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Practice: What Makes It Perfect?
Advertisements DISCLAIMER: In what follows, I can tell that my Christian religious background heavily flavors the material and my perspective expressed therein. I have tried to make the focus more general, to turn it into a subject from which different followers of religious or spiritual traditions can benefit. But again, my thoughts are shaped by […]
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Systemic Privilege and Impostor Syndrome: A Weird Balance in My Life
Advertisements I am a White Male Heterosexual Cisgender Christian. This means a lot in American society. I am of the political view – and I recognize there are disagreeing ones – that that means I have five tickets punched in terms of systemic privilege in the Land of the Free. Life has been easier on […]
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Integer Factorization: Quick Observation
Advertisements Examining the series of real values of x for which f(x)=x2+2cx+r is a perfect square, when m=c2-r is the number we wish to factor, c is the Ceiling Root, and r is the difference between m and the Ceiling Square, is not evidently any better – and is in fact a slower and unenlightening […]
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Integer Factorization: When x^2+2cx+r Yields a Perfect Square
Advertisements For odd positive integer m=c2-r, define the characteristic polynomial f(x)=x2+2cx+r. We are looking for the least nonnegative integer x for which f(x) is a perfect square. Completing the square of the polynomial may give us a way to find values of x given f(x). I decided to try to determine when f(x) = 0, […]
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Integer Factorization: A More Uniform Test, and a Similar Result
Advertisements For 100 pairs of randomly-chosen p and q less than 100,000,000: the Perl routine factor_it_4.pl performed as shown in the following scatter plot of m=pq vs. the number of iterations it required to factor m: Notice, as I mentioned in my blog post about the previous, less uniform test, that the number of iterations […]
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My Integer Factorization Study: Leading Me Ever Back
Advertisements As I’ve previously shared, my math study seems to lead me in kind of a circular path, between periods of great excitement at potentially profound discoveries, and “letdown” periods where I realize what I “discovered” is something not only already evident, but blindingly obvious. I still want to remain happily agnostic about which of […]
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Integer Factorization: Performance Stats/Graphs for factor_it_4.pl
Advertisements I ran factor_it_4.pl tonight on the collection of 10-digit and 12-digit discrete semiprimes I had generated earlier in my study. An image of the table I generated is below, along with scatter plots of particular behaviors. If someone wanted, I could certainly supply them with the raw data used to generate the graphs. I […]
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Fear of Learning (copied from a Twitter Thread of Mine)
Advertisements Fear of learning, especially the kind of learning that makes a human being less susceptible to manipulative indoctrination, is at the core of radically Conservative state governments’ school curriculum policies. It is unsubtle anti-intellectualism. The reasons are clear. To the @GOP and the Radical and Religious Right movements within you (to include Dominionist politics): You have […]
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My Fastest Factorization Script So Far
Advertisements This won’t set any algorithmic speed records, but I am happy with it, for now. It comes in at 48 lines of Perl code. factor_it_4.pl is definitely faster than factor_it_3.pl, and routinely gets its answer in fewer than half the iterations of factor_it_2.pl. Once again, I am not experienced with writing arbitrary-precision arithmetic scripts […]
JCSBimp's Hexagonal Orthogonal
BEWARE: There Be Fearfful Symmetries Here!
