माया अविद्यायाः (māyā avidyāyāḥ - paradox of nescience)

 A classic illustration of the माया अविद्यायाः (māyā avidyāyāḥ - paradox of nescience). There is विद्या (vidyā – wisdom) inherently encapsulated in अविद्या (avidyā – nescience) which is nothing but [अ ]विद्या  ([a]vidyā – [ne]science) and yet to be realised, just as परिपूर्णता (paripūrṇatā - perfection) is built in अपरिपूर्णता (aparipūrṇatā - imperfection) - which is nothing but [अ ]परिपूर्णता ([a]paripūrṇatā – [im]perfection). Hats off to mother nature! Swami Vivekananda declares

Original

Education is the manifestation of the perfection already in man. Religion is the manifestation of the Divinity already in man.

English Reference: The Complete Works of Swami Vivekananda (Volume 4)

In fact, modern neuroscience very categorically states that “Every cell in your body knows how to replicate DNA, yet you still have to spend hours studying to understand why”.  In spiritual terms, this translates as ब्रह्म विद्या (brahmzvidyā – divine wisdom) is inherently eternal, omnipresent and can be realized as अपरोक्षज्ञान (aparokṣajñāna - immediate wisdom) which is निष्काल (niṣkāla – timeless/tenseless) while it's discovery is through the पञ्चविधकोशाः परोक्षज्ञानस्य (pañcavidhakośāḥ parokṣajñānasya – fivefold sheaths of mediated knowledge) experienced as नियोज्य देशकालनिमित्तस्य (niyojya deśakālanimittasya – function of space-time-causality). 

Take another example from the domain of mathematics, the fact that 1+1=2 is an obviously self-intuitive no-brainer to all of us, even to a kindergarten student. Yet, proving it mathematically is very complex and in fact needed very complex non-intuitive mathematical proof running into pages even for subject matter experts like Bertrand Russell and Alfred Whitehead in their magnum opus “Principia Mathematica”.

Let’s now take a different kind of mathematical example, explained in this video

 and

and

    This is a very beautifully explaining video on the concept of dividing any number by zero. Philosophically, in my humble opinion, the video echoes the metaphysical doctrine of अनिर्वचनीय माया खयाति (anirvacanīya māyā khyāti - undefinability measurement constraint) as to how the original number शून्य अव्यकत (śūnya avyakta - unmanifest / noumenal vacuum) divides itself to the अनेकता अशानि (aneka aśāni - phenomenal many).

    Verbally putting expressing it “किञ्चित् सप्तिक सङ्ग्ख्या भाहित शून्य भवति अनन्त” (kiñcit saptika saṅgkhyā bhāhita śūnya bhavati ananta – any finite number divided by zero equals infinity).

किञ्चित् सप्तिक (saptika saṅgkhyā – positive number) ÷  शून्य (śūnya) = अनन्त (ananta - infinity)

(n) ÷ 0 = ∞

Metaphysically, this can be stated as शकलरूप भाहित निष्कलरूप भवति अनिर्वचनीयानन्त  (śakalarūpa bhāhita niṣkalarūpa bhavati anirvacanīyānanta   - partial-form divided by partlessform equals indeterminate infinity). In other words, the mystery of how multiple divisions emerged from undivided, is an indeterminable paradox.  

Original

I came into the unknown and stayed there unknowing rising beyond all science. I did not know the door but when I found the way, unknowing where I was, I learned enormous things, but what I felt I cannot say, for I remained unknowing, rising beyond all science. It was the perfect realm of holiness and peace. In deepest solitude I found the narrow way: a secret giving such release that I was stunned and stammering, rising beyond all science. I was so far inside, so dazed and far away my senses were released from feelings of my own. My mind had found a surer way: a knowledge of unknowing, rising beyond all science. And he who does arrive collapses as in sleep, for all he knew before now seems a lowly thing, and so his knowledge grows so deep that he remains unknowing, rising beyond all science. The higher he ascends the darker is the wood; it is the shadowy cloud that clarified the night, and so the one who understood remains always unknowing, rising beyond all science. This knowledge by unknowing is such a soaring force that scholars argue long but never leave the ground. Their knowledge always fails the source: to understand unknowing, rising beyond all science. This knowledge is supreme crossing a blazing height; though formal reason tries it crumbles in the dark, but one who would control the night by knowledge of unknowing will rise beyond all science. And if you wish to hear: the highest science leads to an ecstatic feeling of the most holy Being; and from his mercy comes his deed: to let us stay unknowing, rising beyond all science.

English Reference: St. John of the Cross

Let us now take the case of multiplying by Zero

    Mathematical jokes apart,  as food for thought, if we extend this thought provoking  message to deeper philosophical interpretation, IMHO the message reflects the  शून्यवाद माध्यमकदर्शने महायानबौद्धधर्मस्य (śūnyavāda mādhyamakadarśane mahāyānabauddhadharmasya - emptiness doctrine in the centring philosophy of Greater-Vehicle Buddhism), according to which the बहुविधभेधाः सम्वृतिसत्यस्य (bahuvidhabhedhāḥ samvṛtisatyasya - multi-fold differences of the concealed realm) collapses into the महानिर्वाण शून्यकैवल्यस्य (mahānirvāṇa śūnyakaivalyasya -  grand deliverance of vacuum  singularity). Interestingly, सम्वृतिसत्यस्य (samvṛtisatya - concealed realm) and शून्यकैवल्य (śūnyakaivalya - vacuum  singularity) closely (but not exactly) corresponds to व्यावहारिकसत्य (vyāvahārikasatya - phenomenal / conventional realm) and परब्रह्मकैवल्य (parabrahmakaivalya - supreme divine  singularity) respectively according to the अध्यास्यवाद  उत्तरमीमाम्सकेवलाद्वैतवेदान्तदर्शने हिन्दुधर्मस्य (adhyāsyavāda uttaramīmāmsakevalādvaitavedāntadarśane hindudharmasya- absolute non-dualistic posterior inquiry philosophy of Hinduism).  In modern physics, this can be equated to the wave-function collapse of the expanding महाब्रह्माण्ड (mahābrahmāṇḍa - cosmic megaverse) back into the महासङ्कुचन कैवल्यम् (mahāsaṅkucana kaivalyam - big-crunch singularity).  Again, to quote Swami Vivekananda, 

Original

My idea is that what you call a Personal God is the same as the Impersonal Being, a Personal and Impersonal God at the same time. We are personalised impersonal beings. If you use the word in the absolute sense, we are impersonal; but if you use it in a relative meaning, we are personal. Each one of you is a universal being, each one is omnipresent. It may seem staggering at first, but I am as sure of this as that I stand before you. How can the spirit help being omnipresent? It has neither length, nor breadth, nor thickness, nor any material attribute whatsoever; and if we are all spirits we cannot be limited by space. Space only limits space, matter matter. If we were limited to this body we would be a material something. Body and soul and everything would be material, and such words as "living in the body", "embodying the soul" would be only words used for convenience; beyond that they would have no meaning. Many of you remember the definition I gave of the soul; that each soul is a circle whose centre is in one point and circumference nowhere. The centre is where the body is, and the activity is manifested there. You are omnipresent; only you have the consciousness of being concentrated in one point. That point has taken up particles of matter, and formed them into a machine to express itself. That through which it expresses itself is called the body. So you are everywhere; when one body or machine fails, you, the centre, move on and take up other particles of matter, finer or grosser, and work through that. This is man. And what is God? God is a circle with its circumference nowhere and centre everywhere. Every point in that circle is living, conscious, active, and equally working; with us limited souls, only one point is conscious, and that point moves forward and backward. As the body has a very infinitesimal existence in comparison with that of the universe, so the whole universe, in comparison with God, is nothing. When we talk of God speaking, we say He speaks through His universe; and when we speak of Him beyond all limitations of time and space, we say He is an Impersonal Being. Yet He is the same Being.

English Reference: The Complete Works of Swami Vivekananda (Volume 8)

    While mathematically, this is not an accurate explanation  but in a lighter vein, if we take an example of if 1000 people multiply themselves zero times (i.e.) do not multiply themselves, then they remain as 1000 and do not disappear...!

    Let us go back to our example, I am  physically there, for sure, but i do not multiply  myself or in other words I  multiply no (zero) times, then...if I claim I am still there, then I am a भाववादिन् / सत्त्ववादिन् (bhavavadin /sattvavadin - realist / existentialist) on the other hand if I say, I do not exist, I am nihilist अभाववादिन् / शून्यवादिन् (abhāvavādin/śūnyavādin - nihilist). It all boils down to a matter of interpretation!

    On the other hand if one technically argues that even if I say I do not multiply myself, it is mathematically  implied that i multiply once, or in other words I multiply one time by default...then I am an एकवादिन् / केवलवादिन् (ekavādin / kevalavādin - monist / absolutist) and alternatively if I justify both claims are true from their relative standpoints, then I am a अनेकान्तवादिन् (anekāntavādin - relativist) 

    This is how our the ऋषिमुनिः (ṛṣimuniḥ - seer-sages) variously interpreted the same truth, like the famous महावाक्य छान्दोग्योपणिशदस्य (mahāvākya chāndogyopaṇiśadasya - grand declaration of Chandogya Upanishad) viz. "तत् त्वम् असि (tat tvam asi - that thou art)" ....to suit their ideological narratives of  भेदवाद (bhedavāda - doctrine of difference), अभेदवाद (abhedavāda - doctrine of non-difference), भेदाभेदवाद (bhedābhedavāda - doctrine of difference cum non difference) etc...,  As the great Vedic wisdom emphatically declares 

Original	Transliteration	Translation
इन्द्रं मित्रं वरुणमग्निमाहुरथो दिव्यः स सुपर्णो गरुत्मान् ।  एकं सद्विप्रा बहुधा वदन्त्यग्निं यमं मातरिश्वानमाहुः ॥	indraṁ mitraṁ varuṇamagnimāhurathō divyaḥ sa suparṇō garutmān ।  ēkaṁ sadviprā bahudhā vadantyagniṁ yamaṁ mātariśvānamāhuḥ ॥	They have styled (him, the Sun), Indra, Mitra, Varuṇa, Agni, and he is the celestial, well-winged Garutmat, for learned priests call one by many names as they speak of Agni, Yama, Mātariśvan. -translation by H.H. Wilson
Sanskrit Reference: ऋग्वेद (ṛgveda) (1.164.46)

    Take another example, which is a very well narrated demonstration of abstract mathematical mysteries in the following video

Of course, in my humble opinion, if we take an open holistic view, these topics have never been unique to mathematics as a discipline. Elsewhere the mysteries (paradoxes) dealing with self-referential, inconsistent, undecidable truths are similarly proposed (discovered), discussed, debated and formally doctrinized in the domain of ancient philosophical (metaphysical) quest. In a nutshell, what I want to highlight is the fact that there are परसत्यानि (parasatyāni - abstract truths) that are अप्रमेय (aprameya - non provable) is recognized both in abstract mathematics (science) and abstract philosophy (spirituality)

For instance, the अनिर्वचनीय मायावाद (anirvacanīya māyāvāda - doctrine of indeterminable epistemic measure) is integral to the प्रतिबिंबवाद विवरणप्रत्शानसंप्रदायस्य (pratibiṃbavāda vivaraṇapratśānasaṃpradāyasya – reflection doctrine of vivarna-treatise-tradition), one of the main sub-schools of दर्शन केवलाद्वैतवेदनातौत्तरमीमाम्सयाः (darśana kevalādvaitavedanātauttaramīmāmsayāḥ – philosophy of absolute non-dualistic final-gnosis  posterior inquiry), deals with the स्वनिर्देश विसङ्गत अविषह्य सत्त्व (sva-nirdeśa visaṅgata aviṣahya sattva - self-referential, inconsistent, undecidable realm).   Of course, the language, symbols and ways of explaining the doctrine varies between mathematical model (hypothesis, axioms, theorems, numbers, letters, operators, algorithms, equations, analogies etc.) and philosophical model (aphorisms, hymns, mythologies, verses, logic, dialectic, poetry, sculptures etc.)

The समावरण आत्मस्य (samāvaraṇa ātmasya – encapsulation of self) as the अहमिदं/विस्षयिन्विषय सम्मेलन (ahamidaṃ/visṣayinviṣaya sammelana– I-this / subject-object parity). परब्रह्मन्/परमात्मन् (parabrahman/paramātman – supreme divinity / self) encrypting (covering) itself as the 

• अहंभाव (ahaṃbhāva –  self-attitude):  पशु/जीवात्मन् (paśu/jīvātman – bonded / corporeal soul)  tied by पाश त्रिमलानां (pāśa trimalānāṃ - chord of triple impurities)  viz. मूलमल अणवस्य /अणुत्व (mūlamala aṇavasya / aṇutva – root fetter of minuteness/atomicity), कर्ममल (karmamala – action fetter / fate)  & चलक मायामल (calaka māyāmala – delusive paradox fetter).  In other words, it is पुरुषतत्त्व (puruṣatattva – soul principle) who is the  ज्ञातृ  / चित्-तत्त्व (jñātṛ  / cit-tattva – knower / sentient principle)  
• नाहंभाव / इदंभाव (nāhaṃbhāva / idaṃbhāva – non-self-attitude/ this-attitude):  It is प्राकृतिकतत्त्व (prākṛtikatattva – material principle) which is the  ज्ञेय / अचित्-तत्त्व (jñeya  / acit-tattva – knowable / insentient principle)

 

     Please be noted of the term “माया अविद्यायाः (māyā avidyāyāḥ - paradox of nescience)”. Here, I have prefixed अविद्या (avidyā - nescience) with the term माया (māyā - paradox) because here अविद्या (avidyā - nescience) here does not refer to पूरणाभाव ज्ञान्स्य (pūraṇābhāva jñānsya – complete absence of knowledge) but only असम्ग्रविद्या (asamgravidyā – partial / incomplete knowledge).

 

    In other words, it is the परिमितविद्या उद्देशात् व्यवहारिकसत्त्व (parimitavidyā uddeśāt vyavahārikasattva – limited knowledge relative to phenomenal realm) in terms of पुरुषतन्त्र (puruṣatantra – subjective-science), वस्तुतन्त्र (vastutantra – objective science) and their corresponding चोदनातन्त्र  (codanātantra – injunctive science)

Please remember that अनिर्वचनीय मायावाद (anirvacanīya māyāvāda - doctrine of indeterminable epistemic measure) is a epistemological constraint of what is called in quantum physics as मापनसमस्या (māpanasamasyā - the measurement problem) relating to Wave-Function Collapse of Schrödinger Equation, and also related to Heisenberg's Uncertainty Principle on the famous Wave-Particle Duality. I am reminded of the following verses from the sacred केनोपनिषद् (kenopaniṣad)

Original	Transliteration	Translation
यदि मन्यसे सुवेदेति दहरमेवापि नूनम् | त्वं वेत्थ ब्रह्मणो रूपम् यदस्य त्वं यदस्य देवेष्वथ नु मीमामँयेमेव ते मन्ये विदितम् ॥ नाहं मन्ये सुवेदेति नो न वेदेति वेद च । यो नस्तद्वेद तद्वेद नो न वेदेति वेद च ॥ यस्यामतं तस्य मतं मतं यस्य न वेद सः । अविज्ञातं विजानतां विज्ञातमविजानताम् ॥ प्रतिबोधविदितं मतममृतत्वं हि विन्दते । आत्मना विन्दते वीर्यं विद्यया विन्दतेऽमृतम् ॥ इह चेदवेदीदथ सत्यमस्ति न चेदिहावेदीन्महती विनष्टिः । भूतेषु भूतेषु विचित्य धीराः प्रेत्यास्माल्लोकादमृता भवन्ति ॥	yadi manyase suvedeti daharamevāpi nūnam | tvaṃ vettha brahmaṇo rūpam yadasya tvaṃ yadasya deveṣvatha nu mīmām̐syemeva te manye viditam ॥ nāhaṃ manye suvedeti no na vedeti veda ca | yo nastadveda tadveda no na vedeti veda ca || yasyāmataṃ tasya mataṃ mataṃ yasya na veda saḥ | avijñātaṃ vijānatāṃ vijñātamavijānatām || pratibodhaviditaṃ matamamṛtatvaṃ hi vindate | ātmanā vindate vīryaṃ vidyayā vindate'mṛtam || iha cedavedīdatha satyamasti na cedihāvedīnmahatī vinaṣṭiḥ | bhūteṣu bhūteṣu vicitya dhīrāḥ pretyāsmāllokādamṛtā bhavanti ||	If thou thinkest that thou knowest It well, little indeed dost thou know the form of the Brahman. That of It which is thou, that of It which is in the gods, this thou hast to think out. I think It known. I think not that I know It well and yet I know that It is not unknown to me. He of us who knows It, knows That; he knows that It is not unknown to him. He by whom It is not thought out, has the thought of It; he by whom It is thought out, knows It not. It is unknown to the discernment of those who discern of It, by those who seek not to discern of It, It is discerned. When It is known by perception that reflects It, then one has the thought of It, for one finds immortality; by the self one finds the force to attain and by the knowledge one finds immortality. If here one comes to that knowledge, then one truly is; if here one comes not to the knowledge, then great is the perdition. The wise distinguish That in all kinds of becomings and they pass forward from this world and become immortal. -translation by Sri Aurobindo.
Sanskrit Reference: केनोपनिषद् (kenopaniṣad) (2.1-5)

But such a constraint is not an ontological one. Please remember that मिथ्या (mithyā - illusion) is सत्य (satya - truth) in दृशीक (dṛśīka - perspective). Of-course, with a wave-function collapse of a possibility wave into a probability event. In other words, what entity (light) behaves relatively as a wave, relative to specific frame of an observer, simultaneously behaves as a particle from the relative standpoint of another. Yet it is the one and same entity. The same entity behaves either as particle or as wave. Similarly, the same ब्रह्मन् (brahman - divinity) is perceived as सगुणब्रह्ममायाशक्तेः (saguṇabrahmamāyāśakteḥ – qualified divinity of paradox-force) from the relative referential frame of व्य्वहारिकसत्त्व (vyvahārikasattva – phenomenal realm) and as the निर्गुणब्रह्मन् (nirguṇabrahman – divinity beyond attributes) in terms of the परमार्थिकसत्त्व (paramārthikasattva – absolute noumenal realm).

    The next important point to understand is that the तिरोधान शक्ति ब्रह्मस्य (tirodhāna śakti brahmasya – concealing-power of divinity) is responsible for providing माया अविद्यायाः (māyā avidyāyāḥ - paradox of nescience), while the अनुग्रहशक्ति ब्रह्मस्य (anugrahaśakti brahmasya - gracious power of divinity) is responsible for providing the ब्रह्मविद्या (brahmavidyā – divine gnosis). These are the two sides (polarities) of the same coin – referred in Chinese Taoism as the Ying and Yang. Again, I would like to quote the following verses from the sacred ईशावास्योपनिषद् (īśāvāsyopaniṣad) wherein the perfect soteriological synergies between these two realms of polarities:

Original	Transliteration	Translation
अन्धं तमः प्रविशन्ति येऽविद्याम् उपासते । ततो भूय इव ते तमो य उविद्यायां रताः ॥ अन्यद् एवाहुर् विद्ययान् यद् आहुर् अविद्यया । इति शुश्रुम धीराणां ये नस् तद् विचचक्षिरे ॥ विद्यां चाविद्यां च यस् तद् वेदोभयं सह । अविद्यया मृत्युं तीर्त्वा विद्ययामृतम् अश्नुते ॥ अन्धं तमः प्रविशन्ति येऽसम्भूतिम् उपासते । ततो भूय इव ते तमो य उ सम्भूत्यां रताः ॥ अन्यद् एवाहुः संभवाद् अन्यद् आहुर् असंभवात् । इति शुश्रुम धीराणां ये नस् तद् विचचक्षिरे ॥ संभूतिं च विनाशं च यस् तद् वेदोभयं सह । विनाशेन मृत्युं तीर्त्वा संभूत्यामृतम् अश्नुते ॥ हिरण्मयेन पात्रेण सत्यस्यापिहितं मुखम् । तत् त्वं पूषन्न् अपावृणु सत्यधर्माय दृष्टये ॥	andhaṃ tamaḥ praviśanti ye'vidyām upāsate | tato bhūya iva te tamo ya uvidyāyāṃ ratāḥ || anyad evāhur vidyayān yad āhur avidyayā | iti śuśruma dhīrāṇāṃ ye nas tad vicacakṣire || vidyāṃ cāvidyāṃ ca yas tad vedobhayaṃ saha | avidyayā mṛtyuṃ tīrtvā vidyayāmṛtam aśnute || vidyāṃ cāvidyāṃ ca yas tad vedobhayaṃ saha | avidyayā mṛtyuṃ tīrtvā vidyayāmṛtam aśnute || andhaṃ tamaḥ praviśanti ye'sambhūtim upāsate | tato bhūya iva te tamo ya u sambhūtyāṃ ratāḥ || anyad evāhuḥ saṃbhavād anyad āhur asaṃbhavāt | iti śuśruma dhīrāṇāṃ ye nas tad vicacakṣire || saṃbhūtiṃ ca vināśaṃ ca yas tad vedobhayaṃ saha | vināśena mṛtyuṃ tīrtvā saṃbhūtyāmṛtam aśnute || hiraṇmayena pātreṇa satyasyāpihitaṃ mukham | tat tvaṃ pūṣann apāvṛṇu satyadharmāya dṛṣṭaye ||	Into a blind darkness they enter who follow after the Ignorance, they as if into a greater darkness who devote themselves to the Knowledge alone Other, verily, it is said, is that which comes by the Knowledge, other that which comes by the Ignorance; this is the lore we have received from the wise who revealed That to our understanding. He who knows That as both in one, the Knowledge and the Ignorance, by the Ignorance crosses beyond death and by the Knowledge enjoys Immortality. Into a blind darkness they enter who follow after the Non-Birth, they as if into a greater darkness who devote themselves to the Birth alone. Other, verily, it is said, is that which comes by the Birth, other that which comes by the Non-Birth; this is the lore we have received from the wise who revealed That to our understanding. He who knows That as both in one, the Birth and the dissolution of Birth, by the dissolution crosses beyond death and by the Birth enjoys Immortality. The face of Truth is covered with a brilliant golden lid; that do thou remove, O Fosterer, for the law of the Truth, for sight. -translation by Sri Aurobindho
Sanskrit Reference: ईशावास्योपनिषद् (īśāvāsyopaniṣad) (9-15)

    That is why श्री ललितापरमेश्वरी (śrī lalitāparameśvarī) who in the श्रीविद्यासंप्रदाय (śrīvidyāsaṃpradāya – sacred gnosis tradition) corresponds to the सर्वज्ञ परब्रह्मतत्त्व (sarvajña parabrahmatattva – omniscient supreme divinity principle) is eulogized in the sacred श्री ललितासहस्रनामवली स्तोत्र (śrī lalitāsahasranāmavalī stotra) which is part of ब्रह्माण्डपुराण (brahmāṇḍapurāṇa) as:

Original	Transliteration	Translation
प्रभवती प्रभारूपा प्रसिद्ध परमेश्वरी। मूलप्रकृतिरव्यक्ता व्यक्ताव्यक्तस्वरूपिनी॥ व्यापिनी विविधाकारा विद्याऽविद्यास्वरूपिणि। महाकामेशनयकुमुदाह्लादकौमुदी॥	prabhavatī prabhārūpā prasiddha parameśvarī। mūlaprakṛtiravyaktā vyaktāvyaktasvarūpinī॥ vyāpinī vividhākārā vidyā'vidyāsvarūpiṇi। mahākāmeśanayakumudāhlādakaumudī॥	(She is) luminous, in the form of brighness, celebrated, supreme ruler, primary cause, unmanifest, in the form of manifest-unmanifest, all-pervading, polymorphic, in the form of gnosis and ingnorance, moonlight that gladens the red-lotus like eyes of supreme-lover.
Sanskrit Reference: श्री ललितासहस्रनामवली स्तोत्र (lalitāsahasranāmavalī stotra) (137,138)

Here, “विद्याविद्यस्वरूपिनी (vidyāvidyasvarūpinī – in the inherent form of knowledge and ignorance) “ is the 402^nd sacred name of the goddess and the esoteric significance of the same is very well explained in the श्री सौभाग्यभास्कर भाष्य (saubhāgyabhāskara bhāṣya), which is the famous commentary on the above text written by श्री भास्कररायमखिन् śrī bhāskararāyamakhin), the eminently noble आचार्य (ācārya - preceptor) belonging to the orthodox school of श्रीविद्या संप्रदाय (śrīvidyā saṃpradāya).  In this excellent commentary, the भाष्यकार (bhāṣyakāra - commentator) explains by referring to various scriptural testimonies including the above cited ईशावास्योपनिषद् (īśāvāsyopaniṣad) 

Original	Transliteration	Translation
विद्यां चाविद्यां च यस् तद् वेदोभ्यं यह। अविद्या मृत्यं तीर्त्वा विद्याऽमृतं अश्नुते॥' इति श्रुतौ प्रसिद्ये विद्याविद्ये। विद्या स्वात्मरूपम् ज्ञानम्। अविद्या चरमवृत्तिरूपं ज्ञानम्। तद्भयम् स्वरूपमस्याः। उक्तंच बृहृनारदीये 'तस्य शक्तिः परा विष्णोर्जगत्कार्यपरिक्षमा। भावाभ्वास्वरूपा सा विद्याविद्येति गीयत्' इति। देवीभागवतेऽपि 'ब्रह्मैव सातिदृष्प्रापा विद्याविद्यास्वरूपिणी' ति। तत्त्रैव स्थलान्तरे 'विद्याविद्येति देव्या द्वे रूपे जानीहि पार्थिव। एकया मुच्यते जन्तुरन्यया बध्यते पुन'रिति। यद्वा विद्यैव चरमवृत्तिरूपं ज्ञानम्। अविद्या भेदभ्रान्तिरूपं ज्ञानम्। स्वः परब्रह्मात्मकं ज्ञानम्। स्वपदस्यात्मवाचित्वात्। 'स्वो ज्ञातावात्मनी'ति कोशात्। एतन्त्रयं रूपंस्याः। उक्तं च लै`ण्गे 'भ्रान्तिर्विद्या परम् चेतिर् शिवरूपमिदं त्रयम्। अर्थेषु भिन्नरूपेषु विज्`नानं भ्रान्तिरुच्यते॥	vidyāṃ cāvidyāṃ ca yas tad vedobhyaṃ yaha। avidyā mṛtyaṃ tīrtvā vidyā'mṛtaṃ aśnute॥' iti śrutau prasidye vidyāvidye। vidyā svātmarūpam jñānam। avidyā caramavṛttirūpaṃ jñānam। tadbhayam svarūpamasyāḥ। uktaṃca bṛhṛnāradīye 'tasya śaktiḥ parā viṣṇorjagatkāryaparikṣamā। bhāvābhvāsvarūpā sā vidyāvidyeti gīyat' iti। devībhāgavate'pi 'brahmaiva sātidṛṣprāpā vidyāvidyāsvarūpiṇī' ti। tattraiva sthalāntare 'vidyāvidyeti devyā dve rūpe jānīhi pārthiva। ekayā mucyate janturanyayā badhyate puna'riti। yadvā vidyaiva caramavṛttirūpaṃ jñānam। avidyā bhedabhrāntirūpaṃ jñānam। svaḥ parabrahmātmakaṃ jñānam। svapadasyātmavācitvāt। 'svo jñātāvātmanī'ti kośāt। etantrayaṃ rūpaṃsyāḥ। uktaṃ ca lai`ṇge 'bhrāntirvidyā param cetir śivarūpamidaṃ trayam। artheṣu bhinnarūpeṣu vij`nānaṃ bhrāntirucyate॥	Vidyā and avidyā are explained in the īśāvāsyopaniṣad(11):”One who simulatenously knows both knoowledge and ignorance having crossed over death by ignorance attains immortality. By knowledge.“ Or, vidyā, knowledge of the Self, avidyā, the knowledge in the form of the last modification (of duality, i.e. just before realization). The bṛhṛnnāradīya purāṇam says, “The Supreme Śakti of that Viṣṇu, capable of absorbing the universe, in the form of existence and non-existence, is sung as vidyā and avidyā.” The Devībhāgavatapurāṇam also,”She is Brahman himself, very difficult to attain and in the form of vidyā and avidyā.” In another place, “ O King, know, that vidyā and avidyā are two forms of Devī; by one are freed, by the other they are bound.” Or, vidyā, the knowledge in the form of the last modification of duality, or of the false knowledge (caramavṛtt). Avidyā confused knowledge of separateness; sva, the knowledge belonging to Supreme Brahman; because according to one lexicography, “sva means relations and Self”; rūpa, these three are her form. The liṅgapurāṇam says, “Śiva has three forms bhrānti, vidyā and parā. The knowledge of different objects is called bhrānti (confused) by the learned. Knowledge in the form of Self, is called vidyā. Knowledge concerning Brahman without ambiguity is called parā (supreme).” -translation by R. Ananthakrishna Shastri
Sanskrit Reference: श्री सौभाग्यभास्कर भाष्य (saubhāgyabhāskara bhāṣya) (402)

 Yes. the above सदाशिवलिङ्ग (sadāśivaliṅga) symbolizes rather theologizes the अर्धनारीशवरतत्त्व शिवशक्तिसंएलनस्य (ardhanārīśavaratattva śivaśaktisaṃelanasya – androgynous principle of divine polarity) variously expressed as the नित्यब्रह्मसंमेलन (nityabrahmasaṃmelana – eternally divine equivalence) between 

• पुरुष च प्रकृति (puruṣa ca prakṛti – spirit & matter)
• शिव च शक्ति (śiva ca śakti – shiva & shakti)
• नरायण च लक्ष्मी  (narāyaṇa ca lakṣmī – Narayana & lakshmi)
• प्रकाश च विमर्श (prakāśa ca vimarśa – effulgence & broadcast)
• नाद च बिन्दु (nāda ca bindu – wave & particle)
• निर्गुणत्व च सगुणत्व (nirguṇatva ca saguṇatva – attributelessness & atrtributeness)
• निष्कलत्व च शकलत्व (niṣkalatva ca śakalatva – indivisibility & divisibity)
• कामेश्वर च कामेश्वरी (kāmeśvara ca kāmeśvarī – lover & loved)
• धर्मिन् च धर्म  (dharmin ca dharma – substance & attribute)
• स्वप्नदर्शक  च स्वप्न  (svapnadarśaka  ca svapna – dreamer & dream)
• दर्शक च दर्शन (darśaka ca darśana – seer & seen)
• ज्ञातृ च ज्ञान (jñātṛ ca jñāna – knower & knowledge)
• ब्रह्मन् च माया (brahman ca māyā – being & becoming)
• विद्या च अविद्या (vidyā ca avidyā – science & nescience)
• सत्यत्व च मिथ्यात्व  (satyatva ca mithyātva  – truth-hood & false-hood) etc

शशविषाण (śaśaviṣāṇa - hare's horn)

 The analogy of शशविषाण (śaśaviṣāṇa - hare's horn) is a very common analogy employed in भारतीय तत्त्वदर्शनिक परंपराः सनातनधर्मस्य (bhāratīya tattvadarśanika paraṃparāḥ sanātanadharmasya - Indian Philosophical Traditions of eternal spirituality) even cutting across most of its native religions viz. हिन्धुधर्म (hindhudharma - Hinduism), बौद्धधर्म (bauddhadharma - Buddhism) & जैनधर्म (jainadharma - Jainism). For example in हिन्धुधर्म (hindhudharma - Hinduism) one can find its usage in 

• न्यायदर्शन (nyāyadarśana – philosophy of epistemology/logic)
• सांख्यदर्शन  (sāṁkhyadarśana – philosophy of ontology)
• उत्तरमीमांसावेदान्तदर्शन (uttaramīmāṁsāvedāntadarśana – philosophy of posterior inquiry of final gnosis)  
• शुद्धाद्वैतशैवसिद्धान्तदर्शन (śuddhādvaitaśaivasiddhāntadarśana - philosophy of pristine non-dualistic final accomplishment)
• परमाद्वैतत्रिकशैवदर्शन (paramādvaitatrikaśaivadarśana - philosophy of supreme non-dualistic triadic Saivism)

    The fact that such a metaphor has been so widely used from the  ancient times denotes a higher probability of they having witnessed a rare sight of a शशविषाण (śaśaviṣāṇa - hare's horn) across Indian peninsula may be because of same or similar विषाणु रोगसञ्चार (viṣāṇu rogasañcāra - virus infection) (as per modern scientific accounts)

Reference: Rabbits with 'horns' growing from their heads invading the US, experts warn to stay away

    As far as  उत्तरमीमांसाकेवलाद्वैतवेदान्तदर्शन (uttaramīmāṁsākevalādvaitavedāntadarśana – posterior inquiry of absolute non-dualistic final gnosis philosophy) goes, it recognizes ज्ञानशास्त्रीय समाहितीकरणस्य त्रिगुणात्मकाः आवरणशक्तेः (jñānaśāstrīya samāhitīkaraṇasya triguṇātmakāḥ āvaraṇaśaktēḥ - triple dimensions of epistemological encapsulation) with respect to the अनुभवज्ञान परब्रह्मणः (anubhavajñāna parabrahmaṇaḥ - experiential wisdom of supreme divinity) viz. 

1. प्रातिभासिकसत्त्व (prātibhāsikasattva - apparent realm)
2. व्यावहारिकसत्त्व (vyāvahārikasattva  - phenomenal realm)
3. परमार्थिकसत्त्व (paramārthikasattva - transcendent/ noumenal realm)

    Please remember that each of the above from an ontological standpoint corresponds to a सत्त्व (sattva -reality/ realm)  and from an epistemological standpoint corresponds to a सत्य (satya - truth) and not their opposites viz. असत्त्व (asattva - unreality) and असत्य (asatya - untruth) respectively. In other words, borrowing the golden views of Swami Vivekananda, the differences between these realms are in degrees of freedom and not in kind, and the मोक्शयात्र (mokśayātra - soteriological voyage) as part of the अन्तिमपुरुषार्थ (antimapuruṣārtha - ultimate human pursuit) constitutes involutionary progress from  सत्यात् उच्चतरसत्यं प्रति (satyāt uccatarasatyaṁ prati - from truth to higher truth). 

    In terms of the interesting debates around मिथ्यात्व शशविषाणस्य (mithyātva śaśaviṣāṇasya - illusion of hare's horn), we must first understand that the concept "मिथ्यात्व (mithyātva - illusion)" even with उत्तरमीमांसाकेवलाद्वैतवेदान्तदर्शन (uttaramīmāṁsākevalādvaitavedāntadarśana – posterior inquiry of absolute non-dualistic final gnosis philosophy) is highly polymorphic in its definitions and corresponding metaphysical interpretations. For example these are some of the famous definitions across its different sub-schools. Of course this is only an indicative and not an exhaustive list.  

• सदसत् विलक्षणत्वम् (sadasat vilakṣaṇatvam – indefinability of reality-unreality)
• प्रतिपन्नोपाधौ त्रिकालिक निषेध प्रतियोगित्वम् (pratipannopādhau trikālika niṣedha pratiyogitvam – counter correlative of negation in trifold time periods (tenses))
• ज्ञाननिवर्त्यत्वं (jñānanivartyatvaṃ – removable by wisdom)
• स्वसमानाधिकरणात्यन्ताभावप्रतियोगित्वम् (svasamānādhikaraṇātyantābhāvapratiyogitvam –counter-positive of absolute negation located in its own  substratum)
• सद्विविक्तत्वम् (sadviviktatvam- distinct and different from the real)

    आचार्य श्री मधुसूदनसरस्वती (ācārya śrī madhusūdanasarasvatī) deals at length with these topics in his magnum opus masterpiece अद्वैतसिद्धि (advaitasiddhi - non-dualistic accomplishment) as a defense to the polemic criticisms raised by आचार्य श्री व्यासतीर्थ (ācārya śrī vyāsatīrtha) in his magnum opus न्ययनामृत (nyayanāmṛta - logical nectar). Again, श्री  चित्सुखाचार्य (śrī citsukhācārya) further expands on them in his magnum opus commentary तत्त्वप्रदीपिका (tattvapradīpikā).

    In my humble opinion, when we refer to मिथ्यात्व शशविषाणस्य (mithyātva śaśaviṣāṇasya - illusion of hare's horn) particularly in the context of ज्ञानशास्त्रीय समाहितीकरणस्य त्रिगुणात्मकाः आवरणशक्तेः (jñānaśāstrīya samāhitīkaraṇasya triguṇātmakāḥ āvaraṇaśaktēḥ - triple dimensions of epistemological encapsulation) listed above, what is emphasized here is its  आपेक्षिक अनित्यत्व (āpekṣika anityatva -  relative impermanence / transitoriness) rather than its प्रकेवल असत्त्व (prakevala asattva - absolute unreality). 

    Moreover,  मिथ्यात्व शशविषाणस्य (mithyātva śaśaviṣāṇasya - illusion of hare's horn) only reiterates that परमलीला महामायाशक्तेः (paramalīlā mahāmāyāśakteḥ - supreme play of grand paradox power) that विषाणु रोगसञ्चार (viṣāṇu rogasañcāra - virus infection) and शशविषाण (śaśaviṣāṇa - hare's horn) could not be experienced (witnessed) in the प्रातिभासिकसत्त्व स्वप्नावस्थायाः (prātibhāsikasattva svapnāvasthāyāḥ - apparent realm of dream state) but also potentially in the  व्यावहारिकसत्त्व जाग्रतवस्थायाः (vyāvahārikasattva jāgratavasthāyāḥ - phenomenal realm of waking state).

सत्यात् उच्चतरसत्यं प्रति (satyāt uccatarasatyaṁ prati - from truth to higher truth)

Thus, based on the above examples and explanations, it is clear that the phenomenal world is only a kind of मिथ्या (mithyā - illusion) caused by अध्यास (adhyāsa-  superimposition) due to अविद्या उपाधि (avidyā upādi  - nescient adjunct) in the form of नाम (nāma - name) & रूप (rūpa - form) as popularly explained by जगत् गुरु श्री आदिशंकराचार्य भगवत्पाद (jagat guru śrī ādiśaṁkarācārya bhagavatpāda) in the following verses from ब्रह्म ज्ञानवलिमाला (brahma jñānavalimālā) 

Original	Transliteration	Translation
ब्रह्म सत्यं जगन्मिथ्या जीवो ब्रह्मैव नापरः। अनेन वेद्यं सच्चास्त्रम् इति वेदान्तडिण्डिमः॥	brahma satyaṁ jaganmithyā jīvo brahmaiva nāparaḥ| anena vedyaṁ saccāstram iti vedāntaḍiṇḍimaḥ||	Brahman is real, the universe is mithyā (it cannot be categorized as either real or unreal). The jiva is Brahman itself and not different. This should be understood as the correct SAstra. This is proclaimed by Vedanta -translated by S.N. Shastry
Sanskrit Reference: ब्रह्म ज्ञानवलिमाला (brahma jñānavalimālā) (20)

In fact, the revered जगत् गुरु श्री आदिशंकराचार्य भगवत्पाद (jagat guru śrī ādiśaṁkarācārya bhagavatpāda), in the following verses from the beautiful treatise titled आत्मबोधः (ātmabodhaḥ - knwoledge of the self)   

Original	Transliteration	Translation
यदि मन्यसे सुवेदेति दहरमेवापि नूनम् त्वं वेत्थ ब्रह्मणो रूपम् यदस्य त्वं यदस्य देवेष्वथ नु मीमांस्येमेव ते मन्ये विदितम् ॥ नाहं मन्ये सुवेदेति नो न वेदेति वेद च । यो नस्तद्वेद तद्वेद नो न वेदेति वेद च ॥ यस्यामतं तस्य मतं मतं यस्य न वेद सः । अविज्ञातं विजानतां विज्ञातमविजानताम् ॥	yadi manyasē suvēdēti daharamēvāpi nūnam tvaṁ vēttha brahmaṇō rūpam yadasya tvaṁ yadasya dēvēṣvatha nu mīmāṁsyēmēva tē manyē viditam ॥ nāhaṁ manyē suvēdēti nō na vēdēti vēda ca । yō nastadvēda tadvēda nō na vēdēti vēda ca ॥ yasyāmataṁ tasya mataṁ mataṁ yasya na vēda saḥ । avijñātaṁ vijānatāṁ vijñātamavijānatām ॥	That by the light of which the luminous, orbs like the Sun and the Moon are illuminated, but which is not illumined by their light, realise that to be Brahman. Pervading the entire universe outwardly and inwardly the Supreme Brahman shines of Itself like the fire that permeates a red-hot iron-ball and glows by itself. Brahman is other than this, the universe. There exists nothing that is not Brahman. If any object other than Brahman appears to exist, it is unreal like the mirage. All that is perceived, or heard, is Brahman and nothing else. Attaining the knowledge of the Reality, one sees the Universe as the non-dual Brahman, Existence-Knowledge-Bliss-Absolute
Sanskrit Reference: आत्मबोधः (ātmabodhaḥ) (61 - 64)

Swami Nikhilananda (RKM Order) in his famous translation of this texts comments thus on verse  #63: 

Original

This text gives the conclusion of Non-dualistic Vedānta, according to which the Real is defined as the entity that is not changed by time or limited by space or affected by the law of causality. The unreal is subject to time, space, and causality. The man endowed with Right Knowledge sees everywhere only Brahman. What appears as the manifold universe to the ignorant is realized the illumined to be the indivisible and non-dual Brahman. It is ignorance that makes one see multiplicity in nplace of Brahman. But this multiplicity, being illusory, does not defile Brahman. This is explained by the apt illustration of the desert and the mirage. In reality the desert alone exists. An ignorant person sees the desert as the mirage and is fooled by it. All the time that he believes he is seeing water, he sees, in reality, only the dry desert. Again, the ignorance through which Brahman appears as the world, or the desert as the mirage, is itself unreal. Ignorance, which is ultimately destroyed by Knowledge, has no objective reality or absolute existence; it is an inexplicable state of the mind of the perceiver.  "If the perceived manifold really existed, then certainly it would disappear. This duality is mere illusion; Non duality alone is the Supreme Reality." (Mandukya Upanishad Karikā I, 17.) Non-dualistic Vedanta does not negate the reality of the universe, because the universe, as Brahman, cannot be ne gated. All that Vedanta aims at is the destruction of illusion, which projects the universe of name and form and makes it appear as other than Brahman”

English Reference: आत्मबोधः (ātmabodhaḥ - self knowledge)