No hiding theorem Puns

See here (wiki) and here (stackexchange).

>But the no-hiding theorem is the ultimate proof of the conservation of quantum information. The importance of the no-hiding theorem is that it proves the conservation of wave function in quantum theory. This has never been proved earlier.

As you can see from that quote, the wiki article is written in a strange style.
The papers on the theorem seem to have attracted little attention, and the sole answer to the stackexchange question sounds bitter.

But the result looks important. So, what's up? Is it pseudoscience? Was it just unfortunately ignored? Does anyone know any more about it?

I can't add a photo to the post but it's:

the integral from 1 to infinity of (ln(x)*cos^4(x))/(sqrt(x^6 + 513))

Here's an imgur link:

https://imgur.com/a/zBHflYy

I worked on it a bit more and I was thinking you could break off 1/sqrt(x^6) to get 1/x^3, and by the p test that would be convergent, so if you do the comparison theorem like that it's confirmed it is convergent.

imo Euler's identity is something pretty overrated. Which other things would you consider overrated?

I just read in a book -- not some blog article or YouTube comment -- a questionable explanation of the no-cloning theorem. It states that if Bob could clone his qubit many times, that would permit him to determine the teleported state of Alice's qubit. As long as she at least measured her qubits, and as long as Bob could make a sufficient number of z and x measurements, Bob could basically use tomography to determine the unknown state. But, cloning is impossible so the authors left it at that.

However, what if Alice prepared multiple qubits with the same state? Instead of cloning, she uses identical preparation, and then teleports all those qubits to Bob. The no-cloning defense suggests that as long as Alice measures her qubits, Bob could perform a bunch of measurements and figure out the unknown state.

So, where is the error?

The qubits could all collapse differently, but what if the state is on an axis? Or, for simplicity, what if the unknown state is |0> or |1>? The defense of the no-cloning theorem states that the problem arises if Bob can make measurements that are all zeroes or all ones. Bob needs to measure gibberish without Alice's classical bits.

Therefore, there must be some other obstacle that the book omitted. Or, I need to trash the book. Or, Alice can't teleport |0> or |1>?

So... Here I am getting all comfy with a decent uptime and I decided to get fancy. I ordered a Firestick to see if I can watch streaming tv with a VPN app so I can see my favorite show I've been missing out on for a year. Haven't received the Firestick yet but decided to roadtest a VPN on my computer and stream the tv show there. Cue the sharp objects....

SO... after about 9 seconds... BLIP.... VPN disconnects. Fire it up again.... 15 seconds later.... BLIP.

And so on and so on.

Question; is this what I'm in for when the Firestick arrives and I sign up for a VPN app for it? I have used a Roku stick and it streams flawlessly but I'm not going through a VPN with it, primarily because it doesn't support one.

The theorem in question is basically a finite version of Kruskal's Tree theorem. I'm comfortable with my level of understanding of the infinite version. But reading Friedman's work is hard, at least in my opinion. Both due to formatting (I only find scanned versions of what basically looks like typewriter papers) and due to brevity at critical points.

So is there somewhere I can find a proof of the relevant finite version? Ideally refined to modern standards, but at least something that's been texed and easily readably? Online? Ideally free?

Prove me wrong:

“In any BBC Drama with a cast of 5 or more people, at least one cast member shall have been on either the classic Doctor Who, the post 2005 Doctor Who, or a Doctor Who spin-off.”

Definition 1:

The natural numbers are such that:

(I) 1 is a natural number;

(II) S is an injective function which takes natural numbers to natural numbers;

(III) There is no natural number m such that S(m) = 1;

(IV) Given a set A of natural numbers,

>if 1 is in A, and
>
>for every m in A, S(m) is in A,

then A is equal to the set of natural numbers.

S is known as the successor function.

(IV) is known as the Principle of Induction.

Observation 1:

0 is not in the natural numbers, according to this definition. An equivalent definition may include 0, but I like this one without 0. Here, when I use 0, it will be just a symbol.

Observation 2:

A function is well-defined when it has a single result for every entry. If the function can be applied in a way such that, for the same entry, it can lead to two or more different results, then it isn't well-defined.

Definition 2:

Addition is a binary operation on the natural numbers such that, for every m and n natural numbars:

m+1 = S(m);

S(m+n) = m+S(n).

Proposition 1:

The addition of two natural numbers is well-defined for all natural numbers.

Demonstration 1:

For all natural m,

m+1 is well-defined,

because m+1 = S(m)

and S is well-defined for all natural numbers.

Suppose that m+n is well-defined. I will show that, then, m+S(n) will be well-defined.

m+S(n) = S(m+n).

m+n is well-defined, and m+n is a natural number,

then S(m+n) is well-defined,

then m+S(n) is well-defined.

By the Principle of Induction,

since, for all natural m,

m+1 is well-defined,

and for all natural n, m+n is well-defined implies that m+S(n) is well-defined,

so m+n is well-defined for all natural m and n, what was to be shown.

Definition 3:

Multiplication is a binary operation on the natural numbers such that, for all natural m and n:

m·1 = m;

m·S(n) = (m·n) + m.

Proposition 2:

The mutiplication of natural is well-defined for all natural numbers.

Demonstration 2:

For all natural m,

m·1 is well-defined,

because m·1 = m.

Suppose that m·n is well-defined. I will show that, then, m·S(n) will be well-defined.

m·S(n) = (m·n) + m.

m·n is well-defined, and m·n is a natural number,

so (m·n) + m is well-defined,

because addition is well-defined for all natural numbers.

So m·S(n) os well-defined.

By the Principle of Induction,

since, for all natural m,

m·1 is well-defined,

and, for every natural n, m·n is well-defined

Just going through my notes on Ergodic Theory as I revise for my final, found the statement that

> One can show that [; x_n = \alpha^n ;] is uniformly distributed mod 1 for almost all [; \alpha > 1 ;], however not a single example of such an [; \alpha ;] is known!

I love facts like this, where something has been proven to be true almost everywhere (ie. in this case picking a random [; \alpha \in \mathbb{R} ;] gives probability 1 of the statement being true), yet noone can find an example for which the statement is known to hold.

I know I've seen more of these before, and would love to see some more cool examples.

Hey, a quick question: The no cloning theorem states that quantum states cannot be copied. I recently read that during the avalanche effect of LASERs the resulting photons are exact copies in terms of polarisation, amplitude, frequency and phase.

How do these two contradicting observations come together?

This "proof" https://en.wikipedia.org/wiki/Schwarz_lemma of the Schwarz-Pick theorem is highly incomplete and makes seemingly random assumptions out of nowhere, but more disturbingly, there doesn't seem it be a single credible reference anywhere that actually does prove the theorem, so for all I know, it could be a lie. Can anyone actually prove it?

I see No Free Lunch theorems discussed enough that I decided to check my understanding, and sit down with the original paper.

They prove bold (but contextualized) claims, and I feel like the bold claims have really taken on a life of their own (absent context):

> one might expect that hill climbing usually outperforms hill descending if one's goal is to find a maximum [...] such expectations are incorrect

> the average performance of any pair of algorithms across all possible problems is identical

Very interesting, to be sure. But this all hinges on a specific assumption:

> [...] our decision to only measure distinct [oracle] function evaluations

meaning:

> techniques like branch and bound are not included since they rely explicitly on the cost structure of partial solutions.

I think their framework is interesting and useful for describing algorithms like Simulated Annealing or Genetic Algorithms.

But since it doesn't apply to an entire class of algorithms (those that can reason from partial solutions), it seems to me that we should really reign in our claims about NFL.

I must be missing something.

Guess people forgot about this show?

Anyhow, still feeling out the plot, but seems cool enough, especially with the time travel worldline reality hopping remote control. I like Takuya as a character, and the general flow of the episode seemed okay.

Laughed when Takuya got dumpstered across three different timelines.

I spent some time trying to reconcile the implications of the no free lunch theorem on ML and I came to the conclusion that there is little practical significance. I wound up writing this blog post to get a better understanding of the theorem: http://blog.tabanpour.info/projects/2018/07/20/no-free-lunch.html

In light of the theorem, I'm still not sure how we actually ensure that models align well with the data generating functions f for our models to truly generalize (please don't say cross validation or regularization if you don't look at the theorem).

Are we just doing lookups and never truly generalizing? What assumptions in practice are we actually making about the data generating distribution that helps us generalize? Let's take imagenet models as an example.

I need the chest piece for a look I'm trying to get so does anyone know if I can still get it

So there are some bad takes some people have on the Coase theorem. Unfortunatly, transaction costs exist and are substantial, and the Endowment effect also exists so we don't live in a perfect blackboard economics 101 world. This on its own refutes most of these bad econ takes.

Unfortunately Conservapedia has the worst take I've ever seen on the Coase theorem.

It starts off with "The Coase theorem debunks excuses, and proves that limitless opportunities are available to all regardless of wealth." which I found an unusual statement because the Coase theorem is not really about excuses, oppurtunity or wealth.

Reading further >The Coase theorem states that if property rights are well-defined and transaction costs (including costs of negotiating) are zero or negligible, then the most efficient economic activity will occur regardless of who initially owns the property rights. Negotiation and market transactions will ensure optimal allocation of property. Simply put, it means "build a better mousetrap, and the world will beat a path to your door,"[1] no matter who or where you are.

>This simple theorem, first published in a 1960 paper[2] by Ronald Coase who won the Nobel Prize for Economics for this in 1991, has powerful implications for economics, law, politics, and even Christianity. This theorem supports conservative interpretations of the Chicago School of Economics.

No No No. Ronald Coase would be ashamed of you. Transaction costs matter a lot. And this confuses Pareto Efficient for socially optimal. This is obviously not the case.

To see this, lets assume one person simply owns all the property, and the rest of the population is destitute. This can be Pareto Efficient, but its also fucking monstrous.

Some people may assume that this is unrealistic, but its honestly not that different from a situation where a large landowner owns most of the land and tenants are forced to work it for him. Land Reform has had great Success in Countries like Japan, and South Korea. If these countries had simply liberalized without land reform, these peasants would not have been able to afford the land they had been given in reality and on the net, this would have been bad for pretty much everyone.

Conservapedia's article though eliminates the actual nuance of reality in favor of Fantasy Christian Conservative Economics.

Conservapedia doesnt stop there though.

>The implications in law are that the