The Creators

Consider the following syllogism:

Everything that exists has a creator.
God exists.
Therefore God has a creator.

Now, this is clearly valid from a purely deductive point of view. But deduction is nothing more than the mechanical rearrangement of symbols, hence it prove nothing about the true state of affairs in our universe until one considers the premises.

First consider "Everything that exists has a creator". If you accept this as a universal truth than we can move on. If you don't then you can entertain the thought that somethings exist and have no creator. Let's revisit the idea a bit later.

No consider the premise "God exists". If you are a believer than you hold this premis as true, by definition. But, if you also hold the first premise true, then you are logically bound to admit God was created by some prior God and so on ad infinitum. But clearly, this is not in line with the teachings of any mainstream religion. So as, say a Christian, you are forced to deny that everything that exists has a creator. Indeed, Christians would argue that everything that exists has a creator EXCEPT God.

So the rather than presupposing that "the universe always existed" or "some universe always existed", Christians belive in an all powerful, all knowing entity that exists and has no creator. I find that incredulous and any reasonable person should as well.

Personally, it seems obvious that both premises above are false. There are many things that exist and have no creator (but God is not one of them).

All this aside, if you are mathematically literate, enjoy physics and worry about matters of what can exist without having a creator I highly recommend The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us by Victor J. Stenger.

Dashed Lines in HTML5 Canvas

There is a lot of functionality missing from the Canvas API. One obvious facility is support for dashed lines. Here is the start of some dashed line code I am working on as part of a larger project. It is not fully tested yet so caveat emptor. I started with code I found here and attempted to make it more efficient by taking most of the math out of the main loop.

var initDashing = function(ctx) {
 if (!ctx.dashLine) {
  ctx.dashStyle=[3,2] ;
  ctx.dashedLine = function(x1,y1,x2,y2) {
   var dashStyle = ctx.dashStyle,
    dashCount = dashStyle.length,
    sign = x2>=x1 ? 1 : -1,
       dx = x2-x1,
       dy = y2-y1,
       m = dy/dx,
       xsteps = dashStyle.map(function(len){return sign*Math.sqrt((len*len)/(1 + (m*m)));}),
       dRem =  Math.sqrt( dx*dx + dy*dy ),
       dIndex=0,
       draw=true;
   this.moveTo(x1,y1) ;
   while (dRem>=0.1){
         var dLen = dashStyle[dIndex],
             xStep = xsteps[dIndex];
         if (dLen > dRem) {
          xStep =  Math.sqrt(dRem*dRem/(1+m*m));
         }
         x1 += xStep ;
         y1 += m*xStep;
         this[draw ? 'lineTo' : 'moveTo'](x1,y1);
         dRem -= dLen;
         draw = !draw;
         dIndex = (dIndex+1) % dashCount ;
   }
  };
 };
};

Here are some examples of usage (here I am using the Jasmine unit testing framework)

describe("Dashing", function() {
 it("draws a 3-2 dashed line by default", function(){
  var ctx = document.getElementById('test1').getContext("2d");
  ctx.strokeStyle = "black" ;
  initDashing(ctx) ;
  ctx.beginPath() ;
  ctx.dashedLine(0,0,100,100) ;
  ctx.closePath();
  ctx.stroke();
 });
 
 it("draws a 10-5 dashed line", function(){
  var ctx = document.getElementById('test2').getContext("2d");
  ctx.strokeStyle = "black" ;
  initDashing(ctx) ;
  ctx.dashStyle = [10,5] ;
  ctx.beginPath() ;
  ctx.dashedLine(0,0,100,100) ;
  ctx.closePath();
  ctx.stroke();
 });
 
 it("draws a 10-5-2-5 dashed line", function(){
  var ctx = document.getElementById('test3').getContext("2d");
  ctx.strokeStyle = "black" ;
  initDashing(ctx) ;
  ctx.dashStyle = [10,5,2,5] ;
  ctx.beginPath() ;
  ctx.dashedLine(0,0,100,100) ;
  ctx.closePath();
  ctx.stroke();
 });
 
 it("draws a 10-5-3-4 dashed line", function(){
  var ctx = document.getElementById('test4').getContext("2d");
  ctx.strokeStyle = "black" ;
  initDashing(ctx) ;
  ctx.dashStyle = [10,5,3,4] ;
  ctx.beginPath() ;
  ctx.dashedLine(100,13,0,80) ;
  ctx.closePath();
  ctx.stroke();
 });
});

I still have to implement a dashed version of arc, encapsulate better and test this code much more thoroughly. I'll upload to git hub when it is ready.