How to blunder a rook and still win

Changed to a hyperlink for your convenience!

xkcd what if?

First of all, if you haven't been reading xkcd, I recommend you start reading it soon! It's an awesome webcomic, perfect for people who actually bother to research on the multitude of references inside, ranging from movies to quantum physics!


Next of all (after you've convinced yourself of the worth of reading the main strip of comics), do check out the sideline series of articles by the same author (Randall Munroe) "what if?".


Today's article will randomly make comments on the 44th what if? issue: High Throw. Here's the link: http://what-if.xkcd.com/44/ . I'm not of the opinion that what if? is substandard. In fact, I do think it's awesome and enjoy reading it. But that shouldn't stop me from commenting about it and trying my very best to poke loopholes... right? :)


Quote: "A timing error of half a millisecond in either direction is enough to cause the ball to miss the strike zone... To put that in perspective, it takes about five milliseconds for the fastest nerve impulse to travel the length of the arm."


Comment: This might have something to do with systematic errors being cancelled out: since the time to throw the baseball is determined beforehand by the pitcher, possibly in the brain (and if it's reflexive enough maybe part of it is generated in the spine), there is a fixed amount of delay between giving the signal to swing the arm around and the signal to release the ball in order to hit the strike zone, and this is possibly learned through trial and error, since nobody is THAT good when they were first introduced to baseball. An example of a similar phenomenon can be observed when timing the timespan between two of the same events with no warning (eg. 2 lightning flashes), where the reaction times tend to cancel each other out almost completely (In my experience, my reaction time varies less than 0.03 seconds when doing the "drop a ruler to find out reaction time" test, whereas my reaction time is close to 0.2 seconds. Note that this is still out of the 0.5 millisecond range mentioned by about 3 times. Maybe that's why I don't play baseball.)


Quote:"But we could also sidestep the whole problem by using a device like this one:

It could be a springboard, a greased chute, or even a dangling sling—..."


Comment: This is actually unlikely to be efficient. The first problem is that the entry angle is unlikely to be sufficiently exact for it to just slide up as depicted in the picture. It's likely to bounce around a bit, which tends to lose energy quite well. The second difficulty to overcome is, as in most physics problems, friction. No I'm not talking about air resistance, that has already been (somehow) accounted for in the what if? comic. I'm talking about friction with the deflector. Firstly, let's talk about an instantaneous deflector (eg. a stiff, hard 45-degrees-to-horizontal board). This will cause a great big bounce, which loses energy according to the coefficient of restitution (COR). "Generally, the COR is thought to be independent of collision speed...(except when collision speeds are in the range of 1cm/second)". The highest permissible COR for a tennis ball, according to the international Table Tennis Federation, is about 0.92, on a standard steel block (Wikipedia). This means that about 8% of the energy is lost in one bounce, or about 8% of the height is lost (with an uncertainty of a factor of 2, considering air resistance). This is close to half a giraffe of height. For a baseball, this is likely to be much more, although to be fair, colliding with a board at 45 degrees will probably lessen the impact.


The second kind of energy loss through friction with the velocity converter is the friction that comes when the ball slides along the (for brevity) chute. Usually, when dealing with such dynamic (or kinetic) friction, we can use a formula:

"The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together." -- Wikipedia, yes again.

Lubricated steel on steel has a coefficient of 0.16, again from Wikipedia (what a glaring testimonial to the unreliability of this article!). So, where does the normal force come from? It turns out that there has to be normal force acting on the ball, since it changes its velocity, and hence this means it accelerates, and using the standard F=ma, we can see that the Kinetic friction is Fric= ma = m(v^2/r), where r is the radius of the chute (Yes that's the formula for centripetal acceleration). So how much energy is lost? We shall make the simplifying estimate that velocity is somewhat constant throughout the ride (else it would be a bad idea anyway). We get:

Work done (against friction) = 2(pi)m*v^2

Well, not quite. After all, can't the ball roll? (The coefficient for rolling friction tends to be a lot lower, which is why cars are even remotely efficient) Turns out that even if it rolls, it won't go as high anyway, because the kinetic energy will be converted into rotational kinetic energy, which doesn't really cause the ball to go higher. (Note that this is in particular because it is a ball; projectiles such as bullets are typically given spin so that they stabilise in an aerodynamic position, a phenomenon known as the gyroscopic effect)


As an aside, note that r is not quite the radius of the chute (I lied.). r is actually the difference between the chute and the ball (Details are left as an exercise to the reader, but rest assured everything tends to cancel out.). There is an interesting special case, which will probably lead to the discussion of a bounce, which I shall not discuss due to its theoretical complexity (i.e. r=0.). And I've been using ".)." too often (Right.).


Yet another point he neglected to discuss (probably too boring) was whether we could thin out the air resistance, for example by climbing to the top of Mount Everest, where the air is thinner (minus some power to account for altitude sickness), or possibly from a hovering helicopter even higher up (Baseball probably would instantly fall downwards from the downwash of the helicopter's rotors or just plainly crash into it).


And one last thing: I don't get the caption for the last comic drawing.

Runescape skills and their applicability to real life

To start off, I just checked the skills present in Runescape, having unconsciously drifted away from the game for quite some time. As it turns out, the f2p (free to play) world has recently gotten access to p2p (pay to play, aka members) skills up to level 5. This isn't a very significant level, but it is a significant step in the expansion of f2p, since updates to the f2p world are as rare as my blog posts. It turns out there are 25 skills, namely *draws deep breath* Attack, Defence, Strength, Constitution, Ranged, Prayer, Magic, Cooking, Woodcutting, Fletching, Fishing, Firemaking, Crafting, Smithing, Mining, Hebrlore, Agility, Thieving, Slayer, Farming, Runecrafting, Hunter, Construction, Summoning and Dungeoneering.

That's a lot to process.

Firstly, I will begin with a few observations on those skills which will eventually save me time.

Observation 1: Dungeoneering and slayer are very forced skills, i.e. skills for the sake of having more skills.

Observation 2: There are a few almost exclusively combat skills, which can be lumped together to save discussion. These are Attack, Defence, Strength, Constitution and Ranged (as well as the combative part of Magic, but hey, Magic is a dual-purpose beast).

Observation 3: Runecrafting is... specific. Let's disregard this for the sake of a glimmer of hope at conciseness.

So we shall begin with the resource gathering skill. Ah... still uncomfortably many: woodcutting, fishing, mining. Out of these, woodcutting and mining are ridiculously industrialised, and are unlikely to be useful unless you happen to work in one of aforementioned industries. Fishing, on the other hand, is an incredibly useful skill, as I have found out personally. It is one of the most effective ways of countering boredom I know, boasting one of the highest used time to productivity ratio. And unlike staring at chess puzzles, people actually pretend to understand why you're doing it.

Next up, resource processing, the monstrous group of skills. This includes: Cooking, Fletching, Crafting, Smithing, Herblore and Construction. We shall do this in a list form, as any prose will result in an unwieldy paragraph that I have learned to shun.

Cooking: One of the useful skills in life, with applications starting from preparing instant noodles, which can save precious seconds and snag you the unbuyable you never wanted! (See: Neopets restocking) This obviously extends to more complex procedures such as barbeques when you happen to be stranded in a forest! (This has been happening surprisingly often to me; sadly I have yet to acquire such mighty levels of this skill)

Fletching: Another important form of entertainment in abovementioned stranded-in-forest situation. Note: Suitable arrows may actually be tougher to find, would do good to prepare those before getting stranded.

Crafting: The rings I know best are tend to exhibit resonance. I shall pass upon detailed discussion.

Smithing: Despite the apparently relation to fletching, smithing is not a viable option due to the disappointing lack of workable metals in forests. Tools may also be disgustingly unimprovisable.

Herblore: Definitely a useful skill, from forest survival to staying awake mugging the dynamics of Neopets using the power of ginseng (anecdotally proven to work).

Construction: Useful insofar as it relates to making a DIY computer. Speaking of which, it might be time to borrow skills from certain friends to improve on this artefact of a computer (a.k.a. mine). Further uses of this include the design of fantastic physical contraptions to do work such as strategically hold down a specific key on your keyboard for various sneaky purposes ranging from games such as Anti-Idle: The Game to Guitar Hero III (TTFAF intro anyone?)

Next up: combat. As somebody who is low in attack, strength and defence (and ranged too, unless it's badminton), I must say I do prefer agility.

This leaves a mere handful of skills that I have left out, probably by accident: Firemaking, Thieving, Farming, Summoning and Prayer, and last but not least, Magic.

Firemaking: This blog does not advocate arson.

Thieving: This blog does not advocate theft of any physical sort, but *borrowing* puzzles, ideas and questions are always encouraged. After all, information is a public good, defined as one which is non-rivalrous and (to a large extent) non-excludable.

Summoning and Prayer: Prayer can be useful in a wide variety of situations, ranging from international chess to chinese chess to shogi to RJT chess to even unexpected niches such as reversi, Go, Connect Five, Transfer Chess and even crazy things like double board RJT chess! (Do try: you'd probably be too befuddled to regret it!). Also, in a last-ditch attempt to make this post remotely relevant, we shall offer a last-minute prayer and invoke the spirit of U+3374 to offer us insights on the uses of magic.

Magic: Coming next^x *next* Thursday, where 1<=x<=3 is a positive integer.

Great eyepow... foresight!

Finally, the backshadowing has caught up. And it isn't even Thursday yet!

I hereby present to you the following guest post, which incidentally, comes without an explicit title:*

In the interest of not having to appear at a certain location in Serangoon on a certain Saturday evening, this article explores the possible topics which may be interesting enough to warrant appearing in the future. In other words, another post ought to be appearing on Thursday! (“Which Thursday?” “Next Thursday!" ”Isn’t that today?” ”No, *next* Thursday!”)

Clearly there are a few classes of possible blog posts. The kind that probably occurs most frequently amongst most blogs simply talks about recent occurrences in one’s life. But, looking at the nature of the previous posts on this blog (as well as the other blog owned by a certain contributor), this is clearly not the way to go (unless you’re talking about recently occurring chess games). Why write about the trifling details of your daily happenings when you can write about the trifling details of your greatest chess failures/cheapoes? Maybe when the (immensely limited) audience begins tiring of annotated chess games (with pretty unsound annotations at that), we can start writing our thoughts on (gasp) other games, like GGbranch-ferrying DotA. (Actually, writing a blog post thinking of strange handicaps and games you can play on a DotA map might be pretty interesting. Next Thursday might happen earlier than expected yet!)

Other than the category of “things that have happened”, there’s the category of “things that are true without needing to happen to us first”** (also known as “facts”). Like maths. And more maths. And even more maths. However, as kindly pointed out, none of our names are “Galois” (who apparently, while younger than us, did something so imba*^3 I still don’t understand it), so we’re kind of short of interesting true things to talk about, even if they do happen to be true. Our work in this area is most likely going to be restricted to generic surveys and discussion of existing results, or reinventing trivial things that we haven’t seen before, but maybe can be found in one of Ramanujan’s notebooks somewhere (though probably too trivial for that). Maybe if we ask a particular penguin*^4 to write something algorithmy rather than pure maths-ish we’ll get something less trivial. Or maybe we can start attempting some original research in some area that hardly anyone’s touched before, which will probably begin not merely next Thursday, but next *next* Thursday!

However, on a more plausible note, I’ve seen quite a number of interesting and not-hardcore-researchy programs written in quite a few areas. The aforementioned penguin has done a couple of interesting machine learning / AI ones, and there are more, like the Twitter iambic pentameter generator, or the genetic algorithm Mona Lisa painter, or the text classifier for “that’s what she said” jokes.  Perhaps when I go and read machine learning or AI or NLP or whatever stuff I’ll write some funny miniprojects up and stave off badminton for yet another week/month/year/millennium. Computer graphics projects are also pretty cool; got to learn that stuff someday.

Of course, instead of writing “facts”, we can instead be cheapskate and contribute our opinions on such facts. Like annotating our chess games. Or coming up with strategies for strange self-DotA-mods*^5. Or maybe writing the fail thought process of spending 5 hours solving some trivial maths/algo question. Or writing a scathing critique of a post detailing the fail thought process of spending 5 hours solving some trivial question. Scathing critiques of scathing critiques could probably be worth a week of writing by themselves!

The last category I can think of is “things that aren’t really constrained by trivial details like fact”. This doesn’t include just fiction (which I’m not really sure any of us are good at writing anyway, but maybe we’ll try someday), but other creative thingumajigs. If a text game ever gets round to being created (coming next next *next* Thursday! My, our Thursdays are going to be really busy, aren’t they?), some interesting aspects would probably end up here, like quest and storyline creation ideas. Art and music also spring to mind, except that we can’t draw and we can’t compose. We can do passable imitations of noob people playing certain instruments, though, but nothing we’d really dare to unleash upon the world online, lest civilization collapse. I suppose what we *can* do is make stuff like puzzles (ought to write another cryptic crossword someday too!), though that borders on fact instead of being pure unadulterated smoke. Also, come to think of it, we do have a decent poet, at least judging from the contents of his other blog. Maybe he can  throw some on this side as well! In addition, next next next *next* Thursday  I’ll probably write a series of articles attempting to formalize a magic system for fantasy settings, so you can wait for that as well.

Thus ends some thoughts on stuff that might appear on this blog in the future. If any of our limited audience has further requests for articles, written by guest posters or otherwise, he or she should feel free to contribute further ideas. Note that the list of banned topics include anything to do with certain units of pressure, especially pertaining to atmospheric pressure, as well as certain martial arts moves featuring in karate. Do will die, don’t ask why.

Happy waiting for future articles! Hope you’ve got a really thick book to read in the meantime.

*Annotations by pH42, yours unfalsely; changed some typos/speeling errors

**Read Anathem for a discussion about this at great length. Like, really great.

***Imbalanced, typically used to refer to something on the overpowering side. Alt. spelling: Imbar

****Preferred spelling: penquin, to better distinguish for penguins.

*****Note parallel to RJT Chess.