Here is very interesting letter from Kurt Gödel to Von Neumann. In the letter, Godel says that if we have fast enough computer which checks, within few days, that if a proof of a mathematical theorem can be written in few hundred pages then only it is worth trying for humans to look into the problem. Otherwise, proof will be so long such that it is impossible for human mind to find the proof. If such computer can exist then all the creativity expected from a mathematician is to ask computer to prove a right theorem. So far, we haven’t developed such computers. So, we have to rely upon human creativity to find a proof for a theorem.
Implications of above statement are much wider. Finding a proof of a mathematical theorem is strongly related to difficult decision-making process in ordinary life. We face such difficult problems also in our ordinary lives. For example, you have 2 job offers and you have to choose one. Lets see how you might evaluate that which job is better for you. You will consider the amount of salary. You will also consider how the pay will change over the years. This follows that you need to evaluate the company under many criteria. You need to evaluate the work environment of the company, kind of career paths you would like to take in the company, stability of the company, flexibility of the company in future market conditions. This list can go on and on and on. You may get overwhelm with the difficulty in choosing the better job. This example suggest that there can be following problems in evaluating these criteria.
- You may have too many criteria to evaluate. ( Large problem )
- You may have too much data to process for some criterion. ( Large Input )
- You may not have enough information to evaluate some criterion. ( Insufficient information )
- You may not know how to evaluate using the data. ( Undecidable )
- You may know how to evaluate the criterion but it takes too long to evaluate. ( High Complexity.)
Above problems limit our decision making capacity. So, you are faced with the similar problems as mathematicians. Mathematicians can choose not to prove the theorem and attack some other problem but you have to pick a job, you have to pick a spouse, or you have to pick a health insurance. Life presents you situations in which you have to make a decision with limited resources and well reasoned decision is just impossible in limited resources.
Above observation shows that reasoning and logic is insufficient to live ordinary human life. There you need wisdom. In difficult situation, people follow the known wisdom of the society, follow advice of elders, or just-do-something-and-see-what-happens. It is one of the reasons why we have prevailing superstitious believes in our societies. Superstition have this positive aspect then there are huge drawbacks. People tend to drawn into ease of superstitions. They don’t want to analyze or may not be aware that matters life can be analyzed. This leads to highly dogmatic society. Once society takes a bad decision then it continues for centuries. Even if in future due to learned experience and analysis, it becomes possible to show that traditional wisdom is a bad decision, people resist too hard to change their life.
In last 300+ years of industrialization, thinkers have observed that we have been using too much wisdom compare to logic. Many questions of life can be decided using logic and we simply depend upon traditions and wisdom. So, there has been a grand shift of paradigm in thought process in which people have been applying more and more logic and reasoning in ordinary life. We have seen in the past there have been philosophical ( Rene Descartes, Friedrich Nietzsche) and political (Ayn Rand) movements which says that logic and reasoning is the only guide line of human life and all the traditions which can’t be demonstrated via logic should be abandoned or at least questioned. These movements have gained significant support time to time but lost their appeal to people soon. People find that logic can’t answer all of their problems. There are limits as we have seen at the start of this post.
We see more clear evidence of the difficulty of decision making in public policy debates. For example, health care debate in US. US government has been trying to design a health care system which is most fair and effective. The system will run over 300 Million Americans which will be eventually highly complicated. No one can logically demonstrate that some health care system is the best effective choice. At the end, you see in public debate in which people are arguing over different conclusions which they didn’t logically deduce but concluded using their wisdom. The debate soon reduce to a cock-fight.
We need to build a culture which tries to apply as much logic as possible and when logic is unhelpful then we can depend on a good set of wisdom, which is passed from one generation to another generation.