Different Perspectives

 

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The same world is viewed differently by different people. Religious people, atheists have their own beliefs according to which they justify the happenings in the world. People stick to their belief systems most of the times. When confronted with contrary evidence, they try to shut it out of their view.

People also have different levels of thinking capabilities. Some can go deep using a particular set of rules and can find inconsistencies in them. Others who cannot go deep are comfortable having opinions which are contradictory.

The beautiful nature of human mind is its ability to hold thoughts which are contradictory as long as it doesn’t perceive them to be inconsistent. This is what makes life move ahead even when faced with difficulties.

Each of us start with a set of axioms we believe in. As we face experiences in life, situations arise where we need to consider our axioms and derive some conclusion from them leading to some contradiction with the event at hand. Note that life always throws things at us so that we don’t have the luxury to derive conclusions from our axioms at leisure. We have to eat, sleep, work and etc. Hence only when faced with some urgent issue, we get to derive that conclusion.

Now, when faced with such situation, we may try to hold on to our axioms and defend them blindly. This may lead to arguments. But over time, when we repeatedly face the same contradiction, we change our axioms which cause the conflict. We may adjust to very similar axioms of others which can justify that particular outcome.

This way we keep on evolving in terms of our worldview. But again, as we repeatedly face everyday situations, we don’t get the luxury to explore all possible conclusions of our new set of axioms. And the cycle repeats.

Difficulties arise when people who have radically different set of axioms come into contact. Both can explain some aspects of the world and both have some limitations. But both cannot co-exist. Also, there is no logical way to disprove others’ axioms without assuming truth to one’s axioms and vice-versa. This leads to conflicts.

Some people may shift from one such perspective to another one. It may be due to bowing down to majority opinion when others are in majority, or an inherent desire to disobey the rules in which they are born into. Or it may be due to brainwashing where repeated exposure to the other perspectives makes one believe in their conclusions.

On the other end of the spectrum are people who are hard to change. Even if their peers change, they try to stick to their set of beliefs.

Whether we believe in some axioms or the other, we assume the world is consistent in some ways that can be explained by those axioms.

But is it really the case?

Take the real numbers between 0 and 1 e.g. 0.023, 0.045 … etc. Cantor’s diagonalization argument shows that natural numbers cannot be mapped to real numbers through bijection. Natural numbers correspond to the set of thoughts or the conclusions that we can derive from them. For e.g. we can number our axioms from 1, 2, and so on say 100. Each derivation of a conclusion involves some steps, which too can be numbered as 101, 102 etc. Now, if the conclusion is a real number, it gets a corresponding natural number N. Since the whole set of natural numbers cannot have bijection to Real numbers, their subset too cannot. Hence, we cannot derive real numbers, ie we cannot explain real numbers using our axioms.

Now the world is clearly composed of more than real numbers. Hence the world which is a superset cannot too be explained by our axioms.

The number of real numbers is called N1. Can we have N1 number of axioms to start with? Our brains have a finite size; hence they cannot produce infinite thoughts. But again, Penrose says consciousness arises at quantum levels. Hence, if thoughts correspond to consciousness, and since quantum states can be in complex superpositions, we can potentially have infinite axioms in our brain.

Hence, it seems that any finite set of axioms cannot explain the world. This effort looks as if trying to make a 3D sphere using planar tiles. We may approximate the sphere, but there will be places where the tiles don’t fit.

Trying to find meaning in scientific theories

Joke

Science is based on rationality.  We start with certain axioms which we assume are true and then derive new conclusions based on them. We test the conclusions by doing experiments which can be repeated by multiple independent scientific teams.  When the experiments confirm the conclusions as true we accept the theory as a model of reality.

The axioms are stated in unambiguous ways using solid mathematics and logic. For eg Newton’s laws are stated using second order differential equations. The process of deriving conclusions also uses mathematics. To find the motion of a particle, we integrate these equations.

The math required to do these are sometimes invented along the way as in the case of calculus for Newtonian mechanics.

newtonian_velocity_equation

These equations are valid for a particle at a particular position r and work well in real-world situations where these are used to send satellites into space.

Now, a particle is defined as something which has zero dimensions. It has no length, width or breadth, occupies zero volume in space. However, if we think about it, can such a thing be possible? How can a thing of zero dimensions exist? What about the instantaneous velocity and acceleration defined here, if you consider anything at a particular instant of time, if such a thing is possible, why would it have a velocity or acceleration which involves change in something with time? It is clearly just an approximation of the real world.

Sometimes the math is invented much before like in the case of quantum mechanics, where the Hamiltonian operator was invented in the early 1800s.

the-schrdinger-equation

Where the Hamiltonian operator is H.

The meaning of wave function Ψ is not clear. Its square is defined as the probability of finding an electron at some point.

Also of interest is the presence of the imaginary number i which is defined as the square root of -1.

Now, quantum mechanics works well to predict the energy levels of Hydrogen atom and other such properties.

So, we are using some abstractions which are not clear to us to derive meaningful conclusions.

In the book The Brief History of Time, Stephen Hawking talks of a cosmological model which has imaginary time that makes the universe self-sufficient with no requirement for a first cause. Now, what exactly is an imaginary time is not clear. It helps in solving equations to get real-world results, but what meaning can we ascribe to it?

Looking at these above examples, we can see that our theories are based on some assumptions which may not have any meaning.

These raise several questions in my mind:

  • Are these abstractions a reflection of higher dimensions? Is imaginary time another dimension of the normal time we experience that somehow influences our universe but at the same time cancels out in the end?
  • Why do abstractions work? Why does a point of 0 dimensions somehow is able to describe real-world objects? Is it just a coincidence that it somehow works? If so, it is of interest to understand what properties of the universe make this coincidence possible.
  • Or is the universe inherently unyielding to rationality? Is rationality just an approximation of what there is, and we may never know the whole truth?
  • Or is there no real truth in the sense we understand? Is the universe inherently self-contradictory with paradoxes, imaginary quantities and quantities like Ψ which have no meaning?

 

These are some philosophical questions to ponder over for everyone.

On the acceptance of inequality in society

When we look back at our previous generations, we see how regressive they were. They treated people differently based on their caste in Indian cultures and their social status in western cultures. We often wonder how could they not see the flaws in their thinking? How could they believe someone born in a noble family is superior to someone born in a peasant family? How could they treat blacks as inferior beings, women as lower in intellectual capacity and unable to make financial decisions?

A person born in a higher class thinks of himself as superior to someone born in a lower class. And surprisingly the lower born thinks of himself as inferior to the higher born. Women think that men are the ones who can make sound decisions and they restrict other womenfolk to kitchen. All of these look very wrong to our generation.

But are we much different from them? Let us examine if we too have such biases.

A lot of talents we have are innate. Someone is intelligent by birth, someone can run faster since childhood. We attribute these abilities to our good genes. While its true that we still need to work really hard to succeed, we actually have a head start in certain aspects.

The current accepted norm in the society is that whoever has certain abilities can use them to make money, earn fame, get what he wants, while those who don’t have the ability should accept the second place. If someone is beautiful, she can become Miss Universe and earn fame and money while an average looking person cannot make a fortune out of their beauty. A highly intelligent person can earn billions whereas an average person can have an average life and we don’t see any issue here.

In all these scenarios it’s not just the society, but the successful person as well as the average Joe, too accept the fate of themselves and others. The successful person thinks he is where he is because of his abilities and the average guy too thinks the same. No one questions the validity of the situations.

While its one thing to question the correct social constructs to be in place for a just society, we should realize that we too are in the same thought process as our previous generations, of someone superior accepting his superior abilities and the consequent fortunes and someone inferior having their own reasonings.

If we think about the reason why this is the case, I think its probably because all these equalities and inequalities are our own social constructs and don’t have any objective ontologies. These inequalities are reinforced by the beliefs of people on both sides and sometimes they are opposed and things start to change.

Is Entropy just a psychological construct?

Introduction

I studied some thermodynamics earlier but am not an expert in statistical mechanics etc. I am also reading the book “Cycles of Time” by Roger Penrose in which he tries to explain the notion of Entropy in the first few chapters. From that understanding some questions came into my mind which I am trying to elucidate here. This is not a rigorous treatment of the subject but many terms are vaguely considered.

What is Entropy?

From Wikipedia here Entropy of a system is the number of microscopic configurations that a system can be in for a given set of macroscopic variables.

For example, gas in a container with known volume, pressure, and energy could have an enormous number of possible configurations of the collection of individual gas molecules. But all these different configurations give the same macroscopic look to the system. The higher the possible microscopic configurations, the greater is the disorder in the system. A well organized system like a boiled egg has low entropy whereas the same egg before boiling if smashed on the floor has many possible random configurations hence a higher entropy.

Second law of Thermodynamics

This law states that Entropy always increases for an isolated system. So, when we take any orderly system, the amount of order in the system decreases and randomness increases with time.

For e.g. if we leave a hot iron ball in a bucket of water, it rapidly cools until the water and the iron ball reach the same temperature. Drop some ink in water and it quickly disperses. Hence, any form of order eventually disappears.

Arrow of Time

Now, as second law states that with time disorder increases, we can in a way say that second law determines the direction of time. Hence, it’s the reason why we observe time to move in only one direction and not into the past.

Fate of the Universe

Now, given that second law is observed to be true and any order in a system eventually disappears into randomness, what will happen to our entire universe?

All stars will at some point of time stop radiating and settle down, and with black holes present in our universe, ultimately everything will fall into them. Black holes too radiate through Hawking Radiation and hence that will be the ultimate fate. Read about it here.

Hence, all kinds of structures, orders will disappear ultimately into uniform randomness.

So what’s the point of anything?

It looks like all human efforts will ultimately be in vain. If the universe itself is going to dissolve into randomness why bother about anything? All results will be temporary until destroyed by randomness.

Psychological constructs?

Let us re-consider the definition of Entropy again. It is the number of microscopic configurations which give rise to the same macroscopic setup. The larger the number, the greater is the entropy.

A circle can be defined by one parameter, its radius. A square has one parameter, its side length. A quadrilateral needs three side lengths etc.

But if we want to define a random squiggly shape, we need to specify multiple parameters. Now, each of these parameters can take vast number of possible set of values and still be considered a squiggly shape of a given area whereas for a circle or a square, only one value is possible for a given area.

EntropyCircleSquareEntropySquiggly

Clearly circle and square of a given area is a well-defined shape.

We can see that more number of squiggly shapes are possible for the same macroscopic quantity area of a shape. Hence, it has higher entropy than the circle or square.

Now, second law says that if we let an organized system like a circle to evolve, it will evolve into one of the squiggly shapes. This we observe in real world too and doesn’t come to us as a surprise.

If on the other hand someone shows a disorganized system evolving to an organized one, we would not believe it to be true. We think there must be something behind the scenes happening.

Here is where I consider the psychological part of Entropy. We consider a lot more microscopic states to be equivalent to the same macroscopic state. The important point here is that it’s we who are looking at multiple microscopic states to be the same macroscopic state!

We easily distinguish between a circle and a square. Even kids who don’t know what a circle or a square is can easily categorize them to be distinct entities. Whereas for random shapes we group them all into one category random. Remember how difficult it was to draw a heart in high school? Whereas everyone’s favourite was drawing an amoeba where we have a lot more freedom in choosing arbitrary values for the drawing!

So, my thinking is what if it’s the human psychology that is playing tricks here?! For some reason we don’t distinguish between random shapes. If we assume all possible shapes to be equally probable, we can easily see that a macroscopic entity having many random shapes has a higher probabillity than a well-defined shape. There are many number of shapes of amoeba for which the teacher gives full marks than for the heart which needs a well-defined pattern for getting full marks. So, here the teacher has no difficulty in identifying more random shapes as those of an amoeba but will accept only a few well-defined shapes as those of a heart.

So, it looks like it is the human psychology that is dictating Entropy! So what if there is nothing called Entropy in reality but just a human construct?! We find things to be useful when they are well-organized, whereas disorganized systems are not useful. We can extract work from an organized system where it transforms into a disorganized system. But here work too is defined to be something which gives organization. We will appreciate a kid who maintains his things in a good organized way, whereas scold a kid who just throws things randomly. It’s this outlook at things that’s making us look at a vast majority of configurations to be of less use and only some configurations to be useful that looks probably to be the reason behind the second law!

So, what I like to think about is what if the universe has no heat death as defined above… what if the universe is randomly evolving all the time but its a just our perception of microscopic configurations which is giving rise to this second law and the hopelessness and heat death that follows!

There are many definition of Entropy and work I haven’t studied mathematically, but these can be re-viewed in light of the above discussion and they will be interesting to consider in this perspective.

Causality – Why anything exists?

Causality – Why anything exists?

 

As we go through our daily lives, we experience many moments of struggles, many moments of happinesses, many times passed as routine chores. Once in a while, we stop to think and ask what is all this around me ? Why is there something ? Where was I before I was born?

Different people with different ideologies give different answers to these questions. Atheists say you didn’t exist before your birth and that they don’t know why anything exists though. Religions give different views depending on their books. So, what answer do I accept?

Most of the time, some pressing work comes into the scene which distracts us from this line of thinking and takes our attention to some other task. We forget about this question and get on with our lives.

Deep down in our thinking, there are certain assumptions which we may not be aware of which work silently and give rise to our thoughts. We see that things change, become other things by joining or breaking. We attribute causality to these changes. Causality is taken for granted unknowingly. Whenever we see something, we “know” it’s in that form due to something else. If there is a cat in our room, we know it came from outside through  the window. This is something which comes naturally to us. We feel this should be the case.

As some people had more time available to think, they started tracing the source of each such cause. What caused the window to be open ? Someone must have opened it. How did the window come to be? Because of the tree from which it’s cut… and so on. By question in this way, we come to the final question why anything exists or what caused this existence.

Now, some say God created this. Then question comes as to who created God? Answer comes as God always existed. Some others say this existence always is there. Some people get satisfied with these answers. But those who believe in causality cannot accept such an answer. How can it always be there or how can God not have an origin?

But maybe such people should be careful about applying causality everywhere. What guarantee is there that causality should always work? It’s just an empirical observation which always succeeds in our environment. We may not be able to apply it to all times.

But the problem with accepting that causality may not apply here leads to situations which defy common sense. Then anyone can say anything about the origin of everything and not be questioned about it. People can say a single God created this. Others can say a trinity created this and so on. It’s okay till this point but then they continue to say the single God wants all of us to do this, or the trinity wants us to do that. And these commandments conflict with our common sense.

But what exactly is common sense? Do we all have the same common sense? I think no. For a person raised religiously, God created this universe is part of his common sense. For a person raised otherwise, it’s not. So, how to deal with the before situation where they want us to behave along their particular doctrines? Well, we can say let’s take majority opinion along the lines of democracy but that’s just submitting to the majority common sense which may not be the correct view theoretically. Or some say let’s take the opinion of the intellectuals but we just doubted the application of causality at the origin of everything. Most of the times, people at this point say it’s beyond our understanding or we don’t know the answers yet and get on with their daily lives.

But for those who cannot do that they try to find an answer through causality to break the doctrines they find are against their common sense. So, we resort to causality again as it empirically works!

It looks like we are freed through these rational thoughts but are also bound by them!

Reductionism in our daily life

We are always under the idea that everything that happens around us has a deeper underlying reason. We try to reduce problems we face everyday into their deeper basic aspects. We try to think of all the complex phenomena that happen around us in terms of basic principles which guide them.

Our education system is based on this idea. In any scientific discipline, a theory is studied by giving it’s basic postulates. Consider Bohr’s model of the atom. We all can try to recollect its postulates about orbits, quantum numbers etc. Now Hydrogen spectral lines can be deduced to be due to electronic transitions from one orbit to another. Similarly ionization energies and others can be calculated using this model.

Let us now consider an entirely different field of say Psychology. Consider the model for memory. I remember reading that there is a short term memory and a long term memory involved in this model. Short term memory deals with things which we can retain for sometime say 30 mins or so. Long term memory is for remembering for ages, recollecting childhood events etc. This model has some postulates about there being cues to retrieve the associated information from the brain etc. In case of short term memory, information is stored in 7 or so buckets, which number recently is further reduced. Now these postulates are used to explain all kinds of phenomena associated with memory retrieval and storage.

In a similar way we can consider other models and how they derive results.

The common theme across all these is that a set of phenomena can be reduced to be derived from certain assumptions. Those assumptions can be taken to be true as axioms as in the case of the Bohr model or can be tested using experiments as in the memory model where the tests reduce these models into further basic models. Going this way we get reduced to a primitive model which we assume to be true axiomatically.

So we are minimizing the information which we need to store to deduce results. And in this process we believe that the minimized information is the reality underlying the observed phenomena. This can be considered as an act of Reductionism.

All is well and good till this point.

But if we think carefully about the reality of the world, a phenomena observed is equally as real as it’s underlying model. In some cases the underlying model may not be real, as in the case of imaginary time. This is one aspect of reducing to models.

In this way, reducing to a model is more of a mathematical convenience than a reflection of reality.

Now, this reductionism is very deeply ingrained in our thinkings. We always try to reduce to basic facts. We don’t even know we are doing this many times. We think this is the correct way to look at things. But the above point can put into perspective the validity of such assumptions.

I didn’t realize I was doing and probably still doing this everyday till I came across Susskind’s book The Cosmic Landscape. There in the initial chapters he talks about reductionism and that’s when I realized that I am doing the same all the time.

As I think about this another thought comes to my mind. We have different branches of sciences, all starting with a set of hypotheses. We believe that they can be reduced to further basic sciences. For e.g. that biology can be reduced to chemistry which can be to physics etc. Some such unifications also are done as in Electricity and Magnetism to get Electro-Magnetism.

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Waves inside waves inside waves ad infinitum

May be the reality around is reducible in parts. At each level it collapses into a set of fundamental principles, but the process may not be continuous. (Here I am vague in explaining because I don’t know how to explain clearly 🙂 .) This discontinuity may result in the theorized reduction of biology to chemistry and others not realizable. We don’t know, but this is a possibility. So we should be a little careful about what we can do.

My intention in writing this article is to tell how deeply ingrained this belief of reductionism is in our thoughts. We humans don’t have a choice but to try to understand phenomena in terms of simpler principles, so we should keep trying taking along with us a pinch of salt 😀 .

 

Induction, Generalization Limits

Induction is something we all are taught in schools in Maths. Prove that if something is true for the number n, then it’s true for n+1 and hence from the base case that it’s true for all numbers.

What are the implications of this?

  • If n is a number, so is n+1, which means numbers keep increasing without any bounds. There is no such thing as the largest number, as we can always add 1 to it to get the next larger number.

  • We see causality in the world around us. If something is there, it’s caused by some other thing. This also leads to infinite causal chains. If there is something, it must have been caused by something else, which in turn must have been caused by some other thing, and the sequence keeps continuing till inifnity in the past.

  • The laws of physics that we have on Earth are generalized to apply to all planets, and even to galaxies. This is more of a generalization, but the essence is the same, whatever applies to a particular case, if another situation looks similar, should apply to it as well.

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Infinite application

 

In the real world around us, we see induction to be valid in lots of cases, hence we strongly believe it to be true.

What if this induction is not valid after some number N?

Why wouldn’t it be valid? Isn’t it based on sound logical arguments?

The logical steps in induction are:

  • To take any number n – what if we cannot chose any number n that we want? One way to think of this is to ask a question – if what we are thinking applies to the real world? I can think of anything but that may not correspond to reality – e.g. I can think of an astronaut crossing the event horizon of a black hole and come back safely – but it doesn’t correspond to reality as we theorize it. So if I chose any number n, and it doesn’t correspond to reality in some sense, how valid is my choice?

  • To extend the property to n+1 – well, same argument here – n+1 may not exist, or it may exist but it doesn’t satisfy the property under consideration

  • Hence to generalize to all numbers – if the above two don’t apply, this cannot hold.

The reason why I am thinking in this sense is because of all the confusion we see by applying induction to things we know. We don’t know what caused the universe – but maybe the causal chain is not infinitely applicable! We don’t understand dark matter – may be General Relativity is not universally applicable!

Then what choice do we have than to apply induction and generalization? I don’t know – the only thing I want to think of is to take these with a pinch of salt 🙂

I may not have clearly articulated but this is the best I can say at the moment and I guess my point hopefully came through good enough.

Happy Life

I recently started reading articles on medium which are generally a little bit lengthy and thought-provoking. It is written by people from all over the world about their life experiences, insights, motivations etc. You can search for articles using tags and as I was going through self-improvement I found a very interesting article here. It’s quite a lengthy one with estimated read time of ~30 mins, which is one nice feature which helps decide when to read which article, so I thought I would write a short article on the same. It covers changes in life-style modifications from various angles. Some of the interesting things I found are:

  •  Read a book per week – I find this rather impractical for me. I generally like to read non-fiction which mostly comprise of science books, and they take a long time to complete. So, what I do is I switch between books so that I am not stuck with one for a long time. I think the benefits of reading books is to gain insights through a different and more experienced angle. We are stuck with our own world view. Reading gives us new ways of looking at things and this in turn can help understand others, not to mention the amount of general knowledge we can get.
  • Write a journal 5 mins a day – I found this suggestion at several places in slightly different forms like writing down the day’s accomplishments, writing down the positive things that happened. This is suggested to improve our self-satisfaction and probably can make us better persons. I tried doing this but somehow lost track of it.
  • Stop eating refined sugar – This one is something most people are not aware of. We take sugar for granted. But recent studies are suggesting to do away with refined and added sugar. We will be surprised to see in how many items added sugar is present. A very nice video on the same is here. Although the video came out in 2009, I saw this only recently.
  • Do some kind act daily – This can really be a small thing like keeping the door open for the person behind you, which is something most Indians don’t do or any such small act. This definitely will make us feel better.
  • Relax daily – The above article mentioned about doing it for 1 hour, but given our busy lifestyles, that would be asking for too much :). So, we should at least try to spend sometime  everyday without bothering about what we are achieving then. Maybe that will help us get closer to ourselves and see what we truly want in life.
  • Define meanings of wealth and happiness – This step will definitely bring focus to our attention how we should plan our lives. But this is something which takes time as what makes us happy today may not make us happy a year later!
  • Track a habit you are trying to improve – This doesn’t need any explanation. Anything which we keep doing, we get better with time. There is a Telugu Vemana poem

           Anagananaga Raaga Matisayillu chunundu

  Tinaga tinaga Vemu Tiyyanundu

Saadhanamuna Panulu Samakuuru Dharalona

Viswadabhi Rama Vinura Vema

                    which says that a Raaga becomes better as you keep singing, even neem leaves taste sweeter as you keep consuming them… with time you can achieve your goals!

                        Hence, this is something we all can try.

  • Be grateful – More and more studies are pointing out how being grateful about what we have in our lives make us really happy.

 

So, these are the things I thought are important for me which I have written here, so that I can come back to them once in a while to remind myself of these positive changes.