I don't take offense. That is a highly brave action. The picture is so iconic that it even looks 'beautiful' even though it's very tragic.

But I don't see how it relates to free will. And it's unlikely I'll reconsider it since it's one of my 'specialties' for more than a decade! In fact I consider it a fact that both science and philosophy have proven, quite independently of each other, that there is no free will.  It's just a remnant of our belief in the soul, basically. Once you understand that everything is material, and our brain is made of matter, and consciousness entirely depends on it, then the rest follows. Maybe a stone has no feelings and a human has feelings, but with determinism it's different: there is no sum that is greater than its parts. If material particles have 0% free will, then it doesn't matter how many of them you stack together and in what order, you will never get something that has 1% free will. There are some things that all material objects have in common, like having a position in space and time for instance. One of those things is being 100% determined.

There are famous free will experiments in psychology that you probably read about, but recently there was a new one (of the same kind) that a friend posted on fb: 
https://medicalxpress.com/news/2019-03-brains-reveal-choices-aware.html

> causal mysterious other reason

It's not mysterious in a magical sense. It's only mysterious because we don't know, cos there's so many things... If you toss sand in the air, can Science predict the trajectory of each grain of sand? No. But we *know* it's all determined. Because nothing else makes sense. If something isn't determined, then it's magic. And it's easy to say 'it's magic', but actually we have no idea what that would even mean.

> man is nothing but a machine

Well we are a very complicated machine. An admirable machine. Not all machines are the same. So we are not just another machine!

> I call this denial of what science itself could actually claim to represent as great knowledge: That the identification of causes, as soon as they were found, again resulted in new and even more intensive searches for further causes, and that in this way we can go on indefinitely without ever finding a real causal origin.

Those are two different things. I can know that A was caused by B, without knowing what caused B. I could then say that A is 100% determined, even though I'm unaware of the ultimate cause of everything.

So yeah, you are right, it's a problem in philosophy: does everything go back infinitely? Does infinite causation that never ends make sense? Is infinite causation better and more sensible than saying that everything started with the First Cause? (usually identified as God). Basically, there are only two games in town: infinite causation and First Cause (or many First Causes!) But, like I said, this has nothing to do with whether human actions specifically are determined.

> the power of the predetermined destiny 

Fate and destiny have nothing to do with determinism. Fate is like the movies Final Destination. It's like, whatever you do, something will push you, in increasingly intricate ways, toward what was meant to happen, toward what was 'written'. Fate is also necessarily against randomness, whereas determinism, strictly speaking, is not. Determinism is simply the idea that if I toss a coin, whether it lands head or tails is determined by the laws of nature, so that if I knew everything that came before the toss, I could tell you what will happen after I toss the coin. It's like that article I sent in my previous reply. Scientists use science to predict what you'll choose before you choose it. And we're only getting started, cos our science is still so primitive.

> nothing a human being does has any influence whatsoever on this already determined mechanics

But why are you separating the human being from the mechanics? Does it make sense to say 'nothing a clock does has any influence on what time it shows'? No, what the clock does has 100% influence on what the clock shows! You do what you do, but what you do is 100% influenced by all your nature and nurture, the brain that you inherited + all the information that was received by that brain since the moment of its birth.

> Is then human compassion basically worthless feeling and only pure imagination?

I don't see how this is related. Human compassion is not at all worthless.

> In so far as I declare this present to be an illusion, I deprive myself, so to speak, of my only possibility to exert influence and leave others to control the situation.

Well this is a contradiction. You are basically saying that (if you don't have free will) all matter is determining you to do X, and therefore you feel you are powerless. But you just said that matter determines you! And you are matter too. So you are not powerless! You are affecting other things just like everything else.

Basically, I think it's just a psychological reaction, let's say like if I tell someone they don't have a soul. All the things you appear to be worried about have nothing to do with determinism and free will. You get to keep all those things, and add knowledge on top! You don't lose anything, and you gain much! It's interesting because you're also a psychologist/therapist, and I would think that your profession would believe that people can be influenced, and that because of that we may both help them and learn about them. If people's actions happen because of some mysterious 'free will', then psychology is doomed, and there's no reason to ask questions such as "why did Jane do X?" Just put them in jail or something and never answer the question and never try to help them.