Having said that, mathematics is unreasonably effective in the natural sciences
There is nothing unreasonable about mathematics. They are effective in natural sciences to the extent that they mathematics allows for working models. Working models prove nothing, They just work. Thye do not necessarily represent truth or "reality."
Infinity is an unbounded quantity greater than every real number Mathworld
In your previous post you defined infinity as bound by time and space.
And any number sequence, e.g. -3, -2, -1, 0, 1, 2, 3 – can be extended or projected, in either a positive or negative direction to infinity, i.e. an unbounded quantity greater than every real number
So what? Besides, positive and negative directions is irrelevant in infinity.
I am not sure what is the point you are trying to make. Can you reduce it to a single sentence or at least a paragraph?
Nevertheless, mathematics is unreasonably effective in the natural sciences.
That term was coined by Physicist Eugene Wigner is his famous article The Unreasonable Effectiveness of Math in the Natural Sciences.
Most of what will be said on these questions will not be new; it has probably occurred to most scientists in one form or another. My principal aim is to illuminate it from several sides. The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories….
As I recall, you and I have been down this road before – your mathematical worldview (and perhaps your theological belief) is Aristotlean whereas mine is Platonic. Every atheist and agnostic has an Aristotlean worldview - but not every Aristotlean is atheist or agnostic. Platonists, on the other hand have a worldview which is "beyond" space/time - so if they are not Judeo/Christian they are at least theistic in some sense or have some concept of a collective consciousness (e.g. Eastern mysticism.)
Aristotle and Plato did not resolve the debate, neither did Einstein and Gödel, neither did Hawking and Penrose. Max Tegmark (a Platonist) described it this way (formatting mine):
If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix.
To the frog, the world is described by Newton’s laws of motion and gravitation. To the bird, it is described by the geometry of the pasta — a mathematical structure.
The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds to a cluster of particles that store and process information. Our universe is far more complicated than this example, and scientists do not yet know to what, if any, mathematical structure it corresponds.
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.
Now the frog is a nominalist. He would say that universals do not exist, such things as redness, sound, threeness, and so on. He would call them language only. To him, mathematical constructs such as pi are invented by the mathematician to describe the world the frog sees. Physical laws don’t exist in themselves, they are “observations.” The soul, mind, or consciousness is merely an epiphenomenon of the physical brain. To the frog, when a tree falls in the forest it makes no sound if no one is around to hear it.
F: Hullo! Did I hear you mention my name? How goes it on your lily pads, lady frogs?
TSB: Hello Brother Frog! So nice of you to join us! How was your trip?
F: What trip? I’m sitting here on my lily pad in my happy pond, sunning myself. Then I heard you two talking about me…. What’s up?
TFB: You are most welcome to join us. We were chatting about the differences in worldview of frogs and birds….
F: I don’t believe in birds.
TSB: (Aside to Timothy) And he doesn’t believe in you either, Timothy….
T: Be that as it may. I continue to believe in him.
Brother Frog is most welcome here. He brings a certain point of view regarding the issues you want to discuss, which promises to be important to their illumination.
And so I shall be very glad to attend to your exchange of ideas.
TFB: Well, Froggie, you know that my sister and I do believe in birds — we are birds! As I was saying (though you may disagree), the bird is a realist. He would say that universals such as redness, sound, and threeness do exist, that geometry exists and the mathematician doesn’t invent it, but comes along and discovers it. To the bird, a variable in a mathematical formula is a universal per se. The physical laws exist. The soul, mind, or consciousness exists and may be “in” space/time or “beyond” space/time — or both. And when a tree falls in the forest it makes a sound even if no one is around to hear it.
Infinity is the unbounded quantity which is greater than every real number.
I am not sure what is the point you are trying to make. Can you reduce it to a single sentence or at least a paragraph?
And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you. – Exodus 3:13-14
You don't have to take Alamo-Girl's word for it. Einstein said it. Parallel lines will eventually intersect because the universe is curved.
From a first-up on google...
Parallel lines also behave differently on a plane and on a sphere. Two lines moving in the same direction on a plane will never meet at a finite set of coordinates. However, suppose that two people start at the Equator and head north. They are traveling in the same direction, but since they are on a sphere, they do meet! First they meet at the North Pole, and if they keep going long enough, they will meet at the South Pole as well...The behavior of parallel lines led to one of the most important developments in mathematics, the introduction of non-Euclidean geometry. In Euclidean geometry, a plane is like a tabletop or piece of paper, a flat object that extends forever in all directions. Using the axioms of Euclid, useful theorems can be proved like "the sum of angles in a triangle is equal to 180 degrees". However, this is only true on a plane. If you draw a triangle on a sphere (like a globe), you can measure the angles and show that they always sum to more than 180 degrees!