Human brain is an intelligent machine. One aspect of intelligence is to take examples of some event, understand the patterns in those examples and finally use this knowledge to predict nature of this event in future. An understanding of several events and their natures finally culminates in "experience" of a human being.
For example, lightning is accompanied by thunders. We all know this and expect a thunder when we see lightning. Why? Who told us? Most of us know this from experience. We saw lightning and we heard thunder first several times, after which we "understood" that there is a causal relation between the two. Many such daily experiences result in a set of "rules" we know. When something happens, we know from our experience of what the following events will be. That is easy.
Many such rules are relatively straight-forward with cause-effect kind of relationships. We understand complicated events with a combination of such simple rules. For example, if it is cloudy there is a chance that it might rain. However, if it is cloudy and the wind is strong, there is a lower chance that it might rain. Simple to understand and to explain.
I am not going to talk about first-order logic here because while it was developed to capture similar scenarios, it is technical and may not be appropriate to capture the probabilities that seem inherent to our experiences. What I can say with some confidence is that in some logic space, individual rules like these can be expressed as a straight-line. That is what i mean by linearity.
Example diagrams are in order here.
Here the lines represent a rule describing a certain condition that, if met, separates 'Yes' and 'No' regions. A 'Yes' region is all events where this rule holds and 'No' region is where the rule does not hold. For example, for the rule that lightning implies thunder, if there is a lightning, the answer for whether there will be thunder can be found in region above the line in first diagram and there are no other conditions to check.
Without getting into too much technical discussion, the main thing i want to convey here is that a set of rules can help us predict answers to several questions and that the more complicated the problem, the more rules we are going to need.
Food for thought here is, why are legal documents so lengthy? Why do courts need hundreds and hundreds of pages to outline resolution of cases, which humans can understand in 5 minutes but need hours to read and explain logically? How many rules/lines would it take to represent a simple circle in above diagrams? A circle is non-linear and would take infinite number of rules to describe. But we humans can understand it easily.
It seems we think of human brain as having two distinct parts. A conscious part which we understand and think and a sub-conscious part that we do not directly understand but which gives rise to intuition, feelings and eureka moments. There may not be a real division inside the brain. It is entirely likely that we express this division to explain that there are something that we can think and explain but others where we know the answer but fail to explain why.
If you look at the last diagram above, you can see that it will take a large number of rules to explain it, never fully but we as humans can quickly and easily comprehend the situation and answer 'Yes'/'No' without knowing why (Assuming each assertion of why is linear).
Therein lies the main argument i am trying to make here. Human beings are inherently non-linear. Our feelings, our senses, our intelligence, our intuitions pretty much everything about us is non-linear. We take this non-linearity with ease and comprehend the world around us without a problem. Sure thing that it takes us a long time of adjusting our mental curves to arrive at a good understanding of the world and humans around us but once done, we can get a good grasp of things….. until, we start writing a book or laws or trying to explain our feelings to others. All of a sudden we find ourselves filling pages after pages trying to convey simple information and ideas and even then we do not always succeed. Why?
Is it that language is a linear tool which we cannot use to express 'complicated' feelings and ideas? Is it that the part of our brain that we use to explain is linear and cannot find words to describe? Why is it that we find it hard to explain intuition?
Why do our societies have rules which occupy 100 pages but amount to saying 'use your common sense' ? If we had a society that had rules like 'use your sense', why do we feel it would be hard to enforce 'common sense'? What is so hard about explaining what is 'common sense' and 'sound judgement'?
I am not sure whether i made my point to the reader or not. Honestly, i am struggling to put the message across though in that struggle lies the success of my argument here. I had a thought which took no longer than 5 seconds to pass through my brain but which has taken no less than 2 hours to explain here and even then i am struggling.
For example, lightning is accompanied by thunders. We all know this and expect a thunder when we see lightning. Why? Who told us? Most of us know this from experience. We saw lightning and we heard thunder first several times, after which we "understood" that there is a causal relation between the two. Many such daily experiences result in a set of "rules" we know. When something happens, we know from our experience of what the following events will be. That is easy.
Many such rules are relatively straight-forward with cause-effect kind of relationships. We understand complicated events with a combination of such simple rules. For example, if it is cloudy there is a chance that it might rain. However, if it is cloudy and the wind is strong, there is a lower chance that it might rain. Simple to understand and to explain.
I am not going to talk about first-order logic here because while it was developed to capture similar scenarios, it is technical and may not be appropriate to capture the probabilities that seem inherent to our experiences. What I can say with some confidence is that in some logic space, individual rules like these can be expressed as a straight-line. That is what i mean by linearity.
Example diagrams are in order here.
Here the lines represent a rule describing a certain condition that, if met, separates 'Yes' and 'No' regions. A 'Yes' region is all events where this rule holds and 'No' region is where the rule does not hold. For example, for the rule that lightning implies thunder, if there is a lightning, the answer for whether there will be thunder can be found in region above the line in first diagram and there are no other conditions to check.
Without getting into too much technical discussion, the main thing i want to convey here is that a set of rules can help us predict answers to several questions and that the more complicated the problem, the more rules we are going to need.
Food for thought here is, why are legal documents so lengthy? Why do courts need hundreds and hundreds of pages to outline resolution of cases, which humans can understand in 5 minutes but need hours to read and explain logically? How many rules/lines would it take to represent a simple circle in above diagrams? A circle is non-linear and would take infinite number of rules to describe. But we humans can understand it easily.
It seems we think of human brain as having two distinct parts. A conscious part which we understand and think and a sub-conscious part that we do not directly understand but which gives rise to intuition, feelings and eureka moments. There may not be a real division inside the brain. It is entirely likely that we express this division to explain that there are something that we can think and explain but others where we know the answer but fail to explain why.
If you look at the last diagram above, you can see that it will take a large number of rules to explain it, never fully but we as humans can quickly and easily comprehend the situation and answer 'Yes'/'No' without knowing why (Assuming each assertion of why is linear).
Therein lies the main argument i am trying to make here. Human beings are inherently non-linear. Our feelings, our senses, our intelligence, our intuitions pretty much everything about us is non-linear. We take this non-linearity with ease and comprehend the world around us without a problem. Sure thing that it takes us a long time of adjusting our mental curves to arrive at a good understanding of the world and humans around us but once done, we can get a good grasp of things….. until, we start writing a book or laws or trying to explain our feelings to others. All of a sudden we find ourselves filling pages after pages trying to convey simple information and ideas and even then we do not always succeed. Why?
Is it that language is a linear tool which we cannot use to express 'complicated' feelings and ideas? Is it that the part of our brain that we use to explain is linear and cannot find words to describe? Why is it that we find it hard to explain intuition?
Why do our societies have rules which occupy 100 pages but amount to saying 'use your common sense' ? If we had a society that had rules like 'use your sense', why do we feel it would be hard to enforce 'common sense'? What is so hard about explaining what is 'common sense' and 'sound judgement'?
I am not sure whether i made my point to the reader or not. Honestly, i am struggling to put the message across though in that struggle lies the success of my argument here. I had a thought which took no longer than 5 seconds to pass through my brain but which has taken no less than 2 hours to explain here and even then i am struggling.