Objects in diving goggles are NOT closer than they apperar

So I read somewhere that light travels faster in water than by air and thought it would be useful for divers to know.

More on Our Number System

There is a tribe in Dontknowwhere that only has words for 1, 2 and many… as they don’t need to count more than two, they has restricted their number system to accommodate their needs… and limits (of the way they see and interact with nature)

* For more on this subject please do some research on the Sapir-Whorf Hypothesis

Our Numbers System - A candidate for reengineering

"Die ganzen Zahlen hat Gott gemacht, alles andere ist Menschenwerk"

-  Leopold Kronecker

At one point numbers were only used to count. The number system was created by men based on their own observations of reality, for instance: 1 sheep, 2 cows, 3 rocks, etc. Later on, the definition Number was extended, not just to count things, but also measure their properties. Therefore, the numbers used for counting were grouped as “Natural Numbers” and the new extended system became known as “Real Numbers” to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and finally complex numbers.

Zero

What is zero? Is it a number? How can it be a number if it does not count anything? Does it even behave like a number? The definition of a mathematical operations states that they are certain procedures that take one or more numbers as input and produce a number as output. This how normal numbers act, therefore, the “zero” should behave as this.

Test 1:  0 + 1 = 1

Test 2: 3 – 0 = 3

Test 3: 1 × 0 = 0

Test 4: 2 ÷ 0 = #¡DIV/0!

Thus, we cannot divide a number by 0, because there is no solution to the equation “X × 0 = 3”

Negative Numbers

Afterward, mathematicians were forced to fill a void when they had 4 sheep and wanted to subtract 5 of them. It was like playing god, creating a sheep out of the blue (Actually they were trying to solve the equation X + 1 = 0, not playing god) But this meant that numbers no longer represented reality. Therefore, negative numbers were the first imaginary numbers.

Rational and Irrational Numbers

Additionally, this sheep has also 2 ears, 4 legs, 231 bones, millions and millions of cells and so on. So, how exactly do these numbers explain reality? Is 1 leg the same as 1/24 of a sheep? As I was told in school: "Es como comparar papas con camotes" ("It´s like trying to compare apples and oranges")

Complex Numbers

Mathematicians love to solve equations, so let us consider this equation: X – 1 = 0

This equation has only one “real” solution… x = 1

Another would be:  x² – 1 = 0

This equation has two “real” solutions… x = 1, -1

Nevertheless, what if we have the equation: x² + 1 = 0

Actually, this equation has no solution because there is no number that when squared the result is -1. Thus, what should we do? As we need to have an answer for everything we cannot have this unsolved equation over our heads, consequently, why not extend the number system one more time to include solutions to equations of this type? So everyone settled and said: “OK, as there is no solution for √-1, let us call it “i” and save us the trouble”

Subsequently, this equation has two “imaginary” solutions… x = i, -i

However, why does this number appear? Why is there a mathematical operation that we cannot do?

If mathematicians have created a symbol for an operation we cannot do, why don't they create another for the division by zero (“X × 0 = 3”)?

Taken from: http://xkcd.com/

Reengineering

What if we don’t need to settle? What if the problem is our numbers system?

As stated before, our number model was developed by people and then patched up as new discoveries appeared. As it is a system developed by men, it has the same restrictions and constrains as men.

As I see it, this model can be only applied until certain level, but if we want to reach the next level (or go back one level, or go to a level within a level) then it gets complicated and we have to settle for negative numbers, fractions and even “i”.

We need to start by assessing the reason for negative numbers existence. Negative numbers are the lack of something, meaning something being lost. If someone loses something, then another one gains that something. First example would be debt: If I owe the bank $2,000 in my credit card, it show as negative in my balance; but it is also positive from the banks perspective (apart from the interest rate). Another example would be heat transfer: if we put ice on a glass of water then we need to see it not as the water loosing temperature, but as the ice gaining it. 


It is all a matter of perspective.

Dis-CORPORATE

It means: To leave your body

A PDCA cycle for Continuous Improvement

PDCA is a management technique developed by Charles Deming for continuous improvement of processes (or products, or services, etc.), I read somewhere that he always called it the "Shewhart cycle" and that he based his idea on his work.

The Deming Cycle is the scientific method for process improvement, you may think that “yeah, but isn’t it common sense?” You might be right, the cycle is pretty logical, but you didn’t theorized it, you didn’t make it common sense.

The steps for continuous improvement are:

PLAN: Establish the objectives and processes necessary to deliver results in accordance with the expected output (the target or goals).

DO: Implement the plan, execute the process. Collect data for charting and analysis in the following steps.

CHECK: Study the actual results and compare against the expected results.

ACT: Correct any significant differences between actual and planned results or standardize if the result was as expected.

This has worked for decades and who am I to question it, but, as one of the names of this cycle states, this a CONTINUOUS IMPROVEMENT CYCLE. This means that you are improving something that already exists so (for me) you cannot start with planning; you would have to check first to see what the differences are (or if there is even a problem)

First, let’s define what a problem is:

A problem is any result that is not what expected, I always find diagrams very useful for understanding.

So, for a continuous improvement process, my proposed cycle would be like this:

The Ant and the Bumblebee

Today I decided to start this blog, actually it is an old blog I had that I have translated to English now that I'm living in Berlin and am not yet capable to write it in German.

The idea for this blog came from a story that a college professor once told in class about a study of how ants where able to only see in 2 dimensions, that's why they can continue walking up a wall or on the ceiling. For them is all a big plane, they don't notice the height. If they could notice the third dimension, then they wouldn't be able to do this... since they don't know, then they can.

Kind of like the bumblebee... even though the laws of physics state that because of it's wing size and beats per second, it wouldn't be able to fly, they do anyway because they don't know that they can't (or perhaps they know they can and that's why they do it?)