You have to surround the 2 with ^s:

R^2^ = 0.11

R^2^ = 0.11

Note that this'll bork if you put spaces between the carets: ^2 2^ gives you ^2 2^

That's how a standard error with normal-ish data works. The more data points for the estimation of a conditional mean you have, the fewer of the data point will be within it. For a normal distribution, the SE=SD/√N . Heck, you can even just calculate which proportion of the distribution you can expect to be within the 95% CI as a function of sample size. (Its a bit more complicated because of how probabilities factor into this, but for a large enough N it's fine)

For N=9, you'd expect 26% of data points within the 95% CI of the mean For N=16, 19% For 25, 16% For 100, 8% For 400, 4% Etc

Out of curiosity: What issue did you take with the error margin not including most data points?

I don't think this is neuroplasticity, as much as it is having a broader experience to bring to bear. I have so much knowledge and experience with a variety of things that I can apply and relate to new skills to learn things fairly quickly.

I also find there's a ceiling on my abilities, like you mentioned. I'm never going to learn something to the same depth as someone who learns it as a kid and carries it forwards, things just don't seem to sink deep into intuition and instinct like that, but I can certainly pick up something well enough to enjoy it and enjoy the process of improving at it. I love learning new skills and pushing myself, and I don't mind the idea that that's the way to age gracefully and stay sharp.

A lot of things are easier to learn when you have a base foundation.

Also, a lot of skills have interrelated mental pathways, so once you have enough exp with one, learning the other means, you are actually plasticising your brain, less than what you would have, had you learnt the other skill without knowing the first.

Played a reflex-based video game against a teenager lately?

I feel like the first time you notice that you have lost some mental capacity is a middle age right of passage.

That's stupid, though. If you can explain 11% of the variance of some noisy phenomenon like cognitive and behavioral flexibility, that's noteworthy. They tested both linear and quadratic terms, and the quadratic one worked better in terms of prediction, and is also an expression of a meaningful theoretical model, rather than just throwing higher polynomials at it for the fun of it. Quadratic here also would coincide with some homogenizing mechanism at the two ends of the age distribution.

This. I could have produced a more insightful scatter plot with a barn door and a twelve gauge.

I've been there and all I can say is that the brain is a miraculous organ and can heal really well from a lot of trauma. You just have to stop damaging it, learn how to work with your brain rather than having your brain work for you, and exercise it. Challenge yourself to learn an easy skill, then another, then another.

I have no scientific basis for this, but my suspicion is that what you do with your brain is more important to cognition than whatever raw intelligence you start with. the more languages you study, the more music you play, the more subjects you study and skills you develop and hobbies you tinker with and deep conversations you have... you learn to learn, you learn to think, it all gets wired up and cross-connected and you become more than the sum of your parts.

how much decline is truly biological vs. being stuck in a rut?

also there's nootropics that could be helpful for concussion recovery/etc. but they haven't been too well-studied, there's many different ones with different sketchiness and sources aren't always trustworthy... but piracetam (iirc) is actually prescribed in the EU for recovery from brain injury, and it's fairly safe and well-studied. I'm not recommending it either way though.

From a completely unscientific but 'experienced' perspective I think the problem is that life just gets in the way as you get older, and you prioritize your own life rather than trying to learn.

Whether neuroplasticity means you can learn things later or not, the opportunity to learn things later just isn't there without effort.

Having a job, kids, a mortgage and no social obligation to learn in a structured and organized way probably impacts you more than anything neurological.

As long as you continue to learn new things, then no, it doesn't become harder with age. In fact, studies show that people who are lifelong learners can actually increase their ability to learn as they age. Learning, for example, a foreign language in later years has been shown to be just as attainable as in childhood, and might even give some protection against dementia. Your brain can actually become more plastic as you age if you continuously push it to do so.

The idea that learning capacity naturally* diminishes with age seems to be a widely accepted myth (which may have roots in sociological and cultural biases), and the opposite may actually be true.

e: those biases and environmental stressors may also contribute to people becoming less able – or less prone – to try, though, and if you don't use it, you might lose that plasticity. So keep learning.

I started doing Capoeira and learning Portuguese with 40 years. I am fluent in Portuguese now after three years. My Capoeira skills are still pretty basic, but I progress and for the first time in my life I feel like I really have a grasp on any kind of sports.

I also changed from marketing to IT last year and I am getting really good at what I do.

It helps if you have a reference system for your new knowledge. I studied computer science which helps in my new job and I had French in school which helps with Portuguese.

So don't worry. Keep learning, avoid stress and drugs and prioritize getting enough sleep. You'll be fine!

Why does that fucking Thing require my Google account?