Story of a 'spinning lady'

Did you notice the figure above? To see the spinning lady, click this link and return back. Is it a spinning lady? In which direction, you feel the lady is spinning? clockwise or counter-clockwise? One can feel the spinning of the lady in either clockwise or counterclockwise. But once you feel lady spin in one direction, your brain continues in that state and insist to be in that state. If you feel that the lady is spinning in clockwise, it is too difficult to see the motion in counter-clockwise direction. But sometimes our brain switches from one state to other state automatically, but changing the state of feeling of brain is difficult to achieve manually.
This is a beautiful eye illusion. Do you know how that beautiful lady, cheated your brains?
Answer is, the lady didn't cheat you, but the cheater is her shadow. Actually, the image shows the shadow of a spinning lady. In this, a 'shadow' plays in important role in cheating you. The pure shadow of an image will not provide the entire information about an object to the brain. From a shadow, we can't predict whether the front side or backside of the object we are viewing. If you didn't understand what I just said, please go through an example.
Look at the picture below.
The middle picture is photo-shot of the spinning lady. Concentrate on the picture and tell what you are viewing- the frontside or backside? It may be both. Look at the left picture. It is the modified version of middle one by adding eyes in her face. Now you feel that you are viewing the front side of the lady. At the same time, you see the backside of the lady in the right picture, but that also a modified version of middle picture with marking of a hair bud. This is important to be noted. While you are viewing the middle picture only, your brain fall in to the mess of finding whether the shadow is of the front side or backside. Then your brain 'randomly' choose one possibility (not actually). But in other pictures, your brain has powerful proof that indicates the state of the lady's body.
Now the problem associated with the spin direction of the lady is not vague. If your brain 'assumed' a side of the lady's body you are viewing, this will determine which direction, she is spinning.

A lady who travelled faster than light....

I recently read and much inspired by this old poem:

Once there lived a lady
She could travel faster than light
She left out of home today
And returned back yesterday!

Sometimes the real things are stranger and mysterious.....

How do we think? A brief introduction

Thinking about how we think is difficult, because thoughts of thoughts are limited by thoughts itself. But learning of how we think is essential in computing as well as AI powered robots. The basic reason of our thinking ability is a special type of cells in brain - neurons. A neuron is not perfectly known to human yet, but many similar models are proposed. The power of neurons is in its networking ability. Neurons are connected to each other and these complex networks may called as neural networks. I am not describing much about neurons because it is beyond our task. It's well enough if you just get an overview from Wikipedia. As I said, many convenient models are there to explain the behaviour of a neuron (Of course, a networked neuron is complex than a single one), but I am just touching simplest one named Perceptron. I will also mention back propagation during the example. I have pasted one figure from Wikipedia because you need it.The area in the shaded square can be considered as a neuron. x1,x2,......x7 are the inputs and w1,w2.......w7 are the corresponding weights (I will tell you what it is). and f is simply a function and outputs y. If the weighted sum of the inputs exceeds a particular threshold (which is previously be set), output y fires out. In actual neurons, y depends on other parameters such as input frequency. Since whole process in actual neurons are chemical, the explanation become rather complicated. But in all models we consider input as well as output signals are electrical in nature.I am explaining once again: first find

x1*w1+x2*w2+.........+x7*w7

If the resultant value is greater than a threshold (Typically 0), y=1; otherwise y=0.
I hope you understand something. But I know most of you are not satisfied because, you don't know what is really going on! Right?
Let me tell an example. This is a story. Here is you, Heroin is you.
Consider you have three friends and you(your brain) thinks that they are:

• Albert - Your best friend. You have a confidence level of 0.7 on him. You trust him and ask his opinion before every important attempt
  
• Deepika - Your classmate. Confidence level 0.3. Good personality.
• Tom(me) - Confidence level of -0.55. Always say lie. Cheating personality.

These prejudice are taken by your brain from your experience. May be true or may not be.
The problem starts here. You are getting ready to go to your office/college. There are two ways to go. One is short path (easy way). Other is long. But short way has a problem is that sometimes it will be blocked. If you take the long path, you may reach the destination late. But if you choose the short path and in any case if blocked, you can't reach the destination on that day.
Then you come to know that today short way will be blocked. Then you consult your friends. Check their opinion:

• Albert - Short road is not blocked. Damn sure.
• Deepika - Someone told me about it. Short way may not be blocked. But I am not sure.
• Tom - Hey man, road is blocked.

Can I go straight away through the short path?
Let's look how your brain solve the problem. Albert surely says that road is not blocked. Put a value of +0.95 for his opinion. The positive sign indicates that he is opposing. If Albert says sure that road blocked, the value may be -0.95. You don't know much about Deepika. But she may be right. Put a value of +0.1. Tom says it is blocked. So put -0.8.
Here threshold value is 0. If weighted sum is greater than 0. road is blocked. It is good to choose the long way. I not, road is not blocked, choose the short path.

Weighted sum is:
signal strength of Albert * confidence level+ signal strength of Deepika * confidence level+ signal strength of Tom * confidence level
=0.95*0.7 + 0.1*o.3 + (-0.8)*(-0.55)
=0.66+0.03+0.44
=1.13 which is greater than 0.

The brain successfully derived a decision for you. It is almost sure that road blocked with a confidence level of 1.13. Did you notice the analysis of Mr.Tom's opinion. You think tom is cheat. So the opposite of what he tells will be right. If you didn't understand the meaning of previous sentence just read one more time because some interesting things hidden in that sentence.

Ok, let's continue our story. Then you started going straight away through short path. You started journey in your own car but Alas! road is blocked. You couldn't just believe your eyes. but suddenly you realize the fact that you can't reach your destination today - you trapped in a huge road block.
Here, your brain attempts to rewire the entire circuitry inside it. Your thoughts were entirely wrong. Both Albert and Deepika was wrong, but Tom was right. You change the congedence level as,

• Albert - 0.4 - I can't blive he cheated me.
  
• Deepika - 0.1 - no coments.
  
• Tom - 0.2 - oh, sorry Tom.

The actual working principle of neural networks is far deviated from the above story, but the fundamental thing in both is same. Actual neurons has a lot of diifernces and complexities than the neuron models

Don't believe your eyes!

Don't believe your eyes, because everything you see, touch and feel is just a feeling only. Consider you are traveling in a space ship. No way to look outside. Space ship is traveling with higher velocity. If there is an obstacle present in front of the spaceship, sensors feel the presence of obstacle and it is reported on your computer. Then you turn the spaceship left or right. Then sensors feels that obstacle is removed (not obstacle, you!) and computer indicates that you can go straight way.
The above explained is a successful turning. But here I go in a something different way. The sensors are intelligent enough to send a fake signal that "there is some sort of obstacle" on the monitor. Actually, there is nothing in front of it. But your computer shows some obstacle. So you put a signal to turn right. Then the sensors shows that "now obstacle is removed. Go straight". You feel that you done well, but the sensor and the computer system really cheated you. Sometimes it was not a cheating, because ,there will be a possibility of thinking that there is an obstacle.
Our brain is not much different or error free in similar cases. If you are think that you know the universe, I think it is actually bad. Things you feeling from the surroundings may be different from reality. Your eyes are similar to the spaceship sensors. Not only your eyes, every sensors just see one phase of the reality. That really implies that knowing reality is too difficult.
I am not going too inside. I am not a philosopher. So let's have a fun. just go thruogh this link. A number of good eye illusions are included. Here I give a puzzle from eyetricks.com - Find which is longer?

Why there is so many constants in equations?

I will tell you the secret of constants in mathematical equations. They are not intruded or the error or nothing, but it is essential part of the equation. I will tell you some facts while going on your story. I will exemplify what you want in this story.
Consider you are a young scientist. You close your room's door and start experimenting on something when you get leisure time on Sundays. You are doing something seriously on your table, with an electrical circuit. Your aim is to find the dependence of a node voltage X (ie, a voltage in a part of the circuit). You came to know that X depend upon the supply voltage V. You start experimenting and plot graph of X for different values of V. Then you
got a graph like this:
It is perfectly linear. So you write,
X is directly proportional to V
To be more specific, X increases for an equivalent increase in V. You repeated your experiment and plot another characteristics with time. This time, your supply voltage kept constant. Plot X with time t.

From the plot, it easy to find that dependence is,

X is directly proportional to e^(-t)

Then from the above town experiments, you can write that,

X is directly proportional to V*e^(-t)
ie, X = K*V*e^(-t) where a K is the proportionality constant.

You can find K from single experiment. Once you got the value X when for a particular V and t,

K = X/(V*e^(-t)

But I want to tell you that your experiment as well as your mathematical expression is not perfectly true. A true dependence of X on it's environment will be very complex and tedious to express in mathematical form. Your X may depend on the atmospheric pressure, temperature, material properties,...raining in New Delhi,.....war on Iraq and so so.
After several years, you repeated your experiment and find that X depending on temperature also. Temperature has a direct linear relationship (like V) on X. But last time, you didn't got it. What's the reason? You were not aware of that, you did the experiment in room temperature itself. But this time you get different answers in day and chilled night. Now you modify your equation as,

X is directly proportional to V*T*e^(-t) where T is the temperature
X = L*V*T*e^(-t) where L is the proportionality constant.

Here I want a point to stress. Do you think your previous equation was wrong? Not at all. It is correct in an isothermal environment. But it become wrong in a temperature varying environment. A single measurement depending upon many things in the surroundings. But many of them can be ignored, because, they have less relationship with X. Something can't be ignored, but they may not be measurable (such as number of electron collision per second).In such cases, just put a constant for that, as long as they are constants. To be more clear, if your experiment depends upon the radius of earth, just put it as a constant in your equation. But when you do the experiment in moon, your experiment may troubled, unless you replaced the radius of earth with moon. I meant that variables can be considered as a constant or variable according to the environment.

What's the value of 0/0 ?

Do you know what's the value of 0/0 ?
Most books just don't care about it. Also many teachers are not interested to touch anything like this. Students are fearing to see this, especially while they are doing some calculations on the exam paper!
Anyway, it is good to be aware of 0/0. I continue this article assuming you know basic addition, multiplication etc.
One question: What's the value of 10/2 ?
It's 10/2 = 5. Is it?
We got the answer as 5. Is that mean 5*2 =10 ?. For example, if you have money Rs.10 and distributed to your two friends equally. Then your friends get 10/2 = Rs.5 each.
From the above example, we can generalize that if a fraction exist in the form x/y=z , then z*y =x.
please note the above line. I will tell you more about that line!
Then the question is if you divide your Rs.x to y people equally, each will get  Rs.z. Then what is z?
The answer z is a number which satisfies z*y=x. In the above example, you put different values for z such that, z*2 =10. Then z is the amount in your each friend's hand. Here 5, the only 5 satisfies the equation when it put to z. Thus each of your friend get exactly Rs.5.
Then consider the case of 0/0 . Like the previous example, if 0 is divided to 0 people, how many rupees each of your friend get? If  the answer of this question is z, we can write z*0 = 0. Put some values for z in order to satisfy the equation. All values of z which satisfies the above equation are the solution. We know that multiplication of any value with 0 is 0. So z can take any values to satisfy the equation.
If the solution of z is written in a page, your page may not be sufficient to include all solutions of the equation because solution is 'any value'. More mathematically,
z = -infinity.......................0.......................+infinity
So, 0/0 = any value
It seems very interesting on the first sight. You have nothing, and you are dividing that to nobody. Then the amount in the nobody's hands may be millions, trillions or anything. If you think, this is like a magic to generate millions from nothing, you are absolutely wrong. Think about it.
Let's go for an example to describe what's actually I am trying express. To understand this example, you should aware of a great law named Ohm's law in Electricity (The circuit shown below is stolen from Wikipedia). If you don't know anything about Ohm's low, you must make yourself aware of that before going to continue.

According to Ohms law (refer picture), R is V/I.

R=V/I

If V=10V and I=2A, then R = 10/2 = 5 ohm. In the above picture, if Voltage V=0, Current I will also be zero (without voltage there will no current). Then R = V/I =0/0.
According to our previous result 0/0 can be 'any value'. So R = 0/0 simply means R can take any value. R can be anything.
R*0 =0 can be treated like this: R is the values that exists when V=0 and I=0.
If you put a resistor in your pocket, the applied voltage V = 0 and hence current I = 0. So you can put Resistances of any value in your pocket. Think about the world of 0/0 = a fixed value. For example, take the fixed value 0/0 = 100. Then Resistance R =100ohm is the only value that can put into your pocket and others can't!
Seems funny? but it is fact.

About our knowledge

We dig everything from the centre. Every experimentation of any branch of science starts learning our world neither from the beginning nor from the ending,but from in between. We don't know the beginning and the ending. But we dig to above and below from the middle, but never reaching anywhere.
For example, a man start to learn about the world. He first learn about the present things -trees, birds, humans etc. He digs to the past and also digs to the future. Here time is the base. When size becomes the base, that man start to learn back to molecules, atoms, sub atomic particles, quarks....And when going up, sun, Milkyway...Here again we don't know the ending. It seems that, man's knowledge is isolated in every axis didn't touch the starting or ending yet. Yes, it's really floating!

Physical Interpretation of DeMorgan's law

I am asking you what is De Morgan's law. This may be the answer.
If A and B are two events,

(A+B)' = A' . B' and (A.B)' = A' + B'

(Here the operator ' represents the compliment of the operand. That is If A is 'yes' then A' is 'no' and if A is 1 then A' is 0 and vice versa). I assume you have basic knowledge of Boolean algebra. Now I am giving a physical interpretation of the law which is very useful in analising the law.

Consider first law,

(A+B)' = A' . B'

Here '+' is OR operator. That is A or B. Let Y be an event of shutting down your computer. You can do it in two ways and B.

A=>shutdown manually by pressing the power button of CPU.
B=>click 'shtdown' using your mouse.

Then,
Y=A + B ie, Y= A OR B

Another iterpretation is that, you can turn off your computer by either clicking 'sht down' or by pressing power button. If any one event occured, the computer turns off. ie, Y become true.

One day, your friend came to your home and want to learn about computer. He did something in your computer in order to turn off.Unfortunately, the computer didn't turn off. He reported you in the other room. Then you think in this way, what may be the reason why the computer didn't shut down. The output occured is Y'. ie, computer didn't turned off.

Then from the previous equation,

Y' = (A+B)'
Applying De Morgan's law,
Y' = A' . B'

Here the interpretation is that, The event A is false and event B is false. ie, he neither clicked 'shutdown' nor pressed power button.

Take De Morgan's second law (A . B)' = A' + B'
Consider two dependent events. For example,
let A and B be two dependent events. If your friend dont know how to call someone using a coinbox telephone. The procedure written on the side of the machine is first put the coin and then dial the number. They are dependent events.
A => Put the coin.
B => Dial the number.

Here the output Y is to call somone successfully. ie Y = A.B
(Here A.B is not equal to B.A which is another boolean theorm. Here just don't think about it.It will be explained later)
Unfortunately, your friend could not call the other. He asked for help. Then you analise the problem why he didn't call.

Y' = (A . B)'
By, De Morgan's law,
Y' = A' + B'

ie, he either didn't put the coin or dial the number properly. The above example is conditional events.

Open electronics - Philosophy

Electronics is nowadays being a part of modern human life. Computer, Television, PDAs, Mobile phones, ,Vehicle Engines, and every field of communication, Medical science, Military requirements and everywhere….A similar boom was taken place years ago in the software field. The necessity of software with less cost and freedom opened the windows of open source software foundations like GNU. Thanks to GNU/Linux.

But the case is different in the case of electronics. Here the real source is the circuit schematic and logic. Here the source is more valuable than software distributed under GPL License. But as development goes on, the nomenclature of “opensource” is becoming relevant in electronics also. In modern digital control, the logic is not only the part of hardware and is shared by the software also. That means, hardware is likely to be same in all devices, but the complexity of logic completely depend upon the program itself. That is what is I want to emphasize “opensource” is being relevant in the filed of electronics also.

In older age, it was easy to 'hack' the circuit by the method known as 'Screw Driver Engineering'. But as micro electronics development goes on, a single chip can hide most of the important logic to the end user. The arrival of microcontrollers again increase the complexity of hacking. These technology is extremely useful where security is required. The same security issues exists in software field also. But a programmer can hide important parts of program from the user. This is considered to be severe from the perspective of openness. The similarity in the electronic field and the computer software field gives us a way for a new revolution - open source electronics.

Read more about the open electronics philosophy here.
Another good website concerning open circuits.

About random numbers

Nothing is random in this world. But something feels to be random if we do not consider some of the associated parameters. If we consider all parameters (ideally), and can feel things in every perspective, it becomes a definite process. The lack of determining the parameters associated with a process is the reason why some process likely to be random.
For example, consider a coin is tossed, it appears a random process to get an outcome of 'head' or 'tail'. But if we simulate the whole process in a computer oriented mechanics simulation program, the process definitely depend upon the orientation of the coin while tossing and air friction, gravity, and so many other things. It is clear that one can say definitely what will be the outcome of the toss. Then why are you saying that it is random? All called random process definite in the other kind. Nothing is random. Nothing should be random.