64 = 65 ?
64 = 65 ?
There is, on Youtube, a puzzle that appears to prove 64 equals 65.
https://www.youtube.com/watch?v=QTxQDjGQh-0
A square of 8 units, covering 64 sq. units, is divided in four pieces, two triangular and two trapezoidal. They are then rearranged in such a way that they look as if they form a rectangle of 13 x 5 units covering 65 sq. units. This is shown so fast that the viewer does not get a chance to catch the trick. The result is shown in the attached graph.
In the fast video clip the hypotenuse of the red and green triangles seem to coincide with the slant sides of the blue and orange quadrilaterals. The colors are chosen so that they kind of blend in at the contacts of the pieces. In reality, they don't coincide. The small gaps left along the line BD shown on the attached sketch add up to one unit and causes the delusion of 64=65. Thirteen small areas totaling one square unit are surreptitiously sneaked in along line BD. To open the sketch, please click on the image name at the bottom of this page.
This trick is worth examining from a different perspective. Tricks like this are used by many 'leaders' in different fields, religious, politics, business etc. In many religions, they are used to sneak in undesirable practices like guru-worship etc. Some others use them to spread atheism. Many use them to cover up their true intentions.
Human life is multi-faceted. For a simplified initial analysis, the various constraints we face can be sorted into two groups, those governed by emotions like love, faith etc. and those like legal, financial matters etc. requiring logic. They can be depicted as a x-y graph similar to that in the trick above. Let us say the overall weight we assign to emotional aspects are plotted as x values whereas that for logical considerations as y values. Ideally neither of them should be close to zero or hundred. The different situations will get plotted as points on a square like the 8x8 graph.
Some people use the trick of dividing and rearranging the field to make rectangles of their choice. Those in favor of emotion would plot it as 13 x 5 horizontal rectangle, logic lovers would present it as 5 x 13 vertical one. The former misguide their followers as spiritualists, the latter as materialists. We need to beware of both. We should never give up our common sense. Of course, we do have to expand our considerations to include other relevant factors to make a comprehensive determination before choosing our options.
Also, the decisions we make should not bind us for ever. As and when the situation changes, we should reconsider the past actions and make suitable corrections in the interest of all current stakeholders.