## Posts Tagged ‘Time’

### Numbers and mathematics are possible only because time flows

August 13, 2022

It is probably just a consequence of ageing that I am increasingly captivated (obsessed?) by the origin of things. And of these things, I find the origins of counting, numbers and mathematics (in that order) particularly fascinating. In that order because I am convinced that these developed within human cognition – and could only develop – in that order.  First counting, then numbers and then mathematics. The entire field of what is called number theory, which studies the patterns and relationships between numbers, exists because numbers are what they are. All the patterns and relationships discovered in the last c. 10,000 years all existed – were already there – as soon as the concept of numbers crystallised. Whereas counting and numbers were invented, all the wonders of the patterns and relationships that make up number theory were – and are still being – discovered. And what I find even more astonishing is that the entire edifice of numbers is built upon just one little foundation stone- the concept of identity which gives the concept of oneness.

#### Croutons in the soup of existence

The essence of identity lies in oneness. There can only be one of any thing once that thing has identity. Once a thing is a thing there is only one of it. Half that thing is no longer that thing. There can be many of such things but every other such thing is still something else.

Numbers are abstract and do not exist in the physical world. They are objects (“words”) within the invented language of mathematics to help us describe the physical world. They enable counting and measuring. The logical one or the philosophical one or the mathematical one all emerge from existence and identity. Neither logic nor philosophy nor mathematics can explain what one is, except that it is. Every explanation or definition attempted ends up being circular. It is what it is.

Given one (1), all other numbers follow.

#### Where numbers come from

Numbers start with one (1), and without a one (1) there can be no numbers. …… . Given the abstract concepts of identity (oneness, 1) and arithmetical addition (+), all natural numbers inevitably follow. With a 1 and with a +, and the concept of a set and a sum, all the natural numbers can be generated.

1 + 1 + 1 + 1 ……

…. Numbers, ultimately, rest on the concept of identity (oneness).

Equally fascinating are the questions that existence, time and causality are answers to. I am coming to the conclusion that the flow of time (whatever time is) does not emerge from existence but, in fact, enables existence.

#### Revising Genesis

…. What time is remains a mystery but the first act of creation is to set it flowing. Note that the flow of time does not need existence. To be, however, requires that time be flowing. Time itself, whatever it is, is a prerequisite for the flow of time and the flow of time is prerequisite for existence. ………. For even the concept of existence to be imaginable, it needs that the flow of time be ongoing. It needs to be present as a permanent moving backdrop. The potential for some particular kind of existence then appears, or is created, only when some particular rules of existence are defined and implemented. These rules of existence must therefore also be in place before the concept of things, whether abstract or material or otherwise, can be conjured up.

It is inevitable that my views have evolved and they may well evolve further but my current conclusion is that for mathematics to exist time needs to be flowing.

The bottom line:

1. All branches of mathematics, though abstract, are existentially dependent upon the concept of numbers.
2. Numbers depend on the concept of counting.
3. Counting derives from the concept of oneness (1).
4. Oneness depends upon the concept of a unique identity.
5. The existence of a unique identity requires a begin-time.
6. Beginnings require time to be flowing.
7. Existence is enabled by the flow of time

Therefore

### Where and when we are – a dimensional conundrum

September 7, 2021

“In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it”. – Wikipedia

In the concept of spacetime one might think that (x,y,z,t) are the four dimensional coordinates which are necessary and sufficient to specify the location of any object at any time within our universe. But that would be an oversimplification. It is true only for a relative location and not for any absolute location.

In reality we have no idea – in absolute terms – of where we are or when we are.

The place where I was born on the surface of the Earth has – during my lifetime – drifted along with the continents some 2.3 m North-East across the earth’s surface. The Sun (along with the Earth) has moved 6.9 billion km around the centre of the Milky Way Galaxy. Using referents outside the Milky Way Galaxy, it has, during the same time, moved some 55 billion km in space. So, I was born some 60 billion km away from wherever in space we actually are now. In the context of the Universe this is still local space, and I do not need to account for the very expansion of space. The looming collision of the Andromeda Galaxy speeding towards us is still 4.5 billion years away and irrelevant in the scale of my lifetime. Taking my present location as (0,0,0,0) and the X-axis as the straight line from where we were then to now, the coordinates of my birth location become (-60, 0, 0, -73 years) where x, y and z are measured in billions of km.

Everything is relative to here and now.

It is not even certain that time is actually a dimension of the same kind as the 3 physical dimensions we perceive. Some think it emerges together with the Universe and everything. Others think it is just a facet of existence. In any event, we only experience it as a backdrop for, but separate to, our own individual existences. On the stage of our existences, we strut and fret our hours away, but we cannot interact with or impact the relentlessly moving backdrop. Just as with nonsense rhymes using language, nonsense equations by learned physicists about the theoretical access to past times is just nonsense. As with any language, mathematics can also describe the unreal and the nonsensical. Speculative cosmologists have more in common with Edward Lear than they would like to think.

Considering time to be a dimension is no more than a convention or, at best, an analogy. It does not help either, that

1. we have no clear definition (or understanding) of what a dimension is, and
2. we can take a dimension to be anything that can be counted.

We can measure the oscillation of apparent motions and assume that such motion is regular and then infer the passage of time. But what time is other than a magical, necessary backdrop for everything is beyond our comprehension. We cannot be certain that a second now is the same, or longer, or shorter, than a second at some other time. (

The world is what our perception tells us it is. But our perception is limited, and it limits the boundaries of our reality. We perceive space and everything around us as having 3 dimensions, yet we cannot truly conceive of any real thing having other than three spatial dimensions. In our 3-dimensional world we can define one- and two-dimensional things only as concepts (lines and surfaces) but we cannot identify any real-world objects which have only one or two dimensions. Moreover, real things having more than 3 dimensions are beyond our comprehension. How a fourth spatial dimension could be manifested lies outside of human reason. We have the language to describe – but only conceptually – any number of dimensions. Scientists and mathematicians speculate about 3 or 7 or 9 or infinite dimensions and claim either that 3 is the most probable or theorise that the others are hidden in the strings that make up the world, but the human brain can only perceive 3. (I note in passing that invoking the infinite is itself an admission of incomprehensibility). It is a fruitless and inevitably circular discussion to question whether it is our perception which is limited to 3 dimensions or whether the universe has only three to be perceived. Our universe is enabled, and strictly constrained, by what our cognition allows us to perceive. Every real thing in our universe has three spatial dimensions; no less, no more. Our universe has 3 spatial dimensions because that is all, and only what, we can perceive.

I probably read “Flatland” as a teenager where a sphere in Flatland can only be perceived as a circle.

Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by “A Square”, the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella’s more enduring contribution is its examination of dimensions. – Wikipedia

No matter how many dimensions the universe may have, three dimensions is all human cognition can ever perceive. It is that reality which constrains all our thought. It becomes a fundamental assumption for science which the scientific method cannot penetrate. If other dimensions exist, then what we perceive in three are projections. As a shadow is perceived to be two-dimensional. But to have a projection or a shadow in our 3-dimensional world we would need some kind of cognitive light from the other, higher dimensions to create what we perceive.

But human cognition is limited. We cannot perceive what we cannot perceive. And we have no clue – earthly or divine – as to where and when we are.

### Dimensions: where and when we are

May 10, 2021

“In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it”. – Wikipedia

In the concept of spacetime one might think that (x,y,z,t) are the four dimensional coordinates which are necessary and sufficient to specify the location of any object at any time within our universe. But that would be an oversimplification. It is true only for a relative location and not for any absolute location. In reality we have no idea – in absolute terms – of where we are or when we are.

The place where I was born on the surface of the Earth has – during my lifetime – drifted some 2.3 m North East across the earth’s surface. The Sun (along with the Earth) has moved 6.9 billion km around the centre of the Milky Way Galaxy. Using referents outside the Milky Way Galaxy, it has, during the same time, moved some 55 billion km in space. So, I was born some 60 billion km away from wherever in space we actually are now. In the context of the Universe this is still local space, and I do not need to account for the very expansion of space. The looming collision of the Andromeda Galaxy speeding towards us is still 4.5 billion years away and irrelevant in the scale of my lifetime. Taking my present location as (0,0,0,0) and the X-axis as the straight line from where we were then to now, the coordinates of my birth location become (-60, 0, 0, -73 years) where x, y and z are measured in billions of km.

Everything is relative to here and now.

Considering time to be a dimension is no more than a convention or, at best, an analogy. It does not help that either

• we have no clear definition of what a dimension is, or
• a dimension is anything that can be counted.

We can measure the oscillation of apparent motions and assume that such motion is regular and then infer the passage of time. But what time is other than a magical, necessary backdrop for everything is beyond our comprehension. We cannot be certain that a second now is the same, or longer, or shorter, than a second at some other time. (A second now must be longer than a second was then).

The world is what our perception tells us it is. But our perception is limited, and it limits the boundaries of our reality. We perceive space and everything around us as having 3 dimensions, yet we cannot truly conceive of any real thing having other than three spatial dimensions. In our 3-dimensional world we can define one- and two-dimensional things only as concepts (lines and surfaces) but we cannot identify any real-world objects which have only one or two dimensions. Moreover, real things having more than 3 dimensions are beyond our comprehension. How a fourth spatial dimension could be manifested lies outside of human reason. We have the language to describe – but only conceptually – any number of dimensions. Scientists and mathematicians speculate about 3 or 7 or 9 or infinite dimensions and claim either that 3 is the most probable or theorise that the others are hidden in the strings that make up the world, but the human brain can only perceive 3. (I note in passing that invoking the infinite is itself an admission of incomprehensibility). It is a fruitless and inevitably circular discussion to question whether it is our perception which is limited to 3 dimensions or whether the universe has only three to be perceived. Our universe is enabled, and strictly constrained, by what our cognition allows us to perceive. Every real thing in our universe has three spatial dimensions; no less, no more. Our universe has 3 spatial dimensions because that is all, and only what, we can perceive.

I probably read “Flatland” as a teenager where a sphere in Flatland can only be perceived as a circle.

Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by “A Square”, the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella’s more enduring contribution is its examination of dimensions. – Wikipedia

No matter how many dimensions the universe may have, three dimensions is all human cognition can ever perceive. It is that reality which constrains all our thought. It becomes a fundamental assumption for science which the scientific method cannot penetrate. If other dimensions exist, then what we perceive in three are projections. As a shadow is perceived to be two-dimensional. But to have a projection or a shadow in our 3-dimensional world we would need some kind of cognitive light from the other, higher dimensions to create what we perceive.

But human cognition is limited. We cannot perceive what we cannot perceive. And we have no clue as to where and when we are.

### Living in time

January 24, 2019

Most fish are probably unaware that the water they are living in is a bounded environment. I write “most” because flying fish must have some notion of the surface and are able to break through it for short periods and small distances. Similarly, bottom-dwelling fish must have some notion of the boundary they burrow into, and all fish must have some notion of coastal or river boundaries. Nevertheless, we can conceive of fish completely surrounded and dominated and constrained by the watery environment they live in. They are completely powerless to change that environment.

And so it is with humans and time. The difference is that we perceive no boundaries to our time environment. Like fish in a river, we perceive only one direction for the flow. Unlike fish, we perceive no local eddies or reversals of the flow of time. Unlike salmon we cannot conceive of moving against the current. We perceive only a smooth, steady, implacable uni-directional flow.

We have no idea of the structure or the nature of time. The flow we perceive may just be a consequence of our language. We have no idea why the perceived flow should be steady. Could there be a condition where no flow occurs? Or where the flow is a different rate or in some other direction? Or even whether the flow itself is just illusion and does not exist at all. We are used to thinking of many futures but only one past. There is speculation of multiverses where every possible future exists. Why only one present?

From what I have read by physicist Carlo Rovelli (“the new Stephen Hawking”), he takes the view that time is an emergent property and the flow of time we perceive is an illusion. Past, present and future are all emergent. His book “The Order of Time” has received wonderful reviews even from those who do not agree with his views.

It is time to read his book and see if it stops me from staying awake at night trying to imagine many pasts and only one future.

Related:

The magical speed of an inconstant time

Idle thoughts: On time and change and states of stasis

Time precedes existence

### Atheism cannot cope with the unknowable

July 8, 2018

I take atheism to be a “lack of belief in gods”.

A lack of belief does not lie in the realm of knowledge. Neither does it lie in the realm of the unknown. A lack of belief is silent about the state of knowledge about the subject in question. A lack of belief does not imply a state of knowledge. A lack of a belief is not in itself a logical negation of that belief. Many extend this and take atheism to be a denial of the existence of gods as professed as a belief by others. I suspect that most of my acquaintances who claim to be atheists use the latter definition when they present arguments to support their denial of the existence of gods to try and negate the beliefs of others. But a denial of some belief is then an attempt to shift something unknown into the realm of knowledge. It shifts the conversation from ” I don’t myself believe in X” to “I know that your belief in X is false”.

This shift from the realm of belief to the realm of knowledge, I think, is incorrect, illogical and invalid. We are inevitably drawn into epistemology. The known, the unknown and the unknowable. The known and the unknown are realms that are self-apparent. Science is the process at the interface of these regions which leads to the growth of the region of the known. All beliefs by definition lie in the region of the unknown. Any statement and its negation ( X and not-X) must both either lie in the region of knowledge, or both in the region of the unknown. It is not possible for one to live in the realm of knowledge and its negation to live in the region of the unknown. A belief in gods lies in the unknown. A lack of belief in gods (which is atheism) is not in itself a commentary on that belief. A denial of the belief in gods cannot then be anything other than belief and cannot shift into the realm of knowledge. A denial of a belief – which by definition lies in the unknown – is to claim knowledge of an unknown thing which is self-contradictory.

Known, Unknown and Unknowable

Is some part (and maybe the major part) of the unknown then unknowable? Some scientists – and some atheists – would claim that the unknowable does not exist; that everything – eventually – can be explained. But I think they delude themselves. This trifurcation into the known, the unknown and the unknowable does not address who the observer is or the time element. “To know” requires cognition. Cognition requires a brain. Known to whom? when? for how long? What is “known” depends upon the brains alive to know. Facts which were once part of knowledge may become unknown, though they may well remain facts. I observe that most of past events are now unknowable, though they were once known. What was once known, may have first passed into the region of the unknown (but was still knowable) and then with the further passage of time may have passed into the region of the unknowable. Most of the past events in my own life are already in the region of the unknowable. The most basic questions of science that we can formulate always lead us first into the unknown and then into the unknowable.  When the unknowable is reached we use labels. Gods, The Big Bang, Dark Energy, Dark Matter, …….. . But they are all just labels for Magic.

But more fundamentally, the Great Unknowable – throughout all of space and all of time – is time and its nature. What came before time, when “before” was undefined, is unknowable. At the most basic level, our causal universe and all its laws and all our logic rely upon the existence of an inexorable and inexplicable Time Magic. (I take all events which occur but which are inexplicable to be Magic. It is my label for that which lies in the region of the unknowable). Beliefs in Gods or the Big Bang also lie in the region of the unknowable.

Atheism is about belief and does not address the nature of knowledge or confront the unknowable. An atheist’s lack of belief in gods then lies in the realm of the unknown and perhaps in the realm of the unknowable (Magic). Even an atheist believes in Time Magic (whether he acknowledges it or not).

### The flow of time precedes causality

April 26, 2018

All origins, all beginnings presuppose the existence of a flow of time. Our imagination, our language and our thought are incapable of conceiving the non-existence of a beginning. We cannot conceive of anything in the world where a non-beginning is not also a non-existence. If it exists it must have had a beginning. There is no branch of science or field of study or area of thought which is not based on causality. We perceive the world around us through the eyes of causality. We perceive what is and look for what caused what is. We do not question that what is must have had a cause. We do not question either that what will be, will be caused by and follow what is. But causality pre-supposes the existence of a flow of time.

But there is no philosophy or theology or science which can explain

1. what time is, and
2. what causes time to flow

One could say that it is the existence of the flow of time which brings about causality. Causality is itself caused by time.

“Perhaps the simplest and easiest to understand is the argument of the First Cause. (It is maintained that everything we see in this world has a cause, and as you go back in the chain of causes further and further you must come to a First Cause, and to that First Cause you give the name of God). That argument, I suppose, does not carry very much weight nowadays, because, in the first place, cause is not quite what it used to be. The philosophers and the men of science have got going on cause, and it has not anything like the vitality it used to have; but, apart from that, you can see that the argument that there must be a First Cause is one that cannot have any validity. I may say that when I was a young man and was debating these questions very seriously in my mind, I for a long time accepted the argument of the First Cause, until one day, at the age of eighteen, I read John Stuart Mill’s Autobiography, and I there found this sentence: ‘My father taught me that the question, “Who made me?” cannot be answered, since it immediately suggests the further question, “Who made God?” ’ That very simple sentence showed me, as I still think, the fallacy in the argument of the First Cause. If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu’s view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, ‘How about the tortoise?’ the Indian said, ‘Suppose we change the subject.’ The argument is really no better than that. There is no reason why the world could not have come into being without a cause; nor, on the other hand, is there any reason why it should not have always existed. There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our imagination. Therefore, perhaps, I need not waste any more time upon the argument about the First Cause.”  Bertrand Russel – 1927

Time, or space-time nowadays, is sometimes considered as a river. The analogy with fluid flow does not help greatly and only raises further questions. Fluids flow (over time and space) as a causal consequence of forces and energies which are not in balance and which seek balance. Fluids flow from a higher pressure to a lower (in a gas pipeline), from a higher level of potential energy to a lower (in a river) or by being physically forced from one location to another (in a pump or a compressor). In the fluid analogy it is particles of the the fluid which are transported over space and time.

If the flow of time is a river then what exactly is being transported? What then is the imbalance, and in what property or state which causes the transportation of the magical thing called time? Rather than addressing the First Cause, perhaps we should be addressing the First Questions.

What is time? and Why does it flow?

The existence of time precedes beginnings. The flow of time precedes causality. The problem of course is that without time, beginning and precede are undefined.

### The imbalance at the core of time, the universe and everything

April 11, 2018

Without imbalance there is no change.

When all forces and energies are in equilibrium, nothing happens. Nothing can happen. At equilibrium there can be no motion, no waves no vibrations, no change. If the origin of our universe (or the universe) was in the Big Bang, then that must have been in response to some great, prevailing non-equilibrium, the Great Imbalance which caused the Big Bang. (It always seems to me a little unsatisfactory that a Big Bang can be postulated without also having to postulate why a Big Bang would need to occur). All change is always in the direction of eliminating the imbalance which caused the change. If the universe is expanding then it must be in response to an imbalance and the expansion must work towards eliminating that imbalance. The physical world is driven by imbalances. Fluid flows and heat flows and electricity flows are achieved by creating imbalances which force the flow. Human and animal behaviour is driven by imbalances. In fact all life is driven by imbalance.

All motion and even the vibrations of the most fundamental particles (whatever they are) can only be in response to some imbalance. The earth spins and the planets move because gravitational forces are not in balance. Geology happens in response to imbalances. Imbalance always causes change in the direction of eliminating the causal imbalance. Change can only therefore be a response to an imbalance. One change may cause another imbalance to come into being, leading to further change and so on ad infinitum. Though a change may be in the direction of eliminating the initial imbalance, the chain of change may not necessarily converge to stasis. All change needs time to flow. We do experience that time flows – even if we cannot define or experience what time itself is. But then the flow of time must itself be due to an imbalance which the flow of time seeks to eliminate. We do not – can not – experience any lapse of time without change or observe any change without the lapse of time.

Chemistry (which is just applied physics) causes material to combine and merge and split but always as a consequence of some initiating imbalance. Sometimes this chemistry produces living cells which then maintain not only a cyclical chemistry (now biochemistry) but also a code for maintaining the particular, cyclical biochemistry in a changing environment.  The state we call “life” is a state of change. All life and its evolution must therefore be in response to some causal imbalances. Furthermore the direction of life or evolution must therefore be to eliminate the initiating imbalance. But here too there is no certainty that the chain of life will converge to stasis.

If any change – including the state of change we call life – can be said to have a purpose, it is to eliminate the imbalance which caused the change or life in the first place. It would seem then that the ultimate purpose of all change must be to return to a state of complete equilibrium where even time does not have to flow. A state of stasis.

Our universe and everything within it is then a “state of change”, moving from one equilibrium state of stasis to another.

Time and change and states of stasis

The very concept of Change carries within it the concept of No change – which I call a state of stasis. Without a state of Change there is no framework within which Time can – or needs to – exist. It is this state of No change – changeless and timeless – which defines stasis. The concept of Time and duration would seem to emerge simultaneously with or after the commencement of change. But can there be Change without a concept of Time? Stasis was/ is /will be where Change is not. There may be many different states of stasis. Whether states of stasis can precede or follow periods of change is indeterminate since without change – and therefore without Time – there is no before and there is no after.

In stasis there can be no change of any kind, no material, no energy or even dark energy.

Stasis will be reached again when time runs out.

### The speed of time (2)

April 1, 2018

The magical speed of an inconstant time (1).

Once upon a time (till about the 15th century) timeless meant badly timed. Since the 16th century it has been used almost exclusively to mean eternal and untimely is now used for badly timed. What puzzles me is that a time period – however measured – is not – and cannot be – time itself. A time period is to distance as time is to length. Time periods are all measured by observing a change which is assumed to be regular. We once thought the length of a day to be unchanging and took the day to be a period of time. We made the second fixed part of an unchanging day. Then we found that the rotation of the earth around its own axis was not regular. The period called a day was not an absolute measure. We have now shifted to the assumed regular frequency of vibration of a caesium atom in a particular state. This frequency is itself a time derivative – a change assumed to be regular (constant over time). But the regularity is an assumption. But even if this frequency eventually decays, and a second becomes longer than it is today, what is it that actually passes?

Does time flow? If it does, something called time must flow with respect to something else and it must therefore have a speed (a derivative).  Modern cosmology would have us believe that space and time are inextricably intertwined to make up a continuum – a la Einstein. Before the Big Bang there was no space and there was no time. And then came the Big Bang Singularity and both space and time were created (which is remarkably like a Creation Event). Time began to pass and there was space for the universe to expand into. But if time was not flowing, and then began to flow, it follows that it accelerated from a zero speed to whatever speed it flows at now. If the speed of time changed once, it can change again. It could go negative. In some other universe the omelette would give rise to the egg. But this brings us no closer to what time is.

We have to distinguish between the consequences of the flow of time (duration) and time itself. Without the flow of time there is no change, there is no motion. There is no life without the flow of time. It could be that if no change occurs, then time has not flowed, that the flow of the thing called time is necessary for change to occur. But change and motion are not themselves time. If the postulated space time continuum exists then there is no flow of time without space. If time does not flow there is only stasis. For matter of any kind to exist, even a fundamental particle, time must flow. For energy to exist, time must flow. And even if the wave theory prevails, the flow of time is required. Causality depends upon the flow of time. Not time, but the flow of time, is necessary for before and after and cause and effect.

Whether time is an intrinsic property of the universe or an emerging property it would seem to be a quantity that is unknowable within the dimensional constraints of the human mind. Perhaps the flow of time we observe is merely the shadow cast by something from a higher, unknowable dimension. But there is nothing that requires the flow of time to be constant or regular. As the universe and space expand perhaps the speed of time slows down.

It’s just magic.

### Stephen Hawking 1942 – 2018

March 14, 2018

It was Fred Hoyle who first used the term “Big Bang” but it is difficult not to associate Stephen Hawking with the Big Bang Theory.

But for me Stephen Hawking will forever be my inspiration for considering the ultimate question — What is time?

### A second now must be longer than a second was then

December 12, 2017

We cannot measure time. We have no idea why time is unidirectional.

We claim to measure time periods and the passage of time, though we have no idea what it is that is passing.

We impute time periods to the observation of changes. We assume that the changes being observed are stable and regular. We used to assume that the earth orbited the sun in a stable and regular manner with every completed orbit taking what we called a year. We now know that the orbit is neither stable nor regular and is no longer accurate enough for use as the standard measure of a time period. We used to assume that the earth’s rotation around its own axis was stable and regular but now know that this rotation is slowing and days are getting longer by about 2.3 milliseconds per century. Of course, to be able to say that, we need a “second” defined independently of a “day” defined by the rotation of the earth. The modern definition of a “second” is now based on the vibration of a caesium atom.

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom in its ground state at a temperature of 0 K.

This assumes that this radiation is stable and regular. We assume that the 9,192,631,770 periods taken to constitute a second are each identical to the other. (Why it should be so is of course magic). For all practical purposes and relative to the duration of the lifespan of the human species it may well be so. But over the long, long term it cannot be so.

The earth-moon-sun system, the solar system and even our galaxy are all losing energy. Even all vibrating atoms must be losing energy for any radiation to occur or for any vibration to take place. For the “radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom in its ground state at a temperature of 0 K” to remain stable for ever requires an energy input which does not exist. Why any radiation should be regular is still a matter of magic.

What a “second” was at the Big Bang and before is unknown. But since then, it follows that “seconds” then were shorter than “seconds” are now. Every “second” now must be shorter than every “second” to come.

Of course what is even more magical is our fundamental assumption that the passage of time itself is stable and regular. We have no clue as to what laws of the universe require such stability or regularity and the why of any such laws is still in the realm of magic.

The magical speed of an inconstant time