The temptation appears to be that pondering the “ideal” realm, one could come closer to God’s thoughts. This is far from the case. This type of postulate can only be put forward in a situation utterly devoid of a model for the thinking process, i.e. what is really happening as this or that entity “thinks.” Such ideation is tragically and pridefully cut off from its own existential realities. This happens because looking within is the hardest task.
Socrates gave a seemingly offhanded model in saying that thoughts in the mind are like imprints in wax. The East has a similar answer, though it has not been examined or its consequences understood, saying that thoughts are forms in the “chitta” or “mind-stuff.” If there is a spiritual soul, then during the thinking process the mind is forming images and using power to retain and recall these images, in what must be a vast inner array of its own spiritual domain. One further sees immediately that in the case of the souls there must be a process of miniaturization, as the thoughts of a lifetime are somehow retained.
Once the nature of a thought is understood, then you see there is no bridge to God or even to another thinker. Each soul is self-enclosed, having perceptions and thoughts about these perceptions. The example of numbers is cited, and if you think of “one” or “two,” at first it seems you should approach unity with others and with God. That is not the case, and to understand this you should notice at best you are generating your own private abstractions, and furthermore the roots and nature of these abstractions are all your own.
With regard to the second question, one should note there isn’t an “actual infinite” amount of ANYTHING. Minds which think this are generally lacking discrimination, making a leap in hopes of dominating everything though the mental categories are inadequate and fail to describe anything real. Infinity is something that cannot actually exist. The mind of man holds almost nothing of the cosmos, but once he can count to three he grows bold and asserts, “Now I have conquered all.” He imagines the counting can go on infinitely, though he actually only counted to three and his imagination is vain.
John referred to Jesus as the “Logos” because the Lord is the only Voice of God. Also this is a nice way to refer to the third and spiritually least side of the Trinity, similar to how Prabhupada continued to refer to the Lord as “the Supreme Personality of Godhead.” Now, there IS infinity in the time domain, that we are unfolding. Creation will not cease.