James Randi Does His Stuff

I am often surprised at how even highly educated  people can sometimes be fooled by slightly unusual things. In my opinion it's nothing but intellectual laziness. If intellectually lazy people see something that's not in the textbooks they immediately jump to the conclusion that something mystic is going on rather that trying to find out what might have happened.

This is a video I found on Youtube about a "mysterious" reaction which apparently has no explanation. As a person who has learnt quite a bit of Chemistry I tried to figure out what could possibly have happened. My explanation may be slightly off or even completely wrong but I have to start somewhere.

Here's what I think happened. If you look at the video you'll see that a few drops of liquid is added to the distilled water before the blue universal indicator is added. Since the Indicator is blue in alkali that "something" was probably an alkali. I remember that pH indicators are frequently weak acids or weak bases and that only a few drops of alkali was added at to the beaker at the start of the experiment so the concentration of alkali must be very very low.

The universal indicator solution is made up of a mixture of several pH indicators, some of them weak acids. From my experience in doing titrations with I've seen that near the endpoint if you keep swirling the flask the solution turns clear (using phenolphthalein as an example) but the titration is not quite done yet because once the swirling is stopped the solution turns a very very  slight pink. You then have to add one more drop to complete the titration. I reason that the agitation may may be affecting the reaction to a certain extent (I still haven't figured out how but I will soon.). I think this is a similar situation. 

One of the acidic indicators in the Universal Indicator mixture reacts with the miniscule amount of base and neutralizes it. After neutralization, the remaining mixture of indicators take on a yellow colour either because the new ions formed are yellow or because the remaining portion of the Universal Indicator has a yellow colour. The colour will probably return to blue if the stirring is stopped.

I hate to burst the bubble of that aspiring magician (He did look awfully pleased with himself) but sometimes the truth is more important.

Refuting Intelligent Design: The Game of Life and Irreducible Complexity

A long time ago I wrote a blogpost about John Conway's Game of life, which used simple set of rules to make dots on a page evolve. This zero player "game" is an excellent example of how complex systems can evolve from simplicity. All we have is a grid in which each cell has two possible states dead (shaded) or alive (empty) and four simple rules:

1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

 If the system is then left to evolve on it's own given certain initial conditions highly complex patterns emerge that seem almost unthinkable with such simple rules. Here's an example.

This pattern was created by humans who worked out the initial conditions using computers. But think about what would happen if you took a huge grid containing millions of squares and kept populating them randomly while allowing the system to evolve for millions of years. Although the probability of such complex patterns forming on their own is pretty low, because of the huge timescales involved, complex patterns will inevitably develop. In fact I wouldn't be surprised if some apparently lifelike systems which replicate themselves evolved. Now if someone who had absolutely no idea of the starting conditions observed this complex system and tried to work backwards he would find find himself with an outrageously complex problem. Although this person may be able to work out how the little structures in the system function and replicate he would have little or no idea about how the system came about. 

Now think about the world as it was nearly 4.5 billion years ago when our planet was in its infancy. We had a big primordial "soup" of chemicals as the "initial conditions". The laws of physics and chemistry were the rules which our "system" which is the Earth and the primordial soup of chemicals followed. Considering the fact that the laws of physics are considerably more complex than the set of four rules for John Conway's Game of Life and that atoms and molecules have a substantially larger set of possible states that alive or dead is it not conceivable that after a about a billion years--the estimated time it took for the first life forms to appear-- by some lucky coincidence very simple prokaryotic life forms had developed?

Irreducible complexity is a concept that is very commonly used by Intelligent design proponents and creationists to justify the existence of an Intelligent Designer. They claim that in it's current state, life is too complex to have evolved by chance. This is another example of the inability of our brains to intuitively grasp extremely small probabilities. "Common sense" is often misleading when we look into the world of the very small. I think the Game of life provides an excellent example of how seemingly irreducibly complex systems can arise from some initial conditions and a set of rules. We may not have the computing power to reverse engineer evolution at present but I think the day will come soon enough.

The illusion of irreducible complexity in a bacterial flagellum. The complexity of the flagellum was shown to be reducible by  Zvonimir Dogic.

Large Numbers and Premonitory Dreams

Ever heard of the saying "If at once you don't succeed, then try, try, try again."? Have you ever thought of approaching the problem mathematically? The idea just popped into my head today during math class. So now I shall play the role of a theoretical Mythbuster and explore the validity of age old adages using a a purely theoretical approach.

First let's simplify the problem. Let us assume that the probability of you failing horribly at something (and succeeding at it) remains constant and does not depend on whether or not you failed horribly in your previous attempt. We need to find the minimum number of repetitions of a particular task you need to carry out before the probability of success is 99%.

Mathematically this is a trivial problem which can be solved using a binomial distribution. If $X$ is the Random Variable that represents the number of successes, then $X\sim B(n,p)$ where $n$ is the number of repetitions and p is the probability of success. Let us assume for the purposes of this discussion that you are such an incredible moron at doing this task that your probability of success is only on in hundred or 0.01. We want to find n when the probability of succeeding at least once is 99%. So doing the math,

$X \sim B(n,0.01); P(X\geq 1) = 1-P(X=0) >0.99$

$1-(0.99)^{n}>0.99$

$n>\frac{\log 0.01}{\log 0.99}\Longrightarrow n>458.2$

Repeating the task over 458 times ought to do the trick! So this old proverb does have a mathematical basis!

Premonitory Dreams

So what does all this have to do with Premonitory dreams? As it turns out a similar concept can explain in a very simple and elegant manner why people have premonitory dreams.

There are thousands of reports every year of people dreaming about the death of a friend or close relative days before it happens. The superstitious always think of this as "evidence" for the existence of the supernatural. But despite the fact that science cannot explain individual premonitory dreams, a very simple explanation exists if you consider the population as a whole. Read this extract from an article by Michael Shermer.

We can employ a similar back-of-the-envelope calculation to explain death premonition dreams. The average person has about five dreams a night, or 1,825 dreams a year. If we remember only a tenth of our dreams, then we recall 182.5 dreams a year. There are 300 million Americans, who thus produce 54.7 billion remembered dreams a year. Sociologists tell us that each of us knows about 150 people fairly well, thus producing a social-network grid of 45 billion personal relationship connections. With an annual death rate of 2.4 million Americans, it is inevitable that some of those 54.7 billion remembered dreams will be about some of these 2.4 million deaths among the 300 million Americans and their 45 billion relationship connections. In fact, it would be a miracle if some death premonition dreams did not happen to come true! -  Michael Shermer,September 3, 2008. Why Our Brains Do Not Intuitively Grasp Probabilities. Scientific American, Retrieved from http://www.scientificamerican.com/article.cfm?id=why-our-brains-do-not-intuitively-grasp-probabilities 

As we can see from this article, our brain is not very good at intuitively grasping probabilities, especially when the numbers involved are disproportionately small. This results in the intolerably widespread delusion that premonitory dreams are a result of supernatural influences. It doesn't help that most people are prone to what is called a confirmation bias. When people believe in something they tend to look for events or pieces of evidence that confirm their belief and tend to "filter out" anything and everything that contradicts their beliefs. All those who claim to be psychics take advantage of this cognitive bias. Take tarot card readers as an example. People always remember the time the street psychic predicted their promotion of pay raise but always forget the times they failed to predict anything substantial. In fact if you measured the success rate of psychic predictions you'd probably find that they are not much better than what you would expect from someone who was guessing intelligently. So in the future if you meet somebody who claims that premonitory dreams are proof of the supernatural you can gleefully prove them wrong!

How to (Legally) Jump a Red Light.

So I went on an extended hiatus from blogging for a while because I was very busy by my AS-Level examinations. Now with only one exam on physics (MCQ) left I shall temporarily re-enter the blogosphere.

With physics buzzing about in my mind I thought I'd do something about physics. So today I am going to tell you how to jump a red traffic light and get away with it (even if you're caught) using the indomitable power of physics.

Imagine yourself in this situation. You're speeding down a long deserted highway, it's an emergency and you're confronted with one of those annoying red lights. You need to get home as quickly as possible but those sneaky cameras are always on the watch for people who want to bend the rules a bit. What do you do?

Use the Doppler Effect.

I wonder how many will get this reference?

Many people are familiar with the Doppler Effect that's observed with sound. They may be able to recall that the sound of a train which is speeding towards them is at a higher pitch that the sound of the same train when it has passed you and is moving away from you. In simple terms this is because the sound waves in front of the train get squeezed together and has a shorter wavelength and consequently a higher frequency that the waves in front which are stretched out.

The amazing thing is that this Doppler Effect will work with light too because light essentially consists of electric and magnetic fields oscillating at right angles to each other. The colour of the light depends on it's frequency and wavelength. In light it is called the Relativistic Doppler Effect because the effect was first brought to light by Albert Einstein.

So to jump the red light, all we have to do travel fast enough for the red traffic light to be blushifted to a green colour. 

So we apply the equation for the Doppler shift of light. $\frac{\lambda_s}{\lambda_0} = \sqrt{\frac{c-\nu_s}{c+\nu_s}}$.

$\lambda_s$ is the wavelength at the source, which is equal to 650 nm (Typical for red light).

$\lambda_0$ is the wavelength observed, which is equal to 520 nm (Typical for green light).

$c$ is the speed of light which is 299792458 m/s .

$\nu_s$ is the speed of the source away from the observer which is what we need to find. 

If the calculation is carried out you will find that the required speed is about $6.6 \times 10^7 m/s$ or about 237 600 000 km/hr.

And there you have it! Travel at 237 600 000 km/h and you can legally jump the red light because at that speed the red light is no longer red. It is green.

By now, the more intellectually keen reader might have spotted a huge gaping hole hole in this grand plan. A big question will be burning in their minds. The will say, if we are travelling at 237 600 000 km/h are we not breaking the speed limit? However, as it turns out my plan is unbelievably foolproof. At 237 600 000 km/h, you're travelling so fast that any speed trap foolish enough challenge you (which by the way utilizes the Doppler Effect to measure the speed of your car) will find that by the time, it's microprocessors are done calculating your speed and ready to snap a photograph of your numberplate, you'll be miles away. Even if there existed a microprocessor that could calculate fast enough, you'd just be an unrecognizable speed blur on the photograph. 

Well now, we have a another problem don't we? Have you seen it yet? You might be thinking, that if the cameras are too slow to photograph you when you travel that fast, why did I go to all that trouble to calculate the blueshift of light? Why didn't I just tell you at the very beginning, without going through all this rigmarole, that all you needed to do was zoom by at 237 600 000 km/h?

I just felt that getting around the problem using Relativistic Doppler Shift Equations were a more elegant way of bending the rules than just "speeding". That's all.

[EDIT: I watched an episode of the famous Mythbusters in which they showed that all you need to do to beat the speed camera is a car that travels at over 300 miles per hour which translates to about 483 km/hr. So that's the minimum speed you need.]

Warning

Disclaimer: The author is not responsible for any unpleasant effects the enthusiastic experimenter may suffer from as a result of carrying out this experiment. Any damages suffered by the experimenter such as those due to relativistic time dilation, time paradoxes, getting lost int time, changing the course of human history etc. are the sole responsibility of the experimenter

LaTeX Testing

I've started using $\LaTeX$ for so that I may embed mathematical equations in my blog without resorting to uploading images each time I want an equation up here. This is just a test to see if everything is working properly.

[Note: Those viewing the mobile version of this website will just see lines of meaningless code unless of course you are adept at coding in $\LaTeX.$]

$R_{{\mu}{\nu}} - \frac{1}{2} g_{{\mu}{\nu}} R + g_{{\mu}{\nu}} \Lambda = \frac{8{\pi}G }{c^{4}} T_{{\mu}{\nu}}$

$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu}$

$e^{ix} = \cos x + i \sin x$

$G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$

$\sum_{n=1}^{N-1} 3^{-n}cos(2n\theta)= \frac{9-3^{-N+2}cos(2N\theta)- 3cos(2\theta)+3^{-N+1}cos[2(N-1)\theta]}{10-6cos(2\theta)}$

$\sum_1^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$

$t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$F_e = \frac{1}{4\pi \epsilon_0} \frac{Q_1 Q_2}{r^2}$

And for
$CH_3COOH_{(aq)} + CH_3CH_2OH_{(aq)} \longrightarrow {CH_3COOCH_2CH_3}_{(aq)} + H_2O_{(l)}$
$K_c = \frac{[CH_3COOCH_2CH_3][H_2O]}{[CH_3COOH][CH_3CH_2OH]}$

A Chess match with my father.

Had quite a long and drawn out chess match with my father. We were quite evenly matched. I was almost going to beat him, but I made a slip up at move 47 (can you find it?) and in the end he beat me.

Play online chess

An Interesting Observation

 

Crazy..... 

An Unexpected Finish

A very unexpected finish to a chess game. I was really tired and playing a bit blindly, not thinking much more than a move ahead. I made a move only expecting to fork the opponent's king and rook but as it transpired that move checkmated my opponent. I checkmated my opponent without realizing it! Imagine that.

This was blitz chess, played in under 2 minutes with 12 extra seconds awarded to the player after each move. I'm playing as white of course.

As this is the first time I am embedding a chess game in my blog I will give some directions. Look underneath the chessboard. Click on the button with ">" in it to see the game move by move. You can also click on one of the moves in the list on the side to jump directly to that move.

Play online chess

PS: I'm not sure why the scroll bar of the move list suddenly decided it was more comfortable -> lying between my blogposts like some freakish cyber bridge. No amount of fiddling with the code could correct that issue...