Mahāyāna Buddhism "Emptiness" Explained.

What is the "Emptiness"?

1. "Emptiness" is a major topic in Mahāyāna Buddhism.

"Emptiness", or Sanskrit "Śūnyatā", is a major topic in Mahāyāna Buddhism. Famous Heart Sutra is all about this "Emptiness". It is explained in the Sutra (Translated by Max Müller, 1894 version) as below:

Sariputra! Form does not differ from Sunyata, nor Sunyata from form. Form is identical to Sunyata, and Sunyata is identical to form. So also are reception (vedana), conception (sanjna), mental conduct (samskara) and consciousness (vijnana) in relation to Sunyata. Sariputra, the Sunyata nature of all things is neither created nor annihilated; neither impure nor pure; and neither increasing nor decreasing.

 "Form" is Sanskrit "Rūpa". "Rūpa" have another meaning "material". It says "Śūnyatā is identical to Rūpa." Okay then, what is Śūnyatā and Rūpa? Why don't we check what it looks like? Let's see:

Fig.1: What a "Śūnyatā" and "Rūpa" looks like.

This is what "Śūnyatā" and "Rūpa" looks like. It's not just a bowl. You are seeing an "Emptiness" and a "Form" now. Let me break down with some more Fig.s.

Fig.2

In Fig.2 left, I put some guidelines on the bowl picture. That is what is filling the bowl: emptiness. When you feel needs on bowls, I don't think there is anyone presumes that you need to grab some wooden clustered matter―what you need is the emptiness expecting filled with some liquid or food (Fig.2 middle). 

Okay, go get some emptiness! No, you can't. You need to have some kind of form to get emptiness. In other words, the emptiness, which is what you want, is depend on "Rūpa", material which surrounds it. 

The Sutra continues(translated from Japanese ver. into English by me):

Shariputra! In this world, everything has the nature of emptiness. 

Not a single existence in this world is not dependent on the others―everything is depend on the circumstance.

2. "Emptiness" is an alias.

"Emptiness" is closely examined by Indian philosopher Nāgārjuna. In his main article Mūlamadhyamaka-kārikā,(a.k.a. "中論", a Chinese translation by Kumārajīva, Japanese Taiśotripiṭakaṃ) he said

空則不可説　非空不可説　共不共叵説　但以假名説 .

It says "Emptiness can't be explained, not emptiness can't be explained. Whether or not it is shared, it is hard to say. Only explained by using aliases." 
c.f. "十八不共仏法 " "Eighteen unshared(special for Buddha) Buddha Dharma" (wikipedia here). So "共不共叵説" means "I don't know you are shared the idea".

Therefore, "emptiness" is an alias. It represents "something whose existence is established on interdependences".

Appendix 1: In Sanskrit version, the part is below: 

śūnyam iti na vaktavyam aśūnyam iti vā bhavet  ubhayaṃ nobhayaṃ ceti prajñaptyarthaṃ tu kathyate

English translation(by me, with help of Google Gemini): 

It is emptiness, or not emptiness, both or not both, it should not be talked. For the sake of prajñapty-purpose, it is talked about. 

So what is "prajñapty"? Kumārajīva translated it into "假名" (an alias). According to this article, "prajñapty" is hypothesis, or alias, constitution("施設") which is temporary set up for the sake of explanation. Other Buddhism concepts, like "Pañcupādāna-kkhandhā", is also called as "prajñapty".

Appendix 2: The famous 18th verse, Chapter 24 explaining "Śūnyatā" from Nāgārjuna "Mūlamadhyamaka-kārikā", is

yaḥ pratītya-samutpādaḥ śūnyatāṃ taṃ pracakṣmahe / sā prajñaptir upādāya pratipat saiva madhyamā.

English translation(by me, with help of Google Gemini): 

 We call it "pratītya-samutpāda" "śūnyatā" . With it, we practice, which is the mid-way. 

"Madhyamā", or the mid-way, is a key concept of Buddhism practice. It has multiple meanings depend on the context, but in this context, check this for further reading. (According to Google Gemini, it is an alter name of the Kingdom of Magadha, which is known as a main stage of the Buddhism development, which was a news to me.)

Appendix 3: According to Japanese Taiśotripiṭakaṃ, Kumārajīva had vocabulary "施設"(constitution), "假施設"(temporary constitution), or "假名施設"(a temporary defined alias). I'm checking it now whether it is the translated term of "prajñapty".

"成實論" is a lost script. I'm looking for the "摩訶般若波羅蜜經", "Prajñāpāramitā sūtra".

 摩訶般若波羅蜜經卷第二 (鳩摩羅什) (5)

菩提菩薩摩訶薩行般若波羅蜜名假	施設	受假
受假	施設	法假
法假	施設	如是應當學復次須菩提菩薩摩訶薩
薩行般若波羅蜜時當作是知名字假	施設	知假名字已不著色不著受想行識不
訶薩行般若波羅蜜時當知諸法名假	施設	須菩提於汝意云何色是菩薩不受想

 摩訶般若波羅蜜經卷第三 (鳩摩羅什) (1)

住亦不不住世尊諸法因縁和合假名

施設

所謂菩薩是名字於五蔭中不可説十

 摩訶般若波羅蜜經卷第六 (鳩摩羅什) (4)

無相法出如上説若人欲使名字假名	施設	相但有語言出是人爲欲使無相法出
若所以者何名字相名字相空故乃至	施設	亦如是是人欲使不生不滅法不垢不
空故若欲出無相法爲欲出名字假名	施設	相但有言語何以故名字不出三界亦
若所以者何名字相名字相空故乃至	施設	亦如是若欲出無相法爲欲出不生不

 摩訶般若波羅蜜經卷第二十四 (鳩摩羅什) (1)

等是名何等是相佛言此名強作但假

施設

所謂此色此受想行識此男此女此大

 成實論卷第三 ( 訶梨跋摩, 鳩摩羅什) (1)

者何如經中佛語比丘但以名字但假

施設

但以有用故名爲我以但名字等故知