I spent a lot of time in the previous section establishing the argument that the properties that define information vectors can be represented mathematically. Why is it so important? Because:

The comparison of similar defining properties of information vectors is a quantifiable, not arbitrary. The comparison of red to dark red is quantifiable and mathematical. You may disagree and think “that’s not true, I just consider dark red somewhat darker than red”. But later in the document I will discuss how “somewhat darker” is really a concept with a mathematical foundation. Since information vectors can be composed of other information vectors, each with its own defining properties, there are many comparisons that can be made. When Billy sees his first apple and his first fire truck, he can compare the objects on their similar redness (as we call it conceptually) and the difference in the size of the objects. When Billy sees his first penny and his first F-22 Raptor jet fighter plane, there aren’t many properties he can compare across those two objects. So from an information vector perspective, those objects aren’t strongly related. That factor will come into play more as we delve into concepts.

We have to prove that information vectors are mathematically comparable because:

I feel it is important to include this statement here although I am deferring most of the detail until the next chapter that involves concepts. In summary, this statement means that the building blocks of our intelligence rely on the many ways in which we compare information vectors. For example:

- We can compare sounds by the variation in their decibel level (volume) or wavelength frequency (pitch)
- We can compare objects by their measurable dimensions (size)
- We can compare objects by their variation in in 3D space (location)

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