2∆ The Present.

- Does it make sense to say that the present moment is in some sense an 'infinitely thin  moment of time'.

The essence of this book is that direct observation really seems to tell us that the present is 'all' that there is. Now make no mistake this is remarkable in itself. I cannot in any way explain how or why all this 'stuff', including ourselves, is here. I also couldn't explain how or why it could not be here.

On top of the mystery of how and why everything exists, we seem to think that perhaps we can use our intellect to deduce that not only does all this stuff exist, but it exists 'over time'. But perhaps it is just as valid if we can use our intellect to realise that in fact all this stuff 'just' exists now. And there is only the constantly changing present? does suggesting that an extra, mysterious, and invisible thing called time also exists - really add anything to our understanding? I saying 'it all appeared in the past' really saying any more than 'it all just appeared'?

(Sample section from book follows)

1.                 Is the present moment ‘infinitely thin’?

If time is constantly flowing, and everything is happening now, then just how long is the ‘present moment’, and can it really be infinitely thin? if so, that really doesn’t leave us much time to get everything done;


If we express speeds in terms of distance and Time, such as ‘100 kilometres per hour’ then this generally seems to make sense, although we know the object, say a car doesn’t have to travel the whole 100 kilometres and take an hour to do so, we know that we are talking about its particular speed at one point in a journey.

So we could say for example that precisely 300 seconds into some particular journey our car was travelling at 100 kilometres per hour.

The problem here is that this moment, ‘300 seconds into the journey’ is just an ‘instant’. That is we are not talking about how far we actually travelled in say one second, or between 300 and 301 seconds into the journey. We are declaring that we knew, or could calculate and express the speed of the car at one particular moment or infinitely thin slice of Time.

This leaves us thinking we have in some way confirmed that Time exists, and in some way confirmed that it makes sense to think about infinitely thin slices of Time. And thus that the present moment may be an infinitely thin slice of time, and thus that we are all ‘In’ one.

This becomes nonsensical however because Einstein concluded that there was a maximum speed limit in the universe, given by Einstein's constant ‘C’ and generally referred to as the speed of light XXX clarify why key here XXX. So if an infinitely thin moment of Time may be expressed as ‘zero seconds’ then whatever speed we claim our car is travelling at, 100, 200 or even 300 kilometres per hour, to work out how far it travels in zero seconds we just multiply the speed by zero.

So at 100 km per hour the distance covered in zero seconds is zero km.

But if we express speeds in terms of fractions of the speed of light then we don’t have to consider over what distance a thing may be moving to still sensibly talk about its speed.

No magic no Time.

This may not satisfy your mind at this point because you may want to say ‘yes but we are still talking about how fast the car was going say 300 seconds into its journey, so still talking about an instant of Time’.

The problem here is that if you try to understand how ‘Time may be nothing more that a man made notion’, from the point of view that ‘Time really exists’ then you may never see what I am suggesting is true.

Consider as a parallel trying to convince someone that ‘magic’ did not exist who listened to you from the point of view that ‘magic was real’.

If you show them how one trick can be performed yet appear to be magic they may accept the point but still claim you haven’t disproved all possible types of magic.

What I am trying to say is that if you start with the view that Time does exist then it might seem nonsensical to think of a world in which things just move and change wherever there is energy flowing.

But if you start with the view that there may be just objects moving and changing wherever there is energy present, then the idea that there is also a thing called Time, and infinitely thin slices of it etc sound equally implausible.

In other words, I personally cannot explain how or why the universe could possible exist, but that clearly does not mean that I does not exist.

With equal conviction however, I personally cannot explain how the universe could possible vanish so that it did not exist.

So I personally confess, and I'm guessing I'm not alone, that I cannot explain how the universe either could or could not exist.

Similarly when it comes to Time the idea that there is - a completely intangible thing called ‘Time’ that permeates absolutely everything but can never be seen, but connects an ever growing ‘past’ that can be seen but not changed, to an infinitely expansive ‘future’ that can’t be seen but is unstoppable – seems equally or in fact more unbelievable that the idea that thing just move and change if there is energy present.

So the idea of Time can seem just as odd as the idea of no Time.

So at this point it makes sense to go back and reconsider what you actually see in the world around you.

Cutting out the abstraction, what do you see?

Figure 131 If time is dilated in different ways everywhere there is gravity or motion, then 'the present' must be an extremely distorted, infinitely thin, '3D' slice through '4D' space time... or is it?

Ultimately all this abstract reasoning may not convince you, so it can be a good idea to actually go outside, walk around and take a fresh look at the world around you and confirm what you actually see.

Does everything just exist and move as it appears to do so right in front of your own eyes, or do all of these moving things ‘require Time’ in which to carry out their motion?

If so do you actually see this Time go by? Or do you just see objects, including yourself just constantly moving and changing.

When you are looking at a clock hand going round is clock face really divided into an infinite number of infinitely small segments that the clock hand passes through infinitely quickly but one by one? And do an infinite number of slices of zero thickness add up to ‘one’ revolution? Or is that whole idea abstract over-interpretation?

You may not like the idea of things just existing and just moving because this word seems to sidestep logic and reasoning, while discussions on Time usually contain a lot of reasoning.

But by ‘just’ here I mean it as in ‘only’ not as in ‘for no reason’.

There may or may not be a ‘reason’ why things exist and move and we may or may not be able to know it, but adding the concept of Time to the mix doesn’t prove or solve anything at all because without Time the question is…

 ‘How can things just exist and move’?

But/and with Time the question is…

 ‘How can things exist and move, in an infinitely thin moment of ‘Time’,

 and be connected to and sandwiched between a massive and ever growing kind of visible but not really ‘thing’ which apparently can’t even be called a thing but is ‘the past’,

 And, be connected to a probably infinitely large, and completely invisible, though partially predictable ‘thing’ that isn't a thing, that also can’t ever be directly seen, called ‘the future’?

So the second version of the question, which includes the notion of Time, doesn’t answer or explain the first, it is just the first question again with a lot of extra unexplained baggage.

So is it day time? or night Time? Or is it just light or dark depending on whether the part of the globe you are on is facing the sun or not? Do things just move if they get a kick in the right place, or do they do so over an infinite number of infinitely thin slices of Time?

Is every clock you see fundamentally different from a rotating playground ride, or a spinning bus wheel?

Does every clock you see ‘measure Time’? Or is it just another moving object but one specially designed to copy the speed at which the Earth rotates because we are all stuck on the spinning Earth and knowing whether we are heading to the sunny side or the dark side is very useful to know?

As with the illusion of vision after too much thinking it is a good idea to actually go out for a walk and confirm what you actually perceive, it may be simpler than you think.

The present, and the infinitely thin moment in detail.

In the previous discussion I touched upon the idea of an infinitely thin slice of Time.

Having read a lot of books on the Time this is a notion that comes up quite often and is seen as one of the mysteries of Time, but I believe that the idea of the present moment being an infinitely thin slice of Time in which, even more incredibly everything happens, can be shown to be the result of incomplete analysis and misunderstanding of some of the more basic elements of mathematics and logic.

Does the idea of an hour, minute or second hand constantly marching through an infinite number of infinitely thin slices actually make sense?

Mathematical confusions.

The problems of zero and cutting things up.

Mathematics is an incredibly useful tool, it allows us to expand and express our knowledge in incredible ways but problems arise if we misuse it.

Consider some basic maths. We have a sheep pen in a field with 6 sheep in it.

If we take 4 sheep out of the pen then 6 minus 4 leaves 2 and we have 2 sheep left. If we take out these 2 sheep then we say 2 minus 2 equals zero, so we have ‘no’ sheep. And a quick inspection of the pen will confirm that the number of sheep we have is zero.

But to say there are zero sheep in the pen isn't quite right because it gives zero the status of a number and suggests that ‘zero sheep’ or ‘no sheep’ can in some way exist.

In other words would someone else turning up at the scene say the same thing? Would they look into an empty pen and declare that what they saw was ‘zero sheep’ there? what, apart from perhaps some suspicious droppings, would make them mention sheep, surely our observer is just as correct in saying there are ‘zero fridges’ or ‘zero footballs’ in the pen.

The point here is that although the number of sheep in the pen seems to have gone from 6, to 2 to zero, ‘zero’ is not really a number it is more accurate to call it a ‘place holder’.

If we start thoughtlessly confusing the ‘map’ of mathematics with the ‘territory’ of the real world we are exploring and in doing so we also blindly treat zero as a number and expect things to work out we can be lead into seeing anomalies and paradoxes which really do not exist, for example...

Normally we can divide a given number of things, say 6 sheep, by some other chosen number say 2 or 3.

If two farmers what to share the sheep then 6 divided by 2 means they should get 2 pens and put 3 sheep in each. If we have 3 farmers they each get 2 sheep but different numbers of farmers might cause serious problems for the sheep, if we have 6 sheep and 5 farmers then to be shared out fairly one of the sheep will have to be killed and then chopped up! This is a shame but not impossible.

Dividing by zero. (Use your loaf).

If we have a loaf of bread we can cut it into a number of slices and the thickness of the slices will determine how many slices we can get from the loaf. Basically it is fairly obvious that the thinner and thinner we choose to make each slice the more and more slices we will get from any particular loaf.

A problem might seem to arise if we try to cut the loaf into slices ‘zero’ cm thick, we might be tempted to say that 1 (loaf) divided into pieces or slices of zero thickness would give us an infinite number of slices.

But if we look at the actual actions we have to take to cut a loaf into slices the process is as follows,

If we were cutting slices 2 cm thick and we choose to start cutting the loaf from the right hand end we would place the knife just at the right end of the loaf then move it left 2 cm and make a cut, hey presto a 2 cm slice is made. From here we just repeat the process, moving the knife 2cm to the left and making another cut, until we run out of loaf.

So, as said if we make the slices thinner, say 1cm then we only move the knife to the left 1 cm before making each cut, and so we end up with more slices before we run out of bread.

If we wanted to make slices of zero thickness though we can do the same thing. Line up the knife with the right hand end of the loaf, then move it left zero cm and start cutting.

We would find however that we wouldn’t be cutting the bread at all, just moving the knife down right next to the end of the loaf. And we could repeat this action a thousand, or even an infinite number of times and we would always in fact still have a whole loaf.

If we choose to start cutting from somewhere in the middle of the loaf a similar situation arises, we make the first cut at any point, thus splitting the loaf into two. Then we move the knife zero distance away from the first cut, effectively of course not moving it at all. And we cut again to no effect. This is to say we do not actually create an infinitely thin slice. As before we could repeat this action of moving the knife zero distance and cutting again any number of times, up to ‘infinity’ but nothing would change, we’d still have a single loaf cut in two.

This is why mathematically any number divided by zero is not said to be infinity but more accurately declared as ‘undefined’.

So using this simple loaf of bread example the idea of an hour hand on a clock face being something that adds up a infinite number of infinitely thin slices of Time to make one whole revolution seems hard to explain, but there is an extremely powerful and practical branch of mathematics that uses such a process to produce genuinely useful results.

The record player conundrum.

Another interesting feature of mixing mathematics, ‘time’, and ‘zeros’, is the way we can seem to make logic and common sense seem to fall apart, or even be fundamentally wrong if we chase zeros and moments in too much of a frenzy. Consider for example an LP record spinning at a steady rate on an ordinary record deck.

At any ‘moment’ speck of dust on the outer edge of the record will be travelling at a certain speed and in a certain direction, while a similar speck of dust on the opposite edge of the record will have the same speed but be travelling in the opposite direction.

If we move both specks of dust closer to the centre of the record, say half way to the central spindle, then they will both still be moving in opposite directions but at a slower rate. Now the problem is that if we keep moving the dust specks closer and closer to the central spindle, they still keep moving, and in opposite directions, but at a slower and slower rate. So logically, or mathematically, at the very centre of the rotating record deck, there must be an ‘infinitely small’ ‘point’ that is rotating at a constant rate, while its ‘edges’ are not moving at all!

Now how something infinitely small can rotate is beyond me, but I can see for myself that record decks ‘work’, and so it must be within the reasoning or mathematics where the problem lies. So when considering things like this, and perhaps matters like ‘is what exists at the very centre of a black-hole ‘an impossible singularity’?’ we should bear in mind that nature tends to make things constantly ‘work out’, and ‘add up’ just fine, even if our understanding and mathematics suggests nature may ‘become impossible’.


Differentiation and integration.

In mathematics one of the most powerful and widely used tools is the function of ‘differentiation’. At this point I can already sense non-mathematically minded readers shutting down and the mathematicians smelling blood, so I will tread carefully.

In its simplest form differentiation allows us to work out the gradient of a line on a graph at any ‘point’. And by point here we mean a mathematically infinitely small location.

If you were to plot a graph of y = x * x you would see a curve that started off with no gradient but got steeper, and steeper and steeper as you followed it to the right of the graph paper.

The gradient or slope of the curve is in fact never a fixed value such as 1 in 10 or 1 in 5 but mathematically always constantly changing and different at every point along its length.

Differentiation however allows us to say precisely what the ‘slope’ or rate of change of the line is at any chosen infinitely small location.

Integration is a related mathematical tool that allows us to work out the area underneath a section of the kind of graph described above.

Integration works by considering the chosen area beneath such a graph to be consisting of an infinite number of infinitely thin strips or rectangles.

To work out the area of a rectangle you multiply its base by its height, but in this case whatever the height of each rectangle, its base would be zero. So if we tried to do this, in reality we would be adding up an infinite number of rectangles each with zero area, and our answer would be zero.

However integration provides us with the correct commonsense answer – by leaving us with an equation that has an error margin within it, but, numerically this ‘error’ ends up being one number or expression, divided by ‘the number of strips’ we imagine chopping the area under our graph into. And so the more ‘strips’ we choose the smaller the error, until we effectively, mathematically, reach an error of ‘zero’[1].XXX simplify and shorten description? XXX

The point here is that while differentiation works with the concept of an infinitely thin point on a line still having a gradient or slope, and integration works with the concept that an infinite number of infinitely thin slices can add up to a real value, these are in fact both mathematical tools, that are in reality used in a three dimensional world by three dimensional mathematicians with 3D brains and 3D pencils just constantly moving and changing, and transferring graphite to paper in interesting patterns if they have the energy to do so.

This may sound facetious but I'm just trying to be clear about what reality is and what is useful but essentially too ‘academic’ here, because otherwise we may have problems further down the line.

 For example although we can work out logically how things like an ‘area beneath a graph’ can be ‘thought of’ in terms of ‘infinitely thin slices of area’, or how the motion of an object can be thought of in terms of infinitely thin slices of Time, and although these methods can produce extremely accurate and useful answers, does this really clearly and directly prove the existence of infinitely thin slices of physical areas or infinitely thin moments of Time?[2]

You may see this more clearly from another point of view, consider how things might look if you had never thought of the idea of Time existing.

Would you consider a mathematical proof that one can work out the rate at which a gradient on a graph changed over a theoretically infinitely small span, or the existence of a mathematical method that allows you to work out the area beneath a section of a graph by dividing it into an infinite number of infinitely thin strips and adding them together also as proof that because these operations can be carried out with equations, the world itself must follow the mathematical tools and therefore also operate this way.

In other words does the mathematics describe a way of understanding the movement and change around us, or does it prove that the movement and change around us is comprises of an infinite number of infinitely small steps constantly being joined together perfectly, and that a thing called Time is therefore possible and therefore probably exists? (XXX REPEATED)

How mathematics stops the world just spinning.

The trap is this, when we ‘Time’ the motion of an object we are generally comparing its motion to the rotation of the Earth. If something travels 240 km per day then we are really saying that while the Earth smoothly and constantly rotates (once) the object smoothly and constantly covers a measured distance (240 km).

To make our figures smaller and more manageable we take on the idea of imagining that the Earth’s rotation ‘starts’ at some place, and the idea that we could slice the Earth’s rotation into 24 sections and then we each of these fictitious or imaginary constructs ‘hours’.

As with basic mathematics as long as we carry out the same operation on both sides of the equation everything remains equal, so we divide ‘240’ km by 24 to get 10 km. and we say that 240km per day is the same thing as 24 km per hour.

This is not too bad, the problem arises because mathematically we are able to handle the concept of logically or metaphysically??? Dividing things up into infinite numbers of infinitely thin pieces and then adding these infinitely thin pieces back together in what turns out to be a very useful and sensible way.

But then, we make the massive and unfounded assumption that because we can do this with numbers, and because dividing the ‘day’ into 24 hours (or 1,440 minutes or 86,400 seconds) ‘worked’ then if we can mathematically divide a day into an infinite number of slices and add them back together ok, then this in some way proves Time exists and works the same kind of way our maths does.

How much fuel do you have to pick up as you go along?

We can take a more practical view of this idea of looking at moments of Time by considering how much fuel a family car might use on a simple journey.

A car cruising on a motorway at a sensible speed might burn a single litre of fuel to cover 10 kilometres, but how much fuel does it burn in ‘an instant’?

To understand just what 10 kilometres on a single litre of fuel equates to take a look at a litre bottle of water then try to imagine how thin it would be if it was heated up and stretched out to be 10 km long !

In other words imagine a straight piece of transparent pipe, 10 kilometres long, sealed at both ends and with a diameter such that the entire 10 km length only held a single litre of fuel ![3]

Now instead of fuelling up a car for a particular journey we could rig up a somewhat dangerous and highly impractical system whereby the car picks up all the fuel it needs as it goes along!

To do this we just need a pipe or trough of fuel running alongside the motorway and to equip the car with a suitable side mounted fuel scoop.

Now I'm going to take a risk and not patent my above idea, but here’s the reason for considering it. If you set up a system where by a car cruising along a motorway is constantly picking up precisely the right amount of fuel it needs as it goes along then you can always clearly and directly see and know just how much fuel the car will need for any given distance. In fact, you wouldn’t even have to measure the distance your were considering.


Figure 132 If a car very dangerously scooped up its fuel as it went along, the cross-section of the trough would show the fuel it needed to travel 'zero distance'.

If you set up the fuel trough to have the right cross sectional area for the particular car, van, bus or tank etc you were running then it would obviously be a smaller cross section for more efficient machines, the car or van, and a larger cross section for the bus or tank. So if you make a pen mark at any point on the ‘fuel trough’ and then another pen mark any distance away from the first, the amount of fuel in that part of the trough is automatically, precisely how much fuel the vehicle needs to cover that distance[4].

What is more significant though is that you need only make one pen mark ! in other words, if you just cut through the fuel trough at any point the ‘infinitely thin’ cross sectional area of the fuel tells you how much fuel the vehicle needs ‘in an instant of time’, or ‘ to cover zero distance’ !

Now at this point the discussion might start to both make sense and sound ridiculous, so I refer you back to the notion of Time existing, and therefore the present moment being an infinite collection of infinitely thin moments of Time. (And say if it sounds ridiculous… then you started it).

It’s interesting to note here that you could use this system to express the fuel efficiency of any vehicle, or compare the fuel usage of a group of vehicles, just in terms of hypothetical  ‘fuel trough cross sections’.

XXX check notes on ‘3d static engine’ are included.- note static forces and pressures – but all have a direction – not an arrow of time.

The fuel scoop, summary.

The thing to realise here is that if you consider the cross sectional area of the fuel at the point it is being scooped up by the vehicle you can see that this area is constant and unchanging.

If you then imagine how the whole system looks, in ‘an instant’ you can see that while the cross section of fuel can be in some sense thought of as an infinitely thin 2 dimensional slice, the rest of the car, its scoop, fuel pipe to the engine, the engine (and car) itself, including all the cogs, pistons, and cylinders, and fuel exploding in those cylinders, all still exist as three dimensional things (whether you are thinking about them as moving or as being stationary in an instant or not).

And if we could magically freeze all this motion, there would still be ‘frozen’, forces and pressures, stresses and strains in the system, and even ‘frozen’ momentum in all the ‘moving’ parts. Thus when the ‘re-lease’ button is pressed the whole thing could carry on as if nothing had happened.

The reason for suggesting this odd contraption here is because this book is about explaining how the world and the motion in it can be described without the notion of Time, and thus also about describing how the notion of Time, in this case infinitely thin slices of Time, can be shown as seeming nonsensical when its consequences are examined. And also the idea of stopping all motion – although impossible to actually do – can still be thought about sensibly in a timeless view.


The trick here is to see that the word ‘instant’ may be invalid. Similar to how the word ‘vanish ‘in the context of ‘magic’ is invalid.  If we assume magic exists then we have to explain what vanishing is. But if we see we have no legitimate reason to assume ‘magic’ then the word vanish is seen to be the problem. We cannot fully explain how the above set up would be in ‘an instant’. But this is not because the view of timelessness fails, but because the theory of time is shown up to demand the existence of concepts or things, that are named – but never shown to exist. In reality we just see three dimensional objects and motion, so it only makes sense to imagine how the fuel scoop car set up might seem if it was running very slowly or completely stopped. Not in a frozen, infinitely thin, instant of time, but just simply all here now but stopped.

[1] Without going in too far into the details this means that if we imagine the number of slices we cutting our graph area into as being say 2, 3 or 4 we will have quite a big error (some number divided by 2, 3 or 4); but, if we choose a bigger number of ‘slices’, say 10,000 the error is much smaller (some number divided by 10,000). And ultimately if we imagine choosing ‘infinity’ slices then our error becomes ‘some number, divided by infinity’, which tends to give and error of ‘zero’.

[2] Consider for example, the very idea that we can mathematically calculate an objects exact speed, at some precise ‘moment’ in a fall, say exactly 10 seconds after release, tends to start with the unspoken agreement that we are just seeing the object as being an’ infinitely small point’ that can ‘be’ at precise locations or infinitely small places, in space.

[3] If you work out just what the diameter of the pipe would be it may turn out to be much smaller than you might think. Consider that a litre of volume, water, fuel or whatever, is 1,000 cubic centimetres, and a cubic centimetre is quite easy to visualise, it’s about the size of a large sugar cube (CHECK).

If we divide our 10 km, or 10 thousand metres, by 1,000 we get ’10 metres’, and this tells us that our family car uses one sugar cubed size amount of fuel per 10 metres.

So the car actually uses 1 cubic millimetre of fuel per 10 millimetres of distance ! therefore the actual cross sectional area of the ‘pipe’ would be one tenth of a square millimetre (mm squared?) CHECK FIGURES AND UNITS)

[4] We are assuming for simplicity that the vehicles speed doesn’t matter here.