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.

Redox in Action: Some Batteries plus Corrosion

Now that we've learned a bit more about redox, let's see how the stuff we've learned applies to the world around us! Yay. Now I sound like an overenthusiastic presenter on a children's TV show.

Continuing with the overenthusiastic children's TV presenter theme (because I feel like I need a lame way to amuse myself today)...

Hey, kids! You know all those batteries that you use to power up all your favourite toys and gadgets? Well, we're going to learn allllllllll about batteries. Well, maybe not all about them, because there's just so much to learn! So, today, we're just going to learn the basics.

The most common kind of battery that you'll see around the shops and in your electronic gizmos is the dry cell. The dry cell is probably called the dry cell because it has a kind of paste, rather than a liquid, inside it.

Here's a picture of the cross-section of a dry cell. The cross-section is what you would see if you cut a dry cell in half, riiiiiight down the middle! But don't try this at home, because it is very very dangerous, and we wouldn't want anyone to get hurt, would we?

You know how the different ends of the batteries are labelled positive and negative? Well, they're named that way for a reason. At the anode, which is the negative side of the battery, the zinc casing undergoes a reaction that produces electrons needed for current to flow.

Zn_(s) à Zn²⁺_(aq) + 2e^-

But wait! If the casing is reacting, how come the casing doesn't corrode? Well, that's because the zinc doesn't just react on its own: it's actually reacting with another substance called magnesium dioxide which is normally found in a powdered form around the graphite rod in the middle of the battery. When they make the batteries, they make sure that there isn't enough magnesium dioxide to react with all of the zinc.

2MnO_2(s) + 2NH₄⁺_(aq) + 2e^- à Mn₂O_3(s) + 2NH_3(aq) + H₂O_(l)

After those two reactions happen, the zinc ions from the first reaction combines with the ammonia from the second to produce another ion- a complex ion this time! Ooh, how exciting!

Zn²⁺_(aq) + 4NH_3(aq) à [Zn(NH₃)₄]²⁺_(aq)

Now, eventually, the outer shell of the dry cell does corrode. That's why you sometimes get battery leakages, where the paste inside the battery comes out. This can be very dangerous, so try not to leave your batteries in your electronic devices (or anywhere, really) for so long that they start leaking!

Why does the dry cell corrode even though there isn't enough magnesium dioxide? Well, that paste inside the dry cell doesn't just contain magnesium dioxide- it contains other stuff too, like ammonium chloride and zinc chloride! Ammonium ions in solution can create an acidic environment, which makes the cell corrode after a while.

Since the zinc ions, once formed, are no longer where the original zinc was, dry cells can't be recharged by making the reactions reverse, and you shouldn't try to recharge them either, as that's also quite dangerous! This inability to recharge makes dry cells primary cells, as opposed to secondary cells, which can recharge.

There's also a very similar cell, called the silver oxide cell! These kinds of cells are also primary cells- that is, they can't recharge. They normally appear in button form, like the batteries in watches and in some calculators! They also use the same anode reaction- the conversion of zinc to zinc ions- but silver oxide, rather than magnesium oxide, is consumed at the cathode.

Ag₂O_(s) + H₂O_(l) + 2e^- à 2Ag_(s) + 2OH^-_(aq)

Apparently they've started developing rechargeable versions of these cells, but most silver oxide cells that you'll encounter at this point in time aren't rechargeable. Make sure to only recharge rechargeable batteries, kids!

The next type of cell that I'm going to tell you all about is the lead-acid accumulator! Unlike the dry cell or silver oxide cell, which produce relatively small currents of electricity, the lead-acid accumulator is created to produce lots and lots of current in a very short amount of time. It's often used in cars.

The lead-acid accumulator is actually made up of a bunch of different cells, each with an anode and a cathode. Each electrode has a lead alloy grid, but the anode's grid is packed with finely divided lead and the cathode's grid is divided with lead (IV) oxide powder. You see, when you finely divide something, it makes the reaction proceed much much faster than if you had it all in one single thick lump!

Anode: Pb_(s) + SO₄^2-_(aq) à PbSO_4(s) + 2e^-

Cathode: PbO_2(s) + SO₄^2-_(aq) + 4H⁺_(aq) + 2e^- à PbSO_4(s) + 2H₂O_(l)

Also, unlike the previous two batteries, these cells are secondary cells. They can recharge, which makes them much more useful for much longer! You can't recharge them too fast, though, or water might be electrolysed to hydrogen gas and oxygen gas, which would mean that you'd have to top up the battery with distilled water. Not only that, but it might explode and that would defeat the whole idea of the battery being useful for a long time!

2PbSO_4(s) + 2H₂O_(l) à Pb_(s) + PbO_2(s) + 4H⁺_(aq) + 2SO₄^2-_(aq)

There are many other kinds of batteries, but there's not enough time to cover them all in today's show. We might be able to talk about them in a future episode. So that's all for now, kids! Stay safe, and look after your batteries!

...

Whew. Now that the show's over, I can go back to being an obnoxious teenager.

By the way, one of my friends' older sisters was watching a whole bunch of kids' shows just to look out for any mistakes that the producers made. Once, she was watching Play School and, at the end, right before the camera was turned off, you could hear someone in the background say, "I hate my job!"

Just some random trivia for you. No, I don't know what episode that is, so I can't help you find it.

Anyway. I'm not going to talk about the other types of batteries, for now at least. Instead, I'm going to talk about corrosion. Yay?

Metals rust and corrode when they're exposed to water and oxygen. How so? you may ask. Well, if you have a look at your data sheet, you'll notice that water and oxygen can be reduced to form hydroxide ions!

O_2(g) + H₂O_(l) + 4e^- à 4OH^-_(aq)

And, as you probably already know if you've become familiar with the basics of redox, many metals can oxidise. Therefore, what we have here is a redox process of sorts, with the metal oxidising and the oxygen and water reducing.

Bear in mind, though, that those metals right at the bottom of the Standard Reduction Potentials table aren't likely to corrode in the same way. This is because these metals oxidise so readily they tend to react really violently with water to produce hydrogen gas, metal ions and hydroxide ions. Take potassium, for instance:

K_(s) + H₂O_(l) à K⁺_(aq) + OH^-_(aq) + H_2(g)

Also, some of the metals near the top of the table won't corrode simply because they're more likely to reduce than water and oxygen are. These metals include gold and silver.

Most other metals, like iron and zinc, will corrode. In fact, iron is very commonly referred to in corrosion questions and examples. My textbook only gives the equations for the rusting of iron. I highly doubt this is really breaching copyright, since you'd probably be able to find all the equations on Google anyway, so here they are:

1. Hydroxide ions produced from the reduction of water and oxygen and iron (II) ions produced by the oxidation of iron combine to produce iron (II) hydroxide: Fe²⁺_(aq) + 2OH^-_(aq) à Fe(OH)_2(s)
2. Iron (II) hydroxide is easily oxidised (more so than iron) to produce iron (III) oxide: Fe(OH)_2(s) + OH^-_(aq) à Fe(OH)_3(s) + e^-
3. The iron (III) hydroxide is then partially dehydrated to produce hydrated iron oxide, or Fe₂O₃·xH₂O. This is basically just rust, that flaky reddish stuff.

Also, as iron (II) ions are consumed to produce the two hydroxides, the reaction producing these ions is favoured in order to partially restore the number of ions- remember good ol' Châtelier? Since the reaction producing these ions also happens to be the oxidation of iron, the rusting process essentially speeds up the rusting process. Brilliant.

Now, we like our things to last, don't we? So, how can we stop our iron tidbits from corroding? Here are some ways we can prevent a metal from corroding:

1. We can coat it with a more reactive metal or connect it via a wire to another more reactive metal. This metal acts as a "sacrificial anode" and will rust instead of the iron or whatever metal that you're trying to protect. If you coat the metal with a less reactive metal, however, then any small scratch on the coating will cause the metal inside to corrode faster. Ditto with linking the metal up to a less reactive metal.
2. Cathodic protection: In cathodic protection, the metal to be protected is linked up to the negative terminal of a DC (direct current) power source, while some scrap metal is linked up to the positive terminal. The negative terminal of the power source provides all the electrons that the iron needs to stay as a metal- if any iron dares become an ion, it will simply collect the electrons being fed to it and become iron again.
3. Some metals are awesome and actually stop themselves from corroding in the long run. Take aluminium, for example. When aluminium oxidises, it forms aluminium oxide, which actually forms a protective coating that stops any further oxidation. Pretty handy, huh?

That's pretty much all from me on corrosion, unless you feel I haven't covered enough. I might do another post on the different kinds of cells if I can be bothered, but for now I'll just go on to thinking about writing posts about organic chemistry. (Actually writing them might be a little tougher.)

Redox reactions (including the T-word)

The first thing that you have to know is how to write equations for and interpret observations for redox reactions. But we've already done writing equations! you might say, and you're right, since I've already talked about them in my post aptly titled "Redox Equations."  We haven't done observations, though, because observations are totally a whole new ball game. Not.

Basically, the first thing that you need to do is write the equation. Then have a look to see if any of these things happen:

• Gases are bubbled through the liquid
• Gases are produced
• Solids dissolve
• Solids form
• The solution changes colour (use your data sheet to determine the colour of reactant and product ions)

Once you've determined these things, you need to make sure to provide detail. If a gas is bubbled through or if a gas is produced, what colour is the gas, and what does it smell like? Most gases are colourless and odourless, but some have a colour, like chlorine gas which is greenish-yellow. Additionally, most gases are odourless, but there are some that are considered to have a "pungent odour" like hydrogen sulfide (and maybe nitrogen dioxide, I can't remember). If a solid is dissolved or formed, what colour is the solid? (By the way, you have to use what the data sheet tells you. So yes, that means you have to say that copper is "salmon pink.") Also, generally, in a redox reaction, where one solid dissolves and another forms, you can just say that the first solid is coated with the second. I think.

A couple of common ion colours that you should know are the permanganate ion (purple) which can be reduced to manganese (II) ions (pink) and the dichromate ion (orange) which can be reduced to chromate ions (yellow). They're on the data sheet anyway, but they're so common in redox reactions that it's almost worth getting to know them.

What's next? Hm. Stoichiometry. Well, stoichiometry here works the same way as stoichiometry everywhere else, so if you need to brush up on that, head on over to the following posts:

• Simple Calculations Involving Moles
• Reactions and Equations, part deux
• Simple Chemistry Calculations
• Empirical Formulae and Limiting Reagents and Some Other Stuff

Next up: Explain the use of self-indicators in redox titrations. You know how you need an indicator of some kind in acid-base titrations? (If not, go to my post on titrations.) Well, in redox, you generally don't, because common oxidising agents used, like permanganate and dichromate ions, change colour when they're reduced anyway, and it's this colour change that helps you to work out an end point.

Redox titrations are a bit more complex than acid-base titrations because you normally have to go to all the work of sufficiently acidifying the permanganate or dichromate ion solutions otherwise you'll end up with manganese dioxide or chromate ions later on.

Now, a bit more about redox titrations. A primary standard needed here is something that's going to oxidise or reduce, otherwise you wouldn't end up with a redox reaction! Oxalic acid (H₂C₂O₄ , otherwise known as HOOCCOOH which is kinda like Ho-oh with some extra letters added in) is often used for redox titrations as a primary standard because it can be prepared to a high degree of purity and whatnot (my first post on titrations outlines the main characteristics of primary standards).

When using potassium permanganate solution, you have to take all kinds of precautions because it oxidises stuff easily and also decomposes in solution, especially in sunlight. When you prepare the solution, you sometimes have to cover the beaker and boil the solution before filtering it through glass wool into a dark storage bottle. Now, I'm not 100% sure on the science behind all of this, because we haven't really done a lot of redox titrations, but I think the boiling might be to get rid of stuff within the solution that the potassium permanganate might oxidise? I'm not sure exactly what stuff needs to be removed, but there you go. As for the glass wool, I have absolutely no idea whatsoever (and I'm feeling too lazy to look it up right now), so if someone could enlighten me, that would be great! If not, that's okay, you don't have to do all my dirty work for me.

The rest of the titration proceeds in pretty much the same way as an acid-base titration, except for a couple of differences:

1. You have to add sulfuric acid (NOT hydrochloric acid, as the chlorine ions will be oxidised by the permanganate ions) to the solution so that the permanganate or dichromate or whatever solution will form your desired products (i.e. manganese (II) ions rather than manganese dioxide).
2. You have to heat the conical flask before reaction because the reaction proceeds too slowly at room temperature. (Well, too slowly for our purposes, anyway.)
3. You don't have to add indicator because permanganate ions are purple and they should turn pink (or a murky brownish colour if you didn't add enough acid) and dichromate ions are orange and they should turn deep green (or yellow if you didn't add enough acid). However, I've also heard that occasionally the permanganate solution might turn clear instead of pink despite what it says on the data sheet.

Whew. That wasn't so bad. I guess it's easier talking about titrations than actually doing them.