Sunday, May 31, 2009

On Abstracts


Summing it up perfectly...

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On Common Language


I find it really intersting that my cell phone's predictive text, which I've always believed will find me the word I'm most likely to want, suggests that if I type 75283, the word I'm most likely to want in my message is 'slave', when in fact I really wanted to type 'plate'. And then we still go around claiming to be a civilised society.

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On Balancing Galloping Chipmunks


I’ve never really seen the ability to balancing a galloping chipmunk in a peanut butter jar on my earlobe as a really useful skill, unless I was stuck in a monsoon in the jungles of Bangladesh, trying to save numerous genetically modified animals which could trigger massively destructive explosions when even slightly wet. In a desperate attempt to save the world, with an animal in plastic bag under each arm, and nothing else to put the chipmunk in, I’d be forced to grab the nearest peanut butter jar, eat it all in seconds and shove the chipmunk in. Anyone who has watched me walk in rain will notice that I tilt my head to the right (or probably not, since its not the sort of thing people look out for, but if they know to look out for it, they will see it). This makes balancing the peanut butter jar on my head impossible. I will be forced to balance it on my left earlobe. The thing that prevents me from learning this skill is that my sense of balance is a bit below average (for the same reasons that I tilt my head in the rain). In the meantime, I have been making every effort to stay out of Bangladesh during the monsoon season, just in case.

The most useful skill I have been able to learn is the ability to operate the bath taps with my feet. This means I have complete control over the water temperature without even having to lift a finger. Having been able to do this for most of my life, I began trying to use my feet for various other things. Not so successful attempts were made at operating the kettle and the stove, however the microwave was mildly successful (Luckily, it’s a digital one). Opening doors is easy, except for the garage door, which is on a step and used to be slightly out of my reach. Especially if there is a car parked next to it, preventing my leg from stretching to its full reach. With practice, I have been able to reach even that door easily in the last couple of years.

(On a side note: Please understand that I don’t do this all the time. It is far more efficient to use my hands to open doors, but if my hands are holding something heavy, it is far easier to use my foot to open the door than to put whatever it is down and pick it up again.)

There are only two doors that force me to use my hands. The first is the bathroom. After a bath, the floor is often wet and slippery, and standing on one leg on a wet floor with a below average sense of balance is definitely not a smart idea. Anyway, I’m hardly ever carrying anything, so using my hands is the safest, simplest and most efficient option. The second type of door is a car door. The designers of most car doors do not think of feet. Barefoot I can usually manage to get the door open, but closing it is a mission. However, when I want to get into a car, I’ll typically be wearing shoes, which really makes it impossible.

If only my toes weren’t so clumsy, I’d also be playing the piano with my feet by now.
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On Google Part V - yet again...


Google

Needs no comment...
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Sunday, May 24, 2009

On Winter Problems


It is winter, and the nights are getting colder. Actually the nights seem to be staying the same temperature, while the early hours of the morning seem to be getting freezing, which is what is causing the whole problem. After waking up too cold one morning, I decided that it was time for my winter duvet. So I dragged the massive down duvet (which weighs more than I do) from the top of the cupboard and replaced my flimsy summer duvet. The problem is that evenings are still warm, and my duvet ensures that I am kept uncomfortably hot, and unable to sleep.

Lying awake last night, my mind went wandering. Eventually it settled on something which I’d read, maybe six or seven years ago. Apparently, in a group of 50 people, the chance of two or more people having a birthday on the same day is around 97%. I found this slightly incredible, and my subconscious mind seemed to want verification.

(Note: Not a side note. Anyone not mathematically inclined may find themselves slightly lost in the rest of this post. You have been warned.)

So I set up a statistics problem in my head to calculate the probability of two or more people sharing a birthday in a sample size on n. Starting with the obvious, I set it clear in my mind that for n = 1, the probability is 0. For a sample size of 2, the probability would be 1 in 365.25 (to take leap years into account). For three people, the probability that the third person shares a birthday with either of the first two is added in. Eventually I came up with the nice simple equation of n*(n-1)/730.5. Unfortunately, this equation did not satisfy the obvious conditions from the other end. You’d expect the probability in a group of 366 people to be 100%. In fact, my formula gives 18000%. A slight overestimate. A little annoyed, I finally fell asleep.

The problem returned to me this morning. Some vague recollection of the statistics course I did last year made me realise that the focus should not be on the probability of two people sharing a birthday, but rather on the probability of two people not sharing a birthday. This would make the probabilities multiplicative rather than additive, which would solve the whole problem.

This meant that the probability of not sharing a birthday with anyone already in the group when the nth person is added is (1-(n-1)/365.25) multiplied by the probability for the rest of the group. That gave a nice iterative solution, but I don’t like iterative solutions (Actually I do. I love iterative solutions, but I also love it when something horribly complicated comes down to one simple formula). Wherever possible, I want a nice short equation that requires no understanding of advanced maths to solve. So I wrote down the iterative solution, and multiplied it out and got a simple expression involving factorials – the largest being 365!. So I pulled out my little scientific calculator, forgetting that it squeals when shown anything more than 70!. Since I happened to be sitting in front of a computer, I turned to that, and started Microsoft Excel.

(On a side note: If I’d been at home, I would have opened Python. If I’d been at university, I’d have opened Matlab. But I was at work, and Excel was the most powerful numerical computational tool I had available. Excel is limited, but has more power than most people give it credit for.)

Excel, however, was only mildly more powerful than my calculator, and pronounced its unintelligible death cry of “#NUM!” at 171!. With no tool more powerful, I had to think more broadly. I thought, “If I was some super genius, what would I do?”, and came up with an answer. I’d reprogram Excel. Unfortunately, I’m not a super genius and wouldn’t know where to begin. I’m only a moderately smarter than an average genius, and had to settle for creating a whole new technique for handling very, very large numbers. Luckily, I was saved the trouble by whoever it was that invented scientific notation. Using this principle, I set up a simple algorithm for finding the factorial of really large numbers.

I realise I only needed the algorithm to work up to 365!, but I do have a tendency to overdo this sort of thing. Limited only by the 65536 rows available in Excel I set out to prove that I could not be defeated. Upon reaching the end, and finding that 65535! is in fact 7.878034e287 188 (A number almost 300 000 digits long), I realised that there were 256 columns available, and I’d only used 7. Laughing, I started the algorithm with 65536 in column H, and double clicked the little black box to copy the cell contents to the bottom of the spreadsheet. The computer laughed back as its RAM was used up. It is incredible annoying how the computer just displays a white screen and refuses to do anything. The nice thing is that when it does finally give you a message, it allows you to drag the message over the screen, and doesn’t refresh anything behind it, which lets you get rather fascinating patterns, depending on how quickly you can drag the message box..

Eventually, I worked out a way past the RAM limitations of the computer and was driven by an overwhelming desire to find out when my algorithm would cease to work.. So I copied the algorithm all the way to column IR and created a spreadsheet that took several minutes to process a save request (and produced a 499 MB file). I finally found that 2 359 260! is 1.073258e14 010 425 (that’s a 14 million digit number). I hate it when I overdo things like this, but I’m always driven by curiosity.

So driven in fact, that I typed exactly 1000 words on it, and forgot completely about the probability of people sharing birthdays.

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On Functional Structure of a Pen


One of the biggest downfalls of the modern design of the pen is that more than two thirds of the pen sticks out of your hand when you use it. I have never really understood why this is necessary, and the designers of modern pens should be ashamed of themselves. When an engineer designs an aircraft, every effort is made to remove unnecessary weight. Any structure that does not carry out a function that is absolutely critical to the safe operation of the aircraft is left out.

I decided to apply my engineering knowledge to make modifications to a pen, in order to eliminate some of the useless components. I identified the function that a pen is required to fulfil, and noted that 55% of the structure and 25% of the mechanical components played no part in fulfilling this function.

With the aid of a concrete floor, a shoe and some sticky tape, I managed to make the necessary modifications to make a 45% weight saving on the pen, while increasing its effectiveness by 15%, and reliability by 50%.

The only problem with it is that the tape slips because the spring needs to be compressed 15% further to make it louder...

It clicks louder, and fits perfectly in my pocket, and that other bit that sticks out of my hand is no longer a problem, and it has a 0% chance of leaking. (I could never work out why they needed to put a tube filled with ink in pens anyway)
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Wednesday, May 20, 2009

On Google: Part IV - Not on Google Searches


Typing ‘Google’ into Google won’t break the internet, but embedding a script into Google that types ‘Google’ into Google and click’s Google’s “I’m Feeling Lucky” button whenever anyone tries to load Google will certainly be good for a few laughs.

Also, it would be quite funny if this post about Google could become the most relevant Google result for a “Google” search on Google, which would make me Google’s leading authority on Google after Google themselves, at least according to Google. I wonder how many times Google needs to be mentioned in a post for one of those Googlebot-Image-0 things from Google to list this blog on Google, so that any search for ‘Google’ will put me high up on Google’s list. I need just one more Google to make 23 in this post alone (Unless I include the title).

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On Cheese in Simple English


I didn't realise how many big words Wikipedia used until I discovered that there is a language called 'Simple English' on Wikipedia.

Normal English Wikipedia says that "Cheese is a food consisting of proteins and fat from milk, usually the milk of cows, buffalo, goats, or sheep. It is produced by coagulation of the milk protein casein. Typically, the milk is acidified and addition of the rennet causes coagulation. The solids are then separated and pressed into final form.[1] Some cheeses also contain molds, either on the outer rind or throughout.

Hundreds of types of cheese are produced. Their different styles, textures and flavors depend on the origin of the milk (including the animal's diet), whether it has been pasteurized, butterfat content, the species of bacteria and mold, and the processing including the length of aging. Herbs, spices, or wood smoke may be used as flavoring agents. The yellow to red color of many cheeses is a result of adding annatto. Cheeses are eaten both on their own and cooked in various dishes; most cheeses melt when heated.

For a few cheeses, the milk is curdled by adding acids such as vinegar or lemon juice. Most cheeses are acidified to a lesser degree by bacteria, which turn milk sugars into lactic acid, then the addition of rennet completes the curdling. Vegetarian alternatives to rennet are available; most are produced by fermentation of the fungus Mucor miehei, but others have been extracted from various species of the Cynara thistle family.

Cheese has served as a hedge against famine[citation needed] and is a good travel food. It is valuable for its portability, long life, and high content of fat, protein, calcium, and phosphorus. Cheese is more compact and has a longer shelf life than the milk from which it is made. Cheesemakers near a dairy region may benefit from fresher, lower-priced milk, and lower shipping costs. The long storage life of cheese allows selling it when markets are more favorable.
"
- from Cheese - Wikipedia (English)

If that was a bit to complicated, the entire thing may be translated into simple english: "Cheese is a solid food made from milk. It can be soft or firm. It is made by removing water from milk. People may store cheese in a refrigerator, to make sure it does not go bad. Its color varies, most commonly pictured as yellow.

Cheese is rich in proteins and fats. It also contains vitamin A , calcium and phosphorus.
"
- from Cheese - Wikipedia (Simple English)
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On Google: Part III


More idiots have found Google. I will do my best to answer them.

"is there such thing as half pig half sheep" - No

"can ants eat brick" - No. They dig through brick. They eat leaves and sugar and dead things.

"pig with sheep hair" - Are you serious?

"sheep poison potatos" - Unlikely, since potatoes generally don't eat sheep, and I am not aware of anything in sheep that would be toxic to potatoes.
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Monday, May 18, 2009

On the Speed of Sound and Marking Times...


... or more precisely, the speed of sound squared, which, as we recall form our compressible gas dynamics, in chapter… uh… 2, is nothing but what? You see, it is nothing but the rate of change of pressure with respect to a change in density. You see what is coming out here? It is your favourite derivative:



Marking is nothing but what? It is mechatronic system. And the project assignment is the plant, the derivative is the actuator, and a flu would be nothing but what? It is such disturbance signal. (*Said while leaning forward, and pretending to stroke a short, but slightly tall dog.*)
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On Existentialism...


... which has become one of the main philosophical ideas since the 19th century, and it’s actually scary how seriously existentialist writers get taken. If I came across some guy rambling on about how useless he was, and how he just didn’t know the meaning of life, I’d advise him to get on with it and be useless somewhere else.

The truth is that if a human can be useless, then how on earth do tortoises get along? And when last did you read an existentialist text written by a tortoise. To the best of my knowledge, there are none, and tortoises achieve pretty much nothing in life. What are they supposed to do, apart from deep philosophical thinking? And they don’t even bother writing any philosophical essays. I think this gets across the point that writing deep philosophical works is really pointless.

And what does that mean about me? I don’t even think that deeply. Does that make me even more useless than a tortoise? What’s the point in these rhetorical questions? I’m really grateful that I’m so awesome, otherwise I’d have some serious doubts about myself.

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Sunday, May 17, 2009

On Security Check Points


Especially the guys who stand at the entrances to certain shopping centres and have little hand held metal detectors. I can’t help wondering how effective they actually are. I generally wear shoes with steel capped toes, and a belt with a metal buckle. My wallet has a number of key rings in it, as well as a magnetic bus tag. My other pocket contains a bunch of keys and a cell phone. All of these are items which would be picked up, even just slightly by the metal detector. They all set off alarms at the airport (especially my shoes).

Why then do they not make a sound half the time? The obvious reason is that they are not always switched on. It’s quite hilarious to watch a security guard with a serious expression on his face scan you with his little metal detector, which is not even turned on.

I have to pass through one of these checkpoints at work every week. I make sure I carry as many bags as possible, and ask him, “Are you sure you don’t want to check the side compartments too?” It annoys the people behind me, but I’m thinking of sneaking a piece of steel pipe past them one day to see how easy it is.
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On Automatic Doors...


... Which have motion sensors and open automatically when you approach. These doors are the biggest pain in the neck for unfortunate OCD sufferers like me. As much as I try, I can’t help but follow the patterns of the bricks or colours on the floor. This is especially annoying if a dark stripe follows the edge of the passageway. I am compelled to follow it, and it brings me to approach the door from an angle that only brings me into range of the sensor as I am immediately at the door. I then have to wait as the door opens.

There is also enough evidence to conclude that they have sound detectors. Very sensitive sound detectors and all the voice recognition and interpretation software that can go with. On one occasion, I swore quietly at a particularly slow door, and ever since it has opened even slower for me. I have watched it open for other people, and I’m sure that both its response time and speed are quicker than for me.

Now, whenever I encounter a new door, I smile and greet it politely. Doors have feelings too, and it will do you good not to break them.
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Sunday, May 10, 2009

On Rabid Laminated Plastic Chairs...


... with hairy armpits, and an unusual obsession for throwing polystyrene from the boxes of old electronic appliances at passing cats, and then cleaning up the mess afterwards. It is a terrible problem. You wouldn’t have noticed it, unless you were a cat. Even the cats are only mildly annoyed with it, since those polystyrene packaging things don’t hurt at all when you are hit by them.

Did you wonder why anyone would want to laminate a plastic chair? Or where you can buy them? Probably not. You were too busy thinking of the whole thing, and didn’t let each concept sink in.

(On a side note: I bet the word random came into your mind, and if it did, then you would have been wrong. There is no such thing as ‘random’. We have to use pseudo-random, which means carefully chosen, calculated based on a set of extremely complex and highly linked set of rules that make the output so difficult to accurately determine, that it becomes unpredictable by any practical means. Whenever I roll a dice, I try to construct Newton’s laws, and set up a system of differential equations. The problem is that I can never seem to differentiate the trajectory of the roller’s hand precisely enough to get an accurate measure of the imparted velocity, and I have no idea of the Young’s Modulus and Poisson’s ratio of the damned dice, so I can never get a good idea of the deformation as it hits the surface – which would allow me to work out the exact trajectory as it bounces. My eye is also a poor judge of surface quality, so I have no idea of the microscopic imperfections that would affect the rebound of the dice, and the weight imbalance from the markings throws me off a bit. The gravity variation as the dice changes height is easy to work out, but by the time it takes me to model the aerodynamic forces on a three dimensional rolling cube, the dice has already been lying still for several hours. It’s difficult to predict, yes, but I could still work it out. Nothing is random. Some quantum physicists may argue, but they poison cats for a living... Why would you trust them? This blog post is not random at all. I really prefer the term “arbitrarily chosen”, which mathematicians like to use instead of “carefully chosen after 6 weeks of sleepless nights and several thousand pages of failed calculations, in order to reveal a single slightly interesting, but mostly pointless phenomena”.)

What I’m trying to get across here is that there is a plot by penguins to agitate domestic cats into attacking furniture (since the laminated plastic chairs are claw proof, they’ll have to take out their frustrations on expensive leather sofas and polished wooden tables, and the TV stand.) This will cause an outrage with trees and cows, whose dreams are being shattered. (Their best aspiration has just been turned to a scratch post. The next best thing for a cow is to become a MacDonald’s burger...) This will cause a trees and cows to revolt, destroying the world, and the penguins will walk in and take over, completely blameless.

The penguins are there... spying on you. If you don’t believe me, refer to the plot in Figure 1 below.


Figure 1: Variation of visible penguin populations with time.

It is apparent that penguins are disappearing, and yet the number of visible penguins in your house remains constant at zero. Where do the remaining penguins go? Invisible penguins in your house... And we don’t know what the initial population of penguins was, so the number of invisible penguins could be anything from a few thousand to several billion...

And, I’m not even getting into the rabies side of things... Not to mention the hairy armpits.

Sometimes, my mind breaks down the little concepts so much, I start scaring myself. I wish I could just see the world as a whole without having to worry about the consequences of the built-in subtleties of every little thing...
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On Names: Part II




... Sorry. I couldn't resist...

www.xkcd.com
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On Diagonally Walking Dogs.


As a dog owner, you notice that sort of thing, and it makes you think. Whenever you take a dog for a walk, it will always pull ahead, as if it knows where you are going. The thing is, you need to vary the routes, to keep things interesting, and the dog knows this. It will always map its own route in its mind, and then try to lead you along it. The result is that the dog and leash form a vector, aligned with the dogs path, but following yours. This leads to the dog walking along diagonally next to the owner.

(On a side note: This only happens if you are lucky enough to own a small to medium sized dog. Things work a bit differently owners of big dogs. In general, the owner gets dragged face down on the ground along the dog’s route, and is given ten seconds to stand up every time the dog finds an interesting tree.)

To me, this is undeniable proof that dogs are mathematically superior than humans. The dog knows where it wants to be – somewhere on the other side of the road – and it has plotted all possible routes to get there. In it’s mind, it has calculated the efficiency of all routes, and worked out that walking diagonally is, of course, 41.4% more efficient than just crossing the road.

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Sunday, May 3, 2009

On the Flying Monkey Dog...


... which launches rockets from it's armpits, and secretes vanilla ice cream from it's elbows. Consider it in your mind. It doesn't make any sense, but it's still so cool... Why? I couldn't work it out either, but sometimes we need to just sit back and accept things for what they are...

... Do you know where they sell them?...
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On Names


It really bothers me that parents can give their child a name without considering the fact that the child will have to live with that name for the rest of its life. Before naming a child, you have to think through all of the embarrassing nicknames that can be easily derived from it.

In South Africa, there is an incredible problem with this. There are thousands running around with names like Surprise, Innocence, Mistake and Success. I once even met someone named Intelligence. Her parents were ever the optimists.

The Dominican republic has a far greater problem. So bad, in fact, that the government has banned giving children unusual names. Unfortunately they were too late to save the child of Mr. and Mrs. Pineapple, who thought it a good idea to name their child Dear. If Dear Pineapple ever reads this, you have my sincerest sympathy.
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On "Aliens Stole My Husband's Skin" and Other Stories


Actually, I lied… partially. This has nothing to do with "Aliens Stole My Husband's Skin", or anything of that nature, but it does have to do with other stories. Two stories in particular, from a certain newspaper (I’m not going to mention names, but they are one of two that prefer to print their advertisements with white writing on a black background, and not the one that reports on finance). Actually, this has little to do with the stories themselves (since I did not actually read them), but has more to do with the headlines.

The first read “Toilet Swallows Pupil”. This is rather alarming, and I sincerely hope that this is an isolated incident and that authorities have securely locked up the offending toilet. I was not aware that toilets had evolved dietary requirements. Luckily, toilets are usually firmly cemented into the ground, and must therefore wait for some unsuspecting prey to wonder into its open jaws. I’m sure that if everyone simply avoided using all toilets, then the toilets which have nutritional needs will starve, and eventually die out. I just pray that I did not miss the headline which read “Toilet Learns to Walk”.

The second headline read “My Dog is a … Sheep.” I have no idea what the actual content of the article was, but it lead me to a search. In April 2007 in Japan, a company called “Poodles as Pets” was shut down, allegedly for selling sheep as poodles. Apparently, sheep are half the price of poodles, and Japanese people, who are not familiar with sheep, were easy to deceive. Suspicions grew when people began to notice that their “dogs” were not barking or eating dog food.

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