Chapter 3: Food and Diet

What is this post going to be about?

Take a guess. Take a wiiiiiiild guess.

...

It's going to be about... FOOD AND DIET!!

(Sorry, no prizes for getting that one right.)

The most important topic to cover here is nutrients, or all the helpful stuff that you get in food that help your body cells to function normally. Some also provide energy for the cells. Today I'm going to write about a wide variety of nutrients, namely sugars, amino acids, fatty acids, vitamins, minerals and water.

First up are simple sugars. Remember those carbohydrates that I talked about yesterday? Yup, I'm talking about them. We get these sugars from the carbs in our diet, mainly in the form of sugar, starch and cellulose. Carbohydrates are the main energy source for the cells. They first get broken down into simple sugars (remember, starch and cellulose are polysaccharides, which are long chains of molecules made up of monosaccharides, or simple sugars), which are then broken down further to release energy. Excess carbohydrates are stored as glycogen in the liver and muscles, but if there's way too much then the remaining carbs get converted into fat, which is stored all around the body.

Aside from obvious sources of sugar, like lollies and other things that should be eaten in moderation (hehe... "should"), sugar can also be found in fruit. Starch, a long-chain carbohydrate, is found in cereals, wheat, rice, oat, corn, bread and certain vegetables such as potatoes, peas and dried beans. Cellulose is found in foods of plant origin, particularly unrefined foods, since it is the material that plant cell walls and fibres are comprised of. Cellulose, however, cannot be digested by humans and therefore cannot provide energy for cells or matter for building new ones, though cellulose can stimulate the contraction of the muscular walls of the intestine. Cellulose, and foods like it, can therefore be called insoluble fibre or roughage (since it can't be digested but it promotes movement of food in the intestines).

Next up are amino acids, which I also talked about yesterday as they're the building blocks of proteins. Unsurprisingly, we get amino acids from proteins. The body breaks down proteins into amino acids and then uses the amino acids to build required proteins- kinda like breaking apart a Lego house and then using the pieces to build a dinosaur. Proteins, as explained yesterday, are part of the structural material of the cell. Some are enzymes in cellular reactions. Excess proteins can be converted to carbohydrates in order to be used as energy or stored as fats. By the way, protein and carbohydrates provide the same amount of energy per gram: roughly 17kJ/g.

There are 20 different amino acids, some of which can be produced in the body. There are, however, nine amino acids which cannot be produced in the body. These are known as essential amino acids. Proteins containing sufficient quantities of these amino acids are known as "complete proteins" or "first-class proteins." These can be found mostly in animal-based foods. Plant-based foods tend to have "incomplete proteins" or "second-class proteins," but if a wide variety of foods are eaten you will still be able to obtain all of the essential amino acids.

Fatty acids have a pretty bad rep at times but they are necessary too. They are, however, only necessary in small quantities. Fatty acids allow cells to make certain fats which are necessary for body functioning. Also, foods containing fatty acids also contain fat-soluble vitamins, like vitamins A, D, E and K. Fatty acids are probably best known for being stored as a reserve of energy- and they contain a lot of energy! When utilised, they contain 37kJ of energy per gram- more than double the energy yield of carbohydrates or proteins!

You've probably already had a list of foods containing fatty acids drilled into your head from various sources, but here's a quick list: butter, margarine, milk, cheese, oils etc.

Next up is vitamins. There are several different kinds of vitamins, and they all come from different sources and have different functions within the body. You can get all of the vitamins that you need from a varied, balanced diet, but they cannot be manufactured in the body. Vitamins do not provide energy, but they're essential for regulating cellular reactions and for cells to gain energy from proteins, carbohydrates and fatty acids.

Minerals are taken into the cells as ions from mineral salts. These include phosphates and sodium chloride (a.k.a. salt). Just like vitamins, a balanced diet should provide you with adequate amounts of minerals, except for a few notable exceptions, like calcium, iron, iodine, zinc and fluorine. In order to balance this, water supplies in several countries are fluoridated (bringing a lot of protest from some people, especially conspiracy theorists), and table salt is often iodised.

Just like vitamins, different minerals have different functions within the body. Secretory cells in the stomach require chloride ions to produce hydrochloric acid (HCl), cells in the bone marrow that produce red blood cells require iron to produce haemoglobin and bone cells require magnesium and calcium. Of course, there are many other processes that require minerals- these are just some examples.

Water! The essence of life! You need plenty of water to live- an average person loses around 3L a day, and you obviously lose more if you're in a warm climate or doing lots of exercise- but you don't need to guzzle lots of it, as most solid food is half water. A small amount of water is also produced in chemical processes in cells. (That's not to say that you don't need to drink water. You do, since the water in food and produced in chemical processes is not adequate.)

So why is water so important? It's an important solvent in the body- many chemicals are dissolved in it. It also regulates body temperature, and is important in the excretion of bodily wastes. If you don't have enough water, you can become constipated and/or get kidney stones, and if you are really really dehydrated, you can even get kidney and heart failure. So drink yo' water, kids!

Now that I've gone through all of the main essential nutrients, it's time to talk a bit more about energy, that stuff produced by carbohydrates, proteins and fatty acids. We all know that we need energy to go about our daily activities, but what else does the human body need energy for?

Answer: the human body also needs energy to grow and repair tissues, to maintain body temperature and to maintain normal body functions. You wouldn't want your heart to go without energy!

The process by which carbohydrates, lipids and proteins are broken down to provide energy is called respiration. The energy comes from the bonds between the atoms in the molecules. If more energy is consumed than required, the excess is stored as fat, as you probably know already.

How much energy do you need? That's not a super straightforward question, as it depends on a lot of factors:

1. Basal metabolic rate, or BMR (i.e. how much energy you need when you're resting. Obviously you're still using some energy when you're resting, as your heart needs to beat and you need to breathe.)
2. Amount of physical activity.
3. Body size: more body mass = more energy required to move around
4. Gender: women generally require less energy since they have a higher proportion of body fat, which weighs less than muscle (see point 3 about how more mass = more energy required)
5. Age: you need more during periods of rapid growth (such as adolescence), but older people generally require less due to decreased metabolic rate and often decreased physical activity.
6. Climate: you need more energy in colder climates to maintain body temperature.
7. Pregnant women need more energy for the developing foetus. Lactating women (lactation = milk production) also need more energy to produce all of that milk.

Aside from each individual having different energy requirements, certain groups also have different requirements for particular nutrients. For example, pregnant women need to consume more folic acid, calcium, iron and protein and lactating women need more calcium. Vegans might need to take some supplements, as certain vitamins might be lacking in their diet, particularly B12, which is only found in foods of animal origin. (Normal vegetarians are normally fine but they do need to be careful to maintain a balanced diet.)

Some foods nowadays also have particular beneficial ingredients added to them. For example, some flour now contains vitamin B1 (thiamine). Some yoghurts contain probiotics, margarines might have extra calcium or fish oil, or drinks might have some extra fibre included. These are known as functional foods.

Diffusion, osmosis, enzymes and organic compounds relevant to human bio

Now I've had a shower I'm feeling kinda drowsy and all I want to do is curl up and dig into that book that my Comprehensive Class teacher, 罗老师, recommended to me, but in my last post I promised y'all that I'd write about all this stuff!

Diffusion and Osmosis

Diffusion and osmosis basically just involve the spreading out of the particles of a substance over a given area so that they become evenly distributed. My old post on the Kinetic Theory of Matter is kind of related to this. But by "kind of" I mean very slightly. As in the only two important lines are:

1. Particles move in random straight-line motion until they collide with each other or another solid object (like the inside of a glass jar) [according to the Kinetic Theory].
2. For example, you can explain why gases spread through the kinetic theory idea of random straight-line motion.

Now for a bit more explanation on how diffusion works!

In a nutshell, particles will tend to move from an area of high concentration to an area of low concentration. For example, if you open a bottle of perfume, the gas particles carrying the odour of the perfume will move from the bottle (where the particles are in high concentration) to the rest of the room (where the particles are in low concentration). The process will continue until the particles are evenly distributed- or, should we say diffused? (I'm actually not entirely sure if you can use the word this way in a scientific context, but I'm assuming you can)- throughout the room.

Now, why might this be the case? Is it because the particles have egalitarian principles and believe that every inch of space should have an equal amount of particles? Nope, I don't think so. Diffusion can be explained by the kinetic theory, as stated above. The particles inside gases and liquids are constantly moving, and they occasionally collide with each other. They continue moving in their straight-line motion until a collision occurs. Once a gas or liquid particle "breaks free" of the giant mob of concentrated particles down at the concentrated end, it can continue on, relatively uninhibited, while it passes through areas of lower concentrations. Eventually this happens to all of the molecules until they are evenly spread out over the available space, where the chances of collision are roughly equal no matter which direction the particle moves in next.

Now for some terminology: The difference in concentration that causes diffusion to occur is called the concentration gradient or diffusion gradient. The greater the difference, the steeper the gradient, and the faster diffusion will occur. The movement of particles along a diffusion gradient is called the net diffusion. "Net" or "overall" is used as a reference to those particles that are moving in the opposite direction (since the kinetic theory states that particles move in random straight line motion. I have no idea whether this is true or whether this is yet another drawback of the kinetic theory).

Also btw if you dissolve something in solution, making the particles of the solute (substance you're dissolving/ substance in smaller quantity) spread out amongst the particles of the solvent (substance you're dissolving things in/ substance in larger quantity), the solute and the solvent will BOTH have diffusion gradients, just in opposite directions. If you're dissolving sugar, for example, sugar will have a diffusion gradient in one direction, while water will have a diffusion gradient in the other direction.

I was about to wrap up the topic right there but then I realised that I haven't spoken about osmosis yet. Oops.

Osmosis is basically the same thing as diffusion. In fact my book says that it's "a special case of diffusion." It's special because while diffusion just spreads the particles throughout any gas or liquid or whatever, osmosis also involves a differentially permeable membrane. That sounds all technical unless you break it down: a membrane is basically like a dividing wall of some sort (okay, not very scientific, and probably the worst explanation ever, but works for now), "permeable" means that things can pass through it and "differentially" means that it discriminates between different substances (also not a very scientific explanation, and makes the membrane sound almost racist or sexist or something-ist). In short, a differentially permeable membrane is a divider of some sort that allows some substances to pass through, but not others. Let's see how this can impact diffusion.

Since differentially permeable membranes only allow certain substances to pass through, osmosis looks at not only of the diffusing substances but at how substances that can't pass through the membrane affect diffusion.

Here's a diagram of a container with a differentially permeable membrane dividing it in half. As you can see, the water molecules are evenly distributed on each side:

As the concentration of water molecules remains the same throughout the liquid, equal numbers of water molecules pass through the membrane in each direction, and the net movement of the molecules is zero (or at least I think it is).

If you take a substance that won't pass through the membrane and dissolve it into the water on one side of the container, however, something interesting happens:

Since the other substance can't pass through, each side has a different ratio of water to other substance molecules. To make up for this, more water diffuses from the left side to the right side, where water now has to compete with the other substance for supremacy. Or something. (My book says something about water molecules moving from a place of higher concentration to a place of lower concentration, but I have trouble writing that after being told in Chemistry that liquids like water generally aren't considered to have concentrations, unlike aqueous solutions, which do.)

Now for some fancy words! I've talked a lot about osmosis without really using the word much. Aside from my earlier description, osmosis is also considered to be the diffusion of water across differentially permeable membranes like the membranes of cells (water is considered most often since it's so darn common and so important to the human body). Osmotic pressure refers to the pressure caused by osmosis when solutes that can't pass through the membrane are added, like in the example above where the water level rises because of the added substance. (Or at least that's what I think the word means.) The higher the number of solute particles, the higher the osmotic pressure.

Enzymes

As you may well know, there are many ways of speeding up the rate of a chemical reaction, and using a catalyst is one of them. There's a bit more about speeding up reactions on my post titled Reaction Rates.

Enzymes are catalysts, or organic catalysts, to be exact- they speed up the reactions of living organisms. They are proteins that decrease the amount of energy needed to start a reaction so that reactions can begin at normal body temperatures. (See the aforementioned Reaction Rates for more details on activation energy.)

Molecules involved in a reaction are called substrates. Enzymes combine with these to make an enzyme-substrate complex. But not just any enzyme will do- each enzyme has a specific function and can only combine with a specific substrate in a specific reaction. This is because each enzyme and each substrate have different shapes and structures, and only complimentary ones will work together [insert lock-and-key analogy here]. After the enzyme-substrate complex reacts with another molecule, the enzyme will combine with a different substrate to start the process all over again. It's a lot quicker than it sounds, though- an enzyme can interact with millions of substrate molecules every minute.

Enzymes are kinda complex in that they are pretty sensitive and are affected by temperature and pH. For an enzyme to function at its best, temperature and pH need to be optimal. Normally, the higher the temperature, the faster the reaction, but if enzymes are present, you shouldn't raise the temperature past the optimal range. Also, an increased concentration of enzymes will do the job faster. More hands mean light work after all. Finally many enzymes are lazy buggers who won't do anything by themselves require the presence of certain ions or non-protein molecules (a.k.a. co-factors) before they will get off their asses and work catalyse a reaction.

Finally it's time for the last topic!

Organic Compounds: Carbohydrates, Proteins, Lipids and Nucleic Acids

(This is where I wish that last year I had hardened up and written more Chem posts because then I could link to them rather than have to write more about them now. The stuff we did about soaps and detergents in 3AB is actually quite relevant to the bit about lipids in that they both involve glycerol and long chains of organic molecules. Oh well.)

I'm tired so I'm just going to super summarise things now. Or, at least, I'm going to do my version of "super summarising" which is basically not really summarising anything at all. I'll just type faster. Meh. In any case, don't expect pictures. Google 'em yerself.

Carbohydrates (what most people prefer to refer to as "carbs" because "carbohydrates" is too long)- contain C, H and O (carbon, hydrogen and oxygen to the uninitiated). There are always twice as many hydrogen atoms as oxygen atoms. Simple sugars (e.g. glucose, fructose, galactose) are also known as monosaccharides. Not sure how these three were classified as "simple sugars," though the fact that they do seem to be relatively small molecules with a 1-ring structure probably has something to do with it. Two monosaccharides can combine via condensation reactions (basically a reaction that combines two small molecules by releasing water- it's in the 3AB course but haven't gotten around to speaking about them, sorry) to form a disaccharide (since di- means "two"). For example, glucose and fructose can combine to make sucrose. Finally, if loads of monosaccharides combine in this way, you get a polysaccharide, like glycogen (the form in which carbohydrates are stored in the body), starch or cellulose. Carbohydrates are important as they provide energy to the body cells.

Proteins- contain C, H, O and N (N being nitrogen). Many also contain S or P (sulphur or phosphorus). To understand proteins we need to first look at their building blocks- amino acids. There are about 20 different amino acids, and they can be combined in various ways through condensation reactions (just like how monosaccharides can be combined in various ways to make di- or polysaccharides). There's a fancy name for the bond between two amino acids: it's called a peptide bond. Because of this, two amino acids joined together are called a dipeptide, while ten or more joined together are called polypeptides. (I suppose those in between are just given prefixes like tri-, quad-, quin- etc.) If there are over 100 amino acids joined together, you have a protein. Proteins make make up much of the structure of body cells as well as take part in many chemical reactions in the body. They're necessary for building big muscles too :)

Lipids- really big molecules that are stored in the body as energy reserves and are insoluble in water. Fats, the best-known lipids, contain C, H and O (but not much of the latter), and are formed from condensation reactions between glycerol and fatty acids. Glycerol is an organic molecule with 3 carbon atoms and 3 OH groups. Each OH group can undergo a condensation reaction with a fatty acid (essentially a long chain of carbon atoms with the carboxylic acid group -COOH at the end). Fats are sorted into mono-, di- or triglycerides depending on how many fatty acids react with the glycerol (those with one fatty acid are monoglycerides etc.). 98% of fats in foods are triglycerides (product of glycerol and three fatty acids). Aside from fats, other lipids include phospholipids, a part of cell membranes, and steroids, which include cholesterol and the sex hormones.

Nucleic Acids- contain C, H, O, N and P. First discovered in the nuclei of cells, giving rise to their name. Just like the other types of molecules described previously, they are made up of many smaller molecules joined together in many different ways. This time, the basic unit is called a nucleotide, and consists of a nitrogen base, a sugar and a phosphate group. The two main types are RNA (ribonucleic acid) and DNA (deoxyribonucleic acid). They differ in the number of chains of nucleotides (RNA has one, DNA has two) and the type of sugar (RNA has ribose, DNA has deoxyribose).

All right, enough rambling from me. Here's the REAL summary:

Looks like the next couple of chapters of this book are going to cover the digestive system. Stay tuned...

Classification of Humans and "The Chemistry of Life"

Yesterday I found my sister's old Year 11 human bio book... some fodder for a whole bunch of new posts! Yay! (Or "Nay," depending on your point of view)

The first chapter doesn't have very much for me to comment on. Firstly it mentions that human bio is related to a whole range of fields of study, such as cytology (study of cells), anatomy, molecular biology etc. Different fields generally study different "levels" of human beings: for instance molecular biology or biochemistry focuses on  the chemical level, cytology focuses on cells, etc. The second important thing mentioned is how species are all classified into different groups in a hierarchical system, from Kingdom all the way down to Species or Sub-species (actually Wikipedia and about.com says that there's a level higher than Kingdom known as "domain," based on differences in RNA structure). You've probably already heard all of that but I'll provide a brief run-down anyway.

The highest level of classification (a.k.a. "taxonomic rank" but that's just too technical for my taste) consists of several large groups, each of which consist of lots of living organisms. As you move down the levels of classification, however, the number of organisms in each group as well the differences between the organisms become smaller and smaller as the requirements for being classified into that particular group become more stringent. There is hardly any difference between members of the same species or sub-species (the lowest rank on the food chain classification system). I mean that compared to the differences between members of two different species there are RELATIVELY small differences between members of the same species, so don't go on about how you have absolutely nothing in common with [insert other person here] or whatnot.

As an example, here's how the human being is classified:

Our kingdom is "animalia," because we have a helluva lot more in common with animals than with plants, fungi, bacteria or whatever else is in the other kingdoms.

We're in the "chordata" phylum. This is because we have a "hollow, dorsal nerve chord." Now I have no idea what "dorsal" means so I just looked it up. First attempt didn't work well because a long time ago I changed the language on Google to Chinese. Then I searched up "dorsal nerve chord" and came up with http://www.indiana.edu/~ensiweb/iho.da.pdf which says that a dorsal nerve chord is "A spinal cord that runs down the back of an animal, attached to its brain at one end." Yup, we definitely have one of them, so we're in the "chordata" phylum.

Our subphylum is "vertebrata" which seems like it just encompasses everything with a backbone. Including us.

Then our class is "mammalia" which encompasses mammals- y'know, those warm-blooded hairy creatures that produce milk (well the females do, anyway).

Our order is "primates": forward-facing eyes and nails instead of claws.

Suborder- "anthropoidea"- human-like primates. How they objectively classify something as "human-like" is beyond me, so maybe there's something else to it. Monkeys and apes are in here with us humans.

Superfamily- Hominoidea. No external tail. Just apes and us now.

Family- Hominidae- extinct ancestors of humans as well as modern humans.

Genus- Homo- some extinct ancestors of humans as well as modern humans. As my year 8 science teacher put it to our rather immature class, "Yes, we're all homos together."

Species- sapiens- modern humans.

Next chapter is on working scientifically, i.e. how to plan an experiment, make a hypothesis, use a microscope, set out data etc. This probably warrants a few posts on its own, but not for a while because I can't be bothered.

And now we're onto the meaty stuff!

Chapter 2: The Chemistry of Life

(They didn't give a chapter number to the "working scientifically" chapter. Hence this is Chapter 2 :) )

A lot of stuff in this chapter is basic chemistry which I have already covered on this blog. Here are some links:

Elements, compounds and ions:

•  Atomic Structure and Periodic Table (Probably a bit more info than you really need for human bio.) (P.S. I still don't really understand the difference between a molecule and a compound so if someone could explain that would be great :) )
• Atomic Structure and Periodic Table, take 2 (the 3AB Chem version, builds on the stuff in the first post)

Solutions:

• Classification of Matter (Explains homogeneous and heterogeneous mixtures)
• Solutions (Probably also more info than you need)
• A Bit More on Solutions (Calculating the concentration of solutions. From what I've read in this chapter it looks like this post might be the most useful)

Acids, bases and pH

(Since the Chemistry course does quite a bit on acids and bases, all these links might be way more than you need. For example the Human Bio book I have in front of me right now uses the Arrhenius theory of acids and bases which is simpler to understand than the Bronsted-Lowry theory preferred in the Chem course, but doesn't explain the behaviour of bases that don't contain OH- ions.)

• Acids and Bases part 1 (physical differences, Arrhenius and Bronsted-Lowry theories, indicators, strong and weak acids, standard reactions involving acids)
• Acids and Bases part 2 (standard reactions with amphoteric- i.e. can act as either acid or base- substances, complex ions, monoprotic and polyprotic acids, calculating pH, properties of metal and non-metal oxides)

Organic Compounds

• Basics of Organic Chemistry
• Naming and Drawing Organic Compounds (not that relevant, but might help you to see those funny chemical names didn't come out of nowhere)
• [insert a whole bunch of posts that I was meant to write but didn't. Including one about functional groups which is still a draft.]

This leaves us with only a few more topics to cover:

• Diffusion and osmosis
• Organic compounds relevant to human biology (carbohydrates, proteins, lipids, nucleic acids)
• Enzymes

This post is getting somewhat long, though, so I'll split it into two posts. Second post will contain those three topics above. I'll begin writing soon. I'll begin after I've had a shower. I promise. *nervously sweats*

Study Techniques

Okay might seem a bit hypocritical for me to be telling people how to study when I'm not doing a whole lot of it at the moment, but I thought I might jot down a few things that worked for me when I was in China, plus a couple of study techniques that my friends and I used last year in Year 12.

The Brainstorming Method

One revision technique that our music teacher taught us was to get a blank sheet of paper and pick a topic related to your subject (for example, if you're doing music you could do one of the periods of music or one of the set works) and then brainstorm everything that you can think of related to the topic. You'll be surprised at how much you actually remember, particularly if the topic in question is one that hasn't been covered in class for a while. While brainstorming, I normally make a mental list of things that I'm not sure about or just can't quite remember no matter how hard I try (normally stuff like dates or composer's names or whatever). After brainstorming, I go back through my notes and find out the stuff that I wasn't sure about, and then add a few more details based on interesting facts that I find in my notes.

The Annotations Method

This "method" of sorts is basically my way of being obnoxious and getting away with it. There are two ways I use dumb annotations to help me in my studies:

1. When reading through the textbook or through notes, I sometimes write annotations in response to interesting facts or anything else that catches my attention. This helps me stay focused when reading while also helping me engage with the text.
2. When I was in Year 10, a technique that worked well for me was to compile all my notes onto a OneNote document during the term, and then at the end of the term I printed out my notes and wrote annotations on my notes. (Yep, notes on my notes...)

So where does the "obnoxious" part come in? Well, some of my annotations were a bit obnoxious. When I was in said Year 10 Modern History class, my notes included some stuff about the Tsar wanting to expand Russia's territories or something along those lines and so every time I saw something about that I would just write "As if Russia isn't already big enough..." in the margins. That might not sound so bad though I'm pretty sure I wrote some really obnoxious stuff on my music notes in Year 12. Unfortunately, I can't quite remember.

The Summarising Method

Haven't really used this method myself, but it was a favourite of my friend who studied Human Biology in Year 12, a rather content-heavy subject. Her method of studying was to continually summarise her notes until they fit onto a small sheet of paper that could easily fit into her shirt pocket. Each time she summarised her notes she'd be refreshing her memory as to what was on them in the first place.

Sentence Method (Languages)

I have a couple of different techniques for studying languages. When I was in China, I started using my own variant of the sentences method, which can be found on several language learning websites, perhaps the most notable being All Japanese All The Time. The basic idea is that you add a whole bunch of sentences in your L2 to an SRS (Spaced Repetition System) program, which is basically a flashcard program that uses spaced repetition to help get things into your long-term memory. (Basically, in Spaced Repetition, you get shown hard things more often and easy things less often so that you don't waste your time reviewing easy things.) On one side of the card you add a sentence in your L2, on the other side you add the translation in your L1. You could also add other things, like notes on grammar points or definitions of new words. As you get more advanced, you might also put these notes in using your L2.

Since I had to learn certain vocab for my Chinese language course, and I was worried that some words would slip by the wayside if I just used pure sentences, my variant was this: I'd put the new word on the card, and then a sentence containing that word beneath it. The back of the card would just have the definition of that word. Then I would tweak the settings so that I could be tested on both sides of the card (i.e. give the definition of the word OR provide the word from the definition). However I wasn't super strict on myself when going back the other way (providing the word from the definition) as there are so many synonyms or near-synonyms in Chinese (or in any language really).

When reviewing cards, if I get the side containing word and sentence, I read the sentence out loud (or whisper it if there are other people around) and then check the definition of the word and give myself a score depending on whether I was right or not and how easy it was for me to remember the answer. If I get the side containing the definition, I write down the word and then check the answer. If I wasn't right because the word was a near-synonym or something, I normally mark it right anyway (though with a lower score, never with full points) and write the other word down as well.

Another thing I could do with my cards that might help me with writing would be to write out the sentences when I get the word/sentence side of a card. I'm too lazy to do this though :P

One thing to remember is that there's no set-in-stone "sentence method," so feel free to tweak around with the basic framework and find out what works for you.

Before I forget, I should probably mention which SRS programs are available. There are a plethora of them available and you could probably find them quite easily by Googling "SRS" or "flashcard program." One of the most popular is called Anki. It's good because you have a lot of control over the formatting of your cards, being able to add in colours, pictures, audio clips and so on. However, while Anki is free on Android and Windows, Anki is not free on iOS (it's over $20) so if you are a cheapskate using any Apple products you might want to consider an alternative. I used Repetitions Free on my iPad when I was in China, and it did the job though it certainly doesn't have any of the bells and whistles that Anki has (i.e. you can't add in pictures, audio clips or even coloured text). There are many others though, so feel free to experiment and see which ones work for you.

Other Language-Learning Websites

A couple of other language learning websites that I've dabbled with are Memrise and Duolingo.

Memrise- I've only used the Memrise iPad app- I haven't used Memrise online. Memrise is basically a flashcard program with a vast library of mnemonics to help you remember words. Some of the mnemonics are quite witty and amusing too, so it might help you learn those few tricky words that just don't seem to stick whatever you do. It also uses spaced repetition to remind you when to revise and make those words stick. I found the app quite fun but in some ways it was quite limited because most courses just test you on words and phrases (and like Language Perfect it suffers from that issue where you have to have the exact, sometimes bizarre, wording in your English translations for it to go through). However I'm fairly sure you can create your own courses on the web version.

Duolingo- I pretty much just got introduced to this website via a "quest" on HabitRPG (basically a to-do list where you get EXP and gold for completing tasks) and I really like what I've been seeing so far. I've been working my way through the French course (figured I might as well pick up some French again since Duolingo doesn't have Chinese on it). Duolingo is a bit like the sentence method in that it teaches you languages through whole sentences at a time. Each new sentence will contain only one or two new words. The lessons mainly consist of translating sentences back and forth (and it's reasonably lenient in that you don't have to get the super exact wording, but you still have to be more or less right) as well as dictations of phrases and sentences in the language that you're studying. If you have a microphone, you'll sometimes be asked to read sentences aloud. I used this at first but I found that my microphone never seemed to pick up my first couple of words and it begun to annoy me, so I stopped using it. (I've heard that some people have had the opposite issue- they've deliberately said the wrong thing and Duolingo has marked it correct.) Aside from these lessons, there's also the opportunity to read articles in the "immersion" tab and translate them or correct the translations of your fellow students. The main drawback with Duolingo is that there is only a limited language selection at the moment. At the moment, English speakers can learn Spanish, French, German, Italian, Portuguese or Dutch (Dutch is in beta). Other languages being developed are Danish, Irish, Hungarian, Swedish, Russian, Turkish, Polish and Romanian. Speakers of many other languages can use the website to learn English. I'm almost tempted to use the "English for Chinese speakers" course to see if it will help me practise Chinese :P

I'm back!

So after months of being away... I'm back! Back to write more random stuff on this blog, which probably needs a new title now that I've not only completed Year 11, but I've also graduated from high school and studied Chinese in China for a semester! (Don't worry, I'll keep the blog title and address the same so that you can find it easily. Also, "Gap Year Misadventures" might sound better but it doesn't really hint at what this blog is about, i.e. learning.)

So what are my plans for the rest of my gap year? Well, my main plan is to get a job and/or some volunteer work to gain some experience and learn some new skills. I'm trying to keep up clarinet practise and Chinese study. Also I bought loads of books while I was in China, so I'd better get around to reading them to make the arduous task of carrying them all home worth it. (My two pieces of luggage weighed 38kg combined. That doesn't include my 8kg backpack that I took on board as hand luggage. Thankfully Mum and I pre-booked 40kg on Air Asia and Scoot.) The book I am reading right now is called 致我们终将逝去的青春 by 辛夷坞. It was recommended to me by my Comprehensive Class teacher when I was in China.

Another thing I intend to do is continue with this blog. That means that I need to do some study of some sort, so that I can find some fodder to feed this blog. I mean, I could always just post up stuff about learning Chinese, but that would probably get boring after a while. At the moment all I can think of is reading the non-fiction Chinese children's books that I bought but I didn't exactly choose a diverse range of topics (pretty much all the non-fiction Chinese books I have- and there aren't actually that many- are about human bio or Chinese history) or maybe going through my old maths books and writing about maths but EEK I DON'T WANT TO TOUCH THAT SUBJECT UNTIL I REALLY HAVE TO!!! *gasp* *breathe*

(Nothing just happened! I'm fine! I swear!)

Okay. Now, where was I?

Right, I remember now. I was talking about what to write about on this blog. If there's any particular topic that you want me to write about, feel free to suggest it and I'll do what I can to accommodate you, even if that subject is maths. Don't worry about me. My stomach is strong (though the bins in Terminal 2 of Kuala Lumpur International Airport might tell you otherwise). I am strong. I can handle this. I CAN DO THIS!!

*faints*

Permutations and Combinations

Right so apparently someone my mum knows needs some 3CD help, but I'm kinda worried that I might have forgotten half of it, so I'm going to blog to refresh my memory.

First up we have counting techniques, which is a relatively straightforward concept but sometimes the questions can be annoying (as with so many other areas of maths...). The main types of counting techniques you need to know for 3CD are permutations and combinations.

Permutations are basically about how many ways a group of objects can be arranged. For example, if you get three characters, say, Azizi, Bentley and Cynder, and put them in a line, in how many ways can they be arranged? You'll find that the answer is six:

ABC
ACB
BAC
BCA
CAB
CBA

It's easy to work that out when you've got so few people. But what if you have 100 people? How many ways can they be arranged? (Not that you'd ever need to know the answer to this question, but still.) This is where the concept of the factorial comes in.

Let's go back to our 3-character example. Instead of thinking about who's going to go where etc., let's slow right down and think of an empty space with 3 spots waiting to be filled with the three characters:
_ _ _

Now let's choose who's going to fit into the first slot. There's 3 options, since nobody's been picked yet.
3_ _

When we move over to the second slot, since one person has been taken, there's only 2 options left.
3 2 _

Finally, that leaves only one person to fill the last slot.
3 2 1

For each character that goes in the first slot, there are 2 different permutations, as there are 2 different characters who can fit in the second slot (the last slot is then a given since there's only 1 character left by that point). Since there are 3 characters who can go in the first slot, this gives us 3 characters x 2 permutations each = 6 total permutations.

Sorry if that wasn't a good explanation. Here's a tree diagram that might help:

There's a logical pattern that holds true no matter how many people you have to arrange. Let's say you have n people to arrange. Therefore there will be n possibilities for the first slot, (n - 1) for the second, (n - 2) for the third and so on. This gives you n(n - 1)(n - 2) x ... x 1 as the total number of permutations.

Thankfully, you don't have to write it all out in full, thanks to the handy dandy factorial symbol (which is just an exclamation mark: !)

Hence, the number of ways you can arrange 3 people is 3! (3 x 2 x 1)

The number of ways you can arrange 4 people is 4! (4 x 3 x 2 x 1)

and the number of ways you can arrange n people is n!

That's easy, isn't it?

Now on to combination!

Combinations is basically the number of different subsets you can get from one big set.

I'm going to use my year 10/11 maths teacher's example for this one, because it's so awesome. I'll just change the characters' names though since I don't remember what the original names were.

Darius, Ember, Flame, Gaul and Hunter all like earthworms, so they all decide to set up an Earthworm Appreciation Society. At first, they decide to create a subcommittee, with a president, vice-president and secretary, appointed in that order. This is where you draw on your permutations knowledge, as first you've got 5 options for president, then 4 for vice-president, then 3 for secretary, resulting in 5 x 4 x 3 = 60 ways in which the subcommittee members can be elected.

Later on, instead of having different ranks within the subcommittee, the Earthworm Appreciation Society members decide that they're going to make all 3 subcommittee members of equal rank (which leaves you wondering what happens to the other two... well, I guess all animals are equal, but some are more equal than others). How many ways can the subcommittee be selected?

No, the answer is not 60. Why? Because, this time, everyone's of equal rank, so Darius-Ember-Flame is the same subcommittee as Ember-Darius-Flame.

How do we get around this problem? you must be asking. Well, first consider how many ways each subset can be arranged. Each subset consists of 3 characters. From the previous thingo on permutations, we know that they can be arranged in 3! = 3 x 2 x 1 = 6 different ways. Hence the Darius/Ember/Flame subset appears 6 times:

DEF

DFE

EDF

EFD

FDE

FED

and each other subset would, likewise, appear 6 times. Hence, to get the number of possible subcommittees, you need to divide 60 by 6 in order to avoid counting subsets 6 times each. This leaves us with 10 possible subcommittees:

DEF

DFG

DGH

DEG

DEH

DFH

EFG

EFH

EGH

FGH

There's also a general rule for this too. Let's first take a look at why it works.

When working out the total number of permutations (remember, permutations is where order matters) for n objects in r [number of] slots, it's a case of multiplying n x (n - 1) x (n - 2) etc. all the way until you've filled up all r slots. An easy way to express this is n!/(n-r)!

I'm not sure how to explain this without being super confusing, but I'll try. n! is the product of all of the numbers from n all the way to 1. The thing is, you only need the product of r of these numbers, because you only need r slots. The remaining number of numbers that you have remaining (i.e. the numbers between 1 and n that don't need to be used) can be expressed by (n - r).

To find the product of just the numbers that you need, n!/(n-r)! works because n! is essentially n x (n - 1) x (n - 2) x ... x (n - r) x ... x 1 and (n - r)! is (n - r) x (n - r - 1) x ... x 1. Hence when you divide n! by (n - r)! you'll find that all of the terms from (n - r) and beyond cancel each other out, just leaving you with the product of the top r numbers. Nifty, right?

Now, as I stated before, working out the total number of permutations isn't enough- you have to then divide by the number of permutations within each subset of r objects, which is r!. This leaves us with a final equation of (drumroll):

The thingo on the left is the notation for combinations (well, one kind of notation anyway. You might see other notation involving P for permutations or C for combinations, with the two numbers on top left and bottom right). The number on the top is the total number of stuff you have to choose from, while the number on the bottom is the number of stuff you want in the subsets. Make sure that the brackets are roundish, otherwise it'll look like a matrix.

That's pretty much all the main basic stuff on permutations and combinations. Because I can be bothered, however, here's some pointers on how to tackle the problem solving varieties of these questions.

Problem Solving: Permutations and Combinations

The problems that you will encounter when it comes to permutations and stuff generally involve some restriction, such as that someone must be on the end of the line, or two people must stand together, or something. I'll show you some basic techniques for solving these, but some are a bit trickier. Just do as many as you can to develop that problem-solving brain of yours!

Oh yeah and, apart from reading the examples in the textbook to get a feel for the types of questions they might ask, I'm making up these questions on my own, which is why they're so weird.

Question 1

Eliona, Sharon, Karyn, Maria and Sarah are lining up for their flu jabs. In how many ways can they line up if:

a) Sarah must go first?

b) Sarah must go first and Karyn must go fourth?

c) Maria is behind Sharon? (Sarah doesn't necessarily have to be first this time)

Question 2

a) Out of 8 humans and 6 Vulcans, a crew consisting of 4 humans and 4 Vulcans is required. How many possible crews are there?

b) One of the humans is Captain James T. Kirk. How many of the crews contain Captain Kirk?

Question 3

Hienuri Kayleuetski is on a chat room with her friends, Diani, Ashleigh and Fiona, who are all using Ashleigh's computer together. To distinguish themselves, they refer to each other as "meep," "moop" and "murp" and encourage Kayleuetski to guess who is who. Kayleuetski's first guess is that Diani is "meep," Ashleigh is "moop" and Fiona is "murp," but is then informed that all of her guesses were wrong. How many possible combinations remain?

Question 4

Neisure has 10 uni books to arrange on her shelf, 4 Psychology, 3 Education and 3 Magic (she lives in an alternate universe where magic is possible!!). How many ways can she arrange them if:

a) they don't have to be arranged in any particular order?

b) books of the same subject are to be kept together?

c) the 3 Magic books must all be together on either end of the shelf, but the other 7 books can be arranged in any order?

Question 5

A TV talk show host wants to invite 3 characters to his upcoming show. His list of potential candidates consists of Alakazam, Blissey, Charizard, Loudred, Miltank, Seviper and Zangoose. How many possibilities are there if:

a) there are no restrictions?

b) he decides not to invite both Seviper and Zangoose (since they hate each other)?

c) he decides not to invite either Seviper or Zangoose, fearing that inviting either would just incite more rivalry?

d) he decides to invite both Seviper and Zangoose just to add some excitement to the show?

Answers

1a) Since Sarah must go first, that only leaves us with 4 characters in 4 possible positions. Hence the number of possible permutations is 4! = 24 ways in which they can line up.

1b) Since two positions are fixed, that only leaves us with 3 characters in 3 possible positions, leaving us with 3! = 6 ways in which they can line up.

1c) To do a problem like this, I generally split it up into different categories and then add them together: if Sharon is first, second, third or fourth (she can't be fifth since Maria has to be behind her). Then I draw boxes for each position and then write numbers in each box corresponding to how many options I have (see my explanation for permutations).

If Sharon is first, Maria will definitely be after her. And since Sharon's position is fixed, that leaves us with 4 characters in 4 possible positions, with 4! = 24 ways.

If Sharon is second, only 3 characters can be in front of her (Sarah, Karyn or Eliona). The other three can be arranged in any order.

[3][1][3][2][1] = 3 x 1 x 3 x 2 x 1 = 18

If Sharon is third, only 3 characters can be first (Sarah, Karyn or Eliona) and 2 characters can be second (those three minus whoever goes first). The other two can be arranged in any order.

[3][2][1][2][1] = 3 x 2 x 1 x 2 x 1 = 12

If Sharon is fourth, Maria must be last, and the other three can be arranged in any order, giving 3! = 6.

Hence the total number of ways in which they can be arranged is 24 + 18 + 12 + 6 = 30 + 30 = 60.

2a) Use the Combinations technique to "choose" 4 humans and to "choose" 4 Vulcans, then multiply the two together.

For humans: nCr(8, 4) (that's the notation used on many calculators) = 70

For Vulcans: nCr(6, 4) = 15

Hence total number of possible crews = 1050

The reason why this works is, for every subset of humans chosen, there are 15 Vulcan subsets that they could be partnered up with. Hence you need to multiply the 70 different groups of humans with the 15 different groups of Vulcans that they could be partnered up with.

2b) Since one of the humans has been "chosen," that leaves us with only 7 humans left to choose from and 3 slots left to fill. Hence, the number of human teams is nCr(7, 3) = 35 and the number of Vulcan teams remains the same (15) which gives us 35 x 15 = 525 different crews all containing Captain Kirk.

3. Yes, I actually did get given a similar problem in real life once, except I skimmed over the part where my friends said "all wrong" and then thought "there's 3! permutations, and I've already guessed one, leaving me with 5 more to go!" No, this is not the case. (I was told to "learn to math" at this point.) And yes, this was a bit of a trick question.

Since Diani is definitely not "meep," this leaves us with two other possibilities: Ashleigh or Fiona.

If Ashleigh is "meep," this leaves us with Fiona and Diani. Fiona can't remain "murp," hence there is only one other option for her: "moop." Diani then takes the last available slot.

If Fiona is "meep," this leaves us with Ashleigh and Diani. Ashleigh can't remain "moop," hence there is only one other option for her: "murp." Diani then takes the last available slot.

Hence there are only 2 possible permutations remaining.

4a) The answer's just 10! = 3 628 800.

4b) To do this, I prefer to think of all of the books of the same subject as just being one book, and then adjusting the number of "slots" accordingly. Therefore I would think of it as 3 books needing to be arranged in 3 different slots, which gives us 3! = 6 ways in which the subjects can be arranged.

After that, you have to multiply by the number of ways books of the same subject can be arranged amongst themselves. The four Psychology books can be arranged in 4! = 24 ways, and the Magic and Education books can be arranged in 3! = 6 ways each.

Then you need to multiply the lot together, to give 6 x 24 x 6 x 6 = 5 184 possibilities.

4c) As in 4b), just think of all three Magic books as simply being one book. This "book" must be at either end, leaving us with 7 slots in which the 7 other books can be arranged. The Magic books themselves can be arranged in 3! = 6 different ways. This leaves us with (7!)(3!)(2) ways in which the books can be arranged (the x2 is because the Magic books can be at either end). Total number of possibilities is 60 480.

5a) nCr(7, 3) = 35 different ways

5b) First see how many possibilities there are if Seviper is definitely coming and Zangoose is definitely not coming. Since Seviper takes up one slot, and Zangoose can't come, that leaves us with 5 potential characters remaining and 2 slots, or nCr(5, 2) = 10 ways. Multiply this by 2 to get the other possibility (i.e. Zangoose comes and not Seviper), and you've got 20 different ways in which to select 3 candidates.

5c) Since neither Seviper nor Zangoose can come, we only have 5 characters to fit into the 3 slots. nCr(5, 3) = 10 possibilities.

5d) Seviper and Zangoose fill up one slot each, so that leaves 5 potential characters and only 1 slot, so only 5 different ways in which to select 3 candidates by this criteria.

An egocentric-sounding passage from 秘密 (The Secret)

Last year, I stumbled across a copy of the Chinese version of The Secret in a university book store. Having never read The Secret, and being curious to know what exactly it's about, I bought the book. Later on, I stumbled across it again in the Self-Help section of a book store in Singapore, and upon opening it and finding out that The Secret is mainly just about positive thinking, my first thought was "This is just an example of very, very good marketing." Back home, curious as to whether people really believed stuff like the "Law of Attraction," I googled reviews of The Secret. Apparently at the end the whole book really does boil down to Byrne's commandment that we all "Feel good now," or something, which is all nice-sounding and stuff, but the truth is, I don't believe that we have that much control over how we feel, though we can control how we handle our feelings. I wanted to see what that looked like in the Chinese version, but on the last page (before the summary and background information on people referred to in the book), I instead found an even more egocentric passage. I couldn't understand all of it at first, but what I could understand made me raise my eyebrows until they'd practically rocketed off the top of my head (gee, I'm glad that my thoughts aren't going to manifest such an occurrence in real life). By the way, the emphasis is not added: the word "你" is actually written in bold print, just to drive the egocentric message even further.

地球为你而转动，海洋为你潮涨潮退，鸟儿为你唱歌，太阳为你朝升暮落，星星也是为了你而出现。你所看到的一切美丽事物，所体验到的一切美妙经验，都是为了你而存在的。看看周遭的一切，没有你，它们没有一个能存在。不论过去你认为自己是谁，现在，你知道真正的自己的真相了。你是你自己宇宙的主宰，你是你自己王国的继承者，你是生命的圆满。现在，你知道这秘密了。

Now, I'm not sure if I've translated this right, so I'll post my translation here just to make sure that I'm not imagining things (or "attracting" things!) and that this really is one of the most egocentric-inspiring passages that I've ever read.

"The world turns for you, the ocean tides rise and lower for you, the birds sing for you, the sun rises and sets for you, the stars also appear for you. Every beautiful thing that you can see, every wonderful experience you have had, all exist for you. Look at everything around you- if you didn't exist, these things also would not be able to. No matter who you thought you were in the past, now you know who you truly are. You are the master of your universe, the ruler of your kingdom, life's satisfaction. Now you know this Secret."

I don't know about you, but I do not necessarily want the birds to sing specifically for me. Let the birds sing for themselves, or for whoever they choose to sing for.

And that is my two cents into the matter.

EDIT: Wow, I was pretty much right about the translation. From http://www.shiningthelightonthesecret.com/whatpeoplearesaying.htm, the actual ending of the book is:

The earth turns on its orbit for You. The oceans ebb and flow for You. The birds sing for You. The sun rises and it sets for You. The stars come out for You. Every beautiful thing you see, every wondrous thing you experience, is all there, for You. Take a look around. None of it can exist, without You. No matter who you thought you were, now you know the Truth of Who You Really Are. You are the master of the Universe. You are the heir to the kingdom. You are the perfection of Life. And now you know The Secret.