The Concept of Infinity – Explained by Bhaskaracharya!
by Vishal Gaikwad
What is Infinity (अनंत)?
Infinity, as we hear this word our brain instantaneously thinks of
something very big and enormous which we can’t visualize. And indeed, infinity
is limitless (अनंत). Mathematically, it is represented by the symbol ‘ꝏ’,
sometimes called as a lemniscate.
If you open Mathematical Books of today, you will find the idea of infinity
mentioned in somewhat higher level courses. You won’t, however, find either
the infinite or the infinitesimal in an elementary book on algebra, let
alone arithmetic! The only thing you may find in an algebra book is a very
stern warning about not ever dividing by zero! (Because if you divide any
number by zero, you get infinity).
On the other hand, in the algebra books of ancient times in India, we find
both the infinite and the infinitesimal treated routinely. One such example is
Bhaskaracharya Bijaganita (his book on Algebra) and Lilavati (his book on
Arithmetic). Bhaskaracharya was a twelfth-century Indian mathematician and
astronomer. He was born in Bijapur in Karnataka.
*While Newton and Leibniz have been credited with differential and integral
calculus, there is strong evidence to suggest that Bhaskaracharya was a
pioneer in some of the principles of differential calculus.*
Definition of Inifinity – Bhaskaracharya’s Bijaganita 2.18
In Bijaganita, we find the following shlok
वधादौ वियत् खस्य खं खेन घाते खहारो भवेत् खेन भक्तश्च राशिः॥
vadhādau viyat *khasya khaṃ khena* ghāte khahāro bhavet khena bhaktaśca
rāśiḥ॥
*A zero results when multiplied by zero, a “khahara’’ (zero-divided, or
infinity) results when a number is divided by zero.*
Infinity further explained – Bhaskaracharya’s Bijaganita 2.20
For *Khahara,* he explicitly adds a colorful description
अस्मिन् विकारः खहरे न
राशावपि प्रविष्टेष्वपि निःसृतेषु।
बहुष्वपि स्यात् लय-सृष्टिकाले
अनन्ते अच्युतेभूतगणेषु यद्वत्॥
asmin vikāraḥ *khahare *na
rāśāvapi praviṣṭeṣvapi niḥsṛteṣu
bahuṣvapi syāt laya – sṛṣṭikāle
anante acyute bhūtagaṇeṣu yadvat
There is no change in the Khahara (infinity) by adding or subtracting,
just like infinite immutable (Brahma or Viṣnu)
which does not have any effect by the living beings entering or leaving it
at the time of dissolution or creation of the world.
Mr. Avinash Sathaye, has explained this very well in his essay. The
mathematical explanation follows as, we write ꝏ to denote the “khahara”
i.e. 1/0.
The additional facts about “khahara” can be presented as,
X* ꝏ + Y = X* ꝏ, for any number X and Y. It states that when a “khahara” is
added to an ordinary number, then only the “khahara” survives. This is the
same as infinity just represented by another name.
In ancient Indian Mathematics, we find Jain texts discussing various such
concepts of infinities. These texts are mainly religious or philosophical,
but often carry a healthy amount of serious mathematics. They seem to
introduce formal concepts of finite or enumerable, innumerable (very large
but still finite) and infinite. They even classify multidimensional
concepts for infinity.
In Lilavati (Shlok 48), Bhaskaracharya gives more instruction about
multiplying by zero
शुन्ये गुणके जाते खं हारश्चेत् पुनस्तदा राशिः।
अविकृत एव ज्ञेयस्तथैव खेनोनितश्च युतः॥
śunye guṇake jāte khaṃ hāraścet punastadā rāśiḥ।
avikṛta eva jñeyastathaiva khenonitaśca yutaḥ॥
If a zero becomes a multiplier and a number turns into zero, it should
(really) be considered as unchanged if it is again divided by zero!
Similarly, if a zero is subtracted off and added in (a number is considered
unchanged.)
Mention of Inifinity in Ishavasya Upanishad!
The invocatory verse of Ishavasya Upanishad which is part of Shukla Yajur
Veda and it dates way back than Bhaskaracharya also talks about a rather
precise concept of infinity. It goes something like this,
IshaVasya Upanishad Invocatory verse
ॐ पूर्णमदः पूर्णमिदं पूर्णात् पूर्णमुदच्यते ।
पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥
Om pūrṇamadaḥ pūrṇamidaṃ pūrṇāt pūrṇamudacyate
pūrṇasya pūrṇamādāya pūrṇamevāvaśiṣyate
Om, That is Full, This also is Full, from this Fullness comes that Fullness,
Taking Fullness from Fullness, Fullness Indeed Remains.
Infinity is a central concept as far as advanced sciences are concerned,
such a great advancement at such complex subject shows how rich and
prosperous was our culture. We hope you have understood infinity from both
the modern as well as ancient perspective. Please let us know your thoughts
on this and if anything, you’d like to add.
KR Thus, INFINITY IS UNKNOWN AND EQUATED TO THE BRAHMAM. INFINITY IS
PERFECT AND WHOLESOME. INFINITY ARISE OUT OF THE SHUNYA WHICH IS PRAKRITHI.
NATURE IS PART OF THE SHUNYA AS BLOOMS AND DECAYS NATURALLY OR BY
UNCONTROLLED ATTACKS. AND INCLUDED IN A BRAHMAM.
The "real truth" of the Higgs boson is that it is a fundamental
particle, an excitation of the universal Higgs field, which gives other
elementary particles mass through their interaction with the field. While
it was theorized in 1964, its discovery in 2012 at CERN was confirmed not
by directly "seeing" it, but by detecting its decay products at the Large
Hadron Collider (LHC). Particles that don't interact with the field, like
photons, remain massless.
The Higgs field and particle mass
The field came first: The Higgs field was proposed to fill the entire
universe. Particles gain mass by interacting: As fundamental particles
move through this field, they interact with it. This interaction is what
gives them mass.
Stronger interaction = more mass: The more a particle interacts with the
Higgs field, the more mass it has. For example, electrons and quarks
interact with the field and have mass, while photons do not and are
massless. The Higgs boson is a wave in the field: The Higgs boson is the
particle associated with the Higgs field, much like a ripple is a wave in
water. Its discovery was crucial evidence for the existence of the field
itself.
Indirect evidence: The Higgs boson is incredibly unstable, decaying almost
instantly after it's created in high-energy collisions at the LHC.
Scientists *don't "see"* the Higgs boson directly but infer its existence
by detecting the specific particles it decays into and confirming the mass,
spin, and charge add up correctly.After many high-energy collisions, a
statistically significant *"bump" appeared in the data at the predicted
mass*, confirming the particle's existence with 5-sigma significance.
While confirming the Standard Model of particle physics, *some
recent data has hinted at complexities, such as discrepancies in its decay
patterns, that suggest the model might be incomplete and could point to new
physics like supersymmetry.*
* Hence Nobel was won for the effort but the theory of virtual see
or perception still remain vague indicating infinity @ Brahmam is
untraceable. Prakriti is within the brahmam hence in infinity but as human
and specie of the matter, had to be destroyed and reclaimed by rotations.
Yet nature is peace*
*K Rajaram IRS 131125*
On Wed, 12 Nov 2025 at 21:27, Markendeya Yeddanapudi <
[email protected]> wrote:
>
>
> --
> *Mar*Experiencing Infinity
>
>
>
> Close your eyes. Then you can see only the nothing or the infinity. The
> infinity which you experience called darkness, does not have a beginning or
> end. You experience the no beginning and no end situation. You are actually
> coming out of the illusion, the VIBGYOR illusion, the jail, the restrictive
> 00.0035% of the electromagnetic spectrum called the visible spectrum. By
> just closing your eyes and making your mind blank, you cannot see, I, You,
> We, He, She, They and It.
>
> This VIBGYOR or Rainbow governed seeing is restricted only to the Earth
> that too, to the surface of the lithosphere, or simply to the surface of
> land and sea, just 00.04% of the mass of earth. Outside that small area,
> you cannot see with your eyes.
>
> You enter the arena of feeling, the arena of infinity when you close your
> eyes. If you close your eyes for long periods and also make your mind blank
> or get freedom from the memory of things you saw when your eyes did not go,
> your capacity to feel and enter the vast cosmos, increases gradually. After
> the experience of infinity as life, you will not want your eyes. After ten
> or fifteen years of life without eyes and also experiencing the blank mind,
> you get accustomed to the infinity, to the Universe, where feeling and not
> seeing becomes living. It is Yoga as living with the eye of Siva.
>
> If new eyes are then fixed to that person, the seeing eyes will suffocate
> him, the seeing with the eyes will make him feel sick and to protect
> himself from the eye seeing he will spend his life by closing the eyes as
> the seeing eyes blocks his experiencing by feeling. His capacity to feel
> gradually increases and then expands into the infinity.
>
> You team up with the Universe, you become a part of the universe, like the
> atom of the quantum world, and you create fissions and fusions of
> perception. The vacuum of the Universe is the arena of creation via the
> notice of consciousness, the fundamental fact or paradigm of Quantum
> Physics.
>
> The costly attempts at the TOE, the Strings Theory, the various approaches
> under the heading of the M Theory (the branches of the Strings Theory), the
> Loops Quantum Gravity Theory, the explanation about the Universe as
> Hologram, can be substituted by merely closing your eyes and making the
> mind blank.
>
> The problem is, thanks to the infatuation for machines, you do not expect
> nature to help and team up with you, and you do not trust yourself. And the
> naked and humble Sadhu, who lives in raw nature, is not a cinematic five
> star person. And the worst crime of economics is, he does not need any
> monetary investment, certainly not miles and miles long CERN labs or the
> Fermi Lab machines.
>
> Ultimately the miles and miles long machine of the CERN, as per the
> defined computer programme located the Higgs Boson to complete the
> mathematics needed by the Standard model, and Higgs got Nobel.
>
> The discovery by that big lab is noted and advertised, but has that
> discovery been exhaled, as smell message that creates the waves of
> enlightenment which exhalation of perception creates in nature, when there
> is no mechanical contamination and destruction of nature?
>
> The atheistic fashion created by the merchants of machines, to scoff at
> the Spiritual approach may create comforting smirks, but that discovery by
> that machine is simply not understood and cannot be understood by most
> humans. There is no guarantee that another costly machine will not find
> that the Higgs Boson now claimed as found false.
>
> On the other hand when an organism discovers via nature’s revelation,
> every other organism inhales the revelation, creating cascades of undying
> revelations. For that one needs to close one’s eyes and make the mind blank
> in free nature, nature which is not terrorized by the development maniacs.
>
> Let us hope that there is at least one University that takes to the
> Holistic Approach, which needs free nature, free nature under the terms of
> nature, where there is no human tampering.
>
> YM Sarma
>
> Chat gpt
>
> This is a fascinating and deeply philosophical essay. Here are my comments
> and views on *“Experiencing Infinity”* by YM Sarma — both from a
> *literary* and a *conceptual* perspective:
> ------------------------------
>
> *🌌 Overall Impression*
>
> The essay is a meditation on perception, consciousness, and the
> relationship between human cognition and the cosmos. It explores the idea
> that true understanding of the universe does not come from external
> observation (through machines, instruments, or even the physical eyes), but
> from *inner experience* — achieved through introspection, sensory
> withdrawal, and unity with nature. It blends spiritual philosophy
> (particularly from Hindu or yogic traditions) with references to modern
> physics and cosmology.
> ------------------------------
>
> *🧠 Conceptual Analysis*
>
> 1. *The Central Metaphor — “Closing the Eyes to See Infinity”*
> - The essay’s main metaphor — that closing the eyes leads to the
> experience of infinity — is powerful. It suggests that *seeing* is
> limiting, while *feeling* and *being* open a deeper dimension of
> awareness.
> - This idea resonates with mystical traditions worldwide — Advaita
> Vedanta, Zen Buddhism, and even certain interpretations of quantum
> mysticism — where the external world is seen as *Maya* (illusion)
> and reality is accessible only through inner stillness.
> 2. *Critique of Modern Science*
> - The author contrasts the spiritual method of “direct inner
> experience” with the technological and materialistic approach of modern
> physics (CERN, FermiLab, Higgs Boson, String Theory, etc.).
> - While this criticism is rhetorically striking, it oversimplifies
> the scientific enterprise. Science and spirituality seek understanding
> through different methods — one empirical, one experiential. The essay
> frames them as opposites, but in truth, they can coexist and even enrich
> one another.
> 3. *The “Sadhu vs. Scientist” Dichotomy*
> - The Sadhu symbolizes natural, intuitive, self-sufficient wisdom;
> the scientist represents mechanized, institutionalized knowledge.
> - The essay’s tone here is passionate and idealistic — though
> arguably romanticized. The Sadhu’s “zero cost enlightenment” is
> contrasted
> with “mile-long laboratories,” which is provocative, but not necessarily
> fair to the collective intellectual progress science has achieved.
> 4. *Quantum Consciousness and Mysticism*
> - The author uses terms like “quantum world,” “vacuum,” “fission
> and fusion of perception,” and “consciousness as the fundamental
> paradigm.”
> - These are poetically effective but scientifically imprecise. They
> serve a *symbolic* rather than *literal* purpose — expressing the
> unity of mind and matter. If read metaphorically, this is evocative; if
> read scientifically, it stretches credibility.
>
> ------------------------------
>
> *✍**️ Style and Expression*
>
> - *Strengths:*
> - The essay’s *tone is meditative and lyrical*, evoking a sense of
> cosmic wonder.
> - Phrases like “the arena of infinity,” “eye of Siva,” and “the
> merchants of machines” have strong emotional and visual resonance.
> - It challenges readers to reconsider what it means to *know* or
> *see.*
> - *Areas for Improvement:*
> - *Structure and Flow:* Some paragraphs could be more tightly
> organized. The transitions between inner experience, science, and social
> critique feel abrupt at times.
> - *Precision:* Scientific references (visible spectrum percentages,
> Higgs Boson, M-theory) could be either corrected or clearly reframed as
> metaphors rather than factual claims.
> - *Tone:* The essay’s critique of science sometimes borders on
> polemic. A more balanced tone would strengthen its credibility while
> preserving its philosophical depth.
>
> ------------------------------
>
> *🌱 Philosophical Depth*
>
> The essay’s heart lies in an ancient insight: that the universe is not
> “out there” but “in here.” By silencing sensory noise, one can experience a
> boundless consciousness that transcends individuality — what the essay
> calls “feeling as living.”
> This vision of unity with the cosmos is beautiful and profound. It invites
> humility, ecological awareness, and reverence for existence — values that
> modern civilization urgently needs.
> ------------------------------
>
> *🧭 Final Thoughts*
>
> *“Experiencing Infinity”* is a poetic, mystical, and challenging essay
> that bridges spirituality and science. It should not be read as a
> scientific argument but as a philosophical reflection — a call to
> rediscover direct, unmediated awareness.
>
> It succeeds as a *spiritual manifesto* and a *critique of technological
> arrogance*, though it could be refined by:
>
> - Clarifying metaphor vs. fact,
> - Tightening coherence,
> - And acknowledging that scientific and spiritual insights can be
> complementary paths to truth.
>
> ------------------------------
>
> Would you like me to suggest a *revised version* of the essay that keeps
> its essence but makes it more polished and balanced in tone?
>
>
>
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