August 31, 2017 Thursday

Bedtime Story 

Constructing Tarski's Formal Restricted Language

Just look at this interesting temporal deixis “tomorrow”.

We all know that “tomorrow” defines the consecutive next day after every day.

Yet “tomorrow” of the day when I was hospitalized last year would certainly be different from the “tomorrow” of the Sunday that is going to come next.

The point that Tarski was making was that such ambiguous words have no place in the vocabulary of our language.

Formalized languages are those languages that satisfy these conditions with supreme rigor.

What is unique about such formalized languages is that there remains nothing to distinguish in expressions that have the same form used in different places.

They mean exactly the same not having any bearing to the context they were said or written.

Tarski says that on some occasions this technique is also used by linguistics while discussing natural languages that have not been formalized.

This is done to avoid any confusion.

Tarski admits that once a language is so formalized, they are fully geared up for theorizing on logic and mathematics.

He recommends that the other sciences too should get rid of the usage of natural languages and switch over to naturalized languages.

He once again wished to make it clear that when he speaks about formalized languages, he does not wish the formal language to be like the formalized mathematics of Principia Mathematica, comprising solely of untried weird symbols.

Nor do the formalized languages need to be diametrically opposite to that of the natural languages.

Au contraire, he feels that the formalized languages would only be interesting if they consist of fragments of natural languages.

The fragmented language would still have the complete vocabulary that will allow everything to be expressed clearly along with extremely precise syntactical rules.

There are some other conditions that are to be complied with in order to rationally use the word “true” in the languages without ending up in paradoxes like that of the Liar.

One is that a sharp demarcation has to be made between the language which is under discussion about which something is being said and the language that is being used in defining the former.

This point was already brought up in my previous bedtime stories.

The former, as you will recall, is known as the object language and the later the metalanguage.

The metalanguage obviously will be more copious than the object and will encompass it as well.

For truth to be defined adequately in such a system of languages, any equivalent of form [D] will work out.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 30, 2017 Wednesday

Bedtime Story 

Demonstratives or Deixis

Martin Rees is a British cosmologist and astrophysicist, winner of several accolades and possessing a gift for both public speaking and writing.

He is also one of those (like me) who believe that by now, with such astonishing technological progress thanks to the powers unleashed by scientific knowledge, the human ape has become his own worst enemy.

Never before in the history of this planet, and perhaps even the known universe, has there been rendered so much power to so many members of a single species to have a lasting effect on a ecosystem of an entire planet.

Perhaps only bacteria and plants with chlorophyll can seek to come this close.

The writing is beautiful of course, but the idea of writing it down for you was to point out how interconnected all sciences is for after all knowledge is about truth.

There can be no better metaphor than the ouroboros to signify this.             

Just in case if you are interested to know what kind of person Martin Rees is and how he thinks and speaks, you might like to watch this short video clip:

https://www.youtube.com/watch?v=E0zdXj6fSGY

Let us return once again to Tarski’s paper.

Just as everything in the universe is connected, either intimately or remotely, for the very same reason, this paper by Tarski “Truth and Proof” essentially on logic involves study of linguistics.     

Now in languages there are certain words that are known as demonstratives.

In terms of linguistics, they are known as deixis.

Deixis are those words or phrases that can only be understood, or rather fully understood depending on the frame of its reference or context.

Deixis can be either of person, place or time.

For example consider the word “here”.

Now we all know what here means but it can be used in tremendously many ways each time giving it a whole new interpretation.

For instance, when I say, “please come here”, here is a deixis of both person and place.

The word ”here” is determined by my spatial position.

But when I say “Here is where we will build a new hospital”, it is primarily being used as deixis of place.

Here my personal position is irrelevant.

Demonstratives and deixis can be pronouns, adjectives and adverbs.

Adverbs include words like “now”, “later”, “soon” and so on which are deixis of time have totally different meanings depending upon the context.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 29, 2017 Tuesday

Bedtime Story 

Stupefying Link Between the Vastness of the Universe and Our Existence 

I shall yet again continue with the extract from “Just Six Numbers” and end it tonight.

“A universe that didn’t involve large numbers could never evolve a complex hierarchy of structures: it would be dull, and certainly not habitable.

And there must be long time spans as well.

Process in an atom may take a millionth of a billionth of a second to be completed; within the central nucleus of each atom, events are even faster.

The complex processes that transform an embryo into blood, bone and flesh involve a succession of cell divisions, coupled with differentiation, each involving thousands of intricately orchestrated regroupings and replications of molecules; this activity never ceases as long as we eat and breathe.

And our life is just one generation in humankind’s evolution, an episode that is itself just one stage in the emergence of the totality of life.

The tremendous time spans involved in evolution offer a new perspective on the question ‘Why is our universe so big?’

The emergence of human life here on Earth has taken 4.5 billion years.

Even before our Sun and its planets could form, earlier stars must have transmuted pristine hydrogen into carbon, oxygen and other atoms of the periodic table.

This has taken about ten billion years.

The size of the observable universe is, roughly, the distance travelled by light since the Big Bang, and so present visible universe must be around ten-billion light-years across.

This is a startling conclusion.

The very hugeness of our universe, which seems at first to signify how unimportant we are in the cosmic scheme, is actually entailed (entail = necessitate, require) by our existence!

This is not to say that there couldn’t have been a smaller universe, only that we could not have existed in it.

The expanse of the cosmic space is not an extravagant superfluity; it’s a consequence of the prolonged chain of events, extending back before our Solar System formed, that preceded our arrival on the scene.

This may seem a regression to an ancient ‘anthropocentric’ perspective – something that was shattered by Copernicus’s revelation that the Earth moves around the Sun rather than vice versa.”

But we shouldn’t take Copernican modesty (sometimes called the ‘principle of mediocrity’) too far.

Creatures like us require special conditions to have evolved, so our perspective is bound to be in some sense atypical.

The vastness of our universe shouldn’t surprise us, even though we may still seek a deeper explanation for its distinctive features.”

I end the extract here.   

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

Advertisements

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 28, 2017 Monday

Bedtime Story 

The Ouroboros and the Scale of Our Universe

I am continuing the extract from “Just Six Numbers”

“It is actually no coincidence that nature attains its maximum complexity on this intermediate scale; anything larger, if it were on a habitable planet, would be vulnerable to breakage or crushing by gravity.

We are used to the idea that we are moulded by the microworld: we are vulnerable to viruses a millionth of a meter in length, and the minute DNA double-helix molecule encodes our total genetic heritage.

And it’s just as obvious that we depend on the Sun and its power.

But what about the still vaster scales?

Even the nearest stars are millions of times further away than the Sun, and the known cosmos extends a million times further still.

Can we understand why there is so much beyond our Solar System?

In this book I shall describe several ways in which we are linked to the stars, arguing that we cannot understand our origins without the cosmic content.

(Exactly the point mon ami keeps emphasizing).

The intimate connection between the ‘inner space’ of the subatomic world and the ‘outer space’ of the cosmos are illustrated by the picture that I will try to show to you – an ouroboros, described by Encyclopedia Britannica as the ‘emblematic serpent of ancient Egypt and Greece, represented with its tail in its mouth continually devouring itself and being reborn from itself.

It expresses the unity of all things, material and spiritual, which never disappear but perpetually change form in an eternal cycle of destruction and re-creation.’

On the left in the illustration are the atoms and subatomic particles; this is the ‘quantum world’.

On the right are planets, stars and galaxies.

This book will highlight some remarkable interconnections between the microscales on the left and the macroworld on the right.

Our everyday world is determined by atoms and how combine together to form molecules, minerals and living cells.

The way stars shine depends on the nuclei within those atoms.

Galaxies may be held together by gravity of a huge swarm of subatomic particles.

Symbolized ‘gastronomically’ at the top, is the ultimate synthesis that still eludes us – between the cosmos and the quantum.

Lengths spanning sixty powers of ten are depicted in the ouroboros.

Such an enormous range is actually a prerequisite for an ‘interesting’ universe.”

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

The Cosmic Ouroboros that was probably first portrayed this way by Sheldon Lee Glashow, the physicist who shared the Nobel Prize for Physics of 1979 with Steven Weinberg and Abdus Salam for the theory of electroweak interactions   

                

             

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 27, 2017 Sunday

Bedtime Story 

Mon Ami's Gardener Analogy

It may sound strange, but fascinatingly enough, in this paper concerning truth, proof and logic Tarski takes us into linguistics.

When you study something out of interest, you will realize that one cannot merely stick to one’s chosen subject of liking.

There is this strange irony in the fact that you will be forced to venture into other subjects if you really love your subject deeply.

There is this example often given by mon ami.

Consider for instance a gardener.

You might not even remotely associate a gardener with science, least of all theoretical sciences.

But if a gardener is curious enough and loves to read and takes not just a cosmetic interest in his endeavor, he is bound to end up ultimately studying molecular and cellular biology and evolutionary biology to come to terms with the origins of the stuff he works with everyday.

Once you have interest in cells and molecules, you are bound to end up studying astrophysics.

And if astrophysics will grip and fascinate your mind, you are bound to get tangled up with particle physics.

This might be a good place to digress from the paper of Tarski and talk about the ouraborus, Martin Rees and his book “Just Six Numbers: The Deep Forces that Shape the Universe” (1999).

I shall quote a very interesting excerpt from this book as it directly validates the point that mon ami makes.

I begin quoting the book from here:

“Large Numbers and Diverse Scales:

We are each made up of between 10²⁸ and 10²⁹ atoms.

This ‘human scale’ is, in a numerical sense, poised midway between the masses of atoms and stars.

It would take roughly as many human bodies to make up the mass of the Sun as there as atoms in each of us.

But our Sun is just an ordinary star in the galaxy that contains hundred billion stars altogether.

There are at least as many galaxies in our observable universe as there are stars in the galaxy.

More than 10⁷⁸ atoms lie within range of our telescope.

Living organisms are configured into layer upon layer of complex structure.

Atoms are assembled into complex molecules; they react, via complex pathways in every cell, and indirectly lead to the entire interconnected structure that makes up a tree, an insect or a human.

We straddle the cosmos and the microworld – intermediate in size between the Sun, at a billion meters in diameter, and a molecule at a billionth of a meter.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

Advertisements

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 26, 2017 Saturday

Bedtime Story 

Developing Semantically Restricted Language

As we concluded last night, depriving natural languages of names of its linguistic objects would restrain it from becoming semantically universal.

In short, limiting its vocabulary can safeguard a natural language from generating paradoxes.

But there is one hitch or glitch.

What about the science of linguistics?

Linguistic is a science that studies languages.

So how can one possibly deprive the language of linguistics with the names of linguistic objects?

Surely that can’t be done.

The language of linguistics got to contain all the names of linguistic objects.

Yet there is a way out.

We need not identify the language of linguistics with the universal language and that can be done by excluding the names of its own components.

In each specific discussion on the subject of linguistics, certain section of the names of certain linguistic objects has to be curtailed.

   

This will prevent it, at least temporarily at each discussion, from becoming semantically universal.

We can play it the same way as with metalogic and metamathematics.

Thus we seem to have managed to have developed semantically restricted languages at least in the arena of various scientific disciplines.

Now the question that arises is whether in such languages we can precisely define the notion of truth such that it is both consistent and adequate?

Tarski says that under certain conditions it would be possible to do so.

It will come with certain conditions though.

The syntactical rules that determine the formation of sentences and meaning from the words has to be very precisely formulated.

Another very important condition is that the syntactical rules have to very formal.

In the case of language here, formality has a different meaning.

The syntactical rules should explicitly define the form or the shape of expressions that can form sentences.

The rules should be so rigid that it should not allow an expression should behave like a sentence at one place but not the other.

Similarly, it must not allow an expression to be a sentence in one context but not the other.

Looking at an expression, one should instantaneously be able to say if that particular expression is a sentence or not.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

Advertisements

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 25, 2017 Friday

Bedtime Story 

Understanding Natural Languages (and its weaknesses)

Linguistically, a natural language can be said to be comprising broadly of two primary components: linguistic objects and semantic terms.

Linguistic objects include stuff like sentences and terms that are one of the components of the language.

Furthermore, even the names of the linguistic objects such as sentences and terms are included in the language without the requirement of enclosing them either inside quotation mark or parenthesis.

Same is the case with semantic terms such as “truth”, “name”, “designation” etc, that even though they refer to the relationship between linguistic objects, they form part of the language without any kind of formal treatment.

Though it all seems harmless and benign, but what it does is that it gives us ordinary apes an extraordinary power that is highly vulnerable to misuse.

For every sentence that can be constructed in a natural language, it allows us to form another sentence in the same language that can declare the first sentence to be true or false.

In short, a natural language allows us to generate self-referential sentence.

Hence a sentence S can assert itself to be either true or false.

In some cases where S can claim its own falsity, then as we have seen in the case of Liar Paradox, it can clearly be reasoned out that S is both true and false.

So how do we get out of the trap that is laid out bare for us in all the natural universal languages?

Or how do we avoid them or go around them?

One way, Tarski says is to avoid the use of universal languages as much as possible since in many places we can do without them.

I know you are not going to accept this so easily so let me elaborate on this.

One place where the natural languages can surely be done away with is the sciences.

Take for instance chemistry.

The primary topics of discussion in chemistry are elements, molecules, chemical reactions and so on but not linguistic objects such as sentences or phrases.

In such a case the language can be restricted possessing limited vocabulary.

It will largely contain names of chemical objects such as “elements”, “thermal”, “equations”, “equilibrium”, “entropy” and so on.

This language will be largely deprived of the names of linguistic objects thus depriving it of being semantically universal.

Other branches of sciences can be given the same analogous treatment.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

Advertisements

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

August 24, 2017 Thursday

Bedtime Story 

Unwanted Consequence of Nihilistic Approach

To show the unwanted consequence of taking nihilistic approach to the word “true” Tarski gave the following example.

Consider for a moment an ancient mathematician who is long since dead has published lots of serious papers.

In all his work there is one certain term that keeps repeating that is open to different interpretations in different places.

Now there is a mathematician existing in the present who also happens to be a historian who comes across the works of this great guy who is long since gone.

After studying all the works assiduously, the historian mathematician comes to the conclusion that under one of the interpretations of that term, all the theorems worked out by the past mathematician turn out to be true.

This means that all the proofs turn out to be valid.

Now it is obvious that this historian mathematician would consider this interpretation of that specific term as true.

In that case he might even stick his neck out and make a claim that any future mathematician who uses this term in its same interpretation would also eventually end up in proving his theorems.

Yet if our historian mathematician wants to be very formal and adopts his new nihilistic approach, then he would not allow himself to make this conjecture.

So what has this truth-theoretical nihilism has unwittingly done?

It has alienated the very conceptual notion of truth from our mind.

So we are back to our old quandary.

There has to be a solution to the problem of notion of truth such that it will not rock the classical concept of truth and yet not allow such paradoxes such as Liar to arise.

For this to happen, there has to applied some restrictions on the notion of truth yet at the same time keeping it available for the purpose of intellectual discussions.

We need to go back once again to the Liar Paradox and examine it closely.

What is it that actually generates the paradox?

To be more precise, what is or are the features of common natural language that gives origin to the antinomy.

Tarski says that one feature that starkly stands out of the natural languages is their universality.

The all tend to be all-comprehensive and that is exactly the basic intent of any common natural language.

It is the very medium that allows to express anything and everything that is capable of being expressed.

To fulfill this requirement, its vocabulary is constantly expanding.

A natural language has linguistic objects and semantic terms.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

Advertisements

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg