True vs Valid

Another very nuanced, but majorly important blog topic that will take a series to properly outline is the difference between True & Valid (or Facts). I've had some eye-opening realizations watching human behavior as a result of operating social media accounts with sizable followings. Seeing in real-time somebody incorrectly conclude something, and then utilize that faulty conclusion as the foundation for a series of responses. 

In mathematics, while outlining valid manipulations to equations to take steps towards potential solutions, entry-level algebra will teach you that you can divide a value to one entire side of an equation so long as you repeat that exact process to the other side. So, for example, if you are attempting to solve 2x = 4x you might decide to divide both sides by 'x' and resulting in something that doesn't make any sense 2=4 or a false statement. Your parameters you were given were valid, as were apparently your steps. Up until this moment this process always yielded a solution, yet now something is off. 

You will then need an addendum to your protocol to be aware, when dividing by a variable, it is no longer valid if said variable has a value of 0 because you can not divide by zero. Correctly solving the previous equation will show that the value for x there is zero, therefor when you thought you were valid by mirroring procedures on both sides of the equation, you unwittingly were not.

Another example comes with the commutative property of multiplication. It would appear with the operation of multiplication, that any two items, when multiplied together will yield the same result no matter which order you put them in. 

2x3 = 6    and   3x2=6 
5x7 = 35  and   7x5=35

...and so on. You may begin to select any two sets of values to try out this property and it will seemingly be the case that ANY combination will hold. And indeed for most number systems and variable sets, that will be the case. Until you get into matrix algebra. AxB is NOT always the same result as BxA

A = | 2  5 |         B = | 4  2 |
       | 3  8 |                | 5  1 |


AxB = | 33   9 |    BxA = | 14 36 |
            | 52  14|               |  13 33 |

If I haven't lost you with all the numbers, hopefully the concept can transfer. An ignorance level and/or incomplete/incorrect set of information can and usually leads to incorrect results. Connecting dots with conspiracy theories which have seemingly valid facts can definitely be found to not actually be the truth.

In simplest terms you can have something out of context, something completely misconstrued (like the media does) or in between those you'll find most click bait conspiracy stuff. People emphatically connecting valid data points, revealing a faulty truth.

-Codd

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