It is comparable to flat Earthers I guess. People can’t believe that some infinities are greater than others. They dismiss the idea and say there is only one kind of infinity and that people worshiping math can’t see the wood for the pulp. One might rely to such incredulously…
People are worshiping math? That’s a startling development. Might have developed from those cardinal numbers and sets with some being greater than others. Cantor’s theorem undermined the Pope of a Largest Cardinal number. Here is the heretical theorem; “The cardinality of a set’s power set is strictly greater than the cardinality of the set itself”. That means there are an infinite number of degrees of infinity. The smallest infinity is subversive and known as Aleph-null.
There are infinities besides mathematical degrees of infinity such as physical and metaphysical. The metaphysical infinities cultists don’t worship degrees of mathematical infinities unless they have no choice. Instead they surge religiously into physicalism and prostrate themselves toward tax cuts.
Georg Cantor showed that some infinities are bigger than others. It’s a fascinating matter to consider -useful for contemplating cosmology in addition to Godel’s incompleteness theorems. https://www.transfinite.com/content/transfinitenumbers
Georg Cantor was brilliant and infinities were a topic mathematicians were recalcitrant about facing. He was oppressed by regular academia, although his work is accepted now. Wikipedia notes that he was “a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. Cantor’s method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor’s work is of great philosophical interest, a fact he was well aware of.[2]”
https://www.transfinite.com/content/transfinitenumbersI suppose that infinities in extra dimensional spaces are greater than those with fewer dimensions. Cantor’s theorem would still be valid. Pythagoreans would need to add a metaphysical liturgy to the mysteries.
I suppose that infinities in extra dimensional spaces are greater than those with fewer dimensions. Cantor’s theorem would still be valid. Pythagoreans would need to add a metaphysical liturgy to the mysteries.
As a practical matter and with math there are different places and kinds of infinity. One may of course refer to the greatest infinity holding all others- one containing the yo yo universe and all others theoretically even though God may not sponsor such a place because he is spirit and also can’t be defined in terms of distance or scale.
One might want to know if there is a finite or infinite number of regular polygons for making three-dimensional puzzles or for manufacturing containers.
https://youtu.be/ciM6wigZK0w?feature=shared
An equilateral triangle, square and the regular hexagon can fill a plain with no gaps, an infinite one, yet nothing else can. Infinity is an attribute that may be applied to some sets with real applicability. In exploring the shape of a structure or universe calculations for geometry and quantity may involve infinities of scale.
The Universe may have an open, closed or flat shape gravitationally speaking. If it is flat, the most popular model, it extends into infinity perhaps because there isn’t enough gravity to collapse it to a big crunch nor too little such that it would fly apart in expansion. Why could it be balanced just right if it is expanding from a singularity? One might think that to be perfectly flat the universe should always have existed infinitely: and that is counter-intuitive to observations of a thermodynamic universe and general relativity.
There is a difference between physical and mathematical infinity. If quanta were infinitely divisible that would create issues. Maybe fields are infinitely divisible yet if so the field overall should lose strength as it subdivides. The system may conserve energy yet monism becoming pluralism may have a cost.
https://www.britannica.com/science/infinity-mathematics/Physical-infinities
https://www.astronomy.com/science/what-shape-is-the-universe/
Theological issues concerning infinity differ quite a bit from space-time concerns about infinity. They are different reference frames. Space-time of this observable universe according to the prevailing theory had a start at time=0. So if it is infinite is that way in one direction like a vector that has not yet achieved infinity. It is just 13.2 light years old and 93 billion light years in diameter. Space-time isn’t empty it is a field that expanded from T=0 in the current model. People have wondered about a theoretical empty volume containing matter at least since Heraclitus and Parmenides.
I think Giordano Bruno was burned as much for real politics as theology. The Inquisition was in full force in reaction to the half millennium war against Muslim invaders of Europe. The ruling powers were Christian and wanted any 5th column Muslims to swear allegiance to European values. Spain was only retaken in 1492, and Muslims attacked Vienna in 1529 and 1683. The Muslims m heresy problem and even the Orthodox Christian schism remained challenges to Habsburg authorities. If Europe was placid I doubt that Bruno would have burned. Science is a bit narcissist on that point in recent media. It was about secular political control. People still want secular political control…look at Ukraine.
