Read addendum at the end of this blog entry.
Although we experience it “all the time”, we all know that ours will eventually be up. It has one direction and it is finite. It is the aspect of our reality which escapes us the most: “Time.”
We have expressions such as time flies, runs or flows. Sometimes we use the image of an hourglass of running sand (a “sand clock“) which we, like time, can’t seize; it escapes us between the grasp of our fingers and mind. This has made the hourglass an enduring symbol of time itself. Sometimes with the addition of symbolic wings, it is depicted as a symbol that human existence is ephemeral, and that the "sands of time" will eventually run out.
So what is “Time”? Why can’t we, it seems, seize it even in its smallest part we know: the “Present” like grains of sand slipping through our "mind's fingers" ?
Is "Time" a reality or an ilusion? Can it be understood objectively or perceived only subjectively ? If both are true, could there be any connection between our personal Time as lived and the physicists' Time?
A flower, a skull and an hourglass symbols for Life, Death and Time
(17th-century painting by Philippe de Champaigne).
"The clock is running. Make the most of today. Time waits for no man. Yesterday is history. Tomorrow is a mystery. Today is a gift. That's why it is called the present."
In "Sun Dials and Roses of Yesterday: Garden Delights..." (1902) by Alice Morse Earle (1851-1911).
"Time" as a personal (subjective) experience
Let's start our exploration with philosopher Sascha Norris on the "personal Time" as we live and experience it.
She writes :
“The capacity for living in the present has almost become a lost art.This text from Sascha Norris hit me like an arrow.
But, we were born to live in the present. We are biologically programmed to live in the now. Thus, we cannot ever truly lose the ability to do so. It is only our own subconscious mind, as well as our past 'conditioning' that prevents us from doing so. This is why we must be willing to struggle for it. We must be willing to fight to make our present a thing of beauty. Each day will not stand the chance of becoming a masterpiece it can be if we do not approach it with a single-minded determination to make the most of it we can. And we can only do this by letting go of both the known behind us and the unknown before us. Only then will we be fully capable of surrendering to the sacred present.”
From Living in the Present, by Sascha Norris, Philosophy Editor at BellaOnline's, 05 September 2013.
In our busy lives, does this “present moment” really exist; does it have some “space” in and for itself, not just lost between two overwhelming yet unreal concepts such as "past" and "future"?
Do we “take the time” for this moment called “present? If real, how long does it last? Does it last just an “instant” like a “zero-point” intersection between the lines of past and future or does it last "longer"?
As an artist, I do sometimes experience this “moment” when I am fully involved creatively in one of my paintings, even when writing this. Then I am losing all notion of a “running time.”Paradoxically I feel closer to my “being” than who I was or will be. Maybe this is what the “lost art of living in the present” means.
Her arrow triggered in me a flow of apparently disconnected ideas, ranging from human psychology, to philosophy, art and science…
So, here we are: what is this “present”?
Sascha Norris wrote:
“Eckhart Tolle, often dismissed by 'serious' philosophers as merely another New Age guru, did make a valid point in his best-selling book, “The Power of Now.” It is essential to our spiritual well-being (as well as, in my opinion, our physical and psychological well-being) to live in the present.”
From Living in the Present, by Sascha Norris, Philosophy Editor at BellaOnline's, 05 September 2013.
I agree with her that Eckhart Tolle the author of “The Power of Now” (PON, 1997), made a strong and valid point for rehabilitating the “present moment” he calls “Now”. He often says:
“Realize deeply that the present moment is all you ever have. Make the Now the primary focus of your life.” (PON, p. 27)We all experience this special time when we relax after a hard busy day’s work, focusing on ourselves only, and distancing ourselves from our past and our future commitments, all our problems in life.
But Eckhart Tolle goes much further than this: he says that in order to find eternal happiness, joy and tranquillity (“Enlightenment”) we should forget everything, forget our past, our future, forget about our life and we should stop thinking, stop using your mind which creates, hew says, this illusion called “time” and should start “feeling” the Now instead. Nothing is real he claims except this “moment”, this Now or “eternal present” so says he without any evidence or demonstration which require the use of this banned “mind”! So this “Now” is wrapped in pure Mystery which Tolle, the self-appointed spiritual teacher, is to unveil us to.
Eckart Tolle: Rejection of Time
“I have little use for the past and rarely think about it; however, I would briefly like to tell you how I came to be a spiritual teacher and how this book came into existence. Until my thirtieth year, I lived in a state of almost continuous anxiety interspersed with periods of suicidal depression.” (PON, p. 8)
Behind his apparent intention to teach us how to live a happier life, self-appointed “spiritual teacher” Eckart Tolle casts a very bleak and pessimistic outlook on our society. He says:
“You will not have any doubt that psychological time is a mental disease if you look at its collective manifestations. They occur, for example, in the form of ideologies such as communism, national socialism or any nationalism, or rigid religious belief systems, which operate under the implicit assumption that the highest good lies in the future and that therefore the end justifies the means.” (PON, p. 41) and “Humans are a dangerously insane and very sick species. That's not a judgment. It’s a fact.” (PON, p. 55)
He asks: “I don't mean to offend you personally, but do you not belong to the human race that has killed over 100 million members of their own species in the twentieth century alone?” (PON, p. 71)
To use the totalitarianisms, murderous regimes to “prove” that aspiring for, dreaming of a better future leads to genocides; millions of deaths is deeply dishonest. The same “mind” which Tolle rejects, has also improved our lives during that same century: many more people live freer with a better lifestyle and life expectancy. More people live. Fact. So Eckhart Tolle is deeply depressed and pessimistic yet as a “spiritual teacher” he aims at bringing joy in our lives….
Tolle elaborates with very basic “101 psychology”. But because of his “dark side”, he assumes that past cannot be full of happy memories, future never with hopes and positive dreams… He explains that all our pains and sufferings are due to our attachment to “time” (past and/or future) which he considers as pure fabrications of our mind, as unreal. He explains:
“The future is an imagined Now, a projection of the mind. When the future comes, it comes as the Now. When you think about the future, you do it now. Past and future obviously have no reality of their own. […] Their reality is "borrowed" from the Now.” (PON, p. 37)
He therefore advises us to stop thinking, stop using our mind and instead to start feeling the “Now”. He says: “Thinking has become a disease.” (TON, p. 16) or “Love, joy, and peace cannot flourish until you have freed yourself from mind dominance. “(TON, p. 23)
From Nothing to Nothing(-ness)
The implications are that he rejects all notion of changes through Time, be them progress or decay which he considers as “illusions”, as unreal. He says:
“Here is the key: End the delusion of time. Time and mind are inseparable. Remove time from the mind and it stops - unless you choose to use it. To be identified with your mind is to be trapped in time: the compulsion to live almost exclusively through memory and anticipation. This creates an endless preoccupation with past and future and an unwillingness to honor and acknowledge the resent moment and allow it to be. The compulsion arises because the past gives you an identity and the future holds the promise of salvation, of fulfillment in whatever form. Both are illusions. […] Time isn't precious at all, because it is an illusion. What you perceive as precious is not time but the one point that is out of time: the Now. That is precious indeed. The more you are focused on time - past and future - the more you miss the Now, the most precious thing there is. Why is it the most precious thing? Firstly, because it is the only thing. It's all there is. The eternal present is the space within which your whole life unfolds, the one factor that remains constant. Life is now. […] Nothing ever happened in the past; it happened in the Now. Nothing will ever happen in the future; it will happen in the Now. ” (PON, p. 36)
So, according to Eckhart Tolle, the “Now” is all there is. This statement is quite disconcerting for us who live in a civilization built on the notion of Time and History. But Tolle goes further: he says that this “Now” is the only “transcendental” reality, a sort of “portal” to eternity (eternal present), to God and to what he calls; the “Unmanifested – the One”, the “Source” which is the “nothingness” from which the Big Bang (and our Universe) emerged, i.e. From Nothing to Nothing (-ness)…
Tolle’s rejection of the reality of time (and space) leads to Nihilist philosophy (Nihilism).
Note: Nihil, from Latin means “nothing”.
“Every physical object or body has come out of nothing, is surrounded by nothing, and will eventually return to nothing.” (PON, p. 87) “Nothing could be without space, yet space is nothing. Before the universe came into being, before the "big bang" if you like, there wasn't a vast empty space waiting to be filled. There was no space, as there was no thing. There was only the Unmanifested - the One. When the One became "the ten thousand things," suddenly space seemed to be there and enabled the many to be. Where did it come from? Was it created by God to accommodate the universe? Of course not. Space is no-thing, so it was never created.“ (PON, p. 90)
So, if we follow him; space (which he claims wrongly to be “nothing”) came out of… nothing.
As King Lear said:
“Nothing will come of nothing: speak again.”William Shakespeare used this philosophical expression “Nothing comes from nothing” (Latin: ex nihilo nihil fit), a known thesis first argued by Parmenides, a “monist” ancient Greek philosopher. King Lear will end up depressed and insane.
Eckhart Tolle adds:
”Nothing (…) cannot become an object of knowledge. You can't do a Ph.D. on "nothing." When scientists study space, they usually make it into something and thereby miss its essence entirely. Not surprisingly, the latest theory is that space isn't empty at all, that it is filled with some substance.” (PON, p. 88)
Tolle’s poor scientific education causes him to confuse nothingness and emptiness (even “empty” space as at least an intrinsic “curvature” which is never “nothing”). In 1887, Michelson and Morley designed an experiment to prove (or not) the existence of æther or ether, a postulated medium for the propagation of light (as air is to the propagation of sound). If such a medium existed it should slow the light speed down which Michelson and Morley intended to measure. But it didn’t… leading to the conclusion that the speed of light is constant in every directions. Einstein took notice of this, leading a scientific revolution since the times of Newton.
Or, maybe Eckhart Tolle refers to the supposed existence of pairs of matter and antimatter? Let’s quote here Professor Hawking on this:
“What we think of as empty space is not really empty, but it is filled with pairs of particles and anti particles. These appear together at some point of space and time, move apart, and then come together and annihilate each other. These particles and anti particles occur because a field, such as the fields that carry light and gravity, can't be exactly zero. That would mean that the value of the field, would have both an exact position (at zero), and an exact speed or rate of change (also zero). This would be against the Uncertainty Principle, just as a particle can't have both an exact position, and an exact speed. So all fields must have what are called, vacuum fluctuations. Because of the quantum behaviour of nature, one can interpret these vacuum fluctuations, in terms of particles and anti particles, as I have described.”
From Does God play Dice? By Professor Hawking (1999)Space is neither “empty” nor “nothing”. Does denying Tolle know better?
|Heraclitus and Democritus, the "crying and laughing philosophers” by Dirck van Baburen (c.1595-1624).|
I cannot help contrasting here Heckart Tolle’s pessimism with Professor Stephen Hawking’s optimism as real life examples of a weeping Heraclitus and a laughing Democritus (more on this later). In his recent book 'The Grand Design,' written with Leonard Mlodinow, Hawking defends the idea that something such as our universe can come out of nothing: “Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist.”
Questioning the reality of things (including Time) is not new. Some ancient Greek philosophers did just that long before.
The paradox of Zeno’s arrow: is time an illusion?
“Nothing comes from nothing” was a known thesis first argued by ancient Greek philosopher Parmenides,. His most famous student was Zeno of Elea (ca. 490 BC – ca. 430 BC) and both were defending what is known today as “Monism”, a philosophical doctrine defending that that “plurality” is an illusion, that there is only “One principle", “One reality”, one single eternal substance, a single unique source giving reality to every things without which they were mere illusions. Its etymology comes from Greek “monos” meaning "alone." Monists defended the idea that things can only be explained in terms of one single reality or substance. This is similar to Tolle’s “Unmanifested – the One”, the “Source” or the “Now”.
This philosophical argument was central to one of the most challenging and inscrutable of Plato’s dialogues: the “Parmenides” written as an account of a meeting between these two famous philosophers, Parmenides and Zeno of Elea, with a young Socrates. Zeno has argued against the “pluralists” who say reality is made of “many” real things (plural) like “atomist” Democritus who defended the idea that matter was composed of different “atoms.”
Note: the name “atom” comes from the Greek ἄτομος (atomos, "indivisible").
Monists denied the reality of “plurality” such as “matter”, “change” or even “time”… Stoics also taught that there is only one substance, identified as “God”. This separates them from Platonists.
Zeno said that the consequence was that “things” would be both “like” (similar) and “unlike” (different); and this is, according to him, an impossible contradiction. Socrates answered that this contradiction disappears, once one “thing” can be both “like” and “unlike”. For example: I am one man, and as such partake to “unity” (the concept/idea and definition of “man”) but I also have many facets and in this respect I partake to “plurality.” To sum up, Socrates argued that all existing things participate in both “unity” and “plurality”, that there is no contradiction.
In this context, Zeno wanted to demonstrate, that matter is not composed of real indivisible units like Democritus’ “hard atoms;” that in fact, matter must be infinitely divisible composed either by one of the Four elements (earth, water, air or fire) or any combination. Zeno tried to demonstrate that our reality is not “discrete” but “smooth and continuous” (One). He also attacked the commonly held belief that motion exists, because motion is a kind of “plurality,” i.e. a change along a plurality of places in a plurality of times.
To do this, Zeno is believed to have conceived up to forty paradoxes, of which only ten are known.
In one of his most famous paradoxes, the “Arrow” he tried to convince us that time is illusory and motion is therefore impossible.
He states that a moving arrow must occupy a space equal to itself during any “instant” in time. But since, in each “instant”, the arrow is occupying a space equal to itself which does not move, and since there is no time in which to move; therefore the arrow is not moving! Put in other words: consider taking a snapshot of the arrow during its flight: at that point, the arrow is motionless because there is no “time” or “space”. So, according to Zeno and Parmenides, an arrow in flight does not move, it is an illusion. Paradox!
Like Zeno, Eckhart Tolle keeps repeating that Time has no existence:
“Let me say it again: the present moment is all you ever have. There is never a time when your life is not ‘this moment.’ Is this not a fact?” (PON, p. 41)
In Tolle’s and Zeno’s footsteps, British physicist and author of “The End of Time: The Next Revolution in Physics” (1999) Julian Barbour says: “If you try to get your hands on time, it’s always slipping through your fingers.” Barbour believes that we cannot capture time because… it does not exist! He sees time as composed of many zero-points he calls “flashes” or “Nows” But these “Nows” would not be understood as passing moments that came from the past to die in the future. He argues that we have no evidence of the past other than our memory of it, and no evidence of the future other than our belief in it. Like Tolle, he considers “Time” as pure construction or invention of our mind. But unlike Tolle, as a scientist Barbour knows as we do since Einstein that these “Nows” are not synchronized “universal clocks”.
American theoretical physicist and string theorist Professor Brian Greene:
“Sensible as Newton's picture of time may seem, Einstein realized it wasn't right. He discovered that time could run at different rates. As strange as it sounds, this means that time for me may not be the same as time for you. Einstein's discovery smashed Newton's conception of reality. […] Einstein realized that time and space are linked, in much the same way that north and west are. And with this surprising insight, Einstein would overthrow the common-sense idea that time ticks the same for everyone. […] And this was Einstein's key insight, that motion through space affects the passage of time.”
From The Fabric Of The Cosmos: The Illusion Of Time (PBS, November 9, 2011).
So, as in a film where no frame is like the other one, each is different: every “moment”, every “Now” is relative.
However different they are, Barbour still believes they all exist somewhere at the “same time” like in an eternal universal mosaic in a special dimension impossible to detect… He adds these moments are like “pictures, self contained snapshots, they don’t change when they are taken in a different order. […] Change merely creates an illusion of time, with each individual moment existing in its own right, complete and whole." For him time is this apparent, illusory change between two “Nows” (frames) which in a film is just a “blank frame”!
Like Eckhart Tolle he concludes: there is no “arrow of time,” therefore no ‘becoming’ or ‘Creation’, Big Bang, etc., just a static ‘being’.
Julian Barbour's interview:
Monism today: Theosophy
The Theosophical Society (TS) was founded in 1875 in New York City. Her founder was Helena P. Blavatsky Theosophy’s esoterism had a defining influence on Tolle as he acknowledges it. He said "And there (in London, note) were other teachers who were just as meaningful whom I never met in person that I feel a very strong connection to. One is [J.] Krishnamurti, and another is Ramana Maharshi. I feel a deep link. And I feel actually that the work I do is a coming together of the teaching "stream," if you want to call it that, of Krishnamurti and Ramana Maharshi. They seem very, very dissimilar, but I feel that in my teaching the two merge into one. It is the heart of Ramana Maharshi, and Krishnamurti's ability to see the false, as such and point out how it works. So Krishnamurti and Ramana Maharshi, I love them deeply. I feel completely at One with them. And it is a continuation of the teaching." (From Eckhart Tolle interview) Both Ramana Maharshi, and Krishnamurti were involved with Theosophy.
Blavatsky is quoted here on the relationship between Monism and theosophy:
“And why cannot a Monist be a Theosophist? And why must Theosophy at least involve dualism? Theosophy teaches a far stricter and more far reaching Monism than does Secularism. […] The Monism of Theosophy is truly philosophical.” (CW XI:336).
© Copyright by the Theosophical Publishing House, Manila
In the late 1920s TS with Besant and Leadbeater advanced Krishnamurti as the “Coming Christ.” When he came of age, he denied that he was the world teacher for the “New age.” This is why the “New age” label is attached to Eckhart Tolle’s,
Eckhart Tolle is a self-appointed “spiritual leader”. He says: “All spiritual teachings originate from the same Source. In that sense, there is and always has been only one master, who manifests in many different forms. I am that master, and so are you, once you are able to access the Source within.” (TON, p. 75) This is consistent with TS’s aims.
Indeed, one of the central doctrinal beliefs promoted by the TS was originally promulgated in Blavatsky ‘s “The Secret Doctrine, the Synthesis of Science, Religion and Philosophy” (1888) the TS “bible”. Her view is that Humanity’s evolution on Earth (and beyond) is part of an overall Cosmic evolution overseen by a hidden Spiritual Hierarchy of so-called “Masters of the Ancient Wisdom”, whose upper echelons consist of advanced spiritual beings where Eckart Tolle believes he belongs to.
The Theosophy network supports Tolle’s ideas.
Theosophy and the NOW:
- For many religions, heaven is a sacred place where God resides. It is a state that we might glimpse through meditation or prayer or attain if we live good enough lives or believe the right things. Heaven is often thought to be synonymous with the kingdom of God, or, as it is sometimes called, the kingdom of heaven. When asked about it, Jesus said that it exists right now in the present time, and also that it exists within us. “The kingdom of God is within you” (Luke 17:21; sometimes this is translated as “among you” or “in your midst”). […] This ideal state where God is supposed to be is not a place we have to “go” somewhere to find. And it is not something we can only find at some time in the future. It exists in the here and now. From Heaven Isn’t Where You Think It Is By Michael Byrne Originally printed in the Spring 2010 issue of Quest magazine (Theosophy).
- The Future is Now
- One Life
Theosophy in artsMonism had some significant impact in visual arts. It has contributed to the development of “pure abstract art”. Its philosophical rejection of “plurality” which in arts means being “figurative” helped convince several to develop “pure abstraction” along with esoteric thought, in the name of “oneness” and “purity”. This was the case of influential painters such as Wassily Kandinsky in Germany, Frantisek Kupka in Czechoslovakia, Kazimir Malevich in Russia or Piet Mondrian in the Netherlands.
Abstraction involved a sort of stripping away of the material world and had the ambition of revealing the world of the spirit.
Mondrian’s evolution toward pure abstract art:
Kazimir Malevich: Black Square 1915
Tolle even argues that not only “Everything is illusion”… even death is!
“Every portal is a portal of death, the death of the false self. […] You then realize that death is an illusion, just as your identification with form was an illusion. The end of illusion - that's all that death is. It is painful only as long as you cling to illusion.” (PON, p. 92)
So death is an illusion and is, at the same time, the end of illusion! Therefore death becomes the end of… death.
All of this sounds very depressing. When Tolle approached us with the hope we can attain enlightenment, happiness and peace, all we find is: “nothingness” he calls the “Now”. The likely place where such a peace can be found is that in a graveyard.
As King Lear said: “Nothing will come of nothing…” Indeed.
Sascha Norris came up, in another paper on “Nothingness”, with a solution to this nihilist impasse:
“Though we may imagine it (nothingness, note) to be capable of being defined, it is too nebulous, for it is neither a state or a condition. It is an illusion. Yet, it exists as a reality in our own minds. We give it both mundane and novel names such as “boredom,” “inertia,” “ennui,” apathy,” and “dissatisfaction.” These names represent a feeble attempt on our part to describe that which is more like a slumber of the soul than anything else. It flourishes in those of us who go through life without noticing the wonder and beauty of the world. It makes its home in the heart of the man who has closed himself off to experiencing anything that will affect him deeply. It is existence, without life. […] Nothingness, if we identify it for what it is, can teach us something. It can serve to motivate us towards change. […] We have to believe with both our hearts and our minds that we exist for something other than our own self-fulfillment. Otherwise, the nothingness will keep drawing us back to us. Jean-Paul Sartre said in his chef de oeuvre, Being and Nothingness, “Nothingness lies coiled in the heart of being, like a worm.””
(From Nothingness: An Investigation By Sascha Norris, 2010)
|The Young Rembrandt; self-portrait as “Democritus the Laughing Philosopher” at human follies (1628-1629).|
In The Beginning was…. The Beginning!
“Time” has puzzled mankind since its discovery when men became aware of cycles (patterns) in the sky; days and nights, recurring planets, yearly cycles, giving birth to the invention of calendars and clocks but also to mathematics, number theory or music. We, as a species, discovered “past” and “future”: History. This is one of the most important differences which sets humans apart from animals: the conscious control of our own life, our own history, our own destiny.
Consequently the notion of “Present” was being, as Sascha Norris noted… forgotten, to be replaced with the “Genesis”, the beginning of Time.
The First Day: Light
3 And God said, Let there be light: and there was light.
4 And God saw the light, that it was good: and God divided the light from the darkness.
5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
(Genesis 3:5, King James Bible)
So in order to have a “beginning” one requires the existence of... “Time”! So, in the Genesis story, God’s first task during the “First Day” was... to create the “First Day”!
From nothing to something
The author of a “Brief History of Time”, Professor Hawking has given us the scientific demonstration of the existence of a “beginning of Time” (Big Bang).
Today, according to physical cosmology, this “First day” called “singularity” is considered far shorter! Approximately 13.8 billion years ago, at this “singularity” called the “Big Bang” our universe started as a “spatial point” during an infinitely small “instant” called the “Planck epoch” (or era) to expand to the size and time we are living now. This era is considered as the earliest period of time in the history of the universe, starting from “zero” to approximately 10−43 seconds (a bit longer than the “Planck time”) during which “cosmic inflation” (or “inflation”) took place. Inconceivably hot and dense, the state of the universe was unstable, very sensitive to the smallest conceivable variation at the quantum level, giving birth through a process known as “symmetry breaking” to our known fundamental forces and Universe.
First cosmologic “Day”...
Even though this concept of Time “works”, nobody really knows or understands what it really is! All we know for sure is how to measure it.
Solving Zeno's paradox?
There is s obviously something wrong in Tolle’s reasoning. His conception of the “Now” as the only reality but equal to “Nothing” as a portal to “Nothingness” (aka the "One") leads us to universal Nihilism, denying so the reality of everything… except his bank account of course" ;-)
Likewise, there is also something wrong in Zeno’s own reasoning. His conception of a time composed of zero-duration “instants” (Nows) is comparable to Tolle’s.
Yet it took more than two thousand years to solve Zeno’s paradox.
Aristotle’s treatment of Zeno’s paradox involved accusing him of failing to accept that a real line cannot be composed of “zero-points.”
As in his “arrow” paradox: since the “time-line” is entirely composed of such “durationless instants” (“zero-points”) … nothing can ever move, which is Zeno’s point!
A visual illustration can easily help to spot Zeno’s error…
Like in his arrow’s case, a projected film is just a succession of still images, giving us indeed the illusion of motion. Hence its name: “motion picture.” Our human visual system (eyes and brain) can process 10 to 12 separate still images per second, perceiving into a continuous motion picture. At a slower rate, the “motion” won’t appear smooth, ie “continuous.” Since silent films gave way to talkies in the 1920s, the standard filming and projection formats are 24 frames per second (fps), which is the PAL format for TVs. This frame has become standard in the film industry.
Does this mean Zeno was right, that motion is just an illusion, that we live in an “illusionary world?” Nope, “moving pictures” technology proves the opposite: that we live in a “discrete world,” where “discrete values” are at work; in this case the “motion” is visually possible because our human visual system requires “discrete frames”, i.e. discontinuous images separated by “empty frames”. Without them; “motion” would not be recognized by our human visual system.
|“Nude Descending a Staircase, No.2”(left) is a 1912 painting by Marcel Duchamp.|
The “Infinitesimals” at the Rescue?
In mathematics the continuum (continuity) could be considered as a line. A mathematical line is “smooth”, i.e. “undivided” yet infinitely divisible into an infinite number of “zero-points” which are so close together that no point can have a point immediately next to it. Yet between any two “zero-points” there are always other “zero-points”, ad infinitum (that is, it is gap-free). The same situation occurs in Number theory. For example, an important property of “real numbers” is their continuity (continuum, known as the “Dedekind continuity of the real number”); when rational numbers do not have this property. This continuity of the set of real numbers may be described, in an illustrative manner, by saying that it contains no "empty spaces".
|Between two rational numbers, there is an infinite number of real numbers.|
The Math Is Not The Territory: Physical time
Zeno’s error lied in this: he considered Time (or any “plurality”) from a purely mathematical point of view (even though math as we know them didn’t exist but did as “pure geometry.”) But math are unreal, they are a splendid and powerful tool, but they are just a tool, not the reality.
The expression "the map is not the territory" first appeared in a paper that Alfred Korzybski in 1931. In “Science and Sanity” (1933), he acknowledged his debt to mathematician Eric Temple Bell, whose epigram was "the map is not the thing mapped," questioning "mathematical formalism." But already in 1928-29, Belgian surrealist artist René Magritte had illustrated this very concept in his painting “This is not a pipe” (or the “The Treachery of Images”).
|“The Treachery of Images” (1928–29) by the Belgian René Magritte.|
The source of Zeno’s paradoxes comes from his error of considering the real world as smooth as a mathematical line which is divisible ad infinitum. Between any intervals of two points on such a mathematical line, we could find, potentially, an infinite number of points. Therefore an infinite mathematical line could contain an infinite number of infinities… Yep the “map” (or Maths) is not the “territory.”
For a “moving picture” to appear to us “smoothly”, it requires a minimum of time whose duration is not zero. Likewise, Zeno’s “arrow” moves in reality because the “instant” duration is also not zero. These are “infinitesimal indivisible minima”, like atoms, like quanta.
A mathematical line is continuous therefore it does not exist in the physical world because this last is discrete. When mathematicians had to solve physical problems such as calculating the instant velocity of a moving object, they had to develop the concept of “infinitesimals”. They turned also to be the most important step in the solution to Zeno’s paradoxes. Monist “One” is similar to “continuum” or “infinity.”
“Infinitesimals” were used in the calculus of Leibniz (and fluxions in the calculus of Newton.) They helped to define “instantaneous speed” as seen in Zeno’s paradoxes. Whether in the cases of Achilles, the tortoise or the arrow, its motion depends on how much finite distance it travels in a finite interval of time (duration). A speed is a “ratio” between a distance and a time, but if this speed is variable, the “instant speed” must be a ratio of an infinitesimally small distance and an infinitesimally small duration (a “derivative”). But what happens at this “point” on its trajectory? At this smallest limit, it travels 0m in the 0s the instant lasts. But 0/0 m/s leads to any number, so it seems indeterminate and “motion” is impossible!
Thanks to “infinitesimal calculus” this ratio is calculable and this, in essence, is what infinitesimal calculus is about (much appreciated by engineers.) It is therefore wrong to consider (as Zeno does) that a moving object’s instantaneous speed is indeterminate and equal to 0/0.
At the end of 18th Century, Leibniz and Newton produced a system of calculating variable speeds that was very fruitful. But nobody in that century or the next could adequately explain what an “infinitesimal” really was! Sometimes an “infinitesimal” is treated as equal to zero, sometimes it has a non-zero ”value”. Newton had called them “evanescent divisible quantities,” and Leibniz “vanishingly small”… as in the case of a perspective. The "infinitesimal" in other words, was assumed to have strange properties.
The inventor of infinitesimal calculus as we know it today was Gottfried Leibniz. In his “Justification of the Infinitesimal Calculus by that of Ordinary Algebra”, Leibniz constructs this geometrical diagram:
Imagine these two triangles BDC and EAC. Because EA and BD are parallel, we know since Euclid that they are both proportional and therefore their ratios remain constant: the angles remain the same, so too will the proportions of their sides.
Let’s imagine now that their common side ECD moves parallely to itself (keeping all the angles constant): we see that in the process, points E, A and C are merging as this triangle’s sides vanish. Although the triangle EAC has “vanished to zero” (to an infinitely small size), has disappeared we still know its proportions, in relation to the large triangle, have not disappeared. So this vanished triangle is NOT nothing. We know that its sides are not nothing, because, if they both equalled zero, then their ratio would now be equal to 0 / 0 which is indeterminate whereas the large triangle has kept its proportions! This is an impossibility since there is no discontinuity in this process.
Imagine now that this zero-triangle is like Zeno’s “instant”, a zero-point. As an infinitesimal, this instant although apparently equal to “zero” would not, in reality, be nothing!
Infinitesimals help to measure changes. Zeno denied change exists, hence his paradoxes. Same error with Eckart Tolle; for him “present” or “Now” as he defined it (i.e. an “instant”) is all there is, and therefore it is nothing(-ness)…
Infinitesimals demonstrate that an instant, although its duration equals to “zero”, not only is it not “nothing” but it is NEVER the same: it does change … “all the time”. This is the fundamental reason why change (progression, regression, etc), time exist.
So BOTH time and instant exist. Denying one (e.g. “time”) leads to denying the other one (“present = nothing-ness”). And vice versa. The infinitesimal calculus contributed successfully to solve simple cases of objects moving at varying speeds: their “instant speed” is not equal to “zero” (although their duration is equal to an “instant “ equal to zero). Zeno’s paradoxes solved.
The infinitesimal calculus requires understanding what realy happens to the limit; at "point zero", i.e. ad infinitum. An analogy can be drawn with the “vanishing point” in a perspective.
For example, consider a line segment: it can be split in half, that half split in half, the half of the half split in half, and so on. This process can continue ad infinitum, for there is always another half to be split. The more times the segment is halved, the closer the unit of measure comes to zero, but it never reaches exactly zero because there is always another half to be split! It is a situation analogous to a visual perspective with its “vanishing point”. “Infinitesimal calculus” informs us that this “vanishing point” is like a “limit,” an “infinitesimal,” which is unique and indivisible yet not equal to “zero.”
This is the key concept: an “infinitesimal”, although infinitely small like Democritus’ “indivisible atom”, is not equal to zero. In Chemistry, the existence of “atoms” was conclusively proven and it worked (ending the reign of medieval “alchemy” with its ancient Greek “Four elements” doctrine). Later in the late 19th and early 20th centuries, physicists discovered there is an inner structure inside these chemical atoms, thereby demonstrating that atoms were in fact further divisible. Subatomic components such as protons, neutrons and electrons were discovered. Today physicists seem to have discovered something like “indivisible subatomic particles” such as leptons or quarks.
The concept that matter is composed of “discrete” units which cannot be divided further has been around for millennia, but these ideas were only founded in abstract, philosophical reasoning rather than experimentation and empirical observation. In the West, in approximately 450 BC, Ancient Greek philosopher Democritus, popularly known as the “Laughing Philosopher” coined the term átomos (Greek: ἄτομος), which means "uncuttable" or "the smallest indivisible particle” composing “matter”. He defended the idea that “matter” is “discrete”, ie not “continuous” or smooth, but composed of “atoms”, that it has a “texture.” Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name as this hypothesis was proven right by scientific experimentations in the field of chemistry.
It is all analogous to quantum physics: we don’t know what “quanta” really are but, like the “infinitesimals,” they are real, the theory works! But the search is on... like a “vanishing point” which is non-zero in a real non-mathematical perspective.
Quantum theory: A theory developed in early 20th century, according to which nuclear and radiation phenomena can be explained by assuming that energy only occurs in discrete amounts called “quanta.”
Contrary to Einstein's view, Quantum physics accepts the fact that our reality at its "infinitesinmal;" level is NOT "continuous" or smooth: it is "discrete" made of "quanta".
Time as a "fabric"?
An artist view from S. Dali.
|Salvador Dali, The Persistence of Memory|
What Is The “Present” Then?
Since the discovery of Quantum mechanics, this idea of “quantization” is even today considered for Space, Time or Gravity. Scientists even use the term of “grainy space,” for a quantized space. Could then Time be “quantized”? My answer is: yes, for the same reason that our universe is not infinitely large (it is finite); so nothing it “contains” is therefore not composed of infinitely small units not equal to zero: Quanta! A quantized spacetime is “discrete”, therefore Space and Time are not “smooth”, they have a “texture” like the “pixels” of this picture.
|We often use the finite to approximate the infinite.|
Could “Present Time” Be “Quantized”?
Could Time then be quantized? How long does an “instant” (the Now) last in the physical world?
In other words, is there a fundamental unit of time that could not be divided into a briefer unit like an “atomos” (Greek ἄτομος, atomos, means "indivisible")? It could be “quantized”.
Note: In physics, a “quantum” (plural: quanta) is the minimum amount of any physical entity involved.
The consequence is that a physical phenomenon can be "quantized." This means that the magnitude can take on only certain discrete minimum values: quanta. It started with the concept of quantization of radiation discovered in 1900 by Max Planck, when observing the emission of radiation from heated objects, known as black-body radiation. He realized that energy can only be absorbed or released in tiny, discrete packets he called "bundles" or "energy elements." As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant. After his theory was validated, Planck was awarded the Nobel Prize in Physics in 1918.
In this context; the “Planck time” (the time required for light to travel, in a vacuum, a distance of 1 Planck length) is the unique combination of the gravitational constant G, the relativity constant c, and the quantum constant h, to produce a constant with units of time ≈ 5.39 × 10−44 s. Despite being “infinitely small”, the “Planck time” is not equal to zero! It is during that “instant” that the Big Bang is considered to have taken place.
A chronon could also be such a candidate for a “quantum (particle) of time.” Such chronon corresponds to about 6.97×10−24 seconds for an electron. This lasts much longer than the Planck time, the other proposed unit for a “particle“ (atomos) of time, the “instant”. Could Time be “grainy” made of such “particles of Time”?
This brings us back to our “hourglass” or “sand clock” seen at the beginning of this paper.
Its shape resembles intriguingly to the recent scientific concept of “wormhole” which could in theory be a “portal” for “time traveling”.
American theoretical physicist and string theorist Professor Brian Greene explains:
“But what about time travel to the past? Well, that might be possible too, using something predicted by Einstein's equations, known as a wormhole. If wormholes exist, they would be kind of like, like shortcuts through spacetime, tunnels that link not only one place with another, but also one moment with another.” From The Fabric Of The Cosmos: The Illusion Of Time (PBS, November 9, 2011).
|The hourglass’ shape shows the “present” as a neck, a “singularity” between Past and Future through which the “flow of time” passes.|
But of course, “wormholes” are just a concept, they never were found in real.
Interestingly, an hourglass requires grains of a certain shape and… the action of Gravity!
Time and Gravity have an intimate relationship as Einstein demonstrated it. Gravity bends spacetime, and that alters Time itself as a consequence. In a field of high gravitation Time’s flow moves more slowly. On the other hand, Gravity field is relative to Time. That means that without Time, Gravity would not exist.
Because Eckhart Tolle or the Monists reject Time (past and future), consequently Present (Now) becomes empty, nothing. And without it, Time itself becomes unreal, meaningless.
Like in a film, we need “frames” (the “Nows”) but also a “projector” that will connect them to create the “moving picture”. By analogy, we need a writer who will conceive these “moments” and weave them into a “story”. This writer could be us writing our own story.
Back To Time: Does Time Fly Like An Arrow?
As I said in the introduction, although we experience it “all the time”, we all know that ours will eventually be up. Time has one direction (it is irreversible) and is finite.
It therefore has been compared to a river, a flow or an arrow.
So much so that even our clocks’ arms look like arrows!
This English expression comes from Tempus fugit, meaning in Latin "time flees". It is frequently used as an inscription on clocks. It was first recorded in the poem Georgics written by Roman poet Virgil (70 BC - 19 BC): "But meanwhile it flees: time flees irretrievably, while we wander around, prisoners of our love of detail."
Interestingly, the phrase "the arrow of time" was popularized in 1927 by British astrophysicist Arthur Eddington. Newton also believed that time was like an arrow; once fired; it soared in a straight, undeviating line obeying his laws of mechanics.
Basically, it is the idea that time flows in only one direction, as opposed to dimensions in space which have no preferred orientation: we turn right or left, move forwards or backwards, up or down without creating paradoxes. Space is “symmetrical” and has no preferred direction. Time isn’t. It has only one direction: Past is NOT equivalent to Future. Time introduces an asymmetry. It is a “symmetry-breaker” of our Universe‘s known fundamental forces at this singularity point called “Big Bang”.
Does Time Flow Like A River (Flux)?
“Einstein gave us a much more radical picture (than Newton’s, note). According to Einstein, time was more like a river, which meandered around stars and galaxies, speeding up and slowing down as it passed around massive bodies. One second on the earth was NOT one second on Mars. Clocks scattered throughout the universe beat to their own drummer.”
(From Is Time Travel Possible? By American theoretical physicist Michio Kaku)
Heraclitus of Ephesus (a pre-Socratic Greek philosopher), also saw time as a river. But unlike Einstein, he saw it as an unpredictable stream. He famously said:
“No man ever steps in the same river twice, for it's not the same river and he's not the same man…All is flux…Everything flows, nothing stands still" or “The Only Thing That Is Constant Is Change.”Heraclitus is painted as the “weeping” or “sad philosopher” because of his renowned lamenting about change.
Sounding like Eckhart Tolle’s skepticism, Heraclitus also said: “Thinking is a sacred disease and sight is deceptive.” He was a fundamental influence on Nietzsche’s philosophy well known for his defense of (passive or active) nihilisms. Tolle is also influenced by nihilist Nietzsche.
It all sounds a bit like Buddhism’ “impermanence” but without any pessimistic, nihilist outlook. Buddhism informs us that all existence, all beings (even the “mortal gods” devas), are in a constant state of flux, or change, a concept very different to “Monism”. The Buddha taught that because phenomena are impermanent, attachment to them becomes the cause for future suffering (dukkha).
Einstein was himself very discontented by the “Copenhagen interpretation” of Quantum mechanics which put “chance” and “probability” center stage. It holds that Quantum mechanics does not give an objective description of reality but deals only with probabilities because observing, or measuring, affect the observed Quantic phenomenon. Its reality is considered de facto… unpredictable: “flux” and “change” stand at the core of matter this interpretation ends the hope of laplacian “determinism”. It is known as the Heisenberg’s Uncertainty Principle.
Unhappy Einstein replied:
"As I have said so many times, God doesn't play dice with the world."
(William Hermanns: “Einstein and the Poet”)
Professor Hawking replied (posthumously) to Einstein: yes God plays dice, and it is “big” and sounds like a “bang”… ;-) !
“Thus it seems that even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion.”
(From Does God play Dice? By S Hawking, 1999)
Cupid’s Arrows Of Love
“For like life, love is a stream, ever flowing outward and inward in its true, eternal form. It’s never passive but always a moving, acting force.”
(From Shall We Love? By Sascha Norris.)
If we are just squeezed between Past and Future, do we exist in the Present? Is our script written? Are we determined by fate or by chance? Ever struck by the arrow of “luck”? Is this chance or God-sent fate? Does God play dice? Is the “arrow of Time” like Cupid’s?
So many times has Cupid hit hearts of men poisoned by love. Cupid carries two kinds of arrows: a person wounded by the golden arrow is filled with uncontrollable desire, but the one struck by the lead feels distaste and wishes only to run away. This “chance” factor has been used by many writers such as William Shakespeare:
“Helena: (…) Love can make worthless things beautiful. When we’re in love, we don’t see with our eyes but with our minds. That’s why paintings of Cupid, the god of love, always show him as blind. And love doesn’t have good judgment either—Cupid, has wings and no eyes, so he’s bound to be reckless and hasty. That’s why they say love is a child. because it makes such bad choices. Just as boys like to play games by telling lies, Cupid breaks his promises all the time.”
(A Midsummer Night’s Dream, Act 1 Scene 1, William Shakespeare, Modern Text)
So contrary to the Monists such as Zeno or the Theosophs such as Eckhart Tolle that claim that the “Now” is the only transcendantal reality and Time is just an illusion is a dangerous nonsense. Philosopher Sascha Norris is right: “Present” does exist in its own right, so does Time ! The discrete “Now” does exist because we live in a “discrete world.” We can now embrace our Time as Past and Future... Welcome back to Life!
Conclusion: Is This The End?Plato might be right after all when he called Time as a “moving image of eternity”:
“Wherefore he (the Creator) resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity; and this image we call time.”(From Timaeus, 37c-e, translated by B. Jowett)
Using analogy, we can imagine the expansion of our universe after the Big Bang…. with expanding ripples on water. These ripples behave as a shockwave which has a singularity as departure point in space and time (an “Big Bang instant”).
This singularity expands, giving birth to our expanding universe as space-time: Space expands, so does this “primordial instant” as Time.
|Cosmological inflation: a “particle of time” expands as a “timeline”.|
To see a world in a grain of sandAnd a heaven in a wild flower,Hold infinity in the palm of your hand,And eternity in an hour.
- William Blake
Living a “discrete” lifeDiscrete: apart or detached from others; separate; distinct, “finite” as opposed to continuous, smooth, “infinite.”
"If I am not for myself who will be for me, and if I am only for myself who am I and if not now, then when?!"This is my meaning of “living a discrete life”.
(Pirkei Avot 1:14). Hillel, Jewish rabbi who lived at Jerusalem in the time of King Herod (c.110 BC - 10 AD).
I watched it by accident just a few days ago this last December a BBC Horizon "Do You Know What Time It Is? " documentary. What a delight it was to hear comments from eminent scientists such as Prof. Brian Cox and Prof. Fay Dowker on the question of Time, pointing at its possible "grainy nature" as I concluded in my blog entry. I swear I never watched it before.
When the documentary was first aired five years ago I was indeed very busy painting my portrait of Prof. Stephen Hawking (see below) whom I met a few months earlier that year in his Cambridge office, UK.
I approached the question of Time from a different (ie artistic, non-scientific) angle yet it appears we "look" at the same "thing".
As an artist encountering Prof. Stephen Hawking was my first attempt to try "bridge the gap" between the so-called "Two Cultures" phenomeon in our society, a "gap" between arts and sciences. Painting Stephen Hawking was part of a project very dear to both my heart and intellect.
I approached the question of Time from a different (ie artistic, non-scientific) angle yet it appears we "look" at the same "thing".
As an artist encountering Prof. Stephen Hawking was my first attempt to try "bridge the gap" between the so-called "Two Cultures" phenomeon in our society, a "gap" between arts and sciences. Painting Stephen Hawking was part of a project very dear to both my heart and intellect.
- Is time quantized? In other words, is there a fundamental unit of time that could not be divided into a briefer unit? By John Baez is a member of the mathematics faculty at the University of California at Riverside.
- Discrete and Continuous: Two sides of the same? By Laszlo Lovasz (Microsoft Research).
- The Beginning of Time By Professor S. W. Hawking.