Numbers

Numbers don't distinguish between entities. Consider 5 - apples, houses, cars etc. What is in a number that I can have 5 items of anything? Or what property is common to an apple, house, car, box etc. that there can be something the same, irrespective of which of these items it is? This has to be something cognitive. Firstly, this has to be about boundaries of entities. Boundaries is where sameness ends and difference begins. It is on the basis of this sameness existing (till a boundary, after which difference begins) that we are able to call anything, a thing, in the first place! This is the cognitive meaning of a ‘THING’. This concept has extended metaphorically to abstract things like class, strength, Math, cricket etc. wherein the sameness is in some or the other regard (than physical appearance). So the world is made up of only “same” and “different”. ‘Sameness or Difference’ is the only distinction that can exist between any 2 things in the world.

THE ALL-KNOWLEDGE PROJECT - PURE FUN!

Take a humongous source of data. All the possible kinds of sentences (on the basis of their parts-of-speech-combinatorial structure) will be covered in it. For each distinct type of sentence-structure do this : Say, the structure is NVN - John was doing his homework. Make combinations of all possible Ns and Vs in it from the dictionary. You will have a set of all possible sentences in the English language of the structure - John is doing his homework. Similarly generate all the possible sentences from all the various different structures of sentences. You will thus have all the possible grammatically correct sentences in the English language. Some of them will make sense. Some won't. If you distribute this set on the internet for kids to play with and just say whether this sentence is “possible” or “not possible” (which in fact will be a commonsense test), you will have a set of all possible sentential English language knowledge.

What is the meaning of INSIDE ????

What is our cognitive undestanding of containment? Closed from all sides. What is our mind’s commonsense understanding of closedness, and thus of insideness? Firstly, there is something particular about all solids - all things. It is that anything that is solid is full-dimensional (which happens to be 3 dimensions) in its existence. That is, its surface covers all “sides” POSSIBLE, locally. Consider a foot-ball. You see its front curved surface facing you; then you rotate it, say, to the right. Then you happen to see that whatever was remaining, which was not seen earlier in the front view, is closed. The right side now is closed because your memory tells you that it is the same thing as what you saw upfront in the beginning. So the football is closed throughout. And closedness throughout leads to the concept of insideness. Anything which has a closed surface on ALL POSSIBLE sides is said to be inside that surface (3D), or loop (2D). So the key check for insideness is the ‘boundary’ or the ‘border’, ON ALL POSSIBLE SIDES.

Psychology v/s Logic

Suppose the given data is - David is teaching vectors to Bryan. And they are in the same class (same age). One commonsense inference - So David is better at vectors than Bryan. The question is - why does a particular inference strike us with more likelihood when we come across a piece of data? Here, there are other inferences like - 1) So Bryan is learning. 2) So Bryan knows (would know) what a vector is. 3) Davis seems to be a helpful student. etc. to name a few. The machine and humans would know the piece of commonsense fact that ‘Teachers are generally older than their students’. This would contradict line no.2 of the given data. And in the LIGHT OF THIS CONTRADICTION, this very inference should be inspired - i.e. So David is better at vectors than Bryan. (They would now be compared in their abilities since they are now known to be fellow-students). This wouldn't have been the primary inference if it wasn't given in the data that they are of the same age. This implies there is a motivational fluid of impending conclusions running through, while the mind is doing commonsense reasoning. That is why some inferences get a preference over the others i.e. humans are more likely to jump to them than others. Logic cannot distinguish between these (unless of course these internal motivational rules themselves are somehow fed in as additional logic-statements into the machine).

The Laws of Thought : Psychology + Logic

The Laws of Thought : Psychology + Logic.

Suppose someone tells you a statement which is new to you and you comprehend well - say - John is highly intelligent.

The first point, in my view is - why does this statement get registered/impacted in your head? 1) Is it because of the word "John"? Say, you are pre-interested in John 2) Is it because of the word "intelligent"? Say, you are pre-interested in intelligence. 3) Is it because of both the words - "John" and "intelligent". Say, you have a fascination for both John and the concept of intelligence.

In case 1 - If I am pre-interested in John, what will get registered or impacted in my mind is 'intelligent' because 'John' is something I already know about, but today I came to know that he is highly intelligent. The new part is the "intelligent" (that he is intelligent), and the 'John' is already something I am used to in some ways (since I was pre-interested in him and hence knew some things about him). The 'intelligent' is the new part in contrast with all that I knew till now about John. So "intelligent" is the impact word.

Case 2 - Similarly, if I am pre-interested in intelligence, "John" is the impact word.

Case 3 - If I am pre-interested in both 'John' and 'intelligent', then the association 'John-intelligent' will get registered/impacted in my mind. Think of one and you think of the other!

Now, if I now come to know something more about intelligence, then in case 1, I will be "drawn to" deductive reasoning from the given statement since intelligent has stayed in my mind and in the very heat of that moment I hear something about intelligent. Hence I will quickly connect John to that new information I have just jumped to (or just been freshly exposed to) about 'intelligence' - say, intelligent people are introvert - and draw the inference that 'John is introvert'. There is a high chance that I will do deductive reasoning.

If I come to know something more about John (say, The Smiths are John's parents), then in case 2, I will be drawn to do abductive reasoning that 'the Smiths must be smart'. This is because John is what has gripped the mind and any new information about John, in the heat of that gripping, would lead the mind to link the impact-word 'John' to the freshly consumed new information about the impact-word itself. Yes, the mind has used an additional information 'intelligent people give birth to intelligent children', but that additional information is general commonsense information floating in the mind  and came in as one of the things you know about the pre-interested topic 'intelligence'. 

I haven't been able to cast the third case into any appropriate logical reasoning format. Probably, inductive reasoning since "one comes along, by default, with the other, always". Yes, probably inductive...

 

The Meaning of MORE

 The meaning of MORE - 

We casually and easily say - more apples, more phones, more trouble, more scolding etc. But what is the technical or Cognitive meaning of the concept? More is more of something. Say, of 'X'. So, firstly, X already exists. And, as the phenomenon - more - says, there is "more of X". Though it is very difficult to define more, one can see 4 properties of MORE :

1) MORE adds to some property/ies of the initial thing. When I get more phones, the property of 'phone'ness or 'something being a phone' is added to. If a computer is added to a collection of phones, the 'electronic-item'ness is added to, and we have 'more' electronic items.

2) Cognitively speaking, there is a detection of a 'match' with what is / has gone into memory (earlier). This is what gives the experiential "feel" of more.

3) 'MORE'ness "fills up" / "takes up" / "occupies" finite space.

4) There is a "location" to X (X is that whose more we are considering), where the more of X keeps piling. This relates to the 'filling up finite space'-point above. There is a location or a space, UNDER CONSIDERATION, where the piling up of X is happening. 

The elementary core of Reason - from Logical and Cognitive perspectives -

 

The elementary core of Reason - from Logical and Cognitive perspectives -

Consider this - John gave Jack a gift. Gifts make Jack happy. So John gave Jack something which made Jack happy.

Lets simplify. John gave Jack a gift. ‘A gift’ makes Jack happy. So, John gave Jack something which made Jack happy.

A gift makes Jack happy. And John gave Jack a gift. How does that imply that John gave Jack something that made him happy? Because, a gift is a gift. Why? When a word is assigned to some piece of reality, any other instance of reality satisfying the criteria of assigning that word to the original reality, will be allowed to be assigned that word. Conversely, that word can refer to that other instance of reality. That is the functional definition of a word.

Cognitively speaking, it is a primary, in-born (the latter is a claim here) instinct “to take note of” something that the mind encounters in reality, which is already in memory (which has been encountered before). A subtle definitive extension of “taking note of” would be “involuntarily applying whatever one knows about the previously encountered entity to the newly, repeatedly encountered one”. That might be the most basic (intelligent) use of what we call ‘memory’.

A very obvious query -

At the heart of reason is nothing but 'DEFINITION' (or definitive substitution). 

Firstly, let's see one obvious point. Given an entity X, if there is any sentence involving the definition/synonym of X, I can cut-paste that definition/synonym into that sentence and the meaning of the sentence remains the same.

Now, a simple point is that given any sentence with entities E1, E2, E3,...., En in it, if I give ANY INFORMATION about an Ei, that information will behave as a "definition" of Ei. And, it will give an inference. (I bought this lamp from 'Laxmi stores'. 'Laxmi stores' was established in 1950. So, I bought this lamp from a store established in 1950).

Question - Can we represent all 'Reason' using hyper-text (or nested hyper-text) pages, since, as we see above, 'REASON' itself fundamentally functions/jumps in that way?

ANALOGY BETWEEN ‘CHEMISTRY’, AND ‘KNOWLEDGE REPRESENTATION IN ARTIFICIAL INTELLIGENCE’ -

 ANALOGY BETWEEN ‘CHEMISTRY’, AND ‘KNOWLEDGE REPRESENTATION IN ARTIFICIAL INTELLIGENCE’ - 

Consider this sentence - 

A gave a ball to B.

There are 6 words. Words are like atoms. They connect with each other to form a molecule called sentence.

There are 2 kinds of words/atoms - stable (independent) and unstable (dependent).

This difference is on the basis of their meanings. 

An unstable word depends upon attachment to other entities for the complete expression of its meaning. A stable word doesn't need that. So unstable atoms form bonds with other atoms in the molecule for stability.

For example, ‘ball’ is stable because you can define ‘ball’ independently of any situation or scenario. The meaning of a ball is ‘a spherical solid object used in games’…..something like that. But when one has to define ‘gave’ one has to take recourse to creating a background and invoking other entities; one says - when one transfers the possession of something to someone. Here, ‘when’,  ‘something’, ‘someone’ are things upon which the meaning of ‘gave’  DEPENDS upon for complete expression. These ‘some-X’ words don't come in while defining a ball or a pen or dance. But come in while defining ‘give’ or ‘preparation’.

When unstable words get into a sentence (molecule) they form bonds with other words. The stable ones don't form bonds with other ones FROM THEIR OWN SIDE. You could think of this as a co-ordinate bond - a directed bond. (Of course the stable words are INVOLVED in the bonds WITH the unstable words).

In the case of the above sentence, ‘A’, ‘ball’ and ‘B’ are the stable atoms. ‘Gave’, ‘a’ and ‘to’ are the unstable ones.

Lets see the bonds - 

1. A - gave

2. Gave - (a ball)

3. Gave - (to B)

4. A - ball

5. To - B

These are the bonds in the molecule - ‘A gave a ball to B’. The atoms in bold are the stable atoms.

Now, every direct (we will come to indirect bonds later) bond indicates a question-answer pair.

The corresponding Q-A pairs for the list of bonds above is - 

1. Who gave? A

2. Gave what? A ball

3. Gave to whom? To B

4. A what? As in, there was one (“a”) of what? Ball

5. To whom? B

Indirect bonds help in answering questions in general about the entities present in the sentence: How?

Bonds like ‘A - gave - a ball’ i.e. the bond between ‘A’ and ‘a ball’ are indirect bonds or ‘pathways’.

Now, any question will involve 2 atoms typically (X and Y) and some blah blah blah in it. Mostly the pathway between the atoms X and Y (i.e. the indirect bond) will be the answer to the question.

For example, ‘what did A do to the ball’? The pathway or the indirect bond says - A GAVE a ball.

Whereas if someone asks - Did the ball give? Here there is no pathway / indirect bond between ‘ball’ and give. So the answer doesnt exist, which  is indeed true. There is nothing like “the ball giving” mentioned here.

Inspired by the above 2 points - direct and indirect bonds - one can say that all the “sub-semantics” of the sentence (i.e. all the sub-information contained in the sentence) can be represented by the BONDS.

We can define Isomers also. Molecules with the same words but different bonds. That is, ‘A ball was given by A to B’ is an isomer of ‘A gave a ball to B’.

All the coordinate bonds have an electron-pair. This “unsaid content” of every co-ordinate bond (the electron-pair) is the commonsense about that linkage that can be placed above the bond. For example, for the bond : ‘A - gave’, what can be written above that bond hyphen is ‘with his hands’ i.e. the hidden unsaid invisible part of the bond.

If the sentence was - A gave a house to B, then on the bond ‘A -gave’ can be placed the commonsense ‘by transferring the papers’ & on the bond ‘gave - (a house)’ can be placed the commonsense ‘all the contents of the house’’. 

What happens when molecules come close to each other? They react with each other - their atoms react. Similarly, when 2 sentences follow each other, their atoms bear relationships with each other (ones from each sentence with the others). Such analysis can be done. (Terms like “reactivity”, “breakage of bonds”, “formation of new bonds” can be invoked…. !!)

For example, the pronoun applicability of a pronoun in the second sentence to the atoms in the first sentence can be seen in this light.

This work can be extended by drawing further analogies between the 2 concept-domains.

Finally, a picture of the molecule - 

WORDS AND ACTIONS

  WORDS AND ACTIONS

The ‘Physical’ and the ‘Semantic’, seen via a problem-solving strategy for making sense of something - 

Here is a problem-solving strategy : “Hold it tightly, upright and steady, in one place, and build other things around it with reference to it.” 

This is both physical and Semantic. Lets see how. 

Consider this sentence - Bill is a Physics undergraduate.

Now, “a Physics undergraduate” (which could also be described as “a Physics-undergraduate”) is “invented” English, after undergraduate programs in universities began in the world. We neither say “undergraduate of Physics” nor do we say “undergraduate of the subject Physics” nor “Physics’s undergraduate” which would be the logical constructions of the same. What have we done to solve this problem of naming when elements like ‘Physics’ and ‘undergraduate’ were floating around in the mind begging to be arranged in a meaningful form as a name? We held Physics tightly upright steady in one place - asserted the word Physics. And then we attached the others - undergraduate (in this case) - to it. We built the world around the word Physics with the rest being arranged with reference to it around it - attached to it. Even a physical scenario is similar. When we have to arrange some physical items and are confused, what do we do? We begin; we take a first step - we fix one of them tightly upright and steady in one place, and then arrange the rest around it with reference to it (on the basis of some relative rationale as regards to it). 

The problem solving strategy - in the Semantic and physical realms - is the same ! 

This shows that in some senses, our ways to deal with words have been inspired by those to deal with physical objects. More importantly, our Semantic and physical realms imitate each other.

Proportionality and Countability

There is proportionality in discrete countability - 

What is 5x? x+x+x+x....5 times. This is equivalent to multiplying the number 5 with x.

Now, what is 2.2x? You can't directly say that it is x + x + .. 2.2 times because - how can the number of times be 2.2? But you can indeed say it actually. Its x + x + 0.2x i.e. one whole x plus one whole x plus 0.2th of x. So, in the third term, instead of a whole ONE x, you have taken a PROPORTIONAL quantity of x which is 0.2th of an x or (x/5) and this works well in the counting scheme above of 2.2x being x + x +..."2.2 TIMES" or the third term being "0.2 TIMES" even if it (0.2) is not a discrete unity integer. 

So countability (which is additive) is consistent with proportionality (which is multiplicative).

Proof that the universe is infinite

Proof that the universe is infinite - 

Consider the term 'all that exists'. Whenever we talk of "all that exists" in the case of finite things, it is always while we are considering some domain (finite) in which all that exists lies. 

Now, if we talk of a (finite) domain we should be able to talk of something which is 'not the domain'. 

Now, since the universe is all that exists, there is nothing like "not the universe". So the universe is not finite. 

Hence it is infinite.

Diversity in Nature - An Intuitive Explanation

Consider 2 bags, each full of numbers - the same numbers (say, 1 to 1000). Pick up a number from the first and one from the second bag. There is more probability of they being UNEQUAL, than they being THE SAME. The chance of picking up a ‘47’ from the second bag too, after picking up a ‘47’ from the first bag is very very less. 

In general, inequality can happen in 'many' ways; equality in only 'one' special case. Thus there is more chance for inequality to happen. When you take 2 things in nature, there is a higher chance of them being different from each other, in some respect, than the same. Difference/Variation is the norm; Similarity/Match the exception, in nature.

REASON - 

The below observation is factually correct, but that it is the REASON for the above or that the above is ROOTED in the below, is an intuitive statement. Is that correct?

Is it so that there is a high chance of "different things being different" and "same things being same"? What I mean is - when you take two things, any two numbers, they being two numbers means that they are (two) DIFFERENT numbers. And that corresponds to the high chance of them being DIFFERENT from each other too. If you take the same thing twice i.e. "take 2 SAME things", so to speak, then there is a very high (100%) chance of them being SAME too (unless of course if the thing changed in the time interval between taking it the two times).

So, DIFFERENT => DIFFERENT. SAME => SAME.

Is there anything like 'infinity'?

Suppose you encounter an algebraic term (n+1), where n is ANY number. Now, what is n? As said earlier, n could be any number. But the question that arises is that how do you know that (n+1) is also a number?  Maybe n is the highest number possible. 

We say things like - "...and this process goes on forever...." which means it goes on infinitely. But what does infinity mean here? That the process goes on forever. What is "forever" here? Forever in time, and time is measured in numbers, and they are precisely what the above argument applies to.

MIND and REALITY

 MIND and REALITY -

Consider a blank paper. There is no line on it (it's blank). Now paint half of it with blue. Now we have a line - the one at the interface of the blue and white patches. Extending this argument, one can say that even on a blank paper, there is a line of the same colour as that of the paper. It's just that we cannot see it. Note that no one is saying that there is a line DRAWN by someone on that blank paper, but the line exists. Going by that argument even further, there is everything that's possibly writable, written on a blank paper, just that it is not detectable by a human being.

When the visual sensation throughout is the same, everything possible "exists" in it.

Is such a thing real, or only in the mind? When there is a mere thought in the mind (without being coupled with any 'action'), there is still a chemical and electrical flow in the brain which makes it a reality, but we cannot detect it. And we say for such things - "it is there only in the mind, not in reality". Extending this fully, we can say that a mind, as a whole, is what a brain does, which cannot be detected by human beings. (Ref : I have used Minsky's definition of the mind here - "minds are all what brains do")

Pair concepts - is it a coincidence?

 Is it a coincidence that almost all concepts which have a related pair of entities are equivalent?

1) Action doer - Action doee

i) container - contained

ii) Owner - owned

iii) .....

....

2) Antonyms or Opposites

3) Function - Inverse function

4)......

......

Take the example of host and guest.

1) i) Host and guest are like the container and the contained. One invites/embraces/hosts/absorbs the other.

ii) One sort of "owns" the other since the former is the container.

iii) .....

.....

2) Host and guest are antonyms

3) Hosting function is the inverse of "Guest-ing/Guest-izing" function.

4) ....

......

Take another example - sin (x) and arcsin (x)

1) i) Sine, the function, is the container which contains x which is arcsin(sin (x)).

ii) The 'sin' owns/hosts/floats the x which is arcsin(sin(x))

iii) ....

.....

2) Sine and Arcsine are antonyms

3) Sine and Arcsine are inverse functions of each other.

4) ....

'SAME' and 'DIFFERENT'

 'SAME' and 'DIFFERENT' -

Same and different aren’t “equivalent” opposites of each other. Because - the comparison checks - 'Same' or 'Different' - applied on 2 entities (while comparing them) aren’t equivalent.

Explanation :

If there is one difference between the 2 entities, they are definitely not same.

But if there is one similarity between the 2 entities, they may or may not be different.

What the two equivalent opposites, instead of ‘same’ and ‘different’, though, are -

‘More same than different’ & 2) ‘More different than same’.

The more the comparison-result between 2 things is of type-1, the lesser it is of type-2, and vice versa.

An example of equivalent opposites is simply, say, ‘Big and Small’; the more big A is than B, the less small it is than B.

THE POWER OF A 'REFERENCE'

 THE POWER OF A 'REFERENCE' -

A reference (real or imaginary) divides anything into (different) parts.

Firstly, for 2 things to be perceived as different, there has to be some property of theirs with regard to which they are different. Now consider a white canvas. All points on it are identical. Draw a vertical line on it in the middle. Suddenly there are 2 parts that are different from each other. But the 2 parts are identical in shape and size and colour. Still how come they are different? What property of theirs distinguishes them? Well, it is that one is to the right of the line and the other is to the left of the line. That's the property. But that is not an intrinsic property of the 2 patches themselves, as such. I am seeing them with reference to something (here, a line) and that's what makes them different. That referencing divides the canvas into 2 parts. So consider anything. And imagine some reference (real or imaginary) anywhere in space. Talking in the language with regard to that reference, every point on that object will be DIFFERENT. Thus, a reference (even an imaginary one) has DIVIDED anything into DIFFERENT parts, even without touching it!

DID THE UNIVERSE GET CREATED?

 DID THE UNIVERSE GET CREATED?

There is 'nothing' only when there is something. Without the existence of something there cannot be nothing. That means there cannot be entirely nothing. So existence is a compulsion. Something has to exist, always. Either this is true or the word 'nothing' is invalid.

Conclusion - the universe was never "created". Something always existed.

THE CONCEPT OF THE UNIVERSE

 THE CONCEPT OF THE UNIVERSE -

You cannot point to the universe i.e. talk about it. This is because you can talk about something only when you can distinguish it from its surroundings i.e. from others. You cannot do that with regard to the universe, since the universe is everything. Now we have a contradiction - we cannot talk about the universe and we have the statement that says 'the universe is everything'. This only means that the definition (that 'the universe is everything' OR 'all that there is') is invalid.

Conclusion - The universe is not everything. Maybe it has another definition. If NOT, the concept is ill-defined and does not exist (the universe doesn't exist).