Geometry as Communication with Nonhuman Intelligences

Daniel Rekshan
School of Integral Noetic Science, California Institute for Human Science
INS 700: Academic Writing for the Human Sciences
Dr. Julie R. Dargis
March 17, 2023

Geometry as Communication with Nonhuman Intelligences

News articles in February 2023 involved the unprecedented use of the term “unidentified flying object” or UFO (Ghose, 2023). These articles described US military action to shoot down three mysterious objects that were only described using vague geometric terms, such as cylinder, octagon, and sphere (Barnes et al., 2023). The US declared these objects to likely be research balloons and called off recovery efforts before finding debris (Rogers, 2023). The US has been engaged in an inquiry into the topic of “unidentified aerial phenomenon” (UAPs), which is simply an updated term for UFOs, since before June 2021 (ODNI, 2021). In this novel political context, the usage of the term UFO in February invites questions. 

However, these objects did not exhibit the qualities of advanced technology associated with some UAPs (Rogers, 2023), like moving against the wind with no known means of propulsion (ODNI, 2021). Most UAP cases resolve into known objects like balloons, but some do exhibit qualities of intelligence and advanced technology (ODNI, 2021). This paper focuses on the identification and communication with UAP intelligences through simple geometry, which is consistently present within UAP reports (Barnes et al., 2023; Haines, 2010) and is a direct means of intuition and implies emotional value such as positive or negative (Larson et al., 2012).

The purpose of this paper is to explore the question, “how can we identify and communicate with nonhuman intelligence (NHI) such as ET or UAP consciousness?” Given that mainstream science has not recognized or integrated the testimony of ET contact experiencers, this paper will examine the role of worldviews in the perception of NHI. The example of shamanic dreaming cultures demonstrates that mainstream culture is unique in its self-imposed limitation of reality to waking phases of consciousness, as opposed to dreams or altered states. Experiential testimony of thousands of individuals across many different modes of experience like ET contact, dreams, and psychedelic states suggest that Western culture is already engaged in NHI contact (Gackenbach, 1989; Hernandez et al., 2018; Luke, 2022). 

Many researchers suggest that mathematics is a universal language. Just as there are many phases of consciousness, there are many types of mathematical reasoning. This paper will explore the use of Euclidean Constructive Geometry (ECG) in NHI communication, which is a special type of geometric reasoning that uses only geometries that can be drawn with the ruler and compass to prove mathematical claims (Beeson, 2012). While most researcher associated with the Search for Extraterrestrial Intelligence (SETI) look for encoded messages in radio waves or stellar pulsations like binary or morse code (Atri et al., 2011), a SETI effort based on ECG may involve means such as telepathy (Ibison & Hathaway, 2011) or the phenomenological appearance of simple geometric shapes. Researchers have demonstrated that this type of geometric reasoning involves intuition, imagination, and emotion (Fujita, 2004; Nathan et al, 2021), which appears to be the same type of reasoning involved in Jungian active imagination (Jung, 1997). The thesis of this paper is that ECG may be the most effective way to search for and communicate with NHI such as ETs or UAPs.

Objective proof and subjective testimony regarding NHI communication

There appears to be two perspectives regarding human communication with the nonhuman intelligences (NHI) associated with UFO/UAPs. On the one hand, scientists and officials deny the significance of firsthand reports of NHI contact. On the other hand, thousands of people report direct interaction with NHI entities in and around their UFO/UAP craft (Hernadez et al., 2018). While most researchers do not deny the lived experience of NHI contact, some skeptically hypothesize that tales of NHI contact such as alien abduction are fantasies or dreams derived perhaps from repressed sexual trauma (Laycock, 2012). 

The skepticism regarding NHI contact stories mirrors the skepticism that some scientists express towards dream reports, who have gone so far as to question if dream reports are made up on the spot to satisfy researchers (Windt, 2013). Ethical guidelines for dreamwork recommend nondual perspectives that honor the dreamer as the final authority regarding the significance of the dream and also require the participation of the research in their own personal dreamwork (IASD, 2019). Mack (1994), in his inquiry into alien abduction cases, exemplifies the ethical principles of dreamwork through his acknowledgement of nondual epistemology and his inclusion of the experiencer’s interpretation of the contact event.

Encounters with NHIs and UAPs often involve dreamlike experiences, which may be why mainstream scientists and officials reject them as fantasies. Notable UAP researchers Vallee and Davis (2004) offered a six-layered model to understand and document UAP encounters. They described the second layer to be “anti-physical” because it involves impossible physics typically experienced only in REM dreams. The authors described the fifth layer as “psychic” because it involves telepathy and dreams. The similarity between dreams and NHI contact has been observed since the discovery of lucid dreaming in the 1980s (Gackenbach, 1989) and continues to be observed in current scholarship (Luke, 2022).

The epistemological and ontological problem of dreams may be contextualized by the shamanic principle and the distinction between monophasic and polyphasic cultures as put forward by Laughlin and Rock (2014). They defined the shamanic principle as an inherent human tendency to use dreams and altered states of consciousness to acquire knowledge and solve problems. They defined polyphasic cultures as those cultures who honor multiple phases of consciousness like altered states. They defined monophasic cultures as those who honor only the waking phase. The authors contextualized mainstream Western culture as a monophasic, which may be said of less than 10% of cultures (Laughlin & Rock, 2014).

Geometry bridges evidence and testimony

Our knowledge of NHI or UAP encounters involves both objective evidence and subjective testimony. The physical evidence may involve photographs, videos, or multiple witness testimony for UAP sightings or NHI beings. The National Reporting Center for UFOs (NUFORC) collected over 90,000 reports of UFO sightings mostly involving simple geometric shapes of the craft like oval, cylinder, triangle, etc. (Nguyen et al., 2018). Several alien abduction researchers have offered mysterious marks on the body, often associated with ET dreams or intuitions, as physical evidence of the encounters (Appelle, 1996; Laycock, 2012; Mack, 1994). 

Both UAP sightings and body marks typically may exhibit simple geometric characteristics that may be objectively described through analysis of the physical evidence, but also subjectively or qualitatively described through the narrative testimony and its interpretation from the experiencer. It appears that the connection between physical evidence and subjective experiences needs to be established in order for mainstream Western culture to consider the dreamlike narratives of NHI contact as epistemologically or ontologically significant. 

A consideration of the history of geometry may serve as a bridge between evidence and testimony because geometry is present within physical evidence like photographs or drawing but must be intuited within consciousness through subjective experience (Fujita, 2004). If we expand our view from exclusively objective or monophasic perspectives to nondual or polyphasic perspective, then we may reinterpret the Socratic myths and Jungian active imagination as historic precedents for communication with nonhuman intelligence through geometry.

Euclidean Constructive Geometry

While there are many different and specialized types of geometry, this inquiry focuses on Euclidean Constructive Geometry (ECG). ECG is based upon the work of Eucild, an ancient Greek mathematician (Beeson, 2012). Constructive geometry proves the existence and properties of mathematical objects through constructing the objects using predefined methods, which is the ruler and compass for Euclid (Beeson, 2012).

Interestingly, the ruler and compass construction of figures relates those figures to a fundamental or basic circle. Geometric reasoning is the process of relating a figure or construction back to the initial Euclidean postulates (Beeson, 2012), which begin with the archetypal dot, line, and circle. In other words, the process of geometric construction using the ruler and compass encompasses all geometric reasoning within a fundamental mandala. This mandala is the circle that you imagine as you relate the figure back to the postulates.

Constructive geometry is different from arithmetic or functional mathematics because it requires concentration and imagination skills, according to mathematical education researchers (Fujita et al., 2004). They defined geometric intuition as the ability to imagine and manipulate geometric figures in creative and integrative ways to solve problems or discover geometric truths. These skills of concentration, creativity, and imagination are also used in active imagination, which was a process that Jung developed to communicate with the archetypes, explore the unconscious, and relate with the self (Jung, 1997).

Geometry is a universal language used by SETI

Mathematics is often characterized as a universal language. Abraham (2017) identified many mathematicians like Pythagoras and Galileo who used geometry to mystically comprehend the hidden order of the universe. The Search for Extraterrestrial Intelligence (SETI) hypothesizes that communication with ETs will likely occur through mathematics (Atri et al., 2011). When Western scientists produced messages for ETs, they encoded meaning in pictograms and binary codes such in the engraved golden record within the Voyager space probe or the radio message sent to a distant star cluster from the Arecibo telescope (Atri et al., 2011). 

Lemarchand and Lomberg (2011) pointed out that SETI has focused primarily on physical-technical cognitive universals like binary codes in radio waves, but have neglected spiritual, ethical, and aesthetic aspects of cognition. They recommended expanding human cognitive maps from physical laws to include means of knowledge like beauty, which may be experienced as geometry. The researchers suggested that SETI has not found an ET signal because its search criteria are culturally limited, similar to their concerns around anthropocentrism. In other words, SETI might be looking in the wrong place because it assumes its worldview is universal, but is merely universal within mainstream culture.

There appears to be a difference between encoded messages using binary and ECG. The encoded messages require several processes of abstraction, similar to how arithmetic is the abstraction of a geometric number line. The famous Arecibo message, composed by Sagan and Drake, consisted of seven complex pictographic concepts, such as a human body, encoded in 1,679 binary digits arranged in a two dimensional grid (Atri et al., 2011). 

In contrast, geometric messaging requires no abstraction because the message is meaningful in itself, rather than as a structure for encoded meaning. Lemarchand and Lomberg (2011) suggest that the beautiful geometries of symmetry and the golden ratio may be characteristics of an ET signal, which may be directly perceived and understood through the universal aspects of geometry.

Geometry, unlike encoded messages, appears capable of directly communicating precise meaning through intuitive, emotional, and rational modes of cognition. Nathan et al. (2021) filmed math experts and non-experts as they solved geometric problems to support empirical claims that geometric reasoning is embodied, gestural, and intuitive. These claims may imply that geometry integrates the rationality of the conscious mind with the irrationality of the unconscious mind. 

Larson et al. (2011) conducted a study with undergraduates that demonstrated that simple geometric shapes, like downward or upward pointing triangles, implicitly convey affective meaning like positive, negative, good, or bad. Their study supported the notion that geometric communication does not require conscious discernment or judgment because the mind may engage in primal threat detection mechanisms. The fact that so many UFO reports may be categorized using simple geometric shapes (Nguyen et al., 2018) begs the question if emotive communication is already happening. Scientists now question the validity of research based on undergraduate subjects (Henrich et al., 2010), which begs the question if our initial assessment of UAP threat is derived from militaristic tendencies of mainstream culture or from the UAPs.

Monophasic culture is WEIRD

The notion that geometry is intuitive, embodied, and unconsciously communicative suggests that it is a universal mode of cognition for at least humanity. However, many notions that appear universal in the dominant culture may not be universal across all cultures. Western scientists are coming to the realization that studies from exclusively Western, Educated, Industrialized, Rich and Democratic (WEIRD) societies require cross-cultural replication to make claims about human nature (Henrich et al., 2010). The researchers found that the interpretation of an optical illusion based on simple geometry differed across cultures, which was previously assumed to be universal and demonstrates the need for cross-cultural studies before making assumptions about potential NHI geometry.

Henrich et al. (2010) used the clever acronym because mainstream culture does not represent the entire human population. For example, anthropologists have observed that around 90% of cultures are polyphasic, while mainstream or WEIRD cultures are monophasic (Laughlin & Rock, 2014). Most cultures honor the dreaming phase of consciousness in addition to the waking phase, which may be respectively understood through subjective and objective means of knowledge. Lemarchand and Lomberg (2011) suggested that SETI may not find ETs until it considers other worldviews because the WEIRD worldview limits our search to physical signals encoded using unknown technological techniques. 

The mystical history of mathematical creativity

It is unclear exactly when and why Western culture became WEIRD and monophasic, but it is clear that the history of Western mathematics and science once honored the reality of dreams and spirit, as evidenced through the work of Socrates and Descartes. Mathematics was once taught through geometric constructions like ECG, but now focuses on arithmetical, algebraic, and formulaic methods that are abstractions of geometry. At some point in history, it seems that Western culture forgot that math is beautiful and that dreams are meaningful. Reintegrating the polyphasic aspects of Western culture may expand our scientific vision enough to communicate with NHI cultures.

The history of mathematical creativity is interwoven with mysticism, as Abraham (2015) demonstrated through a series of case studies of creative and mystical mathematicians. He presented several types of mysticism across cultures and eras: angel or entity encounters, revelation through dreams, awareness of underlying cosmic order, and mystical cultural contexts. John Dee, the 16th century scholar who brought Euclid to England, engaged in the practice of angel communication, which may be understood as NHI telepathy in contemporary language. A similar example from the modern era and another culture is Ramanujan whose dream encounters with deities inspired mathematical creativity (Abraham, 2015). 

The tales of Socrates, as put forward by ancient Greek philosopher Plato, may serve as a primary precedent for the use of geometry as a bridge between the logical and mythological means of knowledge. Plato’s dialog Meno (ca. 380 B.C.E.) related the Socratic inquiry into geometry as a means of recollection from the world of forms, which may be understood as the realm of Jungian archetypes. His dialog Phaedo (ca. 360 B.C.E.) related Socrates’s own recollection of this realm through the mediation of a daemonic entity that he encountered through mystical practice. His example demonstrates that Western culture is originally polyphasic by honoring both myth and logic. 

The work of Jung may serve as an example and precedent for geometric communication with NHI. Jung worked the mandala as an archetype of self and as a vehicle for active imagination (Davis, 2016). He developed the process of active imagination as a way to explore the unconscious and collective psyche (Jung, 1997). Jung documented his active imagination sessions, which he referred to as dreams or fantasies, in a series of illustrated books such as The Red Book (Owens & Hoeller, 2014). These books documented his imaginal encounters with spiritual entities that provided instruction on the nature of infinity, which Harms (2011) connected with the history of mathematics and alchemy. Jung (1979) hypothesized that UFOs acted as mandalas for the modern era, suggesting that they were primarily archetypal events, in addition to possibly physical events. Jung’s imaginative work may serve as an example for communication with whatever intelligence stands behind the archetypal image of the UFO.

DMT, entities, and geometry invite ontological questions

It appears that the NHI contact phenomenon is similar to dreams, OBEs, and psychedelic states. The similarity has been noted from experts in various fields: Gackenbach (1989) observed the similarity from a dream studies perspective, Mack (1994) from an alien abduction perspective, Luke (2022) from a psychedelic research perspective, and Hernadez et al. (2018) from a postmaterialist academic perspective. All these perspectives honor the NHI contact experience like shamanic cultures honor the reality of dreams. Shamanic dreaming cultures honor the reality of dreams, but also have strong processes of discernment and interpretation when deriving knowledge from or taking action about the dreams (Laughlin & Rock, 2014).

Some psychedelic researchers hypothesize that dimethyltryptamine (DMT) is a psychedelic compound universally produced by all living beings and is activated during naturally occurring psychedelic states like birth, death, shamanic consciousness, dreams, and so on (Miller, 2013). The phenomenological similarity of these states implies the presence of DMT, but more research is needed for detailed claims regarding DMT and the pineal gland, which is hypothesized to be the place of DMT activation (Miller, 2013). In any case, the similarity of psychedelic states, dreams, and NHI contact is established and we may look at the DMT experience as relevant to both geometric intuition and NHI communication.

 Luke (2022), in their multidisciplinary review of DMT and anomalous experiences, observed that DMT may induce geometric visions such as perception of multiple dimensions and entity encounters such as aliens or spirits. The geometric visions typically involve more than three dimensions and have a reported feeling of reality, which inspired Luke to question their ontological status. Luke noted the similarity of visions across individuals, which suggests that they are more than mere hallucination. For example, a type of insectoid entity, a human sized praying mantis, has been documented independently in psychedelic and abduction literature for decades before the connection was observed (Luke, 2022).

Reinterpreting history of geometry as evidence for NHI communication

SETI theorists Ibison and Hathaway (2011) considered telepathy as a means for ET communication. They broadly suggested that quantum entanglement may enable faster-than-light two-way communication between humans and an ET culture. They focused on experiment design to authenticate ET sources of telepathy. In order to prove that the source of the signal is NHI, rather than mere imagination, the signal would need to provide new information to humanity. The authors suggested that the location of a crashed UFO, plans for new technology, or novel mathematical proofs would authenticate the source of telepathy as ET or NHI. It appears that the rich mystical history of mathematical creativity may be proof for humanity’s on-going communication with NHI.

This inquiry began with timely references to current events regarding geometric UAPs and ended with the recognition that NHI communication may be as timeless as imagination. The purpose of this paper is to explore the use of ECG in NHI communication. Worldviews or cognitive maps create biases regarding universal assumptions, for example, simple geometric illusions are interpreted differently across cultures (Henrich et al., 2010) . The distinction between monophasic and polyphasic cultures (Laughlin & Rock, 2014) might explain how some universal assumptions from mainstream or WEIRD cultures might limit potential signals of NHI communication (Lemarch & Lomberg., 2011). For example, traditional SETI focuses on radio communications that occur at the speed of light (Atri et al. 2011), but other researchers suggest that dream telepathy may occur faster than light and could be validated using Euclidean geometry (Ibison & Hathaway, 2011).

If the test for NHI contact through telepathy or dreams is to find a solution to mathematical problems, then the history of Western mathematics and science may be seen as proof for NHI contact. There is a well-documented history of creative solutions arising from dreams (Barrett, 1993), including dreams that involve gods, angels, and other celestial beings (Abraham, 2017). Given that geometry requires embodied intuition and imagination, it may no longer be surprising that NHIs communicate through intuition through dreams or active imagination. The shift from monophasic perspectives that reject dreams to polyphasic perspectives that honor dreams and intuitive cognition may be all that is required to reinterpret the history of Western science as an ongoing dialog between human and NHI cultures.. In this view, communication with NHI might be as simple as the appreciation of beauty, embodiment of feeling, and the exploration of imagination.

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