Math-fun moderator Rich Schroeppel had an early mentor who was a Mathematical Creationist. He taught that, in the beginning, the Void was a bilaterally infinite string of cells containing zeros, and every day, God would simultaneously replace each cell with the sum of its immediate neighbors. Then, exactly once, God accidentally said "0+0=1", and Pascal's Triangle exploded into existence. A similarly quaint belief is still taught in the Book of Wolfram. The actual reason God paused on the seventh day was to gaze back over the previous eternity, In[686]:= FoldList[#2 - #1 &, 0, {0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0}] Out[686]= {0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0} In[687]:= FoldList[#2 - #1 &, 0, %] Out[687]= {0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0} In[688]:= FoldList[#2 - #1 &, 0, %] Out[688]= {0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0} In[689]:= FoldList[#2 - #1 &, 0, %] Out[689]= {0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0} In[690]:= FoldList[#2 - #1 &, 0, %] Out[690]= {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} In[691]:= FoldList[#2 - #1 &, 0, %] Out[691]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} In[692]:= FoldList[#2 - #1 &, 0, %] Out[692]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1} In[693]:= FoldList[#2 - #1 &, 0, %] Out[693]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12} In[694]:= FoldList[#2 - #1 &, 0, %] Out[694]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 6, -10, 15, -21, 28, -36, 45, -55, 66, -78} In[695]:= FoldList[#2 - #1 &, 0, %] Out[695]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 10, -20, 35, -56, 84, -120, 165, -220, 286, -364} . . . satisfied that time, like space, was bilaterally infinite, and miracle-free. --rwg