Yes, there are many concepts in mathematics, philosophy, physics and psychology that may be intellectually inaccessible to all humans. One of the oldest and most fundamental questions that has confounded philosophers from ancient times is the question of “first cause.” That is, did the universe exist forever or was it created? If it was created, then who or what created it? If you answer, “God”, then you have to ask who created God. If you say God always existed, then you’re asserting that God had no beginning. This strains our comprehension, because all other entities in our existence have a beginning. Science has no answers about first cause, but the current Big Bang Theory is a model of the universe that suggests it began about 13.77 billion years ago when the four fundamental physical forces began separating. The theory is able to explain what happened from 13.77 years ago to the present, but unable to explain anything before the Big Bang. It is beyond our comprehension, perhaps because the concept of time may be a human construct that Einstein once called an “illusion.”
Another challenge is a recent conundrum from physics. In our macroscopic world, we view objects directly and can accurately measure the location of an object and its speed if it’s in motion. However, in 1931, Werner Heisenberg discovered the famous Uncertainty Principle, stating that we can never know simultaneously the location and speed of an electron with unlimited accuracy because we can only determine its location by bombarding it with another particle, thereby changing its location and speed. The best we can do is create a probability distribution stating the likelihood that it’s in a particular place at a particular time. The Copenhagen interpretation asserts that the electron is not in any particular location until it is observed. In other words, in realms like the microcosms where we cannot perceive phenomena directly through our senses, concepts like “location” may have no meaning.
In realms that we cannot perceive directly with our senses, we are like blind people maneuvering with a white cane. Our white cane is mathematics. Using the power of our mathematical models, we can navigate through these strange worlds, harnessing the electrons as electricity, transmitting messages around the globe and performing calculations through computer circuitry. We know how to manipulate these elements of our natural world without understanding their essence. In his celebrated article The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Nobel Laureate, Eugene Wigner states:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
Indeed, the field of mathematics is based on a system of axioms that are assumed to be correct and consistent. Yet, we never know whether the basic laws of logic that are hardwired into our computers will ever yield a contradiction. Furthermore, Kurt Gödel proved that we will never be able to prove that our logic is consistent and complete. Hence there may be many concepts not accessible through artificial intelligence.
This is a very brief sample of some problems that bedevil the greatest human minds. Our inability to understand these concepts probably results from the fact that our minds evolved to function only in the limited range of our directly perceivable environment.
