Don't worry, apo, you probably didn't miss any philosophical insight of maths.... just calculations and more calculations.
On to a bit more of philosobabble...
To me, it's always been easier to imagine numbers as lying on a straight line... like an axis.
The kind of line that has all the numbers in it. Infinite numbers just between 1 and 2, and pi, somewhere between 3 and 4.
pro tip: if you're doing mental calculations that require pi, approximate it to 3
That said, I've always imagined that numbers just exist. All of them. Not as physical entities, of course, but as abstract ones. Sure they require an intelligence to become aware of them, but they're just there, regardless of the physical world... Just like theists would like their god to be.
You probably can tell that I'm not a big fan of the uncertainty in the Schrodinger's cat dilemma.
The cat is either dead or alive, regardless of anyone's awareness of it. Real numbers just exist, regardless of people's awareness of them.
The significance of the particular number someone defined as pi as the "ratio of a circle's circumference to its diameter" was manifestly discovered, inferred, determined by an intelligence capable of performing that ratio.
I'm not sure if this goes against anything I've written in this thread previously, but, if it does, it just comes to show that you guys managed to change my mind.
On to a bit more of philosobabble...
To me, it's always been easier to imagine numbers as lying on a straight line... like an axis.
The kind of line that has all the numbers in it. Infinite numbers just between 1 and 2, and pi, somewhere between 3 and 4.
pro tip: if you're doing mental calculations that require pi, approximate it to 3
That said, I've always imagined that numbers just exist. All of them. Not as physical entities, of course, but as abstract ones. Sure they require an intelligence to become aware of them, but they're just there, regardless of the physical world... Just like theists would like their god to be.
You probably can tell that I'm not a big fan of the uncertainty in the Schrodinger's cat dilemma.
The cat is either dead or alive, regardless of anyone's awareness of it. Real numbers just exist, regardless of people's awareness of them.
The significance of the particular number someone defined as pi as the "ratio of a circle's circumference to its diameter" was manifestly discovered, inferred, determined by an intelligence capable of performing that ratio.
I'm not sure if this goes against anything I've written in this thread previously, but, if it does, it just comes to show that you guys managed to change my mind.
