Berry’s Paradox and Gödel’s Incompleteness Theorem

A young librarian at the Bodleian Library in Oxford devised an intriguing paradox. He defined a number by means of a statement of the form THE SMALLEST NATURAL NUMBER THAT CANNOT BE DEFINED IN FEWER THAN TWENTY WORDS. This appears to indicate a specific positive integer, which we denote $latex {\mathcal{B}}&fg=000000$. But there is … Continue reading Berry’s Paradox and Gödel’s Incompleteness Theorem →

Does Numerical Integration Reflect the Truth?

Many problems in applied mathematics involve the solution of a differential equation. Simple differential equations can be solved analytically: we can find a formula expressing the solution for any value of the independent variable. But most equations are nonlinear and this approach does not work; we must solve the equation by approximate numerical means. The … Continue reading Does Numerical Integration Reflect the Truth? →

Cornelius Lanczos – Inspired by Hamilton’s Quaternions

In May 1954, Cornelius Lanczos took up a position as senior professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS). The institute had been established in 1940 by Eamon de Valera, with a School of Theoretical Physics and a School of Celtic Studies, reflecting de Valera's keen interest in … Continue reading Cornelius Lanczos – Inspired by Hamilton’s Quaternions →

Buridan’s Ass

``Buridan's Ass'' is a paradox in philosophy, in which a hungry donkey, located at the mid-point between two bales of hay, is frozen in indecision about which way to go and faces starvation --- he is unable to move one way or the other. Jean Buridan was a French philosopher who lived in the fourteenth … Continue reading Buridan’s Ass →

The Ever-growing Goals of Googology

In 1920, a kindergarten class was asked to describe the biggest number that they could imagine. One child proposed to “write down digits until you get tired”. A more concrete idea was to write a one followed by 100 zeros. This number, which scientists would express as ten to the power 100, was given the … Continue reading The Ever-growing Goals of Googology →