This is not a pipe.

Not a pipe

It’s an image of a pipe.

Similarly, this is not the number one:

$1$

This is a symbol which evokes the number one in your mind. The true number one is our name for an abstract concept. It is how many noses you have on your face. It is how many biological fathers you have. It is not some frail collection of pixels on a screen.

Human language is historically bad at making this distinction. We say that $1 \frac{2}{3}$ is written using three numbers. Yet we also say that $1 \frac{2}{3}$ is one number found partway between $1$ and $3$. It is very easy for humans to mix up the symbol with what the symbol means.

Similarly, these scribbles on the screen that you are reading are not words. The true words are a sentiment being passed between you and I. They are qualia, something which these squiggles strive, but fail, to fully capture.

It is easy to forget this distinction. It is easy to say “zero is nothing” rather than “zero means nothing”. Blurring this line is a road filled with land mines. Do not mix up the word “truth” with that which it symbolizes.

Vi Hart explains this in the midst of a fun video about cutting space and time:

It is evolutionarily advantageous for a human mind to blur these lines. When you hear someone shout “Tiger!”, you shouldn’t have to try and remember what sort of real thing your friend associates with those particular syllables. When your friend shout’s “Tiger” you’d better feel the meaning and run.

This is great for surviving the ancestral savannah but confusing when you’re trying to understand how reality works. It’s easy to think that physics is about manipulating symbols in equations, when actually the equations are just one particular representation of the real rules. It’s easy to believe that $2$ is two, instead of remembering that $2$ is a symbol. The real two is how many eyes you have. The real two is how many parents it takes to make a child.

Two is a name for an abstract property – $2$ is just the symbol. Don’t mix up symbols with that which they symbolize.