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What useless things did you understand recently?

In a topological space, defining

  1. X ∨ Y as X ∪ Y
  2. X ∧ Y as X ∩ Y
  3. X → Y as Int( X^c ∪ Y )
  4. ¬X as Int( X^c )

does yield a Heyting algebra. This means that the understanding (but not the explanation) of /u/cousin_it checks out: removing the border on each negation is the "right way".

Notice that under this interpretation X is always a subset of ¬¬X.:

  1. Int(X^c) is a subset of X^c; by definition of Int(-).
  2. Int(X^c)^c is a superset of X^c^c = X; since taking complements reverses containment.
  3. Int( Int(X^c)^c ) is a superset of Int(X) = X; since Int(-) preserves containment.

But Int( Int(X^c)^c ) is just ¬¬X. So X is always a subset of ¬¬X.

However, in many cases ¬¬X is not a subset of X. For example, take the Euclidean plane with the usual topology, and let X be the plane with one point removed. Then ¬X = Int( X^c ) = ∅ is empty, so ¬¬X is the whole plane. But the whole plane is obviously not a subset of the plane with one point removed.

You can get a clearer-if-still-imperfect sense from contrasting upvotes on parallel,

I'm fairly certain that P(disagrees with blargtroll | disagrees with your proposal) >> P(agrees with blargtroll | disagrees with your proposal), simply because blargtroll's counterargument is weak and its followups reveal some anger management issues.

For example, I would downvote both your proposal and blargtroll's counterargument if I could - and by the Typical Mind heuristic so would everyone else :)

That said, I think you're right in that this would not have received sufficiently many downvotes to become invisible.

Hedge drift and advanced motte-and-bailey

Thanks for giving a name to this phenomenon.

Indeed, it would not surprise me if some people actually want hedge drift to occur. They don't actually try to prevent their claims from being misunderstood.

It's much worse. In my experience as an academic, most departments simply pre-hedge-drift their press releases. Science journalists don't - and are often not qualified to - read and comment on the actual papers, all they have to work with is the press release.

Open Thread, Feb 8 - Feb 15, 2016

I mean nationalized, as in the distribution of tobacco products (imports, wholesale, retail) is handled by companies that may or may not have been private at some point, but are now property of the state.

What do you mean by nationalizing?

Open Thread, Feb 8 - Feb 15, 2016

The weight of evidence best demonstrates that control measures have thus far been quite uniformly positive.

I see. The black market effects are well-documented, but I am not familiar with evidence which shows that control measures have any measurable effects on public health. Where could I find that data?

Open Thread, Feb 8 - Feb 15, 2016

Dagon's points are very good. There's another aspect as well:

Tobacco import and distribution (and in some cases, production) are already nationalized in many countries, especially in the EU. National governments try to impose artificial scarcity (winding down operations, tax increases, fixed pricing), and this makes the statistics look better - officially monitored tobacco sales decrease.

Artificial scarcity cannot last: a black market of RYO tobacco, and home-made cigarettes of dubious origin is always ready to serve customer demands. In the end, the health effects of nationalizing the tobacco industry, and winding down operations, can easily be negative.

Consciousness and Sleep

I bet if you phrase the question as "your brain is destroyed and recreated 5 minutes later", most people outside LW answer no. I guess this might be another instance of brain functions inactive vs lack of ability to have experiences.

A note about calibration of confidence

In row 8 of the table, P(D) should be replaced by P(~D).

Starting University Advice Repository

Location-specific advice

Libgen is blocked by court order in the United Kingdom, but if you're a student, you can usually access it through Eduroam.

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