Chapter 2 – The shortest distance between two points

Previous — Chapter 1

On a two-dimensional flat surface the distance between two points is a straight line. So if we were to pin a length of string to a point on one surface of a flat board and stretch it to another point on the surface, the string would pull in a straight line. Were we to try to move the string away from the straight line it would push against us.

On a three-dimensional sphere the shortest distance between two points is not a straight line, it is a curve.

Again, if we were to try to move the string away from its natural curve it would push against us. If we were to look at a surface of a sphere that isn’t smooth but has mounds, the string would take a path that is the shortest through them. If the string went over mounds, they would push back against the natural course of the string.

Now consider the four dimensional space-time continuum. In this case the shortest distance involves time. Time and space is movement (speed is distance multiplied by time) so the straight line here is the natural tendency for an object that is moving to follow the shortest distance between two points. It will travel in a straight line. We know that if we launch a rocket into outer space it will go in a straight line until it gets into the gravitational pull of a planet. Objects which have mass (such as planets) are like mounds on the surface of the sphere that attempt to push (or pull) the natural flow from its shortest, most direct, route. This force that pushes back we call gravity.

Note that when we consider the stretched string the force on the string is always for the string to return to the shortest distance. Gravity is a similar force which is why we don’t see ‘antigravity’ naturally existing.

Einstein’s theory of relativity postulates gravity as a bending of the time-space continuum.

Gravity is the shorted distance between two points in four-dimensions.


Entropy was originally defined as relating to heat through what is called the Second Law of Thermodynamics.

The second law of thermodynamics states that entropy always increases in a closed system. When we use electricity to power a motor, the electricity has lower entropy than mechanical energy and the mechanical energy has lower entropy than heat energy, so the electrical energy gets converted to power and then to heat and the entropy in the system goes up.

A hot substance will transfer its heat to a cooler substance. There is also a different degree of entropy in different forms of energy. So for instance to convert electrical or mechanical energy to heat energy is very easy. Most electrical products get hot in use as do most machines simply as a natural result of this tendency.

Entropy is also related to the degree of order. The natural tendency of the universe is towards disorder. Colloquially we say that you can’t unscramble an egg. The scrambled egg is more disordered than the egg when it has a separate yoke and white, and that is more disordered than when it was in the shell. Like many processes once it has become more disordered, it is very difficult to return to the ordered state again.

As an example of entropy, consider a tray filled with a mix of red and blue marbles.

This appears unordered, it has a high entropy. Now look at this:

This appears more ordered. The blue marbles are on the left and the red marbles are on the right.

When something becomes more disordered we say that we have raised its entropy. Zero entropy would be complete order, infinite entropy would be complete chaos. Examples of rising entropy abound:

  1. When we manufacture a car we take the raw materials, refine them into new substances and assemble them very precisely to form something that has a very specific task. If we left the car for too long it would revert back to its original state.
  2. When we do housework, we remove dust and put it into one place and we move items to where they belong. Left to itself, and to the influence of most teenagers, it will revert back to untidiness and chaos.
  3. Dead bodies decay and rot back to their basic molecules.

In the same way as gravity is a result of the shortest distance between two points in four dimensions, entropy is a result of the shortest distance between two points in five dimensions. It’s as if we are rolling downhill on the slope of time and increasing entropy as we go.

We could say that the fifth dimension is the degree of order. In the same way as time requires matter to exist so entropy requires time and matter.

If we create a sandcastle on a beach we would be said to be lowering entropy — we are creating order out of the unordered sand. The reason the sandcastle is considered to be more ordered (lower entropy) is because there is only a limited number of combinations of sand that would form that sandcastle whereas there is an an enormous number of combinations that would produce a beach.

In Buddhism and other religions, it is sometimes said that ‘everything is as it should be’. God created the perfect world and therefore it is as it should be. In other words, each grain of sand is in a particular place for a reason. It would seem then that each beach is unique. The fact that each grain appears to be exactly the same as every other grain is simply due to our lack of appreciation. Each beach is perfectly ordered. Every grain is exactly where it should be.

What is order?

This raises the question however, ‘what is order?’

Consider our tray of marbles has been set up thus:

An English reader would probably recognise the word ‘TAP’ but a non-English speaker may not. So the English speaker would consider it to have low entropy whilst the non-English speaker would not. In other words, the perception of order is dependent on our knowledge and intelligence. Take the example of a photograph which is made up of pixels, tiny dots of colour which when seen from a distance merge to form an image. The picture of the Mona Lisa is a good example.

If we enlarge the area around the right eye we can see the individual pixels. We can see that it is an eye.

There is still order there. However, if we blow it up far enough we lose the sense of any order.

The order is still there. It is simply that we are too close to the image to perceive it.

If we consider that our three dimensional world exists in a time-space continuum and that the future has, in one sense, already happened, then we can see that we are like someone looking too close to the picture. It appears to lack order simply because we are too closely bound up with what is happening to see the real process. In this light we must reconsider the idea that the universe is gaining in entropy. It is not gaining disorder, it is simply gaining complexity and so the ability to perceive order becomes increasingly difficult. We can’t separate entropy, the amount of order, from intelligence, the process by which we can perceive order.

When we say that the universe is tending towards increasing disorder this is not quite true. To be more precise it requires a greater degree of intelligence to understand the complexity of the universe.


As the human body ages it starts to wear out, but living things don’t simply decay, there is a cycle of development before decaying. With some minor exceptions the only examples of reversal of entropy, of making more order out of the chaos, is where there is intelligence. It could be argued that a definition of intelligence is the ability to make order out of chaos, to reverse entropy. I previously defined intelligence as the ability to predict future events. It would certainly be possible to predict future events and use this ability to produce disorder so this is, as it were, an extra dimension to intelligence.

We previously discussed how the shortest point on a two-dimensional plane is a straight line, on a three-dimensional sphere is a curve and on the four-dimensional time-space continuum is the tendency of objects to travel in a straight line. On a five dimensional universe the shortest point is the tendency towards disorder, the raising of entropy. In this case intelligence is like objects with mass that go against the disorder of the universe.

It is would seem that only when there is intelligence does the natural flow towards disorder become reversed. Plants consist of complex cell structures constituted from a huge variety of elements. The anatomy of all living organisms is highly complex and furthermore the behaviour of living things lowers entropy in the surrounding environment. A bird takes a range of objects to build a nest. It creates an ordered nest from disordered raw materials; humans do this more so, creating highly complex manufactured articles from disparate raw materials.

Entropy is the shortest distance between two points in five-dimensions.

Next — Chapter 3






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