[value of science] -Henri Poincare
when i say it is finished it means two things;
1) Mathematically, the application of the equation is "correct" as less arbitrary
value as possible , course the size of the screen has to be set.
2) Intuitively, it is finished. that means i feel i have explored enough of this curve
in this shape. I feel i need to move on as there is not so much to develop into at
this current frame anymore.
below are the quotes from the reading. They are kind of vague at this point, yet they are very lovely to read if you have time, however i would not recommend thinking them too seriously.
[The creative activity of mind in mathematics is particularly clear . .The axioms of geometry are conventions . disguised definitions or unprovable hypotheses precreated by auto-active animal and human minds].
[Emerson gave his sentiment divine against the being of a line. line in nature is not found . ]
[.... we also know how cruel the truth often is . and we wonder whether illusion is not more consoling. yea even more bracing . for illusion it is which gives confidence .when it shall have banished . will hope remain and shall we have the courage to achieve? thus would not the horse harnessed to his treadmill refuse to go . were his eyes not bandaged? and then to seek truth it is necessary to be independent . wholly independent . if on the contrary we wish to act. to be strong . we should be united. this is why many of us fear truth; we consider it a cause of weakness. yet truth should not be feared. for it alone is beautiful .]
[it is harmony then which is the sole objective reality. the only truth we can attain . and when i add that the universal harmony of the world is the source of all beauty . it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better .]
[today in analysis only whole numbers are left or systems. finite or infinite. of whole numbers bound together by a net of equality or inequality relations. Mathematics . as they say . is arithmetized. ]
[" we have then many kinds of intuition; first . the appeal to the senses and the imagination; next, generalization by induction, copied, so to speak, from the procedures of the experimental sciences; finally. we have the intuition of pure number. whence arose the second of the axioms just enunciated .which is able to create the real mathematical reasoning. I have shown above by examples that the first two can not give us certainty ; but who will seriously doubt the third. who will doubt arithmetic. ]
[without intuition they would never apply mathematics ]
[in mathematics logic is called analysis and analysis means division . dissection . it can have, therefore . no tool other than the scalpel and the microscope. ]
[thus logic and intuition have each their necessary role. each is indispensable. logic which alone can give certainty . is the instrument of demonstration; intuition is the instrument of invention. ]
[i have said how much the intuition of pure number, whence comes rigorous mathematical induction. differs from sensible intuition to which the imagination, properly so called, is the principal contributor. ]
[we therefore choose these rule. not because they are true. but because they are the most convenient. and we may recapitulate them as follow:" the simultaneity of two events. or the order of their succession, the equality of two durations . are to be so defined that the enunciation of the natural laws may be as simple as possible. in other words. all these rules. all these definitions are only the fruit of an unconscious opportunism . ]
The feedback i get from ITP friends are: 1)not understanding what i meant for the method [mathematical + programming exploration] , 1)why it matters for the math and program if it is just beautiful .
I am not confident regarding to the subjects of math + programming. Therefore, maybe i am teaching myself by making the shapes. However, i do believe there is a interesting point in the way i visualize the curve that is different from a geometry book and a computer science. Yet the same intention is based on the equation as what it is, that is nothing emotional or "humanitorary".
The idea/word of beauty is objective and i have no interest in getting into it neither from fine art perspective, philosophical argument nor linguistic opinions. However, i am not denying it. They appear to be beautiful that is why i decided to focus studying on it and hoping the application of such study and work will become clear at the end.