A number is an idea. Maybe, but what is an idea?

Plato believed that all ideas were things - platonic forms as they are now called. Circles existed in the true form in the realm of forms, as did all the numbers.

The representation of a number is certainly a thing. The pixels that are on the screen are things. These pixels exist independently of whatever form they may correspond to. That's the key, isn't it? Do numbers exist independent from our own minds?

So what does exist that is dependent on our minds? Emotions, the labels associated with colors. Some argue that values depend on our mind rather than being universal absolutes. The idea of Beauty is either an independent Platonic form or a dependent idea.

But what about numbers? Pi is part of the structure of the universe. The ratio of the circumference to the radius does not depend upon a human mind to discover it. We did not invent pi: we discovered it.

If our minds worked differently, we would have discovered different ideas. But numbers - they are something different. Is it possible for some mind to think about numbers in different ways? Would a completely alien mind still recognize pi? or other numbers? Numbers transcend opinions and dependent ideas.

Would an alien mind find the universal constant of pi? Would the being understand one and zero? There is something deeper that you and I think than the patterns of of neurons firing when we hear 3.14159...

A number is a thing.