THINK ABOUT THIS: How ‘Hilbert’s Hotel’ Helps Explain God And Infinity
If you’ve ever watched a football game, you may have witnessed your favorite team moving the ball to the opponent’s one-yard line late in the fourth quarter of a tie game. Everybody in the grandstands is on their feet screaming their heads off, either for the winner or to “hold’em!”
But when your team goes for the touchdown to win the game, there is a flag and the referee announces the penalty as “half the distance to the goal.” Then the same thing happens again. And again and again. And again and again.
Your favorite team is getting closer and closer to winning, but never quite gets there because there are an infinity of “half the distance to the goal” movements that can be made without ever touching the front line of the end zone and scoring.
Believe it or not, as Drew Covert of Tent-Making Christianity explains, there is a fascinating application here that helps explain the infinitude of God:
In mathematics, there are some really interesting thought experiments that help illustrate important concepts. One of my favorites is called Hilbert’s Hotel. It’s a thought experiment that was developed by German mathematician David Hilbert in 1924 to illustrate the concept of infinity. Here’s how it works.
There’s Always Room For One More!
Imagine that you are the manager of a hotel with an infinite number of rooms. One day, a woman comes to you and asks if you have any vacancies. You tell her that you do, and she checks in to Room 1. Later that day, another woman comes to you and asks if you have any vacancies. You tell her that you do, and she checks in to Room 2. This process continues throughout the day, with each new guest checking into the next available room.
Now, imagine that at 11 PM a man comes to you and asks if you have any vacancies. You tell him that you do, but all of the rooms are full. The man says not to worry, he’ll just take Room 1. So, you move the woman who is currently in Room 1 into Room 2, the woman in Room 2 into Room 3, and so on. This process continues until everyone has been moved up one room and the man can check into Room 1.
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In his “hotel analogy,” David Hilbert (1862 – 1943) neglected his contemporary Georg Cantor, 1845 – 1918, whose proof of a “consummated infinite” reflected Euclid’s paradoxical Parallel Postulate to effect that two parallel straight lines actually intersect each other at infinity.
Like mathematics’ “imaginary” square-root of minus one (“i”), an algebraic impossibility because there can be no negative square-roots, this magical Aleph-0 point separates –for example– the number-of- all-numbers from the number of curves in n-D spacetime. Defining an infinity as “any number that can be placed in one-to-one-correspondence with a part of itself” –as the infinite number-of-numbers corresponds precisely with the number of all even numbers– Cantor derived a transfinite series-upon-series of infinities, showing Hilbert’s paltry total as the least of them.
As this year’s decades-overdue Nobel award in physics recognizes, theorist Alain Aspect and colleagues’ 1982 demonstration of Bell’s Inequalities (1964, refuting Einstein-Podolsky-Rosen’s [EPR] “hidden variables” quantum-correspondence thesis formulated 1935) renders General Relativity inapplicable on “non-local” cosmic scales. Transcending “local” time-dilation/intervals due to constant light-velocity, our hyper-geometric Reference Frame exists in a holographic Eternal Present (time = Unit-One) “warped” to a 2-D Mobius Strip at four (4) spin-angular coordinate-rotation-points.
Deriving Georg Lemaitre’s dual-dynamic “soap-bubble” interface cosmogony, which Einstein eventually acknowledged, this model’s implications for instantaneous transposition from A to B over any spacetime interval make Elon Musk’s rocket-drives obsolete as Erie Canal boats to an SR-71.