Bridge Washing

One day after service, my cell group decided to play Singaporean Bridge together. In Bridge, there was this concept of ‘washing’. It basically meant that if one player’s hand was ‘weak’ (which we will rigorously define later), that implies that at least one other player has a disproportionately ‘strong’ hand. This justified a re-shuffling of the deck, and a re-dealing of the cards.

As a Mathematics major, I wondered if I could prove this fact. And it turns out that I can. With the proper definitions and the Pigeonhole Principle, we can prove that one player’s ‘weak’ hand necessarily implies at least one other player’s ‘strong’ hand. But first, let us make some definitions.

In a poker card deck, there are 13 values with 4 suits each (Clubs (C), Diamonds (D), Hearts (H), and Spades (P)), giving 52 cards. Denote each card by (V,S), where V is any of the 13 values, and S is any of the 4 suits. For example, we denote the Jack of Hearts by (J,H), and the Ten of Spades by (10, P). Each player receives 13 cards, distributed at random.

Define the set A of ‘strong’ cards as the cards whose values V are Jack (J), Queen (Q), King (K), and Ace (A). Thus, A contains 16 cards, since each value has four suits. For example, (J,H) \in A while (10,P) \notin A.

Define the score function f : A \to \{1,2,3,4\} by f((J,S)) = 1, f((Q,S)) = 2, f((K,S)) = 3, f((A,S)) = 4. Here, S denotes any of the four suits. Thus, f((J,H)) = f((J,P)) = 1 \neq 2 = f((Q,C)). In this set-up, we do not count hands with many non-strong cards of the same suit to be strong, contrary to other existing conventions.

For each player i = 1,2,3,4, let B_i denote the set of cards that player i holds. Then the strength function g : \{1,2,3,4\} \to \mathbb{N} is defined by g(i) = \sum_{x \in B_i \cap A} f(x). A player i‘s hand is defined to be weak if g(i) < 4.

Now we can state the result that we want to prove.

Theorem 1: If there exists a player i with a weak hand, then there exists a player j with at least 5 strong cards.

Proof of Theorem 1: Suppose there exists a player i with a weak hand. Then player i has at most 3 strong cards. Suppose otherwise, that player i has at least 4 strong cards, that is, |B_i \cap A| \geq 4. Since f(x) \geq 1 for any x \in A, the strength g(i) of player i is given by g(i) = \sum_{x \in B_i \cap A} f(x) \geq \sum_{x \in B_i \cap A} 1 \geq 4 \cdot 1 = 4, a contradiction. Thus, the remaining 3 players, which are our ‘pigeonholes’, share at least 13 strong cards, which are our ‘pigeons’. By the Pigeonhole Principle, there exists some pigeon, player j \neq i, with at least \lfloor 13/3 \rfloor + 1 = 5 strong cards.

This mathematically justifies the necessity to wash one’s hand which is rather weak. Note that the converse does not necessarily hold. It is possible for players 2,3,4 to each hold an Ace, and player 1 to hold the rest of the cards. Players i=2,3,4 each have strength g(i) = 4, while player 1 clearly has more than 5 cards. In fact, more is true. By considering the pigeons to be the total number of points 40, we have at least one player j having strong cards totalling to at least 13 points, which implies that player j has at least 5 strong cards by way of contradiction.

Just an interesting mathematical musing over a popular social game.

—Joel Kindiak, 18 Jul 21, 1735H

Double the Loser!

A while back, I had a conversation with a friend, whom we shall give the pseudonym Craig. The conversation touched on serving at National Service. He shared with me how if he did not like his superior, he would take MC out of spite, and in doing so stand up for his rights, rather than let himself be maligned by her.

Craig’s remark was in response to my anecdote of my friend (pseudonym: Alex) and I who, desiring to honour God in our vocations, submitted to our superiors who did not treat us in the best manner. While my superior was not the easiest to interact with, my friend had it twenty times worse. Yet, Alex and I wanted to continue to honour God, and therefore gave the best at work even though we were not recognised.

When Craig gave his remarks, I found myself at a loss for words. Eventually, I did mention that I thought that Craig’s hedonism would backfire in the future, and warned him against it because I cared for his well-being. Nevertheless, I gave no justification for it. I felt weak, since I made a claim I found myself at a loss to defend. I had lost the argument. Craig had won the argument.

A day after the incident, I looked back at what I felt. Apart from feeling weak that I had lost the argument, I felt insulted. I felt like a loser, yet again, since unlike Craig, I did not stand up for my right, and I was a weakling. Furthermore, I was a loser in the conversational exchange. Double the loser!

As usual, I turned to the Lord for help. Who else, right? The Lord revealed to me several truths, new and old, that in a strange twist of events, affirmed me for my interaction with Craig the day before.

Firstly, it was okay for me to lose the argument. The oft-quoted cliche is “win the argument but lose the soul”. Due to whatever reason, I always feel a need to win arguments with robust explanations (which ties in nicely with my current vocation as a Mathematics major). In this instance, I lost the argument, and ended with a rather weak statement. Yet, the Lord reminded me that it was okay to lose the argument. This weak statement could be the very tool that God uses to bring Craig near to him. Beyond being a Christian as his official religion, and into a deep and abiding relationship with Him. And eventually adopting a biblical worldview of his life.

Secondly, this is a taste of persecution for being a Christian. In the eyes of the world, the Christian ideal may appear weak and disadvantageous. Turn your cheek to the other side? Go the extra mile? Why disadvantage yourself like that? And yet, Jesus affirms us in Matthew 5:10: “Blessed are you when others revile you and persecute you and utter all kinds of evil against you falsely on my account.” Was it disadvantageous to submit myself to my rather not-too-great (though not-too-awful either) superior? Possibly. Did I submit out of obedience to God, to work as if for the Lord and not for man (Col 3:23)? Yes. Does God honour that? Double yes.

As I type this, the Lord brought to my mind Isaiah 61:7: “Instead of your shame there shall be a double portion; instead of dishonour they shall rejoice in their lot; therefore in their land they shall possess a double portion; they shall have everlasting joy.” Yes, under the worldly worldview, where pleasure-maximisation is the ultimate ideal, we Christians will be scoffed at. We’ll be mocked for not standing up for ourselves. And at the same time, we have a God who recognises us, who knows us deeply, who pays attention to us, and who honours us in the areas of our lives where we do not receive recognition.

Another piece of Scripture surfaced from Psalm 1:1–2: “Blessed is the man who walks not in the counsel of the wicked, nor stands in the way of sinners, nor sits in the seat of scoffers; but his delight is in the law of the Lord, and on his law he meditates day and night.” Let the world continue in their hedonism. As Christ-followers, let’s meditate on the law of the Lord, delighting in His ways, and enjoying a lifetime of awesome adventures with Him, shepherding us all the way.

And love those who are in the world, even worldly people whose official religion is ‘Christianity’. We who have received grace are in the most privileged position to give grace to those who cannot conceive grace.

In fact, this is the third truth that the Lord brought to my mind. What the world will see is not the rational greatness of Christianity (which is rationally the greatest since we follow the Creator of life, and by extension, live life in the best way that He has designed for us). What the world will see is the irrational love of Christ through us. When love is highly unintuitive, and unmerited favor is incomprehensible, we steward the grace and love that Christ first gave us. Not to win arguments, but to win hearts. To be channels of love and grace and hope to a dying world.

In a strange and unintuitive twist of perspective, God is actually glorified in this exchange. I presented the truth, I build up my friend Craig, and I withheld my emotional outbursts, but processed them with the Lord. And I can only say it is only by His grace that this happened! Who held back my mouth from saying anything that I would regret. God is honoured. And isn’t that one of the fundamental goals of my life, expressed even in submitting to my superior?

Lastly, what so wrong about adopting the biblical worldview? So what if it seems disadvantageous (in the short run, at least)? Does that negate the truth of God’s ideals? Am I intolerant by holding a controversial or unpopular view? And if so, if the truth is that I am loving people genuinely by my unpopular views, thereby following the spirit of Christ’s ideals and not just the technical statements of faith, should I be ashamed? If my glory is Christ alone, then let the insults come. Christ will exact vengeance, if any. I’ll rest, and I’ll simply follow the character of my Saviour.

So double the loser! Mock me more! Accuse me of bring stupid because I want to follow the ways of Christ! Rejoice, for my reward is in heaven! For when I am weak, then I am strong!

—Joel Kindiak, 18 Jul 21, 1643H

Mid Year Update

It’s time for my mid-year update! 2021 is themed ‘The Year of Thankful Praise’, and explores what it means to thankfully praise God in good times and in bad times.

The year kicked off with me entertaining the thought of doing a CS PhD, and preparing myself somewhat adequately by taking two modules on algorithms: one on basic data structures, and the other on online learning and bandits. The latter module achieved its purpose in giving me a much more robust background on my research topic, both UROPS and FYP. The data structures one was an absolute disaster. I did relatively well, but the whole process was hands-down the worst ever.

A few weeks into the semester, and a churchmate joined my LG. He was everything I was not—funny, athletic, responsible (in terms of being closer to adulting than me). I felt weak. For the first time in a long time, I felt weak in my church group. In fact, nearing the end of the semester, the Lord revealed to me my fear of weakness that has influenced a large part of my life for a long time. I will elaborate on this, since it is really not as straightforward as it seems.

Along the way, I got to know a female friend better. We interacted relatively well, and to some extent supported each other in our faith. I developed feeling for her and confessed to her thereafter. She gently rejected me, and affirmed our (rather strong) friendship nonetheless. Within two weeks our interaction pretty much returned back to normal. Nevertheless, the lead-up to confession night was one of uninterrupted fear and trepidation, as I face the real possibility of rejection, which is an expression of failure, and in turn a expression of weakness. I honestly confessed my feelings, knowing full well I would never regret this decision, and paid the price for it. The Lord used Confession Night to push me to face my weaknesses head-on. And face them I did.

But later on, the Lord dropped another bombshell on me. I have been trapped by yet another fear—the fear of broken promises. This has trapped me from fully entrusting myself to people, in the sense of believing people when they mean well and sincerely want to support me in my life. In this regard, I am rather thankful I did not get attached, since this baggage would have exacerbated our relationship. These two fears manifested from my childhood, where I have ben (un)intentionally hurt by various individuals, who on hindsight did not mean it, but in reality impacted me irreversibly.

It is rather unfortunate that unlike others, I don’t look back at my childhood with fond memories. I dread the interactions I had with others, and I dreaded the kid Joel back then too. There was an obvious reason why people despised me—who would befriend an angry and oversensitive crybaby who blames others for his own shortcomings?

As a result, I am going to receive counselling from a Christian mentor (whom my friend helped me link up), to rediscover the foundations of my faith. I will receive the Gospel, and apply these Gospel realities into my childhood, and experience freedom from my childhood bondage once and for all. I don’t know if I will be healed, and if so, immediately. But I know who holds my hand one step at a time.

Meeting with the counsellor figure (he is an ex-pastor, rather than a clinically-trained counsellor) was freeing. He offered me some practical handles to process the emotions I experience that contradict reality, or at least seemingly. In turn, the Lord has given me fresh hope and joy and even thankfulness to feel thankful. I’m also becoming more attuned to my complex emotions, and the Lord has been calling out my childhood fears one at a time (weaknesses, broken promises, neglect, etc). Bring it to the light, place them on a metaphorical vanguard sheet of problems, which in turn is placed in the hollow of God’s hand (Isa 40:12).

I have been accepted into my full-time job as a tuition teacher! For the first year, I’ll be working part-time (even though officially I’m a full-timer), and learn the ropes of the tutor life—student-tutor interaction, HR matters, and so on—from a senior figure in the tuition centre.

Bible study has been operating relatively smoothly. We are currently exploring the book of Philippians, and everyone seems quite engaged in this discovery. Some groups are getting large and may multiply, and I am likely to need a new core team to do just that. I have no idea how I’m going to cope with BS and my work commitments, seeing that during peak season my work commitment will increase, but I’m going to trust in the Lord one step at a time. BS is the Lord’s ministry, so He will make a way, and He will provide the necessary resources to take this dream forward—for the world to know Christ through the Word.

That is my mid-year update. I’m expecting things to develop relatively quickly in my life, so let’s see what happens. I’m not sure when I will update again, but for now this is it.

—Joel Kindiak, 14 Jun 21, 2032H

He Knows Your Name

Last night, the Lord revealed to name yet another one of my childhood fears. He has prepared me twice for this moment, so it hits me less hard. Also, with some practical handles on describing emotions, it definitely helped this revelation induce an exponentially smaller impact on my emotional state.

It is the fear of being neglected.

For a horde of reasons, be it an Asian upbringing, an insensitivity to my sensitive emotions (since Asians tend to come across as strong), I have grown up with a sense that my parents never paid attention to me. And when they do, it is usually negative (because I disobeyed), or comparative (my brother outperformed me in school and obedience). On hindsight, I am sure that is definitely NOT what my parents had in mind, since they verbally make it very clear that they love us equally. Nevertheless, emotionally, I have grown up with this tendency to want to gain attention, highly likely due to my perception of neglect in my growing years.

This causes romance to be at the forefront of my desires, since in my interactions with sisters whom I felt attracted to (over the course of years), they have given me the attention that I find myself lacking. Via constant interactions of texting and meeting up and traveling the same route home, I feel wanted and cherished and belonged. In fact, this is possibly the predominant reason why romance matters so much to me—in many instances it fulfilled a deep longing that not many areas could satisfy.

And yet, these sisters who gave me a sense of being wanted also in their finitude stripped me of that sense, which results in extreme worry when we somehow stop communicating (for good reasons). Perhaps she may be busy with schoolwork, and texting wasn’t exactly the best time. Yet, I would start frantically worrying if I have offended her in any possible way that induced her to not want to talk to me. While these interactions thrilled me in that I felt wanted and therefore cared for and dare I say loved, they were still humans born in the sinful nature, and when I emotionally demanded them to meet my needs, that was when miscommunication ensues, and the amicable friendships dwindled.

This issue of texting actually extends beyond my romantic attempts, and extends to texting people in general. I get concerned when people don’t reply, because I feel that people (don’t) reply because they (don’t) want me. A lack of reply therefore evokes an emotion of neglect, which I have tried to avoid for the past 24 years.

Looking back, it is fair to describe me as an attention seeker. I felt neglected, and desperately sought the attention of others, even bad attention. This explained why I was more than willing to publicly humiliate myself in public, doing things that many would consider mockable or shameful (like dancing for no bloody reason, or screaming ‘Amen’ during service, or being the loudest person in LG, or trying to—thank God this never happened—establish BS as a formal ministry). In gaining the attention, I suppress my feelings of neglect.

This also explain the positive emotion that I felt when I received several specific affirmations from several friends. These friends in various ways conveyed that they noticed me and did not ignore me. They actually remember the blessings I have somehow made in their lives, and how there are many aspects of my life that has been a blessing to those around me. They presented the data and expressed what I perceived to be genuine love. More crucially, they demonstrated to me that they appreciated me, and thereby, they noticed me.

Once again, thank God for revealing to me this struggle at 24 years old, rather than 42 years old. The solution to the feeling of neglect would be the truth that God sees me. God knows my name. He sees the good, the bad, and the ugly, and does these things to them respectively: He responds to the good with affirmation, the bad with past condemnation in the cross of Christ, and the ugly with transformative beauty. God is the one who notices me perfectly, so that I do not need to fear the neglect I experience from time to time—He knows my name.

And He knows Yours too.

—Joel Kindiak, 27 Jun 21, 1546H

My Current Struggle

I have been experiencing emotions akin to that of depression (though I am not formally diagnosed with it, so it is not fair to those who do suffer this officially to say that I am suffering depression).

Just some context: the Lord in the course of various events revealed to me that I have nursed my childhood hurts into my relationships with various peoples, greatly hindering my trust that people genuinely have my best interests in their hearts. These childhood hurts are the fears of weaknesses and of broken promises. The former arising from being teased for being a crybaby, a loser, and a weakling. The latter arising from a fear of abandonment, which reflects dysfunctional assurance in my family’s love for me.

For the past two weeks, I’ve been an emotional wreck. I have not experienced a day where I have not cried. Life was absolutely meaningless by every metric conceivable. I have contacted an informal counsellor who is willing and, considering his many years of helping people experiencing similar troubles to mine, considerably able to walk me through the healing process.

In fact I am aware of what needs to be done in this healing process: complete forgiveness toward every person who have (un)intentionally hurt me in the past. Accept myself in my weakness, being empowered by the grace of God. And experience complete release.

There are some things i can say with certain honesty, even though emotionally I’m a mess:

  • God is real and He really loves me and I can really trust Him
  • God has not given me any verbal reason why I’m experiencing what I’m experiencing
  • I do not doubt the goodness of God in this season
  • God genuinely knows what He is doing, and is working this season out for my good
  • I would rather not have to experience this pain, but know that I must experience it, for this is the path for complete healing
  • I cannot make my emotions the responsibility of my friends
  • God is still working in my life
  • God collects my tears, and sees my sadness
  • God is with me every step of the way, even though I cannot see what lies ahead, and can only rely on the Word one day at a time
  • I have friends who genuinely care for me and who will be there for me, even though I don’t think it is right for me to share every grievance I am experiencing
  • God really loves me, and sees me righteous in Christ, and abundantly blessed

I don’t know where you are in your walk with God. I don’t know if you’re on cloud nine, or deeper than the valley of the shadow of death. But I know Who holds tomorrow, I know Who holds my hand, and I know Who can hold yours too.

—Joel Kindiak, 14 Jun 21, 2047H

AY20/21 Sem 2: Ah Whatever

I intended to enter this semester with a relaxed mindset. Just have fun, and learn things along the way, wreck some bell curves, and get some A’s. I believe I was proved wrong. I made some decisions which on hindsight may not have been the best, but which worked out for good, in particular, enrolling in IE6520 and CS2040, since I made awesome friends through them.

It is with the intent of pursuing a CS PhD that I took the two modules, and also in this semester I discovered that research was not my specialty. All things explored (tuition, TA, research), I still incline the most to tuition. Will blog about that eventually. It is also the semester where I calculated my CAP, and realised that apart from bragging rights (which will fade the first day at work anyway), there is no incentive for me to stress over A’s. Of course I still must learn excellently, since that is my calling as a Christ-follower at school, but to say that I care less about grades is an understatement.

Anyway, without further ado, I present to you the module review for this semester! This time, I’ve arranged the modules by module code, from 1K all the way to, gulp, 6K.

CM1401: Chemistry for Life Sciences

  • Lecturers: Dr Tan Wee Boon, Dr Zhang Sheng
  • Lectures: 2 x 1.5h / week
  • Tutorials: 1 x 1.5h / week
  • Difficulty: 5/10
  • Assessment: 6 x LumiNUS Timed Quiz (40%), 2 x Timed Assignments (60%)
  • Webcast: Yes

I took this module as my (final!!) basket requirement in science: a non-Math science module. Of course with the new CHS arrangement things are rather complicated, this module isn’t exactly offered, but nevertheless here is my experience. Lectures-wise: the first half was taught by Dr Tan, and the latter half was taught by Dr Zhang. Both are articulate, though I learned that from Dr Zhang not through live lectures but through his Zoom recordings of last year’s lectures, which were the teaching mode this time around. Dr Tan in particular is very clear on explanation, and incredibly patient with us non-Chemistry students in our questions. Quizzes were generally doable, though expect a steep competition, since it can be mugged (I did not put in as much effort, since (1) A’s were not as crucial to me and (2) I still had an S/U option for this module). Timed assignments are open-universe, though that information would be useless, since the timed pressure makes comprehending the questions tough, and one really must rely on prior understanding and knowledge of how the different chemical compounds relate to each other. Think of this module as H2.5 Chemistry, where the professors will explain 90% of what we need to learn (the remaining 10% is left as an exercise for Year 2 Chemistry majors).

  • Final grade: B+

CS2040: Data Structures and Algorithms

  • Lecturer: Dr Chong Ket Fah
  • Lectures: 1 x 1.5h / week, 1 x 1h / week
  • Tutorials: 1 x 1h / week
  • Tutor: Low Jiachen
  • Labs: 1 x 1h / week
  • Lab Tutors: Jasmine Seah, Wang Yuchen
  • Difficulty: 9/10
  • Assessment: Participation (5%), 10 x In-Lab Assignments (15%), 4 x Take-Home Assignments (12%), 2 x VisuAlgo Quiz (8%), Midterm (20%), Finals (40%)
  • Webcast: Yes

I took this module as a foundation for my (now-dashed) ambition of pursuing a CS PhD. Also, I took this module with some of my CS1231 students (shoutout to Ming Yong, Maoxin, Kaveen!), and so we struggled and survived (or died) together. This module was hell (CS2030 I heard is worse). Before I explain what is hell, let me explain what isn’t hell.

a) Dr Chong, though articulate in his delivery, spoke in what I felt was a sleep-inducing tone. This isn’t true for most; in fact I think most people would enjoy Dr Chong’s lively and enthusiastic teaching style, but for reasons unexplained I felt like sleeping each Zoom lecture. Eventually I banked on webcast since the 1.5x speed is really helpful in saving time. In short: lectures aren’t the problem. Please get other perspectives on this before you say, “screw 2040 because the lecturer is bad,” because I’m sure he is pretty damned good, but it’s just my experience that I’m recounting here.

b) The tutorial questions, though clearly including black-magic questions, aren’t terrible, since they aren’t graded, but are there for learning purposes. My tutor Jiachen is incredibly enthusiastic and friendly, and has a clear grip of all things CS2040, so I have no quips about that (in fact, I highly recommend you take a lesson under him!). My Lab TAs Jasmine and Yuchen are likewise capable, and likewise I exhort their teaching for you. Therefore, I think there is a high probability that your tutors will be sufficiently equipped to teach you.

c) Midterms and Finals. Apart from several black-magic questions, the assessments are like any other. Give your best, write stuff even if you aren’t clear of the solution, or even have a complete solution at all, and you should do fine. Partial credit is awarded, so not all i lost even if you aren’t the super-genius in the room who can conceive of any possible black-magic question out there.

In part c), however, I alluded to the reason this module was hell. The 15% + 12% = 27% component of the assessment are lab assignments, and if you complete them successfully, you automatically get 27% in the bag. The trouble however, is that these assignments are run on Kattis, and, well Kattis sucks. In fact, it’s really good—which is why it sucks for non-supergenius students like me. If your code passes 99 test cases and fails the last one, you are still considered by Kattis as a loser deserving of eternal damnation in hell (figuratively, since you won’t stop until you solve it, and the process is pretty damned hellish, pun intended). I have spent heart, soul, and sanity trying to solve all the assigned graded problems, regretting every moment I took this module, and regretting it even more if I did it without my friends. I did, but I sometimes wonder if the effort was really worth it. There were extra problems too. I gave up on them. Not worth the energy.

A graver difficulty with this module is one of good-enough. In CS1010S, you could design an incredibly inefficient solution, and still be awarded the marks. Not so with CS2040. It demands you to be good enough. So if your code incurs ‘Run Time Error’, sucks to you. You may be correct, but you’re not good enough. Kattis is designed for competitive programming, and bloody hell I’m not competitive, nor a programmer by any standards. The lab assignments were an absolute torture. Get ready to ask many, many friends, even juniors (shoutout to Russell!) who are way more experienced than you for help. And just get this module over and done with. It’s an absolute bloodbath.

  • Final grade: A-

EC2101: Microeconomic Analysis I

  • Lecturer: Dr Ong Ee Cheng
  • Lectures: 1 x 1.5h / week
  • Tutorials: 1 x 1h / week
  • Tutor: Wang Lu
  • Difficulty: 7/10
  • Assessment: 12 x LumiNUS Quiz (15%), Problem Set Submissions (10%), Tutorial Participation (10%), Midterm (20%), Finals (45%)
  • Webcast: Yes

Ironically, this non-math module was my favourite module this semester. Well, I would call it a EC-coded math module, since the learning heuristics really resembled that of a math module. Concepts were defined (aka definitions), and useful results and intuitions were inferred/deduced (aka theorems), mostly rigorously formulable and provable for a Year 2 math major (most statements are formulated in \mathbb{R}^2, so that shouldn’t be too hard to state and prove). Apart from the FASS paraphernalia (LumiNUS Quizzes, participation, etc), grading-wise you get the usual homework-Midterm-Final format. The problem set submission emphasised effort over accuracy, so 10% is in the bag. LumiNUS quizzes are open-universe and given three attempts a piece, the highest take, so 15% is also in the bag. As long as you contribute answers OR questions in tutorial, you get participation, so yet another 10% is in. Midterms and Finals emphasise economic concepts and the math pertaining those concepts. Algebraic manipulation is crucial in deriving the final answers but not graded at all, so good luck getting partial credit from careless mistakes (note: probably never).

Dr Ong is clear and articulate in her teaching, and fun to banter with in and out of lectures, though eventually I skipped the live lectures and treated this module as a self-study one too, in the interest of time. Wang Lu is legendary: professional and knowledgeable, and I have high praise for his teaching style throughout the semester. I would like to think people-wise this module is friendly, and through them you will learn a ton, clarifying misconceptions and refining your economic intuition.

  • Final grade: B+

MA4266: Topology

  • Lecturer: Assoc Prof Zhang Tengren
  • Lectures: 2 x 1.5h / week
  • Tutorials: 1 x 1h / week
  • Difficulty: 9/10
  • Assessment: Tutorial Presentation (10%), 2 x Assignments (20%), Midterm (20%), Final (50%)
  • Webcast: Yes
  • (Highly) Recommended Textbook: Topology by James Munkres

This is the second-last of my two 4K-modules, and this is a doozy. I call this module MA4266 Munkres, since 99% of the time I’m referring to the aforementioned textbook. A/P Zhang takes all of his material—lecture content, tutorial questions, assignments—from Munkres, so this book really is the bible of topology, not just in NUS, but across all universities almost surely. Lectures were delivered seamlessly, clearly, and quickly. I needed to recap the lectures at my own time to slowly digest the concepts and proofs, and even then I can’t say with confidence I have a very firm grasp on the concepts presented. The lectures could benefit from stipulated 5-min digestion breaks, since many a time we are intaking information for a good consecutive 1.5h at a go. Otherwise, I can’t complain much. Tutorials were facilitated by A/P Zhang too, and students presented solutions, the usual fare. In addition, A/P Zhang required that we typesetted our solutions, so that he could consolidate them into quality TeX files. Part of me thinks we are free labour in this regard, but whatever. I’m going to graduate soon, who cares? Shoutout to Shawn for being my second pair of eyes in this module. Most of the time I’m looking at Munkres anyway, and sourcing for solutions online. Midterms and Finals were tough but not new: a mixed bag of routine, challenging, and black magic questions, as usual. And all surprisingly taken from Munkres. Mug that textbook!

  • Final grade: A-

IE6520: Theory and Algorithms for Online Learning

  • Lecturer: Dr Cheung Wang Chi
  • Teaching Assistant: Wang Xin
  • Lectures: 1 x 2.5h / week
  • Difficulty: 10/10
  • Assessment: 5 x Assignments (75%), Project (25%)
  • Webcast: Yes

Apart from the glaring abnormity that is a ‘6’ in front of the module code (in what sane universe can undergraduates even take 6K-level modules??), this module was exceptionally hard. Thankfully there were no finals. But the homework problems were absolutely brutal. It felt like doing UROPS all over again, Googling and praying for answers to questions I find hard to even comprehend. I crawled through this module black-boxing everything, and banked on Ming Liang and Eloise to carry me through the remaining homework sets. I did offer to tank the project, modifying my UROPS work and submitting that for our project (it is technically original work, though clearly heavily influenced by my research paper), so that we could complete it in O(1) time, rather than see my group-mates struggle in even understanding what my paper is about in the first place. Dr Cheung is a friendly lecturer, though his lecturing could benefit from speaking a bit slower to reduce the probability of stuttering. 3h-lectures are an absolute nightmare, but something I applaud all of my engineering friends for surviving every semester. I’m glad for this lecture though, and the access I have to these materials. These will come in incredibly handy for my FYP, which is a nontrivial extension of my UROPS work.

  • Final grade: A+

What is true with high probability, however, is that academically, my fourth year will be relatively less heavy-loaded. I have the big FYP, one core module, and the rest S/U-able modules. Of course I will spend most of my time on FYP, but this also gives me more time for bible study, weekend rest with my family, possible TA-ing again, and an all-things-considered well-balanced school life.

—Joel Kndiak, 26 Apr 21, 1858H

Musings of a Non-Procrastinator

It has increasingly come to my attention that I am among the few non-procrastinators not just in my society, but all around the world. In every social group I find myself, procrastination is the norm, and I find myself set apart from the norm. It could be the modules I’m taking that warrant less procrastination, but I’ll just share some perspectives on why I don’t procrastinate.

But first, a backstory. In Sec Two, when my life was going downhill due to my sin and my sinful decisions, I did poorly for many of my exams. In Sept 2011, I came to know Christ for the first time ever—that I am the righteousness of God in Christ. Consequently, I devoted my studies to Him, and having a sense that this is what God wants me to do—to glorify Him in my studies. But how? The EOYs were impending in 2 weeks!

I consulted my mom who suggested consistent work instead of last-minute cramming. I am terrified at the idea of last-minute cramming: it’s too much pressure in too little time. And so after the end of Sec Two (which required cramming), I decided in Sec Three and onwards to study consistently. Get a little done every day, rather than push it to the end. The first three weeks were hell. My classmates teased me for being a mugger, and everyone told me to relax. Funny enough, this attitude repeated every year in every social setting (except perhaps J2). This attitude stuck with me all the way till now (that’s 8 years of building and refining this habit of consistency, which some dub “discipline“).

On the whole, this priority on consistent learning/work-producing has brought me many benefits, though it comes with its own costs. These are in no way isolated from my other struggles, but at least contribute in some way. Which may mean that some things I write aren’t logically airtight. I welcome a healthy discussion on this matter. Take what I write as a rough first-approximation.

  1. Getting Things Done With Minimal Worry: By spacing out the workload, I clear what needs to be cleared, tackling each day’s challenge one day at a time. This allows me to complete it with minimal pressure (i.e. pressure that comes from consuming and comprehending information, without external pressure of the nagging responsibility to do it). Each day’s work builds on the previous, and by consistently working through it, on average, my understanding is more robust and prepared for the next day’s challenge.
  2. Systematic Scheduling Works: On a related note, the purpose of scheduling is a clear one, which is to systematically spread the workload out. The benefit here is that I actually stick to my schedule, since I view it not as a social demand, but as a crucial strategy to help me with point 1. On days where I have cleared Day N’s work and I still have brain power to carry on, I’ll carry forward the relatively easier work in Day (N+1) forward, so that in Day (N+1) I have more time and energy for more time-consuming and brain-draining tasks. Especially if the week gets intense.
  3. Intense Prioritisation: With no compromise, work precedes play. Always. Work is the license to play. In secondary school, I would play my Nintendo 3DS and film Mario walkthroughs. In JC, I would (yes, laugh at me) do mathematics for leisure, after slogging through GP and Econs essays. In university, I would try to sleep early, or watch some YouTube. This however means that there will be days with no leisure—when the workload is intense. But I can live without leisure for some time. On a related note, it has helped me build the resolve to say ‘No’ to instant gratification, instead trusting God for the long-term benefits of short-term sacrifices.
  4. Building Responsibility: This attitude of consistency has helped me build a strong sense of responsibility—to take ownership of my work and to give my utmost best, unto the Lord (Col 3:23). Coupled with the reality of bearing the responsibility that comes with helming the bible study ministry as well as just growing up, being consistent has been an insanely useful tool to help me do what I need to do with excellence.
  5. Bragging Rights: I cannot think of one person who laughed at me during Week 1 of whichever study season who did not panic in the last week before the final exam. Literally. I had every right to laugh at every person who laughed at me, especially during the O-Level and A-Level mugging season. And I have to admit: it did feel good being the only person who did not need to cram in the last minute.
  6. Lonely Leisure: This however creates problems. I realise I enjoy spending time with people a lot more than I realise (at least in this season of my life, quality time has regained its spot among the love languages), and ironically in a period of time I find myself enjoying leisure, everyone around me cannot afford it. Which makes for a relatively lonely period of time.

That’s pretty much it. Don’t know what else to say apart from the decision that I want to keep enjoying the joy of being consistent, and use it to fuel my worship unto the Lord in every area of my life.

—Joel Kindiak, 11 Apr 21, 2210H

Christians Can Marry Non-Christians

Disclaimer: This post applies to believers who are currently single. For a treatise on believers who are already in existing relationships/marriage, see Paul’s considerations in 1 Corinthians 7:12–16.

In our modernised society, where religion becomes a part of our lives, we can ask the question: why shouldn’t two people of different religious beliefs (or lack thereof) come together? After all, as long as my partner is a decent human being, it shouldn’t matter what their faith is, right?

That is true. Suppose Christianity were just a religion and relegated to one part of your life, separate from romance, career, education, friendships, family, and so on. Any reason given to marry a Christian can be easily applied, if not applied more so, to a virtuous person of a different faith. In many measures, non-Christians score way higher than Christians. The logic is sound—there is no flaw in argument. So long the person is awesome (by your subjective taste of awesome), it doesn’t matter what religion they belong to. Regardless of race, language, and religion, as per the Singapore creed.

However, if you read carefully the previous paragraph, I’ve included a very crucial premise in this line of reasoning. Can you identify it?

The subtle non-trivial modernist premise is that Christianity is one part of one’s life. With the Enlightenment, secularisation of religion became the norm. This does not mean discarding the religious concept of God, but it does mean separating that belief from the other parts of life shared by people of all (or no) faith. This means that Christianity becomes increasingly seen as being “religious”, and subtly, mutually exclusive to other parts of life. Why then should Christianity influence these other areas of life?

Under the secularist assumption, Christians can marry non-Christians. The logic holds water. (Once again, as a crucial disclaimer: This analysis applies to believers who are currently single. For a treatise on believers who are already in existing relationships/marriage, see Paul’s considerations in 1 Corinthians 7:12–16.)

However, it directly contradicts the biblical perspective.

The rationale is simple. According to the Bible, Jesus is our God. That sounds too trivial. But break it down. What do we mean by God? God is not just all-powerful, all-knowing, and all-present (though there is no denial these things). If God really is God according to the Bible, God is the ruler of every thing that happens—even the disasters (which He can easily purpose for His glory). This means that God is to be viewed as ruler over every part of our lives. This also flies directly in the face of the secularist Christian—which the Bible claims isn’t even a Christian at all (Rom 8:1–7). Thus, Jesus is to reign supreme in every part of our lives—not relegated to a “God box” of our lives. It is logically impossible for God (all-powerful, all-knowing, maximally great in every possible universe) to be lord of all if there are areas He is not Lord of, that is, if we relegate God to a part of our lives separate from other areas. As written in the Gospel Coalition, if Christ is really the God and the Lord of our lives, then Christ must be Lord over our:

  • Relationships
  • Money
  • Possessions
  • Career
  • Kids
  • Time
  • Mouth
  • Mind
  • Body
  • Everything

In the words of Hudson Taylor, “Christ is either Lord of all, or is not Lord at all”. This means Lord over our relationships too. For a Christian holding this biblical truth as the anchor, if they are not yet married, is it consistent for them to fellowship with a person who does not follow Christ? Can a Christ-follower whose Lord (over everything) is Christ consistently date a person who has no intent of following Christ (even if they label themselves as a Christian)?

If Christ commands His followers to follow Him wholeheartedly, the logically necessary conclusion would be to choose a partner who would spur this Christ-follower on in pursuing Christ—a logically contradictory task for a person who has no interest in following Christ, since they won’t even know Christ in the first place. If they know Christ intimately as Lord over every area of their lives, and Saviour of their entire being, then by definition they are Christ-followers. Otherwise, they will only turn a Christ-follower away from Christ.

Can an unmarried Christian marry a non-Christian? Absolutely, under the (rather counter-biblical) secularist view of Christianity. But for an unmarried Christian who is a follower of Christ, who builds his life on the unshakable word of God (Mt 7:24–27), who views Christ as his Lord and Saviour (Eph 1:2), from a logical perspective, this is biblically untenable.

—Joel Kindiak, 31 Mar 2021, 1105H

Chew Slowly

If there is one consistent learning point throughout the last semester, it is this principle of chewing slowly.

It all began when my friend Daniel and I met for lunch. I was very used to gulp down my meals, since I saw meals as simply time-consuming necessities. So get the nutrition but minimise the time wasted on it. Makes sense right? But Daniel shared a different perspective, that by chewing slowly, my body can more effectively absorb the nutrients the food offers. So I took that to heart but didn’t do anything about it yet.

Fast-forward about one month later, I joined my churchmates for a fun day out, where we went on a mayan tour, to eat as much stuff as possible. The Spirit prompted in my heart, “Chew slowly.” So I tried to do that on the trip. Our first food option was dim sum, and I took one food piece at a time, chewing slowly, sucking the juice from the food, savouring the taste of each item. It was delectable. I never knew how much food can be so enjoyable. The idea that people would travel overseas and spend the whole day eating food now made sense to me. I finally appreciated the beauty of chewing slowly. Of course, there are times where I need to eat more quickly, but nowadays if I can, I chew slowly, blocking out the world and the responsibilities that I’m entrusted with, and just enjoy the food.

But interestingly, this concept didn’t stop at the physical. I got back my midterms for two math modules, and I did below median. I did badly for these midterms, and I was discouraged. This was the first time in my life I did worse than the class average in math. Of course I spent the first few days sulking over it, and processing my disappointment with God. Eventually, from a technical perspective, the solution was to change my strategy. I assumed that I could absorbed 4k math concepts the way I absorbed 3k math concepts. I was dead wrong. So my strategy wasn’t working. But here’s the new strategy—chew slowly. Instead of summarising the proofs of deep theorems in one line, as I could still plausibly do for my 3k modules, break it down into bite-sized chunks, understanding step-by-step how the mathematician proved his theorem. It’s okay if a theorem requires 10 key steps as opposed to the usual 1 in my 2k/3k modules. In doing this, I absorbed the concepts much, much more. And by God’s grace, bagged an A- for those modules. Considering that I messed up midterms, I’m not complaining!

Furthermore, this concept can be extended into a spiritual aspect. In October, we were doing a bible study on 2 Timothy 3, which is about being made wise unto salvation by knowing the Word of God. We came to verse 16, the famous verse on the Scripture being the Word of God. And we chewed on it slowly. All scripture—no matter how exciting or boring—is God breathed—personally came from the life and the voice of God—and so on. This principle revolutionised the way we read texts, not rushing over short texts, but chewing on them slowly, and extracting as much spiritual juice as we can from them. And savouring the beauty of Christ in His Word. Even in quiet time, don’t need to rush. Chew slowly, and encounter Christ.

You should try this out! Chew slowly—in all senses of the word. Chew slowly on the phrase ‘chew slowly’?

—Joel Kindiak, 22 Jan 21, 1151H

The Year of Thankful Praise

The theme of 2021 is: The Year of Thankful Praise!

Amazing artwork credits to Faith Chia and Gwyneth Choo.

Enter his gates with thanksgiving, and his courts with praise! Give thanks to him; bless his name! [Psalm 100:4]

There are two words to unpack from this theme. The first is ‘thankful’, and the second is ‘praise’.

  1. Thanksgiving to a person in the Scriptures consistently refers to expressing appreciation to what they have done for the thanks-giver. It is an expression of gratitude, in response to what has been done. Thus, we give thanks to God for what He has done for us.

    What has God done for us? The psalmist declares in Psalm 100:2 (paraphrased) that God created us in His image with great intimacy. In the New Testament, God so loved us that He gave His one and only Son so that whoever believes in Him may not perish but have eternal life (John 3:16). An elaborate list of the implications of Christ’s finished work is in Ephesians 1–3. The list ends with Paul’s declaration: that God is able to do far more abundantly than all that we ask or think, according to the power at work within us, for His glory (Ephesians 3:20). Starting with the Cross of Christ, we gradually thank God for every experience each day with the Holy Spirit. God has done many things for us, and in 2021, let’s thank God every day for what He has done for us.

  2. Praise in the Scriptures can also refer to thanksgiving, that is, a response to what God has done. In addition to thanksgiving, praise is described as adoration that God deserves for who He is.

    Who is God? In Exodus 34:6, the LORD described Himself as “slow to anger, and abounding in steadfast love and faithfulness, keeping steadfast love for thousands, forgiving iniquity and transgression and sin, but who will by no means clear the guilty, visiting the iniquity of the fathers on the children and the children’s children, to the third and the fourth generation.” In Psalm 100:5, the LORD is described as ‘good’ whose ‘grace and truth’ endures for generations upon generations. In John 1:17, grace and truth came through Jesus Christ, who is the radiance of the image of God (Hebrews 1:3). The LORD is perfect grace and perfect truth, and Christ reflects that interplay of grace and truth before humanity. Every morning, let us remember how good God is and how good He has been in our lives!

Furthermore, the phrase ‘thankful praise’ implies that our praise of who God is is saturated with what God has done for us. Though distinct, these two ideas are inseparable. We thank God for what He has done. This expression of thanksgiving informs our view of how good He is. Then we praise Him for how good He is. And this increases our perspective of what He has done. Thankful praise comes together. May 2021 be the Year of Thankful Praise, where we thank Him for what He is done and praise Him for who He is.

–Joel Kindiak, 24 Sept 2020, 1824H