Why is it hard to define something?

[Avichal]

Thanks for all your insights and opinions.
I learned a lot. Even though universe may be following some simple rules, life is complicated, we humans are complicated and I appreciate this complexity. I discovered this in the process: Game of life, which clearly explains my point.

P.S. :- I didn't understand much in the last 2-3 posts but nevermind.

 

[Mk]

The same object can be defined in multiple ways, because the same object can be seen from multiple perspectives.

If you wish to be truthful to your own experience, this is called sincerity, integrity, honesty. The question is not, "is it raining outside?" The question is, am I telling the truth or am I lying?

A 2nd kind of truth is defined by map:territory correspondence, it means your interiorly held symbolic representation of reality is a reflection of the exterior reality you inhabit.

Moreover, math evolves through each individual person in a different way. As a math student approaches math from age 1 to arithmetic, algebra, geometry, finance, probability, infinitesimal calculus, abstract algebra, set theory, sentential logic, model theory, etc. this beautiful and complex thing such as math is one that goes through successive stages of evolution... and different wings of it can be evolved along the way. This is a thing that is constantly changing within each and every individual, so of course it is a thing that would also be constantly changing as a shared concept among a culture. This is another reason why "math" is "difficult to define."

Many of the things that we hold sacred are constantly changing. We hold them to be sacred because of their endurance and diversity of forms produced throughout their evolution.

There is credible argument that some things cannot be defined. Try defining music, or love.

 

[lendav_rott]

Math is logic to me. Logic expressed in a language we happen to call math. Musical theory is math to me, it can be discrete math and yet it can be abstract. It's a form of logic expressed in a language, commonly Italian for music, and a set of symbols just like calculus or algebra.
Languages are logical - their structure follows a certain pattern. If construct I the like sentence this, it wouldn't make any sense to anyone, what happens is everyone recognizes what I was saying anyway, because they reorganize the words and it suddenly becomes logical
Pattern recognition isn't always the same, though. If one were to make a long sentence containing many different plots it can be interpreted differently. Same as math, an assignment gives scrambled pieces of information that you are to reorganize for it to make sense and reach the solution. The solution is a destination just as a conversation about something. If there wasn't any goal to achieve the information becomes unusable. It's like decyphering.

This is becoming kind of philosophical, so I'll stop.

 

[harborsparrow]

You (anyone, actually) might be interested in reading Hassim Nicholas Taleb's latest book, AntiFragile. He addresses what cogitive scientists, buddhists, and others already know--that there are two kinds of knowledge, or mind, or thinking--the logical, and the experiential/inexpressible/unexplainable (a gut-feeling "knowing" based on the totality of life experience one has at the time). He does a good job of exploring these, and also in pointing out some of the limitations of a word such as "science" in some contexts.