Jacob, or “Jisk” when there are too many Jacobs about and I need a nickname. Host of the North Oakland LW Meetups, every Tuesday.
Honestly pretty disappointed with the state of the modern LW site, but it’s marginally better than other non-blogs so I’m still here.
It should be possible to easily find me from the username I use here, though not vice versa, for interview reasons.
I am confused by the introductory statement for #9. Is this an accurate rephrasing?
By representing syntax using arithmetic, it is possible to define a function as follows:
Define with image in , such that:
substitutes the Goedel-number of into (creating ) and then substitutes the Goedel-number of into some fixed formula to get a result in .
For #6, I have what looks to me like a counterexample. Possibly I am using the wrong definition of continuous function? I am taking this one as my source.
Take as the topological space the real line under the Euclidean topology. Let be the point in at radians rotation. This is surjective; all points in are mapped to infinitely many times. It is also continuous; For every and neighborhood there is a neighborhood such that ,
The partial functions f(x) from are also continuous by the same argument.
Ah, yes, that makes sense. I got distracted by the definition of ’s topology
and applied it to surjectivity as well as continuity.
My nontrivial answer for Q7, in Python:
with open(“foo.py”, “r”) as foo:
print foo.read()
And for Q8:
def f(string):
return ″.join([chr(ord(c)+1) for c in string])
with open(“foo.py”, “r”) as foo:
print f(foo.read())
I hit that stumbling block as well. I handwaved it by saying “continue iterating until you have and such that , , and f has no local maxima or local minima on the open interval ”, but that doesn’t work for the Weierstrass function, which will (I believe) never meet that criterion.
Q1
We wish to show that the terms of form a Cauchy sequence, which suffices to demonstrate they converge in a complete space. Take , and WLOG . Then we know from the definition of contraction that . This converges to 0 as m increases, so the sequence is Cauchy.
It’s easy to see that this makes the rate of convergence between terms of the Cauchy sequence exponentially quick. Intuitively that seems like it ought to make the sequence converge to its limit with the same speed, but I don’t think that can be made rigorous without more steps.
Q2
Take a sequence . This converges to some . Suppose was not a fixed point. Then choose an . A sequence which converges to a limit has, for every , some such that . Then we know that but , contradicting the contraction condition. So there is at least one fixed point, .
Suppose there are two fixed points, , for distinct and . If so, , which again contradicts the contraction condition. So there is at most one fixed point.
Q3
Take as the space , with the usual metric. Define . This is a weak contraction (toward infinity) and has no fixed points within this space.
For Q2, I believe you aren’t done:
You have established that there is at most one fixed point, but not that a fixed point exists.
I don’t think that’s a fair description of most holidays, and it’s definitely not a requirement for new ones.
The biggest source of inspiration I have used in my own designs is the Neopagan/Wiccan holidays; Beltane, Imbolc, Luggasnadh , etc. Whatever their proponents may claim, these are de novo holidays they assembled from whole cloth with only scraps of historical practice and misinterpreted or outright fabricated mythology to back them up. And, despite being entirely novel, they’re sticky and genuinely emotionally impactful. In the whole eight points of the wheel of the year, only Yule (winter solstice) can really be construed as “earned”. (Via the standard “we have brought back the Sun” winter solstice narrative. YMMV on how much this actually applies to celebrations of Yuletide.)
So given that, I don’t think holidays need to commemorate things. And actually I think they generally shouldn’t, because a commemoration is backward-looking. We are an extremely forward-looking movement/community, and our holidays should reflect that. Which isn’t to say we should ignore the past—Solstice cares a lot about the past, and how we’ve dug ourselves out of a hole nature made for us, and this is good—but we should focus on the future and the present, doing collective values affirmation and trying to establish a tradition that can sustain us across a couple generations. Values I’ve considered include ‘be ready for tail risks’ (“Prepper’s Night”), ‘community connection’ (“Day of Warmth”), ‘humanity’s potential is enormous’ (“High Summer” or “Awe Summer”), and ‘appreciate skill’/‘share skill’ (“Day of Achievement”).
I think this is a valuable concept to have, but despite thinking about it on and off ever since this was first posted (and reading the Book of the Subgenius) I still don’t really understand it well enough to act on it.
That doesn’t follow. Traditions are self-perpetuating; the more entrenched a holiday is, the more momentum it has to keep being entrenched. Therefore, an old holiday tells us merely that it had something major going for it at some point in the past.
Memorial Day was earned by the sacrifices of the Civil War. July 4th was earned by winning a war of independence against Great Britain. Labor Day was earned by the struggle that working classes endured to gain the right to bargain collectively. Thanksgiving was earned by the starvation and cold that the Puritan Pilgrims suffered in their first winter in the New World.
Also, half of these are serious stretches. Labor Day was ‘earned’ only by the need to supplant May Day to prevent expression of Communist sympathies/solidarity. Memorial Day celebrations, such as they are, never include mention of the Civil War in my experience. Even Thanksgiving’s mythology is much more about commemorating the spirit of cooperation which helped the Pilgrims get through the winter than about the difficulty of the situation.
prediction after seeing the 2009 graph:
15-20% True
8-12% Weakly True
8-12% Undecided
20-25% Weakly False
35-45% False
This was basically taking the 2009 graph and skewing it to the right, pivoting on Undecided. It was still too optimistic.
True: 15-20% vs 12%
Weakly True: 8-12% vs 12%
Undecided: 8-12% vs 10%
Weakly False: 20-25% vs 15%
False: 35-45% vs 50%
Looking at the discrepancy, it doesn’t seem like any systematic skewing adjustment, i.e. adjusting for overconfidence, would have gotten good results. (The closest would be one that pivoted on ‘Weakly False’.) A better model would be assuming that all predictions had a modest chance of being other-than-totally-false which was uniformly distributed over degree of truth, and most were totally false.
Therefore, I predict that if these predictions are examined again in 10 or 20 year’s time, they will still have this uniform distribution over degree of truth property, though presumably a higher chance of not being totally false.
extirpate that which permits them
link is broken, should point to http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.3367
How would this Bardic Conspiracy have any real power?
12 years later, Steven, I have an answer for you. Narratives are very, very good at translating into motivation. In some sense they are the native language of motivation. If you want to keep your motivation fueled while you attack a problem, having a story to tell about how it’s important is incredibly valuable.
And unskilled narrativemancy is quite dangerous; the same things that make it valuable to have a properly-aimed narrative make it very harmful to have a misaimed narrative. It will feel true and important and point you off in the wrong direction and it will take you a long while to recover from the error (and indeed you may never recover).
The initiation ceremony is an example of really good Bardic technique at work; they are presenting the message of ‘speak the truth even if your voice trembles’ in a way that the initiates will never, ever forget. That is a story which will never leave them and permanently remind them of the dangers of succumbing to social pressure.
This is particularly important when trying to harness the power of large groups; I suspect if Conspiracies were joined purely based on the standpoint of how best to optimize the world, the Cooperative and Bardic Conspiracies would have long-since merged.
But also,
Bayes hobbyists, wisdom-of-crowds hobbyists, and moral virtue hobbyists.
These are bad characterizations of the conspiracies. Bayesian Conspiracy is obvious, but is it Cooperative or Competitive which is supposed to be the wisdom-of-crowds faction? And how could either of those be construed as ‘moral virtue hobbyists’?
I’d characterize the four as “Bayes’s Theorem, wielded correctly, is extremely powerful”, “Narrative, wielded correctly, is extremely powerful”, “The human urge to excel, wielded correctly, is extremely powerful”, and “A large group of people working together, wielded correctly, is extremely powerful”. They are each offering, to their initiates, a “Big Secret” of “Learn to master this tool and you will become masters of the world”. Bardic actually has the strongest argument, because the system of Conspiracies is in fact a direct application of Bardic techniques to the world.
I think that’s different but I’ve having difficult articulating how, so I may be wrong about that.
So in the specific original instance, I think there were actually better things we could have been doing. But Edison’s favorite aphorism applies: That would have required thinking.
Possibly there is some more detailed analogy to be made about confronting uncertainty and tending to under-explore and over-exploit.
It has been 2 years. Have said demonstrations materialized?
Minor correction for #7: You probably want to say “nonempty quine” or “nontrivial quine”. The trivial quine works in many languages.