There are several opinion about 'What is Mathematics ?' . I want to start from Some people's view :-
1. Wikipedia :- Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out
patterns and formulate new conjectures.
2. Google Dictionary:- The abstract science of number, quantity, and space. Mathematics may be studied in its
own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied
mathematics).
3. Aristotle:- The science of quantity.
4.Comte:- The science of indirect measurement.
Now see what grammatically it mean :-
1. Mathematics (Eng) <mathematique (Old French )< mathematica (Latin (ars)) means ‘mathematical (art)’ <
mathēmatikē (tekhnē) (Greek) from base manthanein means learn.
So it means a way to Knowledge ( Learning ) [Or Knowledge itself ] .
2. Ganit [ Indian Sanskrit translation ] means Counting
To me mathematics is actually the way of generating symbols/patterns in consecutive time [ The generation of Symbol in consecutive time is called Computation ] .
What does it mean ? See the following:-
1+2=
Now you have 4 Symbols '1' , '+' ,'2', '=' which form a String [Sequence of Symbol] as depicted above . Now you know that this pattern asking you to put another Symbol on right of '=' .Also you know that 1 followed by a + and that followed by a 2 means 3 . So you will put 3 at right of '=' and extend that string to 1+2=3.
This is the basic how Our Brain / Thought Computes.
Similarly ,suppose I am going to tell you :- A box had 3 apples . I took 2 from it and put 8 in it . How many apples will remain in the Box? ------ (1)
A student of mathematics will quickly MAP this into an mathematical problem 3-2+8 = ? And solve it by giving ans 9.
Now look that previous String / Sequence of Symbol which had been given name (1) is a Pattern .
Your Obvious Question will be is it a mathematical expression ?
Obviously ans will be 'Yes' .
Does it contradict what you had learned till now ? It isn't a equation like x+y=z not a geometrical figure like a Circle so how a String can be a mathematical expression .
Well don't fear because it doesn't contradict at all . Just recall your History of Understanding Mathematics .
You first learned Arithmetic with 10 Symbols {0,1,2,..,9} the Operand and initially 2 Extra symbol '+' and '-' named as Operator and '=' '>' '<' . So then mathematics was limited in those symbols .
Later you found out * and / and searched Natural Numbers , Integers , Rational numbers .
Later you increased your span by knowing Algebra [With arbitrary extra symbols ] and ease your Computation.
Then you found out root , power , log and So on...
So day by day the set of mathematics increased to you by introducing new Symbol with new properties .
Thus a straight forward intuition is to insert more and more symbol in mathematical Domain .
So ultimately you will reach what had I told earlier [the Definition of Mathematics].
Every Language actually is a mathematical Expression [ Though meaning of Some Symbol may be Unknown or not well defined but that's a limitation of our knowledge / capability not the fault of Mathematics ] .
So Whenever we right / construct something in some language we actually form a mathematical expression .
You may think that this is just a mere generalization but actually has no Application . But truly this is the most applied mathematical stuff . Computer Science is a study of computation , it use computer as a machine which can do finite no of computation . In Computer Science Automata and Language , Algorithm and Complexity are totally deals with the above mentioned definition and these are consider as mathematics disciplines .
Then is all that we can know reside under the main fold of mathematics . Ans is no . Why ? Because all that we know is obviously a Sequence of pattern but the transformation of the pattern in consecutive time is mathematics / Computation but not the patterns .
Simply Suppose we saw that whatever body we saw when we release them in Space it fall on Earth . Then mathematics will tell that :-
∀x s.t x is body and we had released them in Space <=> They fall on the Ground ----(1)
Number of body we released in space is Large Say N -------- (2)
(1) and (2) => There is a High probability that ∀x s.t x is body when they will be released in Space[By
anybody not only we that is we who did/Saw that experiment ] they will fall on the Ground .
Now if N-> Inf we can Obviously say that for all body that been released in space will fall on the ground.
Similar way if we conduct any Scientific experiment we will have a Statistical data which will direct us to Build Some theorem .
So there is two part -
1. Information Collected from Nature ,
2. Mathematical Stuff to Build a theorem .
The Part 1. is the key factor which differs Science from Mathematics .
What is the difference between Math and Computation ?
Actually Computation means the Ongoing traversal between patterns and Math Says the way of the traversal . Thus Math is the way of Computation [ This part is called Algorithm ] and consist of Some General theorem About Some Abstract Structure We Build to Do ease this overhead of Computation [Mathematical Theorems ] .
And Computation is a Algorithm in Execution .
1. Wikipedia :- Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out
patterns and formulate new conjectures.
2. Google Dictionary:- The abstract science of number, quantity, and space. Mathematics may be studied in its
own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied
mathematics).
3. Aristotle:- The science of quantity.
4.Comte:- The science of indirect measurement.
Now see what grammatically it mean :-
1. Mathematics (Eng) <mathematique (Old French )< mathematica (Latin (ars)) means ‘mathematical (art)’ <
mathēmatikē (tekhnē) (Greek) from base manthanein means learn.
So it means a way to Knowledge ( Learning ) [Or Knowledge itself ] .
2. Ganit [ Indian Sanskrit translation ] means Counting
To me mathematics is actually the way of generating symbols/patterns in consecutive time [ The generation of Symbol in consecutive time is called Computation ] .
What does it mean ? See the following:-
1+2=
Now you have 4 Symbols '1' , '+' ,'2', '=' which form a String [Sequence of Symbol] as depicted above . Now you know that this pattern asking you to put another Symbol on right of '=' .Also you know that 1 followed by a + and that followed by a 2 means 3 . So you will put 3 at right of '=' and extend that string to 1+2=3.
This is the basic how Our Brain / Thought Computes.
Similarly ,suppose I am going to tell you :- A box had 3 apples . I took 2 from it and put 8 in it . How many apples will remain in the Box? ------ (1)
A student of mathematics will quickly MAP this into an mathematical problem 3-2+8 = ? And solve it by giving ans 9.
Now look that previous String / Sequence of Symbol which had been given name (1) is a Pattern .
Your Obvious Question will be is it a mathematical expression ?
Obviously ans will be 'Yes' .
Does it contradict what you had learned till now ? It isn't a equation like x+y=z not a geometrical figure like a Circle so how a String can be a mathematical expression .
Well don't fear because it doesn't contradict at all . Just recall your History of Understanding Mathematics .
You first learned Arithmetic with 10 Symbols {0,1,2,..,9} the Operand and initially 2 Extra symbol '+' and '-' named as Operator and '=' '>' '<' . So then mathematics was limited in those symbols .
Later you found out * and / and searched Natural Numbers , Integers , Rational numbers .
Later you increased your span by knowing Algebra [With arbitrary extra symbols ] and ease your Computation.
Then you found out root , power , log and So on...
So day by day the set of mathematics increased to you by introducing new Symbol with new properties .
Thus a straight forward intuition is to insert more and more symbol in mathematical Domain .
So ultimately you will reach what had I told earlier [the Definition of Mathematics].
Every Language actually is a mathematical Expression [ Though meaning of Some Symbol may be Unknown or not well defined but that's a limitation of our knowledge / capability not the fault of Mathematics ] .
So Whenever we right / construct something in some language we actually form a mathematical expression .
You may think that this is just a mere generalization but actually has no Application . But truly this is the most applied mathematical stuff . Computer Science is a study of computation , it use computer as a machine which can do finite no of computation . In Computer Science Automata and Language , Algorithm and Complexity are totally deals with the above mentioned definition and these are consider as mathematics disciplines .
Then is all that we can know reside under the main fold of mathematics . Ans is no . Why ? Because all that we know is obviously a Sequence of pattern but the transformation of the pattern in consecutive time is mathematics / Computation but not the patterns .
Simply Suppose we saw that whatever body we saw when we release them in Space it fall on Earth . Then mathematics will tell that :-
∀x s.t x is body and we had released them in Space <=> They fall on the Ground ----(1)
Number of body we released in space is Large Say N -------- (2)
(1) and (2) => There is a High probability that ∀x s.t x is body when they will be released in Space[By
anybody not only we that is we who did/Saw that experiment ] they will fall on the Ground .
Now if N-> Inf we can Obviously say that for all body that been released in space will fall on the ground.
Similar way if we conduct any Scientific experiment we will have a Statistical data which will direct us to Build Some theorem .
So there is two part -
1. Information Collected from Nature ,
2. Mathematical Stuff to Build a theorem .
The Part 1. is the key factor which differs Science from Mathematics .
What is the difference between Math and Computation ?
Actually Computation means the Ongoing traversal between patterns and Math Says the way of the traversal . Thus Math is the way of Computation [ This part is called Algorithm ] and consist of Some General theorem About Some Abstract Structure We Build to Do ease this overhead of Computation [Mathematical Theorems ] .
And Computation is a Algorithm in Execution .
No comments:
Post a Comment