British mathematician, logician, philosopher, & public intellectual Bertrand Russell was born #OTD in 1872.
One of Russell's most significant achievements is the co-authorship of "Principia Mathematica" (1910-1913) with Alfred North Whitehead. His works, such as "The Problems of Philosophy" (1912) & "Our Knowledge of the External World" (1914), explored issues related to knowledge, perception, & the scientific method.
"Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover."
An Outline of Philosophy Ch.15 The Nature of our Knowledge of Physics (1927)
"The pursuit of philosophy is founded on the belief that knowledge is good, even if what is known is painful."
“Since the beginning of #Israel’s war on #Gaza, academics in fields including #politics, #sociology, Japanese #literature, public #health, Latin American and Caribbean studies, Middle East and African studies, #mathematics, #education, and more have been fired, suspended, or removed from the classroom for pro-#Palestine, anti-Israel speech.”
I have a question about the aperiodic spectre tile (or the hat/turtle).
I know that the proof of aperiodicity works by showing that the tiles must fit together in a hierarchical structure that eventually repeats itself at a larger scale. But the larger units aren't literally scaled copies of the spectre. I also know that there is some freedom as to how you draw the edges of the spectre.
Is there a way you can draw the edges that allows you to literally use spectres to cover a larger copy of themselves? If so, is this way of doing it unique?