The Secret of Mathematics

Do you want to know the secret of mathematics? It’s practice.

All these great mathematicians, all these college students sucking up the math scores, truly their achievement is not based on inherent talent, skill or genius. It’s based on practice.

It’s based on several long nights; all spent solving practice problems, some with practical applications and some without.

It’s based on several long days; all spent doing the math in their head for simple everyday tasks.

It’s based on days and nights of doing, repeating, the same thing, over and over again, practicing.

The secret of mathematics is practice.

Practice is what makes you perfect, especially at mathematics.

Practice is what tells you, yes, you got the correct change from the merchant. It tells you yes, you gave the correct change to the customer.

It tells you yes, the total price of 3 dollars and 54 cents for 3 pounds of vegetables is correct for the stated price of 1.18 dollars per pound.

It tells you yes, buying this size of the bottle is more cost effective than buying the other bottle.

It tells you yes, with the sale price of so much and the discount of that much, it does make sense to get this brand rather than that one.

It also tells you no, the cashier isn’t doing you any favor or harm by giving you the coupon discount of 25% first and then the store discount of 10% next. (It works out the same regardless of which discount you apply first.)

The secret of mathematics is practice.

Practice is what tells you that you’re going too fast to make that corner. You practice driving everyday, even if you don’t do the math on it.

Practice is what tells you that you put too much salt on the meat. You cook everyday, you don’t need to crunch the numbers on it.

Practice is what tells you there are too many magnets to fit on the fridge. You look at the fridge everyday, you don’t need to pull out the tape measure for it.

Practice tells you all these things about your daily life, abstract as they are. And abstract as mathematics is, you get good at it by doing it daily.

The secret of mathematics is practice.

Practiced is the painter scanning the house telling you how many cans of paint they will need for the exteriors, for the interiors, and for the fence.

Practiced is the house spouse figuring out if the groceries in the cart will fit their monthly budget.

Practiced is the business owner looking at the crowd in the bar and knowing, instantly, that they made a profit this month.

And practiced will you be when you realize math is something you do everyday, you just don’t realize it immediately.

The secret of all mathematical genius is practice.

Random Conversation: I... Can't Argue With That

"The blue of the sky is colour."
"Come again?"
"The blue of the sky is colour."
"I... can't argue with that."
"What is the spelling of colour?"
"C-O-L-O-R."
"In American, yes. But in British?"
"Oh... I see what you mean. By the way, you do know they're no longer really Britain... they are called the UK."
"Yeah, but you can't make UK into an adjective. United Kingdomians? Nah. Plus we knew them as the British when they invaded us, that's our memory of them."
"Well, they could be called the English."
"No, that wouldn't work! Imagine the confusion. English English, versus American or Australian English? Nah, that sounds weird. British is better."
"Okay..."

"British. Britney. Brittany. Britannia. There's a company in India called Britannia. They make biscuits. Wish I could have a biscuit right now. I'm hungry."
"Biscuit?"
"Biscuit."
"What's a biscuit?"
"Oh... that's cookie, in American."
"How does one keep that sort of thing straight?!"
"Heh heh. It gets funnier. You see, international trade has brought in multinational companies, a lot of them are American. And they bring in Americanisms. So we have both Britishisms and Americanisms."
"Like what?"
"Chips. We call 'em chips too. Britain calls them crisps. And fries, we call them fries too, but Britain calls them chips. Imagine a Brit chap trying to get fries in India. He asks for chips, and he'll get chips and he'll walk away with a chip on his shoulder. Too bad he can't eat that one! He won't be chipper for the rest of the day!"
 
"Are all Indians like this?"
Shrug. "Well, you know Rahul. He's fairly normal."
"Yes. Yes, he is!"
"I, on the other hand, am a lucky snowflake."
"What does that mean?"
"Snowflake, coz I'm unique. And when I say lucky I'm being sarcastic. Actually I could be serious. It depends. Maybe I'm both."
"How can you be both?"
"The principle of superposition. From quantum mechanics."
"Superposition."
"Mmm-hmmm!"
"Isn't that only for subatomic particles, and not really for people like you and me?"
Frown. "Well... maybe. But I'm going to ignore that and just say I'm both serious and sarcastic until you collapse the context function to observe which one I am!"
"Are you kidding?"
"Nope! I'm seriously sarcastic. Just like Schrodinger's cat! Except I'm alive. And a lucky snowflake."
"At any rate, that's a good expression. Where'd you hear that?"
"I just made it up."
"Well, you deserve credit for that one."
"I also thought of another one - I'm the only flower with nectar left for the bees."
"What???"
"Well, something like that, I'm still thinking about that one."
"Yeah... that one needs some work."

"I just thought of another expression I could use. It's quite a bit more colorful though."
Silence.
"It's probably not appropriate to say at work."
"Then you probably shouldn't say it."
"I'm the one out of millions of sperm that was successful in swimming to the egg!"
"Wait. What? You can't use that! You're a girl!"
"Well, I was made from two times X, but not two eggs! I had to have a sperm. Otherwise meiosis would toss and turn and cry in its grave. Or its bed or hammock or whatever."
"Amen for meiosis."
"I'm the one out of two thousand eggs and two million sperm that was successful!"
"I... can't argue with that."

The Sugar Detox

My mind is not crazy or rigid any more, which means I often have the inclination, often on a whim, to try a bunch of crazy experiments. The latest one in this series is the sugar detox diet. I got a flyer on Thursday last week which talked about doing the sugar detox, which basically entails going cold turkey on sugar, and I thought I would give it a try over the weekend.

The premise of the diet is to reset the way your body reacts to sugar. You go off sugar completely for three days - and completely means no carbs (which break down into sugar in the body), no dairy or fruit (which contain natural sugars) and no alcohol (which also break down into sugar). After the three days are up, and all existing sugar has left your body, kicking and screaming, and your body has forgotten the taste of sugar, you will re-introduce sugar into your system, albeit only the natural types of sugar, and over time. Starting with an apple per day (which keeps the doctor away).

But the diet itself does strange things to you. All of this serves to show you how dangerous the sugar addiction can be. Here's what happened to me.

I started craving food, to the point where I was almost hallucinating about it. Weird things started going through my mind: daydreaming about stealing my beloved's Coca Cola, remembering the taste of some of my mother's homemade sweets, and arguing with myself about which foods contain starch and sugar and which don't.

I started feeling hungry. All the time. All the time. All the effing time. I mean, for the second day, I made myself a vegetable mixture of cabbage and carrots with oil and spices, and I made a full wok's worth of it. A full cabbage and eight long carrots. I ate the entire thing throughout the day. And invariably, each time, after eating a full plate's worth of it - I was still hungry.

The hunger led to headache and weakness by the third day. My legs were physically tired, moving was painful, and the headache did nothing to help my resolve to get through this stupid diet. Of course, this was expected and the article had warned about this; but I myself was amazed at how I felt. I had zero energy, even though I was eating eggs and vegetables nearly all the time - I ate nine eggs in two days. I could deal with starvation much better as a kid - but then, kids should never have to starve or experiment with starving. My adult body did not take kindly to the carbohydrate deprivation.

Even my poop looked different - after the second day, I saw whole pieces of carrot come out, as though they had not been processed at all. What a horror I felt to see that - my body was just processing all the plain sugar I was consuming from candy, cake and Coke, and using that for my energy supply, and meanwhile all the good stuff was just passing through my body almost untouched.

I finally gave in on the third day in the afternoon. I went to a Thai restaurant, and had a small amount of rice with my curry. But another learning was in store for me - how different the food tasted. The flavor with this particular restaurant is always good, but this time the flavors were beautifully intense. My tongue had not tasted sugar in three days, so I could appreciate the food better, in a way. Interesting theory.

This diet was torture, and since I had done this as an experiment, I had learned the lesson. While not as bad as some other people I know, my body is definitely addicted to sugar, and it is not healthy. Going off it was good as an experiment, though probably not one I want to repeat in a long time. I had originally thought to do it first myself, then force my beloved to do it, but I don't think I have the heart to do that. 

Instead, we will do the bean diet. Hopefully that will be more fun than the sugar detox; I have had good feedback about it.

Alien Thoughts

Much has been written about the structure of the universe, of nature, of matter itself. And a lot focuses too on the nature of life and whether it exists outside the earth we know and love. Through all these discussions and debates, it's pretty remarkable how our theories are tinged with a self-righteous sense of arrogance. 

Early religious cosmologies held that the earth was the center of the universe, because what arrangement could be more perfect? It was religious heresy to argue otherwise. Copernicus, who suggested that a heliocentric solar system made sense with our observations as opposed to a geocentric system, published his ideas in secret. Galileo, who used a telescope to observe that moons orbit other planets (and not the earth), was forced to publicly recant his theories. Kepler was luckier and supported heliocentrism openly, though he was careful not to step on too many religious toes. Through all this, note the intense resistance to the idea that we are not at the center of the solar system and the universe. 

We dropped this idea and replaced it with the general theory of relativity. And the next hot topic is who else exists in the world with us. It's a topic that has gained a lot of treatment in movies, TV shows, comics, cartoons, novels and short stories. And incredibly, we see the same arrogance in all these media, wherever the idea is expressed. 

One prime example of this arrogance is how all these creatures are depicted as being humanoid, with human attributes. Why would we ever assume that alien creatures will be humanoid? Probably because we think that life elsewhere in the universe would develop the way it did on earth. Is this reasonable? Maybe. There is an inherent bias towards the idea, because it's the only way of developing life that we know of. But how probable is this?

How did life develop on earth? It started with the primeval soup, from which arose self-replicating organisms, which diversified and consolidated to form the several kingdoms of life we see today. Conditions had to be just right for life to rise and survive - distance from the sun, composition of the atmosphere, the presence of water, the speed of light, laws of physics, so on and so forth. With the billions of stars and star systems that exist in the known universe, it's quite feasible that one of them will have conditions exactly like our primeval soup, with all the right conditions to produce life. But why assume this is the only initial state that will lead to life? If there is a different initial state that can lead to life, that life form could be very different from what we (carbon-based and self-replicating) are.

Even if a primeval soup existed elsewhere which gave rise to self-duplicating creatures like we are, why assume that the "humans" on that planet are the ones who will ultimately survive? Through the ages, an incredibly wide variety of species have developed within each kingdom. Our species wasn't even the top dog until between 2 and 3 million years ago (compared with 4.6 billion years of earth's existence). Reptiles dominated for a long time, chiefly the large-boned, muscular variety whose brains couldn't develop much beyond "eat food, catch meat". They were mostly killed off 65 million years ago, which paved the way for mammals to diversify and become dominant. 

If aliens are humanoid, are we trying to say that whatever planet they come from also went through all these developments? That they too had dinosaurs who died out and allowed humans to flourish? For all you know, it could be the fish or the mushrooms who are the dominant species. 

The next idea is of course, such humanoids exist, and they have developed technology far more sophisticated that what we've produced. And that these alien humanoids will want to kill us and take over our planet.  

Of all the thousands of species that have lived and died out through the history of earth, only one has developed enough self-awareness to study the laws of physics. How likely is this to have happened on some other planet? Remember, they have to first survive ice ages, dinosaurs and asteroids. 

The fear of conquest by aliens arises, I think, from our observations of our own species. Human civilizations have battled each other, conquered one another, with devastating consequences for the losers of the war. Hence we imagine that an alien civilization would want to do the same with us, if they won the war against us. This is essentially us attributing human tendencies to aliens, who may or may not have developed the capacity for such things. Bacteria don't have emotions. Why would aliens?  

An alternate idea suggests aliens are among us, shape shifting to blend into the crowd, mating with our kind, essentially mingling in. How this might actually work is never discussed. There is also a huge market for horror movies showing humans as incubatory vessels for alien babies. 

Our earth produced carbon-based life-forms. Carbon works because with a valency of four, it is tempted neither to gain nor to lose electrons, but to form perfectly covalent bonds between atoms. Structure-wise, the tetrahedral shape formed by the four bonds per atom is pretty stable. Silicon has the same general properties, being just below carbon in the periodic table, which is why it works well for artificial body parts and implants, with the added advantage that it's easier to manipulate than carbon. It would make sense that alien civilizations are either carbon or silicon-based, but why would they have the exact same anatomy as us, allowing for mating or incubation? We can't even mate with other primates from earth. 

My personal opinion? Any aliens that come to earth will probably be some kind of virus. They will probably be as weird as, if not weirder than, mushrooms. And they will probably end up killing us, but not because they want to; it will just be a by-product of their existence.

Boyle's Law

I remember my high school chemistry teacher, Dr. T. S. Lakshmi.

She is the one that insisted we use logic. The most important lesson we ever learnt - use logic to determine the answer, and you will know the answer. From a high school lecture, that lesson has diffused into every aspect of my being, and defined my personality. One that I am proud of.

She is the one that made us all wake up, no matter how sleepy we felt. I remember feeling drowsy and tired through the day, but the moment the bell rang for the Chemistry period, I'd wake up instantly. Because I knew everyday that today I would be drafted to answer a question.

She put us through the Socrates method of teaching. Ask questions. Of course, there was a twist to it - we'd get asked questions as well, so that we would be forced to think. Her lessons demonstrated who were truly the smart kids in the class.

She taught us the value of examples. No answer in the exam received points if there wasn't a good example attached to it. It seemed purely pedantic at the time, but so ingrained is that attitude, it persists today, eight years later. And it has served me well. I attach working examples to as many customer questions that I answer as possible, and I receive back a lot of very grateful comments and effusive surveys.

And every time that I boil anything on my stove, I remember her. The reason being that I always boil liquids in a vessel that's covered, because that will make them boil faster.

What happens is, when you heat a liquid, it will create vapours that diffuse into the air above the liquid. By covering the vessel, you trap those vapours and leave them with nowhere to go. Thus trapped, they will build up and generate pressure, which gets exerted back on the surface of the liquid, causing it to heat faster (Boyle's law) and create more vapours. If you leave the vessel uncovered, the vapours are free to escape, so they will not exert as much pressure on the liquid. Covering the vessel thus leads to faster boiling. I remember she mentioned this specifically in our lesson that day - to go home and ask our parents if they had ever observed faster boiling when leaving the vessel uncovered.

Thusly did she teach, with meaning and relevance, and thusly do I remember most of my chemistry lessons, though I have never had to touch the textbooks in eight years.

I observe Boyle's law every day, when I cook. And every day, I remember that lesson from 9th grade, and my gratitude towards my dear teacher increases.

Random Thought: Centre of the Universe

They looked at me like I was crazy.

"Wow, you're centre of the universe, aren't you? The world just revolves right around you."

"Well, I wouldn't say the world revolves around me. But you're right, I am the centre of my universe." They stared. "It's logical." They stared more.

"Logical."

"Yup."

"Would you like to elaborate on that?"

"Sure. If the universe is infinitely large and expanding fast in all directions to boot, from my perspective, in the limit to infinity, the edges of the universe are equidistant from me. And if they are equidistant, then no matter what the shape of the universe, I am at its centre.

"So there you go, I am most certainly at the centre of my universe."

The senior ones smiled. "Well, can't argue with that."

The Story of Me and Tomatoes

This all started by thinking about the concept of disgust. We all feel disgust, usually triggered by some specific sense – sight, smell, touch, taste, sound. Sometimes it’s triggered by a thought too. The tendency is natural, but at the same time it might be worthwhile to not base all of our decisions upon the feeling of disgust. 

For example, someone might set down a plate of rotten food in front of me. I will not eat it. Why, because I am disgusted by the sight of it? No. Because I can see the food has rotted, it smells bad, and I know eating this would make me sick. The decision to not eat the food shouldn’t be based upon the feeling that it disgusts me, but the fact that things would not end well for me if I did eat it.

Here’s the thing though – I would feel the same sort of disgust if someone placed a dish in front of me that looked and smelled bad, and yet was perfectly fine to eat. Should I then refuse to eat the food, just because it disgusts me? No, certainly not. Especially if I see others are okay with eating it, or if I know this is a dish frequently consumed by people, there is no harm in at least giving it a try. I may not like it afterwards, but that is no reason to not give it at least a chance.

The most personal example for me, I think, is about me and tomatoes. I don't like tomatoes. I never did. I don't know why. As a child, I simply refused to go near them: I wouldn't touch them in the store, and when they showed up in my food I would pick them out and throw them out at the end of my meal. My mom got mad at me and yelled at me at every meal, and finally gave up, resigned to the fact that I would never touch the darned things.

This continued for quite a while, way into my teens. The first signs of change came about when I went to college. Even there, eating in the mess, I continued with my habit of picking out tomatoes. The other girls found it rather quirky, though it didn't bother anyone.

But then one day I found myself thinking, why do I hate this vegetable (fruit) so much? It's not like it's doing me any harm, people eat it for a reason. Also, there is a distinct flavour that it does add to the food, which is quite noticeable, even if I don't like the standalone taste of it. I could not bring up a single logical reason why I would avoid this vegetable. The only reason was, for whatever reason, I did not like the vegetable.

I realized too, that it wasn't the vegetable itself that bothered me. It was just seeing it in my food. My mom ran this experiment a few times, where she would puree the tomatoes rather than dice them. I ate the food without complaints, and did not even think about the tomatoes. The only difference was I was unable to see them. So the problem was with me, and not at all with the vegetable.

As I realized this, I started to eat the tomatoes rather than pick them out. I took on the tactic of simply ignoring the fact that they were there at all, and got very good at it.

I still don't like tomatoes. And I won't eat a fresh tomato if you just hand it to me. But I can accept that my prejudice really has no grounds, and I shouldn't let it get in the way of what's beneficial to me.

Ailanthus Altissima

My beloved's neighbour has a large tree in his backyard - of course he has several, but there is a particular one that I did not pay much attention to until recently. the same variety grows in another neighbour's yard too - a specimen about six feet tall. I did not notice this tree until a few months ago, when my beloved and I discovered a specimen growing out of one of the basement window-wells, through a crack barely an inch wide.

He didn't want the plant there, for fear it would cause a rupture, so he tore it out and threw it away and thought no more of it. A month later we found the plant had shot up bright back, as though it had never left, about a foot and half tall. He cut it out and threw it out again. The root system remained however, and sure enough, a month later, it was back.

This time, at my behest, he pulled it out as gently as he could and replanted it in another corner of the garden. We also relocated another sapling that I found growing in a rather clumsy place under the deck.

Three months later, both saplings are sturdy and thriving. It has rained several times in the past three months, which I'm sure has done nothing but encourage the young trees. What's more, we found several more saplings sprouting up all over the front and back yards last week, including one very sturdy specimen already three feet tall.

It almost seemed as though this tree was propagating via the root system. It is a common asexual method of reproduction in various plant species. A lot of weeds usually propagate this way, hence leading to my beloved dubbing the plant, "the weed tree". I chose to bestow that more colourful title of "the slutty tree". My beloved suggested going online to find the real name. In the spirit of research, I did.

Ailanthus altissima, it is called. The history and survival of this species is rather interesting. So that I may not unnecessarily repeat what has already been written about this one, you may read all about it here on Wikipedia: http://en.wikipedia.org/wiki/Ailanthus_altissima All I'll say is, there's something pretty remarkable about a tree that could survive the Hiroshima atomic bombing, especially at such close range as 300 metres. It's often said cockroaches will the be the only survivors in the event of a nuclear World War III - but Ailanthus will likely survive too, and revegetate the planet.

There's some comfort in the thought, I think, that organic life will not completely be destroyed. But there's coldness too, given that I and my species won't be amongst the survivors.

For now, I'll just watch my slutty trees grow. In about three years, if they survive the winter snow, we'll have some decent shade in the backyard.

Chicken Basil by Diane Crispell

Dish: Chicken Basil
Cuisine: Thai
Total Preparation Time: 1 hour
Serves: Two

Ingredients: 

For the entree: 

• 2 chicken breasts
• 5-7 red chilies
• 1 bulb garlic
• 1/4 green bell pepper
• 1/4 red bell pepper
• 1/4 yellow bell pepper
• 1/4 white onion
• 1 tbsp peanut oil
• Fresh sweet basil leaves (look for purple stems)
• Salt and pepper to taste

For the sauce:

• 2 tbsp brown sugar
• 1 tbsp fish sauce
• 1 tbsp oyster sauce
• 1/2 tbsp soy sauce
• 1/2 tsp chicken bouillon base

To complete the meal: 

• 1/2 cup rice

Utensils: 

• Chinese rice bowl
• Aluminium wok
• Chopsticks
• Pressure cooker or electric rice cooker

Preparation: 

• If using a pressure cooker, soak the rice in water for 30 minutes to make the grains soft.
• Wash the chicken and cut into big bite-sized pieces and flatten with the blade of a knife. 
• Sliver the bell peppers and onion. 
• Slit the red chilies with a knife. Then soak them in cold water and remove the seeds with your fingers while they soak.
• Chop the garlic and red chilies finely. 
• Wash the basil leaves and remove the stems.

Cooking Directions: 

The sauce:

• Add all the sauces to the Chinese rice bowl and mix using a chopstick. 
• Add water till the bowl is almost full, mix well to even out the sauces. 

The rice: 

• If using a pressure cooker, immerse the rice in twice as much water (1 cup water for 1/2 cup rice, 3/4 cup water will make the rice looser and less sticky) and place in the pressure cooker. Set to medium high heat, and turn the range off after two whistles. 
• If using an electric rice cooker, follow the cooker's instructions to cook 1/2 cup rice.

The entree: 

• Heat the peanut oil in the wok on medium high heat for about 30 seconds. 
• Drop in the chicken pieces and turn to medium heat. 
• Using chopsticks, separate the pieces.
• As the pieces sizzle, add salt and pepper. 
• Try to coat them evenly with oil but do not let them turn brown. (Look for the pieces to turn white with a little bit of pink still in them. This is because they will continue to cook as you proceed to add the sauce and vegetables.)
• Add the chilies and garlic to coat the chicken pieces. 
• Add the bell peppers and onion, and toss to mix with the chicken. 
• Simmer for about a minute, so that the vegetables are still crisp. 
• Add the prepared sauce and turn the heat up to high. 
• Allow the ingredients in the wok to bubble for about 10 seconds. 
• Turn the heat to low and add the basil leaves. 
• Mix well and turn off the heat when done.

Serve: 

• Serve each person a portion of the entree with their desired amount of rice. 
• Serve with a chilled drink to cool off the heat.

Possibility Versus Probability

"I don't believe in ghosts."

"Why not?"

"I don't think they exist, that's all. It's very unlikely."

"You can't know that for sure! What if you're wrong? Science can't explain everything."

"That's true. Science can't explain everything. Doesn't mean the answer only lies in supernatural explanations. Or that I should accept the existence of ghosts as supernatural beings that were once living people. There could totally be other explanations."

"But you admit it's possible ghosts exist?"

"Sure. The possibility always exists. No problem with that. But I don't think it's very probable that they do."

"Huh? What do you mean?"

"It's possible that ghosts exist. It's not very probable that they exist."

"What's the difference?"

"It's possible that ghosts exist - maybe they do and maybe they don't. But that by itself doesn't mean anything. There can be all sorts of explanations apart from ghosts. What really matters is how probable the idea of ghosts is - meaning how likely is this explanation to be true compared to the other explanations."

"You're talking all fancy now. I don't understand you."

"Sorry. All I'm trying to say is being possible and being probable are two different things."

"Those are just words. You're trying to confuse me with fancy words."

"But words are what we use to symbolize what we mean. Yes, these are words, but these are words with specific meanings, and I mean those specific things by using these words. If you don't understand them, I can explain them, but just saying they are words and you don't understand them means you don't really care, and I'm wasting my time."

"Well alright, what do you mean then? Can you explain what you just said about possible and probable?"

"Let's take a simple example. Suppose I tell you we're going to visit these friends of mine, and they have a child who is five years old. I'm busy, so you have to go buy a toy for the child. Now, what kind of toy will you buy? For a boy, or for a girl?"

"I don't know. Is the kid a boy or a girl?"

"I haven't told you. You have to guess. What do you guess?"

"That's not fair. I don't know, I can't guess anything."

"Exactly. From your point of view, there are two possibilities - the kid can be a boy, or the kid can be a girl. But unless I give you more information, you can't tell which it is. What would you say about the probability? How likely is it that the kid is a boy, versus being a girl?"

"I don't know... could be either."

"Yes, again because you don't have more information. You've heard of probability, right? You're probably heard the language somewhere - 50 % chance of something, 10% chance of something, 90% chance, or 10 to 1 odds, or the like? Use whatever language feels comfortable to you. The idea is that because you don't have any other information, there's a 50% chance the kid is a boy, and 50% that it's a girl. Make sense?

"Yeah, sort of."

"But. Suppose I had phrased my sentence like this: We're going to visit these friends of mine. They have a child, and he is five years old. Now what can you say?"

"Well, the child is a boy!"

"Let's put it this way. They have a child, so there are still two possibilities - it's a boy or it's a girl. But my next sentence was he is five years old. That decides it, right? How likely is it that the child is a boy?"

"Ummm... 100%?"

"Yes. Of course, there is still a possibility that it's a girl, and that I made a mistake and said he is five years old, instead of saying she is five years old. But how likely is it that I made such a mistake? After all, I do have a good handle over the English language. Would you agree?"

"That you know English? Yes, you speak quite well. You wouldn't make a mistake like that."

"It is possible, certainly, but very unlikely. Since I'm unlikely to make such a mistake in speaking, it's more likely that the child is a boy. More likely means higher probability - now do you see what I mean? Possibility just tells you what options exist. Probability tells you which option is more likely than the others, and by virtue of being more likely, that option is a better one."

"But it's still just an option right? Other options might be less probable, as you call it, but they can still exist."

"Yes, they can. And sometimes it turns out that a less probable option is actually the correct one. But not usually. And in some cases, an option can be so unlikely that it's almost absurd. You can argue for example, that it's a possibility that the earth is flat, that sailors who sailed around the world, and astronauts who went into space somehow all managed to fool themselves, and the earth is really just flat, and that's certainly a possibility. But it's not very likely, is it? There is enough proof that the earth is round. The possibility that the earth is flat is not just extremely remote, it is patently absurd."

"And you think the same is true for ghosts?"

"Yes. You can explain supernatural phenomena using ghosts and things. But you can also use rational, natural explanations. Guess which set of explanations can be tested using theories and experiments? So yes, I'm not convinced that ghosts exist."