Understanding science topics

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ashwin99
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Understanding science topics

Post by ashwin99 »

When see a clue or something I've never heard about before, so I look it up on Wikipedia or a website on the Internet. Often, though, especially when the clue is something in above-high-school-level science, even reading about it online doesn't help me. For example, when I look at the Wikipedia article for "ladder operator", the article is so technical that I can't really understand it. The closest thing to understanding it is memorizing the clue, but I don't get a deep-level understanding of the concept.

It doesn't seem like this problem is present in other subjects, as they are mainly facts. Advanced math and science, on the other hand, require background knowledge which can be learned only through college courses, it seems.

Does this ever happen to anyone? What are some good ways to actually learn a difficult concept?
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Re: Understanding science topics

Post by Oh No You Didn't »

there are a lot of lecture notes for collegiate science courses on the internet. Some things you need more of a basis in lower level material to comprehend (ladder operators for example, aren't exactly something that are easy to understand if you don't have enough of a linalg background to know what an eigenvalue is etc)

If you want to try to learn QM in particular reading Griffith's is a decent option. It is not particularly difficult to obtain a copy of it and solutions for the associated problems online.
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Re: Understanding science topics

Post by The Dance of Sorrow »

All in all, textbooks and notes are really the way to go to become a great science player. I certainly am not one, but I know that reading Campbell's Biology (a very popular AP Bio book) thoroughly alone should turn you into a pretty darn good bio player at the high school level.

I haven't really read any books for chem, but I'm sure Andrew Wang or someone else who actually knows chem can point you in the right direction.

For physics, if you don't have a background in Physics C-level material, Griffiths might be a bit of a bear to get through. My "freshman physics" course used Halliday and Resnick's massive book and that was good enough for me. Griffiths' physics books are all really good, though, as long as you have the background. Griffiths E&M has even gotten a sucker like me several points on physics questions at very hard levels.
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Re: Understanding science topics

Post by The King's Flight to the Scots »

I don't really think college quantum mechanics textbooks are gonna be the way to go for a high school player.

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Re: Understanding science topics

Post by Steeve Ho You Fat »

If you want to like science, never read any E&M textbooks by anybody.
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Re: Understanding science topics

Post by Steeve Ho You Fat »

While the advice in this thread is correct that you'll only really be good at science by actually learning science and the best way to do that is to learn science the way people learn science, Matt's correct that if you can actually read Griffiths' Quantum, get something out of it, and do the problems in high school, you're like really smart. Read a physics C textbook, and if you understand that, you'll be a top level high school science player - worry about advanced college stuff after you've mastered that.

For that matter, who tossed up ladder operators in high school? Don't do that!
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Re: Understanding science topics

Post by MorganV »

TRIGGER WARNING: MATT JACKSON GIF

One thing that helped me a lot in biology and chemistry courses was to visualize things - if you try to find videos on the krebs cycle, bonding, etc and draw out the diagrams in your notebook, it helps a lot more with conceptual understanding
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Re: Understanding science topics

Post by touchpack »

If you're looking for a non-technical explanation of the ladder operators, you're not going to get one--it simply doesn't exist. If you want to learn quantum mechanics, you're going to need 3 semesters worth of calculus and 1 semester worth of linear algebra. You certainly CAN learn the math if you're smart enough and have internet access (stuff like Khan Academy is great), but you have to consider: is it worth it? It might be better for you to focus your time on making sure you have deep understanding of the high school science canon (not the quizbowl canon, the "this is taught in high school classes" canon) first.
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Re: Understanding science topics

Post by Santa Claus »

When you just need to pick up what one concept is, a lot of the time that can be accomplished by a good ol' Wikipedia chain, where you open a page and just open the page on every concept you don't understand, then repeat. Often this will result in something like two billion tabs being open at any given time, but it helps both by exposing you to a bunch of related topics that you might now have heard about otherwise and by moving to progressively more simple concepts.

This is the first paragraph of an article I personally looked up not too long ago, with all links underlined:
Affine connection wrote:In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity). The terminology is due to Cartan and has its origins in the identification of tangent spaces in Euclidean space Rn by translation: the idea is that a choice of affine connection makes a manifold look infinitesimally like Euclidean space not just smoothly, but as an affine space.
For someone with no significant background in math (such as myself), this is full of nonsense. But fret not! this can easily by remedied by spending some time applying the Wikipedia chain. Presumably you wouldn't need to look up mathematics (you could if you wanted to look over other fields of math I guess), but a brief look at smooth manifold shows that it is a manifold that is locally differentiable (or smooth). From there, you could apply the Wikipedia chain once again, and find out what a manifold is, as well as linear spaces and homeomorphisms, which are on the page for smooth manifold. Moving on to the next link in affine connection, you could find out a tangent space is a real vector space of vectors that pass through a given point tangentially; you would also learn the tangent space of a manifold aids in the generalization of affine spaces to general manifolds (something that could be explored through a separate Wikipedia chain). Vector space leads to a definition (a whole bunch of vectors that can be added together), so you can move on to the next link in affine connection (skipping tangent space, which you've already looked up) to learn about tensor calculus. At this point you have a reasonable idea about what an affine connection is, as well as the what all the terms in its definition mean.

The point of this being, you have a convenient tool already available to you in the form of an extensive online encyclopedia of just about every scientific concept you could possibly want to know about, maintained and linked to other related articles by a series of surprisingly dedicated volunteers. Affine connections (or whatever example you would prefer) are a pretty dang complicated concept, but you can get a reasonably deep understanding of it without the need of a college/graduate level course on differential geometry. Textbooks are amazing resources, but if you want to approach a specific concept or topic, there isn't always a need to learn everything about a subject when you can pick up the context along the way (as well as a lot of useful peripheral knowledge). Wikipedia may not be the best resource, but it sure is a good one.
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Re: Understanding science topics

Post by The Ununtiable Twine »

When you understand the Christoffel symbols, you know it all.
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Re: Understanding science topics

Post by Oh No You Didn't »

to be honest that method just seems like just flashcarding definitions and doing word association?
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Re: Understanding science topics

Post by touchpack »

Black Miao wrote:to be honest that method just seems like just flashcarding definitions and doing word association?
Absolutely.

There's no way a high school student without knowledge of linear algebra is going to gain a profound understanding of graduate student-level mathematics just by clicking around on Wikipedia for half an hour. Sure, you might get just enough surface knowledge to maybe get you qb points, but that's not really what OP was asking for.
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Re: Understanding science topics

Post by The King's Flight to the Scots »

touchpack wrote:
Black Miao wrote:to be honest that method just seems like just flashcarding definitions and doing word association?
Absolutely.

There's no way a high school student without knowledge of linear algebra is going to gain a profound understanding of graduate student-level mathematics just by clicking around on Wikipedia for half an hour. Sure, you might get just enough surface knowledge to maybe get you qb points, but that's not really what OP was asking for.
In my experience, not from learning science myself but from watching others, it's easier to learn biology and chemistry this way than it is to learn physics or math. If you'd like to answer more science and understand, at least superficially, what you're buzzing on, those are probably the categories to emphasize. If you really want to tackle quantum mechanics...well, it's probably possible, but be prepared for what you're getting into.

As a general rule, if you want to really understand any topic asked in quizbowl, be aware that it will take much more diligence than quizbowl studying tends to ingrain. The best players in a given subject, no matter how brilliant, tend to have spent exponentially more time on it than the second tier of players. I think quizbowl can mislead us on how much time it takes to learn.
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Re: Understanding science topics

Post by ashwin99 »

Thanks for all the comments! My question was concerning national-level tournaments. Reading the textbooks for AP Biology, Chemistry, and Physics C and then doing word associations for the rest seems sufficient to get really good only at the regular high-school level.
touchpack wrote:
Black Miao wrote:to be honest that method just seems like just flashcarding definitions and doing word association?
Absolutely.

There's no way a high school student without knowledge of linear algebra is going to gain a profound understanding of graduate student-level mathematics just by clicking around on Wikipedia for half an hour. Sure, you might get just enough surface knowledge to maybe get you qb points, but that's not really what OP was asking for.
I agree, clicking on Wikipedia links is not always very helpful; sometimes at least a minimum background in the subject is necessary just to understand what is going on. What I'm wondering is, if you find a clue that you have no idea about, what is a good way of learning it without it being superficial? Textbooks/courses are great resources but they cover a wide variety of topics -- what if I just want to know what a clue means and not take an entire college course?
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Re: Understanding science topics

Post by Steeve Ho You Fat »

I think the place where you're going wrong is with the idea of learning "a clue". It's nearly impossible to understand anything in physics or math without significant background in the subject. You can't just "know what ladder operators are" without having an understanding of what they do, which requires knowing half a semester's worth of quantum mechanics and a good bit of linear algebra, which require plenty of context themselves.
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Re: Understanding science topics

Post by gustavadolf »

Yeah, to piggyback on what others have said -- understanding ladder operators isn't really possible without the sufficient background in math. If you want to learn about physics or QM, you have to take the subject as a whole or in pretty large chunks, like "thermodynamics" or "mechanics" and not go on a clue by clue basis. Honestly, I'd advocate doing this for any subject. For example, European history makes a lot more sense when you learn it in some sort of order and with a method rather than randomly trying to tie facts from tossups together, and things that make more sense are easier to remember.

On an unrelated note -- am I the only person that hates Campbell's Biology ? I thought it was a terrible book.
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Re: Understanding science topics

Post by touchpack »

Steeve Ho You Fat wrote:I think the place where you're going wrong is with the idea of learning "a clue". It's nearly impossible to understand anything in physics or math without significant background in the subject. You can't just "know what ladder operators are" without having an understanding of what they do, which requires knowing half a semester's worth of quantum mechanics and a good bit of linear algebra, which require plenty of context themselves.
I agree with this--the shortest learning path I can imagine to get to the ladder operators goes something like this:

vector spaces -> eigenvalues/eigenvectors -> wavefunctions -> operators/observables in QM -> Schrodinger equation -> infinite square well potential -> commutators -> harmonic oscillator potential -> ladder operators

At this point, you're probably going to get more mileage out of learning everything you might see in first-semester QM, rather than just the one "clue." Learning all the context will also help you more when playing tournaments written by particularly creative writers.
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Re: Understanding science topics

Post by Oh No You Didn't »

ashwin99 wrote: I agree, clicking on Wikipedia links is not always very helpful; sometimes at least a minimum background in the subject is necessary just to understand what is going on. What I'm wondering is, if you find a clue that you have no idea about, what is a good way of learning it without it being superficial? Textbooks/courses are great resources but they cover a wide variety of topics -- what if I just want to know what a clue means and not take an entire college course?
Read just that part of the textbook/lecture notes/slides. People tend to organize/categorize their material and typically you'll find anywhere from a few sentences (in a book/notes) to a few slides in a powerpoint...

I would note however that it's worthwhile to commit time to going over that kind of material over time because turns out there's all sorts of juicy tidbits (and if you are attempting to get somewhat real knowledge of clues, it's not like the rest of the course isn't covering material that could plausibly come up...)
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Re: Understanding science topics

Post by Sima Guang Hater »

The more math-heavy a field is, the more you're going to run into this problem. Billy's right in saying that if you really want to understand ladder operators, there's simply no way to do it other than sitting down and solving the Schrodinger equation for the QHO by yourself.

However, an almost-as-good method that has worked for me over the years is to try to get a dumbed-down explanation from someone else who actually understands the topic. Unfortunately, this is more helpful for biology (where the entities involved at least behave intuitively in some sense) than it is for chemistry or physics.
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