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Greg Egan Profile
Greg Egan

@gregeganSF

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SF writer / computer programmer Latest novel: MORPHOTROPHIC Latest collection: SLEEP AND THE SOUL Web site: https://t.co/yeU5bLA3mx Also: @[email protected]

Joined December 2016
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@gregeganSF
Greg Egan
3 years
When Cara Leon goes missing, Sam Mujrif is hired to investigate. Cara is 8 times taller than Sam, but evidence points to players much smaller than either of them—and technology with the potential to radically alter the balance of power between the scales.
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@gregeganSF
Greg Egan
45 minutes
Square roots with compass and straight edge. Given line segments AB of length x and BC of length 1, construct D so AD is length x-1, then E so DE meets AD at a right angle and AE is length x+1. Then DE is length 2√x, and can be bisected to find √x.
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@gregeganSF
Greg Egan
21 hours
RT @StartsWithABang: The top quark isn’t a loner after all: “toponium” is real!. The top quark is the most massive, shortest lived particle….
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Greg Egan
21 hours
Link:
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@gregeganSF
Greg Egan
21 hours
Wow, I just (re)discovered Worpitzky's identity, I’m only 142 years behind the times.
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Greg Egan
2 days
“Families Like Ours” is low-key, high-bureaucracy apocalypse, with Denmark preemptively emptied due to the prospect of inundation. It’s all a bit First World Problems compared to real-life refugees, but there are flawed characters, tough decisions and believable human stories.
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Greg Egan
2 days
Just when I thought my digital experience couldn’t possibly get any more exciting!
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Greg Egan
3 days
RT @colin_fraser: I do not believe it tried to do this in any sense that is more real than the sense in which Dwight Schrute tried to oust….
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Greg Egan
7 days
RT @GaryMarcus: Daddy, daddy, what was it like doing a PhD back when people wrote their own articles? . You know, before people snuck in hi….
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@gregeganSF
Greg Egan
7 days
I should add that, with hindsight, the relation:. 1/S(d,n) = d/(d-1) (1/S(d-1,n) - 1/S(d-1,n+1)). is easily proved straight from the formula for S(d,n). Since S(d-1,1)=1, this immediately shows that:. Σ_{n=1…∞} 1/S(d,n) = d/(d-1).
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Greg Egan
7 days
Science writer Amanda Gefter spent more than a decade tracking down the people who knew him, and diving into a vast store of his unpublished work and private papers. A long read, but fascinating and moving. Link:
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@gregeganSF
Greg Egan
7 days
Peter Putnam was a promising student of John Wheeler who became obsessed with a computational model of the mind, was tormented by a pathological relationship with his wealthy mother, and ended up contributing to community politics while working blue collar jobs.
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Greg Egan
7 days
This follows from the definition of H(r,i), and the formula for S(d,n) mentioned upthread. So the infinite sum of 1/S(d,n) is d/(d-1), as we found previously.
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Greg Egan
7 days
This generalises immediately to tell us that the sum of the i=d-1 series that starts at 1/d is just 1/(d-1). But each such series is just 1/d times the reciprocals of the d-simplicial numbers! That is:. 1/(d S(d,n)) = H(d-2+n, d-1).
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Greg Egan
7 days
This in turn means that if you add up the infinite number of entries with a given i, such as those coloured red in the image, you get a telescoping sum:. 1/4 + 1/20 + 1/60 + . = (1/3 - 1/12) + (1/12 - 1/30) + (1/30 - 1/60) + . = 1/3.
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@gregeganSF
Greg Egan
7 days
The general formula is easy to prove by converting the binomial coefficients into ratios of factorials. Now, it follows that each entry [except the leftmost in a row] is the difference between the one above left and directly left, e.g. 1/12 = 1/3 - 1/4.
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Greg Egan
7 days
The key property that makes this so powerful is:. H(r,i) = H(r+1,i) + H(r+1,i+1). That is, each entry is equal to the sum of the two entries below it, e.g. 1/3 = 1/4 + 1/12. for the three green entries in the image.
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@gregeganSF
Greg Egan
7 days
To form the harmonic triangle, take the usual triangle of binomial coefficients, multiply each row by its length, then take the reciprocal. So H(r,i) = 1/[(r+1) Binom(r,i)]. where r=0,. for the rows and i=0,. ,r across each row.
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Greg Egan
7 days
I just learned from @stevenstrogatz that Leibniz himself used a beautiful construction, known as “the harmonic triangle”, to find all the infinite sums of the reciprocals of the simplicial numbers.
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Greg Egan
8 days
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Greg Egan
8 days
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