Amazing Possibilities


Happy new 2009, everybody! 


An understanding of our fundamental limitations is among the most important contributions of science and of mathematics. At the same time, various fundamental limitations stated by many great minds turned out to be wrong, sometimes rather quickly.

There are quite a few cases where things that were considered to be impossible turned out to be possible. Immanuel Kant claimed:  “No finite Reason can hope to understand the production of even a blade of grass by mere mechanical causes.” This quote is from the Critique of Judgment (1790). Elsewhere Kant wrote: “It is absurd to hope that another Newton will arise in the future who shall make comprehensible by us the production of a blade of grass according to natural laws which no design has ordered.”

 Auguste Comte claimed: “Of all objects, the planets are those which appear to us under the least varied aspect. We see how we may determine their forms, their distances, their bulk, and their motions, but we can never know anything of their chemical or mineralogical structure; and, much less, that of organized beings living on their surface …” (The Positive Philosophy, Book II, Chapter 1 (1842)).

Spectroscopy was developed by Gustav Kirchhoff in the 1840s, and the first spectroscopic analysis of the sun appeared about ten years later, less than 20 years after Comte’s statement.

A slightly different example relates to the philosopher Wittgenstein. Continue reading