I came across this article (I read it over a period of many days. It is 10 long pages, and lots of people are interviewed) asking well-known people, most of whom were scientists, what they believe is true but cannot prove. It is from 2005, but I had not seen it before. I definitely enjoyed reading it, and many different perspectives were put forward. I loved reading conjectures on consciousness, religion and more specific topics. I even enjoyed reading some of the physics conjectures, for which I have essentially no intuition (for what was being discussed). Overall though, there were a lot of common themes between the authors.

There are a few people who believed that we will eventually figure out everything in the universe, or perhaps just something that is “easier” such as figuring out how social behaviour works. Conversely, there was a pretty large handful of people who mentioned Gödel, and those people usually discussed how they believed we wouldn’t figure out particularly much about the universe. The difference of opinion is huge. I definitely side with this opinion. There is far more that is impossible to know, than what we do know. Sure, we stumble onto stuff, but that’s the easy stuff.

Discussion of language was definitely a major theme amongst a large percentage of those asked. One entry I enjoyed, which I believe is related to the limits of knowledge, was that of Martin Nowak, a “Biological Mathematician”:

Every special trait of humans is derivative of language. … Mathematics is a language and therefore a product of evolution.

I’m not sure whether it is true or not, but language parsing is powerful. Subtle changes to grammars can make a gigantic difference to what can be computed (see regular grammars versus grammars that can generate anything that can be computed). Seems to me (and other friends, whom I’ve heard mention this idea as well) that once those subtle changes took place throughout evolution, there would be a ridiculous amount of extra stuff that could be done, just by hijacking that same language parsing process.

There was more supporting evidence that even babies can parse these types of grammars, the entry by Psychologist Gary Marcus is very interesting:

For example, in the course of just two minutes, a seven-month-old baby can extract the ABA “grammar” inherent in set of made-up sentences like la ta la, ga na ga, je li je. Or the ABB “grammar” in sentences like la ta ta, ga na na, je li li.

But even still, there are (mathematically provable) limits to language, computation, and even verification in a finite universe. And that is an upper bound for where science and math will hit its limits.