I’ll try to dig out Griffith for a better explanation but has to do with the fact that when you do a partial derivative you kinda lose information I guess?

(Idk, this is heady trying to make math into reality shit and I got a “c” in the class (for reasons partially related to other things) - also, there might be a way to do latex in markdown but I’m a bit too stoned to figure out, look up Schrödinger equation on wiki for maybe a helpful visual aid)

So go back how often we do implicit differential because it’s just an opportunity to look at how sexy the chain rule is. d(xy)/dx = xy’+x’y god fucking dammit that gorgeous

But okay. Think about position and velocity. Velocity is the derivative of position right (and also connected to energy - KE = 1/2mv^2 and E = mc^2 lol)

But since velocity is a derivative of position, it loses information. d(mx+b)/dx turns into m, no way to ever get b back with an initial value condition.

Then - omigod, when you take a partial - you have to ignore dependence. curlyd(xy+by)/curlydx turns into y and then things is really fucked if there was any dependence on y (ie, doing curlyd(xy+by)/curlydy would give you a different answer if you did that first order matters I guess)

There are some operators that are just exclusionary. Once you chose to look for one, you’ve discounted the chance of finding the other. Taking position versus taking energy/velocity. And then the fucky thing there is lots of shits mass is measured in eV/c^2

(I’m neglecting a proper discussion of momentum which is 100% where someone can come in and humiliate me. Please do so.)

The things I think the standard IQ test measures are more about a combination of an ability to quickly visually process information, and some elements of mathematics/logical thinking. I’ve scored +1.3~2.0 z score at various points in my life, and I think that the elements are that I can read extremely quickly and perceive math problems very quickly.

I’ve frequently worked with students who understand math and patterns very well, they just struggle with some element of the visual processing. They transpose numbers and letters when they see them, they switch up letters in geometrical figures, they get so overwhelmed with the stress of reading under eye or the clock that the words mix up and they miss the meaning.

They have the low “IQ” has measured. But they are capable of understanding the concepts - just not conveying them in the way that a standardized instrument can (or even should?) measure.

Ie; I don’t think it’s that great a measure beyond the sub 80 - which is a meaningful deficit and is acknowledged in the process of diagnosing for developmental delays/impairment. (It also can entirely be overcome in some cases with good support - like istfg as someone who has been paid to do this kind of thing the difference is that poor/middle class kids don’t get help)

I’m just scared all of the time. Any time I can get a leg up - I’m not protected. I can lose everything at any time.

If I end up homeless I’ll kill myself. I’ve been sexually assaulted too many times with a place to live. I can’t handle it anymore.

The standard p value in most psych research is 0.05, which means that you are willing to accept a 1/20 risk of a Type 1 error - that you are content with a 5% chance of a false positives, that your results were entirely due to random chance.

Keep in mind that you don’t publish research that doesn’t give results most of the time. Keep in mind that you have to publish regularly to keep your job. (And that if your results make certain people happy, they’ll give you and your university more money). Keep in mind that it is super fucking easy to say “hey, optional extra credit - participate in my survey” to your 300 student Intro Psych class (usually you just have to provide an alternative assignment for ethical reasons).

The issue with CBT is that there are populations that it is not effective for, but because it’s so easy to apply that’s what the majority of professionals are trained to (only) provide. It’s not trauma informed at all - there’s little understanding of how to treat trauma in general. (Considering that ~1 in 4 women and ~1 in 6 men experience sexual violence - why is treating sexual trauma not prioritized in research?)

I have issues with rumination, and CBT makes it substantially worse. I have told every professional that I have worked with that I know it does not work for me, and instead of respecting that, I get stealth attempts at it or they do end up giving me the fucking worksheets.

CBT also can work like a kind of gaslighting - ie, right now I’m terrified of leaving the house because my drivers license is now invalid by state law and EO - my county’s jail has killed quite a few people and a little gay trans man like me is not going to do well. I can’t “replace” that thought with a better one. Ranking how I feel about that just makes me more freaked out.

Artificial selection!

If you think that’s amazing - look up what bananas looked like before human cultivation. Basically any fruit or vegetable you eat is the product of centuries of humans carefully selecting what seeds to save and plant.

I think Sean’s video on the Bell Curve is the best way IQ has ever been interrogated and explored on the internet.

The purpose of IQ is to measure some sort of “g factor” which is a model of “general intelligence.” This was based on the idea that people who tend to do good at some kinds of tests tend to also be good at other kinds of tests.

The IQ test is “reliable” - ie its consistent and you’ll usually get the same results +/- an acceptable amount every time. However, there are lots of concerns about its “validity” - whether it measures what it purports to measure - ie, the “g factor.”

Of note is the “Flynn effect” - that performance on the test in the general population has been improving over time, so the test has to be renormalized. (IQ is a “normalized” test - so about 68% of the population needs to be within 1 standard deviation of the mean. I think standard deviation is about 15 - so 68% of people are going to score between 85 and 115.)

The question then would be - are people getting “smarter” or is it just that people are more adapted to taking tests on pattern recognition and mathematics/logical thinking? How would that measure the intelligence of a tribal person who has not seen abstracted geometrical shapes?

You can bring in alternative models of intelligence - like Gardner’s multiple intelligence - but then that doesn’t really have much of the psychometrics behind it.

(In general, I think a huge issue in psych research is a lack of critically examining the validity of psychometric instruments. It seems we often stop at being reliable.)

That’s wrong though, and further belies my point about math, and perhaps needing to take a quantum class before talking about it.

They are particles and waves.

I think we need to build a time machine to go back to Atlantis, to kill Ramtha and make sure that What the Bleep? never gets made.

Eigenvalues come from linear algebra. I think a difficult think in general with understanding them is often the failure of most middle/high school math teachers to teach matrix operations at all. (I’m guessing because matrix multiplication never shows up on SAT/ACT). Here’s a good explanation for the math on finding eigenvalues and eigenvectors.

But basically eigenvalues are going to be associated with certain matrixes/vectors. You take a “Hamiltonian” of a system, which is a way of describing possible energy values in the system, and it’ll give you a set of possible answers - pairs of eigenvalues and eigenvectors that describe the system.

In effect - you get things like the quantum numbers. That the 1st energy level has 1 subshell can hold 2 electrons, both with opposing spins. That the 2nd energy level has a 2s subshell that holds two, that 2p holds six. You get your n (1st energy level, 2nd so on as you go down periods of the periodic table), l (subshell - don’t get a SPeeDy F), m (which breaks down where in the subshell they are) and the need for opposing spins.

I don’t think you can get the intuitive feel/the “why” without the maths.

I guess I get frustrated when I have to teach algebra based introductory physics for similar reasons - everything makes so much more sense when you understand how the pieces fit together. (Why make them memorize d=d0+v0t+1/2at^2 when all that is integrating a constant twice? That you can set v=0 to find the time of maximum height, because you’re using a derivative to find a max! And then that helps you get why it works, and then even how to possibly explore non constant acceleration!)

I got really fucked over because I didn’t take linear (at all - advising in my physics department was non existent which lead to things like taking classical before Diff Eq lol) and so things like eigenvalues - which tbh I think is kinda the money shot - that things end up quantized and discrete - that took a while for me to get what that meant.

You can put together a version good enough for high schoolers with a laser pointer and some pencils.

To conceptualize though, it might be better to set up some sort of wave table - some sort of tub of water you set up the slits in, then observe the patterns of constructive and destructive interference. (That’s what I did with students.)

Tbh, I think no one who hasn’t solved the Schrödinger equation at least once (at least time independent), should be allowed to talk about quantum.

Like, the uncertainty principle is really really fucking cool when you understand why it works mathematically. But without differential equations and linear algebra, I don’t think it’s possible to really conceptualize what’s going on in quantum.

Idk, I always try to explain to students the deficiencies of the Bohr model and explain the significance of the electron cloud, but probability is hard.

One of my favorite things in quantum was deriving the “quantum numbers” they have you memorize in chemistry (if you don’t remember, you probably got a SPeeDy F) It’s beautiful to watch the way they emerge from the second order diff eq.