Basic Science #3: The Beauty and Power of Mathematics

Natural Numbers

I would like to convey to my readers my love and appreciation for mathematics.  I happened to be able to grasp basic concepts at an early age.  Many of my classmates were not as fortunate.  Decades later I still have friends tell me about their struggles with these concepts.  I believe that with better more diverse teaching methods more and more kids will grow up with a better grasp and understanding of math concepts.
Mathematical constants or natural numbers are the basic alphabet of the laws of nature.  The laws of nature are the laws that govern our physical and biological worlds.
I will start here with one of the very first natural numbers we all hear about the constant Pi. The number Pi is close to 3.14 and is the ratio between the circumference of the circle and its diameter.  This ratio is always the same regardless of the size of the circle or where you find the circle.  It could be in biology or architecture or in space.

I have this vision or maybe you'd call it a dream: any kid who learns to count and recognizes shapes, should be able to understand the concept of pi.  This concept is so basic that every boy and girl could understand it.
This is the blackboard from the movie "The Life of Pi."  The Indian boy named Pi who remembered this number to many decimal points:

Other laws of nature could be explained at a younger age: the power of gravity - why do we fall down?  The power of magnetism - the magnets we stick on our refrigerators.
Many great minds have observed these powers and managed to describe them in mathematical terms.  We have the tools to measure these powers and give them exact quantities.

Next I would like to talk about the number e a relative newcomer on the mathematics scene compared with pi.  This number has a role as the "natural" base for exponential functions and logarithms.  It is also derived from trigonometry and we can find it in many examples as in calculating compound interest.

e = 2.71828182845904523536...

e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ...

The next mathematical concept that is used in many fields of science is the “imaginary” number i.  When you square this number you get negative one: -1.  Or

I would like to bring here one of the most amazing equations that show how these three mathematical constants are related to each other and to the basic laws of life. 
Euler's equation:

If this equation does not blow your mind I don't know what will.  Why is it important?  I hope you agree that this is beautiful!  It shows such promise in the power of math to help solving many complex issues and unrelated problems.

Basic Science #2: Acids and Bases

Thanks to my readers who responded with interest to my basic science post.  Someone asked if the next element is going to be nitrogen?
I am now suggesting this order: we first talk about hydrogen then water then acids and bases.  Next nitrogen, ammonia carbon dioxide.  Then amino acids.
Hydrogen is element number 1.  One proton one electron.  The most abundant element on our planet. Oxygen is element number 8.  Oxygen is what we inhale and is essential for our survival.
These two elements give us WATER which is also essential for our survival.  H2O.

 

The water molecules has two ions in equilibrium: H+ proton and OH- hydroxyl:

When the amount of protons and hydroxyls is equal the pH is neutral, or pH=7.

When the protons are in a higher concentrations, then the pH is acidic.  Examples: When we eat acid is pumped into our stomachs to a pH as low as ONE in order to digest the food.

Vinegar and lemon juice are also acidic.  Interesting to note here that the Hebrew word for acid comes from the rood that means sour.  Any foods with a sour taste are acidic.

When the hydroxyl ion is in high concentrations the pH is basic.  Examples are baking soda and drain cleaners.  Bases usually taste bitter.

 

Now we are ready to talk about nitrogen.  Element number 7.  Nitrogen interacts with hydrogen to form ammonia: NH3. 

 

 

 Ammonia has a bad smell.  When dissolved in water ammonia will become basic:
 

 

 

 

 

 

 

 

Everyone is familiar with carbon dioxide CO2.
CO2 in water:
 Yes, this will be slightly acidic.

Now we are ready to understand what is an amino acid.  Amino acids are the building blocks of proteins in our food and in our bodies.  There are 22 amino acids in life. 
A simple amino acid is alanine:
The amine group is in blue.  The red group is the organic acid COOH.

Here is a chart of the various amino acids categorized by their chemical structure:

 http://rosalind.info/media/amino_acid_table.png

 Hope this post will help those who want to understand better.