Name: Kirtika
Date: 03/09/07
Word count: 1175
"When mathematicians, historians and scientists say that they have explained something, are they using the word "explain" the same way?
What is the most fundamental meaning of the word explain? - To make plain or clear; render understandable or intelligible. The reason that people have to explain anything is in order to be able to communicate to others their thoughts, emotions, discoveries or anything new which people apart form themselves might have a problem comprehending. It is also in order to avoid misinterpretations. However when mathematicians, historians and scientists say that they have explained something, in all three cases it does mean that they have made something clear however the process of this explanation is very different for these various areas of knowledge.
Taking into consideration mathematics, new theorems are explained using numbers and proofs. The means of explanation here is mainly quantitative.
E.g. If you have to explain to someone how
5 X 3 = 15 you would say:
5 + 5 + 5 = 15
The explanation is certain and absolute. There are different ways to obtain the solution but there cannot be different solutions. As long as the proof is true the solution will always be the same. But then again a proof is considered true unless disproved by someone else. Thus when something is explained in mathematics it is more like it is verified. It is based on Logic and reasoning. There is no influence of emotions whatsoever. At the same time mathematics also involves reference to priori. If all Mathematicians explain every new theorem from the basics of mathematics then the explanation would be too long and tedious. Thus the word ‘explain’ is very relative here. It might be explained by the mathematician and yet not clear to every individual. This is because the intellectual level of every individual is different and mathematics being an abstract subject is out of the scope of understanding of some. Thus there is a society of Mathematicians who verify and regulate theorems. It is them who decide if a theorem has been explained. The limitations of this however, is that in case there is an explanation beyond the intellectual scope of the rest of the society then the theorem would be regarded as unexplained.
Historians have a completely different approach towards explanation. History is mainly a branch of knowledge dealing with past events. It entails analyzing past events relating to people, a period, a country etc. History however is subject to interpretation. Historians mainly attempt to explain reasons for certain episodes in the past or the mindset of the people making decisions then. However interpretation of the actions of these people will vary from person to person.
Ex. Interpretation of Hitler’s treatment of the Jews during World War II is despised by some and yet held in reverence by those who believed in maintaining the purity of the Aryan race.
The interpretation of History is influenced by almost all the ways of Knowing. Emotion particularly triggered by Religion and beliefs influences the understanding of history. This is because various Religions and beliefs preach right and wrong to their followers in different contexts. They are taught and not given the chance to listen to their own conscience or differentiate good and bad for themselves. Thus while some religions preach that we must consider the influence of our actions on everyone before implementing them, others say that we can and must do everything to protect our nation. This consequently influences their perception of right and wrong. What might be acceptable by some in history might be considered a blasphemy by others. Language is also a bar when it comes to history. This is because there are many historic documents that have to be interpreted. Revealing of these documents also could entail explaining some fact in history through the information contained in them. Thus history is very subjective and always open to interpretation and scrutiny. It has all happened; we are just trying to explore and understand the circumstances surrounding it and the consequences of it in order to learn from the mistakes of our forefathers so as not to repeat them. Thus contrary to mathematics explanation does not amount to absolute certainty in history.
Science in its most basic form entails the observation and study of nature and all its elements. Explanations in science are mere simplifications in order to understand better, things that are happening around us and to predict how they would act in certain situations in order to prepare us for any future natural hardships. However in science discoveries are being made everyday.
E.g. Earlier the atoms were thought to be like a pie with the electrons embedded at random within it. However as our understanding, observation, and inductive capacities have developed this model has been replaced by the model of electron clouds around the dense nucleus.
Thus every small discovery is altering the realm of the existing scientific reality. At the same time certain explanations are based on models that are derived in such a manner that they correspond to what is happening in reality. Thus science is in itself an explanation of the reality of our daily life. However scientific explanations have their own limitations. Technology has not progressed to such an extent as to allow us to physically observe the constituents of all substances. Thus there is no way of confirming the validity of certain basic explanations of the components of living as well as non-living things. A lot of other explanations are based on these hypothesis or models which imply that the base of science is to some extent is brittle. However, so long as no fault has been found or no exception to the rule has come in the way of our understanding this base holds firm and has been accepted by the scientific society.
Thus different areas of knowledge are explained in different manners and each of these explanations has different implications. Some are open interpretation, some are rigid, some are observations and some are deductions. All these explanations are meant to make their area clearer but the manner in which their explanation is carried out, and its rigidity varies from one to another. That does not make any one area of knowledge more certain that another nor does it discredit any one area. The amount of uncertainty or scope of interpretation corresponding to one area of knowledge is what defines that area. It is what differentiates it from the others. Unless we accept and understand each area for its own characteristics we will not be able to achieve true knowledge from it or completely comprehend it. And only when we put all these different pieces of knowledge together like the pieces of a puzzle will we be able to understand the full scope of our life. Only then will we be able to appreciate the complexities of the reality that we live in. These areas of knowledge are like the different paints. Only when mixed together and spread across a canvas with the bold strokes of a brush will we be able to create a work of art rich in its blend of tints and shades.
Date: 03/09/07
Word count: 1175
"When mathematicians, historians and scientists say that they have explained something, are they using the word "explain" the same way?
What is the most fundamental meaning of the word explain? - To make plain or clear; render understandable or intelligible. The reason that people have to explain anything is in order to be able to communicate to others their thoughts, emotions, discoveries or anything new which people apart form themselves might have a problem comprehending. It is also in order to avoid misinterpretations. However when mathematicians, historians and scientists say that they have explained something, in all three cases it does mean that they have made something clear however the process of this explanation is very different for these various areas of knowledge.
Taking into consideration mathematics, new theorems are explained using numbers and proofs. The means of explanation here is mainly quantitative.
E.g. If you have to explain to someone how
5 X 3 = 15 you would say:
5 + 5 + 5 = 15
The explanation is certain and absolute. There are different ways to obtain the solution but there cannot be different solutions. As long as the proof is true the solution will always be the same. But then again a proof is considered true unless disproved by someone else. Thus when something is explained in mathematics it is more like it is verified. It is based on Logic and reasoning. There is no influence of emotions whatsoever. At the same time mathematics also involves reference to priori. If all Mathematicians explain every new theorem from the basics of mathematics then the explanation would be too long and tedious. Thus the word ‘explain’ is very relative here. It might be explained by the mathematician and yet not clear to every individual. This is because the intellectual level of every individual is different and mathematics being an abstract subject is out of the scope of understanding of some. Thus there is a society of Mathematicians who verify and regulate theorems. It is them who decide if a theorem has been explained. The limitations of this however, is that in case there is an explanation beyond the intellectual scope of the rest of the society then the theorem would be regarded as unexplained.
Historians have a completely different approach towards explanation. History is mainly a branch of knowledge dealing with past events. It entails analyzing past events relating to people, a period, a country etc. History however is subject to interpretation. Historians mainly attempt to explain reasons for certain episodes in the past or the mindset of the people making decisions then. However interpretation of the actions of these people will vary from person to person.
Ex. Interpretation of Hitler’s treatment of the Jews during World War II is despised by some and yet held in reverence by those who believed in maintaining the purity of the Aryan race.
The interpretation of History is influenced by almost all the ways of Knowing. Emotion particularly triggered by Religion and beliefs influences the understanding of history. This is because various Religions and beliefs preach right and wrong to their followers in different contexts. They are taught and not given the chance to listen to their own conscience or differentiate good and bad for themselves. Thus while some religions preach that we must consider the influence of our actions on everyone before implementing them, others say that we can and must do everything to protect our nation. This consequently influences their perception of right and wrong. What might be acceptable by some in history might be considered a blasphemy by others. Language is also a bar when it comes to history. This is because there are many historic documents that have to be interpreted. Revealing of these documents also could entail explaining some fact in history through the information contained in them. Thus history is very subjective and always open to interpretation and scrutiny. It has all happened; we are just trying to explore and understand the circumstances surrounding it and the consequences of it in order to learn from the mistakes of our forefathers so as not to repeat them. Thus contrary to mathematics explanation does not amount to absolute certainty in history.
Science in its most basic form entails the observation and study of nature and all its elements. Explanations in science are mere simplifications in order to understand better, things that are happening around us and to predict how they would act in certain situations in order to prepare us for any future natural hardships. However in science discoveries are being made everyday.
E.g. Earlier the atoms were thought to be like a pie with the electrons embedded at random within it. However as our understanding, observation, and inductive capacities have developed this model has been replaced by the model of electron clouds around the dense nucleus.
Thus every small discovery is altering the realm of the existing scientific reality. At the same time certain explanations are based on models that are derived in such a manner that they correspond to what is happening in reality. Thus science is in itself an explanation of the reality of our daily life. However scientific explanations have their own limitations. Technology has not progressed to such an extent as to allow us to physically observe the constituents of all substances. Thus there is no way of confirming the validity of certain basic explanations of the components of living as well as non-living things. A lot of other explanations are based on these hypothesis or models which imply that the base of science is to some extent is brittle. However, so long as no fault has been found or no exception to the rule has come in the way of our understanding this base holds firm and has been accepted by the scientific society.
Thus different areas of knowledge are explained in different manners and each of these explanations has different implications. Some are open interpretation, some are rigid, some are observations and some are deductions. All these explanations are meant to make their area clearer but the manner in which their explanation is carried out, and its rigidity varies from one to another. That does not make any one area of knowledge more certain that another nor does it discredit any one area. The amount of uncertainty or scope of interpretation corresponding to one area of knowledge is what defines that area. It is what differentiates it from the others. Unless we accept and understand each area for its own characteristics we will not be able to achieve true knowledge from it or completely comprehend it. And only when we put all these different pieces of knowledge together like the pieces of a puzzle will we be able to understand the full scope of our life. Only then will we be able to appreciate the complexities of the reality that we live in. These areas of knowledge are like the different paints. Only when mixed together and spread across a canvas with the bold strokes of a brush will we be able to create a work of art rich in its blend of tints and shades.
A Calvin and hobbes comic just for humour :) !!!
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