Wednesday, February 19, 2014
Mathematical symbols are not a description of the concrete, but are instead in an intrinsic symbol of a property inherent in the concrete.
Mathematical explanations do explain a hidden reality, but the reality explained is a property, not concrete substance. For instance, mathematics, i.e. number exists in a rock much the same as number exists in an ellipse. Mathematical formula can explain an ellipse but an ellipse is not the mathematical formula any more than a cake is its recipe.
Most modern scientific explanations are discoveries of a an intrinsic symbol because most modern scientific explanations are mathematical, that is, what is discovered and explained is a hidden mathematical property that exists in the substance being examined. They're intrinsic symbol because what is explained is not the concrete existence of the object, a concrete existence that is first and best knowable through our senses because God created a world that is not only knowable, but knowable through our unaided senses of sight, and touch, and hearing.
When I draw a structural steel plan, I'm abstracting and using these properties of number that exist in steel beams. My eyes and hands give me true knowledge of the steel while the abstracted mathematical properties in the steel beams give me the capacity to engineer a structure because the mathematical properties can be transformed into formulas allowing us to design with expected results. And so it goes with all of mathematical explanations, they are abstracted mathematical properties that help us understand a hidden reality.
As example, the 3d models of molecules or what have you are mathematical models that explain the mathematical properties, just the same as 3d mathematical model of lines can explain the properties of a steel beam. The lines explain certain properties of the steel beam so that those properties can be put into a formula for practical application, the same with molecules or what have you that we cannot see.
As it stands, there is a disconnect between the modern scientific explanations of nature and our 'unaided' observations explaining nature. When I touch and sit in a chair I understand it as solid, and I use it as solid.
But modern scientific explanations say that the chair is not only not solid, but that it is virtually not even there and nothing solid about it because what takes up almost all of the space the chair occupies is immense void between energy particles. And even those energy particles are are not solid but some kind of force which is in place without breadth or width like a euclidean point or line.
Modern science understands the world not according to what is prior known according to our senses and intellect, but instead according to what it considers is prior known according to technology and numbers. The first act of modern science is to reduce any observation to a quantifiable product capable of being placed into some kind of equation because modern science solely claims to know according to quantity. A red rose only has meaning to science insofar as redness or some other observation can be quantified, which is a very different method of knowing that is done by men.
I should be noted that modern science likewise says that men can also only know by some method of quantification, and thus what modern science is doing is a more perfect way of understanding observation, even though this quantification is not how we see the red rose where we see loveliness or or some sign or some other aspect of none are capable of quantification.
In In other words, modern science says that what we experience through our senses is an illusion and the opposite of what actually does exist. Modern science says our senses deceive us into thinking the world is one way, when it is in reality the contrary and the exact opposite of what we perceive by our senses.
But in actuality it is modern science that is deceived by deceiving itself by its placing number as prior known to our sense and as concrete explanation of what doe exists. Because number is not a concrete explanation, but is instead a tool, a poetical allegory of actual concrete existence.
As an architect I design spaces that can be reduced down to mathematical formulas and equations. That is,they can be explained quantitatively.
All my projects are designed and produced on computer which means that all my documents are in computer language which is mathematical.
All my designs are also engineered, and all engineering is finally reducible to mathematical formula and equation.
Because men are by nature most comfortable in euclidean space, all my designs are euclidean, and euclidean space is reducible to mathematical formula and equation.
The ordering of space according to rhythmic diminution, or one point perspective, or additive and subtractive, or plan to section, or repetitive to unique, or unit to whole, or symmetry and balance and similar can all be reduced in differing manners to mathematical formula.
Any well designed project will contain all of the above and more, with many of the design aspects designed into a project intuitively. In fact the better design is intuitive versus intentional ordering of space.
But what matters here is that even though design can be reduced down to mathematical formula and equations, and thus in turn the build structures can likewise be reduced down to mathematical formula and equations, the mathematical formula and equations is not what concretely exists. What exists are wood, concrete, and similar ordered to human life lived.
(or look at it this way, pie reduces circular motion to straight line motion by changing a circle into a polygon. What exists is the circle, but it must be transformed into a polygon to be manipulated mathematically.)
We use mathematics, and can better manipulate nature by means of mathematics, but human life is not mathematical formula or equations. The mathematical formula and equations are allegorical. They have existence in the design and in the built structure, but the built structure is not the mathematical formula and equations.
Mathematics is a tool created for us and used by us for our benefit, God created us and the world about us so that we could reduce the environment around us down to mathematics. But we are no more finally reduced down to mathematics than love and rational thought can be reduced down to mathematics.
The error the modern scientific explanation makes is mistaking the mathematics for the built structure.
According to modern science we see solid where there is actually only void. We think of ourselves as having some kind of substantial existence when we are actually nothing but tiny bits one dimensional force in a void.
But the modern scientific explanation does not have a cause for common occurrences of human life because the cause must be in the effect. We know that we live in relation with others, falling in love, and into sin. We also know that void and bits of tiny energy cannot anymore fall in love or sin than a light bulb can.
What we have are two explanations that are in contradiction with each other. How can the contradiction be resolved?
God designed the world to be understood on a multitude of levels including much of which is poetic or allegorical.
The mistake commonly made is to think that most modern scientific explanations reflect concrete existence even when those explanations contradict our common perceptions and senses.
The correct understanding is to recognize that our senses reflect concrete existence, and modern scientific explanations reflect some other type of explanation of existence.
So what I propose is that the atomic theory is allegorical, and our perception of the solidity of matter is concrete existence. The concept of energy particles in a void is allegorical because what actually exists is concrete matter, not energy particles.
(It could be that what I'm proposing is rather commonly understood, but I've never ran across it. What I typically find are Catholics trying to explain both contradictory systems as concrete existence.)
Because God is the creator of matter, the relation between the allegorical and actual existence is a perfect melding of the two where the allegorical gives us real insight into the nature of matter. We can "split atoms" not because atoms as energy particles exist, but because the allegorical is sufficiently reflective of what does exist so that we can manipulate what does actually exist through the use of the allegorical.
This understanding explains all the empirical evidence, and not just part of the empirical evidence as happens when the atomic theory is held as reflecting concrete existence.
Second, as Catholics we understand that substantial change is true, with transubstantiation being understood through our understanding of substantial change. That is, if substantial change is not true, then neither is transubstantiation as defined by Trent. The conflict is that the atomic theory as reflecting concrete existence denies substantial change by making all change accidental. But, if the atomic theory is allegorical, this conflict with the Faith ceases to exist.
By making the atomic theory allegorical all conflicts cease to exist.
Or take for instance light theory. Light theory is allegorical, and our perception of rose as actually red is concrete existence. The concept that color exists in our imagination as interpretation of light waves is allegorical because the color actually exists in the object. For instance the color red actually exists in the rose, what we hold in our imagination is what we actually see, not an interpretation of what we see.
Light waves do exist, but they don't move information as light theory says they do.
Mathematical explanations of motion are allegorical. Mathematical explanations are an abstraction of motion into signs. The reduction to mathematical formula, is a allegorical or poetic aspect of creation. Those signs reflect concrete reality not directly, but figuratively.
In other words, God created a world at human scale. A scale where even the most simple among us can know and understand it. Romans 1 : 19-20
Similarly, the created world's virtually unending complexity is also at human scale, designed for those with the capacity to plumb its depths.
As a comparison, St. Augustine writes that the bible is written so that even the most simple can understand the Faith, but yet also written with unlimited intended levels of allegory and other modes of understand for those with the capacity to plumb it's depths
God created a world knowable in the same manner as we come to know. A method of coming to know where we are not deceived by our immediate understanding of our observations which is the most universal human scale. We come to know simply and afterward with greater complexity.
Similarly, the sense of touch is to the most simple, as the sense of sight is to the most complex. The sense is at human scale that which gives us greatest certitude while likewise being the least precise of the senses. So likewise is it that the world is created so that the most simple understanding has the greatest certitude while being the least informative.
The most simple understanding of a red rose is that the color red is in the rose. That understanding is at human scale according to the most simple understanding. It's an understanding that reflects the basic concrete reality. It is an understanding which reflects what does actually exist.
It is not an understanding that plumbs the depth of being, or the nature of light and color which are to understand the nature as it likewise actually exists. Nor is it an understanding that that plumbs the depth of the allegorical as modern color theory does that holds color to exist solely in the imagination.
We live in an age that dismisses the allegorical, the poetic as a good virtually devoid of worth in explaining God's creation, where as we should look at it as another means of perfecting our understanding.
Catholics do look for the poetic and allegorical aspect of creation as sign signified in the capacity of matter such as water in baptism, but the poetic extends far beyond this to where most of creation is better understood as sign.
Upon walking into a basilica style plan church we are moved by a the concrete materials where most of what we perceive is allegorical. We interpret the interplay of light and shadow. We interpret the interplay of spaces and the interplay of the elements in the space. We interpret them to signify a movement from the earthy world outside toward the divine.
We are interpreting what does actually exist, but the existence is not concrete but allegorical or poetic. Which makes them not any the less real for their being allegorical. What we interpret has true existence, but its existence is not concrete but abstracted from the concrete.
The substance of an object fully exists, but we know it and understand it not with our senses, but with our intellect.
Atoms likewise fully exist but they exist as an interpretation of the concrete. That is, they exists as an allegory of what does concretely exist, i.e. prime matter and form. The interpretation of the interplay of light and shadow in a basilica moves us to understand the movement from earth to divine. They are a tool to move us to understand God's creation. Similarly, the atomic theory is an interpretation that is a tool that lets us understand God's creation.