[math-fun] "What Big Bang?" --Pascal
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
On Sep 11, 2016, at 4:28 PM, Bill Gosper <billgosper@gmail.com> wrote:
Math-fun moderator Rich Schroeppel had an early mentor who was a Mathematical Creationist.
And now we have Max Tegman. —Dan
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Max Tegmark? and Bruno Marchal. Brent On 9/11/2016 4:39 PM, Dan Asimov wrote:
On Sep 11, 2016, at 4:28 PM, Bill Gosper <billgosper@gmail.com> wrote:
Math-fun moderator Rich Schroeppel had an early mentor who was a Mathematical Creationist. And now we have Max Tegman.
—Dan
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Yes, I mean that guy. —Dan
On Sep 11, 2016, at 6:13 PM, Brent Meeker <meekerdb@verizon.net> wrote:
Max Tegmark? ...
On 9/11/2016 4:39 PM, Dan Asimov wrote:
On Sep 11, 2016, at 4:28 PM, Bill Gosper <billgosper@gmail.com> wrote:
Math-fun moderator Rich Schroeppel had an early mentor who was a Mathematical Creationist.
And now we have Max Tegman.
. . . . . . . . .
Hello funsters, If we use 10 colors and the Pascal triangle up to about n = 4000 rows it gives this : http://plouffe.fr/binomial/ well, at least it is symmetric, and for stirling numbers 1 and 2, this time it looks like a wing from an aircraft and no symmetry http://plouffe.fr/stirling1/ and http://plouffe.fr/stirling2/ Best regards, Simon Plouffe Le 2016-09-12 à 01:39, Dan Asimov a écrit :
On Sep 11, 2016, at 4:28 PM, Bill Gosper <billgosper@gmail.com> wrote:
Math-fun moderator Rich Schroeppel had an early mentor who was a Mathematical Creationist. And now we have Max Tegman.
—Dan
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Bill Gosper -
Brent Meeker -
Dan Asimov -
Simon Plouffe