What are Hilbert and Banach spaces?
It is dangerous to live without knowing what Hilbert spaces are. One might be spontaneously quizzed on one’s recollection, and it would be very embarrassing to not know the answer! Thankfully, you need only remember that Hilbert spaces are the objects which allow you to generalize linear algebra and apply it to analytic settings.
Localizations of a ring at specific elements correspond to sections of a sheaf
One fundamental observation in algebraic geometry is that there are a number of powerful correspondences between ring localizations and algebraic sheaves. Although elementary, this post will outline one such correspondence, which is that the localizations of a ring to a specific element 
can be exactly thought of as the sections of the sheaf of regular functions over the distinguished open set of . (Consider this post to be a self-directed refresher! It has been a long time since I learned this material.)
Excellent cheeses
Some excellent cheeses follow.
The tenured professor and the sea of cancellation: Gregory Clark on human intelligence
Gregory Clark is a tenured professor of economic history at UC Davis known for studying intergenerational mobility in England from the 17th through the 21st century. Interestingly, he more or less re-derived the additive inheritance of human talent (principally but not wholly composed of human intelligence) from empirical analysis of how social standing fluctuated throughout the centuries. These findings are well summarized in a recent podcast between him and the physicist Steve Hsu. I will highlight and expand upon some points of considerable interest from this podcast.
High-quality studies on education, intelligence, and environmental effects
Heritability of intelligence Effect of gene-environment interactions on intelligence Effect of education on intelligence Assortative mating on intelligence Effect of famine on intelligence Effect of deafness on intelligence Effect of parental death on life outcomes Effect of education on life outcomes
Beware of Gell-Mann amnesia about government quality
Many people are amateur experts in some specific domain of government regulation, such as land use zoning or immigration law, which they know for sure is horribly inefficient and profoundly harmful to the nation. However, they often fail to appropriately generalize these observations to the quality of political governance at large: a form of Gell-Mann amnesia applied to the quality of our rulers.
Advantages of building many castles in the High Middle Ages
Why did medieval rulers like Richard the Lionheart or Edward I build so many castles? Castles were very expensive, especially given poor tax-collection infrastructure; yet the historical record shows that successful conquerors expended great effort (and revenue) on the construction of numerous fortified stone castles. They embarked on these programs of mass construction not out of ignorance but, instead, because of economic and strategic considerations that made efficient use of castles a vital part of conquering and holding territory.
What the Accelerationist’s Political Compass says about us
Every now and then, this “political compass” of acceleration vs. deceleration, hyperhuman vs. unhuman pops up. It’s a pretty interesting breakdown so I wanted to jot down a couple thoughts.
Thoughts on Cixin Liu’s Three-Body Problem series
Several weeks ago I read through the entire Remembrance of Earth’s Past series, which starts with The Three-Body Problem then continues with The Dark Forest and Death’s End. While somewhat disappointing from a literary perspective, the series nevertheless has a fresh perspective on certain aspects of society and culture, which I will briefly discuss.
Meals that are healthy, quick, inexpensive, simple, and tasty
Although I enjoy cooking for its own sake, I am often too occupied by other things in my life to spend time planning and preparing elaborate meals.