Genuine commonsense reasoning

 I propose 2 quite simply distinguished types of commonsense reasoning. Lets call them A and B. My point is that B is tougher to do than A, and truly exploits the diversity and resourcefulness of the mind that commonsense reasoning demands (Minsky, The Emotion Machine).

Lets see type A commonsense reasoning. If there is no petrol, the car wont run. If you close the gate the car won't be able to enter the building. Now, in the first case, petrol is MEANT TO run the car. It is a definitive property or role, as one might say, to run cars. Gates are MEANT TO allow/disallow entrants. So, here the reasoning which is done (thinking of the implication) is in line with what the key entity is meant to do - in line with the definitive role of the entity. So it is easier to do this kind of reasoning. Whatever be the knowledge representation and storage mechanism in the mind, the fact that petrol is required to run cars is stored very "near" to the definition or identity of the entity 'petrol'. 

But now consider something else (type B). Suppose a tree falls on the road, then a car won't be able to move ahead. Here, this calls for genuine commonsense reasoning since it is not a definitive function of trees to "block things in a fallen state". That's not what a tree is (primarily) meant to do - it's meant to purify the air, provide shade, flowers, fruits etc. So this reasoning involves abstractising a tree as a general big mass of solid, which if comes in the way of something, can mostly prevent it from going ahead or block it. This, I guess is a more genuine form of commonsense reasoning since it involves representing/seeing things in ways which are not their key features but are the quintessential feature with regard to the situation/context at hand. That shows agility and a non-stereotypical fashion of thinking of the mind.

A small theory for constructing commonsense-based assumptions about sentences

 A small theory for constructing commonsense-based assumptions about sentences : 

In any sentence we encounter and cognize, there are generally 2 parts - what is explicitly stated in the sentence and what assumptions we make attached to its elements, based upon our commonsense, to comprise our understanding of the sentence. With the help of the latter, we construct a visualization or an assumptive model of whats going on. 

Applying commonsense is synonymous with visualisation.

Lets integrate this theory with how we cognize a sentence in general. That is, building the commonsense model would be a part of the theory. 

When someone says to us - John is standing on the stage - we imagine a man standing upright on his feet and head at the top, on the stage. When someone tells us - John gave a ball to Jack - we commonsensically assume that John gave the ball with his hands to Jack. Here commonsense assumption-making is involved. 

Here is the theory : 

Most text or spoken speech content falls under the category of 'WHAT'. Let me explain this. Whatever is stated in books and speech is the 'WHAT'. Consider 'John flew from New York to Boston'. Here, this sentence talks about 'WHAT did John do?' 'John fell down' talks about 'WHAT happened to John?' John gave a book to Jack talks about 'WHAT did John do?' or 'WHAT did John give to Jack?' or 'WHAT transpired between John and Jack?' A lot of sentences talk about the WHAT, in general. 

Upon hearing the sentence, the first thing the mind does is to think about, if not mentioned, the 'HOW?' As in, how did the 'what' happen? - the way. So upon hearing 'John is standing on the stage', we first think about the HOW i.e. how is he standing? This is important for the cognitive visualisation.

To answer this HOW, we tap our commonsense knowledge. In this we obviously draw forth from our libraries of memory, what are the usual ways of the 'WHAT' happening i.e. the HOW. Commonsense answers the HOW.

Now, here is a Linguistic sub-theory for how the mind finds out the HOW commonsensically - 

Mostly, the WHAT refers to the verb in the sentence - (standing, flew, gave etc. in the examples above). Now, there are 2 kinds of verbs I propose - Dependent verbs and Independent verbs. Dependent verbs are those verbs which require some additional information attached to them (usually a noun) for completion of their meaning. For example, if someone says, 'I am building' or 'I am preparing', one immediately needs to know and ask - What are you preparing or building? The answer could be - building a house/a net/a model and preparing a plan/for an exam/a dish. Independent verbs dont require additional information for completion of their meaning. They are "self-sufficient". For example, when someone says - I am dancing or jogging or running, one doesnt need to know more to understand. 'Dancing', 'running' and 'jogging' are self-sufficient to a great extent. 

So, coming back to our main theory, when the mind encounters a HOW and taps the commonsense knowledge-library for an answer, if the verb is an independent verb, it constructs a visualisation on the basis of the repeatedly seen/known visuals of the verb. For example, in the sentence 'John is standing on the stage', the verb is standing. It is an independent verb. So the answer to HOW John is standing is on the basis of the hundreds of thousands of images of people seen standing - upright, on their legs with their head on the top. Hence the mind visualizes John standing upright on the stage. In the case of 'John gave a book to Jack;, the situation is different, since the verb - 'gave' - is dependent. That is, it is unclear as to 'gave a name' verbally, or 'gave a house' on paper, or 'gave an object' with hands'? In such cases, the additional surrounding data in the sentence is drawn forth. Here, it is 'a book' since John gave a book to Jack. Now, commonsense libraries are tapped for what are the typical, usual, repeatedly-seen visuals of books being given by one person to another. The answer happens to be - with hands. (In rare cases, by emailing e-books as attachments). Hence the answer to the HOW in this case is 'with hands' and in the former case, 'upright, on the legs with the head at the top'. This is what and how commonsense helps construct the assumptive visualisation of the data in the sentence - in other words, the "construction of the assumption", as mentioned in the title.

Going on further, if commonsense can complete the picture by answering the HOW, we keep quiet upon hearing the sentence, and keep our understanding to ourselves, by saying nothing further. If commonsense cannot complete the picture, we ask the speaker or the source - HOW? For example, if your friend tells you - lets go to some restaurant, you dont know how far he is talking of going and there is no way commonsense can answer the HOW - go by bus, train, his private vehicle or walking. So you ask explicitly - how are we going?

Data is the WHAT; knowledge is the HOW. 

This theory explains the basic, broad sentence-cognition framework, with commonsense-based assumptive modeling. 

Commonsense Inferences - definition, technique and theory

What is a commonsense inference? Suppose I say - John is standing on the podium. What commonsense inferences can you draw from it? One is that John is "higher" than the rest of the people. 

How does one go from an original statement to an inference of its? Suppose someone tells you that x > 5. You would say - so, x > 0 or x^2 > 25. How did you arrive at these inferences? By doing certain 'operations' upon the given statement. Can we imitate this for English statements? Can we fiddle and play with given statements to derive inferences from them? Yes. There is a way.

There is a simple technique. Visualise a typical, commonsense image corresponding to the given statement - what the statement is saying. There will be several elements/entities in the image around the subject of the sentence. SEE THE EFFECT OF THE GIVEN STATEMENT ON EACH OF THOSE SURROUNDING ELEMENTS/ENTITIES!! Or, see the surrounding entities in relation to the subject, in the light of the given information in the statement. So, when someone tells you John is standing on the podium, visualise the scene. What do you see? John, a stage, a dias, a mike, the audience, a hall etc. Now just mechanically see each of these elements in the ways described above. It is very easy to arrive at the above commonsense inference - John is higher than the rest

Take another example, in detail - the petrol in the car got over. What are the surrounding elements? car, road, trees, people, other cars, buildings etc.

Element            Related Inference

Car -                 the car cant move ahead

Road -              Car is at a fixed spot/patch on the road.

Trees -              NA

People -            watching this stuck up car

Other cars -       traffic jam

buildings -          NA

I also claim this to be partially/hazily overlapping with a could-be theory of how the human mind does this process.

A question - Machine Learning

We learn commonsense. We arent born with all of it. What does commonsense tell us or makes us want to know about, when we are told about any economic activity - anything involving economics? It is the AMOUNT OF MONEY INVOLVED. How do we learn this? After being exposed to tonnes to examples of economic activities - buying ice-cream from pocket money, learning that someone signed a deal, reading that Microsoft bought Yahoo, hearing that tax rates or interest rates lowered, knowing that uncle bought a house, listening to "we paid some amount to them" etc. The key points or at least the first points of commonsensical relevance/interest here are - how much did the ice-cream cost? how much was the deal for? Microsoft bought yahoo for how much, rates lowered by how much? ....etc. So we LEARN, from repeated experience and exposure, that the most or the first relevant/important/interesting thing in anything that has to do with economics is 'HOW MUCH money is involved?' It becomes a part of our second nature to ask that upon hearing any such thing.

The question is this - can a Machine Learning model, exposed to millions of pieces of economic activities' data, learn this piece of commonsense, from them?

GENERATING COMMONSENSE INFERENCES

 GENERATING COMMONSENSE INFERENCES - 

What is a 'word'? What is a 'gun'? What is 'wedding'? Simply speaking, it is the usage of language for an instance of reality.  When certain instances of reality meet a certain 'n' number of criteria, it is assigned a certain corresponding word 'W'. When there is a ceremony of a bride and a groom, with attendees, with a function......etc., all of these are collectively called a 'wedding'. Similarly, when there is a pipe, a trigger and a handle, they are collectively called a 'gun'. So when these enlisted criteria are met, the respective word is ascribed to that piece of reality. 

Now, when someone describes a piece of reality experienced, with the word 'gun' in the description, it means a gun has been perceived. That means that a pipe, a trigger and a handle have been collectively perceived. This set collectively is a gun. Now, these 3 are the key features - identifiers - for the criteria for a gun to be met for an object. These identifiers don't have any "language" - they are sensory visual and auditory (mostly) inputs into the brain - signals. Now, in the very perception of a gun or the identification of the features which satisfy the criteria for an object to be a gun, there is commonsense involved. This is because the rest isn't talked about and could be anything. But commonsense tells us that if these criteria are met, most often than not, the reality in question corresponds to the word associated with that set of criteria. (In some cases, the perceived features might be even lesser than the required number for the criteria for ascription of the word being met).

So when we talk of 'Commonsense applied to NLP', we have to bear in mind that in the very  perception of the very words which make up the knowledge in the sentence, there is commonsense involved. Lets exploit this commonsense. 

So, a gun = pipe + trigger + handle

Or rather, gun = visual symbol (pipe) + VS (trigger) + VS (handle)  .... VS = visual symbol.

Similarly, fall = visual symbol (at top initially) + visual clip (speedy vertical disappearance) + visual symbol (towards down)

Make a database of ALL the words in the dictionary in terms of the ACTUAL SYMBOLS (not in terms of the words described in the brackets above) and CLIPS, making up the criteria being met for a certain instance of reality to be ascribed that word.

So, we will have an entry in the database like, W = S1 + S2 + ...

Now, write any sentence - The gun fell down.

Break each word into its constituent symbols. So you will have a string of symbols - S1, S2, S3, S4, S5,.........Sn, collectively for all the words in the sentence.

Now is the key trick. Generate all possible combinatorial sub-sets of this set of symbols.

Now,

1) Check each such sub-set against the database. If there is a word in our database matching with a sub-set, it is very likely that the newly-matched word is an aspect in the 'commonsense-inferential-space' of that sentence!

2) Check for a substring standing for another new sentence altogether. Very likely it is a direct commonsensical inferential sentence, as a whole, to the original sentence! How to check this match for a sentence? Well, you would need to have a ready database of all the combinations of all the symbols involved in all the words in the dictionary, and a sentence written, in case there is a meaningful one, corresponding to such a combination.

Is this a complete Q-A theory?

 All questions have 4 components : A = what is being talked about, B = something connected to A, that is being asked (this is the "answer"), C = "connector" of A and B, and D = obviously the 'Wh word'. The target (potential answer) statement on the website is 'S'. 

Consider these 2 simple questions : 1) What do elephants eat? 2) When is Christmas celebrated?

 

A = elephants       B = food ("ANSWER")         C = connector of A and B = eat

A = Christmas      B = date ("ANSWER")          C =  connector of A and B = celebration

* B is the commonsense knowledge indicating the "type" of the answer = Answer to (C + D)? : (eat What)? 'Food' , (celebrate When)? 'Date'

* A and C have to be present, in some form (of course not necessarily as they are in the question) in 'S'. That's mandatory. That is, 

A, or something present along with A in some entry in the commonsense KB, should be present in 'S'. Lets call that A[KB].

C, or something present along with C in some entry in the commonsense KB, should be present in 'S'. Lets call that C[KB].

Remnant in 'S' = S – A[KB] – C [KB] = (Answer), if 'Type' of the Remnant = B (checked from the commonsense KB).

The meaning of an abstract word

The meaning of an abstract word X, is what maps X onto an Event.

When I think of or hear 'ownership' or 'smell', I think of a 0.5-1 second video clip of some event/action related to 'owning something' or 'smelling something', in my mind, to come in touch with the meanings of those words. You need an imaginative actualisation, like is present in the case of physical tangible words. What is the word 'touch' otherwise? Just visual (while reading) or auditory (while listening) signals of a certain frequency going into the brain. For it to 'mean' something, it has to trigger some processes in the brain, whose equivalent is this imaginative actualisation mentioned before. Understanding (not something new), after all, is something external entering the mind and triggering what is already known/understood about it, in there. 

When I hear 'smell', I have to imagine some person smelling something. This is the event that the meaning of 'smell' has mapped the word onto, in the mind. 

When someone tells you - John gave 2000$ to Mary - how do you understand the scene? Or rather, how do you understand 'Gave'? Some part of your mind, quickly, for a fraction of a second, imagines hands transferring something material. This is the source of the commonsense interpretations related to that word; positive ones like - it was given with hands, it moved from possession at one location (hands of one) to another one (hands of the other), it isn't with both at the end of the action etc., as well as negative ones like - the hands weren't ablaze while giving it, there wasn't a gun in the hands simultaneously etc. This is also the Event which the meaning of the abstract word 'Gave' is mapped onto. 

It is impossible to actualise abstract words statically.

Vision isn't commonsensical in the way language is. In language, you skip the parts which are assumed (commonsense). But while seeing something, you would notice the commonsensical thing again, many times too. We all know that phones have a central main button; that doesn't mean we will not look at or notice or think about it when we look at the 500th phone we see in life. This is what makes us draw forth the details from the visual imagination like 'giving with HANDS', 'it cant be with BOTH at the end of the action' etc. - which are related to the commonsense inferences about the scene.

Presuppositions in Linguistics

 Inspired by the concept of Presuppositions in Linguistics, I would just like to float a concept which I call Proactive verbs and Reactive verbs.

Reactive verbs are those actions which require an already existing prevalent reality to which the doer is reacting. Proactive verbs are those actions which aren't reactions to any prevalent reality existing, before doing the action. Technically speaking, every verb will be reactive.

E.g. - 'harvesting' is a reactive verb, because the action of harvesting can take place only when crops have already grown and filled the field. This is the prevalent reality. But 'dancing' is a proactive verb because you can start dancing without the presence or requirement of anything particular in reality. You can just start dancing on the floor or in space. Now, strictly speaking, technically, every action will have some requirements, i.e. the proactive verbs like dancing will require a floor or space and obviously the doer (and some might say intent), or slipping will require a surface and the one who slips, but that is too basic and commonsensical. For all practical purposes, harvesting is reactive and slipping and dancing are proactive. 

This seems to be the basis of the sentences associated with presuppositions like 'John has stopped watching cricket', which implies that John once watched cricket. This is because 'stopped' is a reactive verb. You stop something when something is already going on / in action, before.

An idea for Search Engines

 An idea for search engines :  ‘Splits’ and ‘Wh-words at the boundaries’.

Let me first present a concept of ‘Pauses’ within sentences. Let’s call them splits.

E.g. - 

Put the book on the table.

The splits here are - 

Put the book | on the table. A split is where there is a slight pause, while speaking.

Another example - 

The doctors called the operation team on the next day.

The splits here are - 

The doctors called | the operation team | on the next day.

A more rigorous and technical definition of a split - 

There is a split between 2 consecutive words A and B '....A | B ….' in a sentence, if putting the splits as ‘…. | A B | ….’, and thus pronouncing the sentence with pauses before and after A and B respectively, and pronouncing A and B consecutively quickly, (and also pronouncing the words without a split between them quickly after one another) would make the pronunciation of the sentence sound “odd” (or against the standard rules of pronunciation). 

So, consider the first example above - Put the book | on the table.

The adjusted splits here would be - 

Put the | book on | the table.

Now try to pronounce this with pauses at these splits, and saying the words without a split between them quickly after each other, and thus also say the words ‘book’ and ‘on’ quickly after each other. That would lead to a pronunciation like : Put-the…...book-on…...the-table. That’s clearly odd.

Now that we have defined the splits, here is a crucial property of the splits - 

Every chunk generated with the splits is an answer to a wh-question asked to the immediately previous chunk.

Illustration - 

Put the book |where| on the table.

The doctors called |whom| the operation team |when| on the next day.

This can be exploited in search engines. An answer to a query lies in a chunk in a sentence (on a web-page), if the previous chunk to it contains the “main” part of the query and the Wh-word of the query is the wh-word at the split between the two chunks. 

Illustration  -

Query : Where do flamingos migrate in summer?

Now, just the fact that all the keywords are present in a sentence doesn’t mean that that sentence is answering the query. 

Suppose there is a sentence on the web - In summer, flamingos migrate to the wetlands.

This splits as - In summer | flamingos migrate | to the wetlands.

See the second split. The wh-word that lies at it is ‘WHERE’ which is the Wh-word of the query. And the “main” part of the query, which is ‘flamingos migrate in summer’ is what precedes the chunk to the right hand side of the second split. Since these 2 conditions are met, the right-hand-side-chunk (to the second split) - ‘to the wetlands’ - is the answer to the query. 

This sentence will be spotted by the existing prevalent technique also (of keywords), but there can be another sentence like say - 'In summer, the Indian players migrate to Australian grounds, where wings of flamingos are seen dispersed'. This sentence wont be picked up by the technique described in this write-up, which the keywords-technique would do so.

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So, the help needed is as follows - 

IS IT POSSIBLE TO PROGRAM THESE SPLITS AND THE WH-QUESTIONS AT THE BOUNDARIES (BASICALLY WHAT IS DESCRIBED IN THE TECHNIQUE)?

MIT Moments in Time Dataset

 I saw the moments in time data-set at MIT CSAIL which Jim asked me to have a look at. They are talking about using the video clips to recognize and understand actions and events in videos. They give an example - "opening" of drawers, boxes, curtains, eyes etc. 

Now, these are multiple representations of the same word - in particular, an abstract word like "opening" here. So can this system be said to have an understanding of the meaning of the word "opening"? In that case, why not use this data-set to help computers understand language - meanings of words? Show them 4-5 instances of "opening" (the examples which they have given - curtains, eyes, flower petals etc.) or say, "consumption" (say, mangoes by a person, fuel by engine, sugar in stores) or "absorption" (say, water by a sponge, words by a mind, rays by a shield etc.), and the common aspect of the set is the meaning of the word !!

Consider for example - 'consumption'. After seeing the 3 videos described in the examples in parentheses above - mangoes, fuel and sugar - the machine should understand that the "going in of the mangoes", the "drawing forth and burning of the fuel by the engine" and the "emptying of the sugar from the reservoir and going into usage by the consumers", which all effectively amounts to "something being displaced or drawn forth or taken, for usage in some form" is what is 'consumption'. This gives the machine the real "understanding" of the word 'consumption'. Minsky says that you don't understand anything until you understand it in at least 3 ways. This is an exact match-case of that!

In general (and not just actions and events) abstract words can be taught to the machine this way. Abstract words are understood by demonstrations on physical/tangible words. Abstract word-meanings are mappings from the word onto events in the world. For example, to teach someone, what 'music' means, you expose him to music and say "what you are hearing now is music" or "You hearing = music". The machine understands 'hearing' from this data-set and knows concrete/physical/tangible words like 'you' (required for this data-set). So representations of creation / exposure to / consumption of music (supplemented with descriptive instructions) would teach the machine the meaning of the abstract word 'music'.

After the physical (like computer) and abstract words (opening, hearing, music etc.) are taken care of this way, what remain is the connector words in language - in, and, to, upon, at, if, for etc. These can be taught with multiple exemplary sentences (fragments, as are there in the data-sets) and the corresponding videos. For example, how do you teach someone, the meaning of 'If'? You show the machine videos of - someone hitting someone and the latter crying, someone breaking a glass by hitting it, someone touching a hot stove and his hand burning, and supplement these clips with sentence-fragments like "IF hit person, person cry", "IF hit glass, glass break" and "IF touch hand, hand burn". The machine knows the meanings of all these words (tangible an abstract). So what remains is 'IF', mapped onto the aspect of conditionality/causality in each. So being shown multiple instances, it can be said to get a "sense" of 'IF'.

Do you agree with this theory?

Meanings drawn from sentences - 'Stars' as against logical reasoning.

Consider this sentence - John gave the resignation letter to his boss.

The first meaning of this that strikes you, and strikes you lightning-fast, is that John is leaving his job.

Similarly, upon hearing that 'He presented the Nobel Prize to Mr. James' the first meaning that comes to your mind's notice is that Mr. James is a Nobel Laureate. And upon hearing that 'Jack left a suicide note', the meaning occurs to you instantly that Jack is no longer alive.

What explains this? The popular reason-based explanation given is - when does one give a resignation letter? When one is leaving his job. Hence that flash in the mind, upon reading that sentence which talks about giving a resignation letter. Similarly, when does someone get a Nobel Prize? When does someone leave/write a suicide note?

I go against this explanation by arguing that - consider a normal sentence like 'John gave a book to Mary'. Here nothing comes to the mind's notice like the  strikes or flashes in those examples above. Does that mean it crosses your mind 'when are books given?' and no special or particular answer comes up, and so you keep quiet and hence there is no flash? It doesn't even cross your mind for a second, something odd (i.e. commonsense-wise odd) like 'when are books given by someone to someone?' (upon hearing the sentence).

So here is my theory to explain the above phenomenon - 

I propose something like 'Stars' in the data which catch your attention. These stars relate to your important personal concerns, or important experiences (not necessary having gone through them personally) of the past. Some stars are universal stars i.e. stars for all; for example, Nobel Prize, world cup, suicide note etc. These things have had an impact on everyone's minds and are thus part of their experiences or concerns of life. There might be some stars specific to the individual.

If there is a star in a sentence (or data in general), without any particular context, you draw forth an implication related to the star, about the story. 

One question comes up - Why is an implication always possible/existing? Stars, in line of their very definitions, have something unique connected to them. 

So when you hear 'John gave his resignation letter to his boss', immediately, the universal star - 'resignation letter (which is an impact word) - gets caught and an implication related to it about the story described is drawn which bears a unique connection to the leaving of job, and which predominates all other processes in the mind. Similarly, the star 'Nobel Prize' brings to mind the meaning of Mr. James being a Nobel laureate and the star 'suicide note' brings to mind the meaning - John's death. When there is no star, as in 'John gave a book to Mary', nothing lights up and nothing crosses the mind, leading to no particular or immediate meaning being drawn forth. 

This, in one way, goes further to case-based reasoning because case-based reasoning does overlap with the explanation of the reasoning when stars are present (since the personal concerns and experiences are ultimately cases from the past, in your life), but in case of something regular and commonplace like giving a book it sort of becomes unclear. That is, one has experienced instances of someone giving a book to someone, in his past. Does that mean one will be drawn forth? And more importantly, what would one do with (draw what meaning with) a drawn-forth another regular and commonplace instance of someone giving a book to someone, to supplement the already present commonplace information that John gave a book to Mary?

2 points : 

1) Books might be a star for some overly avid book reader and light up his mind upon hearing the sentence - John gave a book to Mary - in which case he might draw forth some quirky meaning about the act.

2) Whenever something "regular" or "normal" or commonplace comes before you, it doesnt proactively cross your mind that 'this is normal' (unless the context you are in presupposes that you are going to come across something special in there).

Everyday understanding

 EVERYDAY UNDERSTANDING 

Suppose you call up your friend and ask him “Hi, what are you doing?” and he says “Hi, I am shopping”. To this, a typical reaction is “Ok, Ok”. This means you have, in an everyday sense of the word, “understood” what he told you.

What does this understanding comprise of? My first claim (about the first part of this understanding) is that whenever you come across anything in everyday life, you get in touch with why it is so. Now this 'why' is not the actual specific reason as to why that piece of data is the way it is, but you mapping that data as an instance of a commonsense phenomena that is known to happen in the world. That is, the mind gets in touch with the fact that ‘people shop’. This is what comprises (partly) the understanding of the information that he is shopping – the reason for the information as a general commonsense phenomenon known to take place in the world. 

When you see a building while walking on a road, your mind gets in touch with something it knows beforehand that ‘there are buildings alongside roads’. The argument for this is that if there is something that is odd and doesn’t match with a commonsense phenomenon you know happens in the world, you immediately think or ask ‘how come?’ or ‘why?’ or something similar. Suppose your friend had told you “Hi, I am waxing pigeons”, the first and immediate reaction would be “What? WHY on earth are you doing that?” You try to get in touch with the reason, which you cannot do so by mapping what he said with a commonsense phenomenon known to be happening in the world.

The second part of this understanding is that the answer by the friend lights up a related commonsense knowledge-piece in your mind, which is typically, ‘people shop in shops’. (Probably, this extends to ‘people shop by spending money’). This makes you immediately realise that your friend is in a shop, and is what makes you ask, probably something like “Which shop are you in?” The claim of this part of the understanding is supported by the argument that - you would laugh if you followed up to his answer by saying something like “where are you?” to which he said “in a shop!” (You would then say something like “stop cracking jokes, tell me where in the city are you”).

So the understanding of “Hi, I am shopping” comprises 2 parts – 1) getting in touch with the commonsense phenomenon known to take place in the world that ‘people (do) shop’, and 2) Invoking related commonsense knowledge like ‘People shop in shops’ or ‘people shop by spending money’.

Commonsense being hard.

 Minsky says that commonsense is hard.“Commonsense is not a simple thing. Instead, it is an immense society of hard-earned practical ideas - of multitudes of life-learned rules and exceptions, dispositions and tendencies, balances and checks.”(Pg.22, The Society of Mind, Heinemann : London, 1985).

Consider this piece of commonsense - If you use a cab, you will have to pay rent at the end.

The reason why most of this simple knowledge-piece like the one above is hard is that “there is so much” in each piece. When you are talking about a cab, there is so much to a cab. There are so many aspects to it - its parts, processes associated with it, its properties etc. There is the main body made of steel/iron, there are doors, handles, seats, windows, engine, carrier etc. As far as using a cab is concerned, there is the opening of the door, the sitting inside, the actual traveling journey, the talking to the driver about the route, the other things about your life you have in mind which go through it, the goods you are carrying,the people you are along with etc. You are exposed to so much while traveling (which you see through the window as a flow coming at you). You observe the driving of the driver, you experience moving through space automatically, you observe the route you are going along... All this is what is there to a ‘cab’ and to ‘using it’. There is so much possible. So many aspects of each entity involved can be connected to those of the others, leading to various possible thoughts, possibilities, conjectures, concepts and ideas. Out of these just the right, few, precise aspects have to be looked at and picked up to connect with each other, to arrive at the piece - using a cab implies paying rent at end. Here, only the“sitting in the cab while the driver serves you by driving, and your relocation/transfer via the journey” are the important facts connected to the service offered and experience gone through for which you have to pay the charges. If you keep your mind ONLY to this precise set of connected things, it is pretty simple to realise that commonsense fact, even for machines. But that's not the case in real life. The actual experience of going through picking up a cab and finally reaching the destination is made up of such 100-odd things that it is indeed a special cognitive process to keep track of the essentials - the “few, precise and right” - factors to smoothly process, connect and conclude and execute the realisation (before, during and at the end) that at the end, according to the journey, there is FARE PAYMENT.

‘A is taller than B and B is taller than C implies that A is taller than C’ is indeed easy. (So is ‘1+1=2’) This is not hard for humans (as well as machines). This, even though is commonsense, isn’t hard-earned (as Minsky says) since here, there isn't much to everything that’s in there - A, B, C, tallness and greater/lesser comparison between 2 at a time. Moreover, everything is precisely defined. Also,there aren’t many and/or multiply vague aspects to A, B, C, tallness and the comparative inequalities. This makes it less “things to handle on the plate”. You don’t have to focus on just the apt right, few, precise set of connected aspects to arrive at the conclusion. And this is how logic is in general. There is nothing “extra” to lead to the world of other possibilities of probable thoughts, conjectures, fall-outs etc via various combinations of the aspects of the entities involved in the whole picture.

“Common Logic” is easy and “Common Sense” is hard, for humans.

A special class of Commonsense

 I intend to throw light on a certain category of commonsense which, as said just before, is commonsense, but follows a special trend. These pieces of commonsense are easy to agree with, or realize/understand to be correct, after being told about them, but hard to be struck by during the course of being in the situation (or problem-solving situation).

 

Here are a few examples –

 

1)      All that is written in the world – be it magazines, newspapers, books, phones, internet, computers etc. – is written BY A HUMAN BEING. So, all written data is man-made. (Nothing has descended from the sky or nothing that is written in a certain script has been created by a process of nature).

This is commonsense – all written data everywhere in the world is man-made - but not something everyone has realized.

 

2)      Sometimes the key thing to realize in a problem is the “smart” commonsense point, and not, say, the laws of the subject (say, Physics).

Consider this problem- There is a solid disc. It is rotated along a fixed axis which is in the plane of the disc but doesn’t pass through the centre (is not its diameter). There is an ant on the circumference-edge of the disc at the farthest point from the axis on the circumference of the disc, in the beginning and it is moving along the surface of the disc in a straight line. Find the velocity of the ant when it reaches the other end of the disc.

Here, you write the momentum conservation equations of the system (linear and angular). You write the energy conservation equation (potential, kinetic, rotational kinetic energies). And then you fall one equation short considering the number of variables.

The key here is to realize that the angular velocity of the ant at both the end-points is the same! If the axis of rotation was the diameter then this is easy to realize. But the axis being a chord of the disc, it is quite elusive to realize that the angular velocities are the same at the 2 extremes of the disc (initial and final positions of the ant) (even though the linear velocities aren’t (‘r’ X ‘angular velocity’)). The distances of the 2 points from the axis are different making the linear velocities different, but the angular velocities are the same. This is because the angle by which the 2 sectors of the disc rotate in a given amount of time, for any angle of rotation, are the same. They are vertically opposite angles.

Now, this is not a Physics point, it’s a commonsense point. But in the situation of solving the problem (with the ant, the variables of linear and angular velocity, conservation equations etc.) becomes obscure.

 

3)      Consider a graffiti board. It is full. Now, the stuff written near the borders is the recently written stuff. 

This is because people will start writing in the free middle-spaces when the board is blank and move towards the edges once space starts getting used up! The statement in bold, is commonsense but again, quite elusive to realize on seeing a fully-occupied graffiti board.

A Commonsense Addition theorem

 Why will ‘only-addition’ always lead to an increase (irrespective of the initial amount)? (By ‘only-addition’, it is meant “no other activity”).

Proof : For only-addition, you need “something” before (atleast an empty space, which is some space) and that remaining unchanged – by definition.

Case 1 – initial space is occupied. 

(Note : By 'addee' it is meant "what is added to").

Here, for addition you need an addee (since initial space is occupied) and an addendum (something being added; otherwise you are not adding), and the addendum should be of the same type as that of the addee (by definition). By definition, addee remains unchanged. So upon addition, you will have the addee and an addendum – and both of the same type. Now you have 2 things of the same type, earlier you had 1 thing (only addee) of that type. 2 > 1. Hence whatever be the initial amount, adding or inflow will always lead to increase, since ‘increase’, by definition, is in a ‘numerically greater’ sense (>).

Case 2 – initial space is empty. 

Earlier there is nothing – no addee. Later there is the addendum. Something is greater than nothing. In other words, I have 1 thing – the addendum, and earlier there was nothing. Hence ....

Is this a correct explanation for question-answering?

 Is this a correct explanation for question-answering?

Theory - Grammar and thinking.

Suppose someone tells you that A gave a ball to B. Then he asks you - A ball was given by whom? You then answer - A. How does this get processed?

Here is an explanation. You convert the question and the data into different grammatical (but obviously, Semantically equivalent) forms. When the forms match literally, the answer clicks. 

That is, the given data 'A gave a ball to B' becomes ‘A is the giver of the ball’. The question ‘A ball was given by whom?’ becomes ‘Who gave a ball?’, which becomes ‘Who is the giver?’

Now, you have the question as - ‘Who is the giver?’ - and the given data as ‘A is the giver’. These 2 match exactly for grammatical slots. There is an ‘A’ for the corresponding position of ‘Who’. Hence the answer is - A.

A small Linguistics Result

 There are 2 kinds of sentences and 9 tenses. The simple present tense corresponds to one of the 2 types of sentences - GENERALITIES. The rest 8 tenses correspond to the other type of sentences - EVENT.

Generality (E.g. - This is my book. The earth moves round the sun.) and Event (E.g. JOhn stole my book. Jack was born.) are the 2 kinds of sentences. And every Generality implies an Event in the past.

Another way of putting all of the above is that sentences i.e. knowledge can be timeless or time-dependent. The parameter of classification here is Time.

This statement has another deep implication - it means that time existed always and will exist always.

Observations in Maths

5 POINTS :

POINT 1 :

The minus sign is not an EQUIVALENT counterpart (opposite) to the plus sign. Why?

1. The minus sign is both an operation as well as a signing operator (sign) to a number. That is, it is used in (8-3) as well as to portray (-5). 

2. Suppose you have +(+(+(+(+(+(+2))))), it doesnt matter how many pluses are there. The final result is a +2. But if in place  of the plus sign, there are minus signs like in that case, the final answer depends upon the number of minus signs (the parity of it).

POINT 2 : 

Why do we want answers in terms of SINGLE numbers? Why cant I say something is 8+4+3 - thats it. The problem is that you wont know if different representations are the same (i.e. if 7+ 5 + 3 is the same), since  a number can be divided into (even the same number of) parts in various ways.

Anyways, what lesson does this teach us? It is not possible to identify the whole from the parts unless you actually join them! (just like jigsaw puzzles).

Another less strong point is that - if 2 wholes are the same, they (the 2 entities) are the same. But if 2 sets of parts are the same, it doesnt mean that the individual parts are correspondingly the same. 

POINT 3  -

Sense of a number - 

How do you “understand” a number given to you, say 5?

The very meaning of a number is size - indicates HOW MUCH? So the very cognition or understanding of a number is getting a sense of its magnitude, its size.

A number is a size-indicator. 

So, cognizing a number is cognizing its size, which is, comparing it with anything whose (i.e. whose size) you have an understanding of.

You dont cognize anything isolatedly; you compare it with whats in your mind. 

This I guess is where the fundamental genesis of case-based reasoning is. Speaking in a sense, you wouldnt have understood the first thing you saw in life!

POINT 4 - 

B + 5 = 7

Something plus 5 is equal to 7. 

Something is a number. How? Something is added to 5. YOU CAN ONLY ADD NUMBERS, TO NUMBERS. So B i.e. something (here), cannot be a movie or a poem. 

Linguistic commonsensical reversal - Going up takes you close to the cupboard. So, going down takes you away from the cupboard (reversed 2 concepts). 

If something plus 5 is 7, then 7 minus 5 is that something (reversed the order and inverted 1 concept)! Hence B = 2 by mere language! This is just like - The fan is above the floor. Reversal of order and inversion of one concept preserves the truth - The floor is below the fan.

POINT 5 -

Vectors - 

AB + BC = AC

An alternate proof of the triangle rule of addition of vectors - 

Displacement is a vector. The third vector (AC) is clearly the resultant displacement of the 2 steps of earlier displacements - from point A to B (indicated by vector AB) and from point B to C (indicated by vector BC)!

Numerical addition

 Numerical addition - 

‘5 + 3’ 

What's going on here? Apparently, you can't do anything with this; you can’t add ("put together") these 2 “strangers”. Should you merge these 2 shapes? Should you plug them together as '53'?...........

You can only add the same things.

But here you are ACTUALLY adding 5 1s and 3 1s. You are adding 1s - these are the same things.

Addition is holding together the separate added entities as one set, of 1s. 

||||| + ||| = |||||||| 

***** + OOO = invalid numerically. 

When one says what is ‘40+30’, it actually means 40 of the same thing and 30 of that very same thing. In a numerical sense, these are 1s. That is why numerical addition works, without it being stated - ‘things’.