The Right AdiTude

Living in this technology oriented world, we can observe how quickly the devices we use are improving. They are getting faster, smaller and more convenient at an alarming rate. An average computer today is about 1000 times faster compared to a computer 15 years ago. We just accept that this how technology works and rarely think about some key questions. HOW are engineers able to improve the performance of the computers consistently at such a rate? Is it possible to keep improving the speed of our computers at this rate? If not, WHAT is the future of computing? To answer these questions, I will need to first briefly explain the building block of a processor: Transistor. 

Transistors (combination of Transmitters and Resistors) are semiconductors capable of amplifying or rectifying an electric signal. They act as tiny switches that either enable or disable the flow of electricity by physically connecting or disconnecting two wires. This action is triggered by an electric impulse received by transistors. Transistors, being semiconductors, can conduct and enable the flow of electricity or insulate and disable the flow of electricity, thus giving us the basic structure of binary: 1 (conduct) or 0 (insulate). Transistors are usually made of silicon as silicon, after doping, is an excellent semiconductor at room temperature. Therefore, transistors form the basic building blocks for a processor, which means more the transistors, potentially faster the processor. 

Moore’s Law says that the number of transistors in an Integrated Circuit (CPU, microprocessor) doubles roughly every 18 months. This law of exponential growth of the number of transistors turned out to be quite accurate, as the world moved from a computer with 2000 transistors in 1973 to about 350 million in 2006. However after 2010, the world couldn’t keep up with this growth rate. Today, we have computers with about 1.5 billion transistors which is around 5 times less that the Moore’s law estimate. This is because, in order to increase the number of transistors we need to decrease the size of a transistor. In 1970s we started of with transistors that were visible to a human eye. Today, we have transistors with a width of about 30 nano-meters, which is about the size of a few hundred atoms. So, the final question comes down to just how small can we make a transistor?

There is obviously a limit to how physically small transistors can get. For starters, they cannot be smaller than the size of an atom. But, if we do more research and follow basic laws of physics, I don’t see the size of transistors going much below 10 nano meters. Which potentially gives us room for ONLY TWICE the number of transistors that we have now. Even if we go down to this size, there are a lot of challenges we will have to face. First, having this many transistors processing terabytes of data in a small space will lead to significant increase in temperature (by 100s of degrees) and eventually the transistors will reach their melting point. Moreover, if a transistors depends only on a few atoms that makes it less reliable and not affordable. Furthermore, a chip consisting of such transistors will have a huge energy demand that easily exceeds our capacity given the resources we have. And finally, the phenomenon of Quantum Tunneling and Heisenberg Uncertainty Principle: When we’re dealing with distances in tens of nano meters, we cannot ignore the fact that electrons will behave in an unpredictable manner which would further lead to corruption of data and computational errors. 

Mom: Honey, please go and buy milk and if they have bananas, get a dozen.

Dad: Sure!

Dad goes to the store and comes back home with a dozen of milk.

Mom: Why did you bring a dozen of milk?

Efficiency vs Effectiveness, Input vs Output, Result vs Method: These are some key questions that come up in the process of developing any product. 

Efficiency is a way of measuring how well something is done, where as effectiveness measures the usefulness of something that is done. For example if you’re a programmer, you’re efficient if your code runs faster than most of the other code and your effectiveness will be measured in terms of the usefulness of the code. 

Efficiency is clearly method and effort oriented whereas effectiveness is result  oriented. 

Now, the question is: Should you be efficient or effective? It really depends on the type of task that you’re performing. From a programmer’s perspective, if you take the efficient way and make a program which is extremely fast, but if it takes too long to implement it, if might not be what your company/client is looking for. But, if you’re effective and try to finish up a program fast, but someone else comes up with a program that is faster than yours, then again, you’ll lose the deal with the client. Therefore, there has to be a good balance of efficiency and effectiveness while approaching a project. The hard part is coming up with a method that allows us to maintain that balance. 

For someone who is a beginner in project development, it is advised to be effective at first and complete the project before time with minimum requirements and then use the remaining time to work on the improvements. 

But, as you gain more experience in the development area, you’ll get an idea of how much time you have to be efficient while being effective. For example, if you want to make an animation and you have been given a model with a high-poly mesh to work with. You could either be effective, and just continue with the application with the high-poly model, or be efficient and make a convert the high-poly model to a low-poly model to make the animation render much faster. Although, this process might have other hidden costs, such as learning a modeling application like Blender or Maya, and being able to come up with a low-poly model which looks similar to the high-poly model without compromising a lot with major details. If you have expertise in working with animations and know how long it takes to make a low-poly model or to learn a modeling application, then you’ll be able to create a model good enough to load fast within the project deadline, hence, maintaining a good balance between efficiency and effectiveness. 

Personally, I invest a good amount of time in designing a plan that is effective and hardly compromises with efficiency. The more you try to maintain a balance between the two, the better you’ll get at designing a balanced plan.

Here is a really cool vedic method to square a number mentally, that ends with ‘5’. (Not my own)

For a number that ends with ‘5’, say 65.

The square of it will end with  ___25.

Now, the previous digits can be calculated by multiplying 6 with (6+1).

Therefore,

65^2 = (6*7)__25 = 4225.

PROOF:

Let us find square of a number a5.

a5^2 = (a*10 + 5) ^2 = (a*10)^2 + 2*a*10*5+5^2           = 100a^2 + 100a + 25           = 100 * a (a + 1) + 25

Here is a method to square a number mentally, that I came up with. 

For a number, say 92.

Take the closest and the easiest number that you can square:

In this case: 100 or 90

Let’s choose 100.

Now take their difference and subtract it from 92:

92 – (100- 92) = 84.

Now, multiply that number by 100 and add 8 square to it.

84 * 100 + 8^2 = 8,464

Check: 92^2 = 8,464.

Now let’s choose 90.

Take their difference and add it to 92:

92 + ( 92 – 90 ) = 94.

Now, multiply it with 90 and add 2 square to it:

90 *94 + 2^2 = 8,464

PROOF: Let us find square of a number n. Let n be sum of a and b.   Where a is the easiest number we can multiply with and b is a small difference. Therefore, a + b + b = a + 2b And, (a  + 2b) (a) = a^2 + 2ab Now, adding b^2 to it will give us, a^2 + 2ab + b^2 = (a+b)^2 And a+b = n

Let us say we have an if statement,

If ( a == true && b == true && c == true) Do this;

This if statement needs to potentially run three comparison statements in the worst case scenario. The program also needs to keep a track of three boolean variables.

We can replace this statement with an int comparison statement.

Consider an integer x, which is a multiple of 2 if a is true, multiple of 3 when b is true and multiple of 5 when c is true. Which means if a, b and c are all true, it is a multiple of 2,3 and 5. So, it would be a multiple of 30.

Therefore, we can replace the above if statement with:

If ( x %30 == 0) Do this;

This statement needs only one comparison and one variable.