Time Flies

Time is going…fast.

Now this could, admittedly, be a good thing or not. If you are in a huge challenge or are suffering really badly, the quickness of time will speed up the recovery process as the deepest of your metaphysical wounds heal. If you have planned a vacation, the fast flow of events gets you there quickly.

And yet, when you are well, and choose to spend every day bumming around at home instead of doing something useful, the quickness of time will waste it all away. During your vacation, time will eat whatever adventure was not spent there.
Time goes by very fast.

My week sounds something like this: Monday—new week! Tuesday—enjoying it thus far…Wednesday—its midweek! Thursday—nearing the weekend! Friday—weekend! Saturday—party all day err day! Sunday—tomorrow’s yet another new week!

Whether you like it or not, soon it will be the major exams, and then they end. Soon enlistment will take place, and then it ends. Soon you enter university and before long you graduate.

Unless you have a purpose to live, there is practically no reason to. I find my reason in Christ, in knowing Him and making Him known, and that’s the basis on which I choose to live my life on, regardless of what particular event is going on.

Regardless, time will fly.

—Joel Kindiak, 14 Jun 17, 0729H

Death to Instagram

Initially I wanted to use ‘Death to Social Media’, but the problem with that is that I’m unwilling to part ways with Youtube or WordPress (for obvious reasons).

But yes, as the image macros have shown, I have not just deactivated my Instagram account but went one step further to delete it completely. The downsides weighed more than the upsides for me, and my flesh was overwhelmed by the temptation to scroll through ideal yet probably fake lifestyles and keeping up the image of mine. In contrast, once I deactivated my accounts and went for my Australia vacation, I was freed from the need to impress and in fact just need to enjoy my vacation in peace.

Now that I’m back I decided that browsing the lives of others only make me more jealous than inspired, as the craving for attention crept up within my soul once more. Let’s just kill it. So I decided to leave once and for all.

All the photos I keep on my phone will be just that for the purpose they serve: not to impress but for me to reminisce and reflect and be thankful for the year of abundant joy thus far, as well as the many years that have passed.

No couple Insta accounts.

No 21st birthday picture.

No vain inspirations.

It’s time to regain the privacy of my person and to love myself as God first loved me, that I may love others even more. I know that Instagram means different things to different people, and I respect that, but for me its toxicity relative to where I am now as a person overwhelmed its utility.

So, death to Instagram it is, for me at least.

-Joel Kindiak, 5 June 2017, 1129H

A Speck and a Plank

“And why do you look at the speck in your brother’s eye, but do not consider the plank in your own eye?…Hypocrite! First remove the plank from your own eye, and then you will see clearly to remove the speck from your brother’s eye.” ‭‭[Matthew‬ ‭7:3, 5‬]

Last night, I was outraged at my friends’ unavailability and unintentionality. I saw how it’s evident that this friendship wasn’t reciprocal, that some were putting in much more effort than others and that clearly not everyone prioritized one another. I even labeled them, in Moses’ words, “a stiff-necked people” whom I felt like simply giving up on.

Multiple times.

Then the Lord reminded me that I’m guilty of making the same mistake. It’s quite clear that Hope Church isn’t very high on my priority list, or at least the special events like conferences and camps, as I have lost sight of their value. Yet, my cell leader and mentor kept showing me grace in spite of my stiff-necked attitude to church.

Multiple times.

How can I remove the speck in the eyes of my brethren if if have a giant plank in mine? The fact is we are all struggling and growing together in this Christian walk, even when things get incredibly tough. It’s times like these when, after we release that anger, we find forgiveness and grace to show grace to our offenders.

Multiple times.

—Joel Kindiak, 27 May 2017, 0748H

What is Hypothesis Testing?

This was one of the hardest math topics for me to grasp, particularly since the ideas of hypothesis testing and the tools used to quantify it are jumbled up, producing a convoluted Kindiak. I make an attempt to deconvolute any confusion that learning this topic may create.

What is hypothesis testing? At its core, hypothesis testing is about evaluating whether a claim is false or not. I claim to be 170 cm, but when you use a metre ruler to measure me I come short at 160 cm. Claim disproven! Of course, what makes hypothesis testing unique is that it uses probabilities to conclude.

Suppose a cola company claims that the mean volume of their drinks are 300 ml in each can. You smell horseshit and decide to test their claim. You buy 20 cans of cola, poured them out individually, and all of them measure only 290 ml. It would be fair to conclude that the company’s cheating your money right?

After all,

  1. suppose they were right, then
  2. the probability of all 20 cans having less than 300 ml would be miniscule.
  3. It’s too improbable!
  4. Hence, the company is lying!

Take note of the bolded argument. This is the core of hypothesis testing. Step 1 assumes the null hypothesis (that is, the default claim) is true. Step 2 tests that claim with reality. Step 3 evaluates how compatible, or incompatible, the claim is with reality using probabilities (p-value). Step 4 makes the final conviction on whether the default claim is false or not.

Instead of 20 cans, all of which are less than 290 ml, let’s put some numbers and distributions on it (for simplicity’s sake; there are many variants to this).

Let the volume of cola in a can X, follow a normal distribution with standard deviation 3 ml. Suppose we find that the mean volume of cola in 20 cans is 299.5 ml. Not so easy to conclude now, huh? It’s simple, really. We follow the four steps of the argument, but this time use statistics to justify these steps.

Step 0: The set-up

Okay, I lied. We need to first set up the courtroom. We call their claim, that the mean volume, \mu, is 300 ml, the null hypothesis and denote it as H_0. (technically we call it the population mean, since it is the mean volume of ALL the cans of cola, but if this confuses you, disregard until future reference). The alternate claim is that they’re lying, maybe that the mean volume is less than 300 ml. We call this the alternative hypothesis and denote it as H_1. We state the hypotheses as follows:

H_0 : \mu = 300

H_1 : \mu < 300

Step 1: Suppose the null hypothesis is true

We test this claim using 20 cans of cola with standard deviation 3 ml. Assume they are right. That means suppose the mean volume really is 300 ml. The mean volume of 20 cans, \overline{X}, using normal distribution concepts, will follow a normal distribution as follows:

\displaystyle \overline{X} \sim N\left(300, \frac{3^2}{20}\right)

Step 2: Test the claim with reality

If H_0, is true, then in theory, the sample mean will be about 300 ml with small variations. In reality, the sample mean is 299.5 ml. Is that too much of a deviation from the proposed mean? If it is too much, will the probability be too low?

In other words, give that \bar{X} follows such a distribution, what is the probability that the sample mean of the 20 cans of cola would have a value of 299.5 ml? Well, we find the probability simply by computing the value of P(\bar{X} < 299.5), which either by using the G.C. or by using z-values and a z-table can be found. You should get a probability, or, the p-value, of 0.228, correct to 3 significant figures.

Step 3: Is it too improbable?

Improbable or probable are relative words. Some think that a 1/3 chance in winning a dice-based is low, while a 1/3 chance in winning the lottery is mostrously large. In order to assess whether 0.228 is too improbable or not, we need to set a limit. What probability or less do we consider it as ‘too improbable’? This is called the level of significance, denoted by \alpha, and is arbitrarily chosen, depending on the context. In short, for the simplest of questions, it’s given to you in the question (there will be variants asking that you find this value of \alpha)

Anyway, let’s set \alpha=25 \% =0.25 for this question. Any probability less than this is, well, too improbable, GIVEN that we assume H_0 to be true. What’s our p-value? It’s 0.228. Is it less than 0.25? YES. IT’S TOO IMPROBABLE!

Step 4: Final conviction

Under H_0, we assume that the mean volume of cola is 300 ml. The probability that the sample mean volume of 20 cans of cola is 299.5, aka less than 300, is 0.228, which is too improbable (compared to \alpha, 0.25) to occur. Hence, it’s more probable that the company is lying.

We therefore find sufficient evidence to reject H_0 and conclude that the actual mean volume of cola is less than 300 ml (accepting H_1, but writing these two words alone won’t get you credit).

Step E: Error

I lied to you again. What if the company isn’t lying, but we were lucky (or unlucky) enough to pick the 20 cans that gave us a sample mean of 299.5 ml? Then that 0.229 probability was too low, but not low enough to render the company’s claim wrong. The p-value is therefore alternatively defined as the probability of wrongly rejecting  H_0.


That’s the core idea of hypothesis testing and a very simple example to get you started. What about finding the sample mean? What if you use a large sample that doesn’t follow a normal distribution? What if the population variance isn’t known? What if H_1 is not whether \mu is less or more than some claimed value, but just not? What if any of the parameters \mu, \sigma, n, \alpha are unknown?

Welcome to hypothesis testing. Make sure your understanding of distributions and  means of random variables are top-notch before coming here, since they are the ABCs of hypothesis testing.

29 April 2017

In my previous post, I lamented on how this day will be just another ordinary day that passes by without anyone knowing.

This weekend has completely proved me otherwise.

At the picnic that I organized, Alvin, Faith, Xin An and Ting Wei presented me with Alvin’s trademark birthday magazines, and we had an awesome impromptu photoshoot at Sentosa, followed by a sushi dinner and just enjoying one another’s presence. It was the perfect celebration I could ask for. I’m so glad my two groups of close friends finally get to meet each other and have fellowship, even if this is just the beginning.

xin an 8 faith 5 ting wei 8
On Saturday, my life group celebrated my birthday by organizing an Amazing Race full of Math questions. What blew me away was that it’s a team effort that brought this about, in spite of everyone’s hectic NS schedules. It wasn’t just the activity, but the teamwork behind it. That’s taking intentionality to a whole new level! And before the day ended, the Nice Hat guys came to surprise me. The surprise I finally and graciously received.

bravo 2 ting wei 9 xin an 10 may ann 2 justin 2-1
On Sunday, Bryan and Samuel treated me to lunch and Daniel and Jonathan spent time with me over dinner. This weekend sees my birthday the most celebrated in all 20 years, ever.

In Xin An’s words, “YOU SEE! PEOPLE DO CARE!” I guess it’s both a blessing and a slap in the face to stop doubting people so much.

One important thing is knowing that there are people who I can trust. For being there when I needed you the most, for hearing me in my romantic laments, for enduring my public embarrassments, for heeding my advice and for being my friends, thank you. You know who you are.

From the bottom of my heart, thank you for making my 20th the best one yet.

I’m grateful and incredibly humbled to be your friend. No joke.

Thank you.

—Joel Kindiak, 30 April 2017, 2213H


God’s Love


In recent days the Lord has been unveiling a small sample of His heart toward me through my own experience.

He delights in every opportunity He gets to spend with me. Any time alone with Him was precious and cherished to the full. He feels honoured every time I hear Him preach through the various sources and speak through His word.

He loves to give and give and give and bless and bless and bless. Receiving His gifts with a resounding ‘Amen’ brings Him joy. He delights in giving to me. He delights in me being delighted.

When I’m down, He listens and tenderly speaks words of encouragement. He finds ways to make me laugh in my worst moments. He is relieved when I’m okay.

He is sad when I don’t want to spend time with Him. When I just use Him for His blessings. When I chase the world instead of Him. Yet, every time I run back to Him, He leaps for joy. He enjoys not the activities but the person with whom He does them with.

He loves to help. He loves to do whatever He can to solve my problem. He loves it when I ask Him for help, relying on His ability instead of on my own.

He is devastated when I lie to Him, saying that I don’t have time to spend with Him when in reality I have all the time in the world to do so. He is heartbroken when I go against my word. He feels betrayed that I care for someone else more than Him.

He longs to spend time with me. He longs to affirm me with words. He longs to serve me. He longs to embrace me. He longs to give good gifts to me.

He longs to love me in every way possible.

He rejoices when I return after turning away from Him from so long. He is excited to spend more time with me once again.

—Joel Kindiak, Jan 2017