....LawPundit

The basic problem with "hand" proofs as opposed to "mechanical" proofs is that, as noted by Neeraj Suri, Michelle M. Hugue, and Chris J. Walter in Synchronization Issues in Real-Time Systems:

"As hand proofs are sensitive to the skills of the prover, mechanical proofs are sensitive to the correctness of the theorem prover and its underlying logic. "

In other words, to employ a phrase used by Thomas Kuhn (The Structure of Scientific Revolutions), if the paradigms (viz. "mechanical" proofs) underlying a given view of "shared knowledge" are wrong, then that knowledge is likely also wrong. What this means is that someone along the way has done an intuitive "hand proof" which does not conform to the judgmental mechanical proofs in vogue. A hand proof made by a skilled prover is thus always at the root of progress, in any field.

Another example of "hand proofs" is the method by which our legal system relies upon the opinions of judges, rather than on computer-produced verdicts applying fixed mechanical theorems. Here, "skilled" provers are viewed as superior to a computer theorem.

Only after an observation-fitting hand proof is made and then compared with the mechanical proofs in vogue does the battle with the inertia of existing paradigms begin.

Mainstream scientists want the ensuing discussion to proceed under their terms and thus demand that their theories be proven false. This, however, does not accurately describe the process of scientific discovery, nor does it describe the primary motivation for overturning precedents in law - and this constitutes Popper's main error in analysis. Popper, by concentrating on mainstream science, does not actually describe the actual process of scientific (or legal) advance - rather, he describes the process of mainstream resistance to advance and the inefficient mechanisms by which that resistance is or can be broken.

The true pioneers in science (or law), on the other hand, and this is where Kuhn's analysis is the more accuracte, have no interest to waste their time on developing proofs to falsify the erroneous theories in vogue, but rather, prefer to be busy building up their own systems which correspond to the evidence at hand. The falsification process of the erroneous prevailing theories is then later carried out by others, i.e. the innovators and early adopters of new theories.

Good examples here are the "hand proof" works of Isaac Newton, which presented new interpretations of observed phenomena and spent as little time as possible wasting time in disproving the erroneous ideas of others.

Another example of new paradigms and hand proofs is the Constitution of the United States, which is a "new discovery" that concentrates on new things to be achieved, rather than on old things to be "disproven". This in fact is still the genius of America, several hundred years later. America is a "Kuhnian" world of new paradigms and "hand proofs", whereas the Old World (Europe, Middle East) is in part still caught in a maelstrom of Popperian inertia of resistance to change, functioning by antiquated and long outdated mechanical solutions (unreformed social systems, entrenched social classes, overemphasis on tradition, no longer state-of-the-art customs, deference to nobility at the cost of modern social innovation, etc.)

As the "hand proof" says, "go for it". That's the American way which is sorely lacking in the Old World.