Psychological Barriers

A city-based retired professor in Nagpur, India claims to have solved Fermat's Last Theorem - twice.

Fermat's Last Theorem is a famous mathematical puzzle. Fermat wrote a note claiming to have proved it, but did not give the proof. For the next 357 years, mathematicians worked on it without success. Finally, it was proved in 1995 using very modern and deep methods. Now, just a few years later, we may have two additional proofs, one said to use methods that would have been familiar to Fermat.

Running the Four-Minute Mile was a goal (thought by many to be unachievable) for many years before it was reached. Now, it is almost routine.

Why did these things take so long to happen the first time, and then suddenly get easier? There's no obvious change between before and after--except the knowledge that success has been achieved.

I even have personal experience with the phenomenon. A certain logic class had a scary-sounding extra credit problem: to implement a universal Turing machine in a Turing-machine-simulator program. The task went uncompleted for several courses. I was the first to do it. A few years later, I heard that several students in each class were doing it. The thing is, it wasn't even that hard--all that was needed was treating it like a computer programming problem.

Part of my concern about the speed with which molecular manufacturing could be developed is the strong suspicion that there are psychological barriers to inventing easier ways to do it--and those barriers could fall at any random time. All it takes is a few people who move forward as though it were possible--and then, if the laws of physics allow, it will be done. This is not to say that the process of research will be unrealistically accelerated, but that shortcuts will be found by people who look for them with the right mindset.

How many shortcuts are there? We don't know--no one has looked. Once molecular manufacturing is known to be possible, shortcuts will pop up like weeds. (This is one factor that will make it difficult to restrict the technology.) But even before it is known to be possible, shortcuts can be found.

Chris Phoenix

Tags: nanotechnology nanotech nano science technology ethics weblog blog

Comments

[Brian Wang]

There is a washington post article that shows the effect of confidence and belief in oneself in getting better performance on tests

Of course the answer is also in Star Wars V, the Empire Strikes Back.

[Using the Force, Yoda effortlessly frees the X-Wing from the bog]
Luke: I don't, I don't believe it.
Yoda: That is why you fail.

Luke: All right, I'll give it a try.
Yoda: No. Try not. Do... or do not. There is no try.

Yoda: You must unlearn what you have learned.

[KAZ]

To be fair, in all of the cases you cite, the solution allowed a reverse-engineering of the problem to find shortcuts. It wasn't merely psychological.

In the case of running, what changed was training and running techniques. If nobody realized the FIVE minute mile were broken, yet they were trained with modern techniques, they'd still break the four minute mile, and probably be wondering why it was so easy.