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Computer & Science \(-\) I

Posted on April 26, 2022

If you glance at the end of this article and think about what Newton and Descartes were saying, the message appears to be bleak. They are cautioning us by saying \(``\)Don't be so sure,\("\) which is surely not a very encouraging outlook to adopt if you want to lead a productive life. Ambiguity begets confusion, and confusion erodes the chances of achieving excellence. However, even Weinberg<sup>1</sup> says, \(``\)I don't think we'll ever be certain about any of the scientific explanations we have announced to be true. But you give up worrying about certainty when you make that turn in your career that makes you a physicist rather than a mathematician.\("\) We could also translate the majestic duo's message to imply, \(``\)Maintain a healthy amount of scepticism.\("\) Moreover nowadays, since most STEM disciplines draw upon probability theory so heavily, Weinberg's observation about viewing everything with a stochastic or probabilistic lens would be true² for anyone working in STEM today.

One way to distance ourselves from such feelings of uncertainty while looking at the big picture is to simply follow some giant (or giants) from some walk of life unreservedly. Another compelling technique to deal with the randomness of the real world is to begin by considering simple thoughtful questions in search of commonsensical answers. Let us say we want to know what affects us the most in the present times. Answers like the sun, oxygen gas, liquid water and others like that do not count because all of these have been crucial to us since our genesis and even before that.

So, what is it that affects us the most today?

The computer, right?

One could list down all the potential candidates and then do a pros & cons analysis at this point. But on the face of it, the computer and all of its accompanying technologies are most liable to be blamed for everything today. One need only look in their vicinity to find themselves surrounded by all kinds of computing devices! Even Koestler warned us about \(``\)the new Baal, lording it over the moral vacuum with his electronic brain.\("\)

Anyone who has been involved with the STEM community, even indirectly, realizes that coding holds such a major sway over researchers that without being able to code, there would be a very little amount of meaningful research left to do in most STEM disciplines. Most of the relevant low-hanging fruits have been snatched already. For any STEM researcher, words like Python, Matlab, Julia, and R (and also the things they represent) have become part and parcel of their lives.

That begets the question: what is a computer? Let us focus on answering this by keeping in mind the non-CSE crowd because the CSE people\(-\)they have been knowing about the new Baal for quite some time now.

First, there is the point of view that comes from the automata theory. But as the name suggests, it is quite a theoretical perspective and not easy to digest even for CSE graduates who lack a theoretical bent. The theory approaches the question of rigorously defining what computation is in the most abstract sense. Kurt Gödel and Alonzo Church made seminal contributions and there is a very interesting history behind their feats: how Lobachevsky and Bolyai rather to the disbelief of everyone came up with hyperbolic geometry (this was a stupendous feat because it was so unexpected) followed by Riemann and Levi-Civita ushering in the mind-bending era of Riemannian geometry. Euclidean geometry is what we are taught even today in schools, but now some mathematical wizards bring to us this magic of curved geometries that will start challenging all of our meticulously curated Euclidean-Cartesian-Newtonian intuition developed over several centuries! And then David Hilbert and his followers waged an intellectual war against the so-called Intuitionists raising the feared specter of consistency, completeness, and decidability. Enter Gödel, and then we know how he slew these demons (especially the last two) or did he! Maybe the average STEM person had already been knowing about these demons intuitively but was unable to articulate well about them, and all Gödel had done was to vividly resurrect these vertigo-inducing demons.

Subsequently, Turing proposed a tape machine along with all the abstract paraphernalia that was later recognized to be the theoretical abstraction of modern computers. A computer could most simply be described as a machine that can simulate any coded piece of logic. Turing's work is what majorly provided the pretext for establishing CSE departments in universities across the world. The discipline of CSE rose to investigate Turing's automata ideas more deeply (if that were possible, and most curiously, it turns out that it is) but CSE's pursuits later became more concrete by focusing on coding efficient data structures and incorporating the study of algorithms from operations research until the present times when it's mostly AI and ML these days. Even the foundations of ML were laid in the Statistics department for tabular data, but we equate ML with CSE these days because CSE with the help of huge funding from Tech Giants started probing such techniques for image data (computer vision) and even text as well as audio data (natural language processing).

So, is the journey suggested by Turing's ideas the one on which a serious non-CSE STEM enthusiast must embark to understand computers? Turing's approach is difficult and requires too much time investment. Pecuniary investment is one thing to ask for and can be digested for the most part but to ask someone to invest their most precious commodity is too much to ask for! Nobody will counter the fact that we need to understand computers given that they influence our daily lives so significantly. But the Turing approach may only suit the mathematical types. Handling abstraction is not everyone's cup of tea. Doron Zeilberger makes a very potent argument for rubbishing Turing's extreme levels of abstraction (can any level of abstraction be extreme compared to Grothendieck!). Reading his terse insight can be very helpful. After all, the golden wisdom of our times says that the universe is finite, so the higher purpose of considering an infinite memory capacity does not strike us, at least not immediately even if there is one! But one must remember that even Newton's writings have unimaginably managed to get themselves attacked as being naive by polemics or those who did not realize the advantage of accrued civilizational insights due to centuries' worth of painstaking scholastic labor. Recall that Tikhomirov said: \(``\)It can happen that the thought of a genius, which we regard as a mistake carries within it the imprint of truth — a truth clear to him but hidden as yet from us.\("\) And the universe is discrete (another golden wisdom of our times), or as Stephen Wolfram and a large section of researchers seem to be more precisely saying, the discrete algorithmic way of understanding the world is the right way. Even in quantum mechanics, the assumption of discrete quanta is the most fundamental. So, Turing deserves a lot of credit for propounding a discrete theory of computation, which might be the only evasive piece of the puzzle we were looking for, having found which may now truly propel discrete mathematics into helping us fully understand everything. And observing the modern trend of using the concrete avatar of Turing machine, the computer, to do science only reinforces the belief that developing an airtight final discrete theory of computation followed by rewriting physics in its new language may be the only perfect way to understand reality. And I think that the coding-intensive research being carried out by the Wolfram Physics Project is doing just that. Wolfram has assembled a remarkable team of promising physicists and computer scientists who have been championing the cause of using computer simulations to explain everything about the universe. However, when all is said and done, Turing's approach is not suitable for mere enthusiasts who lack TCS expertise.

So, is there another more suitable way to understand computers?

Most of us must have heard on the grapevine, through the blogosphere or during the seminar talks that great inventions happen not at the hands of theoretical scientists but those scientists who are more interested in the engineering world, who want to build even if they don't fully understand what it is that they are building\(-\)the real doers of the STEM world. So, if Turing had not given us the abstract theoretical model of modern computers and even Gödel's and Church's proofs were missing, still all the computing devices we see today would have materialized. You may have also heard that all the advances in semiconductor electronics and semiconductor nanotechnology would have taken place even if there were no quantum mechanics to explain the Schottky barrier and other cognate concepts more fully. We would still have stumbled upon the MRI scanner by tweaking and tinkering here and there even if there were no quantum mechanics to explain the complicated phenomenon of magnetic resonance. Never underestimate the imaginative power of a genuinely talented engineer. These doers and makers of the STEM world are the ones mainly responsible for lifting us from physical misery and bringing us all into the paradise of material comfort, albeit obviously facilitated greatly by the necessary assistance provided by the powerful Governments and MNCs.

The crucial factors that led to the invention of computers are well documented by Walter Isaacson. In a nutshell, neither without the tenacity of Shannon (of AMTC fame) and von Neumann (of EDVAC fame) nor the semiconductor electronics work done at the mythical Bell Labs pioneered by Bardeen, Shockley, and Brattain, would we have had the computers. Nevertheless, all the theorizing done by Gödel, Church, and Turing plays an important role in certain philosophical ways, one need only refer to the Nobel Laureate Roger Penrose's ENM book, especially the consciousness question raised there, which comes up when trying to distinguish between computational intelligence and human intelligence.

So, should the non-CSE STEM enthusiast who has an interest in learning about the new Baal switch to this second option? Seems so, because you have to ask: would understanding Turing-Gödel's theory help you to figure out how your laptop or smartphone works? Definitely not! Would laptops and smartphones still have happened without Turing and Gödel developing their cleverly abstracted rigorous theory? Surely yes! This is not to say that understanding the abstract theory of universal computation will not pave the way for a robust understanding of what computers are, but the main question is whether it is the most crucial form of understanding that one may gain about the computers or not. Who is to say that knowing these abstract theories without knowing how to design semiconductor chips that help our computers make logical decisions is not a bigger folly!

But again, this hardware thread is quite challenging to pursue unless you spend a lot of time in the electrical and electronics engineering departments which we cannot expect of the average STEM enthusiast. Most of them would have only opted for the PCM track in schools and that's it\(-\)but they were bright, understood whatever basic knowledge they could learn from their elementary science textbooks, and had gotten a spark of scientific curiosity ignited in their minds to be sustained for the rest of their lives. Moreover, simply listening to lectures about MOSFETs and diodes without having access to labs with a considerable amount of infrastructure that the Bell Labs and the Intel headquarters could boast of, let's say even as far back as the 1960s or 1970s, may turn the whole exercise into a pointless activity. Most STEM enthusiasts will never be able to obtain that kind of access. Take, for example, all the school students who when they read about atoms and cells have a burning desire to see these things with their own eyes. How many of them ever do! And when such practical constraints are not applicable, then usually intellectual constraints kick in. For example, and this is a pretty tangential example only to be taken in an allegorical sense, if one wants to understand topics at the frontier of relativity theory, one needs to learn Riemann's elliptic geometry and if one wants to understand topics at the frontier of quantum theory then one needs to learn von Neumann's functional analysis, both of which require at the bare minimum a concerted and singular devotion of the profesional kind. So anyway, the point being made is that this hardware approach along with its subsequent mapping to the computer architecture is very concrete and practical but is untenable for someone outside the EEE domain just like the previous approach is quite inaccessible to anyone outside the CSE domain.

Does that only leave an inquisitive mind with the option of falling back on pop-science (through sources like YT, Twitter, and stellar websites such as Quanta Magazine or Big Think) for such answers? Should the average STEM person restrict themselves to only coding in programming languages rather than thinking about the device that the computer actually is? Aren't the supervisors in workplaces always asking us to not reinvent the wheel? Well, of course their motivations are different and have to do more with obtaining more profitable work in a given amount of time. However, it appears to be the case that pop-science is the last resort in this ever-complexifying world of ours, at least good quality Gould-type pop-science. But will that be enough to satisfy a STEM person looking for more serious answers?

Anyway, let us reconsider the position of that middle-aged STEM enthusiast willing to understand computers. Also, I am assuming that enrolling in a degree-based continuing education program at a good CSE or EEE department is out of the question. Then according to me, that pretty much only leaves the option of turning to the Knuthian Bible³, his TAOCP! He provides an algorithmic way of understanding computers as opposed to the theoretical and hardware approach. Even if the later volumes are incomplete, for all practical purposes, the first volume should suffice to get a deeper understanding of a computer. It mostly shares the data structures and algorithms point of view which should be good enough because after all, a computer is just a machine engineered to code algorithms. This masterpiece treats the computer from an algorithmic perspective which seems more appropriate to do. Knuth begins by carefully explaining what an algorithm is and then demonstrates how the mathematical analysis of an algorithm can be performed. Then he introduces a simple machine language called MIX and ends by elegantly explaining the massively important tree data structure⁴ against the MIX backdrop. I believe that this book though serious (even intimidating in some ways) should be accessible to anyone related to the STEM community in a professional capacity even without having any CSE/EEE affiliation and should help in demystifying the new Baal. There is another equally (or maybe even more) appealing way to appreciate computers via Chaitin's AIT but that is beyond the present scope. Moreover, TAOCP constitutes a more straightforward, more classical and more comprehensive approach, hence it must be given the higher preference.

However, returning to the original question that was posed, is the computer really that which affects us the most today? Remember, the question was what really affects us the most today, in the most sobering sense. The answer keeps starkly staring us right in the face despite its abstract nature obscuring it from our view at first glance: what other than Science. One might still think of other things (such as that usual trifecta of technology, money, and government—TMG) that may seem to be more in control of our present-day affairs, but providing good refutations for those is beyond the scope of the present essay. One simple heuristic argument that may suffice for the trifecta is that the importance placed by society on all the three grows in tandem with society gradually getting more and more comfortable with the adoption of a scientific outlook to manage all its affairs. For now, we shall stick with \(``\)science\("\) and maybe we could make this answer even more precise by saying that the thing that affects us the most today is the knowledge obtained as a result of scientific pursuits because it is this knowledge that truly has the immense transformative power; that knowledge being the root cause for the creation of modern scientific/industrial society. As Koestler had pointed out, \(``\)Within two centuries it transformed the mental outlook of Homo sapiens.\("\) The crucial concept of Society has now become a recurring theme in modern science. It has even garnered a lot of attention from mainstream physicists that would have been unthinkable only a few decades ago.

One may then ask⁵ what knowledge is. A simple way to understand knowledge is to think in terms of data. Everything that your mind perceives that your sense organs are collecting is data. Everything that your sense organs assisted by your brain can acknowledge is data. Within this unlimited landscape of data, the portion of data that surprises you is information. The cause of surprise may be an opposition expressed by that data to the views you were holding about the world; your mental model of the world has been challenged. More challenge the data poses to your mental model, the more informational it is. But this informational content of data includes both signal and noise, and when you extract the signal and synthesize it with your existing knowledge, this assimilation updates your knowledge. Nassim Taleb's words that \(``\)knowledge is subtractive\("\) ring very true in this context. Now a lot of filtering needs to take place to get rid of the noise. The cerebrum in Homo sapiens probably became more specialized by the process of natural evolution as compared to other primates in order to excel at exactly this sort of filtering activity. Of course, there is a whole host of things the cerebrum excelled in but in the present context, the cognitive process of attention is what is being alluded to. And a good way to get a feel for this process is to draw parallels between the above-mentioned process and that moment when the antenna receiver of a retro CRT television fails to catch a signal and then that classic grainy static noise appears on the screen. Well yes, I am hand-waving at this point because delineating the extraction of knowledge correctly from information is very challenging and not well understood. If someone were to show you an isolated human brain preserved in formaldehyde, then would you be able to find someone to specify exactly how is it that this device in some living hosts excels so particularly well at manufacturing knowledge? My cursory suggestion here is that the sensory data first undergoes certain preliminary analysis. Then upon deciding whether the data is informational or not, a second phase of thoughtful (or critical) analysis may begin that results in the extraction of knowledge from information; the former is probably not consciously done whereas the latter must be a conscious process. The act of naively producing knowledge would make use of a hybrid mixture of the concerned signal and noise resulting in adulteration. Beware of adulterated knowledge as not knowing is far better than to know wrongly. It is only through excessive training and long experience (note that I skip the mention of intelligence as a factor here because it does not seem to be in short supply any more as society is doing something right about this — most likely the internet-powered interconnectivity and free flow of information and even knowledge — otherwise intelligence would also become a limiting factor) that one's ability to generate knowledge could be trusted by others. Therefore, the knowledge-building process has to be a collective and specialized effort.

In light of this Darwinian evolution that created modern human brain, there is no denying the incontrovertible biological evidence that the primary purpose of the Homo sapiens species⁶ must be knowledge-building. Buckminster Fuller would call that \(``\)the important cosmic responsibilities for which humanity was designed.\("\) Even the name \(``\)Homo sapiens\("\) means knowledgeable man. Fuller laments that our species does not seem to understand the purpose of our evolution and just to contrast how much importance we should place on the prefrontal cortex (PFC), he compares our muscle power to that of a grasshopper signifying that nature did not care about these other factors while evolving our species, so out of gratitude for Nature we must always be willing to focus our attention on improving the collective mind or what is equivalently the collective knowledge. Therefore also, a better mode of thinking is significantly more concerned with natural truths rather than man-made rules most of the time. This is one of the main signs that top scientists use to monitor their quality of thinking and distinguish between superior and inferior modes of cerebral thinking. Well, nature also worked hard to evolve dexterous limbs for us. So, not forgetting the parallel importance of honing skills is also a must. But the limbs would be useless sans the mental faculty to plan how to put them to good use, so knowledge-building precedes skill-honing but at the same time is complemented by it. Now please, pay heed to the two ancient phrases below.

परं ब्रह्मज्नानम्‌

Translation: Spiritual knowledge is ultimate.

scientia ipsa potentia est

Translation: Scientific knowledge itself is power.

The former phrase in Vedic Sanskrit and the latter phrase in Latin (relatively much more modern) show that Knowledge has been held in utmost regard in most civilizational societies. The latter emphasizes the importance of knowledge in western traditions and basically encapsulates the crux of western civilization, while the former shows that similar importance to the painstakingly meticulous traditions of knowledge generation and accumulation is equally upheld in Ancient Indian (a more genuine word most would prefer to use here would be Bharatiya as it conveys a sense that is fully detached from our colonial past; another word that had become popular in this spirit was Kumari Kandam or Lemuria although its validity has now been debunked) traditions. To sum it up, knowledge or the pursuit of the ultimate objective reality⁷ is the common goal of science and \(``\)allied\("\) endeavors. There is only one caveat which is already alluded to in the previous paragraph: In turning our sole attention to the pursuit of knowledge by thinkers, we may easily overlook the immense contribution being made in parallel by doers who swear their prime allegiance to the honing of skills. Knowledge and skills denote yet another complex duality but to an academic, knowledge appears more enticing. Knowledge is what occurs when the cerebral cortex encounters the world of thoughts. Skill is what transpires when the cerebral cortex encounters the world of actions.

It is usual to think about knowledge (about the whole universe) as a fixed entity that we are trying to encapsulate within our collective human intelligence, but we must admit that encapsulating the entire knowledge (even for a species as central and unique as ours) is going to remain a major challenge with which we will be grappling for a long time to come because knowledge is seemingly endless (at least tending to countable infinity if we are going to be splitting hairs; one could define useful/essential knowledge which would appear to be very limited but this reductionist approach is fraught with difficulties and is best avoided here) and also appears to get lost even if imbibed at some point in history. But there is one more way to understand knowledge, which shall be considered by most to be a better way. Let us view knowledge as a process rather than a fixed entity. Knowledge is the process of gaining insights and building a coherent as well as a rigorous understanding of the world. Now, for the most part, this process is only accessible to researchers and academics because someone outside a research environment could only hope to gain scientific insights by reading simplified English essays, which lack any substantial mathematical rigor. This will usually not work out for most because most simplified stuff out there usually tends to be too banal and even too scattered. But we could still suggest to such STEM seekers to read authors from different STEM fields who can write as lucidly as say Rovelli does. Everyone should have the right of access to these insights even if their circumstances render them incompatible with seeking rigorous explanations.

Any process entails a description of how the state variables keep changing, thus we first need to lay out all the variables involved. If knowledge is a process, then what variables are we tracking? Only abstract variables come to mind because knowledge is a process in the sense that our species tries to analyze its collective perceptions and it comes up with sensible questions after giving those phenomena much thought. Now if these questions get answered by simply taking help from the current body of human knowledge, then the problem is resolved. Otherwise, humanity strives to improve its knowledge in the context of those unanswered questions. So, coming back to the question of what variables we are tracking, it is fine to say that we are tracking a metric that measures how collaborative the society is becoming because some form of collaboration has got to be emerging based on such collective sharing of knowledge. Is that not what the purpose of science is in the big picture? To create a sustainable scientific society. And what is society? The best definition is given by Carlo Rovelli⁸ who paraphrases Alexander Bogdanov's idea: society is a \(``\)novel culture based on collaboration, mutually supportive rather than competitive, and that which can flower autonomously.\("\) Adopting sustainability requires shifting societal focus from being money-driven to becoming goals-driven. To this end, society's greatest thinkers need to be meticulously and regularly identified who will then collectively decide some good short-term goals that can achieve a well-balanced long-term vision.

Therefore, all mechanisms in society that encourage competition must be revisited and suppressed carefully while simultaneously replacing them with collaboration-enhancing scenarios. A society that is not paying much heed to the need for lessening competition has not yet begun to enter the advanced phases of scientific modernization. A society that essentially thrives on competitive/adversarial interactions for keeping its money flowing is bound to get messier with time. But well, life\(/\)reality is compensatory in nature. When one gets too invested in one extreme of a spectrum whether by design or by fate (aka circumstances out of one's hand), the pendulum of Life has a tendency to swing towards the other extreme sooner than later. So, competition will never be completely eliminated from society nor should it be. In any complex duality involving two entities, say \(A\) and \(B\), we must never attempt to send the contribution of A to \(0\%\) and \(B\) to \(100\%\), or vice versa. Even if \(A\) dominates \(51\%\) of the times (though I am exaggerating here, any number more than \(50\), which is logically arrived at, should work too), then that is good enough for us to claim that \(A\) beats \(B\). That's how close we have to cut it to end the tussle between these two. This fine line is all we should try to achieve. In fact, a shade of gray is all that is achievable, and one arrives at this disturbing conclusion from any stance of complexity induced Systems Theory style of thinking. Hence, the suchness of what-have-you always compels the sentient towards the balancing act. The topic of knowledge has also received immense philosophical attention, but those efforts rapidly take a turn into unresolvable metaphysical and epistemological debates which may be useful but are best suited elsewhere.

Now, you do not have to be a scientist by profession to realize that science has been exerting a very strong influence on modern humans directly or indirectly. Upon such a realization, it is but natural for any STEM person to show a proclivity for retracing the paths already explored by scientific giants, and such a tendency will only lend itself well to producing more nuanced interpretations of existing scientific knowledge. Maybe democratizing science in this way by allowing for different interpretations is not such a bad idea. And anyway, this social phenomenon is unstoppable just like universal suffrage. We already get to observe this among fully industrialized societies and even among some partially industrialized societies. In fact, everyone must attempt once in their lifetime to understand the essence of science even those outside the STEM community. But not everyone can pursue a lifelong career in hard sciences to seek this realization. As an alternative approach, one could pick up a scientific theory of choice and track down its history from scratch. This approach requires the least amount of mathematical ability. But the discovery of scientific theories has often been so collaborative and messy that the science historians, probably due to cognitive overload, simplify the narrative by chipping away the abstruse details (some of which could be carrying deep insights) as long as the overall story appears intact if simulated in a classroom or lecture hall setting. However, in the era where we have gotten used to swift Google searching, it will be way off base to expect someone to spend significant time searching for the unabridged authoritative accounts related to that particular theory's history.

On the other hand, it so happens that there are academic programs in philosophy of science that have been purposefully designed for elaborate discussions along these lines without getting into the intimidating mathematical intricacies and rigorous theory building, which are actually responsible for building these hard sciences. But should a person interested in such philosophical aspects of science have no recourse other than joining a Phil. Sci. program? Didn't we face a similar dilemma with CSE/EEE programs? Now, consider what Weinberg used to say: \(``\)The best antidote to the philosophy of science is knowledge of the history of science!\("\) So, I believe that philsci programs make more sense for fully industrialized societies that had put their complete trust in science, only to later get somewhat (or maybe very much) disillusioned (by the way, this is just normal human nature), and so needed a reality check that could only be provided in a meaningful way by the philosophy of science programs as part of some sort of cleansing and rehabilitation process. On the other hand, it is going to be the \(``\)history of science\("\) programs that would prove more beneficial to the Indian society as they will provide a lot of clarity and perspective helping us to steer clear of complications that may potentially arise during our unstoppable full-on industrialization process; such insights the benefit of which the western population might not have had while their society was industrializing.

I think it would be amiss not to create another category of light science texts that could be very satisfying to read for non-scientists who are STEM enthusiasts to the core. For lack of a better word, we may call it scientific philosophy. By scientific philosophy, I simply mean thinking about nature just like the sixteenth and seventeenth century maestros of natural philosophy (after all, science was called natural philosophy back then) or the eminent \(``\)early modern\("\) philosophers would be thinking about Nature if they could somehow learn all the advances in science that have taken place since then; and only using plain jargon-free English without any mathematics (or a minimal amount of it)! The main bottleneck is where to find good quality scientific philosophy texts to read. Carlo Rovelli and Roger Penrose are the first names to come to my mind. But the most accurate way to define this category would be to refer to it as the collection of all pop-sci books written by Nobel laureates. Thus, for all practical purposes, scientific philosophy may simply be considered to represent pop-sci articles and books written by highly accomplished scientists. Initiatives that are taken by Wolfram and Strogatz to popularize science are also integral to helping STEM enthusiasts develop the most up-to-date way of scientific thinking. Integrating history of science (histsci) programs along with scientific philosophy (sciphil) programs would help the society immensely, whereas the philosophy of science is a bit of an acquired taste. It is also possible for a new STEM entrant to get lost within philsci's abstract questions and then walk away with a muddled style of thinking. The more \(``\ \)histsci\(\ +\ \)sciphil\(\ "\) programs grow at all levels of education, better will be the scholastic development of a student in that society and higher will be the chances of creating a sustainable scientific society (SSS) as opposed to simply creating a successful industrial society (SIS).

The aptness of a STEM enthusiast adopting a philosophical approach to understand science is not debatable. Allow me to briefly explain why. The Giants constructed the world of scientific thoughts (we just live in it) and their underlings built the modern industrialized society inspired by the scientific way of thinking and empowered by scientific knowledge. The last man who is rumored to know everything was Thomas Young and he died in \(1829\). And to think that the electron was only conceptualized in \(1874\) by George Stoney for the first time in a modern scientific way who had then gone ahead and called it that only in \(1891\)! So even for the most well-meaning educated person who is a STEM enthusiast, it is impossible to keep oneself abreast of all issues in science because of this explosion of scientific knowledge. Hence, the details have to be left to the experts. This inevitably launches us into another debate about specialists and generalists: should we suppress the development of generalist inclinations for the good of society? Well yes but if I try to get into this more deeply, I will keep rambling on, so allow me to swiftly move on after quoting (not analyzing) what the great visionary Fuller⁹ said

\(``\)The way the power structure keeps [clever people] from making trouble for the power structure is to make each one a specialist with tools and an office or lab [It would be amiss not to mention a similar argument that one keeps hearing quite frequently: that of regional hegemons trying to induce other competing regions into meaningless rat races even if such induction requires them to commit a major chunk of their own population to be engaged in similar rat races, thereby ensuring that the first-mover advantage that they enjoy over others never gets erased. Well, the thing about cynicism is that it is difficult to refute these days]. That is exactly why bright people today have become streamlined into specialists. Nobody is born a specialist. Every child is born with comprehensive interests, asking the most comprehensively logical and relevant questions. [then he goes on to show how he would explain fire to a child in the most peculiar scholastic style and continues saying that] Conventionally educated grown-ups rarely know how to answer such questions. They're all too specialized. If nature wanted humans to be specialists, she would, for instance, have given them a microscope on one eye, which is what nature has done with all other living organisms\(-\)other than humans... Humans are unique in respect to all other creatures in that they also have minds that can discover constantly varying interrelationships existing only between a number of special-case experiences as individually apprehended by their brains, whose covarying interrelationship rates can only be expressed mathematically... Human mind's access to the mathematics of generalized scientific laws governing physical phenomena in general made possible humanity's production of its own detached-from-self wings to outfly all birds in speed and altitude while being able to loan one another those wings and modify them to produce even better wings.\("\)

Since we have already achieved so much in science, now may be a ripe time to hit pause on the current scheme of things and encourage our education systems to encourage thinking about science more than learning science. I could not make this point better than has already been done by Roger Gerhard Newton back in 2002: \(``\)University teaching is generally very much oriented toward problem solving, and some [STEM professionals], unfortunately, assume that is all there is to their disciplines. No doubt problem solving, in the widest sense, is our bread and butter; but it is surely not all we do in our professional lives. The way we approach obstacles in research is influenced by our more general understanding of what lies behind the solutions to large problems tackled in the past, and we cannot help reflecting upon the deeper and more general issues, spending some time thinking about [science] rather than simply doing it.\("\) The Princeton PUP overview of his excellent book Thinking about Physics gives it crisp and clear: \(``\)Physical scientists are problem solvers. They are comfortable doing science: they find problems, solve them, and explain their solutions. Roger Newton believes that his fellow physicists might be too comfortable with their roles as solvers of problems. He argues that physicists should spend more time thinking about physics. If they did, he believes, they would become even more skilled at solving problems and doing science.\("\) Today, science has reached such an advanced stage that you have to be a professional practitioner having access to a state-of-the-art lab to really understand what is going on. This limitation is what makes the \(``\)philosophical approach\("\) (I exclusively use this phrase in the context of the definition given above for sciphil and not philsci because latter mostly stands for an esoteric philosophical discursive approach which could get pedantic for a typical STEM enthusiast as science becomes secondary \(-\) not that I would mind the pedantry considerably; after all, what academician does not have a penchant for pedantry! But all we want is to primarily focus on scientific insights cutting across all disciplines while avoiding the rigors of mathematics and compromising on fidelity as less as possible. I do not much like philsci as opposed to sciphil because I want science to be primary and philosophy to be secondary despite acknowledging that an obligatory symbiotic relationship between the two is much needed for an individual to make any spirited progress in understanding the overall scientific picture of the world over his or her limited life span, and also acknowledging that philosophy in its own right is quite the formidable and useful tool we have in our repertoire to understand the universe. Let me put it this way, if I had to clear some relevant doubt and I only had the choice to do so by consulting either a scientist or a philosopher, then I would always choose the scientist — the rationale being that anyone can self-study philosophy more or less, but not everyone can self-study science; note also that not many can do science properly.) so much more appealing for the current STEM enthusiast who could at best only afford to nurture generalistic inclinations. The philosophical approach is accessible to anyone who is simply willing to spend time reading the right books. Recall once again that science was not long ago called natural philosophy.

In fact, science has advanced so much already that we may even whimsically claim science to be dead now (or to sound milder, say saturated). We may even claim Science has given way to Technology (or more precisely, in STEM, S & M have taken a back seat as seems quite appropriate while E & T roar ahead towards the driver's seat; again this is an exaggeration but roughly the correct picture overall) because what one would find most science labs to be engaged in these days would really only be some highly specialized sophisticated technology in play. This is not at all to contradict the fact that the existing scientific knowledge is far from complete. There is much more that remains to be discovered in science. However, what we seem to be observing today is that science and technology need to alternate with each other in phases of societal significance to reach the ultimate goal of unified and complete scientific knowledge. Yet Stephen Gould¹⁰ says \(``\)The evolution of consciousness can scarcely be matched as a momentous event in the history of life; yet I doubt that its efficient cause required much more than a heterochronic extension of fetal growth rates and patterns of cell proliferation. There may be nothing new under the sun, but the permutation of the old within complex systems can do wonders. As biologists, we deal directly with the kind of material complexity that confers an unbounded potential upon simple, continuous changes in underlying processes.\("\)

What Gould seems to be saying is that there may not be much in science that remains to be discovered. The prodigious collective effort exerted by scientists in the past centuries is beyond belief and may be difficult to replicate century after century but luckily, we may not need more scientific discovery (technological advancement, sure; but not scientific discovery per se); rather we mostly require more scientific synthesis. What we now need is to synthesize all that we have learned in science into a coherent body of knowledge and exert ourselves towards obtaining a scientific understanding based on our existing scientific knowledge (if, with the aid of better technology, we discover the last few remaining important scientific facts/concepts that have eluded us until now, whatever they may be, then that is definitely going to be a game-changer! But Gould is asserting that it may not be necessary, at least to understand everything that is ecologically or physiologically relevant to us). There is, however, a lesser viewpoint that prefers to set the goal to be the ability to make accurate predictions in all cases across all time horizons as opposed to gaining scientific understanding. One may think both are essentially the same but one is inferior and a drag on the other. One has to accept that indeterminism exists and so we have to remain content with only being able to understand the past as opposed to predicting the future barring few exceptions here and there. Nevertheless, such an understanding will also invariably provide an intelligent estimate of the future but only as a by-product. Since \(``\)understanding\("\) is an abstract notion (nobody even knows what it is, just ask Penrose!) and technology is gaining more traction as the major driver of the current state of society (as it should!), the basic instinct to choose concrete goals ends up placing unnecessarily too much importance on the prediction problem.

Moreover, it is only in this limited sense that one may dramatically claim that science is dead (well, Nietzsche even more dramatically claimed that \(``\)God is dead.\("\) What goes around comes around), or that science has lived its purpose; by saying this we are simply suggesting that we may have discovered all the relevant scientific concepts and now it's just a matter of weaving all these concepts into a comprehensive understanding by gradually integrating all the fields, the so-called connecting the dots. But then the field of biology is only getting started in the twenty-first century and there is no knowing where it will go in the coming centuries. There can be no doubt that biology is the most happening discipline of this century and most probably the next few. So, we are better off keeping our fingers crossed with the assumption that there are some very revolutionary scientific models waiting to be discovered. In fact, it is highly likely that there are some scientific concepts that we have not yet found out that are critical for us to develop a coherent understanding of this universe. However, it will require such a massive amount of technological innovation to uncover those insights that it is necessary to take a hiatus from science for now and engage more in technology for the time being.

Given that scientific knowledge is incomplete, coherent scientific understanding at high fidelity is nearly impossible, and even complete scientific knowledge may fail to fully resolve what the reality is because the map is not the territory. Then our best hope is only to make judicious use of what we know in order to live our lives better. For example, several questions flash into a curious mind on a daily basis. Let us pick one out of those numerous questions that pique our interest while encountering daily life events and try to think what the best scientific answer to it would be. Most of the time, while trying to obtain a rigorous answer, we will soon realize that science does not yet have a perfectly airtight answer because that would require gazillions of research man-hours, and given the shortage of quality manpower, one should expect most questions that keep popping up in our daily lives to remain only approximately answered. To resolve this situation, a mature response would be to correctly draw upon your entire scientific education to guesstimate an answer that will work or at least will not hurt your interests. That is why the quality of education matters so much. Scientists cannot be present to save us from complexity and randomness in every nook and corner and even if they became omnipresent somehow (technology should never be underestimated), then much good that would do! One has to constantly fall back on their education. The quality of the education system determines the success and sustainability of a scientific society.

In a world of self-interested agents, everyone needs to arrive at the Nash equilibrium but at their own pace, and only mathematics-based rigorous scientific education provides the means to achieve that. Rigor is the most important principle that one can imbibe from the STEM fields, and also the most important factor in dissuading someone having lesser tenacity from pursuing a career in science. But this word gets used in so many places that it may have lost much of its precise original meaning. A STEM person knows and understands the original usage of this term within the context of science and mathematics. The best way to explain to someone what rigor is requires talking about the axiomatization process. It is too involved to get into it in a major way in this article. But what we are specifically referring to here is the story behind Dedekind–Peano axioms and Zermelo–Fraenkel axioms. These axioms were not always present in the mathematical world even when number theory and set theory existed. So, what were these serious mathematicians suddenly seized by so that they started charting out this more formal way of thinking?

One has to browse through these axioms and their emergence in order to understand rigor in the modern academic sense. One may think that understanding rigor within the limited context of number theory and set theory may not be helpful at all to those who just want to go about their daily jobs with a scientific temperament — doing jobs that do not involve an iota of abstract mathematics! And while on the face of it, this may look innocently correct, imbibing rigor from abstract mathematics will have that singular effect of conscious understanding, which Penrose talks about at length in his ENM¹¹ book: once you gain a deeper understanding of a mathematical concept, your conscious way of thinking about things changes. This new shift in thinking could then be said to be more rigorous, more logical, and more rational than before and applies to anyone interested in developing a scientific temper regardless of whether or not their livelihood depends on abstract mathematics.

Mathematicians and physicists have worked tirelessly to propound so many theories. What happens when a theory is being formulated in the final phase with the purpose of sharing it with peers for their feedback? This step starts only after much thinking has gone into roughly fixing the main features that the theory is supposed to have. But when a formal theory is written down, it always begins with mathematical definitions and axioms followed by the lemmas and theorems. That is the only rigorous way of mathematically modeling any chosen scientific concept or process. A scientific concept is referring to an abstract idea derived from some real-world observation after lots of thinking whereas a scientific process can be taken to be a specific idealization of some real-world phenomena or lab experiment measured with excessive precision. If you are not stating all your assumptions clearly in terms of definitions and axioms or are evading writing down hypotheses (that you believe to be true) in the style of a mathematical proof, then that means there is still room for going back to the drawing board and thinking about the matters more deeply.

The definitions and axioms rigorously summarize one's assumptions. They are always developed in hindsight, at least that is the intuitive way. It is difficult to imagine someone so mathematical that he or she approaches a topic as a collection of definitions and axioms right from the outset. But a word of caution here: the limits placed on one's imagination should not be allowed to automatically translate into one's beliefs. But still, it makes more sense to assume that intuition always comes first. The intellectual ability of the right STEM professional allows him or her to reach a conclusion first in his own mind's eyes intuitively. Then, because as part of submitting his work for peer review a theory needs to be developed, he forces himself to rigorously work out all of his definitions and axioms. And there may be a significant time lag between these two steps. Sir Issac Newton is supposed to have known about the inverse-square law of gravitation since \(1666\) but rigorously published his results only in \(1686\). That's two decades!

Now unless one is working exclusively with Platonic idealized abstract mathematical objects, one has to realize that the STEM professional always has that lingering feeling that there is some concept that he has left undefined, appealing to the reader's intuition to cement over it. Say, scientist \(S1\) leaves \(80\%\) of concepts to the reader's intuition, then scientist \(S2\) comes and reduces the undefined fraction to \(79\%\), then scientist \(S3\) comes and reduces the undefined fraction to \(75\%\) and so on. That ideally is the rigorous scientific process of knowledge building. But there seems to be a major limitation to this sort of knowledge-building exercise. You will hit the wall much sooner than you realize. Generally, the pioneer leaves little for the progeny to sort out. If this is the case, a strong believer-cum-follower of science should realize that perfect scientific rigor has very limited practical utility vis-à-vis day-to-day matters because it is a near impossibility. In fact, I find Terence Tao's words to be very educative in said context: \(``\)The post-rigorous stage... the emphasis is now on applications, intuition, and the big picture. This stage usually occupies the late graduate years and beyond... is equally important, and should not be forgotten... [Rigor] has the unintended consequence that fuzzier or intuitive thinking (such as heuristic reasoning, judicious extrapolation from examples, or analogies with other contexts such as physics) gets deprecated as non-rigorous... The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition... Then you will be able to tackle [S.T.E.M.] problems by using both halves of your brain at once — i.e., the same way you already tackle problems in real life.\("\) It is also extremely advisable to remember what John von Neumann said: \(``\)There's no sense in being precise [rigorous] when you don't even know what you're talking about.\("\)

But more importantly, does tirelessly achieving the meaningful connecting of the dots lead to some end in sight or this unending process in itself is the end goal to be sustained for however long it may be sustained? Is it possible for us to weave together all that we will have learned into a unified body of knowledge before our extinction so that all that seems magic and mystery to us now finally becomes coherent with nothing more left to understand? This important and difficult question has been considered by many prominent philosophers. But on such metaphysical questions, I constantly fall back on Sri Aurobindo (at least as of now). He says, \(``\)The Energy that creates the world can be nothing else than a Will, and Will is only consciousness applying itself to a work and a result... Science itself begins to dream of the physical conquest of death, expresses an insatiable thirst for knowledge, is working out something like a terrestrial omnipotence for humanity... The idea of limit, of the impossible begins to grow a little shadowy and it appears instead that whatever man constantly wills, he must in the end be able to do; for the consciousness in the race eventually finds the means.\("\)¹² Others have also referred to this notion more explicitly as the Inexorable Will or Burning Desire. Sri Aurobindo is saying that the primacy of Will Power is as much a True universal constant as we assume the surety of death to be.

By now it should be clear that I am avoiding very formal and rigorous definitions, which are otherwise more suited as part of academic programs. But we know that even redefining fundamental terms in informal language albeit maintaining a serious state of mind may lead to fruitful insights. Now autodidacts are sometimes dangerously well-poised to become good charlatans, but one can only sincerely hope against it. I prefer to look at it as being a generalist as opposed to a specialist, as being transdisciplinary rather than being parochial or superfluous. It is possible to be a generalist without being superficial if done correctly. Am I credentialled enough, up in those ivory towers of academia, to talk about science? Not really, but such apprehensions have never stopped anyone from doing so nor should they. At least that is what the academic freedom available to a college faculty member implies. Can academic freedom be misused? Certainly, but worrying about credentials prior to communicating academic ideas is not a healthy sign in any scientific society. Of course, even blatant disregard for credentials and authority is, euphemistically speaking, not extremely healthy in a highly organized form of society. But the importance of having academic freedom has already been realized far back in the day so that what was once supposed to be confined within the hallowed corridors of university campuses has long since been made freely available to the general public in the form of \(``\)freedom of speech and expression.\("\)

Gregory Chaitin very astutely noted that to write about science is to walk on a razor's edge. I would like to add this: \(``\)To write about science without being in the thick of it is like striding on the razor's edge.\("\) However, that should not let oneself be dissuaded from thinking and writing about science because thinking about what affects us the most today should be a compelling enough reason for any STEM enthusiast to ignore the hazards of that psychological razor. As Weinberg said, \(``\)the effort to understand the universe is one of the very few things that lifts human life a little above the level of farce and gives it some of the grace of tragedy.\("\) And what better way to understand the universe today than the scientific way! Weinberg was a man of extensive experience and extreme erudition and surely was quite capable of unbiased rational thinking. Yet even a man of his stature who must have regularly made the acquaintance of members belonging to high-status society (even more surely in the latter part of his life) sensed an unmitigated farcical component to human life at the level of an individual; compelled enough so as to talk about it publicly while stating that he believed in a tragedy to be its only redeeming feature. In his case, the tragedy must have been that despite having accomplished so much as one of the world's leading \(20^{th}\) century scientists and devoting an entire lifetime sincerely to the search for fundamental answers, he would still have been acutely aware of how less we understand about the most crucial long-standing questions involving the universe's existence since the dawn of human reasoning; at least as long as we discount the first answers that scientific studies seem to have revealed, which appear to be too bleak for human taste. It seems important to be paying attention to his thoughts, after all while he was active, he was Public Intellectual No. 1 in some senses. Richard Dawkins made a very apt observation: \(``\)The phrase public intellectual is much bandied about. Just a few real heavyweights in the world merit the title, and Steven Weinberg is preeminent among them. His collection ranges from deep science on the very frontier of human comprehension, through his trenchant views on public policy, to history and the arts.\("\) However, one could always cultivate a meaningful component to their life even in the eyes of Geniuses such as Weinberg. It involves making a motivated choice, which is admittedly easier said than done. But this is where the ultimate duo of Knowledge plus Thinking comes into play. The Cartesian snippet given below just fits here! It signifies that the optimal strategy for transcendental living is to purify and clarify one's stream of conscious thoughts until it becomes a continual stream of unadulterated knowledge. Only then the actual vision of Nietzsche's Übermensch can be realized. However, this is much easier said than done in an information-overloaded world.

Why are you?

I am because I think.

How are you?

I think therefore I am.

Who are you?

I am my thoughts.

What are you doing?

I am thinking.

When are you?

I am thinking now.

Where are you?

I am in thinking and thinking is in me.

From whom and to whom are you?

The world of thoughts!

The most fixating feature of science is the remarkable sense of mystery it creates about the universe we live in and then prods the seeker into assuming a detective-like role to unleash his problem-solving skills to demystify the hidden secrets. It is like that fictional character of David Bowman says, \(``\)My God, it's full of stars!\("\) But since the space has been explored to such great extents, it seems that the human body's complexity is mostly going to captivate everyone's attention for the next several decades. In that case, a similar Bowman character if he entered the human body would remark, \(``\)My God, it's full of molecules!\("\) And if both these characters were to truly probe the root of it all, then they would finally exclaim \(``\)My God, it's so empty!\("\) just like Alan Guth answers the question \(``\)Why is there something rather than nothing?\("\) by saying Something is Nothing. And if such a character were to ever enter the world of scientific thoughts being \(``\)pulled into a vortex of colored light and carried across vast distances of space while viewing bizarre cosmological phenomena and strange landscapes of unusual colors,\("\) then he would probably exclaim \(``\)My God, it's full of theories!\("\) The journey one takes to realize all of this is facilitated by the serious study of STEM disciplines and is very captivating. Now this article is getting too long, so maybe we will continue later.

References