Two simple tricks to month long subjects

[jewish_scientist]

I thought of 2 tricks that turn concepts I spent about a month learning in high school into <30 minute lessons.

Human Nutrition
1) Carbohydrates = Coins
2) Lipids = Bills
3) Everything Else = Building Materials
4) Doing anything cost money
This works until you get to the cellular level.

Dimensional Analysis
1) Replace every unit with a variable of the same power e.g. mm^2 becomes x^2
2) Do algebra
3) When in simplest form, do the first step backwards
This always works.

[ahammel]

I thought of 2 tricks that turn concepts I spent about a month learning in high school into <30 minute lessons.

There's a mistake that I've often seen people make. It goes something like this:

Alice spends a long time studying, say, biochemistry. At first it's difficult, but she gradually becomes more and more confident with it as she absorbs more knowledge. At some point she has a breakthrough, and acquires a metaphor that allows her to recall her biochem knowledge quickly and easily. "Of course!", she says to herself, "it's just (music|economics|football|the Nicaraguan mining industry)!"

Then, and this is where she makes her blunder, she thinks "why didn't they just tell me it was like $metaphor in the first place? I could have skipped all this hard work!" This is backwards. Her private metaphor doesn't give her understanding of biochemistry, her understanding of biochemistry allows her to form a private metaphor. So we she goes to tutor Bob, who knows nothing about biochemistry, and says "it's easy: these enzymes are like the conductor, and this reaction is like the horn section, so when it receives this queue, the electrons (or "woodwinds") do thus and so...", he will say "WTF are you talking about, Alice?". Alice's private metaphor is no good to Bob, because he hasn't done the work yet.

There are no royal roads. These summaries you've made are a sign that you've done the hard work of understanding dimensional analysis and nutrition, not a way to skip the hard work.

[Zohar]

Yeah, it's basically like that joke about the math student who gets told by her professor that something is trivial and doesn't get it, then goes home and works on the assignment the entire weekend. Monday she comes back and tells the professor "Yeah, you're right, it's trivial!"

[doogly]

The nutrition metaphor you've given makes no sense to me at all, I cannot tell what is going on in there.

The second, you have to be careful that if mm^2 is x^2, m^2 is (1000x)^2. You have to do all the same work, but yes, you are free to use different letters.

[Sizik]

The nutrition metaphor you've given makes no sense to me at all, I cannot tell what is going on in there.

I think this is the intended simplification, minus the metaphor.

Human Nutrition
1) Carbohydrates = Low-density energy sources
2) Lipids = High-density energy sources
3) Everything Else = Building Materials
4) Doing anything uses energy.

[Flumble]

And it's not even right on this basic level. For example, cellulose is a type of carbohydrate that is definitely not an energy source in human nutrition (unless "in human nutrition" includes "burning cellulose to cook dinner"), and a lot of the "everything else" can be transformed into energy sources. Sure, you can add "one can sell building materials for energy" to the metaphor/analogy, but it's a non-trivial extension and in most* cases you can't buy building materials for money, because most* types of money lack certain atoms/acid groups.

*I actually have no idea whether there are carbohydrates that include aminoacids or even what 'building materials' encompasses.

[ahammel]

*I actually have no idea whether there are carbohydrates that include aminoacids [...]

Chitin is one.

[eSOANEM]

↶
The nutrition metaphor you've given makes no sense to me at all, I cannot tell what is going on in there.

The second, you have to be careful that if mm^2 is x^2, m^2 is (1000x)^2. You have to do all the same work, but yes, you are free to use different letters.

Also, this is basically just dimensional analysis.

Don't get me wrong, dimensional analysis is great and really should be way more commonly taught but it certainly isn't new.

[Jorpho]

Dimensional Analysis
1) Replace every unit with a variable of the same power e.g. mm^2 becomes x^2
2) Do algebra
3) When in simplest form, do the first step backwards
This always works.

E_K = ½mv².

So no. It doesn't.

[LaserGuy]

Dimensional Analysis
1) Replace every unit with a variable of the same power e.g. mm^2 becomes x^2
2) Do algebra
3) When in simplest form, do the first step backwards
This always works.

E_K = ½mv².

So no. It doesn't.

Dimensionless constants don't matter in dimensional analysis...

[gmalivuk]

Which dimensionless constant? I saw the point as being that the proposed "trick" won't help you go between different derived units if you don't also remember all the definitions.

[LaserGuy]

Which dimensionless constant? I saw the point as being that the proposed "trick" won't help you go between different derived units if you don't also remember all the definitions.

Jorpho bolded the 1/2, so I'm assuming that's what she was referring to as a problem.

The OP specifically said this was a method to do dimensional analysis, not how to go between different derived units.

[gmalivuk]

Oh, huh, I can't see the bolding effect at all but looking at the quoted post I guess it's there after all.

[Tyndmyr]

Analogies are, I think, of less use than teachers believe. They are almost invariably imprecise, and if the student does not understand the manners in which they are flawed, and the subject used to make the analogy, it's difficult to concisely convey meaning.

The teachers which I felt taught the best were not those who relied most on analogies, but those who ensured that the core concepts were taught in a building-upon-basics fashion, and could communicate a given concept in a number of ways to help those who had difficulty with a given fashion.

I think there's an over-reliance on speed, sometimes. I see a lot of "learn x in 21 days" or whatever, particularly in the realm of technical books, and it seems like mostly an advertising gimmick. It isn't how the books are actually used. Yeah, you can learn things swiftly if you immerse yourself in them and marathon it, but that's really not tied to a specific method.

[Jorpho]

But mnemonics are still cool, right?

Lo d hi and hi d lo, E-I-E-I-O...

[jewish_scientist]

There are no royal roads. roads. These summaries you've made are a sign that you've done the hard work of understanding dimensional analysis and nutrition, not a way to skip the hard work.

You missed 2 details I added. The first is that usually the information takes 1 month to teach; the second is that this is being taught in a high school. In my high school*, there was a class called Health that everyone was required to take. Everything it taught me basically boils down to drugs are bad, cigarettes are bad and extremely bare-bones human nutrition. I think that same level of education can be taught in terms of this simple metaphor. Also, you need to remember that a metaphor is a tool used to gain understanding. In this way it is no different than mnemonics or repetition. None of these will work on every student; it is the job of the teacher to identify what tools work best with each student.

*I am assuming my high school's academia is like most other high schools because it is like all other high schools I know about in every other ways.

The second, you have to be careful that if mm^2 is x^2, m^2 is (1000x)^2. You have to do all the same work, but yes, you are free to use different letters.

I think you forgot what happens when you distribute the exponent.

Spoiler:

Question: A sphere has a radius of 5 meters. What is its volume in milliliters rounded to the nearest whole number? Use p to represent pi.

Formula for the volume of a sphere | (r^3) 4p /3 = V
Substitute known information | ((5 m)^3) 4p /3 = X mL
Replace units with variables | ((5a)^3) 4p /3 = Xb
Distribute the ^3 | (5^3 * a^3) 4p /3 = Xb
Simplify | (500p/3) a^3 = Xb

Formula for converting meters into centimeters | 1 m = 100 cm
Formula for converting centimeter to liters | 1 cm^3 = 1 L
Formula for converting liters to milliliters | 1 L = 1000 mL

Replace units with variables
a = 100c
c^3 = d which can be rewritten as c = ∛d
d = 1000b

Do a bunch of substitutions
a = 100 (1,000c)
a = 100 (1,000 (∛d))
a = 100( 1,000 (∛ (1000b)))
Simplify | a = 1,000,000 ∛b

Substitute into first equation | (500p/3) (1,000,000 ∛b)^3 = Xb
Simplify | 5.2 * 10^8 b = Xb
Put units back in | 5.2 * 10^8 mL = X mL
Answer: 5 * 10^8 mL

And it's not even right on this basic level. For example, cellulose is a type of carbohydrate that is definitely not an energy source in human nutrition (unless "in human nutrition" includes "burning cellulose to cook dinner"), and a lot of the "everything else" can be transformed into energy sources.

Cellulose is trivial with regard to human nutrition because cellulose does not do anything in humans. Cases of extreme malnutrition and starvation are not taught in a high school and that is the only time something besides a carbohydrate or lipid is used as an energy source.

Dimensional Analysis
1) Replace every unit with a variable of the same power e.g. mm^2 becomes x^2
2) Do algebra
3) When in simplest form, do the first step backwards
This always works.

E_K = ½mv².

So no. It doesn't.

Spoiler:

Formula for work | w = fd
Formula for force | f = ma
Substitute | w = mad

Formula for acceleration | a = v/t
Substitute | w = mdv/t

Formula for velocity | v = d/t
Substitute | w = md^2/t^2
Substitute kinetic energy back in | E_k = md^2/t^2

Formula for change in kinetic energy | E_ki - E_kf = w
Subtracting identical units has no effect in dimensional analysis | E_k= w
Substitute | E_k = md^2/t^2

Check out the basic dimensions section of the Wolfran Alpha page on Kinetic Energy Notice that substituting the units as if they were variables creates the same result.

[Angua]

I still don't understand how lipids are bills...

Wait, do you mean bill as in paper money, rather than as what tells you how much you have to pay?

I still don't really think that it gives much useful information though. If that's all you're learning about nutrition, then someone's not doing a very good job.

[ahammel]

There are no royal roads. roads. These summaries you've made are a sign that you've done the hard work of understanding dimensional analysis and nutrition, not a way to skip the hard work.

You missed 2 details I added. The first is that usually the information takes 1 month to teach; the second is that this is being taught in a high school.

I missed neither of those details. I stand by my assessment.

Cellulose is trivial with regard to human nutrition because cellulose does not do anything in humans.

Yes it does.

[doogly]

The second, you have to be careful that if mm^2 is x^2, m^2 is (1000x)^2. You have to do all the same work, but yes, you are free to use different letters.

I think you forgot what happens when you distribute the exponent.

I assure you I did not forget how this works, and also, it is not called distributing.

My point is that if you replace a unit with its dimensional quantity, you have to keep around which unit it was. You can't just call all lengths L, you need to know which they were (unless you are happy to gloss over all constants.)

There just are no extra tricks in your trick. The spoilered text you showed is completely normal, for example.

[jewish_scientist]

Wait, do you mean bill as in paper money, rather than as what tells you how much you have to pay?

I meant dollar bills, not notices of payment. I am sorry for not being clearer.

I still don't really think that it gives much useful information though. If that's all you're learning about nutrition, then someone's not doing a very good job.

I agree wholeheartedly; it is a great disservice to provide such little information to high school student. I suppose that the teacher/ principle/ superintendent/ collective school system would argue that this is how much information:
1) the average high school student can handle.
2) is needed to function in daily life.
3) can be taught in the limited time available.

My response would be that this information:
1) could be taught to middle school students.
2) is obvious a rushed, near-useless response to the obesity problem, so it does not attempt to touch on anything else.
3) should be taught to middle school students; thereby freeing time for more advanced studies in high school.

... [This] is not called distributing.

I know that that was wrong; however, I cannot think of a better word.

My point is that if you replace a unit with its dimensional quantity, you have to keep around which unit it was. You can't just call all lengths L, you need to know which they were (unless you are happy to gloss over all constants.)

I apologize for misunderstanding what you meant. I think that most students would understand that each unit, which are given unique abbreviations, need to be given unique variables.

[Angua]

I'm sure you guys must be learning more than that though. You've said this was a month long subject. You don't spend a month merely on the energy density of sugar and fat, plus the extra concept that proteins help build things. At the very least they would probably have mentioned how calories work and what the daily requirements are - which would be easy given that most foods these days come with calories content on them anyways and then people would know what that means.

Still, did they mention fibre? Vitamins? Scurvy or rickets? Iron, iodine and other minerals? Anaemia? These are all basic parts of nutrition that could be easily part of a month long curriculum.

Obviously nutrition is a massive topic, and you don't need to cover all of it at that level. But if you've spent a whole month on this (assuming only 1 class a week) I would have expected that you could cover more than fat has more energy than sugar and proteins are used to build stuff.

[Flumble]

Joules! Not calories!

Surely a month-long subject also teaches you why Joules is the superior unit of measurement.

[Soupspoon]

You also don't have Joules and joules that are magnitudinally different...

[Angua]

They are from the US so I don't think they'll use joules. Also, if all you're using it for is nutrition then it doesn't really matter.

[jewish_scientist]

I'm sure you guys must be learning more than that though. You've said this was a month long subject. You don't spend a month merely on the energy density of sugar and fat, plus the extra concept that proteins help build things. At the very least they would probably have mentioned how calories work and what the daily requirements are - which would be easy given that most foods these days come with calories content on them anyways and then people would know what that means.

Still, did they mention fibre? Vitamins? Scurvy or rickets? Iron, iodine and other minerals? Anaemia? These are all basic parts of nutrition that could be easily part of a month long curriculum.

Obviously nutrition is a massive topic, and you don't need to cover all of it at that level. But if you've spent a whole month on this (assuming only 1 class a week) I would have expected that you could cover more than fat has more energy than sugar and proteins are used to build stuff.

The underline part is the only thing that was told to us. Notice that I used the word 'told' instead of 'taught'. The reason for this is in the first spoiler below and my theory on why this was happened is in second.

Spoiler:

By far the largest factor the contributed to the non-teaching was that science teachers did not give the class. Stop reading for a moment and let that sink in. Information about a scientific topic was not given by teachers in the science department. The class was called 'Health'; not 'Human Nutrition'. We meet every other day for 1 hour lectures and every other month 'Health' had to switch off with 'Gym'. This meant that Gym teachers had to try to teach both 'Gym' and 'Health'. I would estimate that >75% of the classes were simply watching a video and >50% of those videos were designed to "scare straight" student on the 3 largest current health crises in the U.S. (illegal drug abuse, legal drug abuse, and eating disorders). The classes were designed to teach student that calories, fats, sugars, etc. were evil and cause obese people to cry and wish that they could 'go back and change it all'.

This lead to much confusion when the gym teachers tried to explain what calories, fats, sugars, etc. are and why they are important. In particular, how the relationship between exercise and calories consumed effects weight gain/lose was very confusing. My metaphor compares how exercise 'burns' calories to how spending sprees 'burn' money. Another fumbled subject was why eating sugars cause someone to gain fat. My metaphor shows that sugars and fats can be converted into each other the same way different currencies can be exchanged. The fact that this is the only information that was attempted to be taught is unethical; the fact that this information was so poorly mistaught is an embarrassment to American society.

Spoiler:

Setting: Office of Adam, an important person at the Department of Education, one month before school starts.

Stage directions: Adam is rushing through paperwork, desperately trying to finish everything on-time.
Stage directions: Beth enters stage left

Beth: Hey Adam, what's happening?
Adam: I am absolutely swamped! Can we please talk-
Beth: You know, a lot of people are worried about obesity among kids and I promised to do something about that during my campaign.
Adam, who has realized what is about to happen: No! We cannot just add something to-
Beth: Yeah, well. It would be really great if you could put something in the curriculum about that.
Adam: O.k.! o.k. MAYBE we could squeeze in a guest speaker or two.
Beth: Mmmm. Well, you see, stuff like that cost money.
Adam: I know that. We have some money set aside for emergencies. We can just use some of that.
Beth: Well, here's the thing. We actually need to cut your budget by about 20.56% or so.
Adam: WHAT!?
Beth: Yeah, you see. My second car's headlights' retroreflectors are made out of 23.5 carat diamonds instead of 24 carat diamonds. Its a real safety hazard, you see.
Adam: FIne! We can add an elective called 'Nutrition' or 'Health' or something like that.
Beth: Yeah, I am not saying that's a bad idea, but maybe we could make it a requirement or something like that. That way I can tell parents that I am giving all their children a proper education.
Adam: If its a requirement then a lot of students are going to be taking it and we cannot afford to hire new teachers.
Beth: Well, maybe we could have some of the current teachers teach it instead.
Adam: School starts in a month! We cannot give state-wide training to every school in-
Beth: Yeah, well. I though maybe the gym teachers would know a thing or two about obesity so if you could tell them to do it, that would be great.
Adam, whose spirit and hope have been crushed: O.k. I will call the schools and tell the to replace 'Gym' with-
Beth: Oooo, yeah. You see, there was this memo that came out that said exercise improves the grades of students. Did you get a copy of that memo? So yeah, It would be really great if you did not cut 'Gym'. Thanks for taking care of this.
Adam: I wrote that memo.
Beth: Great. I'll send you a copy of the memo just in case. I have to get going; the Chairman of the Ethics committee is waiting for me at a strip club and he has already payed the strippers to let us beat them, so I really cannot be late.
Adam: You are the worst kind of person.
Beth: So, if you could get on that, that would be great. I'll be sure to send a copy of that memo to you.

Stage directions: Beth exits stage left.
Stage directions: Adam uses strength gained from build up rage to throw his desk through the stage right wall.
Stage directions: End Scene

[Angua]

OK, so you're saying it was actually basically the theory part of a gym class? That's not human nutrition at all.

You can't say that you've boiled a whole subject down to a pat metaphor if you haven't even got the subject right.

[Jorpho]

Cellulose is trivial with regard to human nutrition because cellulose does not do anything in humans.

A lack of dietary fiber can be problematic. We learned about that in grade 8 biology.

Check out the basic dimensions section of the Wolfran Alpha page on Kinetic Energy Notice that substituting the units as if they were variables creates the same result.

I tried to find the page you were referring to, and could not..? Anyway, I think something's missing in there on account of the vector dot product; I lack the time and inclination at the moment to concoct a rigorous proof.

[jewish_scientist]

I would like to apologize for being overzealous when I exaggerated the usefulness for the metaphor on human nutrition. I am not being ironic or condescending; I sincerely admit that I made a mistake. In the future, I will try to restrain myself in this regard.

Check out the basic dimensions section of the Wolfran Alpha page on Kinetic Energy Notice that substituting the units as if they were variables creates the same result.

I tried to find the page you were referring to, and could not..?

This is another mistake that I made. Apparently the Wolfram Alpha page on kinetic energy does not provide this information even though the pages on units of kinetic energy do.

[nichi]

Understanding dimensional analysis requires understanding what multiplication is. Just as 14*15 is 14 15s, 14 m is 14 meters. But you can also do 14 pizzas or 14 drinks. If I multiplied the two, I'd get 196 pizzas*drinks. If I divide by drinks*drinks, I get 196 pizzas per drink.

From there it can be clear what's really going on with multiplication by variables. Your heuristic seems to be just trying to avoid actually understanding the material. At which point you can drop out and just use wolfram alpha.