TezlaKoil

Karma: 211

TezlaKoil 1 Jul 2017 22:40 UTC
3 points
in reply to: sen’s comment on: 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.

TezlaKoil 30 May 2017 0:42 UTC
4 points
in reply to: [DEACTIVATED] Duncan Sabien’s comment on: Dragon Army: Theory & Charter (30min read)

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.

TezlaKoil 2 May 2016 11:07 UTC
7 points
on: 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.

TezlaKoil 10 Feb 2016 7:07 UTC
2 points
in reply to: [deleted]’s comment on: 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?

TezlaKoil 8 Feb 2016 16:06 UTC
4 points
in reply to: [deleted]’s comment on: 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?

TezlaKoil 8 Feb 2016 13:07 UTC
3 points
in reply to: [deleted]’s comment on: 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.

TezlaKoil 7 Jan 2016 14:36 UTC
0 points
in reply to: gjm’s comment on: 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.

TezlaKoil 4 Jan 2016 12:17 UTC
0 points
on: A note about calibration of confidence
In row 8 of the table, P(D) should be replaced by P(~D).

TezlaKoil 4 Dec 2015 18:22 UTC
1 point
in reply to: username2’s comment on: 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.

TezlaKoil 10 Nov 2015 19:32 UTC
2 points
in reply to: Pfft’s comment on: Open thread, Nov. 09 - Nov. 15, 2015
Yes.

TezlaKoil 10 Nov 2015 10:58 UTC
10 points
in reply to: SGrouchy’s comment on: Open thread, Nov. 09 - Nov. 15, 2015
In a sterilized and sealed jar, jam made without sugar can last for years. Once you actually open the jar, you have about 7 days to eat it, and you better keep it refrigerated. You don’t need the sugar for thickening—the pectin in the fruit thickens jam just fine.

However, if you don’t add any sweetener, the result will be very sour.

Source: been making my own jam for years, had plenty of time to experiment.

TezlaKoil 14 Oct 2015 8:56 UTC
3 points
in reply to: philh’s comment on: Stupid questions thread, October 2015
In my experience, acid reflux can cause similar sensations.

TezlaKoil 30 Aug 2015 0:37 UTC
4 points
in reply to: Houshalter’s comment on: Open Thread—Aug 24 - Aug 30
I’m not sure that my paradox even requires the proof system to prove it’s own consistency.

Your argument requires the proof system to prove it’s own consistency. As we discussed before, your argument relies on the assumption that the implication
```
If "φ is provable" then "φ"
Provable(#φ) → φ 
```
is available for all φ. If this were the case, your theory would prove itself consistent. Why? Because you could take the contrapositive
```
If "φ is false" then "φ is not provable"
¬φ → ¬Provable(#φ) 
```
and substitute “0=1” for φ. This gives you
```
if "0≠1" then "0=1 is not provable"
¬0=1 → ¬Provable(#(0=1))
```
The premise “0≠1” holds. Therefore, the consequence “0=1 is not provable” also holds. At this point your theory is asserting its own consistency: everything is provable in an inconsistent theory.

You might enjoy reading about the Turing Machine proof of Gödel’s first incompleteness theorem, which is closely related to your paradox.

TezlaKoil 28 Aug 2015 13:27 UTC
2 points
in reply to: David_Bolin’s comment on: Open Thread—Aug 24 - Aug 30

It is not that these statements are “not generally valid”

The intended meaning of valid in my post is “valid step in a proof” in the given formal system. I reworded the offending section.

Obviously such statements will be true if H’s axiom system is true, and in that sense they are always valid.

Yes, and one also has to be careful with the use of the word “true”. There are models in which the axioms are true, but which contain counterexamples to Provable(#φ) → φ.

TezlaKoil 28 Aug 2015 0:35 UTC
5 points
in reply to: Houshalter’s comment on: Open Thread—Aug 24 - Aug 30
Now here is the weird and confusing part. If the above is a valid proof, then H will eventually find it. It searches all proofs, remember?

Fortunately, H will never find your argument because it is not a correct proof. You rely on hidden assumptions of the following form (given informally and symbolically):
```
 If φ is provable, then φ holds.
 Provable(#φ) → φ
```
where #φ denotes the Gödel number of the proposition φ.

Statements of these form are generally not provable. This phenomenon is known as Löb’s theorem—featured in Main back in 2008.

You use these invalid assumptions to eliminate the first two options from Either H returns true, or false, or loops forever. For example, if H returns true, then you can infer that “FF halts on input FF” is provable, but that does not contradict FF does not halt on input FF.

TezlaKoil 30 Jul 2015 15:50 UTC
4 points
on: The horrifying importance of domain knowledge
From Falsehoods Programmers Believe About Names:

anything someone tells you is their name is — by definition — an appropriate identifier for them.

There should be a list of false things people coming from common law jurisdictions believe about how choice of identity works on the rest of the globe.

TezlaKoil 21 Jul 2015 13:52 UTC
0 points
in reply to: zedzed’s comment on: Interesting things to do during a gap year after getting undergraduate degree
Should this be surprising? I briefly worked at a French school in Hungary: the guy who taught Spanish was Mexican, the girl who taught English was American, and so on. A Korean living in Guatemala still needs to learn English.

TezlaKoil 29 Jun 2015 9:43 UTC
17 points
in reply to: [deleted]’s comment on: Open Thread, Jun. 29 - Jul. 5, 2015

looked up monotone voice on google, and found that it has a positive, redeeming side – attractiveness.

My friends tell me that my face is pretty scarred. Research shows that facial scars are attractive. By the word scar, researchers mean healed cut. My friends mean acne hole.

Not all monotone voices are created equal. I’d be really surprised if “autistic” monotone and a “high-status” monotone would refer to the same thing.

TezlaKoil 9 Jun 2015 22:59 UTC
2 points
in reply to: [deleted]’s comment on: Open Thread, Jun. 8 - Jun. 14, 2015
I believe that an ultrafinitist arithmetic would still be incomplete. By that I mean that classical mathematics could prove that a sufficiently powerful ultrafinitist arithmetic is necessarily incomplete. The exact definition of “sufficiently powerful”, and more importantly, the exact definition of “ultrafinitistic” would require attention. I’m not aware of any such result or on-going investigation.

The possibility of an ultrafinitist proof of Gödel’s theorem is a different question. For some definition of “ultrafinitistic”, even the well-known proofs of Gödel’s theorem qualify. Mayhap^1 someone will succed where Nelson failed, and prove that “powerful systems of arithmetic are inconsistent”. However, compared to that, Gödel’s 1st incompleteness theorem, which merely states that “powerful systems of arithmetic are either incomplete or inconsistent”, would seem rather… benign.

^1 very unlikely, but not cosmically unlikely

TezlaKoil 9 Jun 2015 16:04 UTC
6 points
in reply to: Decius’s comment on: Open Thread, Jun. 8 - Jun. 14, 2015
Sure, that’s exactly what we have to do, on pain of inconsistency. We have to disallow representation schemas powerful enough to internalise the Berry paradox, so that “the smallest number not definable in less than 11 words” is not a valid representation. Cf. the various set theories, where we disallow comprehension schemas strong enough to internalise Russell’s paradox, so that “the set of all sets that don’t contain themselves” is not a valid comprehension.

Nelson thought that, similarly to how we reject “the smallest number not effectively representable” as an invalid representation, we should also reject e.g. “3^^^3″ as an invalid representation; not because of the Berry paradox, but because of a different one, one that he ultimately could not establish.

Nelson introduced a family of standardness predicates, each one relative to a hyper-operation notation (addition, multiplication, exponentiation, the ^^-up-arrow operation, the ^^^-up-arrow notation and so on). Since standardness is not a notion internal to arithmetic, induction is not allowed on these predicates (i. e. ‘0’ is standard, and if ‘x’ is standard then so is ‘x+1’, but you cannot use induction to conclude that therefore everything is standard).

He was able to prove that the standardness of n and m implies the standardness of n+m, and that of n×m. However, the corresponding result for exponentiation is provably false and the obstruction is non-associativity. What’s more, even if we can prove that 2^^d is standard, this does not mean that the same holds for 2^^(d+1).

At this point, Nelson attempted to prove that an explicit recursion of super-exponential length does not terminate, thereby establishing that arithmetic is inconsistent, and vindicating ultrafinitism as the only remaining option. His attempted proof was faulty, with no obvious fix. Nelson continued looking for a valid proof until his death last September.