Nothing is smaller than a Planck length. When I say this, I mean: There is no such thing that is smaller than ℓP. Notice, however, that the same sentence could be misunderstood as having the exact opposite meaning: There is such a thing, called nothing, that is smaller than ℓP. Similarly, if I say: ‘Nothing is better than spaghetti alle vongole’, I mean that I like it a lot. But the opposite reading would mean that I hate it, and that I would rather eat nothing, i.e. not eat.
As obvious as this is, there is an astonishing amount of confusion about the use of the word ‘nothing’. The muddle goes back to Zeno’s teacher (and, according to Plato, his lover – which sheds a different light on his leaving the scene at the Dichotomy paradox): Parmenides. To be fair, the only thing Parmenides wrote is an allegorical poem, On Nature, of which we only have 160 lines, as reported in a few fragments by later writers. But, as these were purposeful selections, there is little chance that the rest was any clearer. Parmenides drew a stark distinction between the way of Truth (Aletheia), which he defined, in no uncertain but awkwardly convoluted terms, as ‘the way that it is and cannot not be‘, and the way of Appearance (Doxa), defined as ‘the way that it is not and that it must not be‘ (Fragment 3). According to Parmenides, the second is a no-go area: ‘There is no such thing as nothing’ (Fragment 5). The only way is the first:
Now only the one tale remains
Of the way that it is. On this way there are very many signs
Indicating that what-is is unborn and imperishable,
Entire, alone of its kind, unshaken, and complete.
It was not once nor it will be, since it is now, all together,
Single and continuous. (Fragment 8).
This is Einstein’s and Weyl’s block universe, which ‘simply is’, and where ‘the distinction between past, present and future is only a stubbornly persistent illusion’ (in conversation with Einstein, Karl Popper called him “Parmenides”. The Unended Quest, p. 129). It is a timeless world, governed by the Principle of Sufficient Reason, which Parmenides expressed in his own way, well before Spinoza and Leibniz:
For what birth could you seek for it?
How and from what did it grow? Neither will I allow you to say
Or to think that it grew from what-is-not, for that it is not
Cannot be spoken or thought. (Fragment 8).
Everything has a cause. Hence it is impossible to think that anything can come from what is not. As Lucretius would later put in De Rerum Natura: Nihil igitur fieri de nihilo posse (Book I, 205), which is commonly abbreviated as Ex nihilo nihil fit: Nothing comes from nothing. How could it be otherwise? There is no such thing as nothing.
Here is where the muddle starts. Let’s assume for a moment that the Principle of Sufficient Reason is right: what-is cannot come from what-is-not. Does that mean that what-is-not cannot even be spoken or thought about? Clearly not, as indeed Parmenides himself shows by repeatedly referring to it. We can speak and think of what-is-not, i.e. nothing, as a name for the absence of something. ‘There is nothing on the table’ does not mean that there is a thing, called nothing, that is lying on the table. It means the opposite: the table is bare, there is no thing lying on it.
The ancient Greeks were aware of the confusion. When Ulysses told Polyphemus that his name was Nobody (Outis) and proceeded to blind him, the giant called for help. But when his fellow Cyclopes asked him what was happening, they were mystified by his answer: Nobody is trying to kill me (Odyssey, Book 9). Somehow, however, Homer’s descendants never managed to dissolve the puzzle: how can nothing be something? Amazingly, therefore, they had no sign and no use for the concept of zero, until they later imported it from the East. Zero is The Nothing That Is. But it is not something: it is just a sign that we use to indicate that something is not. As such, not only we can speak and think about it, but we can also observe it. It is what we call negative evidence, or absence of evidence. Look: there is nothing on the table, no thing, zero things. And there is no green rhino – zero rhinos – under the carpet. This is not positive evidence about the presence of something. It is negative evidence about its absence. So it does not presuppose the existence of the absent thing: green rhinos do not exist, nor their existence is implied in the sentence.
Speaking and thinking of what-is-not does not imply that it is. Somehow Parmenides was confused about this and, as per Boileau’s rule, expressed it obscurely:
For the same thing both can be thought and can be (Fragment 4).
It must be that what can be spoken and thought is, for it is there for being (Fragment 5).
By thinking gaze unshaken on things which, though absent, are present,
For thinking will not sever what-is from clinging to what-is (Fragment 6).
What? Surely he did not mean that whatever we can speak and think of must exist – wouldn’t that be wonderful? What he meant was that it is impossible to think that things are not. What-is has always been and will always be. Ex nihilo nihil fit. Nothing cannot be something, or, more precisely, nothing cannot become something. It is, as we have seen, another way to state the Principle of Sufficient Reason.
For the same reason, Parmenides thought that something could not become nothing:
Nor ever will the power of trust allow that from what-is
It becomes something other than itself (Fragment 8).
As Lucretius put it: Haud igitur redit ad nihilum res ulla (Book I, 248). It is the same reason on which Zeno built his paradoxes. Which, as we have seen, are paradoxes precisely because, in reality, something can become nothing: nothing is smaller than a Planck length.
Parmenides was right: there is no such thing as nothing. More precisely, there is no such thing as nothingness – a place or a state in which phenomena are before they appear into existence. But then he went astray, insisting that what-is-not cannot even be thought about, and that there are no phenomena, no creation, no extinction and no change. What-is is an eternal, immutable one, ‘like the body of a well-rounded sphere’ (Fragment 8). In such a world, everything has a reason and could not be otherwise: there is no such thing as chance.
That is as crazy a world as that of Zeno’s paradoxes. In the real world, we can and do think of possibilities: what-is-not but could be. What-is was not bound to be. It is an event that happened, with some probability: one of several possibilities. Events are nothing before they happen and turn into nothing after they cease to exist. They do not appear from nothingness: they be-come from nothing – nothing at all.