a 3D cross-plot like so:

There can also be more than 3 dimensions: 4, 5, 6… it goes on. Doing cross-connective math across multiple dimensions is where vectors, matrices and other linear algebra concepts come in. 

Summary

Thus, numbers and their representations are an integral part of AI. Data in the real world never has only 2 or 3 dimensions. It always has more than 3 dimensions. Still, understanding 2D and 3D can provide a good starting point. That’s why 2D and 3D planes are taught in schools before matrices and advanced linear algebra. Therefore, you should learn all the tricks of 2D geometry, 3D geometry and Linear Algebra, to really be ready to play with AI.