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.
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.
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.
you can reverse the playback, all the physics of billiards bouncing around works equally well in either time direction.
> If the balls start clustered together, they will scatter over time about the box and the replay of their paths has only one plausible time direction.
It is extremely unlikely that all the billiards will, simply by chance at some point in the future, collect together so they are contained within a very small volume. this shows that there is asymmetry in which direction time flows.
Sharing a simple thought experiment that was shared with me years ago that explains (to me at least) why this is an interesting question. Imagine a billiard ball with nonzero velocity bouncing around an enclosed box. When the ball encounters a side of the box, it bounces off elastically. A replay of this ball's path over time is equally plausible if the replay were run forward or reversed. The preceding is also true if one imagines 2 or 3 balls, with the only difference being that the balls may also bounce off each other elastically. Even in this scenario, reversibility of playback holds no matter the configuration of the balls: they could all start clustered or be scattered and the replay would be plausible when played in either time direction. But this is no longer true when the box (now much larger) contains millions of billiard balls. If the balls start clustered together, they will scatter over time about the box and the replay of their paths has only one plausible time direction. This is because it is extremely unlikely that all the billiards will, simply by chance at some point in the future, collect together so they are contained within a very small volume. To summarize, in the "few scenario" we can plausibly reverse time but in the "many scenario", we cannot. The only difference between scenarios is the number of balls in the box, which suggests that time is an emergent property. layer8's answer elsewhere in this thread says the same, but more succinctly.
I thought the article would discuss physics of flight, but it's about physics of iridescence. Cool, but not what I expected. I've seen butterflies fly in a stiff wind. It seems impossible even when you watch it. I was hoping for some insight into that.
your comment introduced me to the term permaculture, looks interesting. Do you leverage numerical optimization - linear programming or integer programming for example - in your work?
That's a clarifying response: I've applied (non)convex programming (LP, QP, MIP, etc) to all the above and a few more, all of which i'd classify as classical applications. Less traditional applications -- I'd like to explore these more --- include data envelopment analysis, which provides a framework for assessing the efficiency of processes based on 1 or more input metrics, and several ideas in papers published at NeurIPS and other conferences that integrate LPs into neural networks in various ways, including AUC maximization. I've also worked on first order methods to solve LPs, and while I'd like to continue in that direction, the area is very crowded with very good existing tools, new and emerging tools that are also often good, and very strong teams building on all of the above. One of the biggest challenges that I see in the OR space is that it requires human expertise to leverage the technology.
LPs (and MIPs) are used for scheduling, planning, and logistics. These are some of the earliest applications of LPs, dating to the 1930's and 1940's, and these applications are still relevant. The wikipedia page has a good overview of the history and utility of linear programming.
https://en.wikipedia.org/wiki/Linear_programming
Martin Gutmann's recent talk ( https://www.youtube.com/watch?v=b0Z9IpTVfUg ) supports your point. While Shackleton is celebrated for overcoming disaster, Admunsen reached the south pole by avoiding disaster in the first place. Yet despite Admunsen being more effective, he is not celebrated to the same degree (at least in the US) as Shackleton.
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.