The basic solution part is working. I am having trouble with locating singularities – though I have had that part working in the past. (I rewrote a great deal of the program – to improve its design – is the reason for the trouble.) I find it hard to work on it very long at a time.
Subjunctive Conditionals and Ethics
I’m reading Rawl’s A Theory of Justice. It along with Hare’s The Language of Morals and Freedom and Reason has convinced me a correct account of subjunctive conditionals is needed for a correct theory of ethics. (And I think this requires a correct account of modal logic.)
More progress on differential equations
Reply
I’ve been working some, the last few weeks, on my program and making some progress.
The Republican Nomination
I have a thought that, perhaps, no one will secure enough delegates to secure the nomination on the first round of voting at the convention. Thus resulting in real drama at the convention.
On Logic
If we assume there are a countable number of signs, and any sentence contains a finite number of signs, then there must be an uncountable number of truths of mathematics that cannot be represented, let alone be proved. This is because there are an uncountable number of real numbers. It is true that we can talk about many irrational real numbers such as pi and e, but these can be specified by a finite number of symbols. There must be many more irrationals which cannot be so specified.
One could take an uncountable number of signs as primitive, i.e. by using points on a circle, varying continuously. The points on such a circle can be mapped to the whole real line. If one did this, I think one would have also to have an uncountable number of axioms – how else could the primitive signs enter in?
It is a valid objection that we could not do this in practice. But it is also true that there is some finite limit to the size of sentences that humans (or machines we can build) can handle, so a countably infinite assumption is also only of theoretical interest, it would seem.
Discovered one problem I had with maxima
I found that when I passed a string (passed from another function – but I don’t know if that matters) to printf using ~a, I got an error, but if I put the string inside a “string(…) function it worked. This may have been what was causing the trouble I had with arrays. I was doing both in the same place – using such strings and 2D arrays.
Progress on diffeq program
I’ve been continuing on mu diffeq program. I call it omnisode.rb. It is to generate a program to solve numerically systems of ordinary differential equations. I am trying to make it generate code in any of Ruby, Ruby with my apfp, Maple or maxima. I have been writing small programs in Ruby and snobol to convert the code I had started to generate maxima to the more general code.
More work on differential equations
I continued to have problems with maxima. I decided to change direction. Now working on the program (still in Ruby) to generate code for any of Ruby, Ruby with my APFP, Maple, or (hopefully) Maxima. I’ve switched the environment from Linux to Vista as well, as that is where I have Maple. I had a earlier version (in Unicon) which would generate code in either Unicon or Maple, so I have a good idea of what I am doing.
Tuesday I started writing more philosophy – will try to work on it more often
It’s on language and perception. It will go on my web pages when finished.
Differential equations program – learning more about maxima
I have solved some problems I was having. Just takes scouring the maxima manual!