2024-02-02

My time at the TRB 2024 Annual Meeting

Last month, I attended the TRB 2024 Annual Meeting. The conference, which was held in DC, was a lot of fun. The graduate student researcher working with me was able to present our work as a poster. Additionally, although I didn't meet as many people whom I had not met before, this was a good opportunity for me to deepen connections with people with whom I had connected more briefly in past conferences in person or remotely. In particular, these included people working like me at the intersection of transportation & disability as well as people working in the autonomous vehicle industry. Strengthening connections with people in the former group was especially important to me because of the relevance of my work, how few of us there are in the US, and being able to feel like I am part of a group of like-minded academic researchers (given that I lead so much of my work essentially alone in the context of academic researchers). Strengthening connections with people in the latter group was important to me because of recent turbulence in the space of autonomous vehicles and the need for consistent pushes for inclusion of people with disabilities as users of such vehicles.

2024-01-01

Variations of Coastal Monsoon Climates with Latitude

I have learned about different aspects of the Earth's climate and shared what I've learned over 5 posts in 2022, including 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], and 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]. Ultimately, my learning about different aspects of the climates of the world was done with the personal aim of understanding why cities on opposite coasts of the US at the same latitudes have such different climates, with those on the west coast having characteristically mild to hot arid rainless summers & cool (but not cold) rainy winters and those on the east coast having typically warm or hot humid rainy summers & cool or cold slightly drier but still rainy or snowy winters. I did learn about that to a great extent, but as I learned more, I started to question whether my previous intuitions (from when I started learning about different climates) were correct. Follow the jump to see more and the resolution to this problem. 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.

2023-12-02

Myth of the Effects of the Gulf Stream on the Climate of Europe

Recently, I happened to come across articles online [LINK] clarifying that there are some competing explanations for why the climate of Europe immediately to the east of the Atlantic Ocean is milder in the winter than the climate of North America at similar latitudes immediately to the west of the Atlantic Ocean but that the Gulf Stream in the Atlantic Ocean only plays a minimal role. It got me to think whether I have unwittingly repeated the myth of the importance of the Gulf Stream for the climate of Europe in recent blog posts like my most recent one about climate types [LINK]. Having gone through that blog post, I can say more confidently that I did not repeat that myth with respect to the big picture of Europe's climate, but there may have been certain aspects of Europe's climate (especially in eastern Europe) for which I overstated the effect of the Gulf Stream, so I want to set the record straight in an effort to not spread known misinformation or myths as if they were facts. Follow the jump to see more details. 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.

2023-11-01

Contravariant and Covariant Objects in Matrix Notation

For many years when and since I was in college, I wondered whether it might be possible to consistently represent contravariant & covariant objects using vector & matrix notation. In particular, when I learned about the idea of covariant representations of [invariant] vectors being duals to contravariant representations of [invariant] vectors, meaning that if a contravariant representation of a [invariant] vector can be seen as a column vector, then a covariant representation of a [invariant] vector can be seen as a row vector, I wondered how it would be possible to represent the fully covariant metric tensor as a metric tensor if it multiplies a contravariant representation of a [invariant] vector (i.e. a column vector) to yield a covariant representation of a [invariant] vector (i.e. a row vector), especially as traditionally in linear algebra, a matrix acting on a column vector yields another column vector (while transposition, though linear in the sense of respecting addition and scalar multiplication, cannot be represented simply as the action of another matrix). At various points, I've wondered if this means that fully contravariant or fully covariant representations of multi-index tensors should be represented as columns of columns or rows of rows, and I've tried to play around with these ideas more. This post is not the first to explore such ideas even online, as I came across notes online by Viktor T. Toth [LINK], but this post is my attempt to flesh out these ideas further. Follow the jump to see more. Throughout this post, I will work with the notation of 2 spatial indices, in which the fully covariant representation of the metric tensor \( g_{ij} = \vec{e}_{i} \cdot \vec{e}_{j} \) might not be Euclidean, where indices will use English letters \( i, j, k, \ldots \in \{1, 2\} \), where superscripts do not imply exponents, and where multiple superscripts do not imply single numbers (for example, \( g_{12} \) is the fully covariant component of the metric tensor with first index 1 and second index 2, not the covariant component at index 12 of a single-index tensor (vector)); extensions to spacetime (where the convention is to use indices labeled by Greek letters) and in particular to 3 spatial + 1 temporal dimensions are trivial. Additionally, Einstein summation will be assumed, and all tensors (including vectors & scalars) are assumed to be real-valued. Finally, I will do my best to ensure that when indices are raised or lowered, the ordering of indices is clear (as examples, distinguishing \( T^{i}_{\, j} \) from \( T_{i}^{\, j} \) instead of ambiguously using \( T^{i}_{j} \) or \( T^{j}_{i} \)), but this will depend on the quality of LaTeX rendering in this post.

2023-10-12

Where Different Climate Types Do or Do Not Occur in Middle Latitudes

As a follow-up to a recent post [LINK], I've been able to somewhat comprehensively catalogue & categorize climates of different population centers roughly in the middle latitudes (23-67 degrees, which are outside of both the tropics and the polar circles) in each continent to understand why certain climate types occur in certain continents and not others. This post explains that further. 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.

For the rest of this post, I will use the modification of the Trewartha categorization that I explained in the recent post. Each climate label in this categorization has four letters, with the first being uppercase and the remaining 3 being lowercase.

Climate categorization definitions

First letter

The first letter can be A, B, C, D, E, or F. Climate types have the first letter F (polar) if if the mean temperature of the hottest month is less than 10 degrees Celsius. Climate types with the first letter B (semi-arid or arid) are defined based on precipitation thresholds regardless of mean temperatures each month; this will be explained soon. If a climate type does not meet a precipitation threshold for the first letter B, then the first letter is A (tropical) if the mean temperature of the coldest month is at least 18 degrees Celsius, C (subtropical) if the mean temperature of the coldest month is less than 18 degrees Celsius but 8-12 months in the year have a mean temperature of at least 10 degrees Celsius, D (intermediate) if 4-7 months in the year have a mean temperature of at least 10 degrees Celsius (which means the mean temperature of the remaining 5-8 months, including the coldest month, must be less than 10 degrees Celsius), or E (subpolar) if 1-3 months in the year have a mean temperature of at least 10 degrees Celsius (which means the mean temperature of the remaining 9 to 11 months, including the coldest month, must be less than 10 degrees Celsius). These conditions are the same as in the Trewartha categorization.

The precipitation threshold for climates with the first letter B is \( H = 10(T - 10) + 300S \), where \( T \) is the mean annual temperature in degrees Celsius and \( S \) is the fraction (between 0 and 1) of yearly precipitation that occurs in the summer half of the year (inclusively between April through September in the northern hemisphere, or October through March in the southern hemisphere). These conditions are the same as in the Trewartha categorization.

If the mean temperature of the hottest month is less than 10 degrees Celsius, then the climate type automatically has the first letter F (polar). This holds even if the climate type would otherwise qualify for the first letter B (arid or semi-arid), because close enough to the pole, the air is too cold to hold much moisture anyway, and features of the vegetation are more influenced by the coldness than the dryness per se; more precisely, as a climate becomes colder, less moisture from the ground is lost to evapotranspiration, so the amount of precipitation needed per year to avoid a climate type with the first letter B (arid or semi-arid) is lessened anyway. If a climate type does not qualify for the first letter F (polar) but the yearly precipitation is \( P \leq 2H \), then the climate type has the first letter B (arid or semi-arid); otherwise, the first letter must be A (tropical), C (subtropical), D (intermediate), or E (subpolar) depending on the mean temperatures of the hottest and coldest months and the number of months with mean temperatures of at least 10 degrees Celsius. These conditions are the same as in the Trewartha categorization.

Second letter

The second letter depends on the first letter. If the first letter is B (arid or semi-arid), then the second letter denotes whether the climate is either semi-arid or arid. A semi-arid (steppe) climate, with the second letter being 's', has \( H < P \leq 2H \). An arid (desert) climate, with the second letter being 'w', has \( P \leq H \). These conditions are the same as in the Trewartha categorization.

If the first letter is A (tropical), then the second letter denotes whether the climate is a tropical rainforest climate or a tropical wet-and-dry climate. If at least 10 months each have at least 60 millimeters of precipitation, then the second letter is 'r' (tropical rainforest climate). Otherwise, the climate is a tropical wet-and-dry climate; the second letter is 'w' if the dry season is during the winter half of the year or 's' if the dry season is during the summer half of the year. These conditions are the same as in the Trewartha categorization.

If the first letter is F (polar), then the second letter denotes whether the climate is a tundra climate or an ice cap climate. If the mean temperature of the hottest month is at least 0 degrees Celsius but below 10 degrees Celsius, then the second letter is 't' (tundra climate); otherwise, as every month has a mean temperature below 0 degrees Celsius (implying permanent ice where water is present), the second letter is 'i' (ice cap climate). These conditions are the same as in the Trewartha categorization.

If the first letter is C (subtropical), D (intermediate), or E (subpolar), then the second letter denotes whether the climate has a dry summer or generally uniform precipitation through the year, as dry summers indicate vulnerability to droughts, wildfires, and related natural disasters. This is the main way that my modification differs from the original Trewartha categorization. If all of the following conditions hold, namely that the driest month is in the summer half of the year, the wettest month is in the winter half of the year, the wettest month has at least 3 times the mean precipitation as the driest month, and the summer half of the year has at least 3 months where the mean precipitation is at most 40 millimeters (including the driest month, by definition), then the second letter is 's', indicating a dry summer. Otherwise, the second letter is 'f', indicating a humid summer. Unlike the Köppen categorization, neither the Trewartha categorization nor my modification to it allow for the second letter to be 'w', which would indicate dry winters, when the first letter is C (subtropical), D (intermediate), or E (subpolar), and this is for two related reasons. First, there is no particular climactic or ecological feature unique to places with dry winters, as the dryness corresponds to the time of the year with the least amount of sunlight and the lowest temperatures; this is unlike when the second letter is 's' (dry summer), because dryness in the summer allows for temperatures to become arbitrarily high in the absence of precipitation (even if average temperatures are somewhat more moderate, as may happen when moisture comes in other forms like fog), which can easily lead to wildfires as is characteristic of places that have climate types with the second letter 's' (dry summer). Second, the threshold \( H \) for precipitation for a climate type to have the first letter B (arid or semi-arid) is defined to depend not only on the average temperature for the year but also on the percentage of precipitation in the summer half of the year, because evapotranspiration rates increase as the temperature increases. This means that for two places that have the same average temperature for the year, the one that has a greater percentage of precipitation occurring in the summer half of the year will experience more evapotranspiration because the temperatures in that half of the year are higher, so the climate type there is more likely to have the first letter B (arid or semi-arid) under the Trewartha categorization or my modification of it even if the Köppen categorization would make the first letter C (subtropical) or D (continental) with the second letter 'w' (dry winter), because that becomes the more salient feature of such a climate; if the climate type doesn't have the first letter B (arid or semi-arid), then there is less of a salient difference in the climates & ecologies of areas with climate types with the first letter C (subtropical), D (intermediate), or E (subpolar) and the second letter 'f' (humid summer) whether the winter is dry or not.

Third and fourth letters

The third and fourth letters are more needed in my modification of the Trewartha categorization for comparison of different climates to make sense, but the actual letters are the same (although at or below 0 degrees Celsius, I may have shifted things by 0.1 degree Celsius). In particular, the third letter indicates the mean temperature of the hottest month and the fourth letter indicates the mean temperature of the coldest month. Both the third and fourth letters come from the following set of letters. These letters are 'i' for temperatures of at least 35 degrees Celsius, 'h' for temperatures of at least 28 degrees Celsius but less than 35 degrees Celsius, 'a' for temperatures of at least 22.2 degrees Celsius but less than 28 degrees Celsius, 'b' for temperatures of at least 18 degrees Celsius but less than 22.2 degrees Celsius, 'l' for temperatures of at least 10 degrees Celsius but less than 18 degrees Celsius, 'k' for temperatures of at least 0 degrees Celsius but less than 10 degrees Celsius, 'o' for temperatures of at least -10 degrees Celsius but less than 0 degrees Celsius, 'c' for temperatures of at least -25 degrees Celsius but less than -10 degrees Celsius, 'd' for temperatures of at least -40 degrees Celsius but less than -25 degrees Celsius, and 'e' for temperatures less than -40 degrees Celsius. Thus, when I speak of the temperature-indicative third or fourth letters being higher or lower when comparing two climate types, such statements refer to this temperature scale.

Effects of mountains

Frequently, when considering transitions between climate types, I will refer to mountains lying in some direction relative to an area with a climate type and not further discuss the climate types on or across those mountains. Mountains have their own, typically polar-like, climate types and significantly break up continuity between otherwise geographically adjacent climate types in a given continent. In particular, as I discussed in a previous post [LINK], a mountain range that lies roughly along a line of longitude (meridian) creates a significant rain shadow that will depend on the direction of the prevailing winds; at more tropical latitudes, the prevailing winds are the trade winds going from east to west, so areas east of a mountain will get much more precipitation than areas west of a mountain, while at middle latitudes, the prevailing winds are the prevailing westerlies going from west to east, so areas west of a mountain will get much more precipitation than areas east of a mountain. A mountain range that lies roughly along a line of latitude usually will not create a significant rain shadow unless there is a specific warm ocean current driving wind from the equator to a pole roughly along a line of longitude (meridian), but it will block warm air going from the equator toward a pole and cold air going from a pole toward the equator; thus, it is more likely to create sharper transitions in temperature profiles (third & fourth letters in the climate type), and if this affects the position of the subtropical ridge especially around the west coast of a continent, then it can further create sharper transitions between precipitation profiles based on whether summers are dry.

Follow the jump to see further discussion of actual climate type occurrences. I will focus mostly on climates with the first letter being C (subtropical), D (intermediate), or E (subpolar), as those are the most common in the middle latitudes; there will be some discussion of climates with the first letter being B (arid or semi-arid), as there are many areas in middle latitudes that have semi-arid or arid climates, and there will be brief discussion of climates with the first letter being A (tropical) or F (polar), as those are rare outside of the tropical or polar regions respectively. I should note that this post contains two large biases in sampling. First, I have only considered population centers that are clear on Google Maps. Therefore, some of these climates may actually be more widespread in area than they look based only on where people live. Second, as I'm most familiar with North America, I may have picked more small or mid-sized cities in North America compared to other continents. Therefore, some of these climates may actually be more widespread in other continents than this post may seem to suggest.

2023-09-18

Stand-Up Comedy and Emotional Resonance

I recently read an article in The New Yorker magazine [LINK] about how the stand-up comedian Hasan Minhaj significantly exaggerated or conflated stories in his recent big stand-up comedy routines. In particular, these stories were about instances of racism or Islamophobia, including being the victim of police brutality, being part of a mosque that was infiltrated by an FBI agent, and being sent a mysterious powder that led to his child's hospitalization, that either didn't happen at all or were significantly exaggerated. As someone who has liked his work in the past and who could identify to some degree with his stand-up comedy material based on experiences as the child of immigrants from India, I found these allegations quite troubling, yet I also found myself struggling to articulate exactly why I found these allegations to be so troubling. This post is my attempt, in the current zeitgeist (as this is a very new story and new details could soon arise that would make this post irrelevant or incorrect), to make sense of these things. Follow the jump to see more.

2023-08-06

Movie Review: Oppenheimer

I should note that the last movie review on this blog was almost exactly 12 years ago, when I had watched the movie Source Code [LINK]; going back to that post let me cringe a little again at my writing style as a college student. In any case, although I have watched many movies since then but haven't felt compelled to review them for this blog, I felt a little more compelled to do so after recently watching the movie Oppenheimer in IMAX (though not 170 mm IMAX), because of the historical & scientific significance as well as the hype around its release. That movie is essentially a dramatized adaptation of the book American Prometheus by Kai Bird & Martin J. Sherwin (which I haven't yet read), covering the life of J. Robert Oppenheimer during his career as a physicist & developer of nuclear weapons for the US and particularly focusing on his involvement in the Manhattan Project & his subsequently being stripped of a security clearance.

There were a few things that I liked about the movie. I understand that Edward Teller was ostracized by the scientific community by giving testimony that would further bolster investigators turning scientific disputes & personal friction between Teller & Oppenheimer into a reason for claiming Oppenheimer to be a national security risk, but considering that Teller's further ostracism came more when he further dug into developing nuclear arsenals & using nuclear weapons in absurd ways that signaled a weird lust for nuclear explosions, I appreciated that the movie stuck with Teller's role in the Manhattan Project (without letting later views of Teller color his portrayal during the time of the Manhattan Project) and made explicit his real-life testimony praising Oppenheimer's integrity & ultimate loyalty to the US (as opposed to other countries). I also appreciated how the movie made clear that arguments against the use of nuclear weapons after the actual bombing of Japan could be seen as facile or hypocritical when compared to similar arguments before the initial test in Los Alamos. In particular, Oppenheimer initially rationalized concerns about the US having access to the destructive power of nuclear weapons by recognizing the far greater threat to humanity of Nazi Germany getting & using such weapons first, so later claims of being disgusted by their use need to be shaped with a lot more nuance than Oppenheimer actually provided. Additionally, as I have read most of the Bhagavadgītā, I could see that Oppenheimer quoting Kṛṣṇa's line (repeating the translation that Oppenheimer used) "I am become Death, the shatterer of worlds" is arguably a misunderstanding of the philosophical implication, considering that Truman essentially had to correct Oppenheimer in the same way that Kṛṣṇa had to correct Arjuna: the US (with the president, at that time Truman, as the symbolic executor), like Kṛṣṇa, was the entity with the will to destroy, while Oppenheimer/Arjuna was the human instrument and the nuclear/celestial weapons were the insentient instruments. I wonder if more people will recognize this and thus not blindly praise Oppenheimer just for quoting the Bhagavadgītā.

There has been a lot of controversy, especially in India and also among Hindus outside of South Asia, about the depiction of a Sanskrit copy of the Bhagavadgītā during a sex scene being sacrilegious. I'm not religious, and I knew of Oppenheimer's fascination with Hindu mysticism, so I initially gave the director the benefit of the doubt that it may perhaps reflect some combined mystical view of sex & spirituality by Oppenheimer in real life, especially given that reactions about these things tend to be much harsher in India than in the US. Now that I have watched that scene, I can say that the presence of a Sanskrit copy of the Bhagavadgītā added nothing to the sex scene or to the understanding of Oppenheimer's life and was probably not something that happened in real life, so it seems to be in gratuitously bad taste. Moreover, I felt like the scenes where Oppenheimer used Kṛṣṇa's aforementioned line, including but not limited to the sex scene, made it feel cheap & unnecessary; in particular, using it first in the sex scene robbed it of the gravitas that it could have had when portraying the nuclear test explosion.

Overall, perhaps because I had some familiarity with the historical events, I felt like the director tried too hard to make an ultimately simply story about the life of a complicated person seem more complicated (as a story) & visually engaging than necessary. It is perhaps damning to the movie that I felt that despite having seen trailers where the cast of the movie encouraged people to watch it in an IMAX movie theater, I felt that I could have enjoyed it equally on a small screen in an airplane. As an example, I could see that the director was in many scenes trying to visually depict the turmoil in & tortured state of Oppenheimer's mind, but the effects often felt too overwrought with crazy pictures & loud sounds. I thus would only recommend it to people who may then be inspired to read the book (as I myself have yet to do).

On another note, there was a scene with a graph on a chalkboard for one of Oppenheimer's lectures showing a single particle tunneling quantum mechanically through a flat barrier in 1 dimension, but the wavefunction was so badly drawn that it didn't seem to show exponential suppression in space in the region of the barrier. When I saw that scene, I immediately thought that if I were a TA for a class in which he was a student and he had submitted that as part of a homework assignment, I would have deducted points.

2023-07-01

More on Climate Categorization

This post is essentially a follow-up to a recent post [LINK] about the Köppen & Trewartha categorizations of climates; that post was in turn a follow-up to a recent post [LINK] about my intuitions of various climates. This post will discuss, more systematically & in more detail, the climates that are impossible or not typically observed in the Trewartha categorization even when consistently using the third & fourth letters to specify the hottest & coldest mean monthly temperatures respectively, the pros & cons of the Trewartha categorization, and a proposal that I thought of to address some of the cons of the Trewartha categorization. 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.

2023-06-11

Book Review: "How Not to Be Wrong" by Jordan Ellenberg

I've recently read the book How Not to Be Wrong by Jordan Ellenberg. As the author states in the introduction, it is an exposition of simple yet profound ideas in mathematics, meant for laypeople. Topics include nonlinear phenomena (in opposition to naïve linear extrapolation), probability, Bayesian reasoning, and statistical testing of hypotheses. All chapters refer to many examples in politics, economics, and everyday life to make the concepts easier for laypeople to digest.

I found the book to be fairly easy to follow. I can't say that I learned much in terms of concepts, as these are all concepts that I've come across one way or another in school, college, graduate school, or my work now, though I did appreciate the discussion of how conspiracy theorists like to add hypotheses after the fact to make a conspiracy theory harder to fully disprove, how the fact that random fluctuations in many phenomena observed over time are time-reversal invariant implies that the phenomenon of regression toward the mean is also time-reversal invariant in a probabilistic sense, and the intuitive explanations of common causes & common effects in leading to correlations between random variables that are otherwise not causally connected. Additionally, I felt like this book did a better job than the book Algorithms to Live By by Brian Christian & Tom Griffiths (which I have reviewed on this blog before [LINK]) in having some structure in the progression from one chapter to the next and in using topics from earlier chapters in later chapters even though this book, unlike that book, didn't pretend to have a unified message. My only quibbles are the claim that the impossibility of accurately running the fundamental equations describing atmospheric & oceanic dynamics for more than 2 weeks implies impossibility in forecasting through other methods (like machine learning models looking for patterns in weather effects & progression) and the fact that the chapter connecting ideas from probability, geometry, and signal processing (particularly around error correction) took me a fair bit of effort to follow (unlike the other chapters, which tells me that laypeople will likely struggle with that chapter much more). Additionally, I think readers should be aware that the author often makes reference to sports that are mostly popular in the US and to US politics and that the author at a few points espouses more liberal or progressive political views (though I think such espousal is not gratuitous but is done in a way that fits well with broader discussions of assumptions underlying mathematical, political, and legal judgments). Overall, I think the author has done a good job of fulfilling the goal of communicating these ideas to a lay audience, so I recommend this book to anyone who might be interested in these ideas.

2023-05-20

FOLLOW-UP: My Rough Intuition of Climate, Especially in the US

The previous post in this blog [LINK] went over my rough intuition of climate, primarily in middle latitudes like those of the US. Most of the broad categories that I described were largely aligned with the Köppen climate classification system (henceforth called the Köppen categorization). However, there is a more recent categorization known as the Trewartha climate classification system (henceforth called the Trewartha categorization) that is supposed to be more representative of middle latitudes like those of the US. Essentially, tropical, desert, and semi-arid climates, as well as polar and ice cap climates, are defined in the same ways between the two categorizations. The differences lie in the definitions of subtropical, continental, and subpolar oceanic/subarctic climates. One benefit of the Trewartha categorization is that it clearly separates boreal/subpolar climates from other oceanic and continental climates, whereas the Köppen categorization uses subcategories that could be a little more confusing. However, the definitions of subtropical, oceanic, and continental climates in the Trewartha categorization seem less justifiable to me. Follow the jump to see more details. 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.