Nothing

What is nothing? Is it a something? Can there even be nothing?

Motivation

Nothingness is and has long been a subject in philosophy, mathematics, theology, and science, perhaps due to people asking questions like these:

Then there’s the mystical and metaphysical musings on one’s own non-existence. Physiologically, that might actually be hard to imagine. What do you think?

Nothing ... has been a subject of enduring fascination for millenia. Philosophers struggled to grasp it, while mystics dreamed they could imagine it; scientists strove to create it; astronomers searched in vain to locate it; logicians were repelled by it, yet theologians yearned to conjure everything from it; and mathematicians succeeded. — John D. Barrow

Sources

Books and articles:

Nothing in Philosophy, Theology, and Literature

Please start with the SEP article.

Okay, now that you’ve read that article, here is a little summary of some of the philosophical musings of nothingness throughout recorded history (and yeah, I know that a lot of stuff is missing).

Exercise: Who was Thales and when did he live? What did Aristotle say about him? What did Russell say about him? What did Thales think about the nothingness?

Why is there something instead of nothing? A lot of people hate that question. Can you prove nothing exists? Can you prove something does exist, without appealing to the existence of things that existed before? If you emptied everything from the universe (multiverse), would the number five still exist? Or do we talk only of concrete things existing? What is concrete? Is positing the existence of a creator acceptable? Does that make the explanation simple? Why do we care so much about simple explanations?

Nothing in Mathematics and Logic

Zero

Some cultures never invented the symbol-for-no-quantity. But once it was invented, there was no stopping it. Humans have perhaps thousands of different languages, but we all (okay nearly all) share the Hindu-Arabic numerals.

Why might zero be difficult? Work through the following.

  1. Empty your mind of all preconceptions of numerals.
  2. Now how would you repsent oneness? twoness?, threeness? And so on? Simple marke? Matching?
  3. Work your way up a bit, say to seven or so. Now “count down.” What happens before “one”? No marks? No quantity? Not a number?
  4. Are simple marks getting tedious?
  5. Let’s look at hieroglyphic numbers now.

    hieroglyphicnumerals.jpg

    (Note how they can be written in any order.)
  6. What did the Romans do? Kind of weird, huh?
  7. The Bablyonians and Mayans had zeros, in a way (you can look those up on line or in Barrow’s book.)
  8. The place-value system, with the wonderful zero we know today, came from India, and spread to China, Arabia, then to the rest of the world. Note how brilliant this was!
    • They started with counting boards, but note that in principle these boards could be as big as necessary! You can keep adding new places.
    • Instead of one mark per stone in the place, they invented symbols to stand for 1 through 9 marks.
    • When a particular place was empty, they used a symbol. But they also connected this symbol to various concepts of nothingness.
  9. Is there a future to this? What about infinities? What about the NaN in many programming languages?
    Exercise: What does NaN stand for? (Hint: see Wikipedia)
    Exercise: In your web browser, find the Developer Tools or JavaScript Console and evaluate the expression typeof NaN. Why is this interesting?
  10. Finally, reflect on this story:
    When I was a kid I was told “The Hindus invented the zero.” I remember wondering what they really invented. What do you mean “invent the zero?” I decided that what they invented was the round symbol we use for zero. Many years later a kindergarten girl appropriately called Dawn taught me to understand what those Hindus really invented.

    Dawn was working (or playing...I don’t see much difference between these things when they are done well) at a computer using a version of Logo that allowed her to control the speed of moving screen objects by typing commands like SETSPEED 100, which would make them go very fast, or SETSPEED 10, which would make them go much slower. She had investigated some speeds that seemed significant, like 55, and then turned to very slow speeds, like 5 and 1.

    Suddenly she became very excited and called over first a friend and then a teacher to show something interesting. I happened to be visiting the class and shared the teachers initial puzzlement: we couldn’t see what Dawn was so excited about. Nothing was happening on her screen.

    Slowly it dawned on me that the point was that Nothing (with a big N) was happening. She had typed SETSPEED 0 and the moving object stopped. She was trying to tell us, but didn’t have the language to do so easily, that those objects that were “standing still” were still “moving,” they were moving with speed zero. She was excited about discovering that zero is also a number, speed zero is also a speed, distance zero is also a distance and so on. Up to that point zero for her was a non-number. A nothing. All, of a sudden it had joined the family of numbers. — Seymour Papert The Wonderful Discovery of Nothing

∀ and ∃ in Dualistic Bivalent Logic

The early Greeks may not have had a zero, but they could at least reason about nothing. They could derive it from notions of some, all, and not, Note that “some” is the same as “at least one.”

They could negate sentences. The negation of “All apples are red” can be written as:

and the negation of “Some apples are red” can be written as:

Symbolically, we use ∃ to mean “there exists” or “some” and use ∀ to mean “for all” and ~ to mean “not.” So if we represent the statement “apples are green” as A, then you should be able to guess what ∀A and ∃A mean. For an aribrary statement P, it seems

or are they the same? Because if we buy this, then the statement “All of my cats weigh 3 billion tons” is true because I don’t have any cats.

Exercise: What do you think of that?

Construction of Numbers from the Empty Set

In Set Theory, a set is a container of things, for example {Yakko, Wakko, Dot}. The container of no things is written like this:

{}

This is called the empty set. It can also be written as ∅. Since the empty set is a thing, it can be put in a set: 

{{}}

The standard construction of the natural numbers goes like this:

0 = {}
1 = {0} = {{}}
2 = {0, 1} = {0, {0}} = {{}, {{}}}
3 = {0, 1, 2} = {0, {0}, {0, {0}}} ={{}, {{}}, {{}, {{}}}}

and so on. Something from nothing, indeed.

Exercise: Or is it?

Some Kōans

Nothing Exists

Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.

Desiring to show his attainment, he said: “The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no relaization, no delusion, no sage, no mediocrity. There is no giving and nothing to be received.”

Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.

“If nothing exists,” inquired Dokuon, “where did this anger come from?”

Basho’s Staff

Basho said to his disciple: “When you have a staff, I will give it to you. If you have no staff, I will take it away from you.”

Joshu’s Zen

Joshu began the study of Zen when he was sixty years old and continued until he was eighty, when he realized Zen.

He taught from the age of eighty until he was one hundred and twenty.

A student once asked him: “If I haven't anything in my mind, what shall I do?”

Joshu replied: “Throw it out.”

“But if I haven't anything, how can I throw it out?” continued the questioner.

“Well,” said Joshu, “then carry it out.”

No Water, No Moon

When the nun Chiyono studied Zen under Bukko of Engaku she was unable to attain the fruits of meditation for a long time. At last one moonlit night she was carrying water in an old pail bound with bamboo. The bamboo broke and the bottom fell out of the pail, and at that moment Chiyono was set free!

In commemoration, she wrote a poem:

In this way and that I tried to save the old pail
Since the bamboo strip was weakening and about to break
Until at last the bottom fell out.
No more water in the pail!
No more moon in the water!

Where to Meet After Death

Dogo paid a visit to his sick fellow monk, Ungan. “Where can I see you again if you die and leave only your corpse?” Dogo asked. “I will meet you where nothing dies,” Ungan replied. Dogo criticized his response saying, “What you should have said is that there is no place where nothing is born and nothing dies and that we need not see each other at all.”

It Is Not Things

A monk asked Nansen: “Is there a teaching no master ever preached before?”

Nansen said: “Yes, there is.”

“What is it?” asked the monk.

Nansen replied: “It is not mind, it is not Buddha, it is not things.”

Nothing in Science

The history of nothing, or the vacuum really, in science, includes the following:

Looking for a good explanation? Star Talk has an Explainer Video!

We now segue into cosmology and nothingness....

Nothing in Cosmology

Creation from Nothing

There’s a lot being made these days about why there’s so much stuff in the universe and what it actually came from. Here’s a intro video:

Interested in books? The books by Krauss and by Hawking and Mlodinow discuss the modern theory of the void and how the Universe can supposedly create itself. Here is the New York Times review of the Kraus’s book by David Albert. What do you think about it?

Exercise: Albert’s review generated its own chatter! Read about the spat from Jerry Coyne, NPR, and Sean Carroll.

A critic of Hawking is Robert Spitzer, S.J. Here’s Spitzer on “the curious metaphysics of Stephen Hawking”:

Note that Spitzer is trying to sell you his book!

Spitzer also has a film Cosmic Origins which shows some of his views of creation from nothing, among other things. You might be interested in the clip from the movie dealing with nothingness.

Also, Spitzer appeared with Mlodinow and Hawking on Larry King Live.

One more Closer To Truth:

Hahaha Kuhn pitches his book in that one.

Nothing in Computer Science

Nearly every modern programming language has a something standing in for nothing. Consider this line of JavaScript code:

supervisor = "Alice";

This says that someone’s supervisor is named Alice. But what about: 

supervisor = "None";

That means the supervisor’s name is None. An odd name perhaps, but it is still a name. But what if you know for a fact there is no supervisor at all. JavaScript has the special keyword null for this: 

supervisor = null;

This models the scenario where you know for certain that no supervisor exists. Incidentally, JavaScript goes further than a few other languages in having a keyword representing the absence of knowledge: 

supervisor = undefined;

This line of code says that we either don’t know whether there is a supervisor or not, or perhaps that we may know but do not wish to tell.

Nothing in Art and Design

The concepts of figure and ground are well known in art and even music.

The ground, or whitespace, or the so-called nothingness between design elements is indeed a design element. For an understanding of this nothing as something as pertaining to design, read David Kadavy’s 1 + 1 = 3 article.