Sample of my handwritings. The one on the left is the handwriting I use for notes and the one on the right is my exam/homework handwriting đ
contains 34 textbooks including etymology, language acquisition, morphology, phonetics/phonology, psycholinguistics, sociolinguistics, & translation studies
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This makes me sound stupid but what does a feynman diagram mean?
You donât sound stupid! They can be pretty confusing at first, and Iâm sure youâre not they only one that doesnât fully understand them (myself included) so letâs learn how to draw Feynman diagrams!
You do not need to know any fancy-schmancy math or physics to do this!
I know a lot of people are intimidated by physics: donât be! Today there will be no equations, just non-threatening squiggly lines. Even school children can learn how to draw Feynman diagrams. Particle physics: fun for the whole family.
For now, think of this as a game. Youâll need a piece of paper and a pen/pencil. The rules are as follows (read these carefully):
1. You can draw two kinds of lines, a straight line with an arrow or a wiggly line:
You can draw these pointing in any direction.
2. You may only connect these lines if you have two lines with arrows meeting a single wiggly line.
Note that the orientation of the arrows is important! You must have exactly one arrow going into the vertex and exactly one arrow coming out.
3. Your diagram should only contain connected pieces. That is every line must connect to at least one vertex. There shouldnât be any disconnected part of the diagram.
In the image above, the diagram on the left is allowed while the one on the right is not since the top and bottom parts donât connect.
4. Whatâs really important are the endpoints of each line, so we can get rid of excess curves. You should treat each line as a shoelace and pull each line taut to make them nice and neat. They should be as straight as possible. (But the wiggly line stays wiggly!)
Thatâs it! Those are the rules of the game. Any diagram you can draw that passes these rules is a valid Feynman diagram. We will call this game QED. Take some time now to draw a few diagrams. Beware of a few common pitfalls of diagrams that do not work (can you see why?):
After a while, you might notice a few patterns emerging. For example, you could count the number of external lines (one free end) versus the number of internal lines (both ends attached to a vertex).
How are the number of external lines related to the number of internal lines and vertices?
If I tell you the number of external lines with arrows point inward, can you tell me the number of external lines with arrows pointing outward? Does a similar relation hole for the number of external wiggly lines?
If you keep following the arrowed lines, is it possible to end on some internal vertex?
Did you consider diagrams that contain closed loops? If not, do your answers to the above two questions change?
I wonât answer these questions for you, at least not in this post. Take some time to really play with these diagrams. Thereâs a lot of intuition you can develop with this âQEDâ game. After a while, youâll have a pleasantly silly-looking piece of paper and youâll be ready to move on to the next discussion:
What does it all mean?
Now we get to some physics. Each line in rule (1) is called a particle. (Aha!) The vertex in rule (2) is called an interaction. The rules above are an outline for a theory of particles and their interactions. We called it QED, which is short for quantum electrodynamics. The lines with arrows are matter particles (âfermionsâ). The wiggly line is a force particle (âbosonâ) which, in this case, mediates electromagnetic interactions: it is the photon.
The diagrams tell a story about how a set of particles interact. We read the diagrams from left to right, so if you have up-and-down lines you should shift them a little so they slant in either direction. This left-to-right reading is important since it determines our interpretation of the diagrams. Matter particles with arrows pointing from left to right are electrons. Matter particles with arrows pointing in the other direction are positrons (antimatter!). In fact, you can think about the arrow as pointing in the direction of the flow of electric charge. As a summary, we our particle content is:
(e+ is a positron, e- is an electron, and the gamma is a photon⊠think of a gamma ray.)
From this we can make a few important remarks:
The interaction with a photon shown above secretly includes information about the conservation of electric charge: for every arrow coming in, there must be an arrow coming out.
But wait: we can also rotate the interaction so that it tells a different story. Here are a few examples of the different ways one can interpret the single interaction (reading from left to right):
These are to be interpreted as: (1) an electron emits a photon and keeps going, (2) a positron absorbs a photon and keeps going, (3) an electron and positron annihilate into a photon, (4) a photon spontaneously âpair producesâ an electron and positron.
On the left side of a diagram we have âincoming particles,â these are the particles that are about to crash into each other to do something interesting. For example, at the LHC these âincoming particlesâ are the quarks and gluons that live inside the accelerated protons. On the right side of a diagram we have âoutgoing particles,â these are the things which are detected after an interesting interaction.
For the theory above, we can imagine an electron/positron collider like the the old LEP and SLAC facilities. In these experiments an electron and positron collide and the resulting outgoing particles are detected. In our simple QED theory, what kinds of âexperimental signaturesâ (outgoing particle configurations) could they measure? (e.g. is it possible to have a signature of a single electron with two positrons? Are there constraints on how many photons come out?)
So we see that the external lines correspond to incoming or outgoing particles. What about the internal lines? These represent virtual particles that are never directly observed. They are created quantum mechanically and disappear quantum mechanically, serving only the purpose of allowing a given set of interactions to occur to allow the incoming particles to turn into the outgoing particles. Weâll have a lot to say about these guys in future posts. Hereâs an example where we have a virtual photon mediating the interaction between an electron and a positron.
In the first diagram the electron and positron annihilate into a photon which then produces another electron-positron pair. In the second diagram an electron tosses a photon to a nearby positron (without ever touching the positron). This all meshes with the idea that force particles are just weird quantum objects which mediate forces. However, our theory treats force and matter particles on equal footing. We could draw diagrams where there are photons in the external state and electrons are virtual:
This is a process where light (the photon) and an electron bounce off each other and is called Compton scattering. Note, by the way, that I didnât bother to slant the vertical virtual particle in the second diagram. This is because it doesnât matter whether we interpret it as a virtual electron or a virtual positron: we can either say (1) that the electron emits a photon and then scatters off of the incoming photon, or (2) we can say that the incoming photon pair produced with the resulting positron annihilating with the electron to form an outgoing photon:
Anyway, this is the basic idea of Feynman diagrams. They allow us to write down what interactions are possible. However, you will eventually discover that there is a much more mathematical interpretation of these diagrams that produces the mathematical expressions that predict the probability of these interactions to occur, and so there is actually some rather complicated mathematics âunder the hood.â But just like a work of art, itâs perfectly acceptable to appreciate these diagrams at face value as diagrams of particle interactions. Let me close with a quick âfrequently asked questionsâ:
What is the significance of the x and y axes?These are really spacetime diagrams that outline the âtrajectoryâ of particles. By reading these diagrams from left to right, we interpret the x axis as time. You can think of each vertical slice as a moment in time. The y axis is roughly the space direction.
So are you telling me that the particles travel in straight lines?No, but itâs easy to mistakenly believe this if you take the diagrams too seriously. The path that particles take through actual space is determined not only by the interactions (which are captured by Feynman diagrams), but the kinematics (which is not). For example, one would still have to impose things like momentum and energy conservation. The point of the Feynman diagram is to understand the interactions along a particleâs path, not the actual trajectory of the particle in space.
Does this mean that positrons are just electrons moving backwards in time?In the early days of quantum electrodynamics this seemed to be an idea that people liked to say once in a while because it sounds neat. Diagrammatically (and in some sense mathematically) one can take this interpretation, but it doesnât really buy you anything. Among other more technical reasons, this viewpoint is rather counterproductive because the mathematical framework of quantum field theory is built upon the idea of causality.
What does it mean that a set of incoming particles and outgoing particles can have multiple diagrams?In the examples above of two-to-two scattering I showed two different diagrams that take the in-state and produce the required out-state. In fact, there are an infinite set of such diagrams. (Can you draw a few more?) Quantum mechanically, one has to sum over all the different ways to get from the in state to the out state. This should sound familiar: itâs just the usual sum over paths in the double slit experiment that we discussed before. Weâll have plenty more to say about this, but the idea is that one has to add the mathematical expressions associated with each diagram just like we had to sum numbers associated with each path in the double slit experiment.
What is the significance of rules 3 and 4?Rule 3 says that weâre only going to care about one particular chain of interactions. We donât care about additional particles which donât interact or additional independent chains of interactions. Rule 4 just makes the diagrams easier to read. Occasionally weâll have to draw curvy lines or even lines that âslide underâ other lines.
Where do the rules come from?The rules that we gave above (called Feynman rules) are essentially the definition of a theory of particle physics. More completely, the rules should also include a few numbers associated with the parameters of the theory (e.g. the masses of the particles, how strongly they couple), but we wonât worry about these. Graduate students in particle physics spent much of their first year learning how to carefully extract the diagrammatic rules from mathematical expressions (and then how to use the diagrams to do more math), but the physical content of the theory is most intuitively understood by looking at the diagrams directly and ignoring the math. If youâre really curious, the expression from which one obtains the rules looks something like this (from TD Gutierrez), though thatâs a deliberately âscary-lookingâ formulation.
Youâll develop more intuition about these diagrams and eventually get to some LHC physics, but hopefully this will get the ball rolling for you.
So Iâm finishing up my Ph.D. and preparing to depart for the real world (no, just kidding, Iâm going to be in school forever, only in a different capacity)Â and I thought Iâd put together a list of some college tips to share with you all. I graduated with my B.A. in 2012, magna cum laude, with 2 majors, 1 honours thesis, 2 on-campus jobs, and 3 music things. Since then, Iâve gone to grad school and also taught six semesters of first-year seminars. Now Iâm going on the job market for teaching positions. All of this means that Iâve seen both sides of the college experience, as a student and as an instructor. There are a lot of great & useful college advice posts going around studyblr this time of here, and I wanted to add my own. I hope itâs useful. So here we go, with a âread moreâ because itâs long (sorry if youâre on mobile):
academics
find your classrooms ahead of time (profsâ offices too)
figure out how long it will take you to walk between places
figure out where your best seat will be & claim it
say hi to the people next to you, learn their names
take notes in class
take advantage of extra credit
try your best not to fall asleep in class (and if you do fall asleep, apologise to the prof afterwards)
bring your glasses if you need them, donât be stubborn about it
check out the library, wander in the stacks, talk to the librarians
figure out how & where to print
buy used books/textbooks, or rent them, but be careful with ebooks (some profs donât allow them)
plan breaks into your class schedule, or block everything together, whichever works best for you
work out the pros & cons of 8am classes and/or night classes
plan ahead â have a planner, put things in it, do them
fake deadlines are a thing (write down earlier deadlines, trick yourself into meeting them, bask in satisfaction)
grades wonât be what they were in high school
keep in mind GPA values: a 3.5 will see you graduating with honours
be nice to the departmental administrative staff, thank them for helping you (even with small things)
office hours versus emailing profs: both will get your questions answered (probably) but if you can go and talk in person, do it
profs & TAs are people too, they have lives, they have bad days
if something comes up, talk to your prof, be honest but donât overshare, just show them youâre trying
on that note, try
Keep reading
august 23, 2016 | 8:08 pm | 10/100
MIDTERMS ARE FINALLY OVER!!! đ€ been studying for philosophy and biology the last two day! here is a mind map for philosophy and flashcards for biology đâđ« now iâm just hoping and praying i get good results back đ«
fiction is my addiction, and since itâs almost the summer, i thought iâd share some ways to get free ebooks or save some money to get more books so you could have something to get lost in over the summer. while this list has a lot of ya resources, thereâs still something at the end if youâre looking for something more academic
free ebooks:
project gutenberg is always worth mentioning, because come on, it has 50,000 books in its collection. thatâs a lot of books, and you can always catch up on the grimmâs fairy tales
riveted lit is run by the publisher simon and schuster, and they put books up that you can read for a limited time. if youâre looking for something more ya, this is a great place to start
bookbub has more discounted ebooks than free ones, but letâs care about the free ones. you get a daily email with a bunch of discounted or free books
free audiobooks:
sync is my absolute favorite thing. it gives away two free audiobooks, one clasic and one more contemporary, every week over the course of the summer. it starts on may 5 for 2016, and thereâs an amazing lineup for anyone who loves to read young adult like i do (theyâre going to have iâll give you the sun, boy meets boy, and on the jellicoe road) and thereâs even a nelson mandelaâs history on week 12. itâs all free anyway, so why not?
audible allows you to get two free audiobooks in your trial, and if you always wanted to hear a celebrity narrate that classic you never wanted to pick up, you can find something to fulfill that.Â
hey, itâs project gutenberg again. not only do they have audiobooks, but they have audiobooks in other languages such as chinese, korean, spanish, and many more. if you wanted to test your comprehension of a foreign language in a new way, well, there you go
cheap books:
the book depository and wordery have free worldwide shipping for all you international people looking for that amazing book that your bookstore refuses to stock
if you live in the uk, the book people has some really amazing dealsÂ
if you live in the us, thereâs book outlet. the prices are phenomenal and i want to cry because they donât ship cheaply to me
saving money
if you buy something using ebates, you can get a rebate. buying something from book outlet? get a 10% rebate while youâre at it. it even has rebates for university bookstores like the stanford university bookstore. also, for your first time, you can get $10 back along with the original rebate. plus, itâs awesome how itâs for more than just books, because you can get a rebate for clothing stores or ebay. you can look at the full list of stores here.
if you have any questions, you could always drop by and ask. i hope these help you to get something to read!
06.10.17 // Constructive details keep getting more difficult every class, but I think until now Iâm getting them!
I personally prefer Java as a first language. Put non-technically, it is a lot less convenient, so you get a more realistic idea of how computers work. Nonetheless, Python is an amazing language (with convenience as one of itâs values) so it makes sense as a gentle introduction. Itâs also a popular language for data science and machine learning, so itâs great to have experience with.
The Python Language Interpreter: when you write some code in a text file and save it as a .py file, the Python interpreter is what turns that code into commands that your computer can then actually preform. This is necessary.
An Integrated Development Environment (IDE): An IDE is like a helpful text editor for programming. Some basic features include auto-complete, typo and mistake catching, and automatic text coloring to make some parts of your code easier to find. This is optional but highly recommended.
Some learning resources: Weâre going to need something about programming basics, problem solving in computer science, using an API, learning how to use google and stackexchange, data types, control structures, and then maybe an object-oriented programming intro, and eventually all the neat advanced features of the python language. Then we need to learn how to use Numpy (for scientific computing), Pandas (for easy data storage), and Tensorflow (machine learning!). Add some handy cheat-sheets for python, numpy, pandas, and Tensorflow, and weâre good to go.
Other posts will adress download, installation, and resources.
Like I said up above, we need to know how to do the following. Save this and make it a checklist.
Learn to use google to answer questions about installing or using python, any packages, or computer science.
This also includes getting to know how to search Stackexchange, the website for coding questions nâ stuff.
How to install python 3 and get set up
How to install an IDE like Eclipse (with PyDev), IDLE, or Notebook++.
Programming basics: how does python work? What does the language look like? How does tabbing work?
Understand basic logic, including AND, OR, XOR, NOR, NAND, XNOR, Implies, and IfâŠElse statements.
Variables: what are they, how do I set one and change it?
Basic math in Python.
Data types: what kinds of variables can I have? How does my computer store data? How do I use those types of data? What are the key commands and operations I know how to do?
Control structures: if, else, elif, for loops, while loops, break, continue
Methods! What are they, how do I make one, what can I do with it?
The open() command, the all() command, other neat built-in methods
<function name>= lambda <your variables>: <single line method>
Problem solving in computer science: now do fizbuzz.
Whatâs a package?
Importing packages, installing packages you donât have with PIP
Using an API: how do I find one and how do I read it?
object-oriented programming in Python: whatâs a class, how do I make one, how do I reference and instantiate one, methods, class vars, etc
Error handling: how to do exceptions
All the neat advanced features of the python language: iterators, generators, list comprehensions, enumerate, range, assert, withâŠas, etc.
Read through the Numpy API (for scientific computing), data types, matrices, stats, methods, etc. A short detour through scikit would be helpful.
Read through Matplotlib.pyplot API, plotting, plotting options, histograms, scatterplots, etc.
Pandas (for easy data storage), data frames, series, built-in operations on columns and rows, loading from a CSV, saving as a csv, apply, etc
Tensorflow (machine learning!) For basic stuff, shoot for knowing how to use the estimator package, which is discussed elsewhere on this blog. Also get to know the nitty gritty, including tensors, layers, tensorboard, etc.
from a second-year classics major. iâve acquired these tips from my seven years of being a latin student and one year of ancient greek.Â
this post can be helpful for classics majors or people interested in self-teaching the classics. my concentration within my major is language and literature, so my tips will revolve around latin and greek. but if youâre studying any other ancient or modern language, my tips may still apply to you :)
~ make word associations. this is a BIG one. there are many nuances to this tip, so to start, iâll explain why associations are useful, and then iâll give several examples with different variations to cover the nuances.Â
since many english words, prefixes, and suffixes are derived from both latin and greek, take the time to figure out one or two english words that come from each new word you learn - these can either be normal everyday english words or pop culture references. (also, latin is semi-derived from greek, so you can make associations between the two languages as well). if you learn any kind of word association, it will make remembering the word so much easier.
examples:Â
pop culture: pane, which means bread in latin, is related to The Hunger Gameâs city of Panem (panem is the accusative singular of pane). food insecurity is a big theme in The Hunger Games, therefore Panem is an appropriate name for the city that the series takes place in.Â
latin/greek to english: in latin, vicina is an adjective meaning âclose, neighboring,â and its english derivative is âvicinity.â in greek, ÏαÎčÎŽÎ”Ï Ï means âi teachâ and its english derivative is âpedagogyâ - aka âa method/practice of teaching.â ÎșÏÎčÏÎ·Ï means âjudgeâ and its english derivatives are âcritic, criticizeâ and âcritical.âÂ
greek to latin to greek: sometimes itâs tricky to find out which word came from which language first, but usually itâs greek to latin. example: dea (âgoddessâ in latin) comes from ΞΔα in greek.
think of those word associations as you learn your ancient language vocab. it will make recalling a wordâs meaning so much easier.Â
anD DONâT FORGET TO LEARN THE GENDER AND THE GENITIVE SINGULAR OF EACH NOUN YOU LEARN BECAUSE IT HELPS WHEN DECLINING THE NOUN AND MATCHING IT UP WITH ADJECTIVES LATER ON OH MY GOD thiS IS SO IMPORTANT
~ make a concentrated effort to remember lots of different sentence constructions. there are so many i literally donât remember them all and iâve been doing this for years. the major categories i can think of off the top of my head are subordinate clauses, conditionals, and indirect discourse, and, more generally, learn the difference between the primary and secondary verb tenses.
~ every so often, brush up on as much grammar and vocab as you can. iâm saying this because iâve procrastinated reviewing greek all summer and i barely remember anything beyond the basics :/ pls donât tell my professor.Â
~ learn authorsâ common themes and literary/rhetorical devices. for example: in the elegies of propertius, a roman poet, he used emptiness and unfulfilled wishes as motifs. learning words associated with emptiness and learning how to recognize the introduction of a wish made translating faster. iâll confess though that i never really brushed up on the use of the optative subjunctive (the device used in wish statements), so i couldnât recognize how exactly to translate certain sentence constructions. if i did review, it would have made translating in class a breeze. but hey, it was my first semester in college and i had no idea what i was doing at that level. please learn from my mistake!Â
~ learn the political, cultural, and historical context of each piece of literature you read. it will make the experience richer. if you know the context of a fiction piece, whether its poetry or prose, you will understand so much more about it. for example: the aeneid, vergilâs masterpiece (and arguably one of the best works in latin literature), is an ode to augustus. augustus commissioned vergil to write the aeneid and to make comparisons between himself and the protagonist aeneas. he wanted people to see him like they saw aeneas - kind, pious, loyal, determined, and in charge. knowing that bit of information makes many parts of the aeneid clearer. you can apply this tip to any piece of literature, no matter the language.
this is also important in terms of non-fiction writing. i took a class on roman letter writers and i wouldâve been completely lost if my professor didnât share anything historical with us. these letter writers typically vaguely referenced local gossip because messengers often read letters that were meant only for the recipientâs eyes. my professor filled in a lot of what was missing from the letters themselves.
~ have fun with it. learning languages is supposed to be fun!! of course languages enrich your mind and bring you into close contact with other cultures and ways of life, but it is supposed to be fun too. example: propertius once wrote a whole poem about knocking on his lover Cynthiaâs closed door while she sat inside⊠and the door was a metaphor for her vaginaâŠ. which means propertius was h0rny on main!! and he published that in a poem!!1! for people all over rome to read!!!!Â
in terms of plays, my friend read one in latin by plautus about a prostitute who subverts the traditional roles associated with customer-prostitute relationships. he absolutely loved it bc the main character was a bad b!tch⊠and bc it was a comedic play.Â
there are lots of metaphors and jokes written within latin and greek literature, so donât be afraid to laugh :) it makes learning that much more enjoyable
~ when reading a work of literature, ask yourself what this reveals about the authorâs culture. (suicide tw: mentions of su*cide as a plot point in tragedy) this tip is kinda related to the cultural context one, but different in that it looks for culture within literature, rather than looking at literature as a product of culture. and like the previous tip, you can apply this to any piece of literature no matter the language it is in. itâs important to think deeply a piece of literature as well as enjoy it for what it is. example: iâve read most of sophoclesâ plays and i can tell you that the greeks were very comfortable with suicide as a plot point. while murder is also common, suicide is much more common no matter the tragedy. the fact that this theme occurs throughout so many plays tells me that greeks viewed suicide as a tragic occurrence that affects people deeply, but also as a common way to die. it raises questions: what percentage of deaths were attributed to suicide in ancient greece? was it viewed as honorable or shameful? etc.Â
and going back to vergil yet again (heâs my homeboy fr), when writing about dido and her people building the city of carthage, he specifically mentions that they are building the theaters first before almost any other building - and these few lines implicitly state that the arts were very important to carthageâs culture as a whole.
~ to sum it up: as a classics major, if you are intentional about learning the languages and truly engaged with the literature, the process will be that much more fun and you will gain that much more out of it. (<- and that sentence has a future-more-vivid construction by the way hehe)
My psychology notes from finals week. Wound up getting the best score on the exam and got extra credit!
a study blog for collected references, advice, and inspiration
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