It's difficult to form a consistent take on AI if you spend all of your time buried in the hype cycle. And there's not much value in staying up-to-date with everything, what that does is it keeps you in a constant state of stress where you're constantly seeing news that worries you and by the time you think through and examine any piece of news something else is coming out to stress you out.
Consume news in chunks. If you don't believe that AI is going to tomorrow take your job away, you don't really need to be learning about what it can and can't do every single day. So start small, only read AI roundups once a week.
I'm not saying stick your head in the sand, I'm saying, what value can their possibly be in you getting AI news at a trickle every single day, rather than as a chunk at specific times with the addition of context.
In addition, if you are going to keep getting news, spend more time reading research papers and less time listening to breathless coverage on Twitter. There are exciting and impressive things that AI is doing, but there is also a very real hype cycle filled with motivated actors that are giving incomplete pictures of where the technology is, what it's capable of, and where they think it's going. Those people should not be your primary news source, people like Sam Altman should not be your primary news source about where the field of AI is. Understand that those people have extremely powerful motivations to hype their technology as much as is humanly possible -- regardless of where the technology actually is. If the technology is going to replace you in 3 years, they are going to tell you that it will replace you in 1.
My experience is that for many topics, not just AI, perspective helps with anxiety.
There are deeper questions you're asking, and I realize this is not actually advice on how to make yourself AI-proof. But if your goal is to understand the technology, understand where the risks are, understand what to worry about and what not to worry about, being constantly inundated in this stuff is counter-productive.
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Take a week, program something, don't think about or read about or look at AI news for the duration of that week. Install a browser extension to filter things out if you have to, block HN if you have to. Give yourself a little bit of space to breathe, realize objectively, if you take a week to breath the world is not going to fundamentally change over the course of that week and you're not going to get fired from your job over the course of that week. Then, do targeted research about the state of the AI industry, play with the technology to get a feel for what it's good at and bad at, come to some conclusions. Repeat, give yourself time to get away from it all.
If you are surrounded by people who are telling you 24x7 that you are going to be expendable, and are constantly throwing random pieces of information and demos at you without context, that is going to make you anxious regardless of anything else going on. If you are constantly getting news and updates about AI and you never time to digest anything or think through anything or just be away from all of that noise, then you never really have time to form plans or execute plans or do anything other than worry about what the next update is.
Even if AI is going to replace your software job eventually, living in the hype cycle 24x7 and being constantly stressed about it is a bad way to approach solving that problem.
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Also, just general advice regardless of the context that therapy is awesome and if you have good health insurance (which you may have as a software engineer) remote/telehealth sessions are often fully or mostly covered. I would avoid some of the weird startups that get advertised on podcasts, I would try for a licensed therapist from a medical practice, but if you can find a good therapist, this is exactly the kind of thing that can be helpful to talk about with one, both for digging into anxiety and for forming actionable plans around what you want to do next.