Why do we love reading some books?

Why do we love reading some books, but not the others?

Inspired by mathematician Roger Penrose's depiction of Platonic Mathematical World, Mental World, and Physical World, I would like to present my theory.

From the book: Roger Penrose, The Road to Reality, Vintage Books, 2005.

I begin by breaking the problem into several worlds.

The world the author perceives, the world he describes, and the world we perceive.

The discrepancies between these worlds are inevitable; they would have cues on their own, as well as hindrances for our view.

Regardless of the author’s intentions, we begin to build our own world from page one. We continue to fit our perception on the world we have been constructing, not on the world that the author saw or described. Similar to divergence in mathematics we diverge from intended world-view.

So the secret to good authorship must be to relieve both the author and the reader from a burden, the burden of mapping author's world.

Rather than pushing an answer down the throat of the reader, the author should pose a question, such that the world he perceives disappears, and the world his reader perceives gradually unfolds.

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Links:

http://en.wikipedia.org/wiki/The_Road_to_Reality

http://aminotes.tumblr.com/post/1025534467/the-concept-of-laws-the-special-status-of-the

References:

1. Roger Penrose, The Road to Reality, Vintage Books, 2005

Time

Time is one of the most enigmatic terms one would have trouble describing. Take a breath and try describing it now. What is time?

Most simplistically time is simply a mathematical dimension describing change in the position of objects in space. It is not a physical quantity like matter but a virtual quantity.

But fundamentally time or more accurately the arrow of time points to a direction in which a quantity we call Entropy increases.

Entropy is disorder in the Universe and it is always on the rise. The order does not come back by itself; it is as if the arrow of time prevents it from happening.

There is also constant loss during the process of making order. Even if we spend energy to restore the order there will always be an amount of entropy we could not restore (conservation of energy).

This is a war we cannot win.

It is for Entropy dust disperses, disorder increases and decay starts to prevail in a room if we don’t clean it up regularly by adding more energy. Ultimately all living species borrow this energy from the Sun so that we could restore stuff and experience living.

The reason we have an illusion that there appears to be an eternal order in the Universe is because in our limited part of the Universe and in our pathetically short life span it appears so.

Life (plants and animals) constantly restores order by spending energy they borrow from the Sun. In our short-life span we avoid realisation of distant-past and far future that have no practical implications.

But in reality the fuel of Sun is not endless end it will die in about 5 billion years into the future. That would be the time when the debt of energy borrowed by all living species for the duration of life would be settled. Entropy will win or rather we would pay our debt by turning into dust.

In its ultimate twilight the increase in entropy will slow down, and the Universe will be in its heat-death. No heat to restore anything.

References:

The Temperature of History

Recommended background music: Blade Runner End Title.

Does God have a meaning?

 Lets discuss in epistemological terms to begin with.

First and foremost comes the Semantics. Semantics is the study of meaning. If we say, “this is a window” it would mean that the window has a “meaning” associated with it. We can then talk about its “existence” and discuss whether we “know” that “this is a window”. In other words, a word should have at least a semantic “meaning” before we can even talk about its “existence” and speculate about our “knowledge” of it thereafter.

If there is a window within my reach and I am not blind, I may claim in great certainty that “I know this is a window”. Or if I am not certain, I may say things like “I am not sure if that bright thing on that tower 2 km. from here is a window reflecting the sun, or a mirror’”. Hence we can speculate about observable things on their meaning and sometimes test our knowledge later even if our knowledge was not full beforehand. We could do so because we associated a “meaning” to a “window” to begin with.

So a word alone, such as “XYZ” does not mean anything, the word “God” included. Therefore God needs a meaning just like other words in our native tongue. If we can’t associate a “meaning” to God the discussion is over.

Even “un-knowableness” requires a “meaning” of, what we don’t know. Hence without a meaning associable to God, we cannot even begin a discussion whether “Joe is an agnostic”.

Lets now discuss the notion of whether we can find God in quantum realm.

I am assuming we all have sufficient knowledge of Quantum Physics. In a nutshell quantum realm is currently beyond our directly observable and measurable Universe. Quantum Physics is the science of studying “very small” particles or strings that fluctuate and make other particles. What we know about them is we can’t measure their position or momentum at the same time and they fluctuate. Also when we make an observation on them their wave function collapses (more on wave function is a little later). But the good news is we can indirectly confirm our assumptions about quanta. We developed technologies such as Laser beam, and MRI based on Quantum Mechanics.

You see, quanta moves around and change their position and can even appear to co-exist in two places at the same time (see double-slit experiment, entanglement). We know these by indirect observations. So each quantum has a wave function, a probabilistic wave that defines probabilistically where about it can or it is likely to be going as a path in space-time fabric. When an observation is made the wave function collapses, i.e. one of the harmonics of the wave becomes reality and we cannot say with certainty which one beforehand. This knowledge depends on overall probability profile of the wave-function and how all harmonics of the probability wave for different paths overlapped to form the resultant wave function in space-time (see Feynman’s sum of histories).

Considering that we are all quanta implies that there is a finite (non-zero) probability that all of my particles, my atoms, protons, neutrons, quarks, etc. can go through that solid wall in front of me (don’t try this at home). According to Quantum Physics even if it is miniscule there is a finite probability that this can happen. But the fact is, and this point is critical for religious to understand, if that happens the wave function still has to collapse.

In other words we should have the sensation that we are going through the wall. Macroscopically we shall be intact, it was just the coincidence that all of our particles agreed to collapse on this weird wave function at a particular point in the history of our Universe. We still have “meaning”, because our information making us was preserved during our weird voyage through the wall. It is weird because it had tiny probability to happen, but it was not impossible, never.

It is important to note that quantum does not bear information. We have information only when a quantum’s wave function collapses and all the information about a foam of quanta is smeared onto the fabric of reality. We observe this as a macroscopic matter or as a form of energy (both often lead to the same). Or if information falls inside a black-hole some speculated that it could have been smeared onto its event horizon, Hawking predicted and confirmed with observation that information may even leak from it (Hawking radiation). Lets not drift too much.

So if God is an entity residing in the quantum realm it does not and cannot have information/orderness therefore it cannot have intelligence, since information is a necessary (but not sufficient condition) for intelligence. I am not sure if this idea would appeal to anyone.

If on the other hand God has information and/or intelligence then this requires that its wave function must have collapsed already, it is “already outside” the quantum realm.

If God is outside then we are entitled to ask these questions:

• God is outside our observable Universe.
• God is somewhere in our observable Universe but we haven’t observed it yet. 
• We have observed God but we haven’t qualified it as God.
• God does not exist.

The problem with the first three is, either way we need the assistance of semantics in order to qualify say Andromeda galaxy as God or even what we haven't observed is God.

We know that for instance Andromeda has finite set of matter and energy that are measurable to a degree of certainty. We also know that Andromeda is a galaxy hence has a meaning based on properties common to other galaxies. But unless we know what God's meaning is, we cannot be sure if Andromeda is in fact God.

This leaves us with the third option.

A toroidal lamp

I woke up in Istanbul around 6am staring at a toroid shaped lamp hung from the ceiling.

Toroid’s surface has peculiar properties compared to a much simpler shape such as a sphere.

On a spherical surface you may start travelling in any direction and end up where you started. This property is valid for any point on the surface.

A spherical surface is a finite two-dimensional surface with no boundaries. It is a finite surface hence you end up reaching the same point. It has no borders or sharp edges that you may fall off.

As a result a spherical surface is a useful model to study a universe with no boundaries but a finite shape like ours.

A spherical surface has also constant curvature. Nowhere on it there is a point that sits on an area that is more or less curved than any other point on the sphere.

On a toroid on the other hand you may find points across its surface sitting on different curvatures. A point on its outer rim is on a surface with positive curvature, where a point on the inner rim is on a surface with negative curvature.

A simplified modelling can explain this “curvature business” that is the essence of Einstein’s general relativity.

You may construct a toroid by bending a cylinder along axis and joining its ends.

Imagine you make a toroid from a rubber cylinder. You will see that the outer surface of the toroid will stretch, and the inner surface will squash forming wrinkles.

Take a rubble rectangular slab, and on its surface paint little circles with identical diameter placed in equal distance from each other. Form a cylinder from the slab by rolling it so that the circles we drew can be viewed from outside. We should observe that despite introducing a positive curvature, the sizes of circles and the distance between them remain the same. There is no stretching or squashing; the curvature is positive but constant.

In contrast when we form a toroid using a rubber cylinder by bending it along its axis and joining both ends, we should observe that the circles on toroid’s outer surface grow in size and the distance between them increases too. The circles on toroid’s inner surface should shrink in size and the distance between them should become shorter. This is because we have introduced variable curvature changing from positive (stretching) to negative (squashing) from outer to inner rim respectively.

Imagine the toroid represents a certain space-time configuration.

It is possible a light beam to travel from circle A to its neighbour B on the inner surface in shorter time than between neighbouring circles on the outer surface. Space-time is clearly stretched on the outer rim, shrunk on the inner one.

A black hole is like a toroid that its inner hole is infinitely small hence the circles you drew on its inner surface collapse onto each other. There is no way to identify or differentiate those circles from one another, the information about them are sucked by black hole’s event horizon.

It is fascinating to think that there may be oddly shaped universes with multitude of curvatures. A universe that its space-time properties are shaped like a toroid is possible. But other weirder shapes too. Some of them may even have collapsed regions where curvature is transformed in odd directions that we may not easily imagine their shape in our Euclidian minds.

The reason we could visualise and construct a toroid is because we may construct it from Euclidian shapes that we are familiar with such as a cylinder. However we should note that we might not do so if we could not stretch and squash the outer and inner surfaces respectively. You cannot construct a non-Euclidian shape without introducing variable curvature.

A toroid is a non-Euclidian shape whereas a cylinder is a Euclidian one. Our education system has given emphasis on shapes with Euclidian geometry perhaps because there are economical benefits of realising them. Euclidian geometry has given us ability to make useful approximations. We can build pipes by modelling them as cylinders for instance.

However studying non-Euclidian geometry such as toroids, can be crucial in modelling and understanding the cosmos.

The Grand Design

This is a popular science book from renowned physicist Stephen Hawking with a righteous agenda, and that is to take on strong anthropic principle.

Being a popular science book doesn’t mean this is beginner’s stuff nor you need to be a physicist to digest it.

However to get around comfortably you need to have consumed considerable hours digging other popular science books, or surfing Wikipedia on things like special relativity, general relativity, double-slit experiment, quantum physics, string theory, m-theory, and multiverses.

This book ties them up to a big picture and if you are lucky enough to be an open-minded person then you may have your ‘aha’ moment.

And your ‘aha’ moment may as well be the realization that god is not required to create the Universe, your dog, trees, the can of red-kidney beans on the kitchen table and everything else you see or you don’t see around you.

“The strong anthropic principle idea arose because it is not only the peculiar characteristics of our solar system that seem oddly conducive to development of human life but also the characteristics of our entire universe.”

This book challenges the strong anthropic principle with the multiverse idea.

“The multiverse idea is not a notion invented to account for the miracle of fine-tuning. It is a consequence of the no-boundary condition as well as many other theories of modern cosmology. But if it is true, then the strong anthropic principle can be considered effectively equivalent to weak one, putting the fine tunings of physical law on the same footing as the environmental factors, for it means that our cosmic habitat -now the entire observable universe- is only one of many, just as our solar system is one of many. Many people through the ages have attributed to God the beauty and complexity of nature that in their time seemed no scientific explanation. But just as Darwin and Wallace explained how the apparently miraculous design of living forms could appear without intervention by a supreme being, the multiverse concept can explain the fine-tuning of physical law without the need for a benevolent creator who made the universe for our benefit.”

To some these may seem preposterous claims as no one witnessed evidence for multiverses. But our limited observation capacity is precisely the problem here. Multiverse idea is strongly linked to quantum theory. At quantum scales our observation interferes with the history of events selected. According to Feynman, a system has not just one history but every possible history.

“The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us.

When one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless. The idea that histories should be closed surfaces without boundary is called the no-boundary condition.

We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics...One can also use Feynman’s methods to calculate the quantum possibilities for observations of the universe. If they are applied to the universe as a whole there is no point A (that it all started), so we add up all the histories that satisfy the no-boundary condition and end at the universe we observe today. In this view, the universe appeared spontaneously, starting off in every possible way. Most of these correspond to other universes. ” 

I thoroughly enjoyed reading this book I hope you too. It is exhilarating and full of trademark humor from Stephen Hawking.

Links:

Michael Shermer on Model Dependent Realism

The shape of the universe

More than four decades ago scientists discovered that the universe is suffused with microwave radiation -long wavelength light- that is a cool relic of the sweltering conditions after the big bang. Earlier on, it was stupendously hot, but as the universe evolved and expanded, the radiation steadily diluted and cooled. Today it is just about 2.7 degrees above absolute zero, and its greatest claim of mischief is its contribution of a small fraction of the snow you see on your television set when you disconnect the cable or turn to a station that isn’t broadcasting.

In 1929, Edwin Hubble, using the 100-inch telescope at the Mount Wilson observatory in Pasadena, California, found that the couple of dozen galaxies he could detect were all rushing away. In fact Hubble found that the more distant a galaxy is the faster its recession.

An essential property of cosmic microwave radiation revealed by precision satellite measurements over the last decade is that it is extremely uniform. The temperature of the radiation in one part of the sky differs from that in another part by less than a thousandth of a degree.

So although the universe is evolving since the big bang, on average the evolution must have been nearly identical across the cosmos.

This conclusion is of great consequence because the universe’s uniformity is what allows us to define a concept of time applicable to the universe as a whole. Thus the universe has enough symmetry to allow us to speak of its overall age and its overall evolution through time.

Using two-dimensional analogy for space, there are three types of curvature that are completely symmetric -that is, curvatures in which the view from any location is the same as that from any other. They are (a) positive curvature, which uniformly bloats outward, as on sphere; (b) zero curvature, which does not bloat at all, as on infinite plane; (c) negative curvature, which uniformly shrinks inward, as on a saddle.

Therefore a short list of curvatures -uniformly positive, negative, or zero- exhausts the possible curvatures for space that are consistent with the requirement of symmetry between all locations and in all directions. And that is really stunning. We are talking about the shape of the entire universe. Yet, by invoking the immense power of symmetry, researches have been able to narrow the possibilities sharply.

So if someone was to wake you in the middle of the night from a deep sleep and demand you to tell him the shape of the universe -the overall shape of space- and grant you a mere handful of guesses, you’ll be able to meet his challenge.

- Compiled from 'the fabric of the cosmos' -Brian Greene-

Quantum Teleportation

Assume that Alice and Bob share an entangled qubit AB. That is, Alice has one half, A, and Bob has the other half, B.

Let C denote the qubit Alice wishes to transmit to Bob.

First Alice entangles A with C.

Alice then applies a unitary operation on the qubits AC and measures the result to obtain two classical bits. In this process, the two qubits are destroyed. Bob's qubit, B, now contains information about C; however, the information is somewhat randomized. More specifically, Bob's qubit B is in one of four states uniformly chosen at random and Bob cannot obtain any information about C from his qubit.

Alice provides her two measured classical bits, which indicate which of the four states Bob possesses. Bob applies a unitary transformation which depends on the classical bits he obtains from Alice, transforming his qubit into an identical re-creation of the qubit C.

Note in this teleportation method classical bits are transferred at the speed of light, so teleportation takes time over large distances. For example if Alice and Bob are one light year apart, Bob can reconstruct C after one year.

Reference:
1) Quantum Teleportation - Wikipedia

Quantum Entanglement

If two electrons are initially vibrating in unison (a state called coherence) they can remain in wavelike synchronisation even if they are separated by a large distance.

The spins of each electron can be pointed up or down. Lets say that the total spin of the system is zero, so that if the spin of one electron is up, then you know automatically that the spin of the other electron is down.

According to the quantum theory, before you make a measurement, the electron is spinning neither up nor down but exists in a nether state where it is spinning both up and down simultaneously.

Once you make an observation, the wave function "collapses", leaving a particle in a definite state.

References:
1) Physics of the Impossible, Michio Kaku