Category Archives: Topical

Includes posts on physics, philosophy, sciences, quantitative finance, economics, environment etc.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

The Ultra Rich

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Let’s first take a look at how people make money. Loads of it. Apparently, it is one of the most frequently searched phrases in Google, and the results usually attempt to separate you from your cash rather than help you make more of it.

To be fair, this column won’t give you any get-rich-quick, sure-fire schemes or strategies. What it will tell you is why and how some people make money, and hopefully uncover some new insights. You may be able to put some of these insights to work and make yourself rich – if that’s where you think your happiness lies.

By now, it is clear to most people that they cannot become filthy rich by working for somebody else. In fact, that statement is not quite accurate. CEOs and top executives all work for the shareholders of the companies that employ them, but are filthy rich. At least, some of them are. But, in general, it is true that you cannot make serious money working in a company, statistically speaking.

Working for yourself – if you are very lucky and extremely talented – you may make a bundle. When we hear the word “rich,” the people that come to mind tend to be

  1. entrepreneurs/industrialists/software moguls – like Bill Gates, Richard Branson etc.,
  2. celebrities – actors, writers etc.,
  3. investment professionals – Warren Buffet, for instance, and
  4. fraudsters of the Madoff school.

There is a common thread that runs across all these categories of rich people, and the endeavors that make them their money. It is the notion of scalability. To understand it well, let’s look at why there is a limit to how much money you can make as a professional. Let’s say you are a very successful, highly-skilled professional – say a brain surgeon. You charge $10k a surgery, of which you perform one a day. So you make about $2.5 million a year. Serious money, no doubt. How do you scale it up though? By working twice as long and charging more, may be you can make $5 million or $10 million. But there is a limit you won’t be able to go beyond.

The limit comes about because the fundamental economic transaction involves selling your time. Although your time may be highly-skilled and expensive, you have only 24 hours of it in a day to sell. That is your limit.

Now take the example of, say, John Grisham. He spends his time researching and writing his best-selling books. In that sense, he sells his time as well. But the big difference is that he sells it to many people. And the number of people he sells his product to may have an exponential dependence on its quality and, therefore, the time he spends on it.

We can see a similar pattern in software products like Windows XP, performances by artists, sports events, movies and so on. One performance or accomplishment is sold countless times. With a slight stretch of imagination, we can say that entrepreneurs are also selling their time (that they spend setting up their businesses) multiple times (to customers, clients, passengers etc.) All these money-spinners work hard to develop some kind of exponential volume-dependence on the quality of their products or the time they spend on them. This is the only way to address the scalability issue that comes about due to the paucity of time.

Investment professionals (bankers) do it too. They develop new products and ideas that they can sell to the masses. In addition, they make use of a different aspect of money that we touched upon in an earlier column. You see, money has a transactional value. It plays the role of a medium facilitating economic exchanges. In financial transactions, however, money becomes the entity that is being transacted. Financial systems essentially move money from savings and transforms it into capital. Thus money takes on an investment value, in addition to its intrinsic transactional value. This investment value is the basis of interest.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

Philosophy of Money

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Money is a strange thing. It is quite unlike any other “thing” that we know. Its value manifests itself only in a social context where we have pre-agreed conventions as to what it should be. In this sense, money is not a thing at all, but a meta-thing, which is why you are happy when your boss gives you a letter stating that you got a fat bonus even though you never actually see the physical thing. Well, if it is not physical, it is metaphysical, and we can certainly talk about the philosophy of money.

The first indication of the meta-ness of money comes from the fact that it has a value only when we assign it a value. It doesn’t possess an intrinsic value that, for instance, water does. If you are thirsty, you find that water has enormous intrinsic value. Of course, if you have money, you can buy water (or Perrier, if you want to be sophisticated), and quench your thirst.

But we may find ourselves in situations where we may not be able to buy things with money. Stranded in a desert, for instance, dying of thirst, we may not be able to buy water despite our sky-high credit limits or the hundreds of dollars we may have in our wallet. One reason for this inability of ours is obvious – we may be alone. The basic transactional value of money evaporates when we have nobody to transact with.

The second dimension of the meta-ness of money is economical. It is illustrated in the well-worn supply-and-demand principle, assuming transactional liquidity (which is a term I just cooked up to sound erudite, I confess). I mean to say, even if we have willing sellers of water in the desert, they may see that we are dying for it and jack up the price – just because we are willing and able to pay. This apparent ripping off on the part of the devious vendors of water (perfectly legal, by the way) is possible only if the commodity in question is in plentiful supply. We need commodity liquidity, as it were.

It is when the liquidity dries up that the fun begins. The last drop of water in a desert has infinite intrinsic value. This effect may look similar to the afore-mentioned supply-and-demand phenomenon, but it really is different. The intrinsic value dominates everything else, much like the strong force over short distances in particle physics. And this domination is the flipside of the law of diminishing marginal utility in economics.

The thing that looks a bit bizarre about money is that it seems to run counter to the law of diminishing marginal utility. The more money you have, the more you want it. Now, why is that? It is especially strange given its lack of intrinsic value. Great financial minds could not figure it out, but came up with pithy and memorable statements like, “Greed, for lack of a better word, is good.” Although that particular genius was only fictional, he does epitomize much of the thinking in the modern corporate and financial world. Good or bad, let’s assume that greed is an essential part of human nature and look at what we can do with it. Note that I want to do something “with” it, not “about” it – an important distinction. I, intrepid columnist that I am, want to show you how to use other people’s greed to make more money.

Photo by 401(K) 2013

Life and Death, Philosophy

How to Live Your Life

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I think the whole philosophical school of ethics serves but one purpose — to tell use how to live our lives. Most religions do it too, at some level, and define what morality is. These prescriptions and teachings always bothered me a little. Why should I let anybody else decide for me what is good and what is not? And, by the same token, how can I tell you these things?

Despite such reservations, I decided to write this post on how to live your life — after all, this is my blog, and I can post anything I want. So today, I will talk about how to lead a good life. The first thing to do is to define what “good” is. What do we mean when we call something good? We clearly refer to different attributes by the same word when we apply it to different persons or objects, which is why a good girl is very different from a good lay. One “good” refers to morality while the other, to performance in some sense. When applied to something already nebulous such as life, “good” can mean practically anything. In that sense, defining the word good in the context of life is the same as defining how to lead a good life. Let’s try a few potential definitions of a good life.

Let’s first think of life as a race — a race to amass material wealth because this view enjoys a certain currency in these troubled times that we live in. This view, it must be said, is only a passing fad, no matter how entrenched it looks right now. It was only about fifty years ago that a whole hippie generation rebelled against another entrenched drive for material comforts of the previous generation. In the hazy years that followed, the materialistic view bounced back with a vengeance and took us all hostage. After its culmination in the obscenities of the Madoffs and the Stanfords, and the countless, less harmful parasites of their kind, we are perhaps at the beginning stages of another pendulum swing. This post is perhaps a reflection of this swing.

The trouble with a race-like, competitive or combative view of life is that the victory always seems empty to the victors and bitter to the vanquished. It really is not about winning at all, which is why the Olympian sprinter who busted up his knee halfway through the race hobbled on with his dad’s help (and why it moved those who watched the race). The same reason why we read and quote the Charge of the Light Brigade. It was never about winning. And there is a deep reason behind why a fitting paradigm of life cannot be that a race, which is that life is ultimately an unwinnable race. If the purpose of life is to live a little longer (as evolutionary biology teaches us), we will all fail when we die. With the trials and tribulations of life volleying and thundering all around us, we still ride on, without reasoning why, on to our certain end. Faced with such a complete and inevitable defeat, our life just cannot be about winning.

We might then think that it is some kind of glory that we are or should be after. If a life leads to glory during or after death, it perhaps is (or was) a good life. Glory doesn’t have to be a public, popular glory as that of a politician or a celebrity; it could be a small personal glory, as in the good memories we leave behind in those dear to us.

What will make a life worthy of being remembered? Where does the glory come from? For wherever it is, that is what would make a life a good life. I think the answer lies in the quality with which we do the little things in life. The perfection in big things will then follow. How do you paint a perfect picture? Easy, just be perfect first and then paint anything. And how do you live a perfect life? Easy again. Just be perfect in everything, especially the little things, that you do. For life is nothing but the series of little things that you do now, now and now.

Image By Richard Caton Woodville, Jr. – Transferred from en.wikipedia to Commons by Melesse using CommonsHelper., Public Domain

Philosophy, Science

Free Will — An Illusion?

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If we can let ourselves be amazed at the fact that our non-material ethereal mind can really actuate things in the physical world, we will find ourselves wondering — do we really have free will? If free will is merely a pattern in the electrical activities in our brain, how can such a pattern cause changes and rearrangements in the physical world? Could it be that this pattern is really causing an illusion of free will?

Logic in the form of Occam’s Razor should direct us to the latter possibility. But logic doesn’t apply to many or most of the fundamental hypotheses of life, which answer to a different set of rules. They answer to the mythos, the sum total of the intangible knowledge and wisdom passed down from the past, from the ancient, forgotten masters talking to us through our teachers and folklore, through the structure of our languages and the backdrop of our thoughts, and through the very foundation of our sense of being and consciousness. The mythos tell us that we do have free will, and the logic that came later is powerless to break this notion. So it may be that these words that flow out of my pen into this notepad and later to your computer screen were all predetermined and I had no choice but to write then down. But it certainly is not the way I feel. I do feel as though I can delete any word here. Heck, I can delete the whole post if I want to.

On the side of logic, I will describe an experiment that casts doubt on our notion of free will. From neuroscience, we know that there is a time lag of about half a second between the moment “we” take a decision and the moment we become aware of it. This time lag raises the question of who is taking the decision because, in the absence of our conscious awareness, it is not clear that the decision is really ours. In the experimental setup testing this phenomenon, the subject is hooked up to a computer that records his brain activities (EEG). The subject is then asked make a conscious decision to move either the right hand or the left hand at a time of his choosing. The choice of right or left is also up to the subject. The computer always detects which hand the subject is going to move about half a second before the subject is aware of his own intention. The computer can then order the subject to move that hand — an order that the subject will be unable to disobey. Does the subject have free will in this case?

In fact, I wrote about it in my book, and posted it here some time ago. In that post, I added that free will might be a fabrication of our brain after the real action. In other words, the real action takes place by instinct, and the sense of decision is introduced to our consciousness as an afterthought. Some of my readers pointed out that being unaware of a decision was not the same as having no free will over it. For instance, when you drive, you take a series of decisions without really being aware of them. It doesn’t mean that these decisions are not yours. Good point, but does it really make sense to call a decision yours when you don’t have any control over it, even if you would take the same decision if you did? If something flies into your eyes, you will flinch and close your eyes. Good survival instinct and reflex. But given that you cannot control it, is it a part of your free will?

A more elaborate example comes from hypnotic suggestion. I heard this story from one of the lectures by John Searle — a man was hypnotically instructed to respond to the word “Germany” by crawling on the floor. After the hypnosis session, when the man was lucid and presumably exercising his free will, the trigger word was used in a conversation. The man suddenly says something like, “I just remembered, I need to remodel my house, and these tiles look great. Mind if I take a closer look?” and crawls on the floor. Did he do it of his own volition? To him, yes, but to the rest, now.

So, how do we know for sure that our sense of free will is not an elaborate scam that our brain is perpetrating on “us” (whatever that means!)

Now I am actually pushing the argument a bit further. But think about it, how can the spaceless, massless, material-less entities that are our intentions make real changes in the physical world around us? In writing this post, how can I break the laws of physics in moving things around quite independent of their current state just because I want to?

Is free will an epiphenomenon — something that emerges after-the-fact? A good analogy is that of froth riding on the waves on a beach. The froth may be thinking, “Oh my god, what a tough life! I have to haul all these big waves back and forth. Every day of my life, no break, no vacation!” But that is not what is going on. The waves are just sloshing around, and the froth just happens to emerge. Are our lives just moving along on their own preordained paths, while we, like the epiphenomenal froth, think that we have control and free will?

Philosophy

Mind over Matter

When I want to write something (this blog post, for instance), I pick up my pen and start making these squiggly symbols on my notebook, which I type into the blog later on. Simple, everyday thing, right? But how do I do it? I mean, how do I make a change in the physical, material world of matter by the mere will or intentionality of my non-material mind?

This sounds like a really silly question, I know. When you want to write a blessed post, you just pick up a blessed pen and write the blessed thing (using “bless” the same way Whoopi Goldberg used it in one of her movies). What is so strange or philosophical about it? This is exactly what I would have said a week ago before reading up some stuff on the philosophy of mind.

How exactly do I write? The pen is made up of matter. It doesn’t move on its own volition and make words. We know it from physics. We need a cause. Of course, it is my hand that is moving it, controlled by a set of precise electro-chemical reactions. And what is causing the reactions? The neurons fining in my brain — again, interactions in the material world. And what causes the particular precise patterns of neuronal firing? It is, of course, my mind. My neurons fire in response to the ideas and words in my mind.

Hold on, not so fast there, Skippy! My mind is not a physical entity. The most physical or material statement we can make about the mind or consciousness is that it is a state of the brain — or a pattern of neuronal firings. My intention to write a few words is again a spatial and temporal arrangement of some neurons firing — nothing more. How do such patterns result in changes in the physical, material world?

We don’t find this issue so puzzling because we have been doing forever. So we don’t let ourselves be amazed by it — unless we are a bit crazy. But this problem is very real. Note that if my intention of writing resulted only in my imagination that I am writing, we don’t have a problem. Both the cause (the intention) and the effect (the imagination) are non-material. And this line of thinking does provide a solution to the original problem — just assume that everything is in one’s mind. Nothing is real. Everything is Maya, and only one’s mind exists. This is the abyss of solipsism. As a philosophical stance, this idea is consistent and even practical. I wrote a book loosely based on the notion that nothing is real — and aptly called it The Unreal Universe.

Unfortunately, solipsism is quite wrong. When I say, “Everything is in my mind, nothing else is real,” all you have to say is, “I agree, I hear you!” And boom, I am wrong! For if you agree, there is at least one more mind other than mine.

So solipsism as a solution to the puzzle that the non-material intention in a mind can make physical changes in the world is less than satisfactory. Then the other solution, of course, is to say that intentionality is illusory. Free will doesn’t exist; it is only a figment of our imagination. In other words, I didn’t really intend to write this post, it was all preordained. It is just that after-the-fact, I kind of attribute free will to it and pretend that I meant to do it.

Strange as it may seem, there are some strong indications that this statement may be true. I will write another post (with or without free will) to list them.

The current view in thinking about mind and brain is in an analogy with a digital computer. Mind is a program (software), and brain is the a computer (hardware) on which it runs. It sounds right, and seems to explain quite a bit. After all, a computer can control complex precision-equipment based on programs running on it. But there is a deep philosophical reason why this analogy is totally wrong, but that will be another post.

Philosophy, Quotes

Love of Wisdom

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Philosophy means love wisdom. But it enjoys none of the glamor that its definition would imply. For instance, in one of the board games that I played with the kids recently, the chance card that would make you bankrupt actually read, “Turn into a philosopher and lose all your money!” This card was particularly troubling for me because I do plan to take up philosophy seriously, hopefully soon.

The lack of correlation between wisdom and worldly rewards is unsettling, especially to those who are foolish enough to consider themselves wise. Why is it that the love of wisdom wouldn’t translate to glory, riches and creature comforts? The reason, as far as I can tell, is a deep disconnect between philosophy and life — as a wise (but distinctly unphilosophical) friend of mine put it in one of those hazy late-night stupors of the graduate years, “Philosophy to real life is what masturbation is to sex.” Yes, the masses see the love of wisdom as pointless intellectual masturbation. This view is perhaps echoed in what Russell said once:

Philosophy busies itself with things that seem obvious, to come up with something grandiose. This apparent obsession with trivialities is a false impression. Dispelling this impression is the purpose of this post. Let me start by pointing out one fact. Philosophy is at the root of everything that you do. You live a good, moral life? Or even a lousy, greedy one? Your behavior, choices and reasons are studied in Ethics. You are a quant, or do stuff technical or mathematical? Logic. Into physics and worship Einstein? You cannot then ignore the metaphysical aspects of space and time. Lawyer? Yeah, Rhetorics. Knowledge worker? Epistemology defines what knowledge is. Artist? Fashion designer? Work in the movie industry? We got you covered in Aesthetics. You see, every avenue of human endeavor has a philosophic underpinning to it.

Pointing out this underpinning is, in reality, not as big a deal as I make it out to be. It is merely a matter of definition. I define philosophy to be whatever it is that “underpins” all aspects of life, and then point out this underpinning as evidence of its importance. The real value of philosophy is in structuring our thoughts and guiding them, for instance, in perceiving the speciousness and subtle circularity of my underpinning-therefore-important argument. Philosophy teaches us that nothing stands own its own, and that there are structures and schools of thought that illuminate questions that befuddle us. There are scaffolds to support us, and giants on whose shoulders we can stand to see far and clear. To be sure, some of these giants may be facing the wrong way, but it is again the boldness and independence that come with philosophy that will help us see the errors in their ways. Without it, learning becomes indoctrination, and in our quest to assimilate information into wisdom, we get stuck somewhere in between — perhaps at the level of knowledge.

All this discussion still doesn’t give us a clue as to the disquieting connection between philosophy and bankruptcy. For when a great man voices his existential anguish as, “I think, therefore I am,” we can always say (as we often do), “Good for you mate, whatever works for you!” and go about our life.

Love of wisdom perhaps facilitates its acquisition, and the purpose of wisdom is only wisdom. It is very much like life, the purpose of which is merely to live a little longer. But without philosophy, how do we see the meaning of life? Or lack thereof?

Corporate Life, Life and Death, Philosophy

Midlife Crisis

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In one of my recent posts, an astute friend of mine detected a tinge of midlife crisis. He was right, of course. At some point, typically around midlife, a lot of us find it boring. The whole thing. How could it not be boring? We repeat the same mundane things over and over at all levels. True, at times we manage to convince ourselves that the mundane things are not mundane, but important, and overlay a higher purpose over our existence. Faith helps. So do human bondages. But, no matter how we look at it, we are all pushing our own personal rocks to a mountaintop, only to to see it roll down at the end of the day — knowing that it invariably will. Our own individual Sisyphuses, cursed with the ultimate futility and absurdity of it all. And, as if to top it off, our knowledge of it!

Why did Camus say we went through the Sisyphus life? Ah, yes, because we got into the habit of living before acquiring the faculty of thinking. By midlife, perhaps, our thinking catches up with our innate existential urges, and manifests itself as a crisis. Most of us survive it, and as Camus himself pointed out, Sisyphus was probably a happy man, despite having to eternally push the rock up the slope. So let’s exercise our thinking faculty assuming it is not too dangerous.

Most of us have a daily life that is some variation of the terse French description — metro, boulot, dodo. We commute to work, make some money for ourselves (and more for somebody else), eat the same lunch, sit through the same meetings, rush back home, watch TV and hit the sack. Throw in a gym session and an overseas trip once in a while, and that’s about it. This is the boring not merely because it really is, but also because this is what everybody does!

Imagine that — countless millions of us, born somewhere at some point in time, working hard to acquire some money, or knowledge, or fame, or glory, or love — any one of the thousands of variations of Sisyphus’s rock — only to see it all tumble down to nothingness an another point in time. If this isn’t absurd, what is?

If I were to leave this post at this point, I can see my readers looking for the “Unsubscribe” button en masse. To do anything useful with this depressing idea of futile rock-pushing rat-race, we need to see beyond it. Or have faith, if we can — that there is a purpose, and a justification for everything, and that we are not meant to know this elusive purpose.

Since you are reading this blog, you probably don’t subscribe to the faith school. Let’s then look for the answer elsewhere. With your permission I will start with something Japanese. Admittedly, my exposure to the Japanese culture comes from Samurai movies and a couple of short trips to Japan, but lack of expertise has never stopped me from expressing my views on a subject. Why do you think the Japanese take such elaborate care and pride in something as silly as pouring tea?

Well, I think they are saying something much deeper. It is not that pouring tea is important. The point is nothing is important. Everything is just another manifestation of the Sisyphus rock. When nothing is important, nothing is unimportant either. Now, that is something profound. Pouring tea is no less (or more) important than writing books on quantitative finance, or listening to that old man attempting the Susannah song on his mouth-organ on Market Street. When you know that all rocks will come tumbling down just as soon as you reach the pinnacle of your existence, it doesn’t matter what rock you carry with you to the top. As long as you carry it well. And happily.

So I try to write this blog post as well as I possibly can.

Philosophy, Physics

Ghost of Gravity

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It has been a while since my last post. I was reading Zen and the Art of Motorcycle Maintenance again just now, and came to the part where Pirsig compares scientific beliefs and superstitions. I thought I would paraphrase it and share it with my readers. But it is perhaps best to borrow his own words: “The laws of physics and of logic — the number system — the principle of algebraic substitution. These are ghosts. We just believe in them so thoroughly they seem real. For example, it seems completely natural to presume that gravitation and the law of gravitation existed before Isaac Newton. It would sound nutty to think that until the seventeenth century there was no gravity. So when did this law start? Has it always existed? What I’m driving at is the notion that before the beginning of the earth, before the sun and the stars were formed, before the primal generation of anything, the law of gravity existed. Sitting there, having no mass of its own, no energy of its own, not in anyone’s mind because there wasn’t anyone, not in space because there was no space either, not anywhere…this law of gravity still existed? If that law of gravity existed, I honestly don’t know what a thing has to do to be nonexistent. It seems to me that law of gravity has passed every test of nonexistence there is. You cannot think of a single attribute of nonexistence that that law of gravity didn’t have. Or a single scientific attribute of existence it did have. And yet it is still ‘common sense’ to believe that it existed.

“Well, I predict that if you think about it long enough you will find yourself going round and round and round and round until you finally reach only one possible, rational, intelligent conclusion. The law of gravity and gravity itself did not exist before Isaac Newton. No other conclusion makes sense. And what that means is that that law of gravity exists nowhere except in people’s heads! It’s a ghost! We are all of us very arrogant and conceited about running down other people’s ghosts but just as ignorant and barbaric and superstitious about our own.”

[This quote is from an online version of Zen and the Art of Motorcycle Maintenance.]

Philosophy, Physics, Science

Only a Matter of Time

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Although we speak of space and time in the same breath, they are quite different in many ways. Space is something we perceive all around us. We see it (rather, objects in it), we can move our hand through it, and we know that if our knee tries to occupy the same space as, say, the coffee table, it is going to hurt. In other words, we have sensory correlates to our notion of space, starting from our most precious sense of sight.

Time, on the other hand, has no direct sensory backing. And for this reason, it becomes quite difficult to get a grip over it. What is time? We sense it indirectly through change and motion. But it would be silly to define time using the concepts of change and motion, because they already include the notion of time. The definition would be cyclic.

Assuming, for now, that no definition is necessary, let’s try another perhaps more tractable issue. Where does this strong sense of time come from? I once postulated that it comes from our knowledge of our demise — that questionable gift that we all possess. All the time durations that we are aware of are measured against the yardstick of our lifespan, perhaps not always consciously. I now wonder if this postulate is firm enough, and further ruminations on this issue have convinced me that I am quite ignorant of these things and need more knowledge. Ah.. only if I had more time. 🙂

In any case, even this more restricted question of the origin of time doesn’t seem to be that tractable, after all. Physics has another deep problem with time. It has to do with the directionality. It cannot easily explain why time has a direction — an arrow, as it were. This arrow does not present itself in the fundamental laws governing physical interactions. All the laws in physics are time reversible. The laws of gravity, electromagnetism or quantum mechanics are all invariant with respect to a time reversal. That is to say, they look the same with time going forward or backward. So they give no clue as to why we experience the arrow of time.

Yet, we know that time, as we experience it, is directional. We can remember the past, but not the future. What we do now can affect the future, but not the past. If we play a video tape backwards, the sequence of events (like broken pieces of glass coming together to for a vase) will look funny to us. However, if we taped the motion of the planets in a solar system, or the electron cloud in an atom, and played it backward to a physicist, he would not find anything funny in the sequences because the physical laws are reversible.

Physics considers the arrow of time an emergent property of statistical collections. To illustrate this thermodynamic explanation of time, let’s consider an empty container where we place some dry ice. After some time, we expect to see a uniform distribution of carbon dioxide gas in the container. Once spread out, we do not expect the gas in the container to coagulate into solid dry ice, no matter how long we wait. The video of CO2 spreading uniformly in the container is a natural one. Played backward, the sequence of the CO2 gas in the container congealing to solid dry ice in a corner would not look natural to us because it violates our sense of the arrow of time.

The apparent uniformity of CO2 in the container is due to the statistically significant quantity of dry ice we placed there. If we manage to put a small quantity, say five molecules of CO2, we can fully expect to see the congregation of the molecules in one location once in a while. Thus, the arrow of time manifests itself as a statistical or thermodynamic property. Although the directionality of time seems to emerge from reversible physical laws, its absence in the fundamental laws does look less than satisfactory philosophically.

Philosophy, Physics, Science

Half a Bucket of Water

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We all see and feel space, but what is it really? Space is one of those fundamental things that a philosopher may consider an “intuition.” When philosophers look at anything, they get a bit technical. Is space relational, as in, defined in terms of relations between objects? A relational entity is like your family — you have your parents, siblings, spouse, kids etc. forming what you consider your family. But your family itself is not a physical entity, but only a collection of relationships. Is space also something like that? Or is it more like a physical container where objects reside and do their thing?

You may consider the distinction between the two just another one of those philosophical hairsplittings, but it really is not. What space is, and even what kind of entity space is, has enormous implications in physics. For instance, if it is relational in nature, then in the absence of matter, there is no space. Much like in the absence of any family members, you have no family. On the other hand, if it is a container-like entity, the space exists even if you take away all matter, waiting for some matter to appear.

So what, you ask? Well, let’s take half a bucket of water and spin it around. Once the water within catches on, its surface will form a parabolic shape — you know, centrifugal force, gravity, surface tension and all that. Now, stop the bucket, and spin the whole universe around it instead. I know, it is more difficult. But imagine you are doing it. Will the water surface be parabolic? I think it will be, because there is not much difference between the bucket turning or the whole universe spinning around it.

Now, let’s imagine that we empty the universe. There is nothing but this half-full bucket. Now it spins around. What happens to the water surface? If space is relational, in the absence of the universe, there is no space outside the bucket and there is no way to know that it is spinning. Water surface should be flat. (In fact, it should be spherical, but ignore that for a second.) And if space is container-like, the spinning bucket should result in a parabolic surface.

Of course, we have no way of knowing which way it is going to be because we have no way of emptying the universe and spinning a bucket. But that doesn’t prevent us from guessing the nature of space and building theories based on it. Newton’s space is container-like, while at their heart, Einstein’s theories have a relational notion of space.

So, you see, philosophy does matter.