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Kurt Gödel brought mathematical completeness to Georg Cantor's math of infinities by the following:

Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century

Excerpt: Excerpt: Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”

http://www.cosmicfingerprints.com/blog/incompleteness/

Hilbert’s Hotel and Infinity – William Lane Craig

http://www.youtube.com/watch?v=lobeX6ft6PA

The "infinite" problem of joining relativity and quantum mechanics:

The Physics Of The Large And Small: What Is the Bridge Between Them? Roger Penrose

Excerpt: This, (the unification of General Relativity and the laws of Quantum Mechanics), would also have practical advantages in the application of quantum ideas to subjects like biology - in which one does not have the clean distinction between a quantum system and its classical measuring apparatus that our present formalism requires. In my opinion, moreover, this revolution is needed if we are ever to make significant headway towards a genuine scientific understanding of the mysterious but very fundamental phenomena of conscious mentality.

http://www.pul.it/irafs/CD%20IRAFS%2702/texts/Penrose.pdf

Yet, this "unification" between what is in essence the "infinite world of Quantum Mechanics" and the "finite world of the space-time of General Relativity" seems to be directly related to what Jesus apparently joined together with His resurrection, i.e. related to the unification of infinite God with finite man:

The Center Of The Universe Is Life - General Relativity, Quantum Mechanics and The Shroud Of Turin - video

http://www.metacafe.com/watch/3993426/

The End Of Christianity - Finding a Good God in an Evil World - Pg.31 - William Dembski

Excerpt: "In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity." http://www.designinference.com/documents/2009.05.end_of_xty.pdf

A photon is made of "infinite" specified information:

Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh

Excerpt: In contrast to a classical bit, the description of a (photon) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1) — Concept 2. is used by Bennett, et al. Recall that they infer that since an infinite amount of information is required to specify a qubit, an infinite amount of information must be transferred to teleport.

http://www.cas.umt.edu/phil/faculty/duwell/DuwellPSA2K.pdf

And can hypothetically be encoded with infinite information:

Single photons to soak up data:

Excerpt: the orbital angular momentum of a photon can take on an infinite number of values. Since a photon can also exist in a superposition of these states, it could – in principle – be encoded with an infinite amount of information.

http://physicsworld.com/cws/article/news/7201

Unconditional Quantum Teleportation - abstract

Excerpt: This is the first realization of unconditional quantum teleportation where every state entering the device is actually teleported,,

http://www.sciencemag.org/cgi/content/abstract/282/5389/706

And a photon can be destroyed by removal of its "infinite" information

Of note: conclusive evidence for the violation of the First Law of Thermodynamics is firmly found in the preceding experiment when coupled with the complete displacement of the infinite transcendent information of "Photon c":

http://docs.google.com/Doc?docid=0AYmaSrBPNEmGZGM4ejY3d3pfMzBmcjR0eG1neg

Thus since Theism holds that only God is infinite and perfect in knowlege (information) then I hold that man will never create a novel photon.

pi is infinite information:

Proverbs 8:26-27

While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,

Euler's Number - God Created Mathematics - video

http://www.metacafe.com/watch/4003905

This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages, for Genesis 1:1 and John 1:1:

http://www.biblemaths.com/pag03_pie/

Michael Denton - Mathematical Truths Are Transcendent And Beautiful - video

http://www.metacafe.com/watch/4003918

Since a physical infinite is an impossibility, as by Hibert's hotel, then the actual infinite only resides in transcendent information. Double slit- quantum erasure proves the infinite transcendent information is conscious. i.e. The Word is Alive: John 1:1

This following experiment highlights the centrality of consciousness in the Double Slit Experiment as to the wave collapse and refutes any "detector centered" arguments for wave collapse:

Delayed choice quantum eraser

http://onemorebrown.wordpress.com/2008/02/10/god-vs-the-delayed-choice-q...

of note; Consciousness must be INFORMED with local certainty to cause the wave to become a particle. We know from the Double Slit Experiment, with delayed erasure, that the simple fact of a detector being present is NOT sufficient to explain the wave collapse. If the detector results are erased after detection but before conscious analysis we see the wave form result instead of the particle result. This clearly establishes the centrality of consciousness to the whole experiment. i.e. The clear implication from the experiment is that consciousness is primary, and detection secondary, to the collapse of the wave function to a 3-D particle. Consciousness must precede 3-Dimensional material reality.

Intelligent Design - The Anthropic Hypothesis

http://lettherebelight-77.blogspot.com/