Well, the worst is over. I have failed to do more than 2 and a half questions in the dreadful geometry test. Terrifyingly unlucky, since I forgot to study Ceva's Theorem due to a lack of comprehension... and that was what came out. 2 times out of 5.
Incidentally, (maybe not, that intro was just to link up, why am I saying all this?) luck is one truly misunderstood phenomenon. How many times have you heard people saying "What a cute kid! You're so lucky?" Well, I haven't and the meaning of luck (pure chance) is wrong there, unless you quantify it by saying "...I've been trying 462 times and they all look like they've come from Mercury." Exaggeration. Where would we be without it?
Luck is the topic of Discovery Channel's "Million 2 One", a program where they explore the unusual, one-in-a-million sort of coincidences. Well, even rarer than that, so they claim. During the show, they give tales of wonderfully absurd coincidences, mathematical (apparent) paradoxes and stuff that either look like they defy the odds or do indeed. One thing I'd like to know: Where do they get their numbers?
They say something about slicing bagels in half, and the chance of getting your finger cut if you take "sin(angle off the table) / something or other"... seems a little far-fetched to quantify their formula. What units would you take all the measurements in? Is the formula even correct? Does anyone care? (I do, but only to poke fun at their maths.)
Calling someone up by mistake, and finding it's your long-lost second identical triplet 8 times removed, standing by a public phone in Siberia. How on earth do they get the numbers for the chance of standing next to a phone in Siberia, answering it, or the number of people who have nothing better to do than answer that phone? Pure conjecture, I would guess.
Finding your lost wallet 2 weeks after you lost it at the bottom of a scuba-diving practice area of the sea. Oh wow, like they can even calculate the odds on that; kudos to them saying the odds are "incalculable." They realise it.
Quantifying such strange things is really none of our business, neither is it accurate. The formulae, chances, units are all entwined in a mesh of speculation. Only when the unexpected happens to us do we care about what's happened, not why. Given the number of people in the world, it's likely that the unlikely will happen (cool) and we shouldn't really attempt to count the odds on those. Odds are that you'll fail, and I'd take that wager.
Monday, September 22, 2008
Saturday, September 20, 2008
...And On Intuition.
Right, this is a third post "On" topics. Intuition be the theme for today (tomorrow? yesterday's day after tomorrow?)
We all possess this amazing skill called intuition. Perhaps it evolved out of our primal instincts; a self-defense mechanism in fight or flight scenarios; a tendency to predict the future. Pick your reason from these and more, many have been forwarded as to how this peculiar sense works. I'm not so concerned about the mechanics of it, but more of the applications we put it to use in.
Gambling, I'm sure, is a "sport" that encourages, indeed revolves around the house taking advantage of players' misguided intuition. Intuition can spectacularly fail where numbers are concerned, giving one false odds and impressions. Take for example the chance of rolling 2 dice and getting a 12. People will reason "2-12 are possible; ten numbers, so there's a 1 in 10 chance of rolling a 12." Of course, this is a rather unsophisticated example; more elegant and subtle methods are employed by casinos. If for nothing else, I respect casinos for their eloquent execution of probabilistic mathematics.
Speaking of maths, here is a double-edged zone where intuition can help, or fall apart completely. In regular maths tests, it is fairly easy to guess all the MCQ answers from 4 options. Intuition can be applied liberally here to choose the most correct-seeming, non crap answer like "2+2 = 4" rather than "2 + 2 = 5^42/89.17". Don't laugh, this sort of thing happens. Maths competitions, on the other hand, screw up my brain totally. Due to circumstances requiring me to appear pro in math, I go for competitions to check my standard. And here is where intuition falls flat on my face, since all the questions appear to give insufficient information to solve (geometry anyone?) or seem obvious but have no short proof like the unacceptable common sense. Intuition is rendered helpless by the high-level questions.
Note, though, that intuition usually doesn't desert me like this; in regular schoolwork I can probably keep up through a combination of guesswork, short-term memory and a healthy dose of instinct. The correct answers just speak to me. In long open-ended questions, the correct method yells itself hoarse. In essay questions, points flow into my head while writing. Not good for Literature, but OK for everything else. The best thing is it's inexplicable, so I AM telling the truth when I say I don't know how I can even pass tests, let alone score well in them.
Luck is another thing related to this. I once won a scissors-paper-stone match, 5 out of 6 with one draw. Moving pieces like I had no idea what I was doing (I didn't) in a chess tournament and drew... twice like this. Guessing the correct answer to an open-ended maths question by flipping a coin. A wallet, actually, but same difference. Luck combined with intuition works wonders; My old eraser could be used to tell fortunes (and guess correct answers in tests.)
The bottom line? Intuition is weird, wacky and wonderously wicked at whacking randomly at wanted answers when wished for. I hope this holds true in the competition-level geometry test next. Waaaargh.
We all possess this amazing skill called intuition. Perhaps it evolved out of our primal instincts; a self-defense mechanism in fight or flight scenarios; a tendency to predict the future. Pick your reason from these and more, many have been forwarded as to how this peculiar sense works. I'm not so concerned about the mechanics of it, but more of the applications we put it to use in.
Gambling, I'm sure, is a "sport" that encourages, indeed revolves around the house taking advantage of players' misguided intuition. Intuition can spectacularly fail where numbers are concerned, giving one false odds and impressions. Take for example the chance of rolling 2 dice and getting a 12. People will reason "2-12 are possible; ten numbers, so there's a 1 in 10 chance of rolling a 12." Of course, this is a rather unsophisticated example; more elegant and subtle methods are employed by casinos. If for nothing else, I respect casinos for their eloquent execution of probabilistic mathematics.
Speaking of maths, here is a double-edged zone where intuition can help, or fall apart completely. In regular maths tests, it is fairly easy to guess all the MCQ answers from 4 options. Intuition can be applied liberally here to choose the most correct-seeming, non crap answer like "2+2 = 4" rather than "2 + 2 = 5^42/89.17". Don't laugh, this sort of thing happens. Maths competitions, on the other hand, screw up my brain totally. Due to circumstances requiring me to appear pro in math, I go for competitions to check my standard. And here is where intuition falls flat on my face, since all the questions appear to give insufficient information to solve (geometry anyone?) or seem obvious but have no short proof like the unacceptable common sense. Intuition is rendered helpless by the high-level questions.
Note, though, that intuition usually doesn't desert me like this; in regular schoolwork I can probably keep up through a combination of guesswork, short-term memory and a healthy dose of instinct. The correct answers just speak to me. In long open-ended questions, the correct method yells itself hoarse. In essay questions, points flow into my head while writing. Not good for Literature, but OK for everything else. The best thing is it's inexplicable, so I AM telling the truth when I say I don't know how I can even pass tests, let alone score well in them.
Luck is another thing related to this. I once won a scissors-paper-stone match, 5 out of 6 with one draw. Moving pieces like I had no idea what I was doing (I didn't) in a chess tournament and drew... twice like this. Guessing the correct answer to an open-ended maths question by flipping a coin. A wallet, actually, but same difference. Luck combined with intuition works wonders; My old eraser could be used to tell fortunes (and guess correct answers in tests.)
The bottom line? Intuition is weird, wacky and wonderously wicked at whacking randomly at wanted answers when wished for. I hope this holds true in the competition-level geometry test next. Waaaargh.
Thursday, September 18, 2008
On technology.
This is not a rant. Glad that's settled; now I shall turn it into one.
Technology, where would we be without it? What defines technology? Is a lightbulb? The Large Hadron Collider? Quark interactions? A fruit fly that can fly through open windows? Well, at our current stage of development, it would seem as though technology generally means something metallic, goes beep randomly, and have so many functions you need a diploma to get through the instruction manual.
What fits the bill? Handphones (go beep when someone attempts to bug you,) computers (go beep in order to bug you,) printer/scanners that print/scan "beep" onto what you want, along with an unfortunate dead bug, and Blackberries/iPhones (I'd rather eat the berries and apples than listen to their bugging beeps.)
As you can probably guess from the tone, mood, diction, assonance and Cow knows what else from the above paragraph, I dislike such technology. It should have stopped at the telephone, the personal computer, the car, and the postman delivering mail. Perhaps bypassing all the intervening rubbish to reach the LHC.
Seriously, who wants to be irritated by technology? You hear handphones go beep and buzz about like a hornet in your pocket, the radiation/noise emission disrupts sensible thought processes and indeed, their manuals look like Coptic to me. Think about this: how intuitive and efficient is an input interface with all of about 20 buttons? The iPod: going the extra mile by removing the buttons altogether. Exercise of the modern generation is designed to train thumb wrestling professionals.
Not to mention, all the cables, accessories and "little dongly things", as Douglas Adams calls little widgets and doohickeys. Those same things that claim to interface computer to handphone, 2 pin plug to 3, step down power rating from 2.5 Volts DC to 1.5 Volts AC. They help you charge your phone from anywhere, provided you have a "little dongly thing" for every place in anywhere you might go to. How anyone can multiply these variables of applications, accessories, cables, power supply and add-ons into design, functionality, beauty, intelligence and space-travel, and STILL select a handphone wisely floors me.
Ditto for handheld stuffses; even hands-off things like little metal earplugs that allow you to answer phone calls by talking to yourself. These things look like they could slither into your ear and hijack your brain (attention corporate gurus, we do NOT need handphone-powered zombies, thank you.) Earplugs also ensure that you focus on your music/phone calls without hearing distractions, or indeed anything at all. The volume at minimum is so loud it blows earwax clear into my brain.
Computers. These things are deadly. I'm typing on one of these television screens with typewriters in front of it, and if something goes wrong, you could practically blame it on NASA. Blue screens could pop up at any second; my thumbdrive appears to have a Trojan; my USB mouse is screwing the scanner; the wiring behind the monitor looks like a plastic Afro. If the Internet connection dies, I have to wrestle this Afro into giving me the cable for the router. Ditto for the mouse, keyboard, speakers and everything else.
Technology is easy to recognise. If it comes with an instruction booklet, it could be technology. If it looks shiny and is as flat as a peanut or whatever it is now, getting more likely. If the instructions are thicker than the thing itself, you're fairly sure it's technology; if the object in question ever appears to malevolently malfunction, nail on the bloody head, that's technology.
Technology, where would we be without it? What defines technology? Is a lightbulb? The Large Hadron Collider? Quark interactions? A fruit fly that can fly through open windows? Well, at our current stage of development, it would seem as though technology generally means something metallic, goes beep randomly, and have so many functions you need a diploma to get through the instruction manual.
What fits the bill? Handphones (go beep when someone attempts to bug you,) computers (go beep in order to bug you,) printer/scanners that print/scan "beep" onto what you want, along with an unfortunate dead bug, and Blackberries/iPhones (I'd rather eat the berries and apples than listen to their bugging beeps.)
As you can probably guess from the tone, mood, diction, assonance and Cow knows what else from the above paragraph, I dislike such technology. It should have stopped at the telephone, the personal computer, the car, and the postman delivering mail. Perhaps bypassing all the intervening rubbish to reach the LHC.
Seriously, who wants to be irritated by technology? You hear handphones go beep and buzz about like a hornet in your pocket, the radiation/noise emission disrupts sensible thought processes and indeed, their manuals look like Coptic to me. Think about this: how intuitive and efficient is an input interface with all of about 20 buttons? The iPod: going the extra mile by removing the buttons altogether. Exercise of the modern generation is designed to train thumb wrestling professionals.
Not to mention, all the cables, accessories and "little dongly things", as Douglas Adams calls little widgets and doohickeys. Those same things that claim to interface computer to handphone, 2 pin plug to 3, step down power rating from 2.5 Volts DC to 1.5 Volts AC. They help you charge your phone from anywhere, provided you have a "little dongly thing" for every place in anywhere you might go to. How anyone can multiply these variables of applications, accessories, cables, power supply and add-ons into design, functionality, beauty, intelligence and space-travel, and STILL select a handphone wisely floors me.
Ditto for handheld stuffses; even hands-off things like little metal earplugs that allow you to answer phone calls by talking to yourself. These things look like they could slither into your ear and hijack your brain (attention corporate gurus, we do NOT need handphone-powered zombies, thank you.) Earplugs also ensure that you focus on your music/phone calls without hearing distractions, or indeed anything at all. The volume at minimum is so loud it blows earwax clear into my brain.
Computers. These things are deadly. I'm typing on one of these television screens with typewriters in front of it, and if something goes wrong, you could practically blame it on NASA. Blue screens could pop up at any second; my thumbdrive appears to have a Trojan; my USB mouse is screwing the scanner; the wiring behind the monitor looks like a plastic Afro. If the Internet connection dies, I have to wrestle this Afro into giving me the cable for the router. Ditto for the mouse, keyboard, speakers and everything else.
Technology is easy to recognise. If it comes with an instruction booklet, it could be technology. If it looks shiny and is as flat as a peanut or whatever it is now, getting more likely. If the instructions are thicker than the thing itself, you're fairly sure it's technology; if the object in question ever appears to malevolently malfunction, nail on the bloody head, that's technology.
Wednesday, September 17, 2008
On Reason.
This is not a random post. OK, so it is a post, and random too, but... never mind.
Today, there was a little lesson about logic (officially Non-Euclidean Geometry, but it seemed like a logic lesson) which touched upon the meanings of the words "axiom", "system", "unidentified term" and "limo". (Fine, not the last one.) It struck me that all such human logic is really, really flawed. The basic reasoning goes like this.
1. I want to prove something.
2. To prove something, I have to start from something.
3. Therefore, I shall start from this. Believe it, or else the intelligence I spew will make no sense to you.
This is a system. Of thought and logic, or the lack thereof. The first 2 statements are axioms, which you cannot question since they are not meant to be questioned. (I have an issue with this, like I have with handphones.) Next, there follows the Unidentified Term, like "prove" or "start from". "What the heck do these words mean?," you are entitled to question. "Go check a dictionary" is the only seemingly sensible response; you may well ask why chickens cross roads, such an answer I have to give.
But wait! A dictionary itself defines words in terms of... more words. You look up "Advice", it gives you "Guidance". Check "Guidance", and it says "see Advice." The thing is essentially a self-defined system, that you cannot accept if you (choose to) know nothing about it. (Incidentally, how do babies learn from nothing? Genetic programming that allows them to? Accepting things at face value?)
Besides, what makes an axiom? Why and how do we (who, actually) defines it? Look at this.
1. A Cow exists.
2. Cows eat pasta.
3. No pasta is left.
1. There is no pasta left.
2. Only cows eat pasta.
3. Cows exist.
Which, I ask of you, are the axioms in these 2 "arguments"? When Euclid proposed his theory of geometry, he defined complex stuff like "Only one straight line passes through any two points" and asked us not to question it, nor ask for explanation. An interesting parallel to school, really. Who sets the standards for defining axioms and undefined terms? All human reasoning is pointless by that token of arbitrarity of reasoning. To end of, a quote with much meaning to me (not to you, since it's my own axiom:)
"Asfafkbad gighwro nefhnvn j kawnda." Enjoy.
Today, there was a little lesson about logic (officially Non-Euclidean Geometry, but it seemed like a logic lesson) which touched upon the meanings of the words "axiom", "system", "unidentified term" and "limo". (Fine, not the last one.) It struck me that all such human logic is really, really flawed. The basic reasoning goes like this.
1. I want to prove something.
2. To prove something, I have to start from something.
3. Therefore, I shall start from this. Believe it, or else the intelligence I spew will make no sense to you.
This is a system. Of thought and logic, or the lack thereof. The first 2 statements are axioms, which you cannot question since they are not meant to be questioned. (I have an issue with this, like I have with handphones.) Next, there follows the Unidentified Term, like "prove" or "start from". "What the heck do these words mean?," you are entitled to question. "Go check a dictionary" is the only seemingly sensible response; you may well ask why chickens cross roads, such an answer I have to give.
But wait! A dictionary itself defines words in terms of... more words. You look up "Advice", it gives you "Guidance". Check "Guidance", and it says "see Advice." The thing is essentially a self-defined system, that you cannot accept if you (choose to) know nothing about it. (Incidentally, how do babies learn from nothing? Genetic programming that allows them to? Accepting things at face value?)
Besides, what makes an axiom? Why and how do we (who, actually) defines it? Look at this.
1. A Cow exists.
2. Cows eat pasta.
3. No pasta is left.
1. There is no pasta left.
2. Only cows eat pasta.
3. Cows exist.
Which, I ask of you, are the axioms in these 2 "arguments"? When Euclid proposed his theory of geometry, he defined complex stuff like "Only one straight line passes through any two points" and asked us not to question it, nor ask for explanation. An interesting parallel to school, really. Who sets the standards for defining axioms and undefined terms? All human reasoning is pointless by that token of arbitrarity of reasoning. To end of, a quote with much meaning to me (not to you, since it's my own axiom:)
"Asfafkbad gighwro nefhnvn j kawnda." Enjoy.
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