Lately there is some discussions about experts and expertise (note: I purposely write the title of the blogpost in a different way). Let me begin with myself (because I prefer not to say much about others). What would I be an expert on? Since my PhD is on quantization, I suppose I can pret-end myself to be an 'expert' on quantization. Having a PhD does not necessarily entail expertise in the area. Normally it will take more than the few years of PhD. Even now, I still learn new things about quantization, but I suppose I can say I know the gist of what quantization is. The other thing that one should also bring up are also the tools that one uses in one's practice of the topics of expertise (the so-called X-factor). For me, it has always been the global aspects of a theory; thus geometry and topology, but it could also go to theory of categories, thinking in terms of maps between objects. So as you can see, these are all very mathematical. That is why, I guess, I do not mind when my younger quantum colleagues get together in the current rave of quantum science and technology, and they were trying to pin-point my expertise. It was said that I am more of a mathematical person. This should not disqualify me from being interested in the physics of quantum systems; I have always been interested of how the mathematical ideas of quantum theory get manifested in the physical world.
Now, I told my younger colleagues things can evolved; definitions evolve, what considered as standards evolve, and one needs to be aware of this evolution. How? Just plenty of reading, sometimes beyond the scope of one's own interest. To my colleagues and past students, they probably know me scouring up the contents of arXiv weekly (after my retirement, daily), most of the time with delays.
Once I was back in Malaysia, I could not simply continue with the topic I know (not many are interested and with no people to talk to), I explore other areas but yet remaining closed to thematic ideas. It was on Maass cusp forms/pseudo automorphic forms. This was an idea brewing when I was visiting Chris Isham; I was saying quantization on punctured surfaces and he relabelled the program as quantization on topologically complex spaces (which is even more general). In a way, I was toying around with the idea of toy models of assembling quantum systems with ever increasing complex topology. Working on the details led me to the type of work I've dreaded, namely computational work (see this post here where I've opted not to do numerical work for my PhD). Since the spectra of such quantum systems will have discrete eigenvalues (from bound states) embedded in continuous eigenvalues (from scattering states), one can only compute the discrete eigenvalues numerically. To help me proceed, I invited two experts on Maass cusp forms for us to learn their computational work. Again, I need to emphasize that our practice to invite overseas experts is to learn from them, though administrators tend to think invitation to overseas experts should end up with collaborations. No we don't, collaborations have to be more organic and not one-sided. As such, I would not consider myself as an 'expert' but merely acquainted with subject. There is so much to learn here and may be connected to fundamental things like Langlands program.
To the above, I have a 'funny' story to tell. Yesterday, I was doom scrolling FB while being half asleep and there was a post that caught my attention. It was a post on an old paper of ours that was wrong and we had already withdrawn the paper from the arXiv. The two invited experts that we have mentioned had already informed us about the wrong eigenvalues and thereafter we have corrected the calculations and published them. Our work has then been confirmed by others (using a different technique) whom we do not know, though it also mentioned that we might have missed some eigenvalues. We were happy about this because the citation is not made by people who are our friends in our circle. This is unlike citations made by friends within one's circle. Just a few seconds ago upon checking the citation, we found another paper citing the same work as well as work done by my MSc student Syaza. Again this is not from a person within our circle. Back to the FB post, when I first saw it, I sort of ignored it and later when I woke up and tried to find the post but could not find it (did not know who posted it). Not sure of what is the intent; humiliation? We are always ready to learn if the person is just pointing that our work was wrong. In any case, it is very unlikely that I return to this type of computational work without access to good computing facilities and good students to work details out (I'm already retired).
Moving on, we tried to shift our attention to quantum foundations and quantum information. I must say the evolution to these topics from quantization is more natural. The only thing is that the former connects a lot to philosophy while the latter has an engineering approach, both of which needs different kind of mastery, which I guess we are still learning. While I have some ideas still (despite retiring) to explore, there are still many things that we need to learn in order to leave a mark; we are not really at the forefront.
On the subject of expertise, I have to say that one should be at ease looking at technical papers in the area, if one is to be called an expert, to say the least. I sometimes cringe when people say they know well quantum theory but what is demonstrated is rather rudimentary. So I have always pushed my former students to be more technical (in this case mathematical, since that is our forte). In the same way, when I tried to understand artificial intelligence some months back and wrote a piece on Mosstaque's MIND, I purposely write at the end that I am no expert in artificial intelligence, just to be clear. I was imagining an expert in artificial intelligence cringing on reading that pieceof mine. That however, does nor prevent me from still exploring some of the ideas there; perhaps I will be interested in latent space geometry or maybe relational intelligence. Let's see ...
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