Now, reading all the analysis above it occurred to me how it is that the group thinking can be more penetrating than one person's thinking. What I thought was simply: "and what if I do not have my right hand?" I can think as much as I can about rising it, and it will not rise - simply because it is physically not there, or it is tied or numb.
But why did I ask this question? Mainly because when I see such a stretching of logic at one place, it tells me something about the author and his/her intentions. The author has a certain goal in mind and will stretch and twist the logic as much as needed to "prove" this idea to other people. This happens not only with esoteric or philosophically inclined writings. It happens also with exact sciences, even with mathematics. Even in mathematics once in a while errors in logic are being made, theorems are being "proven" and they propagate as "truths" for many many years - until someone decides to check every detail instead of just accepting as "truth" because "it has been published and no-one challenged it".
That was how my
On Conformal Infinity and Compactifications of the Minkowski Space recent paper was born. I felt something must be wrong about what some mathematicians "have proven", but it took me many months first to spot the exact error and then to find out what the truth is and to write it all down.
Another example. Recently I became active on
Physicsforums (as "arkajad"). People are asking questions there and they are often getting answers from those who know the subject) (or think thay know). A very useful function. And so yesterday someone asked
a question about the use of group theory in physics and how in physics the mathematics is being twisted and is not always logically accurate. As I knew something about the subject, I replied. But before replying I checked what is actually known about the exact issue involved. So I have found a "Status report" paper:
The surjectivity question for the exponential function of real Lie groups:
A status report
Dragomir Z. Dokovic and Karl H. Hofmann
And what do we find there? Here are exact quotes (and remember - this is mathematics - the most exact of sciences):
From the Abstract: "
Some so far unobserved errors in the literature are pointed out, results are described, and some conjectures are formulated."
And then: "Although Lai's note was published more than 15 years ago, it remained unnoticed so far that Lemma C is false."
So, here is another example where people were using a mathematical result that has been "proven", but both the statement was false and the proof was faulty.
And that is why it is so important always go back to the sources, check the proofs, compare. It is not enough to rely on "
X said that", or "
X,Y,Z are saying that and no one dares to question - so it must be true." Or "
It sounds so convincing and it resonates with me."
Of course the task seems to be impossible for a single person. But for a group of people determined to find the truth? It may take time, but it will work. It is not enough to ask "the expert" or even "the experts" about their "opinion". The right question to the expert is: "did you checked it yourself in all the details?" What exactly did you do? Because quite often the experts use the same method: they glance through a given statement and they find that "it resonates with them".