13. Thinking Machines with Which-Where-When-Why engines.

We have talked about 2 ways to learn: analyze (top-down/break-up) and synthesize (bottom-up/build-up). The 2 ways are really used alternatively when we learn (or think). How do we really learn to think?

We first come to notice an 'object' for thinking (a thing, a challenge or a situation), we analyze this input object by 'identifying' its features or characters or properties
(using 'Sets Theory', we categorize or classify the object by a 'set',
    e.g. 'x' is in set 'A' and 'a' is not in set 'B' -- that is a 'duck', not a small 'goose').

How do we 'learn' that object 'x' is a duck? We analyze it by parts and combine its many parts into one:
    it walks like a duck; it quacks like duck;...

    Why do we put it in the set 'duck'?
    Because, we 'know' (or 'have learned' in the past) 'what' are common features of members in the set 'duck'.

If we analyze the process of identifying a duck, we see that we have 'multiple criteria' (a set of features; a set of question-and-answer pairs: {[question]:[answer]} patterns) in our definition of a duck.

We test each criterion (Q&A: If [question] then [answer] ) and synthesize or construct, combine in (for those logic magicians, we talk about AND, OR, NOT, Which, When, Where,...) the results (answers) of all tests (questions) to make (choose) a decision.

We may (recursively) repeat analysis and synthesis many times. We may picture our thinking as inspecting (traversing) a tree. We can go from a branch to sub-branches to leaves -- analyze. We may come from leaves to a branch, to the root -- synthesize. Those who have played 'I spy...' or '20 questions' (to name hidden objects), would be well familiar with this binary search process also known as (aka) 'merge/divide and conquer'.

We see how we can use 'Which' to learn and solve problems. How do we use 'Where'? Point that out, please. 'When' was it there last? How do we learn about things in this 'space-time' world -- by using 'IF (x.{attribute:"value"}) THEN (x is "a")' construct?

'Why' do we call our learning and thinking: Which-Where-When-Why machine?
Anyone cares to comment?

<NB> Why 'Sets Theory'? We have learned Sets theory in school. We use Sets theory in our daily life without realizing that we are using set theory. Why so? In simple words, a 'set' is a collection of 'things' that have or share specific 'attributes' (or indexes). We say 'this fruit is a mango' when we mean 'this fruit is a member of a set of fruits called "mango"'. We learn that a mango is like another mango (in the same set) but different from a durian (in another set). By giving and learning the attributes of a set, we can accept (include) or reject (exclude) things for that set. So, set is about 'class' or 'category' -- 'What'.

A silent assumption which we take for granted is that of 'space' -- a world we live in and talk about. When we say a P of people, we omit to say many things like 'alive in town X as at time T' or 'as we can see now'. Different spaces may have different sets.
   
Another fundamental is the concept of a 'whole' 'unit' or 'entity' of things. The concept that allows us to count, and to say that we have one of this, two of that, parts of this, this 'or' that, A 'and' B, X is greater than Y, ...

We somehow learn this 'whole' concept before we can use 'set' concept. We can make sets of chickens, students, cars and lemons. But we have problems with things like 'air', 'water', 'sand', 'light' and all difficult-to-count things. (Note that 'infinity' is not 'difficult to count', but, it takes 'too long to count'.) Once, we have learned to identify 'individuals', we can learn 'sets' and how to make 'subsets' (parts of a set) and 'supersets' (combinations of sets or subsets). By comparing one individual (whole unit) to another individual (whole unit), we can tell whether the two are the same or different, bigger or smaller, blue or green, ... (in some ways or by some attributes).

Our thinking, reasoning and scientific methods are built upon simple concepts of 'whole unit' (quantum?), 'set', 'difference' and 'join' (and more difficult concepts like space and time).

วิเคราะห์ (กริยา):ใคร่ครวญ เช่นวิเคราะห์เหตุการณ์; แยกออกเป็นส่วน ๆ เพื่อศึกษาให้ถ่องแท้ เช่น เช่น วิเคราะห์ปัญหาต่าง ๆ วิเคราะห์ข่าว [พจนานุกรม ฉบับบัณฑิตตยสถาน พ.ศ. 2542]
Analyze An"a*lyze, v. t. [imp. & p. p. Analyzed; p. pr. & vb. n. Analyzing.] [Cf. F. analyser. See Analysis.]
 1. To subject to analysis; to resolve (anything complex) into its elements; to separate into the constituent parts, for the purpose of an examination of each separately; to examine in such a manner as to ascertain the elements or nature of the thing examined; to consider in detail in order to discover essential features or meaning; as, to analyze an action to ascertain its morality; to analyse a sonnet by Shakespeare; to analyse the evidence in a criminal trial; to analyse your real motives.
 Syn: analyze, study, examine [1913 Webster + WordNet 1.5]
 No one, I presume, can analyze the sensations of pleasure or pain. --Darwin. [1913 Webster]

 2. make a mathematical, chemical, or grammatical analysis of; break down into components or essential features; as, to analyse a specimen; to analyze a fossil substance; to analyze a sentence or a word; to analyse a chemical compound.
 Syn: analyze, break down, dissect, take apart. [WordNet 1.5]
[-- From The Collaborative International Dictionary of English v.0.48]

สังเคราะห์ (กริยา):(เคมี) ทำให้ธาตุมีปฏิกิริยาเคมีกันเป็นสารประกอบ; ทำให้สารประกอบมีปฏิกิริยาเคมีกันเป็นสารประกอบอื่น; (กริยาวิเศษณ์) ที่สร้างขึ้นจากปฏิกิริยาเคมี เช่น ใยสังเคราะห์ [พจนานุกรม ฉบับบัณฑิตตยสถาน พ.ศ. 2542]
Synthesize Syn"the*size, v. t.
 1. To combine by synthesis; to unite. [1913 Webster]
 2. To produce by synthesis; as, to synthesize albumin. [1913 Webster] Synthetic
    [-- From The Collaborative International Dictionary of English v.0.48]

A challenge: You have 4 rocks to put on display in a park. How do you place them so that the distances between the rocks are all equal?