Sunday School

[UnseenParticipant]

Here’s another weird number from mathematics. It’s called “i” (the letter between h and j in the standard alphabet). I wasn’t absolutely sure mathematicians consider it a number, so I asked the Gemini AI “is i considered to be a number in mathematics?” and got this reply:

Yes, i is considered a number in mathematics.

While it might seem unusual at first, “i” is a fundamental concept in mathematics.

It’s known as the imaginary unit and is defined as the square root of -1.

This might seem counterintuitive, as no real number can be squared to give a negative result. However, the concept of imaginary numbers allows us to solve equations that would be impossible with real numbers alone.  

Imaginary numbers are crucial in many areas of mathematics, including complex analysis, electrical engineering, and quantum mechanics.

[_Robert_Participant]

Unseen wrote:

Here’s another weird number from mathematics. It’s called “i” (the letter between h and j in the standard alphabet). I wasn’t absolutely sure mathematicians consider it a number, so I asked the Gemini AI “is i considered to be a number in mathematics?” and got this reply: Yes, i is considered a number in mathematics. While it might seem unusual at first, “i” is a fundamental concept in mathematics. It’s known as the imaginary unit and is defined as the square root of -1. This might seem counterintuitive, as no real number can be squared to give a negative result. However, the concept of imaginary numbers allows us to solve equations that would be impossible with real numbers alone. Imaginary numbers are crucial in many areas of mathematics, including complex analysis, electrical engineering, and quantum mechanics.

Yes, besides giving solutions to otherwise unsolvable polynomials, imaginary numbers (EE’s use “j”, because “i” is for amps, lol) gives us the “complex plane” and a shorthand system of “phasors”. This trick reduces complex differential circuit equations down to simple arithmetic. What would take like three pages of equations becomes just a few lines. Of course, now I am sure they always use computers to model circuits, but they should make the students use all three methods, so they understand how complicated the physics of a very simple circuit with resistors, caps and coils really is.

[StregaModerator]

@_Robert_
I lived (in sin, haha) with an electronic engineer in the early 80’s.

There are two memorable elements of this story

1. He had one contract building circuit boards that would used in a satellite by the Ministry of Defence in the UK. I had to sign the Official Secrets Act in case he talked in his sleep. Anyway there was a time pressure and he brought 30 boards and pieces home to assemble them over the weekend. So a group of us sat around in the bed-sit and assembled the boards (without soldering) copying the one model he’d put in the middle. He took all 30 back to work, apparently no errors, and that was that.
Except now, when I look up in the sky, I’m pretty sure my fingerprints are on a satellite, roving around up there!

2. Everybody brought him their broken toasters to fix.  He stacked them in a corner and when someone would ask how the toaster was going, he’d hand it back mournfully, saying he’d tried but there was nothing he could do.

Apparently electrical engineers aren’t interchangeable with standard electricians.

[_Robert_Participant]

Strega, that’s cool your prints are in orbit! Yeah, toasters are not my forte either. I did fix an old radio for a friend’s boss. The problem was so basic (broken power wire), I didn’t mention the issue and he got some free brownie points.

[Author]

Posts