**“What is laid down, ordered, factual, is never enough to embrace the whole truth.”** – Boris Pasternak (1890-1960), Russian poet whose novel *Doctor Zhivago* helped win him the Nobel Prize for Literature in 1958 – he declined.

**“The problems of the world cannot possibly be solved by sceptics and cynics whose horizons are limited by the obvious realities. We need men who can dream of things that never were.”** – John F Kennedy (1917-1963), 35^{th} president of the USA (1961-1963).

What is the difference between nothing and nothingness (as well as zero for that matter? I have received so many emails from all over the world asking exactly that, that I have therefore decided to try to elucidate these concepts somewhat more, as promised. I make use of mathematical logic to simplify and expound the different concepts. Therefore, please bear with me; the mathematical concepts used here is extremely simple and nobody should have any form of ‘math anxiety’ in reading the essay.

Grammatically, the word ‘nothing’ is a noun, which suggests that it refers at least to something. However, mathematicians have the distinction of being among the first people in history to recognise the value of nothingness and to understand and express *the difference between nothingness and nothing*.

Even though it may sound like very dull milestones, they were prodigious events in, for example, the development of arithmetic, as we know it today. Some eleven hundred years ago, *nothingness* found its permanent place in arithmetic as the number zero. *Zero* (0) was a seemingly trivial addition to our numerical alphabet, but it enabled us to express numbers more clearly and easily than before.

Positional notation without the use of zero (using an *empty space* in tabular arrangements, or the word *kha* (‘emptiness’ in Sanskrit), is known to have been in use in India from the 6^{th} century. The earliest certain use of zero as a *decimal* positional digit dates to the 9^{th} century. The glyph for the zero-digit was written in the shape of a dot, and consequently called *bindu* (‘dot’ in Sanskrit). The Hindus permanently introduced the *zero* (0), which they called *sunya* (‘the void’ in Sanskrit), into their number system sometime between the 6^{th} and 9^{th} centuries.

One of the many symbols used by the Hindus to represent the concept of zero was that of the thousand-headed serpent *Ananta* (‘endless’), which enclosed the universe like an Orphic egg (0); its tail being swallowed in its mouth represent the re-entrant nature of infinity (∞).

The Hindu numeral system (base 10) reached Europe in the 11^{th} century, via the Iberian Peninsula through Spanish Muslims, the Moors. The Moors called the symbol for zero, *sifr* (‘empty’) – cipher. Therefore, in Europe they came to be known as ‘Arabic numerals’. The Italian mathematician Fibonacci, or Leonardo of Pisa (*circa* 1170-1240[?]), was instrumental in bringing the system into European mathematics in 1202.

Around 300 BCE, when Euclid (the most prominent mathematician of Greco-Roman antiquity, and best known for his treatise on geometry, *the Elements*) used logic to derive geometrical truths from a small number of assumptions, the question was raised of whether the same could be done with arithmetical truths.

When mathematicians finally applied themselves to find the answer to this in the late 19^{th} century, they could not agree on where to start. Some wanted to begin by merely presuming the mathematical existence of the sequence of natural numbers {0, 1, 2, 3 …}, the basic alphabet of arithmetic, and go on from there.

Others, like the German mathematician and logician, who founded modern mathematical logic, Gottlob Frege (1848-1925), wanted to begin further back logically, to derive the sequence of natural numbers itself from some even more primitive concept or concepts.

As one of his logical starting points, Frege chose the common-sense notion of a class, or set. In mathematics, as in any other application, *a set* is simply a group of things; or, as one of Frege’s contemporaries, the German mathematician who founded set theory, Georg Cantor (1845-1918), put it, a set is “any collection … of definite and separate objects of our intuition and thought”.

Frege believed that *the idea of a set was an even more primitive notion than the sequence of natural numbers*, and so he proceeded from it to derive the sequence; from there, using additional assumptions, he could derive the whole of arithmetic. *In the process, he recognised the difference between nothingness and nothing*.

The difference, he discovered, is one of class. *Nothing* is the empty or null set – the set with no members – that mathematicians denote with a pair of braces: { }. It was the only possible set that Frege had to begin with, since he had started out by not assuming the existence of any numbers.

For him, *the null set represented the moment just before creation*, the potential for becoming an infinite sequence of numbers. Even the symbol for it suggested latent being – two braces that envelop emptiness that would eventually be filled by a growing sequence of numbers.

*Nothingness*, by contrast, is the set with zero (0) as its only member, which mathematicians write as {0}. Just by looking at the symbol, we can see what Frege saw: *nothingness* {0}* is not nothing* { }*, but is actually something*.

However, the understanding of ‘nothing’ varies widely between cultures, especially between Western and Eastern cultures and philosophical traditions. For instance, *Shunyata* (‘emptiness’ { } in Sanskrit), unlike ‘nothingness’ {0} is considered a state of mind in some forms of Buddhism. Achieving ‘nothing’ { } as a state of mind in this tradition allows someone to be totally ‘focused’ (in the Western sense of the word) on a thought or activity at a level of intensity that would not be able to achieve while thinking ‘consciously’ {0}. The classic example of this is an archer drawing a bow, attempting to erase their mind and create a mental void { } as a way to better focus on the shot. Existentialism and the German philosopher Martin Heidegger (1889-1976) have brought these two understandings between cultures closer together.

One of the true st physical analogues of the null set, i.e. { } (nothing), is the physicist’s theoretical notion of a *vacuum*. As striking an analogue of the null set as the physicist’s vacuum is the biblical account of divine creation. According to the Bible, God created the universe just as Frege created the sequence of natural numbers – out of nothing { }.

In her play *Sapientia*, the 9^{th} century Benedictine nun playwright Hrosvitha of Gandersheim (*circa* 935-1000) goes even further: “The Author of the world … created the world out of nothing { }, and set everything in number, measure, and weight, and then in time and the age of man, formulated a science which reveals fresh wonders the more we study it”. Incidentally, she is regarded as the first German woman poet.

Since metaphysics is the study of what exists, one might expect metaphysicians to have little to say about the limit case in which nothing exists. However, ever since the Greek philosopher of Elea in southern Italy (he is the founder of Eleaticism), Parmenides (*circa* 515- ), there has been rich commentary on whether an empty world { } is possible, and whether there are vacuums { }.

This brings us to the mystical concepts of nothing { } and nothingness {0}. *Ain* is ‘nothing’ { } in Hebrew. It is interesting to note that the school of Gerona in Catalonia, Spain was the first to establish and develop the doctrine of the *Ain Soph* (‘infinity’ in Hebrew), the ‘hidden God’.

To quote the *Zohar*, “Before having created any shape in the world, before having produced any form. *Ain* was alone, without form, resembling nothing { }. Who would comprehend *Ain* as It then was, before creation, since *Ain* had no form”.

According to the Qabala *Ain* is not a being, it is No-Thing – a complete void and vacuum { }. Not simply ‘nothing’, not even the existence of ‘nothing’ itself – but absolute, incomprehensible ‘*nothingness*’ {0} [?]. [This is clearly a conundrum – a riddle, an answer in the form of a play on words!]

In Chinese, *Tao* (‘the way’), “… resembles the emptiness of space { }. Tao is something beyond material existences”.

The Hindu sages mentioned ‘Infinite Essential Space’. They considered ‘empty’ space { } as a Reality that could not be thought away even by the use of the most powerful imagination. Nevertheless, their conception of space was not that of immense, infinite Nothing { }. The Hindu sages abhor ideas of Nothing { }, and will not admit that Anything (i.e., for example, {0, 1, 2, 3, …}) can proceed from Nothing { } – instead, their idea of Essential Space was that of an Actual Reality {0} – an Absolute Substantial Reality from which all things were manifestations, emanations, expressions, or thought forms.

The Hindu sages thought of Infinite Essential Space as a ‘No-thing’ (in this case meaning {0}), but not as ‘Nothing’ { }. To them Space was not only ‘an infinite capacity for extending objects’, which is the physical aspect of it – but something more – an Infinite Bare Abstract Subjectivity, which the human mind was compelled to admit in all of its conceptions, and yet was unable to think of as ‘in-itself’.

Buddha (Siddhartha Gautama, *circa* 4^{th} – 6^{th} century BCE) taught that the Fundamental Reality, in its Essence, was equivalent to Non-Being, when contrasted with Being as the human mind understands the latter term.

Non-Being {0} is not Non-Existence { }, but rather Existence in a state devoid of attributes, qualities, or activities, as far as manifestation is concerned {0, 1, 2, …}, although all possible manifestation must be latent therein – in fact, the meaning of Non-Being may be stated as ‘Being, in Latency’.

The distinction is highly metaphysical (and even mathematical), but some of the Ancient Grecian philosophers, and those of the modern West, have recognised the distinction, and embodied it in their metaphysical systems; as for instance Hegel (1770-1831), who stated that, “Non-Being and Being are One”.

This conception of Non-being is also recognised by certain Hindu metaphysicians who postulated a *Para-Brahm*, or Supreme Brahm, or Essential Brahm, beyond the Brahman in its phase of the Active cause of the Universe.

Subsequently, Western philosophers have thought that the Hindu metaphysicians taught that ‘All is Nothing’ { }, but the ‘No-Thingness’ {0} of the Hindu philosophers is very far removed from the ‘Nothingness’ (in this case { } [?]) of the Western mind.

In 1973, the English mathematician John Horton Conway (1937- ) picked up where Frege left off by beginning with nothing, the null set, and creating from it not only the natural numbers, the fractions, and irrational numbers, but also some heretofore unknown kinds of numbers, called *surreal numbers*. For Conway, { }:{ } is zero. That is, in Conway’s theory, as in Frege’s, nothingness {0} is the most primitive realisation of nothing { }.

Conway identifies the number one (1) as the number whose left set contains zero, i.e. {0}, and whose right set is the null set, i.e. { }. Thus, at this point in Conway’s genesis, the number one (1) is flanked to the left by nothingness and to the right by nothing. To the left is potential already realised (as zero), and to the right is potential not yet realised.

* *

In conclusion: *Nothing* { } is the mathematical null set, it is emptiness, the Chinese Tao, a vacuum, a mental void, the Biblical account of divine creation, and the No-Thing of the Qabala.

Furthermore, *Nothingness is not nothing, but is actually something*. *Nothingness* {0}, in contrast to nothing, is the mathematical set with zero (0) as its only member, thinking consciously, and it is equivalent to the Hindu concept of No-Thing.

Therefore, the Biblical account (the Judaic tradition) of divine creation, and the No-Thing of the Hebrew and Hermetic Qabala { } differ from the Hindu concept of No-Thing {0}.

**“In thirty-two mysterious paths of wisdom did the Lord write, the Lord of Hosts, the God of Israel, the Living Elohim, and King of the Universe, the Almighty, Merciful, and Gracious God; He is great and exalted and eternally dwelling in the Height, His name is Holy, He is exalted and holy. **__He created His Universe by the three forms of expression; Numbers [information], Letters [vibration], and words [sound]__.” (*The Book of Formation or Sepher Yetzirah*, attributed to Rabbi Akiba Ben Joseph, translated by Knut Stenring in 1923. 2004. Berwick, ME: Nicolas-Hays)

To me personally, the Hindu concept is ‘intellectually’ more satisfying because it conforms with my idea that *Ain* created everything in the manifested universe out of Its own ‘being’ {0} and not from nothing { }.

What will we ever do without mathematical logic as the unambiguous language to simplify complex ideas?