Grounds for an ethics complaint? UK math prof. publicly misrepresenting results from an unrelated discipline

First, and foremost, be very cautious about taking this issue outside of the scientific realm of argument. If you start to file ethics charges or libel lawsuits, then you are likely to be casting yourself in the role of censorious scientific villain, and it is likely to not go well for you.

Instead, if you feel that your work really is scientifically defensible, I recommend that you stick entirely to the evidence to defend it. If you cannot do so, then that is a serious problem --- having not read your thesis, I have no idea whether you or your critic has a better case. Do note, however, that being in a different discipline does not immunize you from a person's criticism: a critic need not have any credential at all to point out a potential flaw in your work, and the nature of science is that if you cannot defend against criticism, your work cannot stand.

Finally, I would strongly recommend talking to your advisor before you take any further steps and strongly heeding their advice. Your advisor is likely to know better than you whether to take your critic seriously, given the state of your work and the field, as well as what types of response are likely to be wise or foolish.

Cases like that are best treated in "cold blood". Get one or two trusted friends to listen to your story and get them to give an outsider's view of how the blog appears. We cannot judge without further details how consolidated your work is, but I'll take here the stance that it is well-founded, scientific work without major methodological flaws.

One thing you have to remember is that in my experience, there is a significant "facultism". Mathematicians, especially, are, in my experience, not prone to any other type of discrimination, but they do look down on practically all other disciplines (with possible exception of physicists, whom they begrudge the ability to get away successfully with the most outrageously ill-founded mathematical sleight-of-hands).

You have to realise this, and that social sciences will not rank very high on mathematician's scale; so, rather than your particular piece of work being attacked here, it may be that it is your whole discipline. If that is the case, this can inform your strategy.

In your responses, you should stick to facts, not too many, but point out where he is wrong. Factually and focused. Don't make long replies, or people won't read it, pick 1 or 2 points where he is clearly wrong.

As for personal attacks, if his blog is satirical, and you attempt to silence it, you will, as mentioned before, get backfired upon. He is much better trained than you to run a smear campaign.

If you do not wish stay silent on the personal attacks entirely, you could try to say something along the line that he is not trained to judge your psychological makeup and should confine himself to make judgement about facts that he understands about. However, it would be even grander if you would just brush it off as not the issue of the moment and completely concentrate on discussing your results.

One thing that strikes me is his accusation of homophoby. You should check where this comes from (if not from the devolution of your interaction with the person): if there is something in your results that could be interpreted in a way that is politically unwelcome to various agendas (and it doesn't matter which one it is), you need to tread particularly carefully. In the latter case, it is particularly important to utterly refrain from any entanglement into personal invectives, and clarify, drily and accurately what your results say and what they don't say; where their limits of applicability lie and where they are valid.

I haven't answered about the ethics complaint. That's because I think, yes, you might have grounds, but, no, it may not be a good idea. Instead, see my advice above.

It might be worth taking some time to familiarise yourself with some related cases. I can only think of one off-hand, but I'm sure that others could point to more. It could be reassuring to know that this sort of thing happens to other people, and that they survive. I'm thinking of Terrance Deacon. In this case, the defendant won the case, but only because the complaint was "without foundation."

As for the "pseudo-science" assertion -- that's an easy term to throw around. It might be useful to read up on that, too, e.g. in the work of Imre Lakatos.

"But what distinguishes knowledge from superstition, ideology or pseudoscience? The Catholic Church excommunicated Copernicans, the Communist Party persecuted Mendelians on the ground that their doctrines were pseudoscientific. But then the problem of the demarcation between science and pseudoscience is not merely a problem of armchair philosophy: it is of vital social and political relevance."

The main thing is to approach the issue in a professional manner. Remember that people say all kinds of rude things on the internet that they wouldn't say in person. A polite phone call to the professor in question might be interesting, though potentially also quite fruitless.