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How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality (Einstein)? How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality (Einstein)? This issue has troubled philosophers as well as scientist since Einstein first posed it. To answer what Einstein meant when he asked the question, a person must understand what mathematics really is. The physical world is very important to understand when looking at the question.
When deriving a meaning from Einsteins statement it is necessary to restate the quote in a simplistic style and understand how mathematics can work for situations dealing with the physical world. I believe that mathematics is very useful to the understanding of reality because we want it to be. For example, in the movie PI, when Max Cohen, a mathematical genius, was looking for the number 216 and he kept finding that number everywhere he looked. All of the problems that humans face are there because they are blocking the answer society or a particular human is looking for. Mathematics is subvert known as a group of related subjects, including algebra, geometry, trigonometry and calculus, concerned with the study of number, quantity, shape, and space, and their inter-relationships, application s, generalizations and abstractions (beckmann 102).
Mathematics is made up of concepts that are composed of universal relationships. One example of a mathematical concept is the number one. One does not exist but we use this number to represent objects which exist. To understand the quote, How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? it is important to realize that when Einstein speaks of mathematics he is speaking of rationalism.
A man named Descartes, a mathematician who lived from 1596 - 1650, first headed rationalism. Descartes argued that all knowledge obtained through direct observation of nature was suspect because it comes through the senses, and such knowledge can notoriously be deceptive, as all kinds of hallucinations and dreams show (Jeans 34). Descartes has a very good point but it is very skeptical to believe that everything is suspect to deception. There must be some puritanical things in the world.
Two reasons why Descartes believed that knowledge from mathematical proofs may be deceptive were 1) mathematicians have often been wrong and 2) people can never be certain that an omnipotent God may not have decreed that people should be deceived even in the things people think they know the best (Jeans 35). I agree with him for the most part but what about people that do not believe in God. How would number two be applicable for them. Also, these statements would discredit the entirety of scientific knowledge because it might be from unreliable sources.
Descartes also believed that were a number of principles already imbedded into the brain i. e. the existence of God. All rationalists believe that all things can be derived through intuition.
Kant, a philosopher, believed so strongly that truth is obvious that he claimed that it would be possible to construct a pure science of nature (Jeans 35). That is a very bold statement but I think that most of the philosophers are just too black and white. If they would just find a medium they would be able to solve more questions. Another word for rationalism would be a priori which means previously to, and independent of, all actual experience of the world. Mathematics is completely a priori and is derived from intuition. Mathematics is very important but it is also a necessity to understand the physical world.
Physics purpose is to identify the most elementary building blocks of Nature and the laws that govern them (Barrow 65). Physics are the physical processes and phenomena of a particular system. In this case, it would be the universe that embodies humans and other lifeforms. The physical world deals with empirical information and is made up of very complex rules.
To understand the quote, How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? , it is necessary to understand Einstein is talking about empiricism when he say s the objects of reality. Empiricism is derived from experiences rather than from logical principles alone. Empiricism is also known as a posteriori. A posteriori means that there are sources in experience (Jeans 35). As I stated earlier, this black and white formula which most intellectuals tend to work with is not the best way to handle the issue. There should be a word in between a priori and a posteriori.
Empirical logic is strictly, not able to be known independently of experience. This is an epistemological property, and hence distinct from the logical property of being synthetic (Jeans 36). Epistemology is the study or a theory of the nature and grounds of knowledge especially with reference to its limits and validity. In opposition to rationalism, empiricism is based on experience alone. The two most prominent empiricists were philosophers John Locke and David Hume.
A reason to why people were persuaded to be empiricists was because many believed that a person could not imagine a mathematical point, line, or triangle unless we had first made the acquaintance of their imperfect representations in the outer world. Locke believed that the truths of pure mathematics were not the only issues which were constructed through empirical views. He believed that the existence of God and ourselves and the morality ought to be admitted to the class of intuitive truths (Jeans 36). These philosopher are journeying into a very touchy subject which has been questioned since man could question. This quote be the existence of God. Locke statement about morality and truths can only be answered to the extent that people can define morality and truth.
The truth of empiricism is what the physical world is based on. When Einstein said, How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? , he was questioning how something as rationalistic as mathematics can explain something as empiricalistic as the physical world. The concepts of mathematics and the empirical physical world are so different most people would find it difficult to be able to comprehend that mathematics, a conceptual view, could explain something as complex as the physical world. Some philosopher believe the physical world is composed of many complex equations. I believe that many of these equations we find are simply there because we want to find them. For example, when a person buys a new car, that person suddenly sees his car all over the place.
The number of cars did not simply enlarge when he bought his new car but simply the equation appeared more translucent. In the book, Character of Physical Law, Richard Feynman says that mathematics is related to physics by stating, it is perfectly natural that the mathematics will be useful when large numbers are involved in a complex situation i. e. the physical world (Feynman 35). In contradictory to that statement, Feynman also says that in biology the action of a virus on a bacterium is un mathematical (Feynman 35).
Feynman and many other scientists and philosophers have tried to answer the how mathematics can explain something so complex as the physical world. This answer will come in time just like the knowledge to these topics will eventually be complete. The question concerning abstract and empirical topics and how one can explain another is simply formed by a biased opinion just like every other philosophical question. Rationalism will always be prominent as long as people believe in intuition. Empiricism will also be just as prominent as long as there are mathematicians and philosophers that believe that everything is a posteriori. One explanation for the two separate ideas could be because the Continentals loved their abstract ideas and the British's love for practical investigation.
The complex physical world is and always will be explained by the a priori mathematics as long as there are people that want it to be explained that way. Word Count 1364
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