A person close to me had to deal with a concussion for years. Of course each situation is different. Also, I am not a doctor. We know this for a fact, that had he taken less drastic measures after the injury, he would have had to deal with less consequences. Moving, changing doctors, he remained unhappy for long. From what I know, he had far more trouble than you with his first doctor. I personally learnt something from his experience, that when there’s a chance that things can go very very wrong, avoiding or taking actions that would shake the status quo too much is a terrible idea.
The unfortunate fact is the possibility that some part of the cognition takes years to return. He appreciates how he has changed now. It’s been years. I think some of his changes are also due to aging and the hardship. In hindsight, alienating the company might seem like a very terrible idea for him. Fact is, if neither of you were injured, there’d be no such conversations. The core of the problem is the concussion and that is tough to deal with. His was very severe and led to a long pause in his career. As for the doctor, and reiterating that I am not a doctor, my understanding is that there’s little a new doctor can do beyond recommending practice sessions. Unless the science has changed very recently or medical practice is different where you are. Best of luck. Feel free to leave a way so I can contact in case there’s more I can share.
Remarks on Stability of Time-Varying Linear Systems. In Automatic Control. It is a relatively recent published paper, and not a note as I had originally thought.
This is not adding to the conversation. Your comment was my impediment in moving past the second page of the paper. Problem is, I never got to study foundations of measure theory, and presumed I could be wrong. Do you have any self-study recommendations, paper or concise books?
I was perusing Princeton’s companion to mathematics a while back. If I recall correctly, after describing the theorems, the author states that much is written about their implications and that there is not enough room to discuss them. It seemed fair to me.
People write many things on the internet, and it is still surprising to me how they choose to do that. I wouldn’t be concerned about most of it, particularly if it is about topics I know to be deep. I for one looked into some articles on the internet at some point, Godel or not, I made the mistake of thinking that they write what they knows of.
As for godel, I’m sure you can find contemporary math/philosophers.
Another example was in grad school in mathematics. I knew one particular thing was off but I couldn’t place it. A long time has passed since. Recently I came across a note from a math professor who had spent the time to go through all books covering the subject, and explains what everyone had missed. I agreed with him.
So asynchronous learning has a name. I was never as bright as these kids. I am older now in my 30s, and my life has played out so I kept on looking for a role model, and I met the first when I was 31. Now I know that I should have taken my option to do a PhD in a proper university, which I declined years back for financial reasons, and worked on some random research topic in a different school. Quite late now.
I have a close family member who is brighter than me. His family chose to not send him to gifted elementary school despite my objections. He is the top student in a gifted highschool now, and will be going to college next year at age 17.. and has been bored and semi-depressed for the last two years as far as I can tell.
My advice to him is to get in a major school and take it from there. I'm sure that's not hard for him. I feel like I should be able to suggest more but aside from life advice, I'm at a loss. Any pointers? I live here but he is in a country with barely mediocre support for special kids.