Das U-Blog by Prashanth

Book Review: "The Book of Strange but True Science"

noreply@blogger.com (PV) — Fri, 05 Jun 2026 01:11:36 +0000

It had been a while since I had read a book, so I recently read the book The Book of Strange but True Science, which does not have any named authors; my family gave this to me as a birthday gift last year. It is a fun jaunt through scientific phenomena, technological & engineering innovations, and the histories of discoveries of those things, covering most major topics in STEM fields and with each vignette being less than 10 pages.

The book is written at probably a middle school reading level (from my time, though with the decline in reading proficiency among school students across the country, perhaps this is more like a high school reading level), and its perspective is clearly American. All of the vignettes were fairly superficial, and most of them felt familiar to me from school. Thus, I might have liked this more in middle school or high school, but at this point in my life, it feels too basic for me. That said, I would recommend it for any lay reader who could be interested in STEM topics.

Differences in Weather Fluctuations in Different Latitude Regimes

noreply@blogger.com (PV) — Sun, 05 Apr 2026 21:08:00 +0000

Recently, I learned more about weather & climate, particularly at higher elevations in the atmosphere; I used to feel a little intimidated to think about those things, so essentially all of my posts on this blog explaining features of different climates only used surface-level weather phenomena to the greatest extent possible (and arguably sometimes to a greater extent than was appropriate or justifiable). Although the insights that I gained from such learning are not especially groundbreaking compared to my previous two posts about wind divergence or seasonal changes to subtropical ridges over oceans, I feel like I have rounded out my basic understanding of weather & climate, and I wish to share that here. These explanations make clear why there are larger weather from day to day at middle latitudes than closer to the equator or poles as well as why certain analogies, like between middle latitudes at west coasts & tropical latitudes at east coasts, have limits.

The sources that I used are many relevant pages from Wikipedia, the Columbia University interactive maps of mean monthly wind velocities, and these meteorology lecture notes from the University of Arizona. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see more.

Differences in Strengths of Subtropical Ridges Over Oceans

noreply@blogger.com (PV) — Fri, 20 Feb 2026 00:56:00 +0000

Earlier this year, I wrote a post about how subtleties in the convergence and divergence of large-scale surface winds can explain many features of local climates. However, as I thought about it more, I realized that I still wasn't satisfied with my understanding of why the seasonal variation in strength of a subtropical ridge over an ocean depends on the ocean in consideration. Specifically, the subtropical ridges over the Pacific, Atlantic, and Indian Oceans in the southern hemisphere as well as over the Atlantic Ocean in the northern hemisphere are stronger (higher pressure) during those respective hemispheres' winter halves of the year, but the subtropical ridge over the Pacific Ocean in the northern hemisphere is stronger during the northern hemisphere's summer half of the year.

Having looked more at the Columbia University interactive maps of mean monthly wind velocities, I am reasonably more confident that I can explain these & related phenomena mostly through surface wind dynamics, though the explanations aren't complete. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see these explanations.

Subtleties of Wind Patterns Affecting Precipitation

noreply@blogger.com (PV) — Sat, 03 Jan 2026 21:02:00 +0000

Last year, I wrote a long post on this blog giving the most general intuitive explanations possible for the existence of different climate types, based on different configurations of land & ocean at different latitudes, and used that to explain broad & subtle features of actual climates of most locations. As I alluded to in that post, I had a lingering question of why, at tropical latitudes, there are so many east & poleward coasts that have dry seasons despite those coasts getting ordinary easterly (sometimes with a poleward originating component too) tradewinds throughout the year largely perpendicular to the coast. My confusion is because at those latitudes, the water & land temperatures are warm enough even in the winter half of the year to suggest that humid air from over the ocean could unstably rise above air over land & lead to precipitation. Examples include but are not limited to the north (poleward)/east coast of Central America, the north (poleward) & east coasts of islands in the Caribbean, some parts of the coast of Brazil, the east coast of the southern part of India, and the east coast of the northeastern part of the mainland of Australia. I also had a question about why the north coast of Egypt did not get precipitation in the summer half of the year despite getting northerly onshore winds from over the Mediterranean Sea, which is warm enough that despite the air over land becoming considerably hotter then, humid air from over the Mediterranean Sea could in principle rise above dry air over land, leading to instability and therefore precipitation. Additionally, I had a question about why the subtropical ridge over each ocean (more prominently over the Atlantic & Pacific Oceans in the northern hemisphere) is more poleward along the eastern edge of the ocean even though the western edge has warmer currents (suggesting lower pressure along the western edge than along the eastern edge along the same latitudes).

I could not think of satisfactory answers until very recently. Ironically, although that linked post from last year referred to concepts beyond surface-level wind patterns & air pressures, these answers depend mostly on surface-level wind patterns along with the knowledge of what different surface-level wind patterns imply for vertical air flow. The sources that I used are many relevant pages from Wikipedia and the Columbia University interactive maps of mean monthly wind velocities; unfortunately, the latter resource will be shut down in 2026 April due to funding difficulties. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see these answers.

Structural Incentives for Abusing PhD Students in Experimental Sciences and Engineering

noreply@blogger.com (PV) — Sat, 20 Dec 2025 20:38:00 +0000

When I was in graduate school and then for a few years afterwards (even though I had changed fields), I found it strange and fascinating that I and other friends who were in theoretical physics groups all seemed to have really good experiences on the whole (even while going through the normal day-to-day & month-to-month ups & downs of doing a PhD), whereas many (but not all) friends who were in experimental physics & engineering groups had noticeably more toxic & micromanagerial advisors who made those friends' PhD experiences correspondingly worse. For several years, I thought that it was simply an issue of the advisor's personality & mindset, because some friends earned PhDs from research groups whose advisors were much more kind & supportive, so on my own as well as when commiserating with friends who had toxic & micromanagerial advisors, I decried such toxic & micromanagerial advisors and expressed hope for cultural shifts that would reward experimental science & engineering research group leaders who could be more kind & supportive toward their graduate students.

Much more recently, at my current job, I have been working on a billable project that involves finding information for the client about building internal organizational trust, especially for encouraging productive conflicts of ideas. As I looked at those materials, I started to believe more strongly that kind & supportive advisors are exceptional in the experimental sciences & engineering despite being the ideal norm in other fields and that, unfortunately, research group leaders in experimental sciences & engineering may actually be structurally incentivized to behave in toxic & micromanagerial ways toward their graduate students. Moreover, I've come to believe that such structural incentives go beyond, though are compatible with, the idea that advisors who behave in toxic & micromanagerial toward their graduate students excuse or even defend those behaviors by claiming that their own advisors behaved similarly toward them and ascribing their own academic career successes to their ability to thrive when their advisors behaved in those ways toward them. (The latter point is essentially a career-specific manifestation of a cycle of abuse; it is often seen in abusive parenting when an abusive parent admits to being a victim of abuse by that person's own parents and claims to have come out of it "OK".)

The ideas underpinning these new beliefs of mine are related to each other and have many analogies in sports & sports management (the latter at least as far as I can tell as a layperson with respect to sports). I should note that these ideas are probably not new. The way that I am writing about them in this post is supported only by anecdotes from my own experiences as well as what I have heard about from relatives & friends, not by more rigorous data. Finally, as a reminder, all of these discussions only apply to the US (and maybe Canada, but I can't guarantee the latter). Follow the jump to see more about these ideas.

FOLLOW-UP: Learning and Making Sense of Differential Geometry in General Relativity

noreply@blogger.com (PV) — Thu, 02 Oct 2025 15:20:00 +0000

This post is a follow-up to the previous post [LINK] in which I tried to make sense of the mathematics of differential geometry, especially in the context of general relativity, and proposed notation that may be less confusing, more consistent, and arguably more powerful than traditional notation given the existence of a metric in general relativity. With similar motivations, this post explores how some of the ideas of electromagnetic (EM) theory may change on curved manifolds. Follow the jump to see more.

Learning and Making Sense of Differential Geometry in General Relativity

noreply@blogger.com (PV) — Sun, 14 Sep 2025 16:53:00 +0000

I have been out of the field of physics for over 5 years, didn't get to make use of my training in quantitative analysis too much in my previous job as a postdoctoral researcher at UC Davis, and make even less use of my training in quantitative analysis in my current job as a transportation planner at Cambridge Systematics. When I was doing work in my PhD in physics and when I was a student in school and college before graduate school, I enjoyed solving problems in math & physics and growing & applying my toolbox of quantitative skills, so since leaving the field, and especially more recently, I have felt a slight itch to recover some of those skills purely for my own personal satisfaction. To that end, I've resolved to learn or relearn some parts of math that I did not learn at all or to the full extent that I should have in college or graduate school (because I could ultimately manage my work in my PhD without knowing those things to that extent). Currently, I'm interested in learning differential geometry as well as complex analysis. It remains to be seen whether there are other topics in physics-relevant math that I become interested in; if they are, then I will certainly make an effort to learn at least a little bit about them. I've enjoyed learning these topics in math to broaden my knowledge & skills, and I've particularly enjoyed pondering definitions & rules of these concepts in math almost like a lawyer (which also makes this useful for my current job in a very indirect way, because my current job in part involves analyzing laws & regulations and creating intuitive explanations of them for public sector clients).

I can't guarantee that I'll write a blog post about every topic in math that I learn about. However, I am writing this post specifically about differential geometry in parts because I feel that I have learned the basic ideas in it in the context of general relativity to my satisfaction (which was my original goal) and because I have some questions/concerns that I have not been able to satisfactorily resolve based on what I have read in lecture notes or textbooks. This post is a way to further flesh out those questions/concerns. Follow the jump to see more.

There are a few conventions & assumptions to note throughout this post.

The dimension of the manifold will generically be denoted \( N \). For most nonrelativistic physics, \( N = 3 \), while for most relativistic physics (including general relativity), \( N = 4 \); exceptions include constrained low-dimensional systems or different physical models that have different dimensions analogous to differential geometry.
I will consistently use Einstein summation unless otherwise specified. This means that indices that are repeated with one as an upper index and one as a lower index will be summed; indices should never be present more than twice at all and more than once in the same (upper versus lower) position.
Although the convention in general relativity is to use lowercase Greek letters for indices, I will keep things easier to read by using lowercase English letters for indices.
The motivation of general relativity means that I will only consider differentiable manifolds and specifically smooth (infinitely differentiable) scalar functions or tensor components on them.
The motivation of general relativity also means that I will only consider torsion-free connection coefficients that can be expressed in terms of the metric.

Disability, History, Wilderness, Natural Parks, and Urban Spaces (Part 3)

noreply@blogger.com (PV) — Sat, 02 Aug 2025 12:00:00 +0000

This post is a follow-up to a post [LINK] explaining my mindset toward the notion of "wilderness" and appreciation of natural scenery versus urban scenery in the US. (That in turn was a follow-up to a post [LINK] about an essay by the environmental history professor William Cronon regarding the delusional or dishonest way that many Americans & Europeans have come to see notions of "wilderness" since the 19th century.) This post, which was not part of my original plan for this series of posts, was motivated by a recent vacation that I took with my family to eastern Washington & northern Idaho (which together form part of the inland Northwest, along with eastern Oregon & southern Idaho). In particular, my family & I, with me sitting in my manual wheelchair being pushed by them, took hikes on trails, usually built on former freight railroad tracks, that were paved with asphalt which was as smooth as advertised (smoother than many roads and much smoother than many asphalt walkpaths, including in some other state parks that we visited in that region).

There were specific instances when hiking on those trails where I felt like I was being hypocritical or unduly entitled, possibly at least superficially in contrast to my views & beliefs that I have articulated in the linked posts preceding this post in the series. This post is an exploration of those sentiments of hypocrisy & entitlement. Follow the jump to read more.

Different Types of Wet Summer Climates in the Plains of the US

noreply@blogger.com (PV) — Tue, 01 Jul 2025 14:00:00 +0000

As I have cataloged climates of places around the world, starting with the contiguous US, in order to categorize them according to the climate classification system that I have in mind (which I alluded to in my previous post [LINK]), I have noticed that climates in the contiguous US which have wet summer halves of the year & dry winter halves of the year, especially those in the northern Plains states as well as in the state of Montana east of the Rocky Mountains, have dry winter halves of the year because of cold air coming from the seasonal system of high pressure from the settling of cold air over the Great Basin or directly from the settling of cold air to form a system of high pressure over those specific regions. However, these climates have wet summer halves of the year for different reasons in different regions. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see the explanation.

Warmer Middle Latitude East Coasts than West Coasts in South America

noreply@blogger.com (PV) — Sun, 01 Jun 2025 13:00:00 +0000

Even though I published a post on this blog a few months ago [LINK] about my intuitions about climates of the world that do a much better job of explaining actual climates than any prior posts about climate on this blog (so I will not link to those posts within this one except for specific reasons) and therefore made me feel satisfied with my understanding of the climates of the world, there was one bit of dissatisfaction that lingered. At the end of that post, I alluded to creating a new climate classification system that would address some of the problems that I have seen in the Köppen & Trewartha climate classification systems. My specific problems with those climate classification systems are in the middle latitudes: at these latitudes, in the Köppen categorization, the climate type "Cfa" commonly found in North America almost never transitions within the same continent to the climate type "Cfb" commonly found in Europe, and in the Trewartha categorization, the Mid-Atlantic & Northwest regions of the US are assigned the climate type "Do" despite having extremely different climates (the latter particularly having noticeably drier & cooler summers, which the the Köppen categorization does a much better job of capturing). Even my modification of the Trewartha categorization didn't fully satisfy me, as there is still almost never any geographic continuity from the climate types "Dfak" to "Dfbk".

The actual new climate classification system that I have in mind will be the subject of a future post. However, thinking through my new climate classification system involved me looking at climate data from various places, and in that process, I saw that in the middle latitudes in South America, locations along the east coast have significantly higher annual average temperatures than locations along the west coast at the same latitudes due to having shorter & warmer winters. This is a significant contrast to the middle latitudes in North America & Eurasia (which are the only other continents that have significant landmass in the middle latitudes), where locations along the east coast have significantly lower annual average temperatures than locations along the west coast at the same latitudes due to having longer & colder winters. This can be seen in the following table of continents, latitudes, locations, and annual average temperatures.

Latitude (degrees)	Continent
Latitude (degrees)	South America	North America	Eurasia
38	West: 11.5 degrees Celsius (Lebu, Chile) East: 14.0 degrees Celsius (Mar del Plata, Argentina)	West: 12.7 degrees Celsius (Bodega Bay, US) East: 13.3 degrees Celsius (Ocean City (Maryland), US)	West: 16.3 degrees Celsius (Sines, Portugal) East: 12.8 degrees Celsius (Sendai, Japan)
38.75	West: 12.3 degrees Celsius (Temuco, Chile) East: 15.4 degrees Celsius (Bahía Blanca, Argentina)	West: 11.9 degrees Celsius (Point Arena (California), US) East: 13.9 degrees Celsius (Rehoboth Beach, US)	West: 17.4 degrees Celsius (Lisbon, Portugal) East: 11.4 degrees Celsius (Minamisanriku, Japan)
42.5	West: 11.6 degrees Celsius (Castro, Chile) East: 13.6 degrees Celsius (Puerto Madryn, Argentina)	West: 12.2 degrees Celsius (Gold Beach (Oregon), US) East: 11.1 degrees Celsius (Boston, US)	West: 14.8 degrees Celsius (Pontevedra, Spain) East: 7.9 degrees Celsius (Tomakomai, Japan)
46	West: 7.1 degrees Celsius (Balmaceda, Chile) East: 13.2 degrees Celsius (Comodoro Rivadavia, Argentina)	West: 10.8 degrees Celsius (Astoria (Oregon), US) East: 6.2 degrees Celsius (Sydney, Canada)	West: 13.5 degrees Celsius (Rochefort, France) East: 7.0 degrees Celsius (Wakkanai, Japan)
49.25	West: 5.8 degrees Celsius (El Chaltén, Argentina) East: 9.8 degrees Celsius (Puerto San Julián, Argentina)	West: 9.5 degrees Celsius (Tofino, Canada) East: 4.4 degrees Celsius (Eastport, Canada)	West: 11.0 degrees Celsius (Cherbourg, France) East: 0.9 degrees Celsius (Poronaysk, Russia)

That table shows that consistently poleward of 40 degrees in latitude, the west coast of South America is colder than the east coast of South America at the same latitudes, whereas the opposite holds for North America & Eurasia at the same latitudes (in the other hemisphere). Especially given that the warm current along the western edge of the Atlantic Ocean in the southern hemisphere turns away from the east coast of South America at a latitude of approximately 40 degrees even around the southern hemisphere summer solstice such that the water temperatures of 10-16 degrees Celsius at those latitudes are comparable to the water temperature along the west coast of South America at the same latitudes (in contrast to North America around the northern hemisphere summer solstice, where the water temperatures of 18-22 degrees Celsius along the east coast are much warmer than the temperatures along the west coast at the same latitudes) and given that the poleward tapering of the shape of South America means that the climates in that latitude range are dominated by the prevailing westerlies blowing throughout the year, this was a surprising result for me. Moreover, although the Gulf Stream being so warm even at the latitudes of Europe along with the seasonal system of high pressure from the settling of much colder air thereby being much stronger over North Asia compared to North America certainly amplifies the temperature difference seen in Eurasia, it does not fully explain this distinction, as the water temperatures along the west coast of North America at those latitudes are similar to those along the west coast of South America at those latitudes (in the other hemisphere). Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see the explanation.

Posting Less Often on this Blog Going Forward

noreply@blogger.com (PV) — Thu, 01 May 2025 14:00:00 +0000

Since I started this blog in 2009, I have been almost perfectly consistent in posting at least once every month on this blog, and even at times when I didn't have much to write about, I would think of something to write about so that I could continue my streak of posting. The one exception was in 2023 January, where my personal travel that month prevented me from posting in time (and I noted that in the post in 2023 February [LINK]). However, going forward, I see myself no longer holding myself to such a strict regular schedule of posting. This is for the following several reasons.

Internal reasons

There are a few internal reasons (in me) to consider. First, when I started this blog in 2009, I was in high school. I was in college during 2010-2014. During those years, my youthful energy surrounding the things on my mind and my enthusiasm about online engagement through blogs led me to post often, even when my posts weren't that well-formed. Since then, that enthusiasm & energy dissipated, so my frequency & volume of posts correspondingly decreased.

Second, in high school & college, I posted a lot of Linux distribution reviews and my takes on news surrounding free software, and this continued to a gradually decreasing degree over the first half of graduate school. In graduate school, especially around the middle, I read many nonfiction books, so I posted reviews of those books, and my youthful energy kept me motivated to read such books quite regularly. Around the end of graduate school and throughout my previous job at UC Davis, I posted about topics from physics & math, especially surrounding functional calculus, and these posts were interspersed with more introspective posts about my life as well as posts about moving away from popular cloud service & social media platforms. In the last couple of years of my previous job at UC Davis and slightly after that, I posted about my iteratively improving understanding of the Earth's climate. Now, I feel like I have said what I want to say about those things and learned & tried those things to my satisfaction, so I don't feel motivated to go further into those things for myself or for the sake of this blog.

Third, more broadly, my greater age now compared to the early years of this blog have led to a more calm & sedate mindset that makes me less motivated to post on this blog just for the sake of doing so. I find that my motivation to try some other things has decreased too, perhaps in part because of the traumas that I have experienced over the last several years (like being hit by a car [LINK]) and because of my current opportunity to fulfill my desire to live a quieter life where I don't have to hustle or live in suboptimal conditions just for the sake of my career. I am quite content to work at my current job, which I enjoy very much, to spend time with friends & relatives in my area and stay in contact with those farther away, and to take care of myself physically by eating right & swimming and mentally through introspection.

Internet-related reasons

Separate from my own internal motivations, there are a few reasons related to the Internet to consider. First, I have seen that most popular search engines on the Internet yield less useful information these days compared to several years ago because so much textual and even video content is garbage generated by artificial intelligence (AI). This both makes it hard stay motivated to post anything on the Internet (as a human) and makes me wary to post anything if my content will be used by AI in unpredictable or even dangerous ways.

Second, I had hoped that this may be of use to people who may come across this on the Internet. However, as almost all popular use of the Internet these days seems to be through social media platforms, especially Facebook, WhatsApp, Instagram, TikTok, and YouTube, blogging seems to have been an abandoned medium within the Internet for a long time. I am satisfied maintaining my own personal diaries for my own use, so I won't necessarily miss posting things on this blog for that reason.

Third, the current political situation in the US is dire. Legal residents in the US are being forced to turn over their social media activity for the federal government to review for activity that may go against the government's foreign policy stances, per the Associated Press [LINK]. Arrests by federal officials have ensnared US citizens and have become arbitrary & seemingly without accountability, also per the Associated Press [LINK]. Even though I haven't posted much political content on this blog in a long time and even though I can't avoid the possibility that the government may arbitrarily punish me for posts from long ago going against the government's stated partisan beliefs, I don't want to increase my liability further by posting more.

Going forward

I will still post reviews of books that I read after I read them, though my reading of books has become less regular over time. If there are things that I ponder about physics, math, climate, or other things that compel me to write about them in this blog, then I will do so. Finally, I may post things about current events if I feel that such events compel me to no longer be silent in public.

With all that said, this post may be the last post on this blog, and even if it is not the last post on this blog, it may be close to the last post on this blog, with whatever post ends up being the last post on this blog likely not noting the fact of it being the last post on this blog. For whoever happens to be reading this, please feel free to peruse this blog, starting with its first post nearly 16 years ago [LINK]. I know that this blog has lost almost all, if not all, of its human readers over the last decade, but I do wish to express my sincere gratitude for every person in my life and every stranger online who read these posts and expressed support or constructive criticism.

Green's Functions and Violin Making

noreply@blogger.com (PV) — Thu, 17 Apr 2025 23:34:00 +0000

A few years ago, a friend of mine, who is a very accomplished player of the violin & viola and who is an amateur builder of violins & violas, sent me a video on YouTube [LINK] of the violin maker Peter Westerlund showing how to create violins (and violas, by the same logic and with only slightly different overall dimensions) that consistently produce sounds that people well-versed in European classical music judge to be of high quality. Many such people have praised the consistent warm & rich aural tones of violins & violas made in Italy by Andrea Guarneri around 1650 & Antonio Stradivari around 1700, yet it has been difficult for any violin maker to replicate such warm & rich tones in the violins that they have made, in part because there is little scientific consensus about the specific acoustic spectral qualities that make those violins so highly valued. Further complicating matters, as explained in a news article by Science magazine in 2017 [LINK], is the fact that many blind & double-blind studies have left musicians & keen listeners preferring contemporary violins over those made by Stradivari or Guarneri. Even if the instruments by made by Stradivari or Guarneri aren't consistently rated the best, they are rated very highly far more consistently than those made by other violin makers (though this may reflect selection bias in such tests), so there may be merit to considering how to replicate those instruments' aural qualities.

Traditionally, violin makers have carefully studied the exact dimensions, shapes, and materials used in instruments made by Stradivari or Guarneri and done their best to replicate them. However, the resulting aural qualities have typically been judged to be unsatisfactory. This is in various parts due to the effects of aging on the material components of violins (which generally cannot be artificially accelerated), one-off differences in instances of even the same materials used, slight deviations in the craftsmanship, shapes, or dimensions, and other factors that have yet to be explained. This motivated Westerlund (who is probably not the first person to come up with this method) to develop a method to reliably create instruments with highly consistent sounds even if they don't replicate sounds from instruments made by Stradivari or Guarneri per se. The method is as follows. Each violin or viola has a top plate and a back plate, and these are initially constructed separately, joined only later on corresponding sides of the ribs. For each plate, after getting the basic shape & thickness correct, the violin maker should further adjust the shape by tapping or rubbing the plate in various locations, ideally using the same tapping or rubbing motion with the same intensity every time. The violin maker should iteratively shape (by cutting or scraping) at & around those locations of tapping or rubbing and then continue to tap or rub at all locations, until eventually, the tapping or rubbing motion produces approximately the same tone at every location. Once that has been achieved, shaping of the plate is finished.

My background in theoretical & computational nanophotonics from graduate school, even though I was already a few years removed from that even by a few years ago (having changed fields to transportation research after graduate school [LINK]) when my friend shared that video with me, made me interested in trying to mathematically & physically understand why Westerlund's process is successful in creating instruments that have strong internal tonal consistency. However, I wasn't able to come up with a satisfactory answer until much more recently. Follow the jump to see more of my thinking about this, leading to the resolution.

More Quantitatively Founded Intuitions About Climates

noreply@blogger.com (PV) — Tue, 04 Mar 2025 03:03:00 +0000

My last post on this blog [LINK] about my intuitions for climates was over 1 year ago, in 2024. Since then, I have continued to read more about climates of the world. Later in 2024, I was particularly more careful to look at maps of mean surface-level wind velocities. This led me to start to carefully catalog the climates of the world and attempt to explain them based on mean surface-level pressures & wind velocities along with qualitative ideas about the differences between air masses at different temperatures & humidity levels. I felt satisfied doing so for Oceania as well as for Africa in the southern hemisphere. I did so for South America at the middle latitudes (which is entirely within the southern hemisphere) too, and I thought of continuing through tropical latitudes in South America, near-equatorial latitudes in Africa, and thereafter all tropical, subtropical, middle, and subpolar latitudes in the northern hemisphere. However, as I looked more carefully at these maps and compared them to actual climate data from various locations, I started to think that my understanding of these climactic processes is too limited, especially by my focus on qualitative understanding of surface-level phenomena, to be able to come up with accurate explanations. (Even looking back at the post linked at the beginning of this paragraph and even older posts linked within that post, I can see how many things I have said in those posts that I know now to be inaccurate.) Because of that, I shelved the idea of continuing with these detailed explanations until much more recently, when I started looking more carefully at maps of sea/ocean surface temperatures and at calculations of air density at various pressure levels, humidity levels, and temperatures. This made it possible for me to reinforce my intuitions about temperatures & precipitation distributions at various locations in the aspects in which they were correct and fix them in the aspects in which they were wrong. Thus, this blog post is meant to be that originally-intended compendium of explanations for climates in various parts of each comment in tropical, subtropical, middle, and subpolar latitudes (excluding Antarctica).

The sources that I used were many relevant pages from Wikipedia, the Columbia University interactive maps of mean monthly wind velocities [LINK] & mean monthly sea/ocean surface temperatures [LINK], the European Centre for Medium-range Weather Forecast static global maps of mean surface-level air pressures in different astronomical seasons [LINK] (though this website has very recently started displaying a warning that the maps are now out of date), and the OmniCalc air density calculator [LINK]. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations. Follow the jump to see these explanations.

Book Review: "Noise" by Daniel Kahneman, Olivier Sibony, and Cass Sunstein

noreply@blogger.com (PV) — Mon, 03 Feb 2025 18:04:00 +0000

I recently read the book Noise by Daniel Kahneman, Olivier Sibony, and Cass Sunstein. I will refer to it as the current book, because it was written after the book Thinking, Fast and Slow by Kahneman (one of the authors of the current book); I will refer to the latter book as the previous book because many concepts from the previous book are briefly reviewed in the current book, and as I reviewed the previous book in the post just before this one on this blog [LINK], I will sometimes compare some aspects of the current book to the previous book.

The current book introduces the concepts of statistical noise & statistical bias in human judgments, discusses the psychological biases that can lead to statistical biases & noise (of which statistical noise can be clearly seen even in the absence of clear information about statistical biases), demonstrates how statistical noise can lead to uncontrolled & large variations in human judgments in fields like criminal justice, medicine, forensic science, insurance claims adjustment, corporate hiring, and college admissions, explains the sorts of systematic techniques at individual & organizational levels that can be used to reduce noise in judgments, and discusses some tradeoffs that may be encountered when implementing these noise reduction strategies. The authors' discussion of many of the psychological biases that lead to statistical noise in judgments reviews concepts from the previous book, especially Systems 1 & 2.

When reading the current book, I found myself generally agreeing with the discussions of techniques to reduce noise in domains where the presence of significant statistical noise in judgments is broadly recognized as a severe problem. These techniques include aggregating predictions or evaluations that are made independently, structuring/sequencing discussions among people judging things so that their decisions don't affect each other through emergent group-based social dynamics, carefully accounting for base rates from external information when assessing various internal probabilities, and breaking up decision processes into smaller steps that are more clearly defined in their intent and in example decisions/anchors. It helped a lot that I had read the previous book first, such that even if I didn't remember every detail of every psychological bias presented in both the previous book and the current book, those things looked familiar upon reading them in the current book.

There were also a few new things that I learned from the current book. I learned about how the process of judgment feels so satisfying and infuses confidence into the person making the judgment specifically from the psychological signal of having completed the judgment, which explains why so many people who make professional judgments in many domains are so reluctant to turn their discretion over to more systematic rules or algorithms. I also learned about how simple models of human predictive judgments, when those predictive judgments are about specific outcomes, may do a better job at predicting the outcomes that are the objects of judgment than at predicting the judgments that humans would make, simply because those models lack within-person noise pervasive in human judgments.

However, my overall opinion of the current book was shaped more by the many major and minor (the latter to an appropriately lesser extent) criticisms of it. These minor and major criticisms as well as my concluding remarks will be presented in separate sections as follows after the jump; the spoiling of my concluding remarks is simply that I do not recommend this book to others.

Book Review: "Thinking, Fast and Slow" by Daniel Kahneman

noreply@blogger.com (PV) — Fri, 03 Jan 2025 02:30:00 +0000

I started reading the book Thinking, Fast and Slow by Daniel Kahneman in early 2024. This was initially recommended to me by a friend, and I became even more motivated to read it upon hearing positive things about it from colleagues at my previous job, as many of the subtleties described in the book are extremely relevant to the appropriate design of interviews, focus groups, and surveys of human subjects in social science research. However, because it is a long book and the middle of 2024 was made busier for me by moving back to Maryland, traveling a lot, and starting a new job (some of which I have discussed in a previous post [LINK]), I could not finish reading this book until much more recently. Because of this large gap between reading the initial 60% and remaining 40% of this book, I admit that I have since forgotten many details from the initial 60% of this book. Moreover, I started making notes to myself in this post based on that initial 60% because I assumed that I would be able to finish reading the remaining 40% soon afterwards and I would therefore remember the book as a coherent whole, but because that didn't happen, many of the notes that I have made in this post that were supposed to form the skeleton of this post now no longer make as much sense to me. For these reasons, this post may seem a bit more stilted than other book review posts in this blog and will likely seem stronger/more coherent when discussing the latter 40% of the book.

The book is a lengthy exposition of novel ideas in psychology & behavioral economics that were empirically validated by the author, most often in conjunction with his longtime academic collaborator Amos Tversky. The concluding chapter does a good job of recapitulating the main ideas of the book. Most of the book explores various facets of individual & group-based human behavior based on the idea that there are effectively 2 modes through which individuals process information, which the author refers to as Systems 1 & 2. System 1 "thinks fast", making snap judgments based on limited information, heuristics, and a bit of laziness, and is the aspect of thinking that drives most day-to-day reactions & decisionmaking, while System 2 "thinks slow", making more deliberate judgments with more of an effort to gather all relevant information but must in turn be consciously engaged and ultimately disengages from mental fatigue (in favor of System 1) if engaged for too long. The book also considers how individuals' typical behaviors when faced with outcomes that are certain competing with outcomes that have known or unknown probabilities deviate from behaviors idealized by microeconomic theories of expected utility, notably that while the commonly observed behavior choosing a certain gain with a lower value than the expected value of an uncertain gain can be explained to some degree by expected utility theory, the commonly observed behavior of choosing a gamble on losing outcomes with an expected loss of larger magnitude than a different certain loss cannot be explained by expected utility theory; this partly explains the risks that people take in business and can be explained in turn by how people in their perceptions tend to overestimate probabilities that are close to but not exactly 0 and underestimate probabilities that are close to but not exactly 1. Finally, the book partly explains notions of hedonic adaptation (the idea that one's sense of well-being is generally similar in many different good or bad medium- or long-term circumstances by adapting to those circumstances) by distinguishing how people rate pleasure or pain when experiencing those things versus in hindsight and shows how people's conceptions of their identities & well-being in the past, present, and future are intimately tied to their actual memories and their abilities to form & retain memories. These aspects of self-conception as well as perceptions of probability can also be tied to Systems 1 versus 2, as many seemingly shortsighted decisions or perceptions can be explained by System 1 making snap judgments lazily & using heuristics based on incomplete information.

Especially as I read the latter 40% of the book, I came to appreciate how many of the ideas of this book had permeated into other things that I had read & heard from others and that I had internalized into my own worldview & view of myself. Professionally, I could see how so many aspects of framing could be important when designing surveys & focus groups. Personally, I could see how especially as I have aged, I have in many cases consciously chosen to not worry too much about certain details and instead make decisions based on lazier heuristics because I didn't feel that the results of spending more mental energy making a decision based on System 2 would be worth the effort. At the same time, I have become more consciously aware of how my memories of things in my own life can be affected by the passage of time and by more recent events in my own life, and I have become more consciously aware of the deep entanglement between my perceptions of my own memories and the narratives that shape my perceptions of my own life & of the world. I thus feel more proud of maintaining detailed personal diaries where I take note (using System 2 as much as possible when considering things outside of the current moment) of how I feel about various things in the moment as well as in hindsight and carefully consider how & why my thoughts & feelings about different events in or aspects of my life have evolved over time. Moreover, I have become more aware over time of when I might be vulnerable (through System 1) to the power of suggestion or to a subconscious desire to align with groupthink, though given that it is System 1, I am not necessarily aware of these things until later (thinking about these things through System 2). Finally, especially over the last several years, I have come to see many things at a very broad conceptual/philosophical level, whether the experiences in my own life, the evolution of different aspects of human society, or the expansion of human knowledge, in terms of perdurantism [LINK from Wikipedia]; although I am not philosophically sophisticated enough to be able to think through & defend all of its implications, it intuitively makes sense to me to think about personal identities, feelings, people, and other things that can be said to exist, in terms of their existence in spacetime and not just in space at specific instants of time. Because of my philosophical inclination in this way, I was particularly pleased to see the author discuss the idea of time-integrated pleasure or pain and of looking at changing identities or overall life courses in terms of spacetime.

Although this book is not technical at the level of an academic journal article, it is fairly technical compared to most nonfiction books aimed at the general public, so I would say that it is aimed at a well-educated reader. That said, I do think that it is written with reasonable clarity for non-academic audiences. Additionally, the book covers many topics, and it is recommended to bear in mind the headings of sections that comprise groups of chapters, because otherwise, it is easy to lose track of the narrative of the book, especially because the book is long enough that I suspect that it would be impossible for most readers (even those who read books, including more technical nonfiction books, relatively quickly) to finish this book in one sitting. I would say that the concluding chapter is a nice way to reinforce the main points of the book in the reader's mind and that the details of each chapter can be treated as a reference when needed as opposed to forming a perfectly coherent narrative in the progression of chapters in the book.

It is important to remember that some aspects of this book are out of date. In some cases, that is just because this book was published in 2011 and had been written over many years before that; for example, the author gives an example of estimating the likelihood of choosing a particular major in college, but that example uses base rates that seem to be quite out-of-date. In other cases, the book is out of date because it is based on academic experimental work in psychology & behavioral economics, and other studies may find contradictory (either null or opposite) results to those presented in this book. The Wikipedia article about this book [LINK] discussed how most of the results from most of the studies discussed in one chapter (as an example) have been found to be not replicable, with the author afterwards admitting to putting too much faith in those studies and therefore falling prey to the same biases as those discussed in that chapter & elsewhere in the book. As a slightly different example, later parts of the book discuss the ideas of nudge theory and its seeming successes in public policy, but the Wikipedia article about nudge theory [LINK] has pointed out that later studies & meta-analyses have found that after correcting for publication biases in favor of positive results & against null results, nudging does not yield statistically significant (non-null) effects on human behavior; in this case, one of the primary researchers (who is named in this book as a collaborator of the author & pioneer of nudge theory) has made some counterarguments that I don't find convincing.

With these caveats in mind, I would still recommend this book to anyone interested in these ideas and with the patience to carefully consider them, though this may partly reflect my own biases in how I view issues of identity & the world. Follow the jump to see my other assorted & disjointed thoughts about this book.

Third Laptop: Lenovo ThinkPad P14s

noreply@blogger.com (PV) — Wed, 04 Dec 2024 23:05:00 +0000

My previous laptop was an ASUS UX331UN, and I wrote a post when I got it 6 years ago reviewing it [LINK]. It served me well, so I figured for a while that when it came time to replace it, I would most likely get another ASUS laptop. Over most of this year, I noticed progressively more often when using that laptop that it would make an odd whirring sound, and that would be especially noticeable when it would be shutting down. This motivated me to start considering to get a new laptop. More recently, the recent US presidential election result forced the issue for me, as I was concerned that the president-elect, once inaugurated, would impose heavy tariffs on many different countries that would significantly impede global supply chains that are essential for the manufacturing of electronic goods, including laptops. Thus, I thought carefully about and made the decision to buy a new laptop. Follow the jump to see more.

Some Dangers of Confusing "Changing One's Mind" with "Bayesian Updating"

noreply@blogger.com (PV) — Sun, 03 Nov 2024 15:52:00 +0000

Recent conversations with friends & colleagues about probability theory reminded me of conversations with a friend of mine in graduate school about the supposed virtues of making one's own reasoning in one's daily life more systematic through Bayesian inference. The basic idea, in rough qualitative terms, is that one's belief in a hypothesis can be quantified through a prior probability, and when one observes some data related to that hypothesis, one can use the probabilities of observing that data when that hypothesis does or does not hold to update one's belief in (becoming the posterior probability of) that hypothesis based on the data. An example of quantitative & qualitative explanations can be found on the site LessWrong [LINK]. However, even in graduate school and again more recently, I realized that it is very easy for one to talk oneself into believing that one is using systematic Bayesian reasoning while actually just rationalizing one's own prior beliefs & changes in beliefs after the fact. This can be illustrated mathematically in a few ways that are not exhaustive. Follow the jump to see more.

Disability, History, Wilderness, Natural Parks, and Urban Spaces (Part 2)

noreply@blogger.com (PV) — Sun, 13 Oct 2024 13:07:00 +0000

This post is a follow-up to a post [LINK] about an essay by the environmental history professor William Cronon, which in turn was about the ultimately delusional, dishonest, or hypocritical (the particular adjective depending on one's viewpoint) way that many Americans & Europeans since the 19th century have viewed the ideas of "wilderness" and of being close to said "wilderness". That essay, recommended to me by a friend, strongly resonated with me because of my own ambivalence, developed over the course of the 3 years that I physically lived in California with my opinions strongly shaped by my lifelong disability and events that happened to me related to that (particularly being hit by a car [LINK]), about the ways that people in the western half of the contiguous US value "wilderness" or natural parks that don't make a lot of sense to me or don't seem coherent to me based on how most natural parks in the US as designed today exclude people with disabilities in many different ways. Because I have written notes about these and other events & thoughts in my life consistently for the last several years, I think it makes the most sense to first structure this post chronologically to lay out the development of my ambivalent mindset toward the extent to which other people have a particular positive view of "wilderness" that they highly value and then summarize these points more coherently in another section. I should warn that the chronological narration is quite repetitive in writing only because similar ideas occurred to me in marginally different from different stimuli at many different points in my life. In any case, I think that presenting the chronological narration is the most honest way to present my mindset, because "showing my work" makes it much less likely to mislead anyone (including me, as my specific memories naturally become more hazy over time) into assuming that I have felt or thought a certain way for longer than I actually have. Follow the jump to see more.

Disability, History, Wilderness, Natural Parks, and Urban Spaces (Part 1)

noreply@blogger.com (PV) — Sat, 28 Sep 2024 16:36:00 +0000

Over the 3 years that I physically lived in California (as I worked remotely for UC Davis remotely from Maryland for 1 year before that), I became progressively more ambivalent about the reverential attitudes that many people in California and more broadly in the western half of the contiguous US (including the Northwest, Mountain West, and Southwest) have toward wilderness and natural parks and a little bitter that such reverence could directly be connected to the way that urban spaces in this part of the US feel far more neglected and bare-bones than urban spaces in the Northeast & Mid-Atlantic do; the bitterness is related to my personal need, as someone with a disability who does not drive, for spaces with good public transit, safely walkable paths, and dense mixed-use development. I had thought about these issues more especially during this year, but thus far, I had not considered writing blog posts about these thoughts. It was only after reading the essay "The Trouble with Wilderness" published in 1995 by William Cronon [LINK], recommended to me by a friend who thought that I might be sympathetic to the arguments in the essay, that I felt compelled to further flesh out & share my thoughts about these issues in this blog.

The essay explains the dichotomies & hypocrisies inherent in primarily middle-class and rich American perceptions of wilderness and how these attitudes arose. The author explains how until the 19th century in North America & Europe, and until even later in many other parts of the world, wilderness was seen by most urban cultures as dangerous, desolate, and leading people through such desolation to despair & amorality, the latter exemplified by Rudyard Kipling's popularization in the late 19th century of the savage "jungle law". Additionally, there were roots before the 19th century of the idea of spending time in wilderness as leading to religious experiences, but such experiences were clearly meant to evoke terrified awe (consistent with the little bit that I understand about Christianity regarding its emphasis on sin & guilt) as opposed to transcendent bliss, and they were associated with people exiling themselves from society for tough religious penance, whether in the cloisters of a monastery or in a forest far from the comforts of urban civilization. The author explains that the transformation of popular perceptions of wilderness from negative to positive came in the 19th century in Europe & North America, as the perceptions of religious experiences shifted to being more uniformly positive & comforting and simultaneously as local governments started building more amenities to tame wilderness into being a natural park for tourists; I suspect that this also coincided with Friedrich Nietzsche's work on the overman (the self-realized man striving for betterment in conjunction with enjoyment of the world) being interpreted as humanity having a greater degree of control over nature and with the rise of prosperity theology in the US, but I am not yet well enough read to comment intelligently on Nietzsche's work, and in any case, the author does not explicitly make such connections or arguments. The author describes how this shift in perception was reinforced at the same time specifically in the US by the promotion of frontier myths; I was previously familiar with how the frontier myth played into those reverential attitudes in the US toward wilderness, but I didn't make the connection until reading this essay of this myth to the way that the people, including Teddy Roosevelt, who pushed this myth & related reverence for natural parks were in fact rich white American men who grew up in urban comfort & benefited from industrialization and were rewriting the frontier myth in their own image, contradicting the reality that most people, including cowboys, who worked on the actual frontier were racially, sexually, or otherwise socioeconomically marginalized by the settled WASP-dominated society in the Northeast & Mid-Atlantic. The author ties this erasure of history to how the reverence for natural parks among many Americans who grow up in urban settings took root because of the combination of feeling alienated from industrial areas (which were genuinely dangerous & polluted places to live in the 19th & early 20th centuries) and being ignorant of what undeveloped land (wilderness) is really like. The author argues that such positive perceptions are counterproductive for understanding how humanity can actually live sustainably with nature as such attitudes unduly compartmentalize "nature" as being irretrievably separate from humanity, and when combined with negative attitudes about urban environments & rigid beliefs that humanity destroys everything that it touches in nature, this leads to the logical (within its own axioms) yet incredibly depressing nihilistic conclusion that humanity should cease to exist. The author emphasizes that comfortable & positive experiences in the wilderness are too often accessible only to rich people in urbanized areas (in the sense of having the time & transportation to get to natural peaks that have a lot of physical infrastructure & amenities built deliberately, irrespective of the level of luxury of a given private tour) and that this has been true since the 19th century in North America & Europe. Finally, the author argues that it would be better to appreciate & cultivate nature closer to home even in urban settings.

My friend was correct; I did indeed feel that this essay strongly resonated with me, as I have had similar thoughts about the effects of the frontier myth on popular reverence for natural parks in the US and about the myth versus reality of human infrastructure & amenities in natural parks being marketed as "true wilderness". It is worth noting too that the word "jungle" came from the Sanskrit/Hindi word "jaṅgala", which originally meant "desert" (emphasizing the aridity) and was later expanded to refer to any place hostile to human settlement, but its application to thick forests with overgrown understories was based on a misunderstanding by British colonizers in India in the 19th century (which does not surprise me); this is relevant to illustrating perceptions in other cultures of wilderness and of shifts in perception in the 19th century, as other scholars who have published similar essays or book chapters in books or collections edited by William Cronon have showed how the shift in English away from the word "jungle", which had negative connotations, to the word "rainforest" was associated with a softening of the popular image of such ecosystems (previously seen in Europe and by white North Americans as harsh & antithetical to humanity).

I have learned over the last few years of discoveries over the last few decades about the ways that indigenous societies in America (considered as a single continent), before European colonization, shaped environments that in the 20th century were assumed to be untouched wilderness. The shaping took the form of light-touch agroforestry, silviculture (forest cultivation), and polyculture (farming many plant or animal species together in ways that are sustainable due to those species' ecologically mutualistic relations, as opposed to the monoculture prevalent in industrialized farming). Examples include the Amazon rainforest [LINK] whose shaping supported large & diverse highly-developed cities [LINK], wildflowers in the deserts of California [LINK] making clear that even the term "wildflower" in that context is a misnomer that erases indigenous American work on cultivating those plants over many generations, and the temperate rainforests of British Columbia where biodiversity was much higher due to human selection near indigenous settlements than farther away [LINK]. These discoveries came after William Cronon published his essay, so I hope that he would be aware of these more recent discoveries (as he retired from his tenured faculty position only within the last few years). Learning about these things motivated me to learn a little more, from Wikipedia, about agroforestry, silviculture, and polyculture. They seem like promising ways to promote soil fertility, biodiversity, greater resilience against pests & natural disasters, ecological health, and human health. However, it is important to recognize the tradeoffs between these benefits and the need for extensive delicate & prolonged human labor, given the implications for our current population level & standard of living in the US, instead of uncritically romanticizing such practices as better in every way than current practices of monocultures & mechanized farms, especially if such romanticism is a reflexive opposition to white dominance in the various countries of America, with that opposition in turn arising from sympathy with indigenous peoples who have been & continue to be oppressed. In particular, livestock & machines currently struggle to work well with any farming method other than monocultures, so scalability would be a problem, though I am optimistic that AI tools could be paired with more carefully-designed machines to more effectively seed & harvest more complicated crop growths in forests or polycultures.

The essay by William Cronon didn't have as much about disability or the neglect of urban spaces, which are more salient to my experiences. Thus, the extent to which the essay resonated with me because of those issues was more because my mind was filling in those gaps. For this reason, I am making this post one in a multi-part series, with this part focusing more on the essay itself and more directly related issues of indigenous land cultivation (as William Cronon's treatment of indigenous issues, which is understandable given the state of popular knowledge & research in the US in 1995, is with a sad tone as if indigenous peoples in America had been completely wiped out & existed only in the past, ignoring the ways that indigenous peoples in America continue to preserve traditional land management practices & shape their lands accordingly, even if those things happen now on much smaller scales than they did before European colonization). The next post in this series will focus more on my experiences & thoughts from the standpoints of disability & urban neglect; I may have more posts afterwards only if there is a clear need to break the material into shorter posts and there is a clean way to separate the posts by topic.

My time at TRB CATE 2024

noreply@blogger.com (PV) — Thu, 08 Aug 2024 12:00:00 +0000

Last month, I attended the TRB 2024 Conference on Advancing Transportation Equity (TRB CATE 2024). The conference, which was held in Baltimore, was probably the most enjoyable conference that I have attended thus far (though I have not attended that many), for the following reasons mostly related to how good it was for networking. First, the number of attendees, which was around 500, was enough for almost all of the attendees to meet new people & network effectively; the presence of fewer attendees might lead to a situation where a large percentage of the attendees know each other, leading to other attendees feeling left out, while the presence of more attendees might lead to most attendees feeling overwhelmed by the prospect of meeting attendees unknown to them and therefore discouraged to do much other than spend time with known attendees (as often happens in the TRB Annual Meetings). Second, the conference was more focused on equity issues in transportation, so attendees were very passionate about this issue, and this led to more positive vibes & more fruitful discussions (in contrast to something like the TRB Annual Meeting, where the breadth of topics means that it is unlikely for someone working on pavement engineering to have much in common with someone working on public transit network redesigns). Third, conference organizers explicitly encouraged (at multiple points during the conference) attendees to network, and the schedule (especially including the presence of multiple poster sessions structured as receptions/mixers) included a lot of time for networking instead of being packed from start to finish with highly structured sessions.

I am especially grateful to my current employer for sponsoring my attendance given that I presented a poster about work from my previous job (and, interestingly enough, this was personally my first time presenting a poster in any professional setting). It reflects well on my current employer's willingness to take chances with their employees and supporting employees' presence at such conferences so that the employer's name is more publicized and the employee gets the professional development benefits of learning & networking. Additionally, I got to meet several of my colleagues in person, which felt even better given that most of us work remotely and many of them live in different parts of the US. As this conference happened during the second week of my current job, it really felt like an auspicious way to start this job.

Starting a Job at Cambridge Systematics

noreply@blogger.com (PV) — Sun, 21 Jul 2024 13:10:00 +0000

I am pleased to share that I have started a job at the transportation consulting company Cambridge Systematics as of 2 weeks ago, being based out of its office in the DC area (where I grew up). (Note that this company, which was founded in Cambridge, Massachusetts in the US, is a different company than the social media data mining company Cambridge Analytica, which was founded in Cambridge in the UK and was notable for its mining of user data from social media sites for the purpose of targeted political advertising in the 2016 presidential election in the US [LINK from Wikipedia].) The company takes on clients primarily from government agencies at the federal, state, and local levels to do work on long-range planning, travel demand forecasting, big data analytics & modeling for passenger & freight transportation, transportation safety planning, public transit planning & operations, and public transit & highway asset management. I will primarily be working on projects related to shared mobility, public transit, long-range planning, and transportation safety, but I will not necessarily be restricted to these areas.

I am excited to be working at this company, as it will give me a different perspective on transportation than I had within academia. Additionally, unlike in academia where I was focused on leading & managing a few projects over a long period of time in which those projects would lead to research products but might not necessarily have any more immediate tangible impact, in this company, I will be able to work on a wide variety of shorter-term projects that will have more immediate tangible impacts for people. I got into the transportation sector to help people with disabilities, and although many of the projects at this company might not directly relate to the needs of people with disabilities, I look forward to bringing up those issues where possible & applicable, using these projects to educate colleagues & clients about these issues where possible & applicable, and having tangible (even if incremental) positive influences on transportation for people with disabilities through the completion of these projects.

Reflection: Leaving UC Davis

noreply@blogger.com (PV) — Thu, 13 Jun 2024 13:53:00 +0000

This week is my last week as a postdoctoral researcher at the UC Davis Institute of Transportation Studies (ITS-Davis). I am glad that I was able to transition from physics to transportation policy within the setting of academia and to particularly to so at ITS-Davis, which is renowned for having multidisciplinary transportation research & education that has included an increasing focus on issues of equity & accessibility in transportation planning. I learned so much, not just about transportation per se (which, in a professional context, was totally new to me when I started this job) but also about hiring, advising, and managing graduate students, applying for grants, managing grant-funded projects, communicating with different audiences beyond academia in many different forms, working on projects that are not just academic research ending in a peer-reviewed journal article, forming & managing relationships with stakeholders from government agencies, community-based organizations, and other organizations, and expanding my professional network on my own. This ultimately became the right time for me to leave ITS-Davis, but I will be grateful for the experiences & opportunities that I had in it and for the people that I got to work with.

Finite Determinants of Linear Operators in Continuous Vector Spaces

noreply@blogger.com (PV) — Thu, 02 May 2024 15:27:00 +0000

Recently, I wondered whether it is possible for a linear operator in a continuous (infinite-dimensional) vector space to have a finite determinant. By "continuous vector space", I mean that the identity operator can be resolved for a complete orthonormal basis \( |\phi(x) \rangle \) for all \( x \) such that \( \langle \phi(x), \phi(x') \rangle = \delta(x - x') \) as \( \hat{1} = \int |\phi(x)\rangle\langle \phi(x)|~\mathrm{d}x \). If an operator \( \hat{A} \) has continuous matrix elements \( A(x, x') = \langle \phi(x), \hat{A}\phi(x') \rangle \), then it is easy to see that the conditions for its trace \( \operatorname{trace}(\hat{A}) = \int A(x, x)~\mathrm{d}x \) to be finite are that the integral must converge, so the "function" \( A(x, x) \) must asymptotically approach 0 strictly faster than \( 1/x \) as \( |x| \to \infty \) and must at most have singularities at finite points \( x_{0} \) that diverge strictly slower than \( 1/|x - x_{0}| \). This can be seen as the continuum limit of a sum over the diagonal. However, the determinant is harder to express in this way because it involves products over diagonals & subdiagonals that are harder to express in a continuum space.

For this post, I will only consider Hermitian positive-definite operators. The conditions that I will list for which the determinant exists for such operators are sufficient for the determinant to exist, but I am not convinced that they are necessary. If such operators have an eigenvalue decomposition \( \hat{A} = \int a(x) |\phi(x)\rangle\langle \phi(x)|~\mathrm{d}x \) where the vectors \( \{ |\phi(x) \rangle \} \) form a complete orthonormal basis and the eigenvalues satisfy \( a(x) > 0 \) for all \( x \), then one can make use of the identity \( \ln(\det(\hat{A})) = \operatorname{trace}(\ln(\hat{A})) \) to say that \( \ln(\det(\hat{A})) = \int \ln(a(x))~\mathrm{d}x \). For the right-hand side to converge, then \( \ln(a(x)) \) must asymptotically approach 0 with \( x \) as \( |x| \to \infty \) strictly faster than \( 1/x \), which means that \( a(x) \) must asymptotically 1 with \( x \) as \( |x| \to \infty \) strictly faster than \( \exp(1/x) \) (which is not the same as \( e^{-x} \)), and \( \ln(a(x)) \) can at most have singularities at finite points \( x_{0} \) that diverge strictly slower than \( 1/|x - x_{0}| \), which means that \( a(x) \) must either diverge to \( \infty \) strictly slower than \( \exp(1/|x - x_{0}|) \) or drop to 0 strictly slower than \( \exp(-1/|x - x_{0}|) \). For example, \( a(x) = \exp(1/(x^{2} + x_{0}^{2})) \) fits the bill; note that this is not the same as the Gaussian kernel \( \exp(-(x^{2} + x_{0}^{2})) \). Intuitively, this condition makes sense, because for a finite-dimensional diagonal matrix as the dimension becomes arbitrarily large, the diagonal elements must mostly be exactly or very close to 1 for the determinant to not grow arbitrarily large with the dimension.

In finite-dimensional vector spaces, it is also easy to compute the determinants of triangular matrices simply as the products of the diagonal elements. (This is why the determinant is most often computed by an algorithm like first computing the LU decomposition and then taking the product of the diagonal elements of the upper-triangular matrix, which for an \( N \times N \) matrix involves \( O(N^{3}) \) operations, as opposed to the Leibniz formula involving every permutation which involves \( O(N!N) \) operations.) In infinite-dimensional vector spaces, a matrix that is triangular in a countable basis can have the determinant computed similarly as in finite-dimensional vector spaces; if an operator \( \hat{A} \) in that basis has elements \( A_{ij} \), then using the definition \( \ln(|\det(\hat{A})|) = \prod_{i} \ln(|A_{ii}|) \), the determinant converges as long as the diagonal elements \( |A_{ii}| \) are mostly exactly or very close to 1, specifically such that as \( |i| \to \infty \), \( \ln(|A_{ii}|) \) decays to 0 strictly faster than \( 1/i \). (Note that \( i \) is an integer index written in slanted font, not the imaginary unit \( \operatorname{i} \) written in upright font.) However, I am not sure how to generalize this to operators that are expressed as triangular matrices in continuous bases.

Transitioning from microscopic to macroscopic and quantum to classical regimes

noreply@blogger.com (PV) — Mon, 01 Apr 2024 15:44:00 +0000

I recently read two things that were of interest to me having previously worked in physics. One was an article in The New Yorker magazine [LINK], in which the author does a good job of going over the successes of mathematical modeling in the physical sciences and contrasting this with the limitations of mathematical modeling in public health (showing, for example, how many models of the spread of contagions fail when governments & societies take fast & drastic collective actions to limit the spread), the failures of mathematical models in social sciences where the outputs of those models can create feedback loops with public sentiment (for example in political polling), and the way that many people who use machine learning models in different domains expect the fancy curve-fitting of those models to represent fundamental understanding when that might not really be so. The other was a journal article published in Physical Review Letters [LINK] about how it can be possible to test the extent to which a massive (as opposed to massless) object which exhibits the dynamics of a simple harmonic oscillator and prepared in a quantum coherent state can be tested for deviations from classical behavior using a protocol that does not depend on the mass of the object (although I question this given that the protocol depends on timed measurements that depend on the frequency of oscillation, and in many physics contexts the frequency does depend on the mass as \( \omega = \sqrt{k/m}\), but this is somewhat of a quibble). These two things got me to think about something that I realized I never got out of many years of formal undergraduate & graduate education in physics. This can be illustrated with the following example.

In introductory physics classes that focus on Newtonian mechanics, a prototypical problem involves a block, modeled as a point mass, sliding (with or without friction) down a fixed triangular incline in the constant gravitational field of the Earth. In the context of those classes, instructors will be careful to note that this is merely a model, and corrections could come from the inclusion of the variation of the Earth's gravitational field & surface curvature, the technical possibility of moving the triangular incline (which must be much more massive than the block in question), the shape of the block, variations in the touching surfaces, air resistance, et cetera. In later classes, instructors may point out corrections due to special relativity (i.e. the speed of light) and general relativity (as it relates to the Earth's gravitational field).

However, in later classes about quantum mechanics & statistical mechanics, instructors explain how different the models are from models of Newtonian mechanics at human scales, but they often promise that appropriate treatments of aggregates of microscopic constituents can consistently recover results from Newtonian mechanics, yet this promise is almost never fulfilled. In particular, wavefunctions that describe pure states of single microscopic particles are quite far removed from the simple dynamical variables describing blocks on inclined planes, although statistical mechanics can probabilistically describe the solid states of the block & inclined plane as well as the gaseous state of the surrounding air, it is not usually extended to describe the dynamics of the block sliding down the inclined plane. For example, if a block sliding down a fixed inclined plane of horizontal angle \( \theta \) in a uniform gravitational field is described as having equations of motion \( m\ddot{x} = mg\sin(\theta) \) where the \( x \)-axis is defined as pointing downward parallel to the slope of the inclined plane for increasing \( x \) and the \( y \)-axis points outward in the normal direction from the inclined plane, then I wish to see corrections of the form \( m\ddot{\vec{x}} = \sum_{\mu = 0}^{\infty} \sum_{\nu = 0}^{\infty} \hbar^{\mu} k_{\mathrm{B}}^{\nu} \vec{f}^{(\mu, \nu)} \) where the lowest-order term is \( \vec{f}^{(0, 0)} = mg\sin(\theta)\vec{e}_{x} \). I have never seen these sorts of quantum or statistical corrections to Newtonian equations of motion in simple (in the context of Newtonian mechanics) systems. Similarly, it is rare to see how quantum or statistical mechanical systems can, in appropriate limits, reproduce classical systems; I can only think of the quantum coherent state of the simple harmonic oscillator as well as how the Moyal bracket in the phase space formulation of quantum mechanics reduces to lowest order in \( \hbar \) to the Poisson bracket, and in the latter case, intuitive construction of the quantum phase space quasiprobability function is made more difficult (compared to construction of a classical phase space probability density function, as I did in a post [LINK] from a few years ago) by the fact that unlike the classical phase space probability density function, the quantum phase space quasiprobability function cannot be arbitrarily localized in phase space, it can take on negative values for certain wavefunctions, it is compressible in phase space with respect to its own evolution over time, and it is not obvious how it should look for a system of many particles constituting a macroscopic object like a block (in contrast to a classical phase space probability density function, which for such a system could just be a product of Dirac delta functions localizing each microscopic constituent to a point in phase space).

These considerations reminded me of a discussion I had last year with friends from college, who also did course 8 (physics) with me. We came to a consensus that while people who do not become physics majors should, as usual, get exposure to Newtonian physics and the basics of electricity & magnetism, people who become physics majors should have a curriculum over 3-4 years that exhibits a sensible conceptual progression. In particular, after seeing Newtonian mechanics, such students should then be exposed to Lagrangian & Hamiltonian formulations of classical mechanics. The Lagrangian formulation of classical mechanics should then be used to develop intuitions about mechanical waves, which in turn can lead to introductions to classical field theory and development of classical electromagnetic theory as a rich example of a classical field theory. (I would also personally recommend using the introduction of mechanical waves to introduce the linear algebraic treatment of waves and then reintroduce the linear algebraic treatment of waves into the treatment of linear classical field theories in general & linear classical electromagnetic theory in particular.) The Hamiltonian formulation of classical mechanics should then be used to develop intuitions about probability distributions in classical mechanics, which in turn can be used to develop intuitions about statistical mechanics. Optionally, at this point, the Hamiltonian formulation of classical mechanics can also be used to develop intuitions about nonlinear dynamics & chaos theory, but while this is good for the broader education of physics students, it is less immediately relevant for the introduction of quantum theory to come soon after (because quantum mechanics is linear). Finally, only after these things happen should quantum theory be introduced, such that there are clear connections of the wavefunction formulation of quantum mechanics to mechanical waves, the phase space formulation of quantum mechanics to classical phase space probability distributions, and the linear algebraic framework of quantum mechanics to linear algebraic treatments of classical field theories (including linear classical electromagnetic theory); this will ensure that students understand how ideas like superposition, interference, rotation through a Hilbert space, statistical uncertainty, and related ideas are not unique to quantum mechanics (which is unfortunately too often a consequence of the way quantum mechanics is typically introduced in undergraduate curricula, at least in the US). We also came to a consensus that in each course, there should be clear explanations of what prototypical systems are analytically solvable, what prototypical systems are not analytically solvable, and why (in each case).

Progression of Winter Storms across the Contiguous US

noreply@blogger.com (PV) — Fri, 01 Mar 2024 16:34:00 +0000

This winter has featured many winter storms over the contiguous US that have swept from the west coast to the east coast. In previous posts, I have discussed basic intuitions for why different climates occur in different regions [LINK], my assessment of the deficiencies of the Trewartha climate classification system [LINK], what I would change about the Trewartha climate classification system [LINK], how my proposed changes to the Trewartha climate classification system can be applied to understand what climates occur where in middle latitudes [LINK], why popular understanding of the effects of the Gulf Stream over the Atlantic Ocean on the climate of Europe is incorrect in many ways [LINK], and why different climates occur in coastal locations on different coasts at different latitudes [LINK]. These posts have suggested, among other things, that many winter storms on the east coast of the US would come from warm moist air from over the Gulf of Mexico or mild moist air from over the Atlantic Ocean colliding with cold dry air over the continent, but these collisions would be somewhat more sporadic because the prevailing westerlies, which would have dumped moisture primarily over the west coast, would be weak & dry by the time they reach the east coast. Thus, it is somewhat surprising to me that these winter storms seem to be driven by the prevailing westerlies over the continent. The following is my attempt to intuitively explain, based only on sea-/surface-level temperatures, air pressures, and air flows, why this happens. Again, I am not a trained climatologist or meteorologist; I can't guarantee that this information is accurate, and I can only say that my intuitions seem through my limited understanding to align with superficial aspects of more detailed explanations.

Why this happens in North America

This happens in North America mainly because of the arrangement of landmasses & seas/oceans. In the winter half of the year in North America, the subtropical ridge is strongest around 30 degrees in latitude (north of the equator) to the west of the continents of North America in the Pacific Ocean & of Africa in the Atlantic Ocean. Prevailing westerlies generated by the subtropical ridge over the Pacific Ocean bring moisture to the west coast of the US and turn clockwise due to the Coriolis force, meaning that around the time the prevailing westerlies reach the Rocky Mountains, they may have turned more toward the Gulf of Mexico, though this is not guaranteed to happen every time. In doing so, the prevailing westerlies, by this point colder & drier, can pick up warm moist air from the Gulf of Mexico. This clockwise turn by the Coriolis force is reversed within the Gulf of Mexico by southerly winds coming from air coming clockwise off of the subtropical ridge over the Atlantic Ocean, so this newly warmed & moistened air turns toward the east coast of the US, bringing moisture there before moving east & turning clockwise (again due to the Coriolis force) over the Atlantic Ocean toward Europe. This is how the subtropical ridge can function like a conveyor belt of moisture. Essentially, the continent of North America & the Atlantic Ocean are both narrow enough (with respect to the ranges of longitudes), and the Gulf of Mexico with warm water is favorably placed, to ensure that this can happen. That said, the prevailing westerlies will not always turn clockwise enough to go over the Gulf of Mexico and then counterclockwise enough to go over the east coast of the US, which is why the prevailing westerlies are more likely to bring moisture to the west coast of the US but only sporadically do so for the east coast of the US.

I should clarify that the storms that sweep across the contiguous US are often localized highly mobile systems of low pressure. They internally turn counterclockwise, but the motion of the centers of these storms is affected by the aforementioned prevailing westerlies coming from the subtropical ridges over the eastern Pacific Ocean & Atlantic Ocean in the northern hemisphere.

Why this does not happen in other continents

This does not happen in other continents because of unfavorable arrangements of landmasses & seas/oceans. I will give details for each continent in turn.

Eurasia

In the northern hemisphere, Eurasia & the Pacific Ocean are much wider (with respect to the range of longitudes) than North America & the Atlantic Ocean, so the conveyor belt effect is lost there; this point is amplified by the much stronger system of high pressure forming due to the settling of cold dry air over the continent in the winter half of the year. Additionally, the Indian Ocean (which would supply warm moist air) is not far enough from the equator and there are too many mountains in between for the Indian Ocean to function analogously to the Gulf of Mexico.

South America

The east coast of South America in the middle latitudes would refer to the east coast of Argentina. There is no major body of water immediately to the north (toward the equator) of Argentina analogous to the Gulf of Mexico, so although the subtropical ridge over the Atlantic Ocean to the west of South Africa is somewhat close by, the prevailing westerlies are largely dry by the time they reach Argentina and have no way of replenishing moisture & warmth before reaching the east coast.

Africa

In the southern hemisphere, Africa does not extend much into the middle latitudes. Thus, this issue is moot there.

Oceania

Oceania does not extend much into the middle latitudes and is surrounded by much more water, keeping the temperatures more moderate anyway (so there is less opportunity for big temperature contrasts between land & water to form, which would lead to stronger winter storms). Additionally, the Pacific Ocean in the southern hemisphere is much wider (with respect to the range of longitudes) than the Atlantic Ocean in the northern hemisphere, so the conveyor belt effect is lost there.