>Pi is considered a priori knowledge because its value is inherent to the geometric properties of a circle and can be known independently of empirical observation.
What does this say about the nature of reality and the relationship between mental and physical?

>>16732200 (OP)
Nothing.

>>16732201
>Nothing.
I assume you're a Zen master who is riddling me with a koan. Your nothing is not trivial but profound. Please teach me master.

>>16732200 (OP)
>we totally knew about X before we knew about X
what more retardation will mathematicians come up with next?

>>16732200 (OP)
>properties of a circle
FOOL!!! circles do not exist

Nothing deep or meaningful. Relationships between arbitrary, but well defined, things are knowable within the constraints of how you defined them.
Pi being the ratio of circumference to diameter is a natural byproduct of how we defined these properties of a circle. So long as you maintain a consistent logical framework.
We don't need to subscribe to any form of Platonism or whatever to establish this as true

A priori is mostly BS imo. Circles are an abstraction from an empirical observation, completely a priori we don't even have language.

>>16732204
You had three cups of the finest wine in China and yet you still say you haven't moistened your lips.

>>16732482
>finest wine in China
Imported from Burgundy, no doubt.
>haven't moistened your lips
I prefer Borduex.

>>16732200 (OP)
>What does this say about the nature of reality
That this equation postulates the entirety of Pi, and that the rational number sequence is incapable of fully equating it. Thus the number 1, to which this sequence is defined by, is an unnatural number. *That* is thinking in base-Pi, 1 becomes a transcendental approximation.

>and the relationship between mental and physical?
Which is a perspective of Number Theory few ever even notice exists.

>>16732200 (OP)
Simply means the mind is primary before matter