Not the best analogy, IMHO. Mathematics is an artificial construct. It is used to quantify, but it is not quantifiable.
As is the scientific method.
you: Not the best analogy, IMHO. Mathematics is an artificial construct. It is used to quantify, but it is not quantifiable.
In the mathematical Aristotlean paradigm, the mathematician invents the mathematical structures.
In the mathematical Platonist paradigm, the mathematical structures exist and the mathematician comes along and discovers them. For example, pi exists, the mathematician discovered it.
The difference in paradigm affects not only one's view of the math but the physics and cosmology as well. And no doubt (at least in my case) extends to information theory and molecular biology.
For instance, all physical cosmologies (e.g. inflationary, multi-verse, multi-world, ekpyrotic, cyclic, imaginary time) presuppose space and time for physical causation. But in the absence of space, things cannot exist. And in the absence of time, events cannot occur.
Moreover, cosmic microwave background radiation measurements since the 1960's accrue to evidence there was a real beginning of space and time in this universe.
In effect, there was no infinite past to support the plentitude argument that anything that could happen, did. There can be no physical origin for space, time and therefore physical causation itself. All such physical cosmologies are "open."
Conversely, Max Tegmark's Level IV universe is "closed" precisely because it is radical Platonism. The mathematical structures really exist outside of space and time - and what the observer "in" space/time perceives is a manifestation of that reality.
The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: The universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.
And there is a comparable irreconcilable difference between the natural man and the spiritual man:
For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit. For to be carnally minded [is] death; but to be spiritually minded [is] life and peace. Because the carnal mind [is] enmity against God: for it is not subject to the law of God, neither indeed can be. So then they that are in the flesh cannot please God.
But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. Romans 8:1-9
In the Tegmark metaphor, the frog cannot see what the bird sees. To him, the bird's sense of reality is a delusion. To the bird, the frog's reality is a reduction, a construct. Nor can the bird accept the frog's sense of reality.
A Christian who is also a bird (mathematical Platonist) like I am may also see the harmony between Scripture and Creation. Indeed, to me, the unreasonable effectiveness of mathematics is like Gods copyright notice on the Cosmos.
Just a question tacticalogic: In what sense do you mean that mathematics is "artificial?" In the sense that it is the creation of an Artificer? Or did you mean something else?
I do agree with your second statement. I'm not sure what the first statement means, however; which is why I'm asking you for clarification.