On dimensions and perspectives

Prof. T: “Have you seen my book on the history of science?”

Prof. C: [pointing to a bookshelf] “Over there”
Prof. T: “Oh, nice. You added a new shelf. Are all these history books?”
Prof. C: “That’s right. I moved all my history books here. Isn’t that what history is? A collection of books? ;-)”
Prof. T: “I suppose that is one way of looking at it :-). I tend to see history as a collection of facts and experiences from which we can learn. I guess what one makes of history depends on one’s perspective.”
Prof. C: “I’m glad you mentioned the term perspective. Just the other day I was thinking about how each observer can bring their own perspective, and how that affects the conclusions one draws.”
Prof. T: “Indeed. I think it speaks to the complexity of the phenomena we observe. A phenomenon can be viewed from multiple perspectives, just like a geometric object can have multiple dimensions; each with a different face or facade.”
Prof. C: “Hmmm. So then it can be argued that most phenomena in real life are not amenable to simple explanations; true insight can only be gleaned by taking multiple perspectives into consideration.”
Prof. T: “Right. Just imagine us scientists making conclusions by analyzing just a single dimension in a high dimensional space, and ignoring all the other dimensions. Except for in certain specific situations, that would lead to disastrous results.”
Prof. C: “I wonder though, in history, politics, social interactions, etc., how come most of us find it extremely difficult to view certain situations from more than one perspective? Any perspective other than one’s own seems alien, and often wrong.”
Prof. T: “That is a very important question; one we should all ask ourselves all the time.”
Prof. C: “Imagine a world where a person could completely understand another’s perspective. One could step into anyone else’s shoes and see the world through their eyes. Perhaps such an individual would see that we, as humans, have more in common with each other than we realize. Perhaps such an individual would be able to appreciate the fact that differences that move us farther apart from each other are, for the most part, merely differences in perspectives; and that the true picture comprises all the disparate perspectives.
Life, it seems, is a complex, high dimensional problem. Unless we learn to appreciate this complexity and to navigate the high dimensional space, there’s little hope we’ll learn how to make things better. Peace is a solution that lies in this high dimensional space. Perhaps complex systems science provides the method to find the solution.”
Prof. T: “Ah, a super hero with the power to put herself into other’s shoes; shall we talk to the folks who write comic books ;-)?”
Prof. C: “:-)”

Prof. T: “There’s certainly no doubt in the significance of studying phenomena as complex systems. Nevertheless, it occurs to me that perhaps the answer to your question lies in the analogy to the term dimension, as used in mathematics. We know how difficult, and at times intractable, it is to solve a high dimensional problem. So we make use of dimensionality reduction. Solution to the problem in reduced dimensions then becomes feasible.
Perhaps it is the case that in real life, we just find it simpler to look at phenomena from a single perspective. Perhaps we often fail to realize that doing away with other perspectives results in loss of information; information which might well be pertinent. We seem adept at following the path of least resistance.”
Prof. C: “To peace, dimensions, complexity, and perspectives.”
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"Our soul is cast into a body, where it finds number, time, dimension. Thereupon it reasons, and calls this nature necessity, and can believe nothing else.” — Blaise Pascal

On the cost of elegance

"In character, in manner, in style, in all the things, the supreme excellence is simplicity.” — Henry Wadsworth Longfellow
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Prof T: “Hey! Did you find an apartment you like?”

Prof. C: ”Well, I've found several, but they are all well out of my price range.”

Prof. T: ”What exactly are you looking for?”

Prof. C: ”Elegance.”

Prof. T: ”Ah, well, elegance will cost you; it always does :-).”

Prof. C: ”Tell me about it :-). I know it is because the material they use is very expensive. It looks great and lasts very long. But this explanation in itself is not particularly elegant.”

Prof. T: ”I believe elegance comprises simplicity and order. An elegant system, be it a mathematical model, a computer program, or an apartment, requires its creator/developer/designer to put a lot of effort into the work; effort in terms of battle against entropy. This battle has to be won; or there would be no elegance. When we see such a system, we often fail to realize the extent of the effort put into winning the battle against entropy. It is only natural for every system to eventually surrender to entropy.

Prof. C: ”I guess that fate is inevitable.”

Prof. T: ”Right. All we can do is to prolong the duration of the battle. I think the systems we perceive as elegant are those for which substantially more effort is put into the design and development phase, as compared to the effort required during their operation. For example, a well designed and properly built apartment requires significantly less maintenance effort than one with poor design and/or construction. The same goes for computer programs.”

Prof. C: ”Nice. Interesting interpretation of the second law of thermodynamics. Although, it would be nice if you'd come up with an original idea one of these days ;-).”

Prof. T: ”LOL. I know. But there's still hope. The meaning of the term 'original' might not be as obvious though; most innovations are just combinations of existing ideas, aren't they? ;-)”

Prof. C: ”And welcome to the wonderful world of combinatorics :-).”
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"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius — and a lot of courage to move in the opposite direction.” — Ernst F. Schumacher

On information, creativity, and free will

Prof. G: Morning! Did you make it to that panel discussion last night?

Prof. A: Morning! Yes, I did. It was fascinating; left me quite confused though.

Prof. G: Oh. How so?

Prof. A: There was a physicist on the panel who mentioned that according to a theory, the total amount of information in the universe is conserved.

Prof. G: So, information can neither be created nor destroyed?

Prof. A: That's what I understood from the discussion.

Prof. G: Well, I guess if mass and energy are conserved, information can be conserved as well. Why the confusion?

Prof. A: I was thinking about the implications. If information can neither be created nor destroyed, what does that say about creativity? Or free will? Life, the passage of time; everything is just a game of combinatorics. Isn't it?

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“The universe is computing its own destiny.” —James Gleick

On constants, variables, and the meaning of life

Prof. C: Hey, I was just wondering, have you ever thought about the meaning of life?

Prof. T: I think the meaning of life is a variable

Prof. C: You mean the meaning of life is variable, i.e., it can change over time?

Prof. T: That too. But also, it is like a variable in a programming language, or a mathematical model. When you simply declare the variable, it does not really have a meaningful value. It is only when you explicitly assign a value to the variable that it comes to mean something. I think you have to assign meaning to your life; it is not a universal constant.

Prof. C: That sounds complicated, and to be honest, a bit scary.

Prof. T: I know. It can be a blessing or a curse. We should choose wisely. We don't seem to put nearly as much thought into it as we should.

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"Challenging the meaning of life is the truest expression of the state of being human." —Victor E. Frankl

On Mathematics as a Foreign Language

"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." ~Albert Einstein

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Mr. A: (closing the book in his hands) “I wish they would write books without equations. There’s so much I’d like to learn, but every time I try, I run into equations that I simply cannot comprehend. I’ve never really liked Mathematics and equations.”

Mr. G: “Oh, I think I can relate to that. I’ve always been fascinated by the mysteries of the universe; just never could understand the equations. And there are so many in Physics. At some point I just gave up, and moved on to more accessible pursuits.”

Mr. A: “Well, I’m glad to hear I’m not the only one facing this problem. I guess it’s true what they say, misery loves company. Professor T, you certainly do not have this problem. You must think of us as a couple of illiterates?”

Prof. T: (putting down his coffee mug) “Au contraire. It is always a pleasure to talk to you Gentlemen over coffee. You tend to bring up thought provoking issues.”

Mr. A: “Professor T, I understand that your work involves a lot of Mathematics. Perhaps you could shed some light on the issue at hand? I’m not quite ready to give up yet. What must I do?”

Prof. T: (with a smile of admiration) “I admire your attitude, and I’d be more than happy to share my thoughts on the matter. Let me start by asking you this, have you had the experience of learning a foreign language?”

Mr. A: “Yes. As a matter of fact I am currently in the process of learning a language.”

Prof. T: “Well then, you might want to consider Mathematics as just another foreign language.”

Mr. A: “Hmmm … I would that I could, I just don’t see how.”

Prof. T: “Let me clarify that by taking a brief look at the process of learning any foreign language. Consider a language with a script that you are not familiar with. When you look at a sentence for the first time, it may be the case that you cannot even pick out individual characters, and you certainly cannot understand the meaning. The whole sentence appears no more than a pattern of lines on the paper. Are you with me so far?”

Mr. A: “I think I follow. There are many languages that appear to me as some incomprehensible pieces of art”

Prof. T: “Right. So how does one get from there to reading the most profound literary work in that language?”

Mr. A: “Well, lots of studying and lots of practice I guess. It takes a lot of time and hard work to reach the level at which advanced literature can be studied.”

Prof. T: “Precisely. Practice is a must. It also requires repetition. The more you use the language, the better you get at it. However, there is a step by step process involved here that we must not overlook. It all starts with learning the alphabet. We then learn how to join the alphabet to create words. Grammar dictates the rules for formulating valid phrases and sentences. Vocabulary provides us with valid words, and so on and so forth. At a certain point we reach the stage where we can understand the everyday use of language. But we continue learning, until we reach the skill level required to understand more complex literature; both poetry and prose. To summarize, we start by working on the basics i.e. by building a strong foundation. And with enough time and effort, master the language. Agreed?”

Mr. A: “Agreed.”

Prof. T: “So if learning any language entails a tedious and lengthy process, why should learning Mathematics be any different?”

Mr. A: “But Professor T, I still cannot quite see Mathematics as a language.”

Prof. T: “Mathematics is the language of abstractions. It is precise and unambiguous. It helps us formulate abstract structures and their properties. Numbers, operators, function, theorems, proofs etc.; these are all what constitutes the elements and style of the language that is Mathematics. You know, the most fascinating aspect of Mathematics is the portability of the abstract structures. It is due to this portability that the same structures can be used across disparate scientific disciplines.”

Mr. A: “But all I see in Mathematics is numbers and computations. What is this abstraction that you speak of?”

Prof. T: “You raise an important point. In my opinion, it is a common mistake to consider the whole of Mathematics as Arithmetic. The computations and calculations are essentially Arithmetic. As you’ve pointed out, this is what we come across most of the time. However, this is not all. Pure Mathematics is about abstract structures and their properties. A Mathematician creates (or discovers) abstract structures that have no physical reality. She proves theorems about the properties associated with these structures. Then, at a later point, someone finds applications of these structures. The numbers and calculations only enter the picture when computations are performed for a specific (concrete) problem.”

Mr. A: “I see. I’ve heard people talk about mathematical beauty. What is that all about? It cannot be about number crunching, right?”

Prof. T: “There’s a certain beauty in every language. However, what we often refer to as beauty in literature is that of the piece; a poem, a novel etc. In Mathematics, a proof can be like a beautiful poem. The step by step process of a proof may be mundane, or elegant. It depends on a specific proof, just like one poem may be considered ordinary, while the other a work of genius. In order to appreciate the beauty of an elegant proof, one must be well versed in the language of Mathematics. It is hard to appreciate (or like) something that one does not understand.”

Mr. A: “Wow! this is all very interesting. I’ve never thought of Mathematics in this manner.”

(Prof. C arrives at the coffee house and joins the others. Mr. A mentions what the conversation is about.)

Mr. A: (looking at Mr. G, who appears to be lost in contemplation) “You’re awfully quite there Mr. G. Bored by our discussion perhaps?”

Mr. G: “No, not at all. My apologies if it appears that way. I have been listening intently, yet I fail to see how viewing Mathematics as a language helps us with the apparently incomprehensible equations that we encounter in books. Would someone be so kind as to enlighten me on the matter?”

Mr. A: “Good point. Professor T?”

Prof. T: “The point I wanted to make is this: Mathematics is just like any other language; one must start with the basics. It takes time and effort to familiarize one with the syntax and semantics, the grammar and vocabulary. It may be a slow and tedious process, but eventually one reaches the level where seemingly complex equations do not pose any significant challenge. Also, the more one works with pure Mathematics, the more one appreciates the elegance and beauty of abstractions. A lot of us never get to experience what pure Mathematics is about. And perhaps that is the reason why it all seems so inaccessible.”

Mr. G: “I think I get your point. It is indeed encouraging to see Mathematics as just another language. Nevertheless, I feel that there is something about Mathematics that makes it a lot more challenging than just another foreign language. Sometimes I find it hard to comprehend even the basic concepts.”

Prof. T: “Ah, you’ve stumbled upon yet another characteristic of language that we often overlook. In certain languages, there are phrases, idioms, proverbs etc. that cannot be translated into other languages. These often have contextual relations to the culture associated with the language. Unless one understands the culture, such language constructs hardly make any sense at all. A major difficulty in Mathematics stems from the way of thinking it requires. It makes us step out of a certain comfort zone, and think differently. Consider the concept of visualization. We often find it easy to understand structures and objects that we can visualize. In Mathematics, this isn’t always possible. E.g. due to our limited sensory perception, we can only visualize structures in three dimensions. Abstract mathematical structures are often explored in infinite dimensional space. To be able to understand the concept of infinite dimensional space requires a new way of thinking. One must develop it over time.”

Mr. A: “So what should I do in order to pursue my passion to understand and unravel the mysteries of the universe?”

Prof. C: “Professor T, if you don’t mind, may I respond to Mr. A’s question?”

Prof. T: “Oh please. Go ahead.”

Prof. C: “First and foremost, take a deep breath. Do not let your passion consume you. Do not let it transform into frustration. You must find a way to channel it towards a productive outlet. Mathematics is a very broad field of study. It might be wise to start by identifying the branch of Mathematics that is the most important to you at this point. You must then build the vocabulary and learn the rules that govern your target field. Once you are fluent in one branch of Mathematics, you’ll find it much easier to learn the others. And so will begin your journey into the world of the abstract. It is a long road, I know. But trust me, it is definitely worth the time and effort. Persistence and perseverance are the key ingredients. It will open new doors for you, and make it possible for you to understand the workings of the universe; from fundamental particles to life, and from this world to the cosmos. It will be a liberating experience.”

Mr. A: “Oh, this is wonderful. I can already feel the power of Mathematics. I am so glad we had this conversation today. Professor T, Professor C, I must thank you for providing me with the insight and encouragement I needed at this point. I’ll start right away.”

Mr. G: “The spirit of Mathematics has been rekindled in me. Mr. A, I think I’ll join you. We share the interest in understanding the cosmos. Perhaps it would be a good idea to collaborate?”

Mr. A: “Certainly. Let’s head to the library and see where we must begin.”

---

"Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever." ~Albert Einstein

On Gravitons, Connections and The nature of Mathematics - Reflections on a plausible purpose of Life

Is there a purpose of one's life? If so, does the purpose vary from person to person, or is there a single purpose shared by all of human kind? Or is life perhaps just a Darwinian accident without any purpose whatsoever?

While you ponder over these questions with profound implications, let us take a detour. Our brief journey starts in the realm of theoretical particle physics, takes us along into the world of mathematics, and back again to the questions you are pondering over somewhere at the back or your minds. So lets begin, shall we?

The force of gravity is something we are all familiar with. It is the force that pulls us towards the center of the Earth, and enables the Earth to maintain its orbit around the Sun. The same orbit that determines the journey of our planet around the Sun can also be perceived as something that connects the Earth and the Sun. Through the force of gravity, the two objects have been bound to each other in a connection that has a life time in billons of years.

It is a hypothesis that a particle called the Graviton is responsible for the force of gravity i.e. the Graviton is a force carrying particle for the force of gravity. Another hypothesis that comes from String theory postulates that there may exist more than the three dimensions of space that we can perceive in our everyday life. A beautiful conjecture connects these hypotheses by stating that Gravitons may possess the capability to travel between our 3-dimensional space, and the space of higher dimensions. The leakage of Gravitons from 3-space to higher dimensions is the reason why gravity is the weakest of the four fundamental forces.

Mathematics deals with abstractions. These abstractions have no physical existence; it is as if the abstractions reside in a separate dimension. Yet, it is these abstractions that are applied to numerous phenomena in the physical world, resulting in accurate calculations that support modern technology. Moreover, these abstractions also serve to find common grounds between disparate sciences. In a way, mathematical abstractions are like Gravitons; they can move freely between the world of abstractions, and the physical world (perhaps with slight differences in manifestation), creating connections.

In Mysticism and Logic, Bertrand Russell wrote:

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."

Does this not stand true for the inner beauty of a human being as well? Perhaps the very nature of mathematics tells us something about the purpose of our lives?

On humans, currencies and emotions

Mr. A: "Which is the strongest currency these days?"

Mr. G: "It must be Euro, although there might be a temporary set back due to the current European debt crisis."

Prof. T: "There is one currency that is always the strongest. It never fluctuates with time, economic situation, or for that matter any other material factor."

Mr. A: "Professor T! Could you please elaborate a bit? I cannot imagine a currency so stable."

Prof. T: "The currency I am referring to is Emotions. "

Mr. G: "Excuse me??? ... How can you consider Emotions as a currency? What do you buy with Emotions?"

Prof. T: "Well, let me explain it to you. The nature of currency and its utility lie in the fact that it enables you to quantify cost. Do you agree?"

Mr. A: "Yes."

Mr. G: "I guess."

Prof. T: "Now, you have to ask yourselves; what is the most important of all human needs? ... I would say it is social contact i.e. relationships of all sorts. And what is it that you invest in a relationship? ... Emotions! ... It is an emotional investment. It incurs the highest of costs, and emotional bankruptcy proves the most challenging in terms of recovery. It has always been the staple currency for all of mankind."

Mr. A: "But Professor T … one’s emotional state varies from time to time. How can you then consider Emotions as stable?"

Prof. T: "Ah, but an individual’s emotional state is not analogous to currency. A shift in the emotional state of an individual does not alter the value of Emotions.  The significance of Emotions remains the same for all of humanity regardless of what an individual may experience. And it is this stability that I am referring to."

Mr. G: "But what of Economics then? How would you relate this to Economics?"

Prof. T: "Economics is a science of the artificial. It is a humanly creation that interposes structure and order into the fabric of society. However, it is one of infinitely many possible solutions to introduce order into chaos. Emotions on the other hand emerge from the complex interactions within biological and physical processes that befall the human mind. Emotions dwell at the highest branch on the evolutionary tree. They are the work of nature; they make us human. If you look closely, you might observe that emotions play a significant part even in rationalizing Economics i.e. perhaps Emotions are responsible for our understanding of right and wrong; profit and loss etc."

Mr. A: "hmmm ... But do you think the general populous perceives the significance of Emotions in the same manner that you do?"

Prof. T: "Oh, you have asked one tough question there; I must admit. I honestly do not know the answer with any amount of certainty. However, my observation is as follows: with any hierarchical design that utilizes multiple layers of abstraction, the only link between two non-adjacent layers is the layer that lies amidst them. As a result, only adjacent layers are visible to each other, even though they do not provide each other with the whole picture. I think technology today, to some extent at least, serves as a sort of layer between human interaction. While the true currency is Emotions, they are not as discernable since the technological layer is what we really see. The mediative role of technology appears to accentuate technology itself, while at the same time trivializing Emotions. Perhaps this is one of the reasons why we feel more attached to gadgets than fellow beings."

Mr. A: "I see. So what do you think is the solution?"

Prof. T: "I am not even sure if there exists a problem to begin with. I have merely presented my perception of reality. Yet, how am I to judge what the true nature of reality is? ... It all appears to be a matter of perspective, point of view, and the angle of observation. After all we are limited in perception by our senses."

Mr. G: "Perhaps."

Mr. A: "Some food for thought at least."

Prof. T: "I must take leave now. Beethoven is playing the electric guitar today … I hope he is in some Universe :-). See you guys later! ... Chao!"

Mr. A: "Tschüs!"

Mr. G: "Hej då"

On Kindness, Experience and Mentoring - A Sojourn in Sweden

"Kindness is the language that the deaf can hear and the blind can see" - Mark Twain

The very first encounter with Swedish Kindness

In the August of 2006, I boarded a plane to Copenhagen with a couple of friends. All three of us were headed towards a small town in Sweden, called Ronneby. The intention was to pursue graduate studies at the Blekinge Tekniska Högskola. We had different programs of study in mind; in my case, it was Artificial Intelligence.

If I remember correctly, it took around 9 hours or so before we landed in Copenhagen. As relieved as we were to have reached Copenhagen, we were soon to find out that the last train to Ronneby had already left. It was about 9:00pm, and there were no more trains until 6:00am the next morning. Tired and perhaps a bit frustrated, we found a few vacant benches and decided to settle down for the night. Since we had a lot of luggage with us, one of us would watch the luggage while the other two would catch some shut eye. But as always, time passes. And soon it was time to board the train.

The train took us from Copenhagen to Malmö. We took another train from Malmö to Kristianstad, and then finally a bus from Kristianstad to Ronneby. On this bus is where we first encountered the kindness that we would later learn is a cornerstone of the Swedish culture.

At one of the stops on the way, a passenger boarded the bus. He took a seat across the aisle from where I was seated. Without wasting any time, he took out his laptop and started working. After about a half hour or so, one of my friends decided to ask him how far Ronneby was. To our surprise, this simple question triggered an interesting conversation about the University and studies. That passenger was a faculty member at the Blekinge Tekniska Högskola.

Finally, around 9:00am or so, we arrived in Ronneby. We had quite a bit of luggage and no idea how far and in which direction the University campus was located. The professor made a few calls to check which bus route would be the most feasible for us. After spending a few minutes on the phone, he realized that none of the bus lines were going towards the school anymore. So he called a taxi for us. He waited with us at the bus stop until the taxi arrived, informed the taxi driver where to take us (since none of us could speak Swedish), wished us good luck and took off to the university on foot (as per his routine).

I can understand that it might not be possible for all the readers to grasp the significance of this particular event. To me, however, this act of Kindness made an ever lasting impression. Almost five years have passed since, but I still remember this event as if it happened just yesterday. I hope that someday, I can extend the same kind of help to someone.

The “Do it yourself” and “All are equal” principles

The semester started about a week after we arrived in Ronneby. Now everything was about studies. Even though the faculty was very helpful, there was something that made the studies feel quite tough. I did not realize this at the time, but it was in fact a combination of two specific aspects of the Swedish education system, which were significantly different from the system I was used to.

Perhaps the most important factor was what I like to call the “Do it yourself” principle. A standard lecture appeared to be a mere attempt by the lecturer to guide the students in the right direction. That's it! … No spoon feeding. I think we were used to spoon feeding; studying to score high on the exams, rather than studying to actually learn and apply the knowledge. The stark contrast in the systems made the initial learning curve quite steep, but thankfully, I was able to adapt quite soon. Then onwards, I could only appreciate how vital the “Do it yourself” principle is in enhancing the student's learning capabilities. I think it makes everything seem possible, and the fear to explore unchartered territory is significantly reduced. This of course is not to deny the significance of good teaching. What I am trying to say here is the following: It is always wonderful to have good teachers. It helps a lot. However, the fact remains that very few teachers actually qualify as the great ones (unfortunately though). Therefore, the ability to learn difficult concepts without a teacher's support can be a valuable asset for the student.

The other significant difference in the education systems is in fact more of a cultural difference. In Sweden, one always addresses a teacher by the teacher's first name. Regardless of whether the teacher is a doctoral candidate, an assistant/associate professor or a professor; there are no titles and no formalities. Students pretty much consider the professors as peers and vice versa. Initially, this was too strange for me to understand. I was coming from a culture where the teachers are always addressed using their titles, and (in general) the teacher is always right :-). But only after a short while, I could see how productive the Swedish system was. Once you eliminate the extreme formalism, the interaction with the teachers becomes highly productive. Arguments and (constructive) criticism are highly appreciated, and for students who are genuinely interested in learning, there are endless opportunities. It is just wonderful!

For the next couple of years or so, I was a studying Artificial Intelligence. During this time, I received extensive support and encouragement from the faculty to pursue my passion for Robotics and Machine Learning. I had never enjoyed the process of learning to this extent. This was a wonderful two years.

Professional life and Mentoring

Prior to arriving in Sweden, I had been working as a Software Developer for a couple of years. It is not uncommon to find very strict implementations of hierarchy in the industry there. This hierarchy is generally based on experience. E.g. employees further up in the hierarchy are the most experienced. There is a clear distinction in the way one interacts with the senior colleagues, as compared to the interaction between colleagues at the same level of hierarchy. In certain cases, this can result in counterproductive group dynamics. This is particularly true when the senior employees have more of a bossy attitude towards the junior colleagues. This is certainly not the optimal configuration. Nevertheless, there is an upside.

So let’s take a look at the positive aspect of the hierarchical system. I'll get straight to the point i.e. experienced colleagues implicitly take the role of mentors. There is a pervasive culture of mentoring, where people take pride in sharing information with the less experienced peers. This creates an environment where the less experienced employees are expected to learn from the more experienced colleagues. I find this particularly beneficial for fresh graduates when they join the industry straight out of the school. In fact, at the company I used to work for, we even used to design learning programs for the newly hired colleagues.

Alright, so let’s get back to life in Sweden :-). In October 2008, I started as a professional software developer in Karlskrona. This was right after finishing my Masters studies. I was now working at a large multinational organization, where there is no concept of considering the difference in hierarchy while interacting with senior or junior colleagues. Employees interact with each other without regards to the difference in hierarchy. Everyone is considered equal, and no opinions are suppressed. I was working with much more experienced colleagues. And yet, we were all working as part of the same team, and working at the same level. This felt great!

The overall experience has been fantastic. I learnt a lot, and met some wonderful people. Everyone was nice and helpful. It was just so much easier to enjoy the work. I think the "all are equal" principle makes things simpler, resulting in increased productivity. Yet, there is something missing. What's missing is the concept of mentoring.

In my opinion, there is just no alternative to experience. There is a certain wisdom that one only accumulates over a period of time. This particular significance of experience is put to use by appointing senior employees to the key positions. This is very much so in Sweden as well. Therefore, one can safely state that the significance of experience is in fact realized in the Swedish industry.

So what of mentoring? When everyone is at the same level, it becomes very difficult for one of the colleagues to take the role of a mentor. Every interaction becomes a discussion between peers. Junior colleagues do not yearn to learn from the experiences of the senior colleagues. I think this is where the concept of "all are equal" becomes a little bit counterproductive. I am not suggesting that senior colleagues should be bossier :-) … not at all, that is certainly not what I would appreciate. However, there should perhaps be a way for senior colleagues to impart wisdom, to share the knowledge they have acquired through all the experience they have. I believe this would further increase productivity.

And soon it was time to leave

Sweden is an absolutely wonderful place. As much as I wanted to stay, I had to move on. And as much as I miss living in Sweden, life goes on. The sojourn in Sweden has been a very special one in many ways, some of which are perhaps quite apparent from what I have said so far. Yet, there is so much more to say; and perhaps I will some other day :-).

Natural selection, economics and coincidence

It is quite a wonder that at times a good book can be as interesting a companion as a fellow traveler with whom one enjoys having conversations. Even though I had enjoyed reading books while traveling before, Easter holidays this year brought along a very special experience (an interesting observation here: even though a considerable population of the homo sapiens tends to grow uninterested in the spiritual world, it is as if religious events sometimes  bring certain  blessings; “Coincidence”?) . I decided to spend the holidays with a dear friend in Düsseldorf. The companion I chose for the journey was “The Selfish Gene” by Richard Dawkins. Having already read the “The Origin of Species” by Charles Darwin, I must say that it was a delight to understand evolution by natural selection from the point of view of the gene. By the time I reached Düsseldorf, I had only been able to read through the initial chapters that introduce the ideas of genes as replicators and bodies as gene machines. I had no idea what was coming next.

During my stay in Düsseldorf I put the book aside since most of the time was spent on site seeing and discussions. At one occasion while we were talking about energy trading and economics, at the back of my mind I began to wonder whether energy trading could be seen in the light of "Game Theory". However, the discussion moved on to other topics and I did not give it much thought. Soon, it was time to leave for home.

At the airport, I continued reading from where I had left and to my surprise the next chapter was about the application of game theory to evolution by natural selection. This is what we now know as “Evolutionary Game Theory”, put forward by Maynard Smith. Introduced in the same chapter is the concept of “Evolutionarily Stable Strategies (ESS)” (a concept from the evolutionary game theory) on which rest of the book relies heavily.

As wonderful as the experience of reading “The Selfish Gene” has been, it did not come without stimulating a myriad of thoughts in my mind. Some of these I have managed to streamline and would like to share with the reader. The book is based primarily on and extends Darwin's theory of evolution by natural selection. It is no doubt a brilliant effort at explaining the origin of species. However, I have come across certain issues resurfacing throughout the text that I find hard coming to terms with. In the following bullets, I try to tackle them one at a time.

• "Coincidence is the last refuge of the uninspired": I have not been able to authenticate the source of this very interesting quote, yet it makes a lot of sense in terms of statistics. Coincidence can be defined as, "a statistically possible yet highly unlikely event", or an anomaly perhaps? Yet, at the heart of the idea of "The Selfish Gene" lies the theory of evolution by natural selection; which in turn is built on a foundation of coincidence. One might wonder, we so arrogantly believe in coincidence (in the particular case of evolution by natural selection) that we do not wait much long to ridicule the concept of the existence of a supreme being; and yet we take pride in calling ourselves rational and scientific ... irony? (Please note here that peer reviewed articles published in scientific journals go through a very thorough process of evaluation in order to ensure that the experimental results bear statistical significance)
• Speculation and the scientific method: The fundamental message conveyed by the text appears to be speculative rather than scientific. One very interesting example appears in the last chapter where the author uses a sentence construct like, "This theory is testable, thought it hasn't been tested yet." which then connects to the sentence, "If I am right about ...., it follows that". Should this not be considered a fairly week argument in the light of the scientific method?
• The kaleidoscope of the sciences of the artificial: As mentioned earlier, the concept of evolutionarily stable strategies is an application of game theory to the theory of evolution by natural selection. Now, game theory (or economics in a broader sense) is one of the “Sciences of the artificial”. This would mean that economics is fundamentally a man-made tool. In essence, when we apply economics to explain the origin and function of life, what we are doing in a broader perspective is enclosing the phenomena of nature in the bubble of scientific progress made by man so far. We try to explain something using what we know, and we completely discard what we do not know. Are we so sure that we know of all there can ever be, that we shut the door to the existence of any other possibilities? It is as if history is repeating itself; as if we are back in the time when Galileo’s idea of heliocentrism met with bitter opposition. Are we not supposed to be open minded?

  The question of the origin of the life can perhaps be viewed from a different yet interesting perspective. Let us consider this problem as an optimization problem. We have an infinitely large search space consisting of all possible explanations for the origin of life. Wouldn’t natural selection be one of the possibilities and most likely a local optimum in the search space? Would it not be wise to continue the search in other directions and look for other possible explanations?

•  The gene and the cosmos: Let us take a step back from the theory of evolution and try to evaluate the place of the gene within the universe. The origin of life is a phenomenon known to have occurred only on the planet Earth. What about the rest of the universe? How did it come into being? These are the questions that have consistently been challenging some of the brightest minds in cosmology. To me it sounds as if the question of the existence of a supreme being is rightfully tackled by cosmology due to the much broader scope of the field. If we analyze the theory of evolution by natural selection in this perspective, does it not challenge the completeness of the theory if the sole focus is on the origin of life without considering the events of the cosmos? I would like to quote “Roger Penrose”  here: “There is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. Some people take the view that the universe is simply there and it runs along–it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment.” On a different occasion he said, “there is what can be called a Platonic world beyond the material world that "contains" mathematics and other abstractions”. My interest in sharing these quotations is merely to bring to the readers attention, once again, to the point that we are very limited by our senses. Our perceptions are constrained by the capabilities of our sensory organs and our nervous systems. What if there is much more to be perceived, only we do not yet have the ability to understand it?
• Existence of God and Ockham’s Razor: The 14th century English logician, William of Ockham presented a principle that is often quoted in a simplified form as, “The simplest explanation is usually the best one”. Applying the principle to the question of the origin of species, what would be simplest explanation; the existence of a supreme being or evolution by natural selection?

Having stated all that, I would like to bring the reader’s attention to the heart of this discussion. The purpose of this criticism is not to encourage a debate about the existence of God, or to defy atheism. The objective here is to highlight the fact that be it science or religion, when used with a political bias, it tends to incline towards extremism. As I understand it, the grand objective of science is to uncover the truth; and the curiosity and search for this truth is what has driven the scientists for centuries to make the most amazing discoveries that we know of today. Let us find a middle ground where our efforts are focused not on argument for the sake of argument, but rather on the search for truth.

Finally, I would like to conclude by sharing this excerpt from the Nobel lecture by "Sydney Brenner": 

“... there are many aspects of humanity that we still need to understand for which there are no useful models. Perhaps we should pretend that morality is known only to the gods and that if we treat humans as model organisms for the gods, then in studying ourselves we may come to understand the gods as well.”

And so it begins …

It has probably been over a year since I started thinking about organizing random thoughts in a manner that would not only make it possible to express them; but also aid in the process of  sharing them with peers. My hope has been to express freely without requiring scientific rigor, yet discussing science and other subjects of daily life in a fairly simple manner. Also, a blog would hopefully spark interest in readers to comment on the posts, thereby enriching and/or critiquing the stochastic thoughts.

Tonight, I feel that I am finally ready to commit to a frequent contribution. And so it begins …

The title of the blog basically encapsulates the major areas I intend to write about. Brains – neural science, Machines – computer science and artificial intelligence, Mathematics – well, the mother of all sciences, and Life – all the various aspects of life including sociology, religion, music and numerous other things that just popup in my head from time to time.

I cannot in good conscience leave out the most significant inspiration behind the title; the book “Brains, Machines and Mathematics” by Michael A. Arbib. The moment I saw this book in the university library, I knew I had to read it.

Apart from the major areas highlighted by the title, I will hopefully be writing about several other interesting topics that I come across. Since by profession I am a software developer, I like to think about issues pertaining to software engineering and development. Also, I am highly fascinated by the theory of complex adaptive systems and other biologically inspired methods.

Having said that, I will move on to a couple of questions that have been bothering me all day long. I will not indulge into the details at the moment, however, a brief description is as follows:

• Boolean logic, Fuzzy Logic, Temporal Logic … “Emotional Logic”? – Would it ever be possible and/or useful to develop a formal model of human emotions, that constitutes a form of logic where truth is ascertained by the emotional state of an individual rather than the conventional models of logic?
• Validity of mathematics as the language of proof – All major branches of science use mathematics as the language to definitively devise proofs. Can we prove that mathematics is the one perfect language for proofs? and what if it is not? Oh, by the way, what language would we use to prove that?

This is a glimpse of what some of the posts might look like. With time, however, I hope the ideas and the posts will evolve in such a way that the variety of topics increases and more and more readers find it interesting to share their ideas.

A word to my friends: please feel free to comment, for that will be a very valuable contribution.