# Your Idea Space has Zero Measure

Your idea space consists of your thoughts, emotions, sensations, perceptions and the empty set, . Your idea space is unique to you, uncountable, and has zero measure

Figure 1. Your idea space consists of your thoughts, emotions, sensations, perceptions, and the empty set, ∅.

Thoughts consists of words, pictures, memories, daydreams, songs, etc. Emotions involve feelings of pleasant, unpleasant, neutral, and everything in between. Sensations include the classic five: touch, sight, sound, taste, and smell. Perception is one’s ability to recognize something. For instance, a pen is a pen. A computer is a computer. Together with the empty set, , or nothing, these elements make up your idea space.

## The Empty Set, ∅

The empty set is nothing, Ø. An easy way to understand it is as follows: Imagine you have three apples. Each apple has distinct characteristics that can be used to describe it (Table 1).

Table 1. Apple characteristics.

Clearly, this table is missing entries. That’s the empty set, Ø! Your mind may quickly try to fill in those gaps by thinking something like, the third apple is yellow! However, you and I will never know what that information is, because it is missing. There’s simply nothing there.

Now extrapolate the same concept of the empty set, Ø, to the idea space. It is simply a place where no ideas exist, or the space between breaths. For instance, by focusing on the breath for a short period of time you can experience emptiness of thoughts.

## Zero Measure

The regular, or Euclidean, distance between any two points is simply $$x-y$$, or $$d(x,y)$$. An object has zero measure if the distance between any two points is less than $$\epsilon$$ for all $$\epsilon>0$$. In other words:

$d(x,y)<\epsilon \textrm{ for all } \epsilon>0.$

Figure 2. Definition of zero measure.

The outer measure of a zero set is $$0$$. The outer measure of the empty set, Ø, is also $$0$$. Thus, zero and nothing look the same. For instance, we can make a pen smaller, and smaller, until it has zero measure. At which point, it looks like the empty set, Ø: nothing.

Figure 3. A pen with zero measure looks like nothing.

To be clear, $$0 \neq Ø$$! Although the two look the same, behind an object of zero measure can lie uncountable depth, like your idea space.

Figure 4. Although zero looks like the empty set, they are not the same.

Your observable universe is a giant sphere centered on you where everything you see is in the past. Why? Because it takes time for light to travel from point A to point B, even when traveling at $$186,000$$ miles per second. Your observable universe is filled with celestial objects, like galaxies, stars, planets, and humans. Since everything you see is in the past, the edge of your observable universe is its beginning: The Big Bang.