If you never had a cassette player or a walkman, if you didn’t adjust your TV’s reception with a Yaggi antenna; if you never watched movies on the VCR or play games on Atari or SEGA; and if you never played the brick game then you were never born. And there used to be a time when 1.44 MB of a floppy disk used to be enough and people transferred data through them. A toast to these extinct technologies without which mankind would never have made the advances it has made.

## Speed Mathematics using Trachtenberg System

16 AprIt is surprising what the human mind can achieve when it is pushed to extreme conditions. One such thing happened when **a Russian Jew Jakow Trachtenberg evolved his own algorithms to do calculations speedily** when he was incarcerated in the Nazi concentration camps.

# Multiplication Algorithms:

## 2 Finger Method:

Suppose we have two numbers 120 and 131 and we want to multiply them quickly without the use of a calculator. The following figure will better illustrate what will happen:

The vertical arrow points to the product where we will get the units digit, and the sloping arrow points to the product where we will get the tens digits of the product pair. If an arrow points to a space with no digit there is no calculation for that arrow. As you solve for each digit you will move each of the arrows over the multiplicand one digit to the left until all of the arrows point to prefixed zeros.

Likewise, Trachtenberg also introduced a number of special algorithms to multiply any number by 3,4,5 and so on up till 13. For example suppose that we wanted to multiply a number by 11 then we’ll add every number to its neighbor i.e the number on it’s right side:

For example 11×37015 = 407165

3 7 0 1 5

(3+0)+1(carry from next) (3+7) (7+0) (1+0) (1+5) (5+0)

= 4 0 7 1 6 5

# Division Method:

The division method is pretty much the same as general multiplication method except that you have to subtract instead of adding. The division will be done in the same digit to digit way.

# Addition Method:

The addition method is the usual one of writing the numbers one above the other and adding the columns together. The carry is taken over to the next digit which is something taught to us from the very beginning.

After the end of World War 2, Trachtenberg who survived the camps started to teach this method to students who did not have confidence in their abilities. It has been proven that the system can shorten calculation time by 20 percent and the results are accurate 99 percent of the time.

## Army and the Robots: A marriage of convenience

6 AprEver since **Isaac Asimov** put forth his famed laws governing a robot, the affair headed towards its logical outcome a marriage of convenience; in which both parties stood to gain. The army is an organization in which commands are followed to letter and spirit and this is exactly the way in which robots are programmed. While research could have been put into using the robots for peaceful purposes, man is making drones and gun mounted UGVs. If humanity understood how better off it would have been without wars, it wouldn’t have programmed humans to make them into soldiers.

It is understandable for soldiers to obey their superiors in the heat of battle without which the chain of command will collapse but in my experience, the soldiers leave no stone unturned in following the orders even in routine work. This is quite dangerous because it can make them dull as they do not make exceptions or deal with a situation in the manner it requires. For them the most important thing is the order; the higher the order comes from, the higher the need for it to be enforced.

We have been given an intellect of our own and given the ability to adapt according to changing situations. We should use those God gifted faculties instead of acting in a pre programmed way; devoid of sensing the sensitivity of the situation.

## An Inspirational Snack

5 AprSome great thoughts.

– Evan Sanders

Read my Book! **Amazon** (*http://amzn.to/Z0xZXT) ***iTunes **(*http://bit.ly/10ix2JQ**)*

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## The blogosphere as I imagine it

5 AprFor me the blogosphere is like our universe on which hundreds of thousands have got their own private spaces. They write whatever they feel like writing like **the infinite scurrying of ants**. Many blogs connect together based on common interests. They like the posts and comment on each other’s blogs and create this buzz which starts slowly and does not stop until it reaches a crescendo.

Blogs are the next thing in media and they are so updated that newspapers are in no competition with them. A huge community of normal people just like me, driven by their passion for writing continue to pour out information after information and accept applause from their peers.

## Implications of the existence of Fourth Dimension

4 AprAccording to recent claims, there can be a total of **eleven dimensions** as opposed to the previously known three dimensions. The theory of dimensions is really simple to understand. If we have got a single point, then it can be represented by just one dimension. Now if we move from one point to another, then a line is formed and we need two coordinates to express its position. The lines join together to form a plane and planes result in 3 dimensional shapes like a cube or a diamond. **Often people think of the fourth dimension as time**. This confusion arises because of Einstein’s theory of relativity and it might be correct to some extent but to interpret the fourth dimension in **spatial terms**, it’s a 4D hypercube.

If you have ever seen the movie Avengers, you’ll remember the light emitting blue colored hypercube which is called Tesseract. A tesseract is the physical form of fourth dimension although such a hypercube doesn’t actually exist. It was just shown in the science fiction movie. However, the presence of a fourth dimension can solve many of the problems that are faced by us today. The reason is that we live in a lower dimension and cannot perceive the phenomenon going on in the higher dimensions.

The famous Greek Philosopher Plato presented the concept of a person living in a lower dimension not being able to perceive what goes on in a dimension above them. He spoke of men who were chained and were shrouded in shadows. The only shapes they could make out were the shadows on the wall so even in those ancient times; he had an idea about how dimensions will be perceived. For example, if a person lived in a 2D world and he was shown a ball he’ll only be able to visualize the face of the ball which is in front of him. That way, the ball which is a sphere in reality will appear to be a plane to him which is a strange phenomenon for him.

**Main Concept**

The same is true for us. Since we can perceive three dimensions, so we have no problem as far as seeing a three dimensional object is concerned. But there are many phenomenon in this world that have no logical explanation until now and perhaps they are happening in the fourth dimension or even a higher dimension than that. It can be a reason why we are not able to comprehend their meaning in entirety. So the universe has got this masking effect in which the higher dimension is hidden or masked from the lower one. The mathematical term to explain this concept is that higher dimensions are perpendicular or at an angle of ninety degrees with the lower one.

**Evidence of The Fourth Dimension**

In order to prove the existence of a fourth dimension, we will have to prove that four dimensional movements and shapes exist. In our space, rotation is about an axis but in the 4D space, the rotation is along a plane. This type of movement will be complex for us to comprehend since we live in a dimension lower than the fourth. In order to completely describe the position of an object in a four dimensional space, we’ll require four points instead of three points we currently need.

It is not possible to prove mathematically the existence of a fourth dimension. That is why we have been deriving all analogies from a three dimensional world. The reason is that if any four dimensional movements happens in the universe, it happens at a very small level in the minute particles and it’s not big enough to be observed by anyone. However, highly extensible and flexible fluids can exhibit the properties of a four dimensional motion.

Let us assume a sphere which has got the usual xyz axes attached to it along with the w axis of fourth dimension. Now to understand the fourth dimension motion in terms of our own space, we explain the phenomenon of a vortex. A vortex can be described as a whirling motion whose most familiar example is a cyclone. The most interesting thing about a vortex is that its ends must be connected to a fluid or they can be connected to each other to form a sort of a ring. The particles remain trapped inside the vortex and cannot get out which would normally be the case if a wheel with water on it is moving; the water will move off. As stated previously, the rotation in a 4D world will be around a plane. The vortex will rotate around a plane and will enclose in the shape of a ring. The simplest phenomenon available to us which shows such properties is current passing through a wire. Actually the field of force is surrounding the wire. So the concept of a fourth dimension can be given by a phenomenon which exhibits characteristics of electricity. One such phenomenon is light which is electromagnetic in nature and it is a universal fact.

**Applications In The Fourth Dimension**

Whenever we talk about the fourth dimension, the discussion inadvertently moves towards complex shapes that’ll be available to a person if a fourth dimension was added. Due to the presence of fourth dimension, we can make highly efficient wheels and mechanical shafts. The energy requirements decrease and size of machines decreases due to inclusion of just one more dimension.

The relation between shapes is another shape. Just like the relation between two numbers is another number. A very simple example is that 20 is a number which is related to 5 by 4. The product of 5 and 4 is equal to 20 and in other words if we divide 20 by 5 we get 5. Similarly complex shapes can be broken down and represented in form of simple ones.

One interesting thing that can be explained due to fourth dimension is that we can describe the concept of levitation. It is a known fact that if a point exists in a circle, we can remove it by taking it up into a higher dimension. Similarly, a being living in a higher dimension can simply pull an object from 3D space to tetraspace. This is quite interesting because if you ever encountered a being from a 4D world, he could remove the contents of your stomach without facing the need to even touch you. The 4D being will be able to look straight through your body inside you. Suppose he thinks of playing a trick on you. He can take any object available in our world which is 3D and take it to tetraspace. Then he can bring the object back to our world and suspend it in midair. This is a very bizarre situation and there is other strange phenomenon in this universe which can be explained due to the fourth dimension.

Let’s revisit the tesseract which appears in science fiction movie Avengers. It is a hypercube which is considered to possess immense amounts of energies. In the move, the Tesseract is used to make highly sophisticated weaponry. However, this is just part of the fiction. A tesseract may exist if there was ever a fourth dimension and these would be just some of the applications in which it would be used. A tesseract would consist of eight cubes connected in four dimensions. If we were to represent it in the three dimensional space, then we will have to cut up the hypercube and unfold it. The result will be four cubes stacked on top of each other and four other cubes which will be present one on each side of the cubes.