1 Corinthians 10:13

"No temptation has overtaken you that is not common to man. God is faithful, and He will not let you be tempted beyond your ability, but with the temptation He will also provide the way of escape, that you may be able to endure it"

This year has been the most gruelling year to date, academically, emotionally, and spiritually. But God has been kind to me. Very kind. He did not deny me the trials necessary for strengthening, and neither did He let me perish under the challenge.

I remember asking countless times to let me tackle my struggles head on, once and for all. The process spanned a couple months and I was tired of dragging this burden. Just let me get over it already! If I must suffer, let it be short and quick. I thought it would be easier that way.

Then I received a stronger dose. It was just enough to stomach safely, but any more could have done me damage. It was one strong dose of temptation. I just wanted out. But everything I had endured up until then, the drag on the tamer incline, allowed me to face a long lasting selfishness of mine.

I like to think of it as the power formula, where P = w/t. God increased the time because He knows that I am not powerful enough, but we still got the work done. Also, I did exercise my power output beyond my usual level. I gained what I needed to, and got stronger from that. So God was kind. Very kind.

After all that God gave me a debriefing. He showed me all the things I could not see back then. Looking back, the whole event was the worst and best thing that happened this year. Had my saddest and happiest moments too.

My time here is far from over. A lot has yet to happen over the next six months. This year is only a precursor to what I must endure later on. I will keep these words close at heart and be reminded that no temptation is too great to overcome.

Nederlands

Prerequisite: none

Hallo!

The Dutch language is classified under Indo European, Germanic, West Germanic, Low Saxon Low Franconian, Low Franconian. English parts at the West Germanic branch, falling into the English category.

This post is only meant to provide a taste of the Dutch language. The grammar is very general and many exceptions are not noted. If you would like to learn conversational Dutch, Duolingo is a great free site to do so.

Here are some Dutch pronunciations given in IPA:

To aid whole words, Google Translate works pretty well.

The Familiar

Nominative pronoun:

*Sometimes je is an unemphasized jij, ze for zij, and we for wij. U is formal.

Verb conjugation:

Possessive pronoun:

Question (vraag):

Demonstrative pronoun:

Number (nummer):



Family (familie):

Colour (kleur):

red (rode)
orange (oranje)
yellow (gele)
green (groene)
blue (blauwe)
purple (paarse)
pink (roze)
brown (bruin)
white (witte)
grey (grijse)
black (zwarte)

Example phrases:

What is that?
(What is that?)
Wat is dat?

Thank you too
(Thank you too)
Dank je ook

I will be hungry and thirsty
(I shall have hunger and thirst)
Ik zul heb honger en dorst

My hand hurts
(My hand does hurt)
Mijn hand doet pijn

The pink pig likes to eat red apples
(The pink pig likes red apples to eat)
Het roze varken houdt van rode appels te eten

What would you like?
(What may it be?)
Wat mag het zijn?

Do we need spoons or forks?

(Have we spoons or forks need?)

Hebben wij lepels of vorken nodig?

They come from The Netherlands

(They come out Netherlands)

Zij kommen uit Nederland

The Unfamiliar

De / Het:

De and het are the "the" articles used for gender and neuter nouns. Here is a general guide to when to use which. I like to think of het as "it". The best way is not to memorize, but to accept the Dutch culture of what is considered "the" or "it", gendered or neutral.

The sandwiches (de boterhammen)
The man and woman (de man en de vrouw)
The artist (de kunstenaar)

The writing (het schrijven)
The cup (het kopje)
The book (het boek)

Lig / Zit / Sta:

Use these verbs when describing where something is. Here is a general guide to which verb to use.

The papers lie between the boxes.
De papieren liggen tussen de dozen.
My jacket lies under the bed.
Mijn jas ligt onder de bed.
A (dead) dog lies on the street.
Een hond ligt op de straat.

There sit women in the house.
Er zitten vrouwen in het huis.
The cat sits on the table.
De kat zit op de tafel.
Yuck, raisins sit in my bread.
Yuck, rozijnen zitten in mijn brood.

The lamp stands nearby the bookshelf.
De lamp staat nabij de boekenplank.
The buildings stand near the city.
De gebrouwen staan dichtbij de stadt.
There stands food in the kitchen.
Er staan eten in de keuken.

Interesting words of note:

zwembad = swim bath (swimming pool)
tijdschrift = time writing (magazine)
ziekenhuis = sick house (hospital)
dierentuin = animal garden (zoo)
schildpad = shield toad (turtle)
neushoorn = nose horn (rhinoceros)
vliegveld = fly field (airport)
hoofdstad = head city (capital)

This is only a sparse quarter of the Duolingo course. Still trying to get comfortable with some very Dutch words and patterns such as om te and er. Might update if I ever do.

Doei~

Braid Theory

Prerequisite: algebra 2

Got more to share from Alexei Sossinsky's Knots: Mathematics with a Twist~

J. W. H. Alexander figured that all knots can be represented as a closed braid. On the left you have a braid between the dashed lines, closed in such a way to make a knot. On the right you have the reverse, a knot split open to make a braid.

So the idea came about that maybe braids can help classify knots, except that not all knots are conveniently coiled. Before we go any further, some terminology:

smoothing: operation on an intersection

orientation (a): curve direction (indicated by arrows)
country (b): curve bounded regions
infinite region (c): the space outside the knot, also considered a country
Seifert circle: smoothed country
desingularization: to make planar representation of a knot with smoothings

nested: two Seifert circles of same orientation inside one another
change of infinity: to bring a point in an unnested Seifert circle out to the infinite region (top right quadrant)

in turmoil: country with two edges of different Seifert circles with same orientation about the country (indicated with weighted arrows)
perestroika: to make new crossings on country in turmoil (bottom right quadrant)

With all that, Pierre Vogel made the Vogel Algorithm, which can coil any knot for making braids. It helps to digitize knot computations as follows:

do smoothing

if in turmoil

--> do perestroika

--> do smoothing

if unnested

--> do change of infinity

done, you have a coiled knot~

(cut it into a braid if you like)

So can braids classify knots? Maybe. Kind of. Not sure.

Let us examine some product properties of braids:

The way of multiplying braids is shown on the left, where you join the bottom of a braid to the top of another. If you think about it thoroughly enough, you can agree that this operation is associative but not commutative. In the middle you have a braid B joined to its mirror image B^-1, which yields the trivial braid e. Note that any braid B joined to the trivial braid is still braid B just as in multiplying by 1.

There is a system of algebraic coding for naming braids, based on elementary braids. The negative superscript indicates an undercrossing.

The subscripts tell which column the crossing is at. The algebraic code of the braid in this example is written at the base.

But there are cases such as these where it does not matter which elementary braid you list first. In this example, i = 1 and j = 3, in which | 1 - 3 | = 2. It is commutative.

Emil Artin went further with this three-braid isotopy. Jeez, what do we do about it. Braids are almost as finicky as knots..

Caresse sur l'océan

First find out about introspective.

caresse sur l’océan
tenderly carry my luve and his luvess
on forth to an expanse of sea and sky
to where the moon is the colour of honey
as they cruise in bliss
a guardian battles the elements
donning cuirass and dress
with spear and petal in hand
to watch over their ship on wings of vigilance
tho’ it were ten thousand mile
to fill their sails with streams of blessing
’til a’ the seas gang dry
I will luve thee still my dear
still as the reservoir in my heart
be it now or then
may my luve and his luvess
caress on the ocean

The Imagery

The soft sea.
A sailing ship.
A guardian.

The Content

This entry is extremely short, but it has given sufficient context. Many references to A Red, Red Rose by the Scottish bard Robert Burns (which I got to sing a version by Rene Clausen at a choir festival).

The actual chronological order in which I wrote this "sea series" is Letting Go, Sea Song, Caresse sur l'océan, written mid October, mid November, and mid December respectively. Each entry was conceived independently. I swear the matching themes are coincidental. Perhaps this is the very wonder of my introspective project, finding things about myself that I otherwise would not have noticed. These little capsules of preserved thoughts may not be much by themselves, but it appears profound in the bigger picture.

Those months were crucial to me in the lifelong run. I finally got myself over this stumbling block and readjusted my motivations. We kids think we are mature, but it is with realizations such as these that prove us wrong. How wrong I was! And I suspect this story is not over yet. Just a little feeling that there is one more thing I have yet to learn from this..

I cannot promise that I will not write about the sea again. It comes back to me all the time.

Letting Go

First find out about introspective.

Chronological order: Letting Go, Sea Song, Caresse sur l'océan

letting go

of what never was

the first word

the final glance

all a dream

but the sorrow is real

to bask in a glow

that meant naught

every breath

gone over the hills

wondering if this brine

can ever be sweet

for the red die

and the green wilt

the aftermath of saline intimacy

drains blue to a grizzle

return, daughter of salt

to the ocean’s embrace

sands may crumble

but the seas will never dry

the plains you love so much

they are no more

the cliffs you love so much

they are no more

let the waves nourish

your diluted veins

as a free spirit leap up high

and as sea foam on the rocks

let go

The Imagery

Salt.
Animals and plants dwindle away.
Blue fades to grey.
Return from land to sea.
Sea foam sloshing off the rocks.

The Content

Another sea themed entry, comparable to Sea Song and contrastable to Caresse sur l'océan. This piece is particularly ambiguous, but if you consider the connotations I associate with certain symbols it will be clearer.

I would very much rather have you make the connections yourself. An excess of words will break the magic.

Size Does Matter

Prerequisite: none

I had a curiosity for gigantic organisms. Gigantic, as in dinosaurs, eighteen meter sharks and five meter sloths. Then I came across the right book. Here are the highlights of John Tyler Bonner's book Why Size Matters: From Bacteria to Blue Whales.

First of all, we all love pictures. This book has tons of cute illustrations. This diagram compares the sizes of various species in the eukaryotic domain. Adorable, especially specimen number 10..

That is a tapeworm.

Some other awesome organisms introduced, such as the rotor flagellum bacteria. Just when you thought humans were cool for using wheels and axles, these bacteria were born with it!

And then some maths. Roughly. The little fishlike squiggle (∝) means "proportional to". This is a summary of general trends that organisms follow:

Some other trends are (diameter ∝ height) and (size ∝ distribution distance). In fact, most organisms seem to aim for a common size-distance ratio. That is very mind blowing.

This book also introduces the Reynolds number, defined as the ratio of inertial force and viscous force. It points out that although microorganisms appear to swim relatively fast with their rapidly beating cilia, that is not actually the case. If you were one of these puny germs, the Reynolds number would be extremely low as viscous environment has way more effect on your microscopic inertial mass.

And my very favourite, this graph:

Organisms of one centimeter appear to be the slowest in the race, while the two extremes of the size spectrum are incredibly fast. So you see, size does matter.

Lorentz Transformation

Prerequisite: physics, algebra 2

Einstein's book Relativity: The Special and the General Theory is not the usual kind of pie that I stomach, but hey, the cover states: "a clear explanation that anyone can understand". Anyone. Hmm.. It is not really anyone's fault, which Steven Pinker explains rather nicely.

Nonetheless, here is my shot at following the derivation of the Lorentz Transformation. I did manage to squeeze out the final result, although I may not have applied the correct maths or logic. If anyone can spot an error that would be great. Even better, tell me about it.

In the below diagram, the coordinate system k' is moving away from k. At the origin of each "point of view" is a photon. The k' photon is moving away from the k photon in the positive x direction at velocity v (which I did not label..).

First, we can agree that the distance a photon covers is (speed of light)*(time). This applies for both k and k'. The two are related by transformation constants λ and μ. In the former case, the photons are moving in the positive x direction; in the latter, negative x.

Add 3) and 4) to isolate x'; subtract to isolate ct'. Introduce constants a and b to unite λ and μ, and for convenience.

Pick the origin of k where x = 0 and substitute into 5) to get 6), recalling that velocity is displacement over time ( v = x/t ). For comparison between scale increments ∆x and ∆x', pick the points t = 0 and t' = 0 to substitute into 5). From k' point of view, ∆x = 1/a as seen in 7).

*The substitution of constant a is from rearrangement of 6).

And from k point of view, ∆x' = a(1-(v^2/c^2)) as seen in 7a). Although ∆x and ∆x' are not the same in different perspectives, they should. Setting the two equal yields 7b).

Substitute 6) and 7b) into 5) as needed, to get 8). Substitute 8) into (x'^2 -c^2t'^2) to confirm that it equals (x^2 - c^2t^2). Except, does (x'^2 -c^2t'^2) really equal (x^2 - c^2t^2)?

There is argument that (x-ct) and (x'-ct') are incorrectly squared, since the correct square roots are as shown below:

But maybe the squaring came beforehand, leading to that conclusion (sorry for the transgender-looking x):

So there you have it. Your final product is equation 8). If the teacher ever threw you the equation for Lorentz Transformation, now you know where it comes from. Kind of. Maybe it is true that "anyone" can understand such things, but it is just a matter of time. And choosing manageable perspectives. Got to keep working at it.

Ai Pioppi

Prerequisite: physics, algebra 2/geometry

The Bicycle of Death. I bet it sounds more menacing in Italian. It is one of the many human-powered rides at Ai Pioppi.

This ride just about sums up my second quarter of AP Physics but I am not supposed to go into that, am I? The Blue Giraffe is protesting now. But I must comment on how much energy goes to friction and moving the hardware itself! While it is tough work for two men, two children would be dealing with even greater percentages of their body masses. It is almost a fancy workout equipment.

But then that is the power of machines, pedalling a greater arc length for moving a shorter arc length along the track.

I see there is also an extension from the carriage, through the center of the circle, to the other side. It may contribute as a counter mass of the carriage to facilitate riding towards the top, and as an inertial mass to uhh, keep people hanging up there.

F = Ia here refers to the weight of this counter mass (the acceleration should have been called g tangent).

I have not quite labelled everything thoroughly, missing a couple tangent subscripts here and there, but whatever. And I put zero at the top. And I should be using degrees in physics. Meh. Point is, gravity does some of the work.

It is also interesting to note the carriage's gradual accumulation of height. This ride makes a visual for the net accumulation of energy, of human input and friction output. And each time the carriage passes through ground level, it does so at a higher speed.

The place has come a long way from welding seesaws and roundabouts for little kids..

Seismic Wave

Prerequisite: earth science

Car crashed about a month ago. "Crash" is an overstatement. "Bump" more like. Yet the impulse was enough to crush the little Toyota. It was a young car too, with a red number plate and not yet one week in possession.

The cracks are almost like the impact frozen in time. Most likely not many cracks are due to material foliation since glass is an amorphous solid. From what I heard, the car hood actually sprung up and smashed itself. Maybe the epicenter of the impact can be pinpointed with these rough circles, or that the effect of P and S waves are distinguishable?

What I am really driving at is that glass smashing might be something worth investigating. Not that I have the means of doing so. But where patterns are concerned, numbers can be introduced~

If you feel inspired to smash some glass, please feel free to do so. Be sure to tell me about it.

As of now we got the headlights repaired. But the spiderweb on the windshield is still there, held by tape.

1 Corinthians 13:7

"Love bears all things, believes all things, hopes all things, endures all things".

Most people are familiar with verses four to six, but it is seven that strikes me the hardest. The last phrase in particular. The Chinese translation is the best: "love never ceases". 愛是永不止息. It is much easier said than done because love never ceases - unconditionally. No requital, no acknowledgement, no nothing.

One of the many tough things love must endure, is nothingness. Especially with being a conversationally inert person, I deal with nothingness every day. I am just a minor character that barely stirs a thing in anyone's life. I should be a master at facing nothingness by now. Or so I thought.

There is one such person that I cared for dearly over the past year or two. For once I felt understood by someone, and that in return I could be more than a human backdrop. I was so moved. Now that I have had a taste of emotional attachment, I do not know how to live without it. This friend is extremely significant to me, although I am maybe not equally significant. A moon can revolve around the Earth, but the Earth still revolves around the sun..

Added on top of the nothingness are the flaws and not so innocent aspects I learned of this friend. Rather than turning away in disgust, it makes me even more determined to hold on. I cannot let go until I have steered my friend away from sin. From hell. If I cannot manage to be of help, I will have failed miserably. The prospect of hell.. will haunt me forever. It is unbearable. I starve hungerlessly and worry sleeplessly.

All that, and unable to communicate.

It is not like I am being ignored, but most people interpret my cursed unresponsiveness as a leave-me-alone. If only I were not so subdued in nature, I could quite simply mend this silence. But no. I am very subdued. I cause a lot of drama for myself and drown in anxiety instead.

What usually happens was my psychological ego defence mechanism steps in. Too much stress. Specifically, reaction formation, inverting an anxiety-inducing belief to its opposite. When it gets tough caring about someone.. I stop caring. And suddenly there is only a meager handful of people left that I care about. My love died. I am such a moron for giving up on people. Presently, I am faced with nothingness from this very dear friend of mine. Do I let this love die too?

Love endures all things. Love never ceases.

Why should it matter that I am lesser in someone's life? Why should I stop praying? Why should I stop caring? If I really cared then I would see it through. We still have six months left, and I am determined to make things right. Sow some seeds at least. Then I will be able to part ways confidently.

But until then, I must wade through the nothingness. It will hurt. It will drive me crazy. But if this truly is love then it will endure.