howto restric a method to being absolutely constant

[potatoCode]

if you want a functor to be "read-only" make its operator(), function arguments, and any other private members const and the compiler will ensure that you aren't modifying anything.

I think what OP wants is something similar to

    void operator()(const Target& obj) const

where the const in red won't get caught by the compiler if any modification is done on the argument.
(which I totally agree with you that it doesn't make sense)

@ssouffri
AFAIK, there's no such thing as "absolute const" for you can a) cast it away,
b) make certain members mutable.
I don't know much about pthread or boost thread functions,
but for win32 api,
even if you some how make the method "absolute const",
the chance is that you will likely pass object as the argument,
in which case data passed to the thread function

    void operator()(const Target& obj) const
    {
        tHandle = (HANDLE)_beginthreadex(NULL, 0, &obj.dispatch, &obj, 0, &tID);
    }

would require, some type of conversion,
of which, the conversion is impractical to pursue or non-thread safe.

I think you have to rely on the design more,
and implement necessary synchronization.