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I would greatly appreciate a harsh review of my SoP

Posted: Fri Nov 20, 2020 8:19 pm
by Nightzeit
Read my SoP and tear me a new one. Mandatory word limit: 1000 words. Thank you.



I am looking for what confines us.

I always wondered about the shape of the universe. Initially, I believed space was connected and finite and sought ways to explain this. Then, imagining space as the closed shell of a glome, I supposed the universe might exist in a background of more than three spatial dimensions.

From contemplations like these, I began to question why I could interact only with exactly three spatial dimensions. This question resonated within me profoundly. Suddenly, I realized that if I had no issues with the concept of potentially infinitely more spatial dimensions, then I should have no hang-ups with the idea of space being infinite. I began to favor a new outlook, one in which space was infinite and globally flat.

I attended X X University because I could commute and study physics there. During my first semester, my professor discussed LIGO’s recent evidence of gravitational waves from two black holes merging. I was intrigued.

Between schoolwork, I drew some conclusions regarding higher spatial dimensions. For instance, by rotating in a fourth spatial axis, one could be orientated into the appearance seen only in mirrors in our universe. I pondered higher dimensional oscillations analogous to the movement of a jump rope, which spiral through multiple planes.

Eventually, I began truly viewing time as a dimension. Currently, I believe time is indistinguishable from space such that, should the number of temporal and spatial dimensions be flipped, the universe would behave relatively the same. However, this does not address the apparent arrow of time, another inquiry paramount to our understanding of the big picture.

By making turns, one moving at constant speed could potentially take an infinite amount of time to arrive at a specific location a given distance away. However, the amount of time to reach this location has a lower limit.

Conversely, if there existed one spatial and three temporal dimensions, I believe the situation would be inversed. Moving at constant speed, one could travel a potentially infinite distance, by turning through temporal dimensions, to reach a specific point in time, a given duration from the initial moment. This duration is not the same as the amount of time elapsed by the traveler. Analogous to the imbalance that appears in our universe, in this hypothetical universe, there exists a minimum distance that must be traversed in order to reach a certain point in time, but no upper bound.

Should it be the case that time and space are truly of the same species, I beg a bold question. Why do we not observe any dimensions of parameters separate from time and space? If this question is naïve, then I seek education to alleviate ignorance.

My ultimate drive is to obtain a deep understanding of the reasons we observe exactly three spatial and one temporal dimension. I intend to study cosmology with specific interest for the geometry of the universe, the arrow of time, gravitational waves, and the theory of everything. I am also curious about black holes, the creation and fate of the universe, time crystals, and, to eliminate or validate my skepticism, string theory. Additionally, I enjoy mathematical physics and the exposure I have had to relativity and quantum mechanics. Unsurprisingly, I have a strong interest in the problem of time and addressing compatibility issues between general relativity and quantum mechanics.

I aim to become a theoretical physicist and physics professor, both to have some choice in the topics of my research pursuit and because I believe I would truly enjoy teaching. I am proficient at explaining content. The tiny physics program at XXU builds a sense of community and led me to the position of unofficial tutor. It is to everyone's benefit that we all work to build each other up. Academically, I benefited directly from the assistance of others and indirectly by teaching others. When a majority of students are struggling, courses run at slower paces and may reach less content. Furthermore, every person counts when trying to get advanced courses to meet enrollment requirements. For one course, I created a petition of interested students to help convince faculty to offer it.

Aside from physics, I am devoted to artwork and engrossed in mathematics. I independently investigated the Lonely Runner Conjecture, but later realized that some of my inferences were incorrect. In need of revision, the project was put on hold while other matters absorbed my time. Recently, I have been independently exploring the 3n+1 Conjecture. I began learning C++ to create a program to aid my advancement on this conjecture, having incentive to use a language faster than those I already knew. The program calculates in base-576 and yielded 13847 lines of data. My work in this conjecture also inspired my birth of an original card game, which I would look forward to playing with the Y community. Before attempting a formal document, I opted to express my ongoing progress with a colloquial explanation including figures, which is currently incomplete at 41 pages long. If requested, I would be happy to discuss this in greater detail.

A friend and I discussed an ambition to create our own scripting language, seeing a need for one that is both relatively fast and intuitive in design. It must be sufficient for both general and scientific purposes and possess the unusual ability to allow users to define new statements within their programs, akin to how one defines a function.

I lack solid opinions on the initial and final conditions of the universe, if any, but I am confident the instruction of faculty members such as Big Bounce advocate Dr. A and physical cosmology frontrunner Dr. B would enable development of my stance. Spacetime curvature, or, less widely-believed, the possible lack of curvature, and Einstein’s field equations allure me. Dr. C's work on the equations and gravitational waves captivates me. Only one institute in [the state] offers a doctorate in theoretical cosmology and it is the only one worldwide with these individuals.

Re: I would greatly appreciate a harsh review of my SoP

Posted: Sat Nov 21, 2020 5:40 pm
by geekusprimus
First, some general tips for writing an SOP:
  • Every department has slightly different requirements for an SOP, but as a general rule, they should explain why you would be a good fit for their program. Focus on your research experience and how you've been prepared for graduate study.
  • Unless the department asks for personal stories (often labeled a "personal statement" rather than a statement of purpose), keep them to an absolute minimum.
  • Don't add filler statements, especially if it's something cheesy or banal ("It's always been my dream to study at XYZ University!", for example).
  • If you know exactly who you want to work with, your statement of purpose should read somewhat like a job application for their research group.
Now, some critiques of your SOP in general:
  • Keep conjectural ideas to a minimum unless it directly relates to research you've done under an advisor or research you're interested in doing with a professor in that area. Even if your ideas are well-founded, you run a strong risk of coming off as a crackpot. Find a better way to get to your point that you want to study spacetime geometry. If you've worked on these ideas with a research advisor, focus on your contributions to the project instead.
  • It's great that you have so many interests. Focus on a few, emphasizing the ones that you have the strongest understanding of. Saying "I'm interested in a theory of everything" isn't going to looked on kindly by most admissions committees because nearly everyone in theoretical physics has some passing interest in a theory of everything. If you're interested in gravitational waves, for example, talk about how they relate to your interest in cosmology. There are a lot of people working on gravitational waves who do absolutely nothing with cosmology, and vice versa.
  • Take out "and, to eliminate or validate my skepticism, string theory," or reword it -- while there are plenty of reasons to be discontented with the current state of string theory, setting yourself up as a contrarian isn't likely to win you much love from the admissions committee. Again, if you have interests in string theory and would like to mention them, connect them to your primary focus on cosmology. String cosmology is a fairly new field, and most string theorists really don't do a lot of cosmology.
  • If you bring up your programming experience, talk about how it will benefit you as a graduate student. For example, I applied specifically for numerical relativity last year, so I made a point to bring up my experience with debugging, numerical methods, and other things that are essential for the field.
  • Streamline your essay and focus on your transitions. It sounds corny and is overused, but "tell a story." There should be a smooth, logical progression from topic to topic, all the way from your introduction where you mention your interests to the very end where you state why you're interested in studying at a particular school with a particular professor.
I hope I didn't come off as too harsh. Your statement of purpose is one of the most important parts of your application, particularly in the absence of GRE scores this year, and you'll likely go through many drafts before you settle into something that can form the core for the various statements you'll write for your specific applications.

Re: I would greatly appreciate a harsh review of my SoP

Posted: Sat Nov 21, 2020 7:34 pm
by Nightzeit
Thank you for the in depth critique. It's very helpful. Here are my thoughts.
Keep conjectural ideas to a minimum unless it directly relates to research you've done under an advisor or research you're interested in doing with a professor in that area. Even if your ideas are well-founded, you run a strong risk of coming off as a crackpot. Find a better way to get to your point that you want to study spacetime geometry. If you've worked on these ideas with a research advisor, focus on your contributions to the project instead.
Coming off as a crackpot has been one of my concerns and I'm glad you have validated this as a threat. One of my issues is lack of any formal research. My university seems to be a school primarily for K-12 gym teachers. It's a state school that has no graduate program for physics. I've only ever had 3 physics professors. As far as I know, I am the only one in my "grade"/class (of 2021) in the pre-grad concentration. The program is so small that Physics courses that run once every 2 years max are being cut by the school due to budget issues from the pandemic, so I have to actually take some classes at other universities virtually in the spring just to graduate. I was also under the impression that there was little undergrad level research to be done in theory and I knew I wanted to go into theory since the beginning. I didn't realize that I should or could be researching other things. Everything I've researched was done by my own oblivious desire. I also had some big personal circumstances (medical issues with myself and family) in the past that made free time very difficult for me. I feel like these are all just excuses and excuses aren't worth anything, but my parents were both highschool drop-outs and I just didn't really know anything about college going into it. Sorry for rambling here, I'm just really at a loss.

Anyway, my purpose for the long explanation of conjectural ideas was to express that I have some clear ideas about what it is that I most want to research, specifically. I do acknowledge, however, and fully wish to express in my SOP that I am not set in stone on my current ideas/beliefs and I am aware that they could potentially be totally naive.

I've struggled to find things that directly correspond to my interest in space and time dimensions and I really wish I had a catagory name to sum up the topic. If there is an official name for this very specific area of cosmology, I don't know what it is.

If you have any other specific suggestions on how to accomplish my goals for these paragraphs, to more clearly express the topic that I am most interested in and to express that I am open to new ideas, please let me know.

I will try to briefen these paragraphs.
It's great that you have so many interests. Focus on a few, emphasizing the ones that you have the strongest understanding of. Saying "I'm interested in a theory of everything" isn't going to looked on kindly by most admissions committees because nearly everyone in theoretical physics has some passing interest in a theory of everything. If you're interested in gravitational waves, for example, talk about how they relate to your interest in cosmology. There are a lot of people working on gravitational waves who do absolutely nothing with cosmology, and vice versa.
I tried to be somewhat broad to make myself more appealing by showing that I am willing to work on topics not exclusively within a super narrow area of interest and also to express that I want to learn more and learning is one of my goals for grad school (obviously).

Will definitely remove the "theory of everything" part, good point.

This is all good advice and by shortening some other areas I should be able to fit some more details in about the topics I listed.
Take out "and, to eliminate or validate my skepticism, string theory," or reword it -- while there are plenty of reasons to be discontented with the current state of string theory, setting yourself up as a contrarian isn't likely to win you much love from the admissions committee. Again, if you have interests in string theory and would like to mention them, connect them to your primary focus on cosmology. String cosmology is a fairly new field, and most string theorists really don't do a lot of cosmology.
I was considering removing this line. Originally I included it because I wanted to show them that I'm not an expert on string theory by any means and that I want to learn more about it because of that and that I'm not just throwing it in as a buzzword because "WHOA STING THEORY WHOA COOL BIG WORDS!" I have a level of understanding of it but my understanding isn't in depth. I justified this because I felt my potential prospective advisor seemed a bit "contrarian," for lack of a less negative-sounding word, himself.

In retrospect, my trying to justify wanting to learn seems like the wrong approach, since grad school applications aren't about proving why you want to study grad level physics as much as they are about proving that you will study grad level physics and that you will produce papers and results.
most string theorists really don't do a lot of cosmology
.

I wasn't really sure the level of overlap the two fields had, this is also good to know.
If you bring up your programming experience, talk about how it will benefit you as a graduate student. For example, I applied specifically for numerical relativity last year, so I made a point to bring up my experience with debugging, numerical methods, and other things that are essential for the field.
Good idea. I'm not entirely sure how I could specifically tie my past experience and my future goals with coding together, but I'll figure something out before deadlines.
Streamline your essay and focus on your transitions. It sounds corny and is overused, but "tell a story." There should be a smooth, logical progression from topic to topic, all the way from your introduction where you mention your interests to the very end where you state why you're interested in studying at a particular school with a particular professor.
I agree it sounds a bit choppy at this point. Noted.

I wish I could express my desire for this school more strongly in my paper. I put a limit on certain locations and then found that most schools do not offer theoretical cosmology doctorates. Then I looked into individual prospective advisors and realized that most of the schools on my list did not have any advisors that I was fully certain would be a good match. I guess if I really want to sound genuine, then I need to look into more of the specific reasons for my appeal.
I hope I didn't come off as too harsh. Your statement of purpose is one of the most important parts of your application, particularly in the absence of GRE scores this year, and you'll likely go through many drafts before you settle into something that can form the core for the various statements you'll write for your specific applications.
There is no such thing as too harsh. Part of physics is ripping everything that you're confident about to shreds until you come across something too strong to tear.

I think I'm at least a decent writer and have at least a few things that standout a bit, so my hope is that I can spin this so that the SoP being weighted more heavily can be used to my benefit.

Re: I would greatly appreciate a harsh review of my SoP

Posted: Sat Nov 21, 2020 8:41 pm
by geekusprimus
I wish I could express my desire for this school more strongly in my paper. I put a limit on certain locations and then found that most schools do not offer theoretical cosmology doctorates.
As another word of advice, there are tons of people doing theoretical cosmology research, but you won't find most schools labeling the degree as "theoretical cosmology." Your best bet is to look in the gravity research groups inside of physics departments and cosmology groups in astronomy departments. If you can specify the general region you're interested in, people on this board can probably guide you to some schools, perhaps including some that you haven't considered.

Re: I would greatly appreciate a harsh review of my SoP

Posted: Sat Nov 21, 2020 9:15 pm
by Nightzeit
geekusprimus wrote:
Sat Nov 21, 2020 8:41 pm
I wish I could express my desire for this school more strongly in my paper. I put a limit on certain locations and then found that most schools do not offer theoretical cosmology doctorates.
As another word of advice, there are tons of people doing theoretical cosmology research, but you won't find most schools labeling the degree as "theoretical cosmology." Your best bet is to look in the gravity research groups inside of physics departments and cosmology groups in astronomy departments. If you can specify the general region you're interested in, people on this board can probably guide you to some schools, perhaps including some that you haven't considered.
Thanks. I'm aware that a lot of the schools all call it something a little bit different or sometimes lump it together with one subfield or another.

I'm a bit confused as to why cosmology seems to inconsistently either fall under astro or not. Is it wrong to assume that usually when catagorized under astronomy it is more observation and experiment based?


Originally I believe my radius was something like New Jersey, Pennsylvania, New York, Delaware, Connecticut or so. Might expand range. Definitely want north east USA in general. I also ruled out all schools in Philadelphia, PA (mainly because I hate that city, but I also want to note that I had a tour of UPenn and was personally turned off by the attitudes of some of the grad students I met there). I also want to rule out New York City and Camden, NJ and wanted to avoid Newark, NJ if possible.

Then of course I looked into what schools seemed to have Physics PhDs and then which of those had theoretical physics and then which of those had some form of cosmology in theory (paraphrasing, i saw stuff like "high energy "physics and cosmology", "cosmology and string theory", "gravity theory and cosmology" "gravity theory and string theory" "general relativity and cosmology theory" etc.)

When I was done my list was:
Princeton University in Princeton, NJ (private, Ivy)
Lehigh University in Bethlehem, PA (private)
SUNY at Albany in Albany, NY (state)
Cornell University in Ithaca, NY (private, ivy)
Bryn Mawr College in Bryn Mawr, Pennsylvania (private)

After looking I'm strongly considering not applying to Bryn Mawr because 1. it's located 15 miles west of Philedalphia and 2. their physics department is hands-down the smallest on my list. If I recall correctly, only one advisor there would potentially be even relevant to me and, not sure if this matters or not, I think they were only and associate.

Lehigh seems alright, but they don't let you pick an advisor until after the first year so that you can explore different things before deciding. While I can imagine this would be good for some people, since I feel confident in my choice of cosmology and theory, I think this might be a drawback for me. Feel free to give input on this, anyone reading.

Princeton is my number one at the moment, probably not a huge surprise.

If anyone else knows any other schools to suggest in the north east in general feel free to, especially ones close to my target area. I'll make a new thread under schools if this doesn't get a lot of replies.

Re: I would greatly appreciate a harsh review of my SoP

Posted: Sat Nov 21, 2020 11:44 pm
by geekusprimus
I'm a bit confused as to why cosmology seems to inconsistently either fall under astro or not. Is it wrong to assume that usually when catagorized under astronomy it is more observation and experiment based?
It's really hit or miss, and it frequently depends on what kind of cosmology they're doing. Stuff like inflational cosmology and particle cosmology tend to be in physics departments, but things like observational cosmology, galaxy formation, and the like will be primarily in astronomy departments. That being said, there is a considerable amount of overlap.

If Princeton is on your list and you think you've got a shot, you definitely need to add Harvard and MIT to that bunch. They both have strong cosmology programs, and they're such huge hubs for string theory that I'd be genuinely surprised if they didn't have string cosmologists. Plus, Massachusetts really isn't terribly far from Connecticut.

Inside your actual area, I know as a matter of fact that Penn State also has quite a bit of theoretical cosmology going on in their physics department. The general tenor of the department definitely leans toward loop quantum cosmology (unsurprisingly, as Abhay Ashtekar and Martin Bojowald are faculty there), but there are a couple more conventional cosmologists, and there are also a couple string theorists and particle theorists who may have interests in cosmology, too.

I don't know if any of these schools have theoretical cosmology research up your alley, but I would also take a look at the University of Rochester, Rutgers, the University of Maryland, and Virginia Tech. A couple of those are a little further than you are really interested in, I think, but it wouldn't hurt to look at the research going on inside their physics departments and/or astronomy departments to see if they look interesting. Especially if you don't have a lot of experience, you really want to cast a pretty broad net so you can maximize your shots. You might also consider applying to some postbacc programs and some master's programs to help you build some research credentials.