Mathditation Equation of Samadhi (4/5) (EN)


D. The Equation of Samādhi


Let me summarize the key points from Section C:

+ WM is the “home” of the restless mind monkeys, and it has a limited capacity.

+ When active attention and WM work together to process the meditation object, they begin to generate load, gradually occupying the space normally used by the mind monkeys.

+ Both attention and WM are influenced and attracted by a shared set of factors.


So, if we replace a static meditation object (e.g., the moon) with a dynamic one (e.g., a sequence of seven numbers), and place certain demands on this object (e.g., solving a problem), then attention becomes increasingly engaged—and anchored—to the object, without straying off to play with the monkeys[1]), The higher the attentional demand, the greater the WM load, shrinking the available space for the mind monkeys to dwell. When the WM reaches full capacity and can no longer process additional information[2], concentration becomes very stable—and a moment of stillness emerges. At that point, we drop the dynamic object and simply rest the mind in that stillness—for as long as possible.[3]

Hence, a more precise equation of samādhi is:


Focus = A*Dynamic_Subject + (1 – A)*Mind_Monkeys

 

where Dynamic_Subject refers to a neutral but dynamic meditation object—such as number sequences, letter-to-number conversions, character-color matching, etc.—structured with properties that strongly capture attention and generate increasing load on WM.[4][5]


What’s particularly fascinating about this samādhi equation is that it inherently embodies the Four Great Elements (Mahābhūta).


+ Earth (Pathavi). If earth is the element of substance and form, then in this samādhi equation, the numbers and letters serve as the earth element. They are the objects of meditation—the raw material of the session. Just as pathavi has the quality of occupying space, numbers and letters do too, especially as we arrange, enlarge, or manipulate them in calculation.

+ Water (Apo). If water is the element of cohesion, then the logical steps and arithmetic operations in the task represent apo—the principle of connectivity and flow. Each computational step relates to the next, creating a smooth, flexible structure depending on how we engage with it.

+ Fire (Tejo). Fire represents the element of energy. In the equation, tejo corresponds to attention. It determines the intensity, clarity, and effort applied to each number or step. Whether one element is sharper or more vivid than another depends on the energy of attention.

+ Wind (Vayo). Wind represents movement and life-force. In this context, vayo manifests as pīti (joy/bliss) and ekaggatā (one-pointedness). These are signs of concentration. Their appearance fluctuates based on the quality of mental stability. At the beginning, when focus is weak, these qualities don’t yet arise. But as concentration deepens, both joy and one-pointedness begin to emerge and strengthen.


But what about monks or lay practitioners who meditate using a fixed object or mantra, such as contemplating a red dot or reciting the Buddha’s name? I can’t speak for their experience. However, I would say that achieving samādhi through a static object requires strong willpower, unwavering faith, and genuine affection for the object. With daily perseverance (which will gradually improve mental stability), and/or by refining one’s external lifestyle (to reduce the influence of the mind monkeys), the path to samādhi is certainly still possible.[6] Of course, karma and merit (puñña) also play important roles—yet we don’t fully know what those forces are or how they operate. They’re not within our clear control. Alternatively, one could “modify” the static object slightly—for example, by focusing on its fine details while drawing it, or writing out the mantra on top of the red dot, one character at a time. But since this modification is relatively minimal, the risk remains that familiarity will dull attention, leading to resistance or boredom.


E. Continuous Thought Regulation


One’s ethics = A*Ethics + (1 – A)*habits

where:

+ Ethics (with a capital “E”) refers to the precepts (Sīla) upheld by monastics, such as honesty, filial piety, and gentle conduct. It also includes abstaining from killing and renouncing sensual craving.

+ ethics (lowercase) refers to moral discipline in daily lay life.

+ habits are unwholesome tendencies—accumulated from past lives—that obstruct our spiritual ascent.


Continuous Thought Regulation (KSTTLT) means going against ourselves—against deeply ingrained habits from previous lives. That’s why it is incredibly difficult. According to the equation above, how can we draw attention toward the precepts (Ethics)? After all, they’re not like meditation tasks we can swap out daily. When a stimulus arises, the instinctual, automatic response will come from habit. It jumps straight into WM and captures our attention instantly. Only when we have enough time to choose a response, we hopefully can redirect attention toward the precepts and consciously guide our behavior. But if life is already chaotic and WM is overwhelmed by bad habits, then there's no room left for attention to even see the precepts. The solution is to gradually reduce that chaos—proactively reorganize our life, create a more wholesome and uncluttered environment in WM—so attention has space to observe the precepts more easily. This method involves both blocking harmful stimuli and preparing wholesome responses ahead of time.[7]


End of Part 4/5


Notes:



[1] Question: Could we focus on the mind monkeys themselves to overload WM and thus enter samādhi? Answer: No. By nature, mind monkeys jump around erratically, with varying intensity and direction, making sustained attention impossible. Even if one could enter samādhi by focusing on a single wandering thought, the Law of Correspondence would merely align us with a realm matching that restlessness—namely, the kāma-loka (sensual realm).

[2] See page 8 of Fingelkurts and Fingelkurts (2014) - Attentional state_From automatic detection to willful focused concentration: “…individually, each neuronal assembly presents only a partial aspect of the whole object/scene/thought/concept, while the wholeness of ‘perceived’ or ‘imagined’ is brought into existence by joint (synchronized) operations of many functional and transient neuronal assemblies in the brain… synchronization of neuronal assemblies (located in different brain areas) that participate in the same functional act as a group – operational module (OM), e.g. executing a particular complex operation responsible for a subjective self-presentation of complex objects, scenes, concepts or thoughts. Any single OM thus signifies the binding of multiple sensory percepts or motor programs in a context-dependent way as a function of a saliency, priori knowledge and expectancies. It somehow ‘freezes’, and ‘classifies’ the ever changing and multiform stream of our cognition and conscious experiences.” See also Rabinovich et al (PLOS, 2007) - Neural dynamics of attentional cross-modality control - for a computational model of how attention quality can be modulated based on the number of objects and the intensity of their stimuli.

[3] For illustrations of real meditative sessions, and post-samādhi reflections, see Scientific Meditation and Quantum Mind.

[4] Attention can be mathematically modeled. For example, in Vaswani et al. (2017) – Attention is all you need, the core variables include: keys (information), queries (specific demands on that information), and values (their respective parameters). These input structures closely resemble the requirements of dynamic meditation objects as discussed here. See also: Luong et al. (2015) – Effective approaches to attention-based neural machine translation; Bahdanau et al. (2016) – Neural machine translation by jointly learning to align and translate; and https://lilianweng.github.io/lil-log/2018/06/24/attention-attention.html.

[5] According to Brother Alpha, the mandala method from Vajrayāna (Tantric Buddhism) can also induce samādhi, as the sheer number of details within a mandala can overload WM. However, a mandala is not a neutral object—it involves deities and symbols, which may lead to other consequences. Moreover, with prolonged exposure, one may become desensitized to a specific mandala. In contrast, mathematical puzzles and visual patterns (letters, numbers, multilingual symbols) are virtually limitless, so habituation is far less likely.

[6] I believe that during the time of the historical Buddha, people could enter samādhi more easily using static meditation objects because society was simpler and less saturated with information. This naturally reduced the activity of the mind monkeys. Furthermore, when practitioners spent time molding a lump of clay and observing it closely before meditation, they were already cultivating a level of attentiveness. That clay had genuine salience.

[7] See the article Wellbeing and Section I in Scientific Meditation.