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The Mathematics of Meditation

Sunday, February 26, 2017 18:24
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“Learn how to see. Realize that everything connects to everything else.” ~Leonardo Da Vinci

     Understanding geometry can help us understand the physical world around us. Understanding meditation can help us understand the intangible world within us. The benefits of understanding the outside world are stupendous, and the benefits of understanding the inside world are limitless. 


         The Sacred Geometry

           of Asana, Mantra,

           Yantra and Tantra

A mandala is a visual symbol often utilized in meditation practices and teachings. The mandala symbol itself is a geometric construction of geometric points, lines, planes and solids which symbolizes our universe. These geometric symbols can be used as a visual meditation tool, called a yantra. Other designs can similarly be used as meditation tools, but may not be mandalas by definition.

    Mandalas and all other yantras work as visual meditation points of concentration. Pictured (top) is the sri yantra: sri meaning ‘king’ or ‘most important’. Ancient yogis of India and Tibet considered it to be the most powerful of all geometric symbols, representing the geometric structure of the sound of creation — the Om.
    Conversely, a mantra is the audio version of the mandala; an aural meditation tool. Whether the sound of the mantra is a single syllable tone, such as the Om, or a series of metaphysical musings, such as the ancient Gayatri Mantra, mantras are wavy linear expressions of universal connection, voiced as concentrated sound vibrations.
    Meditation tools also extend far beyond the visual and aural; the terms asana and mudra both refer to physical positionings used as meditation tools. An asana is a body posture (such as those used in the practice of yoga) and a mudra is a hand gesture or posture. Asanas and mudras enable our own bodies to become a geometric representation of meditation. The postures transform the physical self into one’s own geometric figure or plane, both among the space and sensitive to the space of self and its surroundings.
    Bringing these concepts and tools together is tantra. Tantra is integration; the integration of yantra (visual), mantra (sound) and mudra (positioning), each of which is an important, intertwined aspect of yoga, and life itself. Essentially tantra is the spiritual understanding of the relationship and connections between individual and universal energies. An ancient spiritual philosophy preceding both Buddhism and Hinduism, tantra signifies confluence and integration — a fusion — and refers to the unification or weaving together of principles and practices, instructions and individual actions. It unifies the macrocosm with the microcosm, the universal and the individual, the feminine and the masculine, the yin and the yang. It also refers to integrative knowledge and its continuation and refinement, through the interaction of teacher and student, and the acceptance, integration and transmutation of knowledge between individuals — like the string of life.
    Etymologically, the word tantra is Sanskrit for loom, the device that weaves together string into cloth. It is an ancient word with many properties and has been variously used to describe the knots of strings weaved together in a rug, the cord on which sacred mala beads are strung, (mala beads are Tibetan prayer necklaces of 108 beads, which are used to assist with the mental or vocal repetition of a mantra 108 times — a number of great spiritual significance) and more broadly, to describe practices that unify the individual with the universal. Although the word tantra is often used in reference to the union of sacred lovemaking, the concept is not necessarily limited to the act of lovemaking. In fact, humanity itself is a tantra; a fused weaving knot or many strings, of many instructions and many individuals.
Unifying meditative principles and practices potentiates the power of tantra, yantra, mantra and asana. This is further enhanced by the incorporation of Yin Yang tantra. The combination of the Yin and Yang potentials and energies within leads to all sorts of aspects of personal development. This can be energetically understood in the idea that there are only two types of energies, straight and circular — straight for Yang potentials and circular for Yin potentials. It can be understood on a tangible level that rest and work are both required. When straight and circular energies combine, a spiral results. A spiral is one of, if not the, highest expressions of life energy.

    There is not necessarily the need for a specific yantra, or specific mantra, or specific asana in the practice of meditation, however each are tools that can be used and considered, and are most powerful when practiced in a unified tantric manner, or tantric mind state. A tantric mind state recognizes unity expansion and aims toward it, rather than cultivating a mind state of separation. Essentially, using yantras, mantras and asanas as meditation tools helps to establish your sacred space and to unite with entirety in tantric balance.

    No matter how one approaches meditation, the unifying tantra of meditation principles and practices bring about the unified expansion from the central source, as symbolized by the mandala yantra (the visual). No matter our level of refinement of posture, we are always in an asana, whether or not we also utilize mantra or yantra. For most of us, we still see and hear, and those who cannot can still concentrate and connect. And no matter the mantra, yantra or asana we utilize, it is the principles and energy behind (and pertaining to) their symbolism that contains the real spiritual power — the highest potential for tantric connection, which is inherently within us all.

Seed of Buddha Meditation 

    One of my favorite meditations is extracted from Buddhist lessons, and relates to the four dimensions of geometry. Known as “the Seed of Buddha Meditation”, this practice is one of the most powerful meditations I have learned. It is believed that the Buddha himself practiced and taught this meditation, just as I learned it from a Tibetan Buddhist monk from Nepal. It is direct and simple, but can open us up to receive profound and infinitely complex spiritual lessons.

    The profundity of each of the ideas in this meditation cannot be understated. Each of the concepts has been elaborated on for centuries since the time of Buddha, and so the presentation here is, of course, a simplification of the ideas and processes that might be endlessly explored and refined as part of our own personal inward exploration.
    The following provides the steps for you to perform this powerful meditation practice, but as always, it is the energy we bring to these principles and symbols that contains the real spiritual power of this meditation — the highest potential for universal connection, which is inherently within us all.

    Like many meditations, this practice is derived from important Buddhist concepts and teachings, The Four Thoughts and The Four Immeasurables. So, there are lessons to be gained for both the secular and meditative practitioners, from beginners to the advanced.
The rhythm of this 3-part meditation moves from mindfulness of a particular idea or thought, to mindfulness of no idea — where as much as possible, we think on nothingness — to mindfulness of the next idea, and so on. These periods of nothingness give us a chance to relax, to break from processing each thought or concept this meditation presents — which can all be quite intense — before moving on. The meditation then concludes with the Buddha Breath exercise.

    Each step of the process can take as long as you like, and the timing may differ each time you practice it. Meditate on each idea as deeply as you feel appropriate, considering your own time constraints, circumstances, realizations and states of mind etc.
The Seed of Buddha MeditationTo begin, sit in a comfortable cross-legged position (on a meditation pillow, if you prefer.) Sit for a time to simply settle into absorption and relaxation, focusing on the breath.

    The first part of the meditation consists of contemplating The Four Thoughts of Buddhist philosophy, which turn the mind toward Dharma; the precious human body, impermanence, karma and samsara. The second part consists of contemplating The Four Immeasurables. Contemplate on each of the following ideas using personal experiences and/or universal understandings as your guide.

The Four Thoughts

Precious Human body
The precious human body idea essentially comes from understanding that every being is precious, and spontaneous Buddhahood could happen at any time, yet we have a precious human body that is particularly capable of gaining enlightenment, and even assisting others in the process. Contemplate the preciousness of your human body, and others’, then allow yourself to come to the point of gentle concentration on your own relaxation. Breathe in a relaxed manner. All beings are capable of attaining enlightenment, however only humans are capable of attaining enlightenment in this life. The practice of compassion and helpfulness among the collective are examples of quality being. Meditate on how lucky we are to be humans, capable of enlightenment and instigation of enlightenment.

Everything is impermanent; ourselves and the condition of our world. Allow yourself to contemplate the changing, dynamic nature of existence at all levels. Then pause again, gently becoming mindful of your own relaxation and breath, taking whatever time you need to clear your mind.

Contemplate the workings of the universal law of Karma; that of cause and effect. In the Buddhist tradition, karma refers to the cycle of actions driven by intention leading to future consequences, and therefore, future actions and intentions. Reflect on personal experiences and/or universal understandings of this concept, then, when you are ready, allow yourself to become mindful of your own relaxation and breath.

Samsara refers to the plane of existence and suffering; the endless cycle of birth, existence and death we are all in, perpetuated by desire, ignorance (relating to concepts of reality) and their resulting karma. It is the opposite is nirvana; the nothingness, the bliss that just IS, and the essence beyond birth, death and duality. Contemplate this concept, then again, when you are ready, allow your mind to return to your breath.
It is interesting to note, The Four Thoughts (not so coincidentally) relate to the four dimensions of geometry; the single point symbolizes the individual precious human body, the line symbolizes impermanence (ie. through movement), karma is illustrated by the circular exchange of energy, and Samsara relates to volume (ie. 3-dimensional shape).

    The Four ImmeasurablesThe second part of this meditation uses the same pattern of mindful focus followed by periods of relaxation, this time, contemplating The Four Immeasurables of Buddhist philosophy.
Buddha is known to have pointed to 4 aspects or stages of love, known as The Four Immeasurables; the love for self, love for others, love for the happiness of others, and love for all beings in equanimity. It is commonly understood that each stage requires the preceding stage of love to be achieved. However, for the purposes of this meditation, we will begin by focusing outwardly — on our love for all beings in equanimity — and end by focusing inwardly — on our love for self.

    So, as with The Four Thoughts, using personal experiences and/or universal understandings as your guide, contemplate on each of The Four Immeasurables, returning your awareness to your breath and your relaxation between each concept.

Love for all beings in equanimity.
Love for the happiness of others.
Love for others.
Love for self.

    Like The Four Thoughts, The Four Immeasurables are also symbolic of the four dimensions of geometry. Love for the self is symbolized by individual point, love for others is symbolized by the linear connection, love for the happiness of others is (like karma) circular and all-connecting, and love for all beings in equanimity is voluminous and all-inclusive.

Buddha Breath
The third and final part of the meditation is Buddha Breath.
On every inhale, imagine you are removing the ignorance and suffering of others (other people specifically, and those generally locally and globally.)
On every exhale, imagine you are sending them compassion and happiness. Imagine you are a conduit of Buddha consciousness, or supreme consciousness. Imagine that you are a vehicle for transmuting suffering and ignorance into happiness and compassion, which happens through you, instigated by you, connecting above and below.
On every exhale, imagine lotus flowers from Buddha consciousness being transported through you, and on every inhale, imagine the fiery pain and suffering of Samsara being drawn into a fiery lotus flower that remains in front of you, burning up the ignorance and suffering that is drawn into it.
Finish the meditation by keeping a lotus flower for yourself, perhaps placing on the crown of your head, and imagining light shining through you and onto you, cleansing you of any leftover negativity.

The Geometry of Energy: How to Meditate’ explores meditation and meditative energies through the sacred dimensions of geometry. Simple and profound, it is an empowering four-step meditation designed to lead to individuation, self-development, and an enhanced understanding of energy and vibration.
Useful to meditation newcomers and longtime practitioners alike, ‘The Geometry of Energy’ provides insights into a variety of meditative processes for psychological and spiritual cleansing and enhancement.
‘The Geometry Of Energy: How To Meditate’ is available here on Amazon.

About the author:
Activist, author and Tai Chi teacher Ethan Indigo Smith was born on a farm in Maine and lived in Manhattan for a number of years before migrating west to Mendocino, California. Guided by a keen sense of integrity and humanity, Ethan’s work is both deeply connected and extremely insightful, blending philosophy, politics, activism, spirituality, meditation and a unique sense of humor.

 For more, visit Ethan on Facebook and check out Ethan’s author page on Amazon.



Meditation And Geometry For The Youth is an introduction to geometry and meditation for young people, and for the youthful. The book is designed to teach young people and everyone for that matter about the fundamentals of meditation and of geometry.  

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