The Known and Unknown: Physics and the Revelation of Baha’u’llah.
“Praised be to God Who made the Point to be outstretched within the Book of Origination, an Ornament through which is the Genesis of Creativity. From it He differentiated the knowledge of what hath been and what will come to pass.”[1] -Baha’u’llah (provisional translation Stephen Lambden)
Recently I wrote two articles exploring some aspects of the correspondence between Baha’i scripture and modern physics. The first was on Plato modern physics and Baha’u’llah, the second was a brief analysis of Abdu’l-Baha’s Tablet of the Universe. In the process of writing, several questions arose which seemed to warrant further study. I also came away with a desire to categorize those ideas contained in the Baha’i writings which seemed to clearly prefigure many aspects of modern physics. This was in part so that I could better identify those that reside in varying degrees of speculation. For example those ideas which, though not established by physics have some considerable likelihood of being right. Also, those which are not understood, but that might point us in directions that might be worthy to consider. Thus to simply put; distinguish the known from the unknown.
As I prefaced in my previous article, these musings represent just that, my very flawed musings. These in no way represent the official views of the Baha’i community. For that you should go here. Also in this article I am unafraid of speculations even wild speculation, however hopefully in this process we are clear in the distinction between what is established by science, what has some probability of being true and what is pure wild speculation. That is so that we can effectively retrieve ourselves from the various rabbit holes we will be going down.
For me the revelation brought by Baha’u’llah and Abdu’l-Baha’s exposition represent an ocean of knowledge for the spiritual and social development of humankind. However I also believe that as Abdu’l-Baha says in the Tablet of the Universe: “These are spiritual truths relating to the spiritual world. In like manner, from these spiritual realities infer truths about the material world. For physical things are signs and imprints of spiritual things;”[2]. So taking this advice I would like to see how far our minds and current understanding carry us in this direction.
This mode of inquiry however is full of peril for a practicing scientist. Faith can be a very powerful force in subverting rationality. One only has to look at the long list of respectable scientists who have at various points in their career fallen down the hole of questionable pseudoscience. Renowned people like Newton, who in addition to creating the foundation of physics out of just about thin air, yet spent a lot of time on Alchemy and esoteric numerology. I know many scientists of faith who dislike this direction of thought. Although they believe that faith and science are not mutually exclusive, still they think that their domains shouldn’t intersect beyond the mechanics of ethics and the vagaries of ‘inspiration’. They may be right. However my reading of Baha’u’llah’s revelation and intuition tells me there is more, much more. So I will stick my toe into this water.
There is another aspect to this process which warrants some discussion. Often when individuals engage in such activities, they spend a lot of time fitting scripture into the current scientific narrative or worse yet trying to fit and distort current science to fit theology. While this might be necessary as a starting point, one should always bear in mind the dangers of ‘over-fitting’. That is anything can be fit with enough variables. Just about any wild theory can be made consistent with observation if we twist it enough. One can see this occurring at the various creation science institutes where they try and cram current science to fit their 6,000 year narrative of the world. Or those who will divine all sorts of modern science or predictions from the numerology of the Bible or the Quran.
To me for these activities to have any merit beyond a curious entertainment, they must produce a valid prediction which is new and verifiable. That is it must generate new knowledge or information in the Adami sense of that word (I will talk about this new definition for information a bit later).
What is known
For completeness I will repeat here many of what I consider the well established items listed in my other articles as well as some new ones.
- The non-existence of absolute rest. “Divine and all-encompassing Wisdom hath ordained that motion be an inseparable concomitant of existence, whether inherently or accidentally, spiritually or materially.” [2] This is a well understood consequence of Heisenberg’s uncertainty principle: the fact that absolute zero Kelvin is impossible to reach.
- The non-existence of a void. “..a void is impossible and inconceivable.” [2] This is required by current quantum field theory for which empty space is not really empty, underlying it is a field from which particles pop in and out of existence. It is bubbly or foamy thing. Actually the vacuum can never reach absolute zero energy.
- The continuum which mediates the propagation of electromagnetic waves is non-physical. “…ether, the forces of which are said in natural philosophy to be heat, light, electricity, and magnetism, is an intelligible and not a sensible reality”[3]. We call it the quantum field, Abdu’l-Baha calls it ethereal matter.
- This continuum gives rise to both matter and electromagnetism. “the substance and primary matter of contingent beings is the ethereal power, which is invisible and only known through its effects, such as electricity, heat, and light — these are vibrations of that power, and this is established and proven in natural philosophy and is known as the ethereal substance” (Provisional translation by Keven Brown) [4].
- Gravity drives stellar formation. “By the operation of this attractive force those holy and resplendent suns, with their luminous worlds, satellites and planets, circling and orbiting in their heavens, at once exerted attraction and were subject to it, induced motion and were themselves moved, began orbiting and set into orbit other bodies, shone forth and caused others to shine.”[2]
- The universe originated from a singularity. “When He purposed to call the new creation into being, He sent forth the Manifest and Luminous Point from the horizon of His Will;”[5] While this verse probably refers to the revelation of Baha’u’llah’s predecessor the Bab who was also known as the Primal Point, I think it also can be applied to the understanding of origination. This theme of creation coming forth from a point or singularity is repeated in many of Baha’u’llah’s writings.
This is of course not an exhaustive list, but these were the ones I could identify which seemed to be rather clear and less debatable.
Moving Towards the Unknown
When I reflect on the statements in the Baha’i writings which seem to prefigure many of the discoveries of modern physics, there is an interesting pattern. Most are in their clearest expression given by explanations provided by Abdu’l-Baha. If one looks carefully it is usually possible to trace it to the original concept provided by Baha’u’llah, however it is ultimately Abdu’l-Baha who is uniquely capable of pulling these concepts out and rendering them intelligible to us.
For example on the question of the ultimate substance of matter if one looks at Baha’u’llah’s Tablet of Wisdom we can see the ideas later expressed by Abdu’l-Baha present.
“..He (Socrates) it is who perceived a unique, a tempered, and a pervasive nature in things, bearing the closest likeness to the human spirit, and he discovered this nature to be distinct from the substance of things in their refined form.”[6]
This I think is the kernel of the idea that underlies Abdu’l-Baha’s statement that, “…ether, the forces of which are said in natural philosophy to be heat, light, electricity, and magnetism, is an intelligible and not a sensible reality” and perhaps the other ideas about non-existence of rest and a void which both flow from the concept of a pervasive and spirit like thing underlying matter. It seems it would behove us to pay extremely careful attention to what Abdu’l-Baha is saying, despite how deceptively simple it may sound.
With hind-sight it is easy to see the many important principles contained in his writings. For example, the understanding that both matter and light arises from the ethereal substance, the understanding that this field represents a non-physical, non-“sensible reality” and that absolute rest is impossible via his statement “that motion be an inseparable concomitant of existence”. These concepts expose some of the core ideas of quantum mechanics and later field theory.
However I wonder how a scientist existing before the advent of the quantum wave function, might have used his statements to hasten these discoveries. One could imagine an insightful individual who might have taken Abdu’l-Baha’s statements on ether and matter to heart and seen as DeBroglie eventually postulated that matter might be modeled as a wave. Or later understood that this same field could also explain electromagnetism. Yet still it requires formulating these principles in terms of the problems and mathematics at hand. Thus I doubt one will discover a fully formed theory of physics hidden in scripture. Instead one will find principles which should inspire and hopefully point the direction towards fruitful inquiry. I also think that at the end we will need to turn towards Abdu’l-Baha’s words in order to hope to grasp these ideas latent in the revelation of Baha’u’llah.
What is probably True
There are several ideas which seemed to be suggested in the Baha’i writings, and I think many physicists think are true, but still haven’t been proven yet. I now list them in descending degrees of certainty.
The Cosmos exhibits Self similarity.
“earthly and heavenly, material and spiritual, accidental and essential, particular and universal, structure and foundation, appearance and reality and the essence of all things, both inward and outward — all of these are connected one with another and are interrelated in such a manner that you will find that drops are patterned after seas, and that atoms are structured after suns in proportion to their capacities and potentialities.”[2] This perhaps should really belong in the known category of known, since this is a plainly observed phenomena of our universe, and in fact is due to the nature of our physical laws and has in part driven the development of fractal mathematics.
The Cosmos is Infinite.
“Know thou that the expressions of the creative hand of God throughout His limitless worlds are themselves limitless. Limitations are a characteristic of the finite, and restriction is a quality of existent things, not of the reality of existence.”[2] Despite the belief that our universe originated with a singularity, there is a strong suspicion that our cosmos is infinite, populated by a multi-verse and in fact its almost a requirement for many existing theories beyond the standard model.
Grand Unification of the physical forces.
It has always seemed to me that the project of grand unification to be very consistent with my understanding of Baha’u’llah and Abdu’l-Baha’s discussion of the nature of reality arising from singularity and the unity of existence. In the Tablet of Wisdom Baha’u’llah refers again to creation: “The world of existence came into being through the heat generated from the interaction between the active force and that which is its recipient. These two are the same, yet they are different. Thus doth the Great Announcement inform thee about this glorious structure.”[6]
Abdu’l-Baha identifies the active and passive force, with the ethereal force: “the substance and primary matter of contingent beings is the ethereal power, which is invisible and only known through its effects, such as electricity, heat, and light — these are vibrations of that power, and this is established and proven in natural philosophy and is known as the ethereal substance (maddiy-i-athiriyyih). This ethereal substance is itself both the active force and the recipient; in other words, it is the sign of the Primal Will in the phenomenal world …. The ethereal substance is, therefore, the cause since light, heat, and electricity appear from it. It is also the effect, for as vibrations take place in it, they become visible. For instance, light is a vibration occurring in that ethereal substance. (Ma’ idiy-i-Asmanl 2:69)”(Provisional translation by Keven Brown)[4]
Here we have the full quote which I gave partially for the previous list. Abdu’l-Baha seems to be saying several interesting things. First as I noted before, that the ethereal substance gives rise to both matter and electromagnetic fields. This is interesting by itself since it is yet another example of Abdu’l-Baha getting right a very important consequence of quantum field theory, namely that both matter and the electromagnetic field arise out of the quantum field. Second the fact that he links the ethereal substance to Baha’u’llah’s active and passive force, seems to point to it being the ultimate origin of all forces including gravity.
The idea that a single field or ethereal substance gives rise to all forces is of course at the heart of all the grand unified field theories. It would seem that Baha’i scripture lends significant credence to this project.
Space-Time arises from Quantum entanglement:
In my previous article I made the observation that the description of gravity contained in the Tablet of the Universe sounded a lot like a description of quantum entanglement. The idea of viewing space-time as a product of quantum entanglement originated with Van Raamsdonk based on the so called AdS/CTF correspondence and is described nicely here.
The question as to how might gravity be related to the quantum or ethereal field is possibly hinted at in the Tablet of the Universe, where Abdu’l-Baha relates that the universal attractive force is derived “ from the firm ties, the mighty correspondence and affinity that exist between the realities.”[2] To me this sounds suspiciously like a description of entanglement. After all entanglement at its heart represents a ‘correspondence’ or correlation between particles.
The AdS/CFT correspondence refers the mathematical equivalence of two toy models of the universe. AdS stands for the Anti-de Sitter space where the rules of space-time gravity work in the usual manner only without the expansion and acceleration which characterizes our universe and with an Escher drawing like topology which gets more compact as the Conformal boundary is approached. Conformal field theory (CFT) refers to conformal quantum field theory confined to live on a lower dimensional surface surrounding the AdS space like a cylinder surrounds its interior. In 1997 Juan Macldeona discovered that the operation of quantum field theory on this boundary gave rise to effects which mathematically ‘looked’ like gravity in the space on the interior. This was an example of the holographic principle where higher dimensional behavior gets encoded in lower dimensions. Later Van Raamsdok showed that the source of the emergent space-time in the AdS/CFT model was due to quantum-entanglement on the CFT boundary.
The idea that space-time is emergent from quantum entanglement seems to have a lot of circumstantial evidence from the resolution of several paradox’s which arose in the study of black holes, entropy and information. The upshot of the conjecture of viewing of space-time as a product of quantum entanglement, is that it provides the ‘holy grail’ of linking gravity with the quantum field and providing a possible pathway towards a ‘good’ grand unified field theory.
As a side note, I personally think that if both space and time are emergent properties of the quantum field that this implicates dimensionality as well. So the very fact of 3 or higher dimensional space may itself be an emergent phenomena of the quantum field. Ultimately the very idea of space and passage of time can be expressed by the rules and modes by which matter interacts.
Holographic principle
This related idea is actually embedded somewhat in the idea that space-time is built-up from quantum entanglement. At the heart of the AdS/CFT correspondence is the application of the holographic principle, where higher dimensional dynamics are encoded into a lower dimension on its boarder and is actually emergent from the lower dimensions. So for example in the AdS/CFT toy models, space-time can be shown to be emergent from the operation of quantum field theory on a two dimensional surface.
I find the manner Abdu’l-Baha describes this physical existence: “..this nether place is only its shadow stretching out. A shadow hath no life of its own; its existence is only a fantasy, and nothing more; it is but images reflected in water, and seeming as pictures to the eye.” [7] as rather suggestive of the holographic principle.
What Might be True
There are several other ideas that Baha’u’llah and Abdu’l-Baha express clearly in many places although they are not current or completely understood in modern scientific thought. To me these seem to probably be fruitful avenues of research and practice.
Nature is possessed of a power which Creates.
“Say: Nature in its essence is the embodiment of My Name, the Maker, the Creator. Its manifestations are diversified by varying causes, and in this diversity there are signs for men of discernment. Nature is God’s Will and is its expression in and through the contingent world. It is a dispensation of Providence ordained by the Ordainer, the All-Wise. Were anyone to affirm that it is the Will of God as manifested in the world of being, no one should question this assertion. It is endowed with a power whose reality men of learning fail to grasp.”[6] Of course its almost axiomatic to say that Nature creates if one is a naturalist and scientists almost by definition are. However it would seem that Baha’u’llah is making a much stronger statement. He appears to be claiming that there is an as yet undiscovered power in Nature which drives and generates order in the universe. This idea is also repeated in several of Abdu’l-Baha’s talks. For example, in a letter to the naturalist Dr. Forel Abdu’l-Baha seems to refer to this as the “the Ancient Power”[8].
Love is the cause of life
Perhaps related to this creative power of Nature, Abdu’l-Baha identifies “Love” with the power to bring forth life. “Love is the very cause of life”. “We declare that love is the cause of the existence of all phenomena and that the absence of love is the cause of disintegration or nonexistence.”[9] He then goes on to make an interesting definitional shift and relates the physical “attractive force” to a primitive form of love.
Gravity seems to play a role here as it appears to be the dominant force which drives the creation of order in our universe. Recent work by Barbour [10] and his colleagues studying toy dynamical models of a universe governed by simple Newtonian gravity show that there is something unique about systems under the operation of an attractive force like gravity. In this paper they say, “self-gravitating systems exhibit “anti-thermodynamic” behavior that is not fully understood.” Thermodynamics as it was originally conceived didn’t take into account gravitation. Indeed the operation of self-attractive forces leads to symmetry breaking and clustering which is very different from how ideal gases behave. They also show that by itself the operation of gravity might explain the origin of the universe from a singular divergent core as one of the systems natural modes.
Information is positively involved in the generation of order
This is a deduction I have made based on my understanding of the description of the creative properties of the Word of God, “(the) Word of God which is the Cause of the entire creation, while all else besides His Word are but the creatures and the effects thereof. Verily thy Lord is the Expounder, the All-Wise. Know thou, moreover, that the Word of God — exalted be His glory — is higher and far superior to that which the senses can perceive, for it is sanctified from any property or substance. It transcendeth the limitations of known elements and is exalted above all the essential and recognized substances. It became manifest without any syllable or sound and is none but the Command of God which pervadeth all created things. It hath never been withheld from the world of being.”[6] If we abstract beyond the profound mystical import of the word of God, we can see that on the simplest level a word is a container for information. That information can help generate order shouldn’t be surprising based our day to day experience with information technology, knowledge and life. However uncovering this fundamental relationship from a physics point of view is much more challenging and only recently are physicists beginning to sort this out.
In a previous article I have already gone into much detail about this subject so I wont repeat it all of it here. The important point is that it implies that the current Shannon definition of information which links the rise of disorder or entropy to the rise of information needs to be rethought. A solution has recently been developed via Adami’s definition of information which relates positively with the rise of order.[11] In his definition information represents the ability to make a prediction better than pure chance. Shannon’s definition on the other hand is really a measure of a systems potential uncertainty and thus its ability to store information.
Meditation can help drive the process of discovery
This is probably a point which most of my more naturalistic colleagues might strongly disagree with. However I believe there are enough instances in the history of science where the process of discovery has occurred in a mystical or a revelatory manner that we shouldn’t dismiss this out of hand. There are plenty of dreams, visions and mystical experiences which fill our science history books. Also I think most researchers may reflect on how difficult problems at times seemed to be suddenly resolved, or an important insight occurs after a dream or a period of mediative reflection.
Baha’u’llah says in the Book of Certitude quoting an Islamic hadith, “Therefore, hath it been said: “Knowledge is a light which God casteth into the heart of whomsoever He willeth.” ” also in the Tablet of Ornaments, Baha’u’llah says, “ In this Day whatsoever serveth to reduce blindness and to increase vision is worthy of consideration. This vision acteth as the agent and guide for true knowledge. Indeed in the estimation of men of wisdom keenness of understanding is due to keenness of vision.”
When Abdu’l-Baha visited Paris during the early years of the 20th century, he gave a very positive account of the practices of the ancient Persian illuminati school. This is where in addition to standard lectures they would engage in collective silent meditative reflection on various problems. Abdu’l-Baha then goes on to make the following comments on this subject:
“Through the faculty of meditation man attains to eternal life; through it he receives the breath of the Holy Spirit — the bestowal of the Spirit is given in reflection and meditation.
The spirit of man is itself informed and strengthened during meditation; through it affairs of which man knew nothing are unfolded before his view. Through it he receives Divine inspiration, through it he receives heavenly food.
Meditation is the key for opening the doors of mysteries. In that state man abstracts himself: in that state man withdraws himself from all outside objects; in that subjective mood he is immersed in the ocean of spiritual life and can unfold the secrets of things-in-themselves. To illustrate this, think of man as endowed with two kinds of sight; when the power of insight is being used the outward power of vision does not see.
This faculty of meditation frees man from the animal nature, discerns the reality of things, puts man in touch with God.
This faculty brings forth from the invisible plane the sciences and arts. Through the meditative faculty inventions are made possible, colossal undertakings are carried out; through it governments can run smoothly. Through this faculty man enters into the very Kingdom of God.”[12]
What is Unknown
At this level of conjecture our task becomes much more difficult. This is because for what follows we don’t have access to Abdu’l-Baha’s explanations since in the existing translated literature I could find nothing bearing on these subjects. So at this point we are left only with provisional translations of some extremely challenging Arabic tablets of Baha’u’llah and a lot of speculation.
Also, although I am a practicing research physicist, I am not by any stretch a string theorist. I have had a healthy interest in the progress of various theories beyond the standard model throughout my career, but I must admit to being very skeptical of the whole string theory project. I recall during my days as a post-doc at Fermilab, reading the famous critic of string theory, “Not Even Wrong” by Peter Woit. I thought rather smugly how my colleagues and I were engaged in “real” physics, hoping to beat the Europeans and discover the Higgs at the Tevatron. We were testing the standard model and not simply engaged in obscure mental exercises which will only lead to things mathematicians might be interested in.
However over time and especially during the past year I have amended my view of string theory. This is in part because of the fact that in recent years there seems to have emerged actually useful insights stemming from the use of string theory in the AdS/CFT context (as I mentioned previously). Also as just a mathematical tool it has already shown its use in calculating accurately a fundamental constant of the quark gluon plasma[13] which we produce at the RHIC collider where I work. In addition, when I began seriously reading Baha’u’llah’s more esoteric works, I was rather struck at how similar it all sounded to aspects of string theory. These writings seem to be invoking the same Greek and Pythagorean ideas of geometric reduction which underlie string theory. As a result I was interested in exploring these connections a little more.
In the following I will lay out some of the basic concepts which underlie string theory and comparing them to aspects of Baha’u’llah’s more esoteric writings. I want to be clear at the outset that I don’t believe Baha’u’llah is trying to do ‘physics’ in the modern sense of that word. Instead I think he is looking at the relationship between the age old practices of Eastern mathematical mysticism and our understanding of mystical truths and cosmology. These ideas have roots in ancient Greek Pythagorean ideas and philosophy. Thus one might argue that these practices share a common Pythagorean root with string theory in the realm of ideas surrounding geometry and numbers.
The fundamental units of matter are string like objects.
In several of Baha’u’llah’s more mystical and alchemical tablets, he links the arabic letter ‘Alif’ to a primal Pythagorean line, thread or string from which creation is generated. Here it is important to note that the Arabic letter for “A” (alif ) is a straight line. For example:
“This Point assumed the primordial shape upon the mirrors of the letters in the beings of the Names. The [Arabic letter] “A” (al-alif) received it [within itself] before all the other letters, in the [pre-eternal] elemental particles of things for thus did this Divine Point take on the form of this Eternal [Arabic letter] “A” (alif). This inasmuch as the merciful breezes blew upon it from the Source of Singleness whereupon the Countenance of the Divine Singularity (wajh al-wahidiyya) was disclosed from behind the Green Veils. The substance (body, temple, form.. haykal) of the Point was made manifest in the shape of the letter “A” (al-alif)”[14]
In another place in this same tablet, Baha’u’llah gives yet another interesting viewpoint on this same theme and in the process we see used the ancient practice of Abjad or numerology. Baha’u’llah, the Bab and before them muslim mystics and scholars made extensive use of this type of numerology to encode ideas or reveal connections they claimed where hidden in the words of God.
“ Know then that should thou make this divine “A” to revolve about its self there would be manifest two upright “A”s . And then after that if thou should raise them both up unto [the value of] the tens then there would be manifest the number of twice ten. Then would surely be made manifest the [letter] ك “K” (al-kāf; abjad = 20)of the [creative imperative] command [= كُن kun = “Be!”] by means of which the “Temples of the Divine Unity” , the Manifestations of Singleness and the loci of abstracted reality were called into being. And this [creative “K” as the imperative كُن ] actualized the [qur’ānic] “and it is” (fa-yakun) [= كُنفَیَكُونُ kun fa-yakūn, “Be and it is!”, Q. 2:115; 3:42; 6:72 etc.] before it was associated with the supportive letter ن “N” [as thou dost know] if thou art of such as are informed. Following this conjoining [ of ك “K” and ن “N” as the creative imperative كُن ] the modalities were created in the worlds of limitation as well as the concrete [worldly] testimonies in the worlds of constructed reality. Unto this do testify such as are privy to the knowledge of the mysteries of wisdom the like of which hath streamed forth from a manifest and mighty Pen .”[14]
Here one sees the linking of two primal lines or strings to creation, only now the numerical value of 10 is inserted which associates it with the arabic letter “K” in the word “Be” (Kun). As we will see later the number 10 might be significant. The primary subject of this tablet are the isolated letters found prior to several verses in the Quran. So throughout the tablet there is a back and forth between numbers and letters and the meanings they imply.
There is yet another description of creation which seems to follow a somewhat similar description. Only now the reference to the primal Pythagorean line is more explicit. In the Lawḥ-i kīmīya, he quote’s the famous Persian polymath Jabir’s[15] rendering of a saying attributed to Plato. “Know then, that God, praised and glorified be He, took a line, split it lengthwise into two, rotated the one about the other, and so made from them the universe. The line, however, formeth only from the point when you move it. Conceive ye then our meaning” (Provisional translation by Keven Brown)[4].
This description Plato gives and others by Baha’u’llah, seem to make clear the link between the straight line of ‘Alif’ and the primal Pythagorean line. The idea of a ‘line’ being at the heart of creation is another expression of the underlying concept of string theory. Firstly the word ‘line’ versus ‘string’ is just semantics. The object that is being clearly referred to, is the one dimensional Pythagorean line, which is exactly what a string represents in string theory. String theory postulates that the primary particles are described using 1 dimensional strings. One of the fundamental actions which these strings undergo are represented by the ‘splitting’ of the string. For example in one version of this theory electron/positron pair production are represented by a photon described as a vibrating string which then splits lengthwise yielding two strings an electron and positron. This is also true for quark antiquark production.
Thus the production of all known particles might be represented in this manner. These strings (particles) end up in orbit around each other in complex manners to yield protons and then atoms. Or another way to look at it is the second rotating line becomes a surface to which the first line attaches. String theory as it turns out requires the postulate of surfaces which strings can become attached to. This is in order for the boundary conditions of the strings to make sense. These are called D-branes (here D refers to the mathematical Dirichlet boundary condition), or also equivalently p-branes. The p-brane terminology generalizes the concept of a string (p=1) to a point (p=0) or to a surface (p=2) and higher. So one could understand the generation of all things from this sequence of processes Plato describes. Finally Plato indicates that these strings are actually produced by a single point. This idea was actually proposed by the well known string theorist Charles Thorn. In a paper on string theory where he claims “Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point like objects.”[16]
Since there seems to be an interesting correspondence between some of the ideas behind string theory and these mystical tablets of Baha’u’llah, I would like to explore this relationship some more to see where this leads us. First lets consider some basic concepts underlying modern string theories.
hidden dimensionality
The basic postulate of string theory is that the fundamental objects in nature are 1 dimensional strings whose modes of vibration represent various fundamental particles. These strings are so small that they make particles look point like at the range we are currently capable of observing. It has been demonstrated that string theory can only support consistent theories which contain either 25 or 9 physical dimensions plus 1 temporal to get (26 or 10 total dimensions). This is because if you apply the requirements of relativity and quantum mechanics to these objects it turns out that you need to assume the existence of 26 dimensions of space-time. The reason for this is, if other number of dimensions are used, then nonphysical mathematical anomalies or ‘ghost states’ appear (in the form of norms which are negative). These states cancel if there are 26 dimensions or one can use 10 dimensions if super symmetry is also assumed. Without going off on too much of a tangent, supersymmetry refers to the theory that claims that every half integer spin particle (fermion) has an integer spin partner (boson) with identical charge and mass and visa versa.
To explain the fact that we don’t observe these extra 22 or 6 dimensions, it has been postulated that these extra dimensions are curled up into hidden or compact dimensions. The analogy of the garden hose is often used to explain this. So looking at the garden hose from high above the surface of the earth it looks like a point. When you descend closer it looks like a line. Move even closer you can recognize width and the interior and thus resolve all three dimensions. So the current accounting of dimensions goes as, 4+6=10 or 4+22=26 dimensions. That is 3 standard spatial dimensions plus time = 4, plus an additional 6 or 22 curled up in compact dimensions.
In the past there were derived 5 types of self-consistent superstring theories. Later it was discovered that what distinguishes the various types of string theories was found to be based on the size and shape parameters of the extra dimensions, basically the nature of the complex geometry which described how they were curled up or compactified. These surfaces are often expressed as what are called K3 surfaces that are very complex creatures which describe the geometry of how the curled up dimensions are shaped. Thus varying the parameters describing these surfaces would move you from one theory to another. It is now believed that there is an overarching theory of which all of these string theories represent a special case. This unknown theory has come to be called M-theory (M is at times referred to Mystery, Magic and other such things). It is believed that this theory lives in a 11 dimensional space and also includes the 11 dimensional supergravity theory as a special case. So each theory actually represents a particular solution to this master theory. In this case the basket of possible solutions represents an enormous space, by some accounting as much as a between 10¹⁰ to 10⁵⁰⁰ possible solutions. So the problem is determining which of these choices represent our universe.
Monstrous Moonshine
As it so happens, there might be some guidance relative to the size and shape parameters for these extra dimensions given by recent fascinating and down right mysterious work done in mathematics. The story behind this quite amazing, full of strange unexplained numerical correspondences, lost manuscripts and religious visions of a mysterious and tragic genius dating nearly a century ago. This rabbit hole is very deep. I strongly recommend reading the recent article which gives a great accounting this story in Quanta magazine.
The Umbral Moonshine conjecture, is an outgrowth of the Monstrous Moonshine conjecture and based in part on the work of the famous mathematical genius Ramanujan, who died at the tragically young age of 32 in 1920. Before he died he revealed mathematical functions which are a fundamental component of this conjecture. He claimed to receive his mathematical knowledge from the Hindu goddess Namagiri in the form of dreams and visions. One vision was described by him:
“While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.”[17]
Umbral Moonshine was motivated by the unexplained and mysterious numerical connection between the dimensionality of what is called the Monster in group theory and the modular j functions in number theory. This was recognized in the late 70’s and the unexplained connection came to be called Moonshine or Monstrous Moonshine. Later in the 90’s the bridge connecting the Monster group and j function was discovered in the mathematics of the 24 dimensional version of string theory. The connection was that the coefficients of the modular j function represented the number of ways that a string can vibrate for a given energy, while the Monster group represented the symmetry of a string vibrating at that energy. The Umbral Moonshine conjecture put forward in 2012, connects 26 new monster groups with many of the mock-modular functions given by Ramanujan. As before now the bridge connecting them to each other are the yet to be determined string theory geometries which are described using the K3 surfaces. The symmetries at a given energy of these surfaces give the new monster groups and the Ramanujan mock-modular functions give the ways the strings with these surface geometries can vibrate at a given energy. If you want to delve more deeply into this topic there is a nice and accessible tutorial here.
Returning to Baha’u’llah’s writings, we find the idea of a hidden dimensionality within the primary ‘Alif’, line or string if you like, repeated several times in this particular tablet. These of course on one level probably refer to the hidden symbolism and meaning. However might it refer to hidden physical dimensionality? On one level I think it is correct to consider the words of God as ‘over-loaded’ operators, to borrow a software term. That is they have meaning which changes based on their context and application. Thus the meaning is not exclusive: either or. For example we have:
“Then observe the devolved cryptic dimensions [of the letter[s] “A”] just as thou dost witness their [mundane] numerical-alphabetical aspect . This [letter] “A”, for example, if thou submerge it in the oceans of the decades the “A” would appear,[maintaining] its own shape through the replication of the [Primordial] “Point” [as 2 dots] and from it would appear the [letter] ې “Y” for its numerical value is ten (yā’ = abjad 10 = 1 & 0) according to the manner of enumeration in which thou dost calculate. In like manner, if thou shouldst cause the letter “A” , to ascend unto the heaven of the hundreds it would appear in its very essence through the compounding of the dual “Points” such that thou would, this moment observe the letter ق “Q” [again with 2 dots]. Wherefore is it that it the letter “A” traverseth until it terminateth at the end of numerical computation when the letter “A” appeareth on the fourth level [of the thousands] [again] through the compounding of the [Primoridal] “Points”. Wherefore is there manifest the numerical reckoning of the thousands. In this respect thou shalt observe the letter غ “Gh” (al-ghayn; abrade = 1,000).”[14]
So the inner letters of “A” are the arabic “A”, “Y”, “Q” and “Gh” letters which represent powers of 10, zeroth to third power. If we continue in this tablet we find the following tantalizing paragraph which appears to refer to these inner dimensions.
“Then know that this [letter] “A” (al-alif) is expressive of mysteries relative to all sciences (kull al-`ulum) inasmuch as God hath bestowed upon it a portion of the wonders of His Bounty. Within it is a foreordainment [measure] of knowledge relative to what hath been and what will be. If, for example, thou deduce the [other] letters (al-ḥurufāt) which are inner dimensions (sarā’ir) of this [isolated letter] “A” in the light of that which We have divulged unto thee previously of the four levels [implicit] therein and thou write down [the secrets of] its power of articulation (استنطاق istintāq) and after that divide it according to its four divisions (taqsīmāt) and thou apply this according to these [four] divisions in line with its requirement in terms of augmentation (الترقى al-taraqqī) and diminution (التنزل al-tanazzul), of ascent (الترفع al-taraffu) and equilibrium (التساوى al-tasāwī) there shall assuredly appear before thee something of such mysteries as shall astonish the intellects. And thereby will be evident that which thou hast heard regarding the all-encompassing [comprehensive science of] jafr (al- jafr al-jāmi` ) and thou shalt attain unto the genesis of the sciences (madbā’ al-`ulūm).”[14]
As this paragraph deals with the “genesis of the sciences” it is particularly irresistible for the scientist in me, so lets spend a bit of time on this to take it as far as we can go. The hope is that perhaps we might be able to glean some guidance as to the geometry of these strings if indeed there is a connection. Of course we don’t offer a resolution to this mystery, however at least some groundwork can be laid for the future.
I believe the “letters which are inner dimensions” refer to the previous paragraph I cited. Here Baha’u’llah instructs us to “write down [the secrets of] its power of articulation” so at surface value I take it to mean writing out the letters as they are pronounced in arabic. Thus we get ( A= “ألف”, Y=“ياء”, Q= “قاف”, and Gh= “غين” ) now if we use the rules of Abjad equating letters with numbers we get the following numbers, A= (1,30,80) summed = 111, Y= (10,1,1) summed =12, Q=(100,1,80) summed = 181 and Gh= (1000,10,50) summed = 1060. If we add them all together we get 1364. Then he says, “and after that divide it according to its four divisions and thou apply this according to these [four] divisions in line with its requirement in terms of augmentation and diminution, of ascent and equilibrium”. This is where we lose things. What does the operation ‘divide’ and ‘apply’ refer to? Are these mathematical operations? as in divide and multiply? or divide as in segment or sort? What does augmentation, diminution, ascent and equilibrium mean in this context?
There is another hint here, at the end of the paragraph reference is made to the “all-encompassing [comprehensive science of] jafr (al- jafr al-jāmi` )”. Al-jafr is an esoteric Islamic practice of number/letter mysticism, divination and gnosis associated with Adjab. It is purportedly associated with ‘letter sciences’ taught to Muhammad by the angle Gabriel, while his son-in-law Ali was present on Mount Paran. It was used to help predict various events associated with the coming of the end times and the appearance of the hidden Imam.
As such the forerunner of the Baha’u’llah, the Bab engaged in some aspects of this practice, since he was primarily concerned with preparing his believers for the advent of Baha’u’llah and linking his mission to that of the fulfillment of Shi’ite millennial expectations. One of the interesting practices involved the construction of so called ‘magic squares’. Magic squares were of great fascination to ancient Chinese and made their way into Islamic culture. They would function as magical Talismans or were used in divination, to predict important events.
Magic squares consisted of a table or matrix of numbers where each row, column and diagonal would add up to the same number. One of the interesting ideas present in the concept of a Talisman in general is the notion that a lower object is a model of a higher object. So there exists this idea of progression of Talismans, the prophet being a Talisman of God, and man being a Talisman of him. So Adam is made in the ‘image’ of God. On another level these magic squares where considered Talismans of the universe or representations/models of the universe.
Apart from the interesting additive properties, magic squares are interesting mathematical objects for a variety of reasons. One property is that if taken as a modern matrix their magic number represents one of its eigenvalues, with the unit vector being its eigenvector. This might be important since the mathematics of eigenvectors can be used to solve coupled harmonic oscillators and a good portion of classical quantum mechanics is cast in this form. If you are curious about this aspect of linear algebra a brief tutorial with its connection to magic squares is here.
Maybe the key here is that the expressions “augmentation and diminution, of ascent and equilibrium” implies some kind of mathematical operation associated with each division or level. At this point it would be helpful to have access to the Arabic terminology associated with the different types of mathematical operations used by practitioners of abjad or al-jafr to understand if these kinds of operations were being invoked. So for example ‘A’ division requires ‘augmentation’ which might be addition, multiplication or even exponentiation. ‘Y’ division requires ‘diminution’ which might imply subtraction, division or taking the negative exponent. ‘Q’ division requires ‘ascent’ and ‘Gh’ requires ‘equilibrium’ for which I have no good guess as to what might be required.
On another level they remind me of the so-called raising and lowering operators which are used in string theory (and in simple quantum mechanical harmonic oscillator systems) for deducing the various energy states including the ground state. These operators move the string system up or down in energy by discreet amounts which are given by the properties of the string. They basically represent the vibrating modes of the string. In this connection it is also interesting that in music theory terms such as ‘augmentation’, ‘diminution’, ‘equilibrium’ and ‘ascent’ are used, which in their basic meaning refer to the nature and modes of vibrations underlying the notes. This in turn might connect it back to the mock-modular functions since their coefficients represent the ways that a given K3 surface permits the string to vibrate at a particular energy.
I have this rather strong belief that we are witnessing the first inkling of a stupendously beautiful and profound mystery in the convergence of mathematics, physics and mysticism. We have the intersection of the mystical visions of mock-modular functions of Ramanujan, its relationship to the monster group, the geometry of string theory and their collective relationship to the strange anti-de Sitter Space which happens to be the key that exposes the nature of space-time as being a product of quantum entanglement. Thus it is tempting to think that along with the strange correspondence between string theory and the descriptions of creation as the product of some cosmic line or lettering that perhaps another piece of this puzzle might be found in this fascinating Tablet of Baha’u’llah’s.
I also am of the opinion that the way forward in understanding these verses and any connection they might have to the physical nature of our universe is to be found not just in the application of overpowering mathematical or intellectual firepower (though it might help a bit). Rather I believe it will come as result of purity of heart and as “ a light which God casteth into the heart of whomsoever He willet.”
Links to my other articles on religion and science:
Plato, Modern Physics and Baha’u’llah
One Physicist’s first Look at Abdu’l-Baha’s Tablet of the Universe
The Known and Unknown: Physics and the Revelation of Baha’u’llah
Does the singularity of God require the singularity of Religion?
The Spirit of Faith and Eternal Life
Links to Short Stories:
Igor (part I), The Refugee (part II), Marion-Jack (part III),
References
[1] Baha’u’llah’s Commentary on the basmala and Qur’an 68:1: “N” (Nūn). By the Pen!” provisional translation Stephen Lambden: http://hurqalya.ucmerced.edu/node/461/
[2] Abdu’l-Baha’s Tablet of the Universe, provisional translation: http://bahai-library.com/abdulbaha_lawh_aflakiyyih
[3] Some Answered Questions by Abdu’l-Baha pp 83–86:http://www.bahai.org/library/authoritative-texts/abdul-baha/some-answered-questions/#f=f6-270
[4] Provisional translation contained in “A Bahá’í Perspective on the Origin of Matter” by Keven Brown published in Journal of Bahá’í Studies, 2:3, pages 15–44 Association for Baha’i Studies North America, 1990 http://bahai-library.com/brown_perspective_origin_matter
[5] The Tablet of ISHRÁQÁT (Splendours) Baha’u’llah http://reference.bahai.org/en/t/b/TB/tb-9.html
[6] Tablet of Wisdom, Baha’u’llah http://www.bahai.org/library/authoritative-texts/bahaullah/tablets-bahaullah/#r=tb_en-9
[7] Selections From the Writings of ‘Abdu’l-Bahá pp 320 http://reference.bahai.org/en/t/ab/SAB/sab-151.html
[8] Abdu’l‑Baha’s Tablet to Dr. Forel:http://www.bahai.org/library/authoritative-texts/abdul-baha/tablet-august-forel/#r=taf_en-title
[9] Promulgation of Universal Peace. Abdu’l-Baha http://www.bahai.org/library/authoritative-texts/abdul-baha/promulgation-universal-peace/#f=f7-500
[10] PRL 113, 181101 (2014)
[11] Christoph Adami, “What is Information” Philosophical Transactions of the Royal Society A mathematical, physical and engineering scienceshttp://dx.doi.org/10.1098/rsta.2015.0230
[12] Paris Talks p184 http://reference.bahai.org/en/t/ab/PT/pt-55.html
[13] https://arxiv.org/pdf/hep-th/0405231.pdf
[14] Tafsīr al-ḥurūfāt al-muqaṭṭa`āt (Commentary on the Isolated Letters) or Lawḥ-iāyah-yi nūr (Tablet about the Light Verse) of Mīrzā Ḥusayn `Alī Nūrī Bahā’-Allāh(1817–1892). Part II. Provisional translation by Stephen N. Lambden :http://hurqalya.ucmerced.edu/node/451/
[15] Based on private communication with Keven Brown; https://en.wikipedia.org/wiki/Jabir_ibn_Hayyan ; I believe Jabir’s quote is possibly a retelling of the following quote from Plato’s Timaeus which follows his description of the creation of the ‘World Soul’ this might clarify the relative geometry of the two lines “..This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse.” (Timaeus 34b-37c). Also Stephen N. Lambden has translated this same verse in the Lawh-i Kimiya as “Then know that God, blessed and exalted be He, took a [cosmic , alphabetical] trace [line] (khaṭṭ an) and cleft it in the middle [lengthwise] (bi’l-ṭūl). Then he made one of these two [lines] rotate about the other. And between the two he made the Cosmos (al-`ālam). But the cosmic [alphabetical] line (al-khaṭṭ) came into being from the Point (al-nuqṭa) and derived its motion from it. So understand that which we say!”
