The SCIENCE OF DESIGN is quantifiable, mathematical and real.
 
The DESIGN OF SCIENCE is qualifiable, anti-methodical and real.

Some eight decades before Christ, Marcus Vitruvius Pollio, a Roman architect, engineer and writer, discovered proportional law from his observations of nature.  Leonardo Da Vinci, also an architect and engineer, a writer and artist, in 1509, described the Law of Proportionality in his rendering of the male body and referred to the Law as "The Divine Proportion".

The Golden Section is an example of the Science of Design, the Law of Proportionality. It is quantifiable, mathematical and real because it can be CALCULATED.
 But the Golden Section is also a perfect example of the Design of Science. It is a Law that occurs frequently in nature (nature having come before science) and is qualifiable, anti-methodical and real because it can be FELT.

Calculations and Feelings. Both real. Left Brain. Right Brain. Science and Design.

Another example: Both scientists and artists (engineers and architects) use the Law of the Golden Section because it is mathematical and is extremely useful in Art.
 
Essentially the law states that two unequal parts of a whole must be in proportional relationship to each other to create a satisfactory image to the eye.

Umm ... mathematics used to justify feelings?

Numerically, the Golden Section is approx. 1.618034 or 38 percent to 62 percent. This proportion reoccurs throughout our lives and can be said to create an Ideal Proportion between two objects or two parts of a whole.

The Golden Rectangle, derived from the Golden Section, is generated by each whole rectangle being sub-divided on the Golden Section ratio of 38 percent to 62 percent.  The Golden Spiral is formed by connecting the mathematically derived corner points of each proportionally descending rectangle.
 
This is simple math yet the Nautilus at the bottom of the ocean does its design without thinking. The Sunflowers in our garden, despite their large heads, don't think either but the counter-rotating spirals of delicious seeds can be perfectly described mathematically.

It seems like simple math is genetically codified into nature, into our very DNA.

The proportion between my forearm and my upper arm is 38 percent to 62 percent. The same ratio applies between my hand and my forearm. My face comes together in this ratio. The relationship between my eyes, my ears, my mouth and my nose, are born from the Golden Section. Even though every one of our faces are different, they are built upon these mathematics and within this poetry.

Conscious or subconscious, mathematical or felt, left or right brain or both, recognition of the Golden Section in living things and in inanimate things and in our artistic endeavors, feels "right to the eye", creating a feeling of satisfaction and harmony within an image.

So, Math Feels good?

You bet you, it does.
 
There are many fascinating and wondrous "secrets" out there and in here, Sacred Geometries, Golden Numerical Sequences, Feng Shui, Chi, even the Architecture of Song. These Golden Nuggets of Nature© can be taught through innate and learned intuitive feeling and through the calculations of mathematics.
 
It is why we are called Living Architecture.