Mathematics Learning - the Indian way

[sravna]

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At the outset let me clarify the purpose of this thread is to present Mathematics in a way that helps one understand its concepts in a holistic way and not to present a typical or text book introduction to the subject. It is my view that not only Mathematics but all the subjects are taught in a way that there seems to exist no connection among their various topics.

Since I view reality as one, I think that the various descriptions of reality such as the various sciences , the math etc can be correlated . There also exists a natural co-relation between the various areas in a particular subject. I would like to highlight this inter-relation when discussing the various areas in Mathematics. I would also like to highlight the natural evolution of a simple concept becoming more and more advanced.

Thus the presentation would be based on the Indian philosophy of teaching. Since this is a novel way of presenting the subject in the present day context, I hope the readers would appreciate that fact and give their valuable feedback for any improvement in the presentation.


So I welcome contributions, suggestions and criticism from the members to make the thread very informative and useful.

 

[renuka]

Dear Sravna,


Two little birds sitting on a tree,
One eats fruits but the other just sees,
One knows all but the other doesn't know,
There's only one though two are in a row.


Please explain how 1 + 1 is NOT 2 here.

 

[sravna]

Dear Sravna,


Two little birds sitting on a tree,
One eats fruits but the other just sees,
One knows all but the other doesn't know,
There's only one though two are in a row.


Please explain how 1 + 1 is NOT 2 here.

Renuka,

Does the last line referring to one refer to the word one in the second and third line lines? Am I on the right track?

 

[renuka]

Renuka,

Does the last line referring to one refer to the word one in the second and third line lines? Am I on the right track?

Dear Sravna,

Ok lets make it simple..

Who are these 2 birds and why are they considered to be 1 even though 2 are seen.

 

[Raji Ram]

......... Two little birds sitting on a tree,
One eats fruits but the other just sees,
One knows all but the other doesn't know,
There's only one though two are in a row.

Please explain how 1 + 1 is NOT 2 here.

Dear Renu,

Sravna Sir might be racking his brain. I Google searched to get this result!!

In the Upanisads the example is given of two birds sitting on a tree.

One bird - the jiva, or living entity - is enjoying the fruits of that tree

and the other bird - Paramatma - is simply witnessing.

 

[sravna]

Dear Renu,

Sravna Sir might be racking his brain. I Google searched to get this result!!

In the Upanisads the example is given of two birds sitting on a tree.

One bird - the jiva, or living entity - is enjoying the fruits of that tree

and the other bird - Paramatma - is simply witnessing.

Dear Smt.RR ji,

I thought of this reply but since Renuka said 2 are "seen" it did not seem convincing.

 

[sravna]

Dear Folks,

Let us keep our discussions as usual in a separate thread which I will create, Thanks for your cooperation.

 

[renuka]

Dear Smt.RR ji,

I thought of this reply but since Renuka said 2 are "seen" it did not seem convincing.

Dear Sravna,

This stanza I coined sometime back and it has a nursery rhyme tune too..so that it makes remembering the Upanishadic verse easier.

Ok you see there are 2 birds here...One is Jeevaatma( the ignorant one that does not know) and the other is Paramaatma(the one that knows all)

Externally there is 2 but in reality there is only One cos Jeevaatma and Paramatma are essentially one and the same.

Or you can look at it as how Raji madam looked at it that is One bird(Paramatma) is only the witness but the other bird Jeeva is eating enjoying the fruits.

 

[renuka]

Ok Sravna,

Now one more just for fun sake.

Goundamani Senthil Banana Mathematics Problem.


Goundamani asked Senthil to buy 2 bananas..

Senthil bought 2 bananas and ate one.

Goundamani asked Senthil: where is the other banana?

Senthil replies :This is the other one.

Goundamani get angry cos he has no idea where is the other banana.



So you see....no mathematical formula can solve this!LOL

 

[Raji Ram]

Google search helps me Renu! I am not a great person.

Hope Sravna Sir will not get upset by our intrusion in this thread!

 

[sravna]

Dear Sravna,

This stanza I coined sometime back and it has a nursery rhyme tune too..so that it makes remembering the Upanishadic verse easier.

Ok you see there are 2 birds here...One is Jeevaatma( the ignorant one that does not know) and the other is Paramaatma(the one that knows all)

Externally there is 2 but in reality there is only One cos Jeevaatma and Paramatma are essentially one and the same.

Or you can look at it as how Raji madam looked at it that is One bird(Paramatma) is only the witness but the other bird Jeeva is eating enjoying the fruits.

Dear Renuka,

Sure, advaita in 4 lines.

 

[sravna]

Ok Sravna,

Now one more just for fun sake.

Goundamani Senthil Banana joke.


Goundamani asked Senthil to buy 2 bananas..

Senthil bought 2 bananas and ate one.

Goundamani asked Senthil: where is the other banana?

Senthil replies :This is the other one.

Goundamani get angry cos he has no idea where is the other banana.



So you see....no mathematical formula can solve this!LOL

Dear Renuka,

May be one has to use mathemagic.

 

[renuka]

Google search helps me Renu! I am not a great person.

Hope Sravna Sir will not get upset by our intrusion in this thread!

Wait till he sees the Senthil Goundamani Banana Mathematics Problem!LOL

 

[sravna]

Introduction

The word Mathematics invokes a feeling of hate or fear in quite a few. So a reasonable way to start an introduction to Math is to ask, "Why Math?" or "What is the need for a subject like Math?". There is an answer for that. In many instances there is a need for making a precise and unambiguous statement of a problem. Languages such as English or Tamil cannot be used to make such statements. There is always the element of ambiguity or lack of preciseness in the expressions of the languages we normally use to communicate.

The subject of Mathematics was born for the sake of precise and unambiguous expression. With such a language as a tool we can venture into exploring nature, and can expect exact answers to questions such as, how fast the light travels or how much does a hydrogen atom weigh or what is the normal temperature of the human body and so on. So we just need not have to say that light travels very very fast but can say it travels at the speed of 3,00,000 km/sec. Since understanding or predicting natural phenomenon needs such precision we can understand the need for something through which such precision can be expressed. There are also applications in everyday life some of which where we can appreciate the need for precision are the financial transactions or the creation of technologies.

So the need for Math is not arguable. So what exactly makes up a tool such as Math?

 

[SANDHYAV]

until recently. earlier i was a strong believer in Maths is mother all of sciences. I used it in my life, expenses, organisational methods and in my field of work. It involved both basic mathematics, tricks and tips in mathematics and high level statistics.

To start the discussion i would put a point against. Psychology is the mother of all sciences. without u Liking science, u cannot learn the mother of sciences. so psychology comes first. of course if u want to learn and excel in psychology u better be good in maths.

but again, calculation is only a tiny part of human brain, may be left pareital lobe. i dont know if u want to do complex maths, u need both frontal lobe which is the thinking brain? if u want to execute a series of formula again it is probably EXECUTIVE MEMORY which is again frontal lobe, i dont know i may be wrong.

to summarise if u dont have the motivation to learn maths then the mother goes out of the window. even if u have the motivation u need the LIKING to learn more in that field, which can be the EMOTIONAL brain and not the DRY CALCULATIVE BRAIN.

but if u USE ABSTRACTION as the magnified view of your maths, then it is PSYCHOLOGY!!

Abstraction - Wikipedia, the free encyclopedia

 

[kk4646]

I do have some facination for Maths... Sometimes a tangential thought will run in my mind..

As we know every society do have different 'thing' as their God and people believe & accept different 'forms' for their worship according to their religion..But we all know it is a common knowldge that one society/religion never accept or identify with the other one's methods..

Now if we look at the Maths..here is the one which is acceptable by every human being irrespective of differences and most importantly .. so far no-body could change any combinations/results..[1+2 is 3 only in any place] In such case why not every society/religion adopt this Mathematics as their GOD and throw away all their myths and accept something which is universal..

TVK

 

[auh]

Who are these 2 birds and why are they considered to be 1 even though 2 are seen.

Choose the practical answer:

Maybe one of the birds is

1) an optical illusion,
2) a hallucination in the eyes of the perceiver
3) both the above
4) any one of the above.
5) the question is wrong

 

[Raghy]

Choose the practical answer:

Maybe one of the birds is

1) an optical illusion,
2) a hallucination in the eyes of the perceiver
3) both the above
4) any one of the above.
5) the question is wrong

One more may be....

A mirror view. A person stands in front of a mirror, others can see two of the same person.

When I was young, I used t think of this every time I went to the barber shop and viewed myself in the large mirror. ( there was no large mirror in our home. The one we had was slightly larger than my palm). Then Barber Mohan could afford to buy one more mirror and placed that on the opposite wall... With the combination of mirrors, I could see myself many times. It could be confusing, the original and the image could be deceiving too! ( the same principle was used when Bruce Lee fought the last fight ).

Cheers!

 

[sravna]

A fundamental unit was required for developing the tool for precise expression, just as alphabets are fundamental for a language. The idea of numbers thus emerged. Note that we already had languages to communicate our thoughts which are formed as a result of perception or just thinking itself. These thoughts are related to real world objects and phenomenon and also what we make of them and are communicated through a language in a structured way. We have the alphabets of the language which are generally grouped together as a word and this is structured into a sentence and so on so that we can convey what we want to convey.

The words of a language represent a specific object, action or idea . For example the world "ball" represents a specific object, the word "hit" represents a specific action. In the real world there would be many balls and many times you hit something. There is a need to express them. The numbers did exactly this, to specify "how many? or how much?". This is however a basic perspective. Words can describe abstract concepts. So we really are not answering "how many " or "how much" but still a number could be associated with them. For example take the concept of speed. It can be expressed in terms of distance and time and can have a number associated with it since distance and time can be quantified. Such quantifiable abstract concepts can be used to quantify even more abstract concepts and so on. The idea is we can try to be precise when we associate a number with something.

 

[sravna]

Dear Folks,

I would request you to make any views or comments in the discussions section as it seems they would really distract from the topic. I hope you will co-operate.

 

[Raji Ram]

Dear Sravna Sir,

If a thread is posted in GD forum, members have to start the discussion in the same thread. If you do not want any one to 'disturb',

you may please post the main thread in 'Share your knowledge' forum and bring only the discussion thread to GD forum.

Just my humble suggestion.
P.S: With scroll facility in the mouse, those who want can easily read ONLY your posts!! :decision:

 

[sravna]

Dear Smt.RR,

That was only for the benefit of the readers. Of course no body can stop a member from making any post in this thread.

 

[renuka]

Dear Folks,

I would request you to make any views or comments in the discussions section as it seems they would really distract from the topic. I hope you will co-operate.

Dear Sravna,

You are kind of restricting the thought flow of members..its not easy to disconnect and then connect again from one thread to the other.

Its like how some people dislike the usage of the barrier method of contraception cos the user has to stop for a while..put in on and then continue..

You are restricting the experience of the members by such "rules" and "regulations"..ultimately if you dont give us the freedom..you might end up just "Dancing with Yourself"..and that's less fun cos the intensity is much less.

 

[sravna]

Dear Renuka,

I cannot take anyone's freedom here. If you think it is convenient for you to post in this thread do post. It is up to you.

 

[sravna]

We discussed how numbers are the basic units of Math. Now, we come to the question of how actually we can answer how many or how much of something which the numbers represent. These things can be as we saw, real world objects or abstract concepts.

We do not have knowledge about everything in the real world. We can answer the question of how much or how many of something based on certain knowledge. Also, many times we can answer the questions of how many or how much of something based on its relationships with some other things. Thus among the various things, the way the value of an unknown is determined is based on the relationships among these things. To do the above, we need to develop certain notions.

In the subsequent discussions we will see what these basic notions are and how these notions naturally evolve and also how there is an underlying commonality among the various areas of Mathematics.