Rakyat Jalan Sendiri

Density

Water crystal (ice).

A basic formula for density of a solid is to weigh its mass m for a given reference volume V and then to divide the mass with the reference volume to yield density ρ. Because a crystal is constructible from many unit cells due to periodic arrangements of atoms, we can use the volume of a unit cell as the reference volume.

There are different unit cells for different crystals, depending on how the crystal's atoms organize themselves spatially. The number of atoms per unit cell, thus the mass of the unit cell, and the unit cell volume are difficult to predict. Experimentally, they are determined mainly from x-ray diffraction, which is also not straightforward.

Let us consider a simpler situation. Suppose a solid has two atoms, A and B, i.e., an alloy AB, then the density can be thought of as equal to

ρ = (m_A + m_B) ⁄(V_A + V_B).

It assumes that we know the unit cell volume V_i for atom i and the number of atoms i within each unit cell volume. It further assumes that the alloy AB adds the individual volumes from atoms A and atoms B to produce the alloy. This is not always the case, which is often surprising for many students. If atom A is much smaller than atom B, then atom A can occupy a tiny space–interstitial site–available between nearest neighboring atoms B. In this case, the density of alloy AB is better approximated by

ρ = (m_A + m_B) ⁄V_B

since atoms A only increases the unit cell's mass. Unfortunately, the formula

ρ = (m_A + m_B) ⁄(V_A + V_B)

and its equivalent expression

ρ = (C_A ⁄ρ_A + C_B ⁄ρ_B)^-1,

where C_A = m_A ⁄(m_A + m_B) and C_B = m_B ⁄(m_A + m_B), are often used indiscriminately. The unit cell volume additive property should work well only for atoms A and B that have the same crystal structures.

The formula

 ρ = (m_A + m_B) ⁄(V_A + V_B),

however, can work well when A and B refer not to atoms, but to phases. Two phases can coexist and each contributes its mass and volume. Both mass and volume are thus additive. The equivalent expression

ρ = (C_A ⁄ρ_A + C_B ⁄ρ_B)^-1

then requires us to determine the density of each phase separately. C_A and C_B are now determined by the lever rule.

Lever Rule

Ni-Cu phase diagram. Ni = A, while Cu = B in this blog. Phase 1 = liquid, Phase 2 =  α (solid phase).

One formula often used in phase diagram calculations is the so-called lever rule. It is a basic and interesting equation.

Consider an example of a binary alloy composed of atoms Ni and atoms Cu. (A ternary alloy has 3 elements.) It is possible for a NiCu alloy to have 2 phases, say phase 1 and phase 2.

A phase of a binary alloy is simply stated a distinct "character" of the alloy. If the alloy is heated to high temperature beyond its melting point, it will turn liquid. We say the alloy becomes a liquid phase when heated above its melting point. When it is cooled below the melting point, the alloy will return solid. A solid is another phase, different from the liquid phase. So, we could assign phase 1 = liquid phase, while phase 2 = solid phase.

A phase diagram then is a diagram that tells us what phase(s) the NiCu (binary) alloy would like to adopt at certain temperature, pressure, and amounts of Ni and Cu.

It is possible for an AB (binary) alloy to have more than one solid phase. Why? Because the diatomic A-A bond strength is different from the B-B bond strength, and the A-B bond strength can be different from both. The relative magnitudes of A-A, A-B, and B-B bond strengths motivate the binary alloy to have more than one solid phase. We can figure out the maximum number of phases using Gibbs' phase rule; for a binary alloy it is 4.

Lever rule is applicable for a region in a phase diagram, where 2 phases occur simultaneously. These 2 phases may be liquid phase coexisting with one solid phase, or two solid phases. Level rule tells us the total concentration of atom B given the concentration of atom B in both phases. It also tells us the total concentration of A if we know the concentration of A in both phases.

For phase 1, atoms A weigh m_A1 while atoms B weigh m_B1. The concentration of B in phase 1 is c_B1 = m_B1 ⁄ (m_A1 + m_B1). For phase 2, atoms A weigh m_A2 while atoms B weigh m_B2. The concentration of B in phase 2 is c_B2 = m_B2 ⁄ (m_A2 + m_B2).

Now, the total concentration of B is not equal to the sum of the individual concentrations of B in phase 1 and 2,

c_B ≠ c_B1 + c_B2,

since the correct expression is

c_B = (m_B1 + m_B2) ⁄ (m_A1 + m_B1 + m_A2 + m_B2).

Rarely though, each mass of A and B in both phases are all known. c_B is, however, often known beforehand. So, the correct expression above is usually solved for the variables on the right hand side of the expression. This is when we need the lever rule.

The lever rule relies on another fractional amount definition W₁ and W₂. It states that the total concentration of B must be equal to

c_B = W₁ c_B1 + W₂ c_B2,

if the sum of these fractional amounts is 1,

W₁ + W₂ = 1.

Solving for W₁ and W₂ using both equations we get the lever rule

W₂ = ( c_B − c_B1 )/( c_B2 − c_B1 )

and

W₁ = ( c_B2 − c_B )/( c_B2 − c_B1 ).

What do these W₂ and W₁ mean? When you substitute the values for these compositions, you'll find that W₂ corresponds to the mass of fraction of phase 2 with respect to the total mass (i.e., the mass sum of phase 1 and phase 2). W₁ is thus the mass fraction of phase 1.

What is interesting is that the lever rule does not solve the equation

c_B = (m_B1 + m_B2) ⁄ (m_A1 + m_B1 + m_A2 + m_B2)

directly. In practice, c_B is usually known, but some of the mass quantities on the right hand side are not. The lever rule makes a consistent connection to the c_B formula. More importantly, the lever rule is based on an assumption that the concentration c_B can be written as a linear combination of the respective concentrations of B atoms in the two coexisting phases. I am not aware of atomistic proof for this linear combination assumption.

Waldjinah

Naik becak dari Solo Balapan
Sarapan serabi di Laweyan
Kerap aku dengar namamu

Kota tempat Ibuku lahir
Tempat berbaring selamanya
Di sudut kota makin ramai

Suara bening halus Waldjinah
Baru aku paham sekarang
Elok anggun indah rahayu

Aku tersenyum ingat dulu
Naik sepeda berburu lagu
Kiss, Queen, Led Zeppelin

Aku terbawa iklan mutakhir
Tanpa tanya tanpa tahu
Budayaku sudah kaya luhur

Spending Control

The urge to write this blog came up when my wife and I were doing early spring cleaning and realized how much stuff we bought despite the efforts to minimize them. I need to remind myself.

I figure sometime ago that spending control is more important than saving plan. On practical level, saving plan is not realistic since it makes me starved. In contrast, spending control teaches me to learn who I am.

My other argument for this spending-control strategy is that whatever I buy is likely worth nothing after the purchase. To test that theory, you can go to IKEA to buy the sofa you've been dreaming about and try to sell it on Calgary Kijiji - a free online marketplace - for the same purchase price, and see if there is someone interested in buying.

As a result, I don't buy clothes unless I need to replace ones that are completely worn out. I keep only two pairs of shoes - one for running, the other for work. I don't wear a wristwatch anymore since my cellphone tells time. My prescription glasses were bought 16 years ago and I still wear them.

I learned the hard way. I bought a new car 9 years ago and learned that it was difficult to sell it one year later when I needed money. The satisfaction of owning a new car also wore out very quickly for me. I never liked forking out $450 every month for the next 5 years. I realized then that I was poor and not cut out for expensive stuff. I told myself that I would never buy a new car again since any new car depreciates very fast.

I am also motivated by my life philosophy. Less is more. My dream is to fit all my clothing and personal amenities in one backpack, and I am still working on it.

On Bullshit: Excerpts

One of the most salient features of our culture is that there is so much bullshit. Everyone knows this. Each of us contributes his share. But we tend to take the situation for granted ... Nonetheless it should be possible to say something helpful, even though it is not likely to be decisive. Even the most basic and preliminary questions about bullshit remain, after all, not only unanswered but unasked.

In the old days, craftsmen did not cut corners ... These craftsmen did not relax their thoughtful self-discipline even with respect to features of their work that would ordinarily not be visible. Although no one would notice if those features were not quite right, the craftsmen would be bothered by their consciences. So nothing was swept under the rug. Or, one might perhaps also say, there was no bullshit.

It is just this lack of connection to a concern with truth–this indifference to how things really are–that I regard as of the essence of bullshit ... It does seem that bullshitting involves a kind of bluff. It is closer to bluffing, surely than to telling a lie ... Lying and bluffing are both modes of misrepresentation or deception ... Now the concept most central to the distinctive nature of a lie is that of falsity: the liar is essentially someone who deliberately promulgates a falsehood ... Bluffing, too, is typically devoted to conveying something false. Unlike plain lying, however, it is more especially a matter not of falsity but of fakery. This is what accounts for its nearness to bullshit.

This points to a similar and fundamental aspect of the essential nature of bullshit: although it is produced without concern with the truth, it needs not be false. The bulshitter is faking things ... A person who undertakes to bullshit his way through has much more freedom. His focus is panoramic rather than particular. He does not limit himself to inserting a certain falsehood at a specific point, and thus he is not constrained by the truths surrounding that point or intersecting it. He is prepared, so far as required, to fake the context as well.

Someone who ceases to believe in the possibility of identifying certain statements as true and others as false can have only two alternatives. The first is to desist both from efforts to tell the truth and from efforts to deceive. This would mean refraining from making any assertion whatever about the facts. The second alternative is to continue making assertions that purport to describe the way things are, but that cannot be anything except bullshit.

Bullshit is unavoidable whenever circumstances require someone to talk about without knowing what he is talking about. Thus the production of bullshit is stimulated whenever a person's obligations or opportunities to speak about some topic exceeds his knowledge of the facts that are relevant to that topic ... Closely related instances arise from the widespread conviction that it is the responsibility of a citizen in a democracy to have opinions about everything, or at least everything that pertains to the conduct of his country's affairs. The lack of any significant connection between a person's opinions and his apprehension of reality will be even more severe, needless to say, for someone who believes it his responsibility, as a conscientious moral agent, to evaluate events and conditions in all parts of the world.

The contemporary proliferation of bullshit also has deeper sources, in various forms of skepticism which deny that we can have any reliable access to an objective reality, and which therefore reject the possibility of knowing how things truly are ... Rather than seeking primarily to arrive at accurate representations of a common world, the individual turns toward trying to provide honest representations of himself ... As conscious beings, we exist only in response to other things, and we cannot know ourselves at all without knowing them ... Facts about ourselves are not peculiarly solid and resistant to skeptical dissolution. And insofar as this is the case, sincerity itself is bullshit.

(The above paragraphs are taken verbatim from the book On Bullshit by Harry Frankfurt. They form a concise summary for us who want to cut the bullshit.)

Value of Education

Education is a way to learn from the past and to chart our future.

For me the value of education is to fight boredom. Brain is one of our organs and it needs regular exercise. We go to gym to make our body healthy. Where do we go to have brain exercise?

I get bored when I don't know what to do. It happens when (i) problems around me are too difficult or too easy for me to solve, (ii) I don't have money to spend, or (iii) I don't have someone to talk to. I can do nothing for the second reason, but the other two reasons are related to our brains.

If one is not educated, he will not know how to occupy his mind. Put it mildly, he does not know how to waste his time well. He has little interest in activities that make his brain sweat. He does not like brain exercise. He just wants to be entertained. What often happens is that he settles for spending money to fight boredom. He thinks spending money buys a cure for boredom. That's why we have the term "retail therapy".

I am not saying an uneducated man cannot be a hard worker. They are not correlated as far as I can see. An educated man can be lazy; in fact, a highly educated man is often lazy since he thinks he can solve world problems by just thinking about it or daydreaming or writing a blog ;-(

What I am saying is a person with education knows how to waste his time. He reads books and thinks about stuff that interest him. This activity gives him knowledge, ideas, motivations, and hopefully a plan of actions. When he thinks about all these things - I can assure you - he will not get bored.

A lack of education also causes one to believe problems in this world are not interconnected. The perspective will be narrow and one-dimensional. He then believes that there is no point to worry about this world since to comprehend it is beyond his wildest imagination. He can be easily misled and manipulated by political parties, advertisements, con-artists, among others, since other people do the thinking for him (or not).

What is funny though is that too much education can cause one to think these problems are too complex to solve. He overthinks them and wants to map out everything in his head. He does not act unless he knows everything. This is unfortunate. Education does not free him, instead it imprisons him. Instead of taking the first small step of action, he worries about the biggest problem in a far distance future. He becomes a constant worrier (not a warrior).

We Make Our Own Problems

Traditional market - Pasar Gede in Solo - is more enjoyable than a supermarket.

Life is absurd. How can it not be? Let me give you an example.

This world is now such that you can find almost any product you can imagine. From disposable plastic stirrers to disposable marathon running shoes. They create convenience. Our lives become easier and more enjoyable. In turn, manufacturing and trading of goods and services create wealth for us to buy more products.

Our lives have indeed become easier and more enjoyable in the past century. The market economy - although imperfect - sustains creation-destruction cycles. Producers that cannot follow changing consumer habits and demands will perish.

The notion of competition comes from our needs to secure raw materials for manufacturing, skills to execute manufacturing processes, and money to buy products. Added to this mixture is the awareness that resources and skills are finite. Some countries are so worried they are willing to go to war or manufacture conflicts to get resources.

Competition then leads to progress. A person or a country needs to generate progress in order to compete. Otherwise, he or it will lose in a battle to secure resources, skills, and money.

The relentless pursuit of efficiency and competition collides with our wish to have enjoyable lives. It demands we work very hard - or else, we don't make enough money to satisfy our shopping needs - in order to lead comfortable lives. We get stressed out to be comfortable, which is a first indication of this absurdity.

Hundreds of stores in Ambassador Mall in Jakarta sell consumer electronics.

We reconcile this contradiction by compartmenting our lives. We work hard during the day and we enjoy our lives in the evening. It happens also in our lifetime scale when we say to ourselves we will get our freedom - that is, retirement - when we reach 55, or 65, or maybe never. Another indication of the absurdity.

What I find amusing is that the stuff of living we enjoy essentially do not change with time. Our brain chemistry has not changed. We like spending time with friends and families. Some do sports, some like eating, and so on. These activities are relatively inexpensive, yet we embellish them to look more expensive and desirable. Because of these embellishments, the cycle of work -> money -> purchases -> perceived status -> work -> ... cannot be stopped easily. We spin in a vicious cycle.

Buta

Aku yakin dunia kiamat
Penuh murka maksiat
Perang mesti kukibarkan
Begitu kata pemimpinku

Aku tadi dilarang istri
Terjang seberang desa
Siapa lagi akan berangkat
Aku tegakkan kebenaran

Jika aku tikam kamu
Karena kita beda agama
Pasti Tuhan akan bangga
Aku yang setia puja

Aku lari berbalut darah
Menang aku telah raih
Bukti padu cinta suciku
Aku tagih janji surgaku

Crash Coffee

Got for free from Starbucks and used once in a blue moon

Making coffee using percolator or even more complicated machines - those expensive Italian capuccino machines - is not my cup of tea (pun intended). I like my stuff simple. I prefer kopi tubruk (crash coffee, literally translated).

I pour coarsely ground coffee and piping hot water onto my cup. Put sugar or milk and stir. Kopi tubruk is ready to serve in < 1 minute with a minimum utensil and dishwashing after that.

Having ground coffee float at the top also helps decide when I can drink my coffee. When the float sinks to the bottom, it is time to drink. Not too hot, just the way I like it.

I like loose leaf tea as well, especially Japanese genmai cha (brown rice tea), although I prefer Earl Grey tea when drinking tea with sugar.

I still don't get it though why coffee making should be as complicated as it is today. Tea is a lot simpler. I often use tea to wash my camping bowl when camping; I drink the tea and the bowl is clean.

Math = Beauty

Math is a powerful tool to make sense of this world. It self-regulates and tells me I did stupid things if I was not consistent. I have to remember my assumptions as I work through calculations. If these assumptions contradict each other, then math simply tells me so.

It happened this afternoon. I was trying to get a physics formula from a series of calculations. I got the formula, but then I realized that there was a contradiction in one of the assumptions. So I had to throw out the formula even though it was exactly the formula I was looking for.

I know my previous calculations were garbage, I needed to think of another path.

I found the path and also got the formula I was looking for. This time, it has no contradiction. I got another payoff: the path gives a clearer and more elegant answer.

I remember buying that "Godel, Escher, Bach" book to understand the beauty of math when I was undergrad, but I never finished reading it. It is too complicated for me. A more satisfying read is "Why Beauty is Truth" as it also tells about history of symmetry. Books that teach me how to appreciate beauty in math.

I sometimes tell students to have faith in math. That is, we have to allow math to run its course and not to interfere with its process. Try not to have expectations when doing calculations. When there is no contradiction, math will simply show its beauty.

Lives We Want

I believe each of us has two life paths. One is what I have, I chose; one that you chose and have. We chose these lives because we know they promise comfortable lives. Not easy I know, but mostly pleasant. Predictable.

Such life is like a nest under a shade of a big tree. It never sees a snowstorm or a monsoon rain. It is sheltered but secluded. It can lull us. For some it may define what life really is.

The other one is what I didn't choose. The one you didn't choose. The one that fills my dreams. You know, this is the life that your heart always tells you to live, but you didn't have the courage to do it. The dream life I still don't have and want to chase.

I know though the life I want to live. But it will take time to get there. I only hope I have enough time.