Maybe numbers cannot adequately describe infinity. Like digital recording, something is always left out.
” ...the landscape of large cardinals...”
Hmmm. Where to start?
I don’t know about anybody else, but I know when I’m crunching numbers on some quantum formula, I hate when I start discovering new infinities. That’s just so annoying.
> This changes completely the landscape of large cardinals. <
I’ve been on Free Republic for 10+ years. So I’m permitted to comment on an article after only glancing at the title. I don’t get why fat Catholic prelates are so very affected by mathematical theory.
I can define infinity as “something the debt ceiling is quickly approaching”
I got through about 5 paragraphs before my head started to hurt.
I say it’s spinach, and I say to Hell with it.
My head hurts from trying to make sense of the article.
Mathematicians can prove, it turns out, that the sets of even numbers, whole numbers, and fractions are all the same size – an infinite number known as ℵ0 (pronounced “aleph-null”). The set of reals, on the other hand – that is, all rational and irrational numbers – is much bigger.
Exactly how much bigger, though, is a question that is already pushing at the limits of what we know and can prove.
This is so not complicated. I learned this particular secret of the universe from a space toy:
"To infinity... and beyond!" ~ Buzz Lightyear
As long as Hebrew has entered the room, "beyond" is based on עבר, the very root of "Hebrew".
the new cardinals nevertheless spell trouble for some mathematicians’ pictures of infinity. The problem lies in a property called Hereditary Ordinal Definability, or “HOD” – the idea that a set, even an infinitely large one, can be understood by sort of “counting up to” it.
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Hod (Hebrew הוֹד Hōḏ, lit. 'majesty, splendour, glory')[1][2] is the eighth sephira of the Kabbalistic Tree of Life. It is positioned on the left side of the tree beneath Gevurah (severity) and directly opposite Netzach (eternity).
Hod is associated with qualities such as submission, humility, and intellectual rigor. It represents the capacity to comprehend and articulate divine truths, balancing the emotive and instinctual energies of Netzach. This balance is crucial for maintaining the flow of divine energy through the sefirot and manifesting it in the material world. Hod is also linked to the planet Mercury and the archangel Michael in Western esoteric traditions.
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Hod... is the eighth sephira:
∞
"Help, I've fallen and I can't get up!"
large cardinals
I can understand why this article is fixated. Tis the Season!
These numerical “cardinals” are like trying to figure out the number of angels dancing on the head of a pin.
You say “infinities” and I say “vanities.”
My cardinals are smaller and like black sunflower seeds.
I was a math major at a university that prided itself on its Mathematics discipline.
Mathematics is a tool. Not always perfect, there is always error, but it will get the job done if you use it within it’s limits just as any tool.
Words, words and nothing but words…
Those who wrote this have too much time on their hands.