Learning for the sake of learning is vastly less impactful than learning for the sake of accomplishing something. As I've gotten older, the scale of the personal projects I've been willing to take on has grown exponentially, and my ability to absorb new knowledge to support those projects has grown as well.

Learning with examples is crucial. Personally, I find it easier to grasp mathematical concepts when I encounter them in various real-life scenarios. Similarly, understanding the rationale behind the introduction of a specific concept or definition in a field helps me comprehend it better.

To me, mathematics is a carefully crafted compilation of concepts devised to provide precise descriptions (like cross product, dot product, determinants, derivatives) or simplify and generalize ideas (such as linear maps, wedge product).

In essence, mathematicians create these tools and then analyze them to uncover similarities and patterns.

Would math "exist", if there were no "sensory inputs" at all?

First thought: it helps if you're using what you've learned in some way. Maybe find someone to talk to about what you're learning. (Rubber-duck learning?) Imagine you're teaching someone, and trying to summarize what you've learned.

It might help to read two books on the same topic -- just so things you read in one give you context for the other. (Someone told me they retain information better when it melds with topics they already have some long history with...)

I've also found talking about what you just learned is very helpful. If you don't have an interlocutor available, ChatGPT is a good stand-in.

Starting from 40 I feel life is mostly about trimming things down instead of stacking them up.

Essentially few matters in my life.

Apparently reading aloud does help retain information. https://www.medicalnewstoday.com/articles/320377

Here's something I've done in the past when trying to get my head round a new programming paradigm. Start learning it in late October / early November and then you should have just enough knowledge at the start of December to tackle this year's Advent Of Code with it.

Note - if you haven't done all the previous years then you don't have to wait till the end of the year :)

Keep notes and write a diary. Writing solidifies knowledge in your mind. It also helps to clear your mind and organise your thoughts.

This might not apply to you but my recent experience of getting my memory back might be interesting, if nothing else.

I'm nearing my 40s and have been seeing a steady decline in my ability to learn. My short term memory was the real problem I couldn't keep enough in there to put ideas together. I couldn't focus on or retain new information. Some was explained by stress. I had a lot going on with work, a new family with a young baby and a dying parent but it was more than that.

At the same time my wife was having trouble sleeping. Since the birth of our first child she was not able to sleep, like she used to. Now every noise would wake her up, especially her snoring husband. My snoring was always bad but she used to be able to cope with it.

So I started talking to the doctor about my snoring. He suggested I try a mandibular repositioning device. It didn't fix my snoring but something happened to my memory. Approximately a month of using the device and my memory began to improve.

The mandibular repositioning device hurt and didn't help my wife sleep so I pressed on. The next step was to work with a sleep clinic. They got me tested for sleep apnea. It turned out I was at the upper end of mild on the apnea index.

The next step was a CPAP trial. They sent out a machine and I was to try it for a month to see if it improved my sleep and snoring. It was not fun. The thing was terrible to sleep with. It hurt, I kept waking up, it filled my stomach with gas and I felt worse than I did with the mandibular repositioning device.

I kept going because it did stop my snoring, so I had hope. Every second day I'd call the clinic and they would mess with the settings on the machine. Almost a month in something switched. I could sleep through the night.

Then my memory and focus really returned. I can now learn at the pace I was used to as a student in my 20s. I could structure my thinking in a way I wasn't used to. My abilities at work improved beyond what I thought possible. Oh, and my wife can sleep next to me. I don't snore, move in my sleep or get up to use the loo anymore.

After this I've been shouting about it everywhere I can. Sorry, if my CPAP evangelism is a bit much.

Interestingly as I reflected on the change I remembered something I'd read in "Coders at work", Douglas Crockford reported something similar with his apnea.

Here is the quote:

Seibel: Do you think that programming is at all biased toward being young?

Crockford: I used to think so. A few years ago I had sleep apnea, but I didn’t know it. I thought I was just getting tired and old, and I got to the point where it was so difficult to concentrate that I couldn’t program anymore because I just couldn’t keep enough stuff in my head. A lot of programming is you keep stuff in your head until you can get it written down and structured properly. And I just couldn’t do it.

I had lost that ability and I thought it was just because I was getting older. Fortunately, I got better and it came back and so I’m programming again. I’m doing it well and maybe a little bit better now because I’ve learned how not to depend so much on my memory. I’m better at documenting my code now than I used to be because I’m less confident that I’ll remember next week why I did this. In fact, sometimes I’ll be going through my stuff and I’m amazed at stuff that I had written: I don’t remember having done it and it’s either really either awful or brilliant. I had no idea I was capable of that.

https://wm-help.net/lib/b/book/2520193410/5

I had a similar experience with CPAP, but also not eating after 5 PM did wonders for my sleep.

Unfortunately I don't abide by that 5PM rule very often, but without a doubt I sleep much more deeply and have more vivid dreams when I sleep on an empty stomach.

This is a very interesting thing I´d never considered. But looking back, it does seem to make a lot of sense. Iĺl try it out!

Yeah especially if you suffer from Reflux. The less in your stomach the better.

I don't try. The things I use enough to remember, I remember. The things that I don't, I can Google.

I mean, I learn whatever interests me. I retain whatever I retain. I don't worry about making that happen; I just let it happen or not happen.

If you're sonsick you don't learn and retain information, double and triple down on your health. Make bigger and bigger responsible, progressive changes til th

sonsick?

I’m gonna guess “finding”.

I learn by doing. So If I want to learn something new, I give myself an easy(but trickier than whatever beginner tutorial exists) project, and just get on with it.

Monks and scribes recorded them in illuminated manuscripts on vellum.

I expect many of these will be readable long after HN has vanished into the ether.

Repetition