one-point connectification

Money is one of the most important inventions of mankind. Just take a moment and appreciate the craziness of being able to express a full body massage in terms of wine glasses.

Mathematically speaking, money acts as the one-point connectification of the graph of tradable pairs of goods and services. (In the same spirit as the one-point compactification of a topological space.) Once it is introduced into an economy all goods and services can be converted to each other. In other words, by definition, there is nothing more liquid than money.

divergence in top talent

Being a sloppy mathematician is a precondition for being a superb physicist. All the greatest ideas in physics involved huge discreet intuitive leaps. Mathematics always came later to bridge and formalise the gaps. 

Einstein doggedly went ahead with his gut feelings. It took him and his mathematician friends years to formalise his intuitional ideas about gravity. Feynman did the same thing in quantum mechanics. He went ahead with his path integrals which mathematicians have still not been able to make rigorous despite continuous attempts during the last seventy years. (Einstein and Feynman are not some random physicists. They are the best humanity could come up with in the twentieth century!)

What seems like a positive correlation in the middle talent range becomes negative at the top. Good math and physics skills go hand in hand until you reach the top echelon of each discipline. Best physicists are not mediocre but horrible mathematicians, and vice versa.

There are similar examples from other domains as well. I will provide you with two. I am sure you can come up with more.

  • Good business and political skills often go hand in hand. This leads most people to mistakenly conclude that top businessmen can become top politicians and vice versa.
  • Best performers on stage are timid and awkward in social contexts off stage.

piyango ve matematik

Piyango oynayan yakınlarımı matematiksel argümanlarla caydırmayı çok denemişimdir. Hep de başarısız olmuşumdur.

Piyango biletlerinin satışından toplanan paranın sadece yarısı bilet alanlara geri dağıtılıyor. Böyle bir oyun oynanır mı yahu? Tabi ki hayır, ama gel de anlat! Olasılık hesapları, beklenen değer kavramı vs hiç bir işe yaramıyor. Karşı taraf bir türlü ikna olmuyor.

Neyse artık sonunda doğru yaklaşımı buldum. İnsanları kıllandıracak doğru cümle şu: "Bütün biletleri dahi alsan kaybediyorsun."

En efektif eğitim karşı tarafı kıllandırarak temel kavramların yeniden keşfini sağlamaktan geçer.

math as sensitisation

In the first iteration of the study, he and the team had started with a totally naive neural network. But they found that if they began with a neural network that had already been trained to recognise some unrelated feature (dogs versus cats, say) it learned faster and better. Perhaps our brains function similarly. Those mind-numbing exercises in high school—factoring polynomials, conjugating verbs, memorising the periodic table—were possibly the opposite: mind-sensitising.

- AI vs. MD (Siddhartha Mukherjee)

I had always suspected that mathematics increases general mental sharpness. Since it is the most rigorous of all academic disciplines, it should also be the most "mind-sensitising" one in Siddhartha's sense. This creates a pragmatic ground for arguing in favor of making abstract mathematics a mandatory part of public education.

Personally speaking, my most challenging intellectual journey involved a deep understanding of category theory. The inhuman level of abstraction caused me headaches. Now, looking back at my experience, I think that pain was literally the pain of adding new layers on top of the already existing layers in my (neocortex) neural networks. I have probably been using those additional abstraction layers ever since, in all areas of my life.

3 pillars of risk analysis

At Urbanstat, our philosophy of risk analysis is all-embracing and rests on three complementary pillars each of which has its own upsides and downsides.

 

Statistical Modeling

Generally speaking, risk analysis has always been about deciphering statistical patterns. What has changed over time is the sophistication of the models employed. Simple linear models have been discarded in favor of ensemble models that combine different types of approaches and go beyond the traditional least square estimation techniques.

Hence, in some sense, the modeling community has embraced the values of the post-modern world where no approach is deemed to be inherently correct. Every approach has its own unique context-dependent set of advantages and disadvantages.

As Urbanstat, we use ensembles consisting of decision trees and neural networks to help insurers detect the high-risk customers. Since we only know the fate of the accepted policies, we can warn the underwriters only about risks that they are willing to accept but should not. In other words, statistical modeling cannot warn about false negatives, policies that are being rejected but should not. Despite this fact that we can only see one side of the moon, we can still create enormous value for our clients, helping them see the complex statistical patterns that go unnoticed.

Models are tailor-made for each of our clients. We clean and enrich the data sets, supervise the variable and model selection processes. We work closely with our clients to ensure that the resulting decision-making assistance suits their risk appetite.

Downsides:

  • Cannot detect false negatives
  • Cannot provide humanly comprehensible reasons for rejection

Upsides:

  • Unlocks humanly incomprehensible complex patterns
  • Improves continuously over time

 

Physical Modeling

Unlike most other types of risks, due to their mechanical physical nature, geographical risks can be gauged even in complete absence of past policy/claims data. In this sense, Urbanstat’s geographical focus has provided it an important fallback option when statistical analysis is not feasible.

Catastrophe modeling is hard because catastrophes are both complex and rare. We either import external models or develop our in-house ones if we believe that we can do a better job than the existing alternatives.

Our ultimate vision is to become completely model agnostic by establishing a marketplace where institutions (companies, universities etc.) can put up their catastrophe models for sale. After all, as in the ensemble approach to statistical modeling, conjunctional use of different physical models often improves the outcomes.

Downsides:

  • Cannot be updated very frequently
  • May have a high margin of error depending on the complexity of what is being modeled

Upsides:

  • Can help the underwriter even in complete absence of past policies/claims within the region concerned
  • Helps build further human intuition via visual layers

 

Human Intelligence & Institutional Policies

Although there are talks of complete automation of underwriting services, we believe that it will not happen anytime soon. Machine intelligence and human intelligence work in different ways and each have their own advantages. That is why the hybrid approach always performs better, even in very well-defined contexts like chess games.

Moreover, one should never forget that it is the humans that provide the data sets that machine learning algorithms get trained on. Hence there is always a continuous need for human inputs.

In Urbanstat, we allow underwriters to easily draw authorization regions and add flexible if-then rules on these regions. Through this general mechanism, they can incorporate into their risk analysis framework all the institutional policies and individual insights.

Downsides:

  • Subject to human and organizational biases
  • Can get complex to manage and monitor as the underwriter team scales

Upsides:

  • Adds anticipative power to the whole framework
  • Improves statistical models that feed on human decisions

domains of cognition

Did you know that emotions correspond to certain bodily states which precede the actual experience of emotions? (Read this interview with Lisa Feldman Barrett) 

Similarly, the instructions we send back to the body upon feeling a certain emotion embark on their journey before we become conscious of them.

The complete correspondence between physical phenomena and cognitive models is as follows:

  • Environment <-> Perceptions
  • Body <-> Emotions
  • Brain <-> Consciousness

By definition, modelling involves reduction in information content. Just like we can not perceive our environment at its entirety, we can not be conscious of every single activity going on inside our brains. (Remember that evolution optimises for survival, not understanding.)

The discovery of the unconscious was traumatic. Similarly, we resisted the idea that there could be stuff out there that lie beyond our perceptions. (e.g. micro organisms, atomic particles, electromagnetic waves) Each such traumatic cultural acceptance process was followed by an outburst of mesmerisation and imagination. A grand belief in mystery reemerged and many speculative phenomena got ascribed to the newly discovered inaccessible realms.


The cognitive models exhibit nestedness, just like the physical phenomena they model. But the order of nestedness is inverted and the relationships are mediated via causality rather than spatiality.

  • Environment > Body > Brain
  • Perceptions <- Emotions <- Consciousness

Perceptions are affected by emotions. The domain of attention changes as the emotional state does.

Both emotions and perceptions are affected by the states of consciousness. For instance, you experience a lot more stuff when you are awake than when you are deep asleep.


You may be wondering how a brain can model itself. Would that not amount to creating a recursive loop? The model of the brain is part of the brain and therefore it too needs to be inside the model. But how can a model be inside itself?

In the timeless world of mathematics, recursions instantly turn into monstrous creatures. But in the world of physics, recursions take place in time and their behaviour get tamed.

A model of the brain at time t contains a model of the brain from time t-1. In other words, consciousness is like a Russian matryoshka doll which has (due to the enormous information loss happening at each step of modelling) a very small number of nested units.

originality and friction

Ideas are amazingly overvalued in the startup world.

Even in precise and theoretical disciplines (e.g. math, physics), a tremendous amount of propaganda is required to get an original idea accepted. Some of the greatest ideas get pushed into the fringes and stay there for decades, either to be rediscovered later by someone with more social capital or to be entirely erased from the collective memory.

In the imprecise and pragmatic world of startups, it should be even tougher for an original idea to propagate since there are additional executional hurdles on top of the already existing social frictions. (If an entrepreneur encounters only executional hurdles, then he should question the originality of his ideas.)

Hence there is no need to panic about a truly original startup idea to be stolen etc. 

mathematics and ux design

Just like mathematics, UX design is a discipline with very few principles and many manifestations of those same principles over and over again. But as human beings we often mistakenly focus on manifestations and forget the underlying structures. Appearances can be fooling.

Notice that the tendency to mistake unity for multiplicity is another fundamental UX principle. (For instance, similar objects should be grouped together to hint at an underlying unity.)

Hence, just like mathematics, UX design is a discipline that is strong enough to take itself as its subject. One can study UX design itself from a UX point of view, just like one can study mathematics itself using mathematics.

philosophy of neural pruning

The difference between math and science is baked into our brains.

Math is perfect knowledge. A mathematical statement is either true or false. But a finite brain can not cope with the incredible amount of data flowing from its environment by using such a perfect knowledge framework. Instead it uses a statistical pattern recognition framework that does not have a black-or-white view on how the world works.

The mind is pragmatic. It builds and discards models on the go without giving a shit about their ontological status. In fact, anything with a sufficiently low probability of occurrence is deemed not to exist at all. (Neural pruning is conducted using non-zero thresholds.)

mystery of two and three

Number one symbolises uniqueness. It is prevalent in both mathematics and physics. Beyond number one, mathematics and physics diverge in a mysterious way.

In mathematics, if you have three examples of a given structure, then it is extremely likely that there are infinitely many other examples as well. In other words, beyond uniqueness, the only finite number mathematics favours is the number two.*

In physics, number three plays the same role that number two plays in mathematics.** It underlies all plural ontologies.

  • There are three spatial dimensions.

  • There are three gauge theories corresponding to the three fundamental forces.

  • There are three generations of leptons and quarks.

  • Only the first three fundamental representations of the double cover of the Poincare group matter for calculating the spins of fundamental particles.

  • Only the first three orders of the generic Lagrangian matter for describing the dynamics of non-interacting particles.

* Hat tip to Prof. George Janelidze

** Hat tip to Physics from Symmetry by Jakob Schwichtenberg