## Sunday, October 14, 2012

### Reflection on the Jungle Confidence Course (JCC)

From 10th September to 3rd October, I was training in the wild jungles of Temburong, Brunei. Part of my training was going through a Jungle Confidence Course (JCC). In this course, we (in teams) were given 48 hours worth of rations to use for 9 days of survival. We walked over 25 km in the jungles and then built up an improvised shelter for 3 days worth of survival. It was a once in a lifetime experience.

My team didn't manage to pass the course because of a tiny screw-up. But nonetheless, we did everything that those who passed the course did. We did our best. This is a reflection I wrote about the course.

JCC Defining Moments

During JCC I was the secondary plotter- meaning that I walked at the back of the team and confirmed our location every now and then with the primary plotter at the front. Because of this role, I wasn’t very involved with the actual decision making that was going on at the front. Since I couldn’t apply my initiative to make decisions during navigation, I took an initiative to make decisions while harbouring at night. Setting up the communal shelter and making a fire came under my charge and I thoroughly enjoyed managing these amenities. Setting up shelter amidst heavy downpours, foraging for dry wood in the wet rainforests and sharing hot food and drinks while drying our soaked hands and feet over the fire- those were my defining moments in JCC.

Learning Points

1.   Before the course, I never appreciated a fire. At the end of a long day in the field, I would rather sleep than put in an effort to make a fire. But during JCC, I came to understand the value of a fire. When you are tired, wet and lonely, a fire can really save the day. The heat from the fire can dry your soaked hands and feet. This can prevent skin related problems such as foot rot. The smoke from a fire keeps away insects like mosquitoes. A fire allows you to eat hot food and drink hot beverages- a real morale booster. Most importantly, a fire somehow connects you to civilization. It makes you feel safe and secure. It also gives you a deep sense of hope- something I believe is essential for survival. Thus I learnt the value of a fire.

2.   Being at the back of my team for most of JCC, I came to understand the dynamics between the front of the team and the back of team. Usually, what happens is that the front members will walk very fast- due to their initiative in navigation and lack of obstructions (people) in front of them- and the back members will walk relatively slower because of their natural lack of initiative and motivation. Sometimes, the front members realize that they are too far off from the members behind and to allow the team to re-group they wait for the back to catch up. The moment the last man arrives at the front, the front members move off again. This is a very common mistake that teams make. Why? While waiting for the back to catch up, the front members get a few minutes of rest, allowing their bodies to recuperate. But since the team moves off the moment the last guy arrives, the last few guys do not have the same amount of rest as the front guys. As this process repeats through the days, the back guys slowly get more fatigued compared to the front. That’s why it’s common to see the last man looking weak- not necessarily because he’s inherently weak but primarily because he never gets to rest like the others do. The solution to this is that rest timing (maybe 5 minutes) should be started when and only when the last man arrives at the rest point. The team should never move off when the last guy arrives but rather after a certain time after which the last guy arrives. This ensures equality. It’s easy to forget the needs of the last man. But remember, you could always be the last man and you could be forgotten too.

3.   Since food rations were very limited in JCC, I learnt how to maximize their utility. One useful tactic I learnt from my teammates is to expand the volume of food. This tricks your body and mind into thinking that you have a lot of food. How does one expand the volume of food? Firstly, add water to your mess tin and add food from, say, your main pack. Mix the food thoroughly and heat it till boiling point. This will expand the volume of the food, making you feel full. Once you’ve finished the food, some traces of unfinished food will remain in the mess tin. You can add water to the mess tin again and heat it. This will make a nice soup to supplement your initial meal. Once again, this adds volume to the meal consumed, making you feel full and ultimately, satisfied.

4.   The killing of the quail was a special experience for me. It made me realize how the hunters actually derived their meat. They really had to kill the animals. They really had to do the dirty work. It made me see the discrepancy between the lives of the hunters and the lives of us modern human beings. Today we eat meat without giving a thought about the animal that was killed. We pay someone to do the dirty work for us.

I felt terrible after killing the quail. It took me some time to come to terms with what I did. Eating the meat wasn’t enjoyable either. The entire experience made me question my meat-eating habits. Are these habits right? I still think about it today. Maybe there is something right about being vegetarian... This is something for me to ponder about.

5.   The last thing I learnt from JCC is being true to yourself. My team failed JCC because we did not acquire sufficient points for navigation. We knew about our failure halfway through JCC, upon the completion of Exercise Explorer. All 7 of us were devastated. This meant no JCC badge- no recognition for our efforts. We could have given up right there. We could have succumbed to the situation and performed poorly for Forager and Trekker. But we knew why we were in Brunei. We came all the way here to learn essential survival skills- skills that could only be learnt in the wild jungles of Temburong. We remained true to ourselves and true to our mission. We carried on with full might and did our absolute best for Forager and Trekker. The result- all of us passed Forager and came up third for Trekker! Mind you, this was us competing with teams that knew they passed JCC. I was very proud of my team at the end. We didn’t get the badge... but hey, we earned the experience of a lifetime.

Pictures-of-Singapore-Armed-Forces/page133

## Tuesday, August 7, 2012

### The grand scheme of things

About 2 years back, I went for a lecture by a Buddhist monk by the name of Ajahn Brahm. He was an English chap who gave up his indulgent city life to take on a monastic one. He talked a lot about Buddhism, most of which was difficult to catch. But there was one thing that really struck a chord.

Brahm was talking about what it means to be a Bodhisattva. Now for those who are not well-versed in Buddhist terminology, a Bodhisattva is a person who sacrifices his own path to enlightenment to help others reach a higher state of life. In secular terms, a Bodhisattva is one who wilfully sacrifices his own benefits for the benefits of others. In Buddhism, attaining a life state of a Bodhisattva is highly regarded.

Now Brahm was trying to tell the audience that failure in life is alright as long as we bounce back from it. He was using an example of a school kid failing a test. Then, he added on something about the school kid’s failure which was very interesting.

This is something along the lines of what he said.

Failure is relative. If you (the kid) have failed, then someone else has to have passed. Even if everyone fails, some (you) will fail worse than others. Despite being on the losing end, there is beauty in being a failure. By you taking up the role of a failure, someone else has not. By you suffering, someone else has not. So by becoming a failure, you have given others success. You have in your own way become a Bodhisattva. Of course, your actions do not resemble a Bodhisattva per se. It's not as if you failed willingly just to give others success. You failed despite trying to succeed. But as a consequence of your failure others succeeded.

This really fascinated me. Even if you screw up on a micro-level, on a macro-level you actually don't screw up. You simply become an agent of the macrocosm- of the system of things to happen.

Interjecting my thoughts here... Think about crime. We all condemn crime. I mean civil society hates thieves and robbers right? After all, they plague our streets. But if you think about it, these criminals give meaning to lives of policemen. They give policemen work to do. They get them incomes too. These criminals even give cities the honour of being crime-free - for if there were no criminals to begin with, then how can you ever be crime-free?

With this in light, isn’t a robber a Bodhisattva in his own way? Yes, his actions are wrong. But he sacrifices his own life and freedom to allow policemen to catch him and send him to jail (not willingly though!). By sending him to jail, the policemen get their own benefits such as income and recognition.

All of this is really fascinating.

But with this there are implications for our conception of sin. Our commonsensical conception of sin is that it is wrong in its entirety. But with these new observations in light, sin can now be right! Sin can now be useful in the grand scheme of things. But does that mean we encourage it? I don’t know and I can’t know.

To give my take on this: I would say we should live our lives to the best of our abilities and free ourselves of sin. But if sin adamantly finds us, then perhaps it's meant to be... and that's the grand scheme of things.

## Friday, August 3, 2012

### Saintly warfare

The past few (very few) posts of mine have been about my thoughts on the military. I just can't seem to think about anything else really. The military is what my life's about now.

Just before I conscripted, I had quite a problem accepting my place in the military. My Buddhist beliefs told me to respect all life, but yet I was going to train to be a soldier... a killer. My nonviolent beliefs told me there was no meaning to violence, but yet I was going to train to shoot... to kill. I saw the military as a violent, immoral organization. To me, there was no moral value in being a soldier.

Over the past months, I've been trying to find some moral meaning in being part of the military. Much to my surprise, I actually came up with something rather convincing... something that even a staunch supporter of nonviolence would believe.

Say one day a stranger barges into my house and decides to hurt my mother and my sister. What would I do? Does being a Buddhist and a believer in nonviolence entail that I do nothing and watch my family get hurt? No! There's something wrong with the nonviolent approach in this scenario. Obviously you can't just sit there! I think a natural and moral approach to this scenario would be to stop the guy with all the strength you have. If I had a rudimentary weapon like a stick or a broom, I'd use that to stop him. To me, this analogy justifies the use of aggression, but only for the sake of defending the people you love.

Now instead of one stranger invading my home, what if 200 of them were to invade the 50 homes in the estate where I live? That would mean an average of 4 attackers per household. Would each man in each household be able to defend his family with a broom or a stick? Would fighting on an individual level be effective? Not really. But if all the men from all the households were to come together, pooling their knowledge, resources and manpower, then it would be much more likely that they’d win against the attackers. Also, if one man dies in the fight, at least he would die knowing that the others left would protect his family. This is because the men will be fighting for the entire estate and not just for their respective families. To me, this idea justifies the formation of a large organisation that specializes in defense, because undoubtedly there is strength in numbers. This, to me, provides a moral justification for the formation of the military.

But all said and done, there are some considerations that I believe every (defensive) military must undertake to ensure its doctrines have good moral groundings. One important consideration is implicit in this question- how much aggression should be used by a military that warrants a good moral grounding of its actions? The answer to this is minimum aggression. A military that is well grounded in moral principles uses minimum aggression- just enough to meet its defensive objectives. Aggression should not be used for cruel acts, like in the torture of POWs, the killing of enemy civilians and the killing of enemies who chose to surrender. Peace, for both the defender and the aggressor, should be the ultimate concern of a moral army. After all, moral people care not only for themselves but for their enemies too. This consideration is reflected in the Geneva Conventions, which are a set of international laws that establish the humane conduct of war. It's a link worth checking out.

With all of this, I see the military in a different light. I see it as a moral organization that defends its land when the necessity arises. Instead of loathing the military, I now feel pride to be a part of it. Of course, all of this is because the military that I'm part of is a defensive one.

## Sunday, July 29, 2012

Since I got posted to the Officer Cadet School (OCS) back in April, I've been learning a lot about leadership. There's one thing in particular that keeps amazing and, somehow, amusing me. If you give a person, anyone really, a role involving leadership, that person will almost instantly feel empowered to do it well. This person would develop this powerful energy, something he never had before, that would help him to surmount and overcome the challenges he faces. I mean I've seen the laziest of people transform into active leaders when given a leadership role. I've seen people, who were otherwise nasty, change into caring leaders when given a duty. Strange? I used to wonder how and why this happens. I thought of some explanations based on my experiences as a leader.

In some cases, the person could feel that his performance as a leader would affect how much he is recognized by his superiors and respected by his peers. Thus, he would feel pressured to lead well. In other cases, he could feel his performance as a leader reflects his character. The desire to see a good reflection of himself, for himself, drives him to lead well.

This interesting observation about leadership taught me something important. If you've been given a leadership role, no matter how daunting, it's good for you. It helps you see yourself as others would and helps you to fix your flaws as you accommodate your behavior to suit others. It also brings out the best in you. At one time, I used to fear being given an appointment. But now that I see its benefits, I treat such leadership appointments with high regard. I even try to volunteer for such roles. The energy you develop as a leader- the pulse that drives you forward to surmount the highest of obstacles- that's something I really love.

But there's a catch to this whole energy business- something I had to learn the hard way. Being a leader, it is easy to make yourself work extra hard to accomplish your task because of all this energy you possess. But the raw fact here is that the people you are leading most likely do not feel this energy. In fact, they probably don't feel the need to work hard, since they don't feel the same sense of responsibility that you, as a leader, do. I realized that this is a dilemma a leader faces- between his personal idealism and the realism of the team.

Different approaches can be used to solve this issue.

One solution is for the leader to take a larger burden and allow the others to take it easy. But this approach is rather individualistic- not efficient and/or good for the team.

A better solution would be to involve the entire team. You could do this by appointing micro-leaders within the team and shift some of the responsibilities below, thereby allowing the team to feel that they are working actively and contributing. Of course, the leader must remind these micro-leaders about how important their jobs are. This will motivate them further. Another approach the leader could adopt is to set up an active feedback channel between him and the team. This feedback channel could help reveal flaws in the way the leader works. If the leader amends these flaws and shows the team that the system can be governed by them, then they would feel much more motivated to work. I've seen this style of leadership work very well in OCS.

I'm starting to find these basic human systems very fascinating indeed. This is all just a glimpse of what I'm learning in the military.

## Sunday, May 13, 2012

### My duty?

If you look at this world objectively, assuming there is some frame of objectiveness, you'll come to see that it's rather arbitrary.

I mean for some strange reason women were wired to suffer physically. Women go through years of painful, periodic cramps. They carry the load of an offspring for almost a year. They suffer 12 hours (and more!) of agony as that very offspring enters the world! Oh yeah, and they have to live with the lustful stares of hungry males... What they go through, I would never know. I do know one thing though- if an intrinsic duty to mankind exists, women by their very nature fulfill it.

Men on the other hand are so different. For some strange reason, men were not wired to live a tough life. They don't have to suffer physical hardship as their female counterparts do. Unlike women, their natural build and toughness protects them from physical harm. The only possible duty a man fulfills is impregnation. But then again, given our nature, I think that's more of a privilege than a duty... If you think about it, men do not fulfill any duty to mankind. If anything, they are a burden.

So what then is a man's duty to mankind?

I asked myself this many times when I conscripted into the army. Then it all made sense. The only advantage a man has over a woman is his natural physical strength. Isn't it then a man's duty, by his tough nature, to physically defend women and children against those who wish to harm them? Isn't it his duty to mankind to use his toughness to defend those who are vulnerable?

This is one of the thoughts that helped me excel in my army training. I now understand the purpose of army and my presence in it. I now know my duty as a man- to protect my loved ones, my nation and my world.

## Monday, March 12, 2012

### An ode to the second week of March: Good and Evil

Oh Destructive one
What did I do?
You cursed me with demons

Oh Heavenly one
What did I say?
You blessed me with angels
When I lost my way

Oh Wise one
Is this what I see?
Of Good and Evil
Only the extremities?

Ah Mighty one
Today good prevailed
To you, my gratitude and my grace.

## Saturday, March 3, 2012

### To help and to be helped

How many times have we heard our parents or teachers say, "Be an asset to society" or "Be useful to society"? I don't know about you, but I've heard a lot of that. Why do they say this? Well, the world lacks helpful people and with more of them, it's likely to become a better place.

But is that it? Are things so simple? I don't think so... There is a catch to this whole becoming-more-helpful business. I realized this during my army training last week.

Imagine a day comes when most of us become super helpful and only a few selfish people remain. How then will those selfish people become helpful, when the people around them only want to help and do not want to be helped?

By depriving a selfish person from the opportunity of becoming helpful, isn't a helpful person being selfish? Think about it...

To be truly helpful is not just to help, but it is also to have the ability and the humility to be helped. That's what I realized.

### What can I do?

What can I do with a woman,
When I have no time for love?

What can I do with conversation,
When I have nothing to say?

What can I do with manners,
When I live without them?

What can I do with control,

## Friday, March 2, 2012

### Some powerful moments

Hello!

For the past 4 weeks, I've been training in the army on an island called Pulau Tekong. It's been a physical and mental roller-coaster so far. But nonetheless, I've enjoyed myself thoroughly. In my time there, I've had numerous moments that made me go "wow!"

One of those moments was during field training (in a forest). My buddies and I had put camouflage cream on our faces so that we blended in with the forest. We had also covered our vests and helmets with leaves and twigs. We were then instructed to lie prone next to a tree and disguise ourselves. We were not supposed to move because that could give up our location. Lying there, next to a tree, I somehow felt one with the forest. I felt one with nature. There were ants and funny-looking insects crawling all over me. There were even insects inside my pants. But none of that mattered to me. I was at peace... And everything felt so right. I could just stay there forever; become a rotting log or even a small tree. That was something.

Another powerful moment was seeing my buddies getting punished and watching them do push-ups in compensation. This sounds rather sadistic, but believe me it's not. The sight of 50 to 60 young men going down to the floor and back up in that push-up position- something about that sight was very powerful.

The last experience that impacted me was during one of our long marches. We were all wearing our full gear, with our huge fatigue backpacks, helmets and rifles. I was at the back of my marching group. All around me was dense vegetation. Looking in front, I saw the rest of my group. Everybody looked the same to me from back there. Everybody looked equal. There were differences in height and shit like that, but that didn't matter much. While marching, our helmets and bulky bags were swaying in cadence, and our footsteps were in tune. There was something simple, yet so powerful and harmonious about that moment. I really enjoyed it.

My army experience so far has been a collection of such wonderful moments and of course, many painful ones too. I look forward to more of these wonderful moments.

## Sunday, February 19, 2012

### Entrapment

To be involved, to be busy, to be immersed... that's one thing. Whatever you do, there's always a way out. You can always say no. If you think life sucks, you can always leave and go somewhere else.

But to be trapped, and I mean it quite literally, that's another thing altogether. To know there's no way out, that every possible struggle for freedom is pointless, that feeling of desolation is difficult to describe... and even more difficult to understand. I mean we're all so used to having life our own way. We're all so used to hope. How can one understand the non-existence of hope?

You'd think there's sadness. Not much of it really. There's more of emptiness, and emptiness is difficult to describe. There's regression too, and that's impossible to explain. The paucity of human (or perhaps my) vocabulary is getting the better of me now... This entrapment is profound.

But thankfully not all is lost. Surprising as it is, the human spirit survives. I don't understand how, but this boundless spirit finds joy, laughter and camaraderie in the darkest of places.

## Saturday, February 18, 2012

### Meaning and derivation of the arithmetic mean

Hello again!

My apologies for not writing in so long a period. During the last 18 days, I've been in a military camp and have had no access to the internet or the real world. If you're wondering why, it's because Singapore has a conscription policy for all able-bodied men, and I happen to fall into that category. As for my army experience so far, I shall the leave that to another post. I have missed thinking about mathematics, so this post will be mathematical.

In the study of statistics, central tendency is a critical concept. Central tendency is basically a value or number around which quantitative data, or sets of data, tend to cluster. Central tendency can also be thought of as a number, or a set of numbers, that conveniently and accurately describes a set of data. There are many measures of central tendency. One simple and commonly used measure is the arithmetic mean, and I'm sure we are familiar with the formula for it. For a set of data (numbers) a_1,a_2...a_n, the arithmetic mean (a bar) is given by the following formula:

$\large \bar{a} =\frac{a_1+a_2+...+a_n}{n}=\frac{\sum_{i=1}^{n}a_i}{n}$

I am going to be explaining how the arithmetic mean actually links with the idea of central tendency, and using that idea, I will derive the formula above. To start off, assume there exists some arbitrary sample of data:
Now, assume a central tendency value or an arithmetic mean for this sample exists, and it, being the central value, exists such that the sum of the positive deviations and the sum of the negative deviations (modulus) from it must be exactly the same. To put this more mathematically, the arbitrary data set will need some re-arrangement. The data that is greater than or equal to the arithmetic mean (assuming it exists) must be isolated from the data that is less than the arithmetic mean in the following manner:

\large \begin{align*} &a_1,a_2,a_3...a_s\geq \bar{a} \\ &a_{s+1},a_{s+2},a_{s+3}...a_n< \bar{a} \end{align*}

Now for the mathematical statement regarding the arithmetic mean:

\large \begin{align*} &(a_1-\bar{a})+(a_2-\bar{a})+(a_3-\bar{a})+...+(a_s-\bar{a}) \\ &-(\bar{a}-a_{s+1})-(\bar{a}-a_{s+2})-(\bar{a}-a_{s+3})-...-(\bar{a}-a_n)=0 \end{align*}

Re-arranging the terms:

\large \begin{align*} &a_1+a_2+...+a_n-n\bar{a}=0 \\\\ &n\bar{a}=a_1+a_2+...+a_n \\\\ &\bar{a} = \frac{a_1+a_2+...+a_n}{n} \\\\ &\textup{QED} \end{align*}

I hope you now see how the formula was derived and how the arithmetic mean actually represents the central value of a data set.

LaTeX source: http://www.codecogs.com/latex/eqneditor.php

### Two days

Two days to walk freely

Two days to speak easy

Two days to care unconditionally

Two days, my free society

## Friday, January 20, 2012

### On the composition of natural numbers

I've finally stopped doubting myself for calling you that. I mean you gotta have some serious readers if your hits reach 7900, right? Anyways, since you do exist, I wanna thank you for reading my blog! I hope I've kept you entertained.

For the past two weeks, I've been in India, my homeland. I've been through many hours of driving... more precisely being driven. These long car rides served as great opportunities for me to think about things.

I have been pouring over how natural numbers are composed. In that, I mean I have been wondering what natural numbers like 27 or 98 really mean and how these numbers are constructed from basic logical principles. A recent car ride to New Delhi gave me great insights.

But first of all, what are natural numbers? David Berlinski wrote in his book "One, Two, Three. Absolutely Elementary Mathematics" that natural numbers function as tools, allowing us to distinguish things from a thing, and one set of things from another set of things. According to him, natural numbers create things altogether! I think natural numbers are the numbers we naturally know. They are the numbers that we use to get about daily life. They help us in counting. They are basically the numbers 1,2,3... and so on towards infinity. They are also known as the non-negative whole numbers.

To get how natural numbers are composed, one must first understand the idea of the number zero. Zero means something, and that something is nothing. Before we arrive at anything, we must first have nothing. The notion of nothing, or zero, is defined by the symbol "0".

The next pillar of this number system is a consistent unit, something we define as "1". This unit is left as a symbol, and is not given an extra descriptor such as 1 cow or 1 dog, to maintain generality and applicability to various scenarios.

With the fundamental ideas of "0" and "1", other unique symbols can be constructed. I'm going to show you the logical basis for the construction of the symbols "2", "3", "4", "5", "6", "7", "8' and "9". All of this may seem trivial to you right now, but if you think about it, none of this has to be. Keep your mind open, and you'll see some amazing implications later on.

(A) Firstly, this condition is "0":

(B) This condition can be understood as "1":

$\bigotimes$

(C) This next condition looks very different from (B) and is greater than (B) by one unit, and thus needs to be given another symbol "2":

\begin{align*} &\underbrace{\bigotimes \bigotimes } \\ 2\! \! \! \! \! \! \! \! \! \! \! \! \end{align*}

(D) This next condition looks different from (C) and is greater than (C) by 1 unit, and is thus given another symbol "3":

\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes } \\ 3\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}

Using the same ideas, the following symbols are inherited by the following conditions:

\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes } \\ 4\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}
\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes } \\ 5\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}
\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes } \\ 6\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}
\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes \bigotimes } \\ 7\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}
\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes \bigotimes \bigotimes } \\ 8\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}
\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes \bigotimes \bigotimes \bigotimes } \\ 9\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}

Well, what comes next? Our educated nature would force us to say 10. But remember, 10 has yet to be invented. We are still in the midst of logical construction.

So here we are... We need to invent another symbol for the condition which has 1 more unit then 9.  Well, that symbol could very well be this:

\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes \bigotimes \bigotimes \bigotimes \bigotimes } \\ \varphi \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}

But that's not what are forefathers chose. They decided that the condition which has 1 more unit than 9 should be recognized as another pillar of the natural number system, and that it deserves a unitary recognition, like 1 has. But of course, the condition which is 1 unit greater than 9 is greater than 1, so it cannot look like 1. It must be unique in its looks. They gave it the symbol "10". "10" means, reading from left to right, 1 complete unit of 1 unit greater than 9 and no other units of 1 (hence the zero):

\begin{align*} &\underbrace{\bigotimes \bigotimes\bigotimes\bigotimes \bigotimes \bigotimes \bigotimes \bigotimes \bigotimes \bigotimes }\Rightarrow \underbrace{\bigodot} \\ 10\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \!\! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \!10 \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \! \end{align*}

I would like to call 10 the "grouping unit", since it groups 1 unit more than 9 units into 1 group. I would also like to call what the grouping unit represents the "grouping unit value". In our system, the grouping unit 10 has a grouping unit value of 1 unit greater than 9. Also, notice that 10 is a construction of the symbols defined earlier on, and not a new symbol altogether. Human economy is at play here, for construction of a new symbol to denote 10's unitary property would complicate life.

You may ask at this point, why was this grouping unit (10) invented? Well for one, if it wasn't, we would have to keep conjuring new symbols and would eventually run out of options. You may also ask, why is the chosen grouping unit value 1 unit more than 9? Why can't the grouping unit value be 8 or 9 instead? A possible answer- our forefathers realized we all have 10 fingers and considered that number sacrosanct. But it should be noted here that the grouping unit 10 could have other possible grouping unit values like 8 or 9. If the grouping unit 10 had a grouping unit value of 9, 10 would then mean 1 unit of 9 and no other units of 1. But the fact is we chose a grouping unit value of 1 unit greater than 9 for the grouping unit 10, and that's that.

This breakthrough allowed us to represent larger numbers conveniently. For example, 27 would represent 2 units of 10 and 7 additional units of 1. 98 would represent 9 units of 10 and 8 additional units of 1. This convenience would last up till 99. One more unit would create 10 units of 10. How can we represent this? Well, a new grouping unit can be invented- "100". "100" reads, from left to right, 1 unit of 10 units of 10, no units of 10 and no additional units of 1 (hence the two 0s).

In a similar fashion, adding a zero to the right of the nth grouping unit creates a new (n+1)th grouping unit, each (n+1)th grouping unit containing 10 occurrences of the nth grouping unit. An example- converting 100 to 1000 by adding an additional zero. 1000 would consequently mean 10 groups of 100s and no other groups of 100, 10 or 1. Adding zeros to such grouping units also constructs and defines the various powers of 10.

With the help of 10 and its powers, we are able to compose natural numbers in an efficient and sustainable manner; using only the symbols of 0 to 9 in a certain order.

QEF

I hope this has been enlightening to you, because it certainly has been for me. Now, for something else. What would happen if we human beings were born instead as funny-looking alien creatures with 6 fingers, instead of 10, assuming we had the same brains and intelligence? By that I mean what would happen to our natural number system? Something really weird!

The ideas of 0 and 1 would be the same to us, but our grouping unit of 10 would no longer have a grouping unit value of 1 unit greater than 9. Because we would have 6 fingers, our grouping unit of 10 would now have a grouping unit value of 6. So now numbers would proceed like this:

$\large 1, 2, 3, 4, 5, \left \{10 \Rightarrow [6(1)+0] \right \}$

The numbers would continue like this, jumping up by 5 units on what we recognize as multiples of 5:

\large \begin{align*} &11\Rightarrow [(6)(1)+1],\: 12 \Rightarrow [(6)(1)+2], \\ &13 \Rightarrow [(6)(1)+3],\: 14 \Rightarrow [(6)(1)+4], \\ &15 \Rightarrow [(6)(1)+5],\: 20 \Rightarrow [(6)(1)+6=(2)(6)]. \\&... \\&... \\&51 \Rightarrow [(6)(5)+1],\: 52 \Rightarrow [(6)(5)+2],\\ &53\Rightarrow [(6)(5)+3],\: 54\Rightarrow [(6)(5)+4],\\ &55 \Rightarrow [(6)(5)+5],\: ?\Rightarrow [(6)(5)+6=(6)(6)]. \end{align*}

What would the last term be? Would it jump up to 60? Just like 10 units of 10 is grouped as 100 in our system... now, 6 units of 6 would qualify as 100. Thus, ? = 100.

The grouping units of 10, 100, 1000... in this system would now represent what we know as 6, 36, 216... in our system. 5 then becomes the last figure that appears on any placement, instead of what we know as 9. For example, 5 + 1 = 10, 15 + 1 = 20, 55 + 1 = 100 and 555 + 1 = 1000.

This is all really mind-blowing! It is also difficult to comprehend because we are so accustomed to our own number system. Imagine the pains involved in switching to another natural number system with a different grouping unit value!

If you liked this demonstration, you can also try to construct numbers for intelligent aliens with different number of fingers, like from 2 till 9 fingers. It'll be an interesting exercise. After that, try doing the same thing for aliens with 1 finger and 10 fingers (us). The last two experiments will be especially eye-opening. You'll get to see how arbitrary our number system is, and how little reason there is for us to prefer one number system (and grouping unit value) over another.

Picture from: http://www.clker.com/clipart-27994.html
LaTeX math codes: http://www.codecogs.com/latex/eqneditor.php

## Monday, January 2, 2012

### My problem of induction

I wrote this essay for an application to a special university program. Because I had to keep within a tight word limit, I omitted lengthy explanations of concepts. For that matter, I'll probably write another post. But anyways, here's the essay:

Back in August 2011, I was taking an evening walk and started thinking about Newton’s Law of Gravitation. The law relates the gravitational force between two point masses to their individual masses and their separating distance. This law is said to hold for all masses at all separating distances.

I began wondering how Newton derived his law. I deduced that he must have carried out experiments on masses which were separated by certain distances. But then something occurred to me. Newton could only have tested a finite number of masses at a finite number of separating distances to verify his formula. This is because it is physically impossible to test all combinations of mass and distance, them being infinite.

But how then can Newton’s observation be called a universal law? Couldn’t there be untested masses and distances over which Newton’s Law doesn’t hold? I was perplexed by this thought.

I read extensively and chanced upon the problem of induction by David Hume. According to the problem of induction, inductive statements, which are generalizations of past experiences, are unjustified because past experiences used for their justification may not be similar to present or future experiences. This principle implies that Newton’s Law is flawed because of its inductive nature.

I used to believe that laws of science were absolute and unquestionable. But the problem of induction made me realize the fragility of scientific theories. This destroyed my love for science.

The problem of induction also convinced me that my everyday actions were unjustified. I’ll explain... Let’s say as a child I touched a pot of boiling water and discovered it was hot. If I were to see another pot of boiling water today, I will remember my past experience and will not touch the pot I see, assuming it to be hot. But philosophically, this decision is unjustified. The pot today may be of a different nature than it was back then. It might just be cold. By extending this idea, I began to realize my everyday actions were unjustified. I became nihilistic. I even began to doubt my own existence, because according to the problem, it is perfectly possible for me to stop existing in the next moment.

I was devastated. But then, I began reading up on solutions to this problem. Regarding the validity of science, I found Karl Popper’s philosophy particularly relevant. According to him, science is not a perfect way to probe the Universe, but it is the best way we have. Understanding that science was the best way to explore the Universe brought back my love for it, and I accepted its inherent imperfection. I began to find the imperfection beautiful, because it creates mystery and fuels curiosity.

Regarding the philosophical validity of our everyday actions, I read and realized that though our everyday actions may be imperfect, they are the most rational options available to us. If we don’t follow these rational approaches, we will be reduced to a state of perpetual contemplation and will become unproductive in the process.

Ultimately, pragmatism is the solution to this problem of induction, or at least it provides the greatest consolation for us imperfect human beings. I learnt the importance of being pragmatic through this experience. I also understood the provisional nature of our existence and of science. I now perceive the world as a huge puzzle, one that I may or may not be able to solve. But I’m going to act morally and rationally, to solve this puzzle in the way I feel is right!

Picture source: http://namestormers.com/company-names-blog/naming-philosophies-from-the-naru-naming-guru/