I generally agree, though direction, intuition, and domain knowledge are still relevant. Your breadth-first-search framing feels right, but you still need a sense of which paths are worth following, and you need to know when to trust the results.
I’ve been doing more math as a hobby in the past few weeks — working on lesser-known conjectures and exploring proofs of hard theorems — than I could have managed over the previous several years. It’s an exciting time.
> I don't think his Usonian concepts have had much impact on society.
The word Usonain has vanished, but the style's influence has not.
> In 2024, I spent $750,000 on a 1200 sqft rancher built in 1962.
The Jacobs First House [1] in Madison, WI was the first Usonian house; it is credited with many features that became common in the mid-century ranches of the 50's and 60's. Stewart Hicks has a good deep dive [2] into Wright's influence on 20th century architecture.
I don't know, man. I mean, I know it's the standard Architecture School answer that Wright was influential. But I feel like that can only be said if you focus on superficial, outward appearance and completely ignore his design philosophy, why he designed the way he did.
The materials he chose were meant to make home ownership accessible to the common man. Your own link to the Jacob's House talks about Mr. Jacobs being "a young newspaper man". The $5000 cost in 1935 is like $120k today. Yeah, if 1500sqft houses cost $120k today, I could believe a journalist just starting out on their career could afford the mortgage on it.
Are houses L-shaped now? Yeah, sure. Are they accessible to the common person? Not at all. People are talking the Little Golden Book version of Wright's philosophy.
Also, my house is not L-shaped. Jacobs got 25% more house for 1/6th the inflation adjusted price. He got a study and a shop; I'm performing my own manual labor in my back yard to build a gazebo that I hope will work as a shop for me. As a newspaper hack with a likely-unemployed wife he got a house near a lake. My electrical engineer with a master's degree wife working at a major military research institution and I got a drainage ditch that kinda looks like a stream when it rains really hard. And we're in our 40s. Everyone massively missed Wright's point.
Wasserstein distance (Earth Mover’s Distance) measures how far apart two distributions are — the ‘work’ needed to reshape one pile of dirt into another. The concept extends to multiple distributions via a linear program, which under mild conditions can be solved with a linear-time greedy algorithm [1]. It’s an active research area with applications in clustering, computing Wasserstein barycenters (averaging distributions), and large-scale machine learning.
There is an analogue of the CLT for extreme values. The Fisher–Tippett–Gnedenko theorem is the extreme-values analogue of the CLT: if the properly normalized maximum of an i.i.d. sample converges, it must be Gumbel, Fréchet, or Weibull—unified as the Generalized Extreme Value distribution. Unlike the CLT, whose assumptions (in my experience) rarely hold in practice, this result is extremely general and underpins methods like wavelet thresholding and signal denoising—easy to demonstrate with a quick simulation.
There's also a more conservative rule similar to the CLT that works off of the definition of variance, and thus rests on no assumptions other than the existence of variance. Chebyshev's inequality tells us that the probability that any sample is more than k standard deviations away is bounded by 1/k².
In other words, it is possible (given sufficiently weird distributions) that not a single sample lands inside one standard deviation, but 75% of them must be inside two standard deviations, 88% inside three standard deviations, and so on.
There's also a one-sided version of it (Cantelli's inequality) which bounds the probability of any sample by 1/(1+k)², meaning at least 75 % of samples must be less than one standard deviation, 88% less than two standard deviations, etc.
Think of this during the next financial crisis when bank people no doubt will say they encountered "six sigma daily movements which should happen only once every hundred million years!!" or whatever. According to the CLT, sure, but for sufficiently odd distributions the Cantelli bound might be a more useful guide, and it says six sigma daily movements could happen as often as every fifty days.
I highly doubt the finance bros pretend distributions are normal or don't know Chebychev, vs. not having enough data to obtain the covariance structure (for rare events) to properly bound even with Chebychev.
I’ll share an anecdote I witnessed in my extended family–it was horrible. When US Air went bankrupt, employees with decades of service, expecting high five-figure to low six-figure annual income, learned they would get roughly $0.20 on the dollar. For many who were entering retirement, the impact was life-changing, and the stress and disruption it caused could well be argued as life-shortening.
PBGC did take over, but that did not solve the problem.
I believe the root cause was mismanagement of the pension, with the bankruptcy merely exposing this. But I wouldn’t be surprised if, at every opportunity during the bankruptcy process, changes were made that eroded the program’s health.
This is an instance where Conway's Law applies: state and county systems were kept separate so that maintenance and repairs crews wouldn’t accidentally duplicate work. https://en.wikipedia.org/wiki/Conway%27s_law
I've seen several, Planet Trek in Wisconsin is a good bikeable one with high quality signage. The sun is downtown, the moon is the size of a peach pit, Pluto is ~20 miles away.
how helpful was ai for this? The paper is light on details, but it says the agent was used to generate a kind of seed set (rank-1 bilinear products) that were then fed into the subsequent steps. Evidently this idea succeeded. Curious if anyone here has insight into if this is a common technique, how this agent's output would compare to random or a simple heuristic that attempts the same. Also interested to see how the training objective gets defined since the final task is a couple of steps downstream from what the agent generates.
My hope is that a lib like this one or similar could rally mindshare and become integrated as the new standard, and adopted by the wider developer community. In near term, it comes down to trade-offs. I see no decision that works for all use cases. Dependencies introduce ticking time bombs, stdlibs should be correct and intuitive, but at least when not they are usually well tested and maintained, but when stdlib don't meet urgent production needs you have to do something.
It's basically what happened in Java. Everyone used jodatime, and they took great inspiration from that when making the new standard time api for java 8.
I’ve been doing more math as a hobby in the past few weeks — working on lesser-known conjectures and exploring proofs of hard theorems — than I could have managed over the previous several years. It’s an exciting time.