There’s a convincing argument all numbers are imaginary. I’ve never seen a million of something in one place. Let alone a billion, or a trillion. Root 2? Get outta here. e, pi. Basically any useful number already has the property that i has (suspending disbelief until we can get rid of it again somewhere later down the line)
Pi can be seen in real life (obviously not with full precision, but close enough). Simply make a 1 cm rod on a lathe and measure its circumference, and you’ll see it’s ~3.141 cm
The same goes for root 2. Simply measure the diagonal of a 1 cm square
Not sure where you’d see e in real life, though (excluding as the base of an exponential, because any exponential can be trivially rewritten with any base)
@glibg10b@Rugnjr I ran this past my (engineer) SO and, after grumbling at being nerd-sniped, he came up with something you could measure to derive e.
He said a capacitor filled through a resistor for a time unit equal to “RC” gives you a simple formula that solves for e.
I think I may have got that right? Most of this is gibberish to me, but he gesticulated wildly and held up random electronic things at me so I think he had something.
I’m a computer engineering student and you remembered correctly, it reaches the final voltage times (1 - 1/e) at the time given by the time constant. Though technically e is the base of an exponential in this case
Mathematically, the thing about e that causes this is the fact that d/dx (ex) = ex. In simpler terms, if a car is driving in a straight line and its speed increases e (2.71) times per second, then its distance travelled always equals its speed (plus some amount that doesn’t change) (ignoring units)
The other cool property about e that I know of relates to complex numbers, but I don’t think I can explain that in a way that’s easy to understand
There’s a convincing argument all numbers are imaginary. I’ve never seen a million of something in one place. Let alone a billion, or a trillion. Root 2? Get outta here. e, pi. Basically any useful number already has the property that i has (suspending disbelief until we can get rid of it again somewhere later down the line)
You see pi every time you see a pie.
Pi can be seen in real life (obviously not with full precision, but close enough). Simply make a 1 cm rod on a lathe and measure its circumference, and you’ll see it’s ~3.141 cm
The same goes for root 2. Simply measure the diagonal of a 1 cm square
Not sure where you’d see e in real life, though (excluding as the base of an exponential, because any exponential can be trivially rewritten with any base)
Oh sure it’ll be close to pi. It could even approach pi, but it won’t be pi. Coastline problems abound
@glibg10b @Rugnjr I ran this past my (engineer) SO and, after grumbling at being nerd-sniped, he came up with something you could measure to derive e.
He said a capacitor filled through a resistor for a time unit equal to “RC” gives you a simple formula that solves for e.
I think I may have got that right? Most of this is gibberish to me, but he gesticulated wildly and held up random electronic things at me so I think he had something.
I’m a computer engineering student and you remembered correctly, it reaches the final voltage times (1 - 1/e) at the time given by the time constant. Though technically e is the base of an exponential in this case
Mathematically, the thing about e that causes this is the fact that d/dx (ex) = ex. In simpler terms, if a car is driving in a straight line and its speed increases e (2.71) times per second, then its distance travelled always equals its speed (plus some amount that doesn’t change) (ignoring units)
The other cool property about e that I know of relates to complex numbers, but I don’t think I can explain that in a way that’s easy to understand