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This is obvious after you learn calculus. The "nth difference" corresponds to nth derivative (a sequence just looks at integer points of a real-valued function), so clearly a polynomial of degree n has constant nth derivative. It would be even more accurate to say that an nth antiderivative of a constant is precisely a degree n polynomial.
Neither finite differences nor calculus are new to me, but I didn't pick up the correlation between the two until now, and it really is obvious.
This is why I love mathematics - there's always a trick hidden up the sleeve!
In response to
Welcome to Less Wrong! (6th thread, July 2013)
Hey there LW!
At least 6 months ago, I stumbled upon a PDF of the sequences (or at least Map and Territory) while randomly browsing a website hosting various PDF ebooks. I read "The Simple Truth" and "What do we mean by Rationality?", but somehow lost the link to the file at some stage. I recalled the name of the website it mentioned (obviously LessWrong) from somewhere, and started trying to find it. After not too long, I came to Methods of Rationality (which a friend of mine had previously linked via Facebook) and began reading, but I forgot about it too after not too long. At some stage about 4 months ago I re-discovered MoR, read about 3/4 of what was available and then started reading LessWrong itself.
It took me about 3 days to get my head around the introduction to Bayes' Theorem (since implementing a basic Bayesian categorisation algorithm), and in the process I realised just how flawed my reasoning potentially was, and found out just how rational one friend of mine in particular was (very). By that stage, I was hooked and have been reading the sequences quite frequently since, finally making an account at here today. There's still plenty more reading to be done though!
A little background (and slight egotism alert, which could probably be applied to everything here); I'm in my final year of school now, vice-captain of the school's robotics program (and the programmer of Australia's champion school-age competitive robot), debating coach to various grades and I've completed a university level "Introduction to Software Engineering" in Python using Tkinter for GUI stuff as I finished the Maths B course a year early. I'm planning to go into university for a Bachelor of Science/Bachelor of Engineering majoring in Mathematics/Software Engineering next year. I've got major side interests in philosophy and psychology which I currently don't plan to explore in any formal sort of way, but LessWrong provides an outlet that addresses with these two.
I look forward to future comments and whatever criticism they attract; learning from mistakes tends to stick rather well.
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I apologize if I misinterpreted your statement:
I was curious what was meant by this.
It's likely that Eliezer isn't tending towards either side of the nature vs. nurture debate, and as such isn't claiming that nature or nurture is doing the work in generating preferences.