hypothesis generation and information

Science is an art of omission. It requires a lot skill to see which details are not terribly relevant to the behaviour of the system that is being analysed. (Especially if the system is a complex one.) If you are lucky though, some of the unessential details may have already been pushed out of your sight. (Perhaps you are simply ignorant of some facts that are already available in the literature. Or perhaps it is the technological limitations - which ultimately define what is empirically available to you - that is working in your favour.) In other words, knowing less can be helpful in the generation of scientific hypotheses. Here are three examples:

- If Darwin knew about Mendelian genetics, he could have been dissuaded from formulating his famous theses. Mendelian genetics does not generate the massive amount of change that is needed for speciation.

- How could Kepler have formulated his (beautiful and simple) laws of planetary motion if he knew about every single irregularity and perturbation in the planetary orbits? For instance, the precession of Mercury's orbit could only be explained after Einstein's invention of General Relativity.

- Theory of General Relativity itself was a product of “ignorance” as well. Here is an excerpt from Philipp Frank’s book on Einstein (Page 249): Hilbert once said: “Every boy in the streets of our mathematical Göttingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work and not the mathematicians.” And he once asked a gathering of mathematicians: “Do you know why Einstein said the most original and profound things about space and time that have been said in our generation? Because he had learnt nothing about all the philosophy and mathematics of time and space.”

Knowing more may not help you neither. Greater information can result in increased uncertainty. An example:

- You receive a tidbit that the existing CEO at Company X may be replaced with an a-lot-more innovative and risk-loving person. The future of Company X is now looking more uncertain. Therefore, due to the increased number of possible future scenarios, creating a valuation model for Company X has become a harder task for you.

algebra vs analysis

I remember reading somewhere the following characterization of the difference between Algebra and Analysis. Unfortunately I can not recall the source: "Algebra is the study of equalities. Analysis is the study of inequalities."

Nice and clean, but not a very accurate picture of the reality...

Why? Because there is a dependency relationship that is being overlooked here. Although you can do algebra without invoking any analytical techniques, the converse is not possible. Why? Because you need to have some structures in place before you can conduct any analysis, and building mathematical structures necessitates employment of equalities.

Algebra tends to be more conceptual than analysis since it places more emphasis on structures.

mathematics and suicide

I wonder whether there is any connection between the following two long-standing observations:

- Theoretical mathematicians are held in high respect in French culture.

- The French are obsessed with suicide.

Some keywords/expressions that may be helpful for unearthing the connections:

- Existential qualms, a desire for the otherworldly, escapism, social disengagement, assertion and expression of individuality, the-individual-who-is-misunderstood-by-others, presence and consequences of a rich inner world, strive for originality, impatience with imperfections, perpetually true ideas / perpetuation of social values, adherence to tradition, respect to historical continuity, self-sacrifice in the name of something greater, inability to share discoveries/emotions with the loved ones.

a small advice

This is for mathematics students who want to delve into a more applied field such as physics, biology or economics:

There is no doubt that you will encounter new sorts of mathematics. Learning these will not be a great challenge for you. The real challenge will be adjusting to the way the practitioners think in their respective fields, the way they reason while they are not scribbling down mathematical equations. Ideas are put into mathematically precise forms only after they are formulated in some intuitive sense. Published papers are very polished versions of a lot of messy thinking.

Being able to generate interesting hypotheses in these fields requires a lot of non-mathematical experience. That is why the transition will be tremendously enriching for you.

recurrence

The concept of recurrence (which sort of covers the idea of self-reference as well) pops up everywhere in science and mathematics. Here is a large selection of examples:

Such conceptual similarities make me worry. Is our mental tool kit really that small? I wonder how many times we will have to subtly repeat ourselves over the next couple of hundred years. Should the presence of such similarities be interpreted as a manifestation of the all-too-humanness that Nietzsche was pounding on?

Or perhaps it is not us but nature who is repeating the same theme over and over again? (i.e. Our models accurately reflect what is being modelled.)

Recurrence was a depressing idea for Nietzsche who put it in its ultimate form in "Gay Science":

What if, some day or night, a demon were to steal after you in your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence—even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again—and you with it, speck of dust!”

If that has not arisen a mystical titillation in you, the following probably will. (Quotation is from an expository introduction to Bell's Theorem.)

The question is a variation on the old philosophical saw regarding a tree that falls in the forest with nobody there to hear the sound. A conflict between the assumption of reality and Quantum Mechanics has been suspected long before J.S. Bell. For example, in referring to the trajectory of the electron, in say the double slit experiment, Heisenberg stated "The path of the electron comes into existence only when we observe it."

People have long known that any measurement disturbs the thing being measured. A crucial assumption of classical sciences has been that at least in principle the disturbance can be made so small that we can ignore it. Thus, when an anthropologist is studying a primitive culture in the field, she assumes that her presence in the tribe is having a negligible effect on the behavior of the members. Sometimes we later discover that all she was measuring was the behavior of the tribe when it was being observed by the anthropologist.

Nonetheless, classically we assume a model where we, as observers, are behind a pane of glass where we see what is going on "out there." With Quantum Mechanics the pane of glass has been shattered. J.A. Wheeler suggests that we should drop the word observer entirely, and replace it with participator. He devised the following figure, whose caption is:

“Symbolic representation of the Universe as a self-excited system brought into being by ‘self-reference’. The universe gives birth to communicating participators. Communicating participators give meaning to the universe … With such a concept goes the endless series of receding reflections one sees in a pair of facing mirrors.”

 
 

linear amortization

Say we are given the following data:

EBITDA Flow: 70, 70, ..., 70
Initial Investment: -500
Amortization: -50,-50,...,-50
EBIT: 20,20,...,20
Tax (20%): 4,4,...,4
Current Value of Taxes: NPV(4,...,4)

Note: Here we limit ourselves to 10 years. Hence, for example, the first line depicts a flow of 70 each year. Initial investment of 500 is assumed to be linearly amortized over 10 years. NPV stands for Net Present Value.

Now imagine that we do not have the usual linear amortization requirement, and we are allowed to write off the investment expenses early on. In that case, amortization will be (70,70,70,70,70,70,70,10,0,0) and value of taxes will be NPV(0,0,0,0,0,0,0,12,14,14) which is lower than previous case's.

When you ask accountants why government requires linear amortization, they usually respond by claiming that investment is not an immediate consumption and therefore should not be amortized immediately. (It is utilized over a certain period and hence should be expensed over that period.) But the above argument yields an entirely different point of view: Governments like linear amortization method because in that case the tax stream generated by the investment assumes a form which has greater net present value.

double-filtration of nouns

Henri Poincare once said the following: “Mathematics is the art of giving the same name to different things.” In other words mathematics filters down the number of nouns.

Similarly physics can be thought of as a linguistic siege against the plurality of nouns. For example, a truly reductionist stance could be described as follows: "Everything is made of a small zoo of elementary particles which are the same everywhere. The dynamics of these particles explain the dynamics of everything."

Since physics employs mathematics in its explanatory framework, we can combine the above two observations and conclude that there is a double filtration of nouns at work here.

reflections on recent past

The economics crisis caused me a lot of misery but it has taught me a lot of lessons as well...

During the summer of 2008, I was looking for a financial job in the City of London. I was a recent graduate with no proper experience and the finance world was in flames. Banks were firing people in masses. There was a great deal of uncertainty and pessimism. No one was hiring. I was not getting a reply for my work permit application neither. Even after 10 weeks of waiting, there was still no word from the Home Office. My plan B had failed long time ago and I had no plan C.

It was an emotionally taxing period to say the least. Sooner or later I was forced to go back to my home country. A lot of things happened later on. I ended up returning to academia. The details are not worth going into. Most of them are too personal to disclose here anyway.

What I want to do now is to emphasize the bright side of those painful days. A lot of practical lessons were learned. But even more importantly a lot of intellectual lessons were learned as well.

In some sense I was very lucky. I was eager to learn more about how economies work and there could not be a better time to do this. The whole system was falling apart and the financial world was teetering on verge of collapse. The machine had broken down and all its pieces were lying on the floor. I tried to analyse these pieces one by one. I read as much as I could. I paid special attention to writings by people who had different interpretations of what was going on and had different solutions for getting us out of the mess. While doing so, I discovered some pieces and connections that I thought never exited.

We care about the internal picture of a mechanism only when the mechanism fails. And the desire to fix the mechanism forces us to learn about its nuts and bolts. The intricate details of a company's cost structure matter only when sales fall to unexpectedly low levels. People start to worry about how central banks operate only when the financial system runs out of liquidity. We care about how a home appliance works only when it stops working.

It was an intellectually stimulating period, full of action and surprises. Gradually I developed an interest in complex systems which are amazingly prevalent in nature. These systems are often mathematically indecipherable. It is tough to break down what-is-going-on into smaller, more-easily-digestible pieces. The only legit way of gaining any insight is by conducting simulations. In other words, you learn about the system by trying to re-create a smaller version of it. The word "small" is very important here. While attempting to build a viable replica, you should not trivialize the system. Yes, you can not re-create everything. Therefore you need to use your intuition and select the aspects that are worth replicating. Even after doing that, you will still end up with a computationally very demanding task. You will be drowned in data and will have hard time trying to get a qualitative grasp of things. It will be impossible to come up with a nice analytical description. You will start with a lot of data. You will end up with even more. That is it. Page of ugly codes and lots of data. There is no beauty in it. At least not for me.

I love complex systems. They are fun to watch unfold in real life. But if I want to understand their behaviour, I like using words rather than formulas. Faced with such complexity, having some basic knowledge of mathematics helps. But having more will not put you into a more advantageous position. For example, in business and economics, the most insightful practitioners are often not even mathematically literate.

Pursuing a further degree in economics was never appealing to me. My interest was amateurish perhaps. But I wanted it to stay that way. Trying to break down what is seemingly-irreducibly-complex is a tough job. It also involves a lot of wishful thinking. I am a pessimist by nature. So it would not have worked for me. Never.

Now I am going back to pure mathematics. I will be fooling myself. Yes. There is no wisdom in pure mathematics. In fact, there is no wisdom in ivory towers at all.

To gain wisdom you need to step down into the real world. Too bad that the world is very complex. Too bad that it does not lend itself to analytical thinking... You will just have to get used to it.

I am making a concious choice here. I need a peace of mind and I am ready to sacrifice some wisdom for attaining it. In the land of pure mathematics, I will be living in ignorance. But this ignorance will be a delightful one, as that of an artist.

against beard

Several reasons why employees are not allowed to grow beard:

- Office is for work. It is not a venue for declaration of character traits, political choices etc.

- Beard is perceived to be a distraction.

- Beard is perceived to signal dirtiness.

- "Groomed-Beard-is-OK-School-of-Thought": Tidiness is what is important. Shaving every morning signals your client that you care about him( and your looks before him). Maintaining a groomed beard is a similar ritual.

- "No Beard" is a convention and conventions self-propagate themselves: “We need to blend in and act like the others in our sector.” (Note that in some sectors growing beard is tolerated.)

- "Only-Bosses-can-Wear-a-Beard-School-of-Thought": This is similar to what happens in military. Lower ranking officers are de-personalized and turned into similar looking peons whose sole function is to execute orders handed onto them by their superiors. Superiors are freer to do what they want to do.

mahalle berberi

- Adamin uzerinde niye beyaz onluk var? Cunku beyaz hijyen demek. Doktorlar da beyaz giyer. Iyi de benim ilkokul hocama da beyaz onluk giydiriyorlardi...

- Devasa aynanin yaninda asililar: Beykoz Futbol Takimi'nin armasi, berberlik locasi uyelik levhasi, Arapca bir kac dua, sararmis bir Ataturk resmi. Biz Ataturk'u de takim tutar gibi sevip, sayiyoruz. Kacimiz nutugunu okumusuzdur ki zaten? Batili, buyuklerine fikirlerinden dolayi saygi duyuyor. Biz ise baska sebeplerden oturu... (Bir resmi guzel yapan cercevesi olabilir mi?)

- Berberin makasi yanagima gotururken yaptigi estetik dansi hic bir zaman unutmayacagim. Bir dirsek hareketiyle beyaz onlugunu sivarken makasi havada guzel bir S cizmisti... Bana bir kez daha "gereksizlik" ile "estetik" kavramlari arasindaki o derin bagi farkettirmisti. Gereklilik hep "duz" cizgiler dogurur. Ornek: A ile B noktalari arasindaki en kisa cizgi duz cizgidir.