Roger Penrose: Mathematical understanding:…mathematical understanding depends upon consciousness, but mathematical understanding is not something of a purely computational character; there is something else which has to come into that. The mathematics only comes in to demonstrate that there is some part of our conscious thinking which you can not simulate on a computer.
Question: Well then, what is the ‘something else’ that might come into play? Well, if you believe as I do, that whatever controls our actions and brains and so on, is the physics of the world, and that tells you that there has to be something else in the physics of the world which is not controlled computationally. It doesn’t mean it is not mathematical; but it is not computational. The distinction between those is important. We have to look for something that is a basic gap in our present understanding. Source: Roger Penrose interview
Mathematics is a principle of a higher order than a system for manipulating symbols to quantify matter, energy or natural physical forces. Mathematics is a fundamental principle and function of using representational symbols that represent the abstract categorical qualities of intelligence. Numerical symbols represent the instantiate natural intelligent order of the universe as well as the unpredictability of seeming randomness. An example is the measurement of the abstract increments of time using mathematics. The numerical symbols of increments of the time continuum are representations of the intelligent order of persistent change and growth. Those changes are the differences that make a difference that define the quality of the duration of that event, season or age.
Mathematics is an innately human fundamental conceptual principle that has objective attributes. Two apples added to two apples are four apples, two days plus three days are five days, even if there are no numerical symbols used to represent the apples or time periods.
In physics, mathematical symbols only represent and are manipulated to measure and explain the function of the underlying physical properties attributes. Logic and math are coherent abstract mental concepts. Mathematics is not a physical force, nor energy or mass. Energy and matter in the universe exist and are only measured and understood through the use of mathematics and logic and are then referred to as laws of physics.
Humans with innate cognitive pattern and sequence recognition through the sense organs and neural and nervous systems incorporate the man made symbols of mathematics and languages which then create the basis of the phenomena of sophisticated consciousness or mind.
As well as the measuring of quantities, mathematics is the basis of representing categorized or discrete abstract phenomenal mental qualities. Objects and symbols are recognized through the senses beginning after birth starting with the subitizing of physical objects by an infant. The natural order of the categorization of human mental and emotional characteristics and expressions are innately instantiated by the mathematical symbols that represent those abstract qualities and attributes of consciousness.
Equality, balance and harmony may be conceptually created through the rules of mathematics and then applied in actuality. The processing and interpretation of abstract information and signals perceived by the human sensory organs are influenced by the principles of balance and harmony governing the interpreting mind. The capacity of the mind to separate and interpret the signals of logic and reason from the noise of the instinctive emotions is a function of mind governed by its degree of conscious awareness.
Mathematics and Language (order isomorphic alphabets)
Language is an extension of the representational symbols of mathematics. Mathematics is a discovered principle of categorical order and alphabets are human created numerical order of representational symbols used by tribal or linguistic groups. The agreed upon order of the linguistic sounds, and alphabets creates the intelligence of the given language. The open vowel sounds and the closed consonants each have their respective resonant influence relative to their respective positions in consistently used alphabets.
Symbols of mathematics (the discovered, natural ordered set, of nine elements.....the place-holding symbol, "zero", facilitates a set of nine numbers to go to an infinity) and language are representations of the discrete informational qualities of intelligence that resonate through the physical senses and nervous system creating relative qualitative mental harmony or discord. The resonation of complimentary qualities creates harmonic synchronicity of desires and mental and emotional qualities of human expression. The instantiated qualities created, over time,by the formal and informal names assigned and accepted by an individual influence the mental characteristics that define that person. Mental stability, harmony and balance are created and influenced by mathematics and language.
Conscious entities consistently referred to by their given names are influenced by the resonance of the forces of intelligence as to the relative balance and harmony derived from the numerically defined qualities of the vowels and consonants that are instantiated mental and emotional qualities.
Quote: "Human concepts and human language are not random or arbitrary; they are highly structured and limited, because of the limits and structure of the brain, the body, and the world."
"1. Exactly what mechanisms of the human brain and mind allow human beings to formulate mathematical ideas and reason mathematically?
2. Is brain-and-mind-based mathematics all that mathematics is? Or is there, as Platonists have suggested, a disembodied mathematics transcending all bodies and minds and structuring the universe—this universe and every possible universe?"
Source: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being” by George Lakoff and Rafael E. Nuez