A MULTI-DIMENSIONAL WORLD VIEW


 
 

7. WHAT MAKES KNOWLEDGE A DIMENSION?



The One-Metre String
Imagine that I held out in front of you a piece of string one metre in length in order to illustrate something about the dimension of length. I know the string has some width and mass-energy as well, but that can be ignored for the moment, because that is not what I am illustrating. You know the string is one metre because I tell you it is, and I have my tape measure there for you to check it if you want to. Now you would probably assume that I have cut the string to that length. Well, you would be right.

Is the particular length of that string a property of its length? All string has some length, and length is the dimension that my string illustrates, but in this case it is a specific length.

It may seem by looking at the string that its length was simply a natural property of the string, and that it could produce that length by itself. However, the specific length was something that had been added to the string that was not part of the string itself. What had been added was information or knowledge. The specific length information contained by that string is an independent reality that is not dependent on any property of the string. The string would not have been able to make itself to be one metre, because it is not a property of length to originate information.

You may argue that a piece of string could randomly be of any length, that by chance a piece of string could be one metre, which could be an integral part of the string. However a random length is not knowledge until you measure it. You may calculate the length of the random sized string and get a value but then you have applied some measurement process that is not part of the string to turn it into knowledge.

My one metre length of string is therefore an illustration of the dimensions of length and knowledge.

What is Knowledge?
Knowledge is true information that is contained in our mind about reality. While not everything that we claim to believe or know is necessarily true, I am concerned here with knowledge that is true and accurately reflects information about what exists such as in objects, events or facts. For this reason, by definition the knowledge that is in my mind and the information that is in reality is the same information. I am talking about informational knowledge.

Everything has properties with some informational value. That value can be transferred to an observer or a computer. The dimension of knowledge is concerned with transferable information, or the informational value in objects, events and facts. The dimension of knowledge is not measured in metres, seconds or tons, but in megabytes of the information itself, its nature and the amount of it, and what is done with it.

To the extent that my brain simplifies or selects information that it wants to observe,  and because my brain is limited in capacity, my knowledge may be limited. But in these days of computers, much of that knowledge can be stored and analysed outside my brain, and in effect my brain is being extended hugely in its capacity to know. Although knowledge may be limited, if it still reflects the reality which is the source of the information, then it must be counted as knowledge.

In the string example above, the length of the string being one metre illustrates knowledge in three ways. Firstly the knowledge was applied to the string from my knowing what one metre was. Then it became information that was contained in the string itself to give it its length. Then finally that information was communicated to others, observed and measured by them. So knowledge has a source, an effect, and is meaningful communication. It is both objective when it is a value of something, but also subjective when the information becomes known and is a thought in our minds.

What would constitute the dimension of knowledge?
Observable and measurable knowledge. Knowledge is normally gained through our senses, and is a measurable value of some property that we are considering. We measure things to find any information about their size, weight, shape, structure, colour, movement, or any other property. It is not the physical properties that we are concerned about, but the information properties of the measurement such as its numerical value or the number of objects.

Knowledge of events. If it is an event, we can record its date or duration by measuring it in seconds, minutes, days etc. Or we can have a description of events such as we get in the latest news. That description may be in the form of numbers, words or images. Knowledge can be very complex and also include financial value, emotional value, or the knowledge of how to do something,

Historical knowledge. What about historical knowledge? Is true knowledge only what is true in the present? If I had cut the string to one metre last year, and since then had cut it to half that size, then it would no longer be true knowledge that the string was one metre. What we do in that situation is to specify a time. 'Last year the string was one metre long', is valid knowledge. This opens the way for how historical knowledge is accepted, an important part of our experience.

Facts. What is factual knowledge? This refers to true derived knowledge, knowledge that is calculated or logically added onto previous knowledge that may not be directly from observation. Where I live in for me is direct knowledge. But for you it may be a derived fact from my address. You can look up Papatoetoe, New Zealand in an atlas to see where I come from, but your knowledge of where I live comes from the observations of the cartographers who drew up your atlas. Your knowledge is not direct, but derived, as much of our knowledge is.

Theories and opinions. What about theories and opinions? Are these knowledge? To the extent that a theory is deduced from reality by formal rules of reasoning we can say that they are knowledge. But there is a sense of our English usage where a theory is merely hypothetical so is not really knowledge. Not every thought, belief or opinion can be counted as knowledge.

Specific or general. The word knowledge is used in a great variety of ways in the English language. It can be used in a specific sense of an item of knowledge as when I say I know how old you are, or in a collective sense to refer to an accumulation of information such as when I say that I have some knowledge of a language. I need to use it in both ways, to refer to specific knowledge to help us define its nature, but then it needs to be also general to refer to large bodies of knowledge.

The cosmic constants. The cosmic constants, such as the speed of light, the force of gravity, the strong and weak nuclear forces, are information contained in the matter and energy of our universe that are measurable. [SOI pg 165] They are an essential part of a description of the universe. These constants are information that effects the properties of matter and energy and even allows them to exist at all.

Boundary measurements. This refers to the initial conditions and measurements of the universe. Some of these are - the speed of expansion of the universe, the properties of superstrings, the properties of elementary particles, the number of dimensions, the ratios of various constants, initial uniformity, atomic properties and ratios between different atoms. [MC pg 372]

Mathematical knowledge. Mathematics and logic are the ways we work or reason with knowledge. Maths doesn't have to have the unit specified though. We can just add 1+1=2. Knowledge on its own is enough. Mathematics shows how knowledge is cumulative and can be added to itself to create more knowledge.

Non-random information. Random information (eg a series of random numbers) does not fit to be included as knowledge, because it has no source, it has no effect, and is not meaningful communication.

Other areas of knowledge. Because knowledge is cumulative there are many areas of life that are included in the knowledge dimension. It is a dimension that has grown from the seed of some essential boundary measurements (such as the speed of expansion of the big bang) and universal constants, into a huge tree of knowledge.

Fig 11. The Tree of Knowledge. Showing some of the ways that
knowledge has built up and the extent of the dimension of knowledge
today.
 
Is Knowledge Truth?
Is the knowledge dimension the truth dimension? I have defined knowledge as being true information about what actually exists. But the question arises if there is an absolute truth that all knowledge depends on, or if knowledge is relative. Is our knowledge merely a subjective model that we build up in order to succeed in this world? Or is knowledge discovering truth that is getting us closer to the ultimate truth who is God?

The problem is that if there is no absolute truth then the statement that there is no absolute truth is not absolutely true also. We are therefore left with the conclusion that it is possible to know the truth which is consistent with absolute truth.

If the study of knowledge is based on reality, then the information we discover from the natural world will be consistent with what we discover from the spiritual world, because both are from God. If we are not looking for truth, then we are wasting our time. As one philosopher said, "I have seen everything done in this world, and I tell you, it is all useless. It is like chasing the wind. You can't straighten what is crooked; you can't count things that aren't there." [Ecclesiastes 1:14-15] We are also wasting our time if we can't trust the truth of what we observe with our senses nor what we receive by revelation in God's Word.

But we haven't arrived at absolute truth yet, or we would be God. So it is best to be humble about what we know and settle for calling this the knowledge dimension rather than the truth dimension.

Is Knowledge A Dimension?
1. Is Knowledge A Unique Property?
Does knowledge have properties that are unique and not dependent on other dimensions?

That we can calculate using maths without it referring to any other property, indicates it is a unique property that is independent from other dimensions. In my illustration, knowledge applied to the string was sourced completely outside of it, and any measurement or observation of properties comes from outside of the object or event itself. We can hold knowledge in our head or in a computer, and also communicate it, completely separately from the object it refers to.

Knowledge is the informational value of the properties of what exists, but in itself does not have any mass-energy, time or space. An object that weighs 1kg  has 1kg of mass at ground level gravity. But the information itself doesn't weigh anything. Nor does it have any time or spatial value. The specific information content of an object is an independent property.
     

Fig 12. Dimension of Knowledge. This dimension represents the
 amount of knowledge in an object, event, or facts. The 'byte' unit is
computer language for one unit of information in the computer language
of '0's' and '1's', which is the simplest way of coding information. The
amount of knowledge so far in this book is 2.5mb or 2.5 million
bytes of information.
2. Is Knowledge Co-dependent?
Is knowledge equally and mutually dependent on other dimensions for its existence in the universe? If I compare it with mass-energy as another dimension for example: Similar arguments can be presented for knowledge in relation to the other dimensions.

3. Does knowledge allow movement?
Can there be different positions within the dimension?

The best way to imagine that is with a slide rule like mine which has one of its scales marked 1-10. The numerals could refer to anything such as the size of the memory that would hold such knowledge, the number of objects, the value of a particular property, or financial values. The slide rule also allows me to calculate with the numerals themselves, which is an amazing new freedom of movement that the dimension of knowledge provides.

Let us see if movement of knowledge is allowed when graphed with mass-energy and space.
      

Fig 13. A Space-Knowledge-Mass-energy Graph. The object 'A'
exists with a particular position in space, has mass-energy and has
some level of information content. 'A' would move to the right if it
increased its knowledge content by being painted in multi-colours
instead of a dull gray, without changing its space or mass-energy
co-ordinates.
4. Is The Dimension Of Knowledge Theologically Valid?
Knowledge was important from the beginning. One of the trees in the garden of Eden was the Tree of Knowledge of Good and Evil. More on that later. Adam was also given the task of naming the animals and birds. Knowledge of them was important for his responsibility to cultivate and guard the world.

John introduces Jesus in his gospel by describing him as the 'logos'. "Before the world was created, the Word already existed; he was with God and he was the same as God." [John 1:1] This 'logos' was truth and wisdom and yet also personal as the Hebrews saw knowledge. Here knowledge is completely separate from the created world.

The Hebrew concept of knowledge was more than intellectual knowledge, and was to apprehend and experience reality. It was more than the possession of information but exercising and applying it also. [EDOBT pg 457] Knowledge was highly personal.

Knowledge in the Bible is to know God and Jesus Christ. "If you obey my teaching, you are really my disciples; you will know the truth, and the truth will set you free." [John 8:32]. To know Christ is to know the truth. There is a spiritual direction to knowledge because knowledge comes from God. All kinds of revelations of knowledge are described in the Bible and Christian experience, proving in our experience the supernatural nature of knowledge.

Wisdom is highly valued in the Bible. "Listen to what is wise and try to understand it. Yes, beg for knowledge; plead for insight." [Proverbs 2:2-3] Knowledge is meant to grow through learning. Daniel prophecies a great increase in knowledge in the world, "Many will go here and there to increase knowledge." [Daniel 12:4 NIV] Knowledge is to be opened to us through our relationship with Jesus Christ, "He is the key that opens all hidden treasures of God's wisdom and knowledge." [Colossians 2:3]

Knowledge fits neatly into the requirements to be a dimension.

C.S. Lewis
I must admit to being a fan of C.S. Lewis because he has helped me to think out the presuppositions of my faith. He was a person who wasn't afraid to think through his faith, and didn't see that as compromising it in any way. In his book on ‘Miracles’ he says “If necessities of thought force us to allow to any one thing any degree of independence from the Total System – if any one thing makes good a claim to be on its own, to be something more than an expression of nature as a whole – then we have abandoned Naturalism. For by Naturalism we mean the doctrine that only Nature – the whole interlocked system – exists.” [M pg 18]

He goes on to show how in fact reasoning is something that operates independently from nature, for it has its own system of logical deduction from knowledge. In nature things happen as a result of cause and event, but in reasoning things are deduced by logic, and are totally independent of any need we may have to eat, for example.

So C.S. Lewis concludes “If our argument has been sound, acts of reasoning are not interlocked with the total interlocking system of Nature as all its other items are interlocked with one another. They are connected with it in a different way…The knowledge of a thing is not one of the things parts. In this sense something beyond  nature operates whenever we reason.” [M pg 37]

While Lewis seems to be talking about reason, by this he includes a knowledge of a thing. Reasoning is working with knowledge. Lewis's arguments support the conclusions that I have reached that knowledge is an independent property.

Einstein
Einstein gave us the Special Theory of Relativity and the formula e=mc2 . The ‘e’ refers to energy, the ‘m’ refers to mass, and the ‘c’ is a constant that is equivalent to the speed of light – this is very specific knowledge that is necessary for the existence of matter and energy.

It is not only a piece of string that needs some knowledge about what its length should be but matter and energy need some information as well. Note that ‘c’, the speed of light, has to do with time as well as mass-energy, so already we have some information from outside the mass-energy dimension itself that is being linked into the equation that is basic to mass-energy. It is not information that is part of mass-energy, that it could have possibly worked out for itself. It is information applied from outside its own dimension like the 1 metre length was applied to my string.

The level of ‘c’ must be crucial for all of our existence, for it affects how much energy it takes to make up matter, or how much energy gets released in a nuclear explosion. Its not the sort of information that would come out of randomness, because atoms don't operate on a variety of values of ‘c’ that they could choose which figure was going to work out the best.

Therefore knowledge is required for anything to exist. Einstein's theory of relativity all along has been showing us that knowledge is a dimension on its own.

Is There More Than One Knowledge Dimension?
One dimensional knowledge. If we think in terms of knowledge being just one dimension, then all we have is knowledge adding to knowledge over time. A line or arrow (see Fig 12 above) of knowledge would show that by moving along that line. That would be how we normally grow in knowledge - through discovery, experience and learning adding to our knowledge. We could lose knowledge too of course, for example if my computer crashes

At the beginning of the universe there would have been a few crucial pieces of information required. But now our world and even my study is filled with huge amounts of information. Even if it is only one, this is a growing dimension.

Two-dimensional knowledge. What would a second dimension of knowledge look like? I wonder if we already have a second dimension of knowledge that has arisen, which is knowledge of knowledge itself - ie consciousness. It could be just an extension of the one dimension of knowledge - ie as knowledge grows it becomes aware of itself. But it makes sense when you have a graph with two axes of knowledge for the two arrows of knowledge that are going in different directions to cross and to interact with each other to provide knowledge of knowledge.

Perhaps also choice is provided where there are two dimensions of knowledge. It could be that when we have the two or more arrows of knowledge crossing each other as on a two-dimensional graph, that we would be able to have any choice. Choice could then be considered to be between two different directions of knowledge. Because the knowledge dimension is independent from other dimensions, then our choices would be genuinely free, only limited by the choices perceived to be on offer.

Each time you are at a road intersection you have a choice of two or more roads to take. The intersection of the 2D knowledge arrows could be what is provides for logical choice as well.

Three-dimensional knowledge. Then what would three dimensions of knowledge look like? It could allow for independent knowledge to enter. Each dimension has independence of course by the nature of dimensions.

But this could be a way for revelation or inspiration where visions or ideas pop into our consciousness. That seems to happen with some scientific discoveries, but it could also be what is behind revelation from God. I have experienced revelation knowledge happening in a variety of ways. There is no reason why God would not be communicating through a third dimension of knowledge for this to happen.

If we draw three dimensions of knowledge on a balloon with our arrows, then the arrows can continue around the balloon and meet with each other, so that knowledge has no beginning or end. That makes the idea of omniscience (all knowledge) possible. Three dimensional knowledge points towards absolute truth (complete knowledge, that is free from limitations, restrictions or dependency from anything other than itself).


Fig 14. Three Dimensions of Knowledge. A 3D knowledge line 'K'
on the surface of a sphere  demonstrates how knowledge can have
no beginning or ending. If that line was our one or two dimensional life,
we can see how revelation (A, B, and C) can intersect our knowledge line.

Genuine Free Will
Proposing more than one dimension of knowledge provides us with a useful explanation of our own consciousness. Haven't you always wondered why there was the ability to think at all? Have you wondered if your choices were really free?

Because knowledge is a dimension separate from nature, we no longer need to think of ourselves as puppets being led along some path pre-determined by nature itself. Counting knowledge as a dimension deals a blow to determinism (the belief that our thoughts are causally linked to the natural dimensions). The transcendence principle of dimensions means that dimensions add their properties to other dimensions, but do not determine effects in those dimensions.

The presence of a second dimension of knowledge provides us also with genuine free choice. This choice is still limited to the actual knowledge available, but it is a genuine choice nevertheless. There is genuine free will in the universe.

Our free will is only going to be helpful if it is based on true knowledge, and we need ways to discern what is true and not true. That drives us to seek the source of truth itself in the third dimension of knowledge.

Jesus said, "The knowledge of the secrets of the Kingdom of God has been given to you..." [Luke 8:10]

There is another benefit of seeing knowledge as a dimension, and that is to explain why our universe is designed. []
 

EDOBT  'Evangelical Dictionary of Biblical Theology', ed Walter Elwell, 1996
MC        'Mere Creation', ed William Dembski, IVP 1998
M           'Miracles', C.S. Lewis, Harper Collins, 1947
SOI        'Signs of Intelligence', ed William Dembski & James Kushiner, 2001

Rev Brian Brandon, May 2004

To go to the Next Page
To go back to the Home Page.