If you have used Matlab, Or R, there is a huge range of data science that only really requires an undergrad in math. Hospitals that run their own Clinical Trials usually have a consistent need.

Really you’re eligible for anything statistics related, and there is a lot out there. Some job titles to look for:

1. Data Scientist
2. Statistical Analyst
3. Statistical Programmer
4. Signal Analyst (this is usually government related)
5. Data curator

The math is describing reality - but that’s why I highlighted that the math predicted it long before there was experimental evidence.

From what we know about the quantum realm (my physics professor liked using that description, as if it’s a whole different existence), it appears that it’s actually the opposite: reality is obeying the math. Consider how wild that is - particle interactions are doing what they do because of how mathematics works. Something that we humans came up with to describe observations.

So the way I “understood” the spin-statistics theorem is that it’s basically this:

A given particle with a given intrinsic spin has a direct relationship to a collection of the same particles as a consequence of quantum math. Yeah. Just “it’s related.”

Proving that math is really freaking difficult and you need to use relativistic quantum field theory. I think it was Richard Feynman who said “We apologize for the fact that we cannot give you an elementary explanation.”

Actually when I graduated there was another professor (can’t remember his name) who was discussing his frustration with how they still can’t explain it without all of QFT steps.

Basically, this is where the shared attitude of “the more you know about quantum physics, the more confusing it becomes.”

It’s a lot more complicated than that even.

Pauli Exclusion Principal is that two or more identical particles of half integer spin cannot occupy the same quantum state. So two electrons in an orbital must be made of a +1/2 and -1/2 spin. This is evidenced by observation, but the prediction was made long before that.

This is because the total wave function for fermions is antisymmetric (bosons, like the photon, are symmetric). It’s sort of hard to describe how this works without paper and pen, but essentially there is different formula of solving a wave function. A symmetric wave function is a sum, and an antisymmetric wave function is a difference. The issue arises when you have two identical particles - symmetric functions can be any state as it results in a solution >0. If you have an assymetric function of two identical particles, the result is 0, which isn’t a valid state.

The very uncomfortable part of physics is here: when we ask “why” the answer based on the math and the observation is quite literally “because that is the way math works.” It’s fundamental - just like x * 0 = 0.

That works too. It just needs to get caught in a single prop for it to go down

You know, there’s no reason we can’t have anti-drone fireworks.

They don’t really even need dangerous amounts of explosives, they just need a strong net to get caught in a prop.

Drones are pretty damn slow if you compare it to a rocket.

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Yes - but more importantly, I am so happy reading the rest of the comments here: I’ve truly found my people.