Can you live in a Fractional Dimension? – I

To simply put, your expression after reading the question is puzzled, right? How can there be fractional dimensions, let alone living in one? Before heading to answer something that tricky, shall we get to ground zero and understand what a dimension is in the first place? Quoting Wikipedia: “In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it”. Did you note the word “informally”? Obviously, there exist some rigid definition, what do you think mathematicians are for :). In fact there are multitudes of definitions in mathematics but will come to that later on.  For now let’s just discuss some amazing thoughts based on the wiki answer which will really be a pleasurable experience. The most important thing in science is to ask the right questions so let’s start by a few interesting questions.

How many dimensions do our eyes see? The answer can be derived from this counter question: How many dimensions can a camera capture in an image? Well, that’s simple it is 2 and because our eye is an organic camera it can see only 2 dimensions. But why 2? Hmm, that’s a decent question. That’s because we live in three-dimensional space and one of the dimension(depth) in the image capture setup will be for light to bounce off the object and form image on the retina(photo sensors of our eye). Also, did you know because we have 2 eyes very close to each other we have stereoscopic vision and thanks to that we can visualize depth too. Okay that was more than asked, but how can you claim that the space we live in has just 3 dimensions? Because every point in space can be associated with three numbers in x, y and z direction. But how can you be sure that there are only 3 dimensions? Because we perceive only 3 dimensions. Isn’t that answer more anthropological rather than scientific? Okay, I will end the soliloquy here but see I made my point. Which one, science has anthropology as its basis or soliloquies suck :). No idiot, the point is that there is no concrete proof of space being three-dimensional. By the way, the picture below shows how a  Tesseract, a 4-dimensional “cube” will look to us when it is rotating, so Yeah.

Okay, you might be thinking where I am going with this. As I said earlier before moving on to a tricky answer let’s get comfortable with dimensions and related concepts. In the nineteenth century a lot of work was done in Mathematics by some of the most brilliant people such as Bernhard Riemann on higher dimensional geometry. These were later used in physics starting with the Special theory of relativity.  In fact it was Hermann Minkowski (Yes, he was a Mathematician and Einstein was his student) not Einstein who gave the 4-dimensional space-time model.  Then came along Quantum Mechanics which was completely probabilistic and too random to make sense, although philosophers loved this and created all sorts of crappy theories using the uncertainty of the new science (as is always the case). The uncertainty of the new subject was obviously taunting to many physicists but in the recent decades the dimension picture is attempting to explain why quantum mechanics may look probabilistic because of our 3-dimensional spatial perception. The amazing video below talks about this new approach, now very well-known as M-theory (apparently M stands for Minkowski) and also shows you how to visualize 11 dimensions.

Cantor Set

The above picture shows a Cantor set also known as Cantor comb. You get this by taking a line and opening up the middle third of the line. As you can see the second line has an open middle which is 1/3 the length of the line and the third line is got by applying the same rule on the second line. What is so special about this? Actually, everything about this set is special and the most amazing thing, before I stop this first part of my answer (I know, I was cheeky for not giving the answer in this part :)), is that the Cantor set which intuitively looks to have a dimension of 1 (as it is a line), actually has a dimension of 0.630929… Yes, I will explain this in the second part and also answer the question in the title. So, stay tuned

……………….to be continued………………….

Advertisements

Introspection by a young Indian

I’m sure most Indians would have heard two contradicting views about India. Firstly, the arguments claiming India to be a prosperous and well developed region (cluster of provinces) before colonization and claims to have proof for their argument. Secondly, the argument (especially foreigners) considering Indians as people who are boastful of their past arguable achievements, without having any present day significance. This contradiction made me think. Initially like everyone else I tried to find which one is the truth but soon realized that I’m missing something bigger and more important.  I started so discover a certain degree of agreement in the contradictory views. So, the soul of this post is to find the implicit fact agreed by both the proponents.

In the former argument there is a call for the Indians to not forget their roots which were apparently glorious and says that latter argument is developed by westerners (in particular by the British) to destroy our self-esteem. The latter argument just points out at our present day reality and asks for our recent contribution to the world development. If we get into verification of authenticity of either of the arguments we will be lost. We can’t deny the second argument but at the same time we can’t fall prey to it since we were indeed a slave nation under the British and we do see lack of self-esteem among Indians, who are willing to accept anything from the west and don’t like to appreciate the east. So let’s move on and check if there is any common ground in these two arguments.

Being a person who likes to define rules of the game before playing one, I want to define what is progress? Here is the way I look at it: Anything which makes us understand our universe better is progress. The only way to understand the universe better is through science. Thus my yardstick of progress is scientific progress. When we contribute to scientific progress it gives a sense of right to enjoy the modern day technological facilities or else metaphorically speaking, if we don’t contribute to science and enjoy its benefits then it is like living on other’s income by theft or robbery. Being a man with moral conscience scientific progress is the epitome of all kinds of progress which will make me proud in front of foreigners. It is the last frontier of a nation’s developmental challenge.

Now coming back to the two opposing views, one fact is accepted in both perspectives i.e., Indian contribution to scientific development (synonymous with development) in modern times is very less if not nil (thanks to CV Raman, Ramanujan, JC Bose). Major chunk of scientific work happens in America after WW2 (though CERN and some European universities continue to hold on) and before WW2 it was Europe which was the knowledge bowl of the world. So in past 400-500 years we are constantly lagging in the quest for knowledge. Whoever claims for Indian contribution inevitably goes before this period and in case they come up with some examples they will be exceptional people with a foreign institute affiliation. So where did we fail? I am forced to accept that we failed, but where?

Scientific progress asks for economic prosperity since the quest for satisfying the knowledge hunger comes only after satisfying the real hunger. India certainly had all the resources for economic development. Any simple study will reveal the reason behind huge population in India as abundance of natural resources here, apart from petroleum. Hence economic progress with men and material power must not have been a problem. But, both scientific and economic progress asks for one key factor which was completely missing in India and it is often neglected around the world. That key factor is political stability. The political instability and lack of governance not just derailed our scientific progress but also our economic and every other forms of progress. This is where our ancestors failed us. They couldn’t give political stability and protection because of lack of foresight, will, interest and presence of selfishness.

Now that I have arrived at some sort of conclusion what is more worrying for me is that we continue to commit the same mistake as that of our ancestors’. We continue our apathy and indifference towards politics. Majority of those who indeed show interest does it for personal gains or to pessimistically ridicule the developments. Politics is something which everyone must know. Irrespective of a person studying science or arts or economics, he must know politics and its implications. He must have a political ideology of his own. He must be able see through the political developments and actively participate in it. Hopefully we will realize this before it is too late.

Why the sky isn’t blue?

Nope, it’s not what you’re thinking. The title is neither wrong nor is it misleading.  I came across this awesome video and the question is quite straight forward “If sky is blue because of Rayleigh scattering, why isn’t it violet because it has a shorter wavelength? ” (to people from a science background). This question just blows away my mind and i am like “wow!  why didn’t i ask this question when i heard the “why is the sky blue?” answer. Check out this video and prepare to be amazed with the explanation.

Fun way to find your nerdiness quotient

Are you ready for the truth? Ok this is how it works. There are 10 nerd jokes below. If you enjoy a joke then +1 for you, if you understand but don’t enjoy it then +0.5 for you, if you just don’t get it then you get zero. After going through jokes you can find your position on the following scale:

nerd scale

so lets start:

  • 1. Two variables discussing about religion:

x^2: Do you believe in god?

x^3: Well, I do believe in higher powers!

  • 2. Meanwhile in another part of universe of the polynomials

Spider-polynomial: “with great powers come great difficulty in factorizing”

  • 3. There are two kinds of people: Those who can extrapolate an incomplete data…
  • 4. There are only 10 types of people in the world: those who understand binary and those who don’t.
  • 5. Geeky pick up line: I wish, I was your derivative.. I could lay tangent to your curves!
  • 6. Another pick up line: I’m attracted to you so strongly, scientists will have to develop a fifth fundamental force.
  • 7. And one last pick up line: I wish, I was Adenine so I could get paired with ‘U’
  • 8. You may think glass is half empty or half full but engineers know that glass is twice large as it should be!
  • 9. A majority of people have an above average number of legs.. think about it.. its true!
  • 10. I’m not lazy, I’m overflowing with potential energy

Hope you got the score that you wanted to get (either more than 5 or less than 5). Let me tell you that my heart goes out for those who wanted to score less than 5 but scored more. Do write a comment below about your position on the nerd scale.

Linearity …..Obvious?

As Humans we think linearly. We use this notion of linearity to such an extent that it loses its significance. I mean, say you do double the amount of work (than told to), what shall you expect to get in return? Of course you will expect double pay (and some praise ……….. maybe). Now why do you expect double the cash, why not 4 times? The question seem to be ridiculous, you may be thinking how in the world anyone can expect 4 times the pay for double the work (……..such a job seriously rocks ). I ask why not? The question is annoying as it is fighting our instincts. The question is so  fundamental that it touches the foundations of our thinking process.

Reason-Humans think linearly. As a science student the first and easiest property to be proved is the linearity property. We neglect it saying it is obvious, but should we? Does everything in nature is linear? No, in fact most of the activity taking place in nature is non-linear.A musician doesn’t play a note on every beat   As a human tendency of linearizing every study we define functions in such a way that they are linear. This has proved very beneficial to science and it is the right approach. All i want to convey is that the next time you approach a problem linearly , reflect just for a moment,  is the characteristic of the problem  really linear