© 2006 Olga López
© 2006 Urantia Association of Spain
Only in mathematics, as Averroes says, there is identity between the things that we know and those that are known in an absolute way. Mathematical knowledge is propositions that our intellect builds so that they always work as true, because they are innate or because mathematics was invented before the other sciences
Umberto Eco, The name of the rose
¶ Introduction
The purpose of this reflection is not to prove the existence of God using something like “meta-mathematics” (in the same way that metaphysics situates itself “beyond” physics). I know pretty well (and The Urantia Book takes care of reminding us more than once; just review UB 1:7.4, UB 12:7.6, UB 12:9.3) that there are no irrefutable proofs of the existence of God . I am also aware that my mathematical knowledge is very limited, even though I had to study a lot of mathematics in the past. It’s just that sometimes, trying to think beyond the mathematical formulas that I had to learn as if they were dogma, and considering certain numbers and their properties, I couldn’t help but feel a certain vertigo at the thought that, somehow, they were showing me concepts like infinity , indeterminacy, unification. Concepts that, in some way, are related to the characteristics that we attribute to divinity.
I have just made an inquiry, refreshing knowledge that I had forgotten, about that part of mathematics that most amazed me in its day. I suppose that someone more expert than me (finding him won’t be difficult) could get more out of these reflections, and warn about other properties and other formulas.
Why is mathematics so useful in formulating the laws of nature?
It is curious how, on many occasions, we take certain things for granted that, after reflecting a little on them, do not seem as obvious as they had seemed to us at the beginning. In relation to this not long ago I read an article by the Nobel Prize winner in Physics Eugene Wigner, entitled The unreasonable efficiency of mathematics in the natural sciences. In this interesting article, the author begins by asking why mathematics is so useful when it comes to formulating the laws of nature. At school we have been taught numerous formulas corresponding to laws that have been verified to conform to the operation of nature: for example, the free fall of bodies as a uniformly accelerated motion, Newton’s laws of planetary motion, and a long etcetera. But, have we wondered why the laws of nature can be formulated mathematically? Furthermore, why hasn’t another way of expressing them been found up to now, if not better, at least as good as the mathematical formulation?
That the laws of nature are written in the language of mathematics is something that Galileo Galilei affirmed more than three hundred years ago. But long before him, the Pythagoreans, back in the 6th century BC, also claimed that the secrets of nature were expressed through numbers; for this reason they allowed to make contact with the divinity.
Once we discover that the suitability of mathematics for understanding the material cosmos is by no means a obvious one, the next step is to ask ourselves the reason for this suitability. Maybe because the math is easy? Eugene Wigner strongly denies this. Furthermore, there are mathematical concepts, such as complex numbers[1], that do not seem to be suggested by what we actually observe. And yet they are concepts that occurred to someone and that have practical utility (for example, in electronic engineering).
If mathematics is ideal for understanding how nature works, it is, according to Eugene Wigner, because it allows us to develop brilliant reasoning and even border on impermissible reasoning. Thanks to mathematics we can, for example, understand the notion of infinity, and the fact that there are infinities greater than others. For example, the natural numbers are an infinite set, but the real numbers are also an infinite but larger set, which also includes the natural numbers. Between 0 and 1 there are also infinite numbers, whether natural, real, irrational, etc.
While the domain of mathematics is beset with qualitative limitations, it does provide the finite mind with a conceptual basis of contemplating infinity. There is no quantitative limitation to numbers, even in the comprehension of the finite mind. No matter how large the number conceived, you can always envisage one more being added. And also, you can comprehend that that is short of infinity, for no matter how many times you repeat this addition to number, still always one more can be added. (UB 118:0.11)
On the other hand, in light of the UB, it doesn’t take a lynx to realize the importance of certain numbers. The seven, for example, is linked to the spiritual world, while the number ten is related to the material level of reality .
But I wanted to go a little further in my ramblings. Is it possible to get a glimpse of God through mathematics (or, rather, “meta-mathematics”)? Eugene Wigner says in his article that “the miracle of the suitability of the language of mathematics for the formulation of the laws of physics is a wonderful gift that we neither understand nor deserve”. Defining it as a “gift” leads me to think that it really is a gift. Or, rather, a tool with which human beings have been endowed and that allows us to discover the laws that govern the physical world as well as look beyond and glimpse the existence of a Supreme Intelligence. In the UB it is said that, in the same way that there are laws that work in the material world, there are laws that are equally true in the spiritual world (UB 7:1.8; UB 44:5.5). I wonder if these laws will have (or could ever have) a mathematical formulation. And even more if we take into account that “in practice, the laws of nature work in the apparently double kingdoms of the physical and the spiritual, but in reality these kingdoms are only one” (UB 42:11.2).
¶ Looking into the unfathomable: the number pi
In mathematics, “magic” numbers are handled, which lead us to think about their reason for being and their importance. Among these numbers, the so-called irrational numbers stand out, of which the best known is undoubtedly the number pi (П), although it is by no means the only irrational number since its number is, how could it be otherwise, infinite. As you already know, the number is the ratio between the length of any circumference and its diameter, for all the circles that exist and will be in the world. This number was known to different ancient peoples, from at least 1650 B.C. (Ancient Egypt), but could only get a rough approximation of its value. In the last 50 years there has been a giant leap in finding out more decimals of this number, thanks to the invaluable help of computers and their increasing computing power. Today a whopping 1,241,100,000,000 decimal digits of the number have been obtained, which has greater merit if possible, since each decimal that is discovered is more hidden, it costs more to make it appear. In any case, its true value is an unfathomable mystery, as it has an infinite number of non-repeating decimals (they are not periodic).
The number is a transcendental (or transcendental) number, as it is defined as a fundamental property of mathematics. As such, it is not the solution of any polynomial equation. There are infinitely many transcendental numbers, but very few are known, and the proof that an irrational number is transcendental can be very difficult.
The relationship of the number with the circle leads us to consider the importance of this geometric figure in the organization of the universe. In the UB, for example, we can find these significant statements:
Even your olden prophets understood the eternal, never-beginning, never-ending, circular nature of the Universal Father. . . . (UB 2:2.1)
The final proof of both a circular and delimited universe is afforded by the, to us, well-known fact that all forms of basic energy ever swing around the curved path of the space levels of the master universe in obedience to the incessant and absolute pull of Paradise gravity. (UB 12:1.1)
And all this confirms our belief in a circular, somewhat limited, but orderly and far-flung universe of universes. If this were not true, then evidence of energy depletion at some point would sooner or later appear. All laws, organizations, administration, and the testimony of universe explorers—everything points to the existence of an infinite God but, as yet, a finite universe, a circularity of endless existence, well-nigh limitless but, nevertheless, finite in contrast with infinity. (UB 42:1.9)
In his book The univocal language of the Sacred Doctrine, Abelardo Falletti deduces from equality , a deep meaning of transmission of the religious fact in man. He affirms that in the decimal system there is something unattainable that science calls “transcendent number”. The number is a transcendental number that cannot be caused or come from rational numbers, including periodic ones. The above formula cannot be reversed so that the square root of 5 divided by two returns without the itself intervening.
According to Falletti, “something coming from ‘the uncaused’ or timeless descends mechanically, through radicalizations and mathematical-geometric calculations, to the measurable” (numbers 5 and 2). This supposes “a perfect analogy with respect to the religious fact in man, since in said brain only and mysteriously appears ‘the uncaused’ without it being able to be explained by classical science (…) something absolutely foreign and unattainable such as the Meaning of Oneself or Feeling of I Am (…) In other words, something from ‘the uncaused’ has mechanically descended into Man and remains caged - trapped in the measurable or temporary existence of the brain”.
Let’s see what the number П gives of itself! But Falletti does not stop there, but wonders: can something from the uncaused fallen in man return to its timeless source from the activity or desires of the measurable? In the following sentence, he responds in the negative: starting from numbers 5 and 2, without the intervention of “the uncaused” the “uncaused” cannot be achieved. “Only what has descended can ascend”.
The number does not only appear when we talk about circles. It also appears in a formula that is said to be the most important in mathematics, since it conclusively (and mysteriously) unites geometry, arithmetic, analysis and algebra. This formula is called Euler’s identity.
Taking into account that is the most important number of the geometry, e (another transcendental number) is the most important number of the analysis, i (whose value is such that ) the most important number in algebra, and 1 and 0 the bases of arithmetic (the neutral elements of multiplication and addition, respectively), does this formula not suggest the idea of unit?
¶ 19. The role of the mind
According to the UB, the material mind and therefore framed within spacetime cannot obtain a “scientific” demonstration of the existence of superior mechanisms. As beings endowed with a finite mind, we tend to consider as automatic and mechanical phenomena that are actually directed by higher intelligences (UB 42:11.3-4 and UB 42:11.7). Does this mean that we are “condemned” to obtain a partial and very limited view of reality? Of course, we will not obtain the total vision with the current mind, but this can be a good instrument to reach higher levels of insight if we are able to harmonize science, philosophy and religion, placing each one in its corresponding field.
“Science teaches man to speak the new language of mathematics and trains his thoughts along lines of exacting precision. And science also stabilizes philosophy through the elimination of error, while it purifies religion by the destruction of superstition.” (UB 81:6.10)
The mind is, of course, the great integrator, the one that relates the material level with the spiritual. Therefore, it is not surprising that “The Conjoint Actor is…the one who integrates the mathematical causes and effects of the material levels with the intentions and volitional motives of the spiritual level” (UB 115:3.14).
The worst that can happen, and the Book often insists on this, is that we focus our attention exclusively on one aspect of reality, to the detriment of other equally important aspects. This is what happens today with the excessive scientism and materialism that surrounds us.
“There always exists the danger that the purely physical scientist may become afflicted with mathematical pride and statistical egotism, not to mention spiritual blindness.” (UB 133:5.4)
It is therefore a question of integrating all the aspects in an overall vision: it will never be stressed enough that all our gifts must serve us to obtain an expanded vision of reality, which encompasses its three levels (material, mental and spiritual) and harmonize and integrate them.
It is not a question of science, philosophy and religion being mixed arbitrarily, but of being harmonized; rather it is human beings who must harmonize them within. As it says in the UB: the universe does not resemble the laws and mechanisms that the scientist discovers, but it would be more like the scientist who thinks, who uses his mental gifts to understand the functioning of the cosmos (UB 195:7.22) .
¶ Definitely…
Abstract reasoning is a typically human quality that allows us to investigate and learn about reality and even takes us to its limits. Mathematics, in my opinion, is a tool of the mind that allows us to glimpse many clues that divinity has been leaving so that we can intuit its presence. In light of all this, mechanism seems, once again, an absurd and incomplete explanation of reality.
“Materialism reduces man to a soulless automaton and constitutes him merely an arithmetical symbol finding a helpless place in the mathematical formula of an unromantic and mechanistic universe. But whence comes all this vast universe of mathematics without a Master Mathematician?” (UB 195:6.8)
Beyond mathematics hides… the Mathematician Master.
¶ References
- The unreasonable effectiveness of mathematics in the natural sciences, Eugene Wigner. It can be read at the link http://pedroweb.dyndns.org/fisica/eficacia/irrazonablewigner.pdf
- Wikipedia: http://es.wikipedia.org
- The pi number page: http://webs.adam.es/rllorens/pihome.htm (as a curious fact, the music that plays when browsing the page is based on the pi number)
- Light and Life Magazine (all old issues): https://aue.urantia-association.org/numeros-antiguos-del-lyv/
¶ Notes
Complex numbers are represented in the form , with being the real part and being the imaginary part ↩︎