What sort of philosophy asserts the speculative identity of zero and infinity?

Question

I know math tells a different story, but it occurred to me that if zero were equal to infinity, than nothing would be equal to everything and that would explain how the universe and everything came to be.

I drew the relationship of the two through the existence of real randomness. My very sketchy understanding is that Quantum mechanics, which seems pretty accepted, depends on the existence of randomness. Furthermore, I find that if something can be random, than it can be anything. I don't even see way it can't be two things at once, or perhaps an infinite number of things; I digress. So, the thing can be both zero and infinity. In this sense they are equal.

Is there any significance to my hypothesis? If so, do you know of any ideas, writings, teachings or anything else that could help me understand or discover more? If this is just baseless and absurd, I think understanding why that is would be just as enlightening.

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Full disclosure, I have no academic experience with philosophy. All I'm really looking for is to be pointed in the right direction. The closest sounding thing I have heard of is Buddhism, but please, no offense if that is incorrect, I'm not a Buddhist and know very little about it other than that some of the smartest and most exuberant individuals I have meet are Buddhist.

Update

Thank you all for the enlightening answers and comments. Much of the feedback has helped me see a few place where I should have been more clear. A better title would have been "Any philosophy that states nothing is equal to everything?" (It's becoming apparent that there are.)

My use of the word infinity was only intended to be taken literally in the context proposed in my question. In retrospect, I can more clearly see the point was to show a physical example in which the two, when interpreted in their literal forms, are logically the same.

I used numbers and context to reason that the two can be equal, and I hypothesize that this is how everything came to be. I am seeking knowledge that will help confirm or dismiss this conclusion. It was not my intention to dispute the semantics of infinity. In terms of the question, infinity means what it means, but such details are only relevant when applied directly to the context of the reasoning.

Another interesting side note. I discussed this idea with a friend last night and his response was, "Welcome to Taoism". A quick google search revealed that Buddhism is based in Taoism, so definitely something I plan to find out more about.

Answer 1

There are a number of things which are problematic with identifying infinity with zero, with entertaining the idea that they are equal.

The first you should ask what you really mean by equality. How serious are you about the idea that "zero" and "infinity" refer to the same concept? How many Bengal tigers are there, for instance, in your immediate vicinity — none, or infinitely many? (If there happen to be one or two, would you expect there to be infinitely many of them if those two went away?) I would suspect that there being zero Bengal tigers nearby to you would appear very differently to you than there being infinitely many. This gets to the heart of what mathematics is actually for: it's for describing features of the world that you see around you — and for being able to express different ways that the world could be, which you could distinguish from one another if you wished to. If it were somehow "really the case" that zero and infinity were equal — that is, if this somehow were a deep meaningful feature of the world — why are we not being constantly assaulted by (or at least crushed to death under the weight of) infinitely many Bengal tigers?

A better response might be to say that "zero" is not the same as "infinity" on the level of tigers or birds, but only for other physical phenomena, such as matter in the universe. (This would already indicate that the two concepts of zero and infinity are meaningfully different, and that what we're talking about is not mathematics, but physics proper.) Perhaps it is only a meaningful way of describing things on the quantum mechanical level. But here it is no better: why are there not infinitely massive balls of neutrons and protons and electrons popping out of vaccuum — not just a handful with some probability, but infinitely many, all the time, because "nothing is the same as everything"? Sure, it would crush the universe to a tiny speck under the instantaneous emergence of black holes all over the place; but this just gives us a way to see that it isn't happening, not of explaining why it doesn't if somehow "zero" equals "infinity". The problem is that even if you restrict yourself to "the quantum mechanical scale", saying that "zero equals infinity" doesn't allow you to describe features of the physical world with enough precision to explain why at any moment we aren't consumed by black holes.

Note that the statement "on a quantum mechanical scale" is itself a vague statement. Most physicists believe that matter behaves according to quantum mechanics at all scales, it's just that for objects which are large and rigid enough, we can use less complicated models of physics such as Newtonian mechanics to describe what's going on. So even saying "on a quantum mechanical scale" is insufficient to save us from an infinite avalanche of bengal tigers. If we want to put teeth into a statement such as this, we need something subtler than equality; we need actual numbers and differences, to describe differences in size and in probability.

This is another problem which is touched on by your question. Quantum mechanics does indeed depend on "randomness"; but randomness is not the same as "anything can happen". For instance, a dice roll is random: but would you expect to roll a seven on a single die, because it is random? More precisely, not everything that can happen will actually happen: if you rolled the die a thousand times and only rolled sixes and twos, wouldn't you come to suspect something was wrong? But certainly it's possible. The problem with the die which rolls only sixes and twos is that it violates your expectations, which is a way of observing that there are limits and averages which you can expect from the die. Similarly, although quantum mechanics is random — and also to our macroscopically-honed expectations, strange — this does not mean that it's a free-for-all of strangeness at all times. The very fact that we have a theory of quantum mechanics that works at all, indicates that it has regularity and predictability about it; it only has less predictability than a deterministic theory of physics in which we can finely control the initial conditions of the system.

So what could it mean for "zero" to be the same as "infinity"? Well: all numbers — including simple ones, such as 1, 2, 3 — are just ideas, and they can mean different things in different contexts. When you roll a die, the number 6 doesn't mean anything, although you might give that number signifcance by doing something specific. In the game of craps in which you roll a pair of dice, 7 and 11 are good rolls and 2, 3, 12 are bad ones; but that does not mean that somehow 7 = 11 or that 2 = 3 = 12 in any deeper sense. These are just human games, of course; but numbers are human ideas with which we try to grasp the world with acuity. The roles of any numbers in a physical theory do not arise from the numbers themselves, but from their interpretation as referring to magnitudes of physical qualities which interact with one another.

So the only way to assess whether or not zero is "equal to" infinity in some physical theory is to see whether the two concepts are effectively the same in that theory, at least for the main quantities of interest. For the physical theories that I know of, the answer is a resounding no. This does not mean that there could not be another, very useful theory in which some quantity such as mass or time somehow might be meaningfully interpreted in such a way that zero equals infinity, but that will be a question of that model of physics, and not of reality itself. In the end, zero and infinity are the names of ideas, of metaphors that we use to grasp the world — they are the map and not the territory.

(If you want to ask about whether the lack of any existence is identical to everything existing at once, without reference to mathematics, that would be a separate question, but one for which I doubt that there is an interesting answer; I would say it is either "no" or "there's no way to find out", depending on what limitations you put on the multiply existing worlds.)

Answer 2

I recommend that you read "Zero: The Biography of a Dangerous Idea" by Charles Seife (Sep 1, 2000). It is for non-mathematicians but has information that even some of my math major friends didn't know. Infinity is a major topic in the book, including its relationship to zero.

Answer 3

Interpreting infinity=0 mathematically is problematic for reasons that Niel de Beaudrap outlined. However we need not interpret those symbols mathematically, but rely on other interpretations. As you have specifically mentioned Buddhism I'll angle my interpretation in that way.

First of all, are we allowed to interpret these mathematical symbols non-mathematically? Given that mathematics imports ordinary language into its own discourse, for example imaginary, boundary, manifold, imaginary, rational I don't see why the reverse should not be allowed.

To quote the answer from this question on Nagarjunas philosophy in Mahayana Buddhism: 'For Nāgārjuna, śūnyatā is definitely equivalent to niḥsvabhāva (the lack of svabhāva.) And yes, this means that both beings and Being had no essence. Furthermore, śūnyatā is itself empty; we can't reify śūnyatā into some kind of meta-essence. So: the essence of all things is that they are essenceless. That's the paradox we live in'.

As you asked 'the more I think the numbers are just a metaphor for something deeper', the question is then what is the referent of that metaphor.

Sūnyatā is derived from the sanskrit Sunya, which is used for zero. If we think of infinity as the totality of all beings, both real (cups, stars, atoms) and abstractions (numbers, ideas, ideologies); we can encapsulate the above quotation as you put it: infinity=zero. That is, all beings, including the totality of all beings have no essence.

Also that 0=infinity, on the face of it is a contradiction, a paradox - and that can allude to the paradoxical illuminations of Nagarjunas thinking.

Given that people give you weird looks when you say this, might be likened to stating a Zen Koan such as 'what is the sound of one hand clapping', which is meant to be provocative and disruptive, to force people out of their normal habits of thinking. Of course people hearing this either are confused, dismiss it as a grammatical game, or airily & knowingly dismiss it as a Koan - which is simply an acknowledgement rather than perhaps illumination. Perhaps, to retain its disruptive element one needs to translate it into an unfamiliar language that recalls its deeply paradoxical nature.

Having said all this, I would hesitate to use this is as some kind of mantra, essentially because mathematics as a subject is far removed from buddhist philosophy, and the similarities are superficial. If anything, that we frame this thinking in these terms, shows perhaps how mathematics is pervasive in anglo-american philosophical discourse and the technocratic aspects of its civilisation. When we think of nothing, we think of zero; when we think of infinity, we think of the mathematical conceptions (for the mathematically trained Cantors infinities, or a one-point or two point compaction), for those not so highly trained (1,2,3,..).

Although to me, 1=infinity, sounds poetic; it's partly because of my mathematical training - in fact it is not. Poetry should use language in its ordinary sense, as its only then evocative and resonant - there's a good reason why poets do not use scientific/mathematical vocabulary (to be precise they use it sparingly). Further, truths such as these should not be dependent on such training and should be taken for themselves in the tradition that they come from. To not do so, is perhaps to distort and pay less than the respect that thought deserves. (Also, it may also stop you from grappling with the Buddhist philosophical tradition itself, if thats where your interest lies).

I'd recommend instead reading about Nagarjuna, the Diamond Sutra or Vajra, rather than coming up with hermetic readings, even when its entertaining...

(As an aside, it might also be worth looking at the sufi mystical tradition in Islam, Al-Hallaj famously said 'Ana Al-Haq' and was executed for it. Al-Haq is one of the ninety nine names of The-One (Al-Lah). In the orthodox Sunni tradition of Islam 'that what is created and the creator' are irrevocably distinct and incomparable. However Al-Hallaj was said to have negated his Nafs=ego, soul & self, to have discovered illumination, to have found that his soul and the realm of the divine is one - which is Al-Haq. If all things are essenceless, are your self & that divine realm not the same, or partake of it?

But then one should not conflate different traditions, even when one can and should. As it says in chapter 8 of the Diamond Sutra 'And yet, even as I speak, Subhuti, I must take back my words as soon as they are uttered, for there are no Buddhas and there are no teachings').

Answer 4

I am not a philosopher. I am a physics major who enjoys philosophy. With that said...

It is an interesting thought indeed. One thing with your hypothesis is that infinity itself is not a number in the traditional sense. In fact, mathematicians don't even acknowledge it as a number at all but rather, an idea. So to say something is the same as infinity doesn't mean very much. (it is the same as saying 0 = "The biggest number you can think of plus more")

Quantum mechanics is a remarkable discovery as well because you do see behavior similar to what you are talking about in that light is both a wave but also a particle; that electrons can occupy a superposition of quantum states at a given time simultaneously. This is the basis on how quantum computers are to work, instead of having 1 or 0s, the quantum nature of electrons opens up the possibility of a gamut of values between [0,1] and both 1 and 0 at the same time.

The type of thinking you are proposing is not terribly absurd, although the idea that "something" = "Nothing" might be a difficult prospect to build off of, for if everything is nothing then the universe has a sort of "zero dimension" to it instead of being able to take on any number of values between the two polarities.

Answer 5

Umm...From my understanding to your question, I can say that you may want to justify this sentence "Coming from nothing to everything is possible", right?!

If that's the matter;

First, the respective users talked about the equility of zero and infinity, as "Niel de Beaudrap" did in the first paragraph of his answer.

Second, in mathematics, the randomness does not have the same meaning of the public one. In mathematics, the randomness may mean "Lack of pattern or predictability". For example: when you look to a waterfall from a distance of about 10 meters, you see water drops are going in random directions and then fall in random places... But, when you use the slow-motion cameras and zoom to those drops, you see that every drop separates when the energy becomes enough to separate the water in a specific mass and time. At the same time, the surface-tension (and other bonding forces of the water) can't hold that mass to it => the result: a drop of water had separated, has an energy equals to {the separator energy - losses}, has a mass of m value, separated at time xx:xx:xx of the day x at the year xxxx, it separated from the coordinates x,y,z heading to the coordinates x',y',z' ... and many other properties... So, actually, there is no randomness, but, there is a very complex event to be predicted, or the knowledge is insufficient to predict it!

The most important part comes here, Question: Why did that drop happened to separate? Answer: because of the irresistible energy. Question: From where did that energy come? Answer: The water hit the rock. Question: Why did the water hit the rock? Answer: Because of gravity. Question: Why did the gravity make that effect? Answer: Because the water came into two places different in elevations, the second one is lower than the first one... and so on, until you reach a this Question: Why the matter exist having those potentials to acts in this very unique way? Answer: There must be a higher forces which is out this system, and is capable of making this system and add/remove from this system, and this force is called "God". There is a prolonged speech about the God, you may want to go through later.

Final conclusion: as the other says, "zero = infinity" is a problematic equation. Also, there is no real randomness, but, a "real inability" does exist.

Answer 6

Yes, there is at least one philosophical idea that addresses the uniqueness of Existence, infinity coming out from one (see e.g. the initial part of this answer), yet not zero albeit but we will reach to that point as well in what follows. A try to better understand the previous notion can be assumed as the proof given in this question, a thing is coming from nothing and then that nothing would evolve into infinity through spawning and causality for example.

However, let discuss things differently. Hypothetically assume a world of a specific living species confined to a one-dimensional curve as their universe. Those living beings move and live but only inside that 1D curve. Now assume a two-dimensional surface containing that curve, with inhabitants being confined inside that surface. Suppose the specified curve inside that surface is such curved that its two ends are somewhat close to each other in the view of the residents of the 2D world. A resident of the curve decides to travel from an end of the curve to the other side of the curve, it should travel the total length of the curve, but if it could just come out of the curve and travel inside the surface its travel was far shorter. Now embed the 2D surface inside a 3D volume and assume the surface to be such curved inside the volume that every point over the surface be more easily and faster accessible from within the volume compared to from within the surface itself. Extrapolate this idea to higher dimensions and in the limit you will have an infinite-dimensional hypersurface. If the material world contained in such an infinite dimensional universe is finite then the residents of the infinite-dimensional hyper-surface can simultaneously access to every points in all the contained lower (finite) dimensional universes, like the universe is zero-dimensional. So that you have a finite universe (comprised of infinitely many points) being confined into a zero-size infinitely dimensional universe. Infinity is now inside a zero. Tic,his is not a magic indeed, it actually make use of the notion of the space-filling curves and an extension of such a concept (the curve being enough curved inside the surface, the surface being enough curved inside the volume and etc).

Answer 7

Yes I really like what you had to say. I think your answer is in Pythagoreanism

"The Pythagoreans, held that the void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature."

"Instead of an undifferentiated whole we have a living whole of inter-connected parts separated by "void" between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using maths, but truly mathematical since it shows numbers and reality to be upheld by the same principle. Both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos — both are a play of emptiness and form, apeiron and peiron. "

-- http://en.wikipedia.org/wiki/Pythagoreanism

Answer 8

I'm not going to pretend I read everything here because alot (i.e. 90%) of it was over my head and it seems to me that most of you placed a value for both 0 and infinity, a qualifier to make it 'of' something, though that could just be my ignorance.

Lets try it this way.

Infinity equals 'everything', all that is, is not, can, cannot, all devoid of limitation and boundary. This is an interpretation that is simplified bad I am trying the reresent it as devoid of individual qualifiers as possible.

Zero equals the absence of anything and everything. The infinite would there-by, in my view 'everything' include the actuality of absolute nothingness which is conceptually impossible for us to fathom. Absolute nothing would have to be devoid of boundary and limit as it would then be definable by the abscence of what it is in contrast to that which we would define it by. The concept of nothing is not the same as absolute nothingness because as we define it it becomes something, or rather a void of something as opposed to the non-exsistence of 'everything'.

Thus, by how I like to define it, Zero and Infinity appear to be equal in that one only exists in the abscence of the other while coexisting in the same 'place' even if you say 'nothing does not exist'. This appears as a paradox to us because we cannot actually understand true nothingness as we are 'something' and we need to define infinity as having a point of origin which would render it finite. The problem of the question, as I propose it, is not the answer but the actual limitations of the asker. We are limited in that we have define most things, boiled down to it's simplest form, as a linear projection between two points.

That is just my take on it and if could just be drivel or I missed the point... Or both.

Answer 9

Contrary to what some may think, mathematicians don't sit around cooking up bizarre axioms: "Gosh, Siegfried, what if we let zero equal infinity and go around in great big loop?"

The axioms that fully describe the natural numbers, the Peano Axioms, have not changed substantially changed in 126 years. Where did they come from? Many of the properties of the natural numbers were established long before these axioms were conceived. There was a sense, however, that there might be a short list of properties from which all others might be derived. The Peano Axioms (today reduced to a mere 5 essential properties) were just such a list. So successful have they been as a basis for number theory and analysis that, for all practical purposes, they have come to define the natural numbers. (See the posting, "What is a number again?" January 22, 2014 at my math blog.)