avz

> aleph-1, which is the size of the power set of aleph-0

In ZFC, aleph-1 is not the size of the powerset of aleph-0. Instead, aleph-1 is the next larger cardinal number after aleph-0. The size of the powerset of aleph-0 is called continuum or beth-1. In ZFC, we can show that the size of the set of real numbers equals continuum, but it is not possible to relate continuum to a specific aleph-k (though some can be ruled out using Easton's theorem).

Now, the statement that aleph-1 is the size of the powerset of aleph-0 is known as the Continuum Hypothesis (CH) and is independent of the axioms of ZFC. Therefore, your claim that aleph-1 is the size of the powerset of aleph-0 cannot be made in ZFC. The statement can be made in ZFC+CH, but then the question which aleph-k is the size of the real numbers has a straightforward answer: aleph-1.

There exist countries with simple tax code, inhabited by people who do not want to pay tax. Therefore any valid explanation why US has a comparatively complex tax code must cite something specific about the US. A generic reference to human nature explains nothing.

I am concerned that the type of defense of privacy exemplified by your argument (that reporting the happy hour to the insurance company was a privacy violation and should be illegal) will backfire sooner or later.

Assuming that the guy was running a happy hour in a place where they are banned, your argument reinforces the view that privacy is only needed for those who break the law.

Explaining why privacy is important is hard enough as it is. Please don't make it harder.

> the human genome is littered with viral genetic material accumulated over time, god knows if it's for good or for bad

In some cases, we know too, e.g. synctin-1 [1] is a viral protein coded by a gene integrated into the primate germ line some 25 million years ago and repurposed by our bodies to facilitate cell fusion in the development of the placenta.

[1] https://en.wikipedia.org/wiki/Syncytin-1

> [...] lots of people see what looks like the "story changing", and distrust anything coming out of their government, [...].

Changing and updating our beliefs as evidence comes in is a fundamental ability that underlies numerous activities from scientific research to debugging software to driving on a congested road network. Why is it a problem for public health officials to update and change policy as we learn more about the virus?

Would it really be preferable if policy remained frozen to whatever people thought best on day one?

I think the presence of international standards like the one potentially being established by GDPR makes outsourcing easier, not harder.

It would make little sense for an Argentine developer to learn the intricacies of Slovenian data protection regulations. It makes a lot more sense for her to learn the intricacies of GDPR (and whatever the US comes up with).

These caveats make sense. I think that the role of computing and automation in law will be similar to their role in many other fields where the new technology does not necessarily eliminate humans completely, but instead increases their productivity by broadening the scope of their work, eliminating the bulk of repetitive and time consuming activities and allowing them to focus their efforts on areas that require nuance and judgement.

An interesting aspect of law-related automation concerns cases that could "be resolved with mathematical efficiency", but for whatever unfortunate reason end up slipping through the cracks in enforcement. Unequal, unpredictable and discretionary enforcement is often source of corruption and inequity, so filling those gaps would be welcome.

> You literally drop heavy stuff from orbit

If you literally drop something in orbit then it stays in orbit. In order to make it fall to the ground you first need to de-orbit it.

This is an entirely sensible position, as long as we don't simultaneously decry winner-takes-all market dynamics.

On second thought, we can in fact do both simultaneously by shifting the responsibility for supporting good journalism onto our favorite other, such as "the government", "the rich", "regulators", "we as a society", etc.

I am personally completely satisfied paying for publications as long as I read at least one article per issue. In fact, due to time constraints, one article per issue has become something of an objective.

> Quantum supremacy is debated, and so not something I can reasonably comment on. From the explanation above however, you can see that supremacy is achieved whenever you do something with a QC that cannot be done with a classical computer. The problem is proving that something is 100% provably beyond the scope of a classical computer (people are clever, and so it's often not).

My understanding was that quantum supremacy occurs when a quantum computer performs a computation that cannot be performed with comparable speed on a classical computer given the best available classical hardware and the best available classical algorithms of the time. In particular, it does not require a proof that no efficient classical algorithm exists. Instead, it is sufficient that nobody knows such a classical algorithm at the time of demonstration.

Otherwise even factoring a large number by running Shor's algorithm on an error corrected quantum computer would still not constitute quantum supremacy demonstration because there is no proof that factoring cannot be done efficiently on a classical computer. After all, it is not inconceivable that people just don't know how to factor integers fast on a classical computer.

> But country-specific things aside: * The DMCA already makes it easy enough to...

DMCA is a country-specific thing. Moreover, it is specific to a country the article is not about.

I want to add a historical remark. Very early forms of human government, such as ancient kingdoms in various parts of the world, had one or a few prominent members of society hold full discretion and decision-making power. Later, we codified rules and decided that even monarchs are not above the law. Endowing the written laws with additional power by making them executable seems like a natural next step.

> No one actually wants a society being ruled by computers, except maybe the people running those computers.

Humans in charge are known for injustice, kickbacks, favor trading, selective enforcement and other forms of corruption and abuse. Properly engineered and regularly reviewed open source systems with balance checks might just get us closer to a rules-based system that provides a level playing field for everyone. Given all the known biases of current AI systems, we are certainly far from ready for it, but the prospect of transforming large parts of government into an open source "social operating system" that automatically and fairly offers basic services according to clearly coded and broadly enforced rules looks like a desirable goal in the (very) long term.

Many laws can be expressed as computer code. Where they cannot is often due to deliberate vagueness built in to leave scope for future interpretation as new cases arise. This suggests that we could express laws in computer code that raises a HumanInputRequiredException in the cases currently handled with deliberate vagueness. The resulting reduction in vagueness would remove a huge amount of discretion that currently facilitates corruption and abuse of power while ensuring ultimate human control and human-directed evolution of the law.

> A decade or two of stagnation would be frustrating for those in the field but probably overall a good thing.

Is a decade or two of a head start given to high-tech totalitarian regimes like China overall a good thing?

> Plus I don't think this would affect research at all so not even.

Limiting use of AI reduces interest of the public and young researchers and engineers, contributes to brain drain and limits availability of large datasets that are an important asset for AI development.

> Just seems odd that somehow the FBI is the best server admin here?

Without arguing for or against it, I can see this new role viewed as a "sysadmin of last resort" wherein an authorized institution steps in to ensure a minimum security level among neglected systems in their jurisdiction.

Developing complexity theory of quantum algorithms without a quantum computer is not any more outrageous than developing complexity theory of Turing machines with oracles. The former might a least be built one day. And yet, people produce interesting research on both.

Turns out water is overrated (as far as complexity theory goes).

> this concept of a 'widely digitally delicate prime' is that you can take such a prime, prepend it with any sequence, and receive a prime in return.

This makes no sense. Let X be a number that satisfies your condition and consider the number XX formed prepending X to itself. You're asserting that XX is prime, but it is obviously composite, because it is divisible by X (just like say 2929 is 29*101).

Perhaps I can share a different perspective. I like unrestored ruins. I perceive a restoration as admixture of modern techniques and fresh touch onto an old and genuine core, and a recreation as a modern construction made to look old. When I explore those without having noticed or been forewarned about their true origins I feel cheated. When I do notice or someone tells me they really are new, I still feel they are inauthentic.

I suppose I expect to see not just how people lived in the past, but also to see the effect that time has had on what they made. I like looking at a fragment of a wall and contemplate the amount of time that separates me from the folks who put it up. Knowledge that the wall was built in my lifetime just completely ruins it for me (no pun intended).

That said, I did see some great recreations and I learnt much more about the past from them than I had from ruins. Some folks do impressive amount of research about what life used to be like and recreations are probably the best way for them to share what they learnt.

This has nothing to do with the alleged erosion of personal lives.

Money is simply not the only aspect of a job that determines how rewarding it is. Other parameters that people find relevant include meaningful mission, ethical concerns, work relationships, power, travel, ability to open source code, to publish and to give talks, access to expensive hardware, innovation, leading others, helping people in need... etc. I find it a bizarrely narrow view to insist that getting paid is the sole motivation to work. In fact, from conversations with folks older and more experienced than me I am under the impression that as we age all these other aspects of our work keep gaining in importance over paycheck.

That said, I understand that in the absence of money the need to get it is an overriding concern. However, I find the focus on money very surprising for a site full of software engineers who by and large can afford the freedom to pursue meaning and self-actualization in their work.

In the absence of a physicist, I suppose that a software engineer in the room might do. After all, the counterintuitive consequences of relativity have their counterparts in counterintuitive effects in distributed systems and concurrent programming. In both cases, the core issue that misleads our intuition is the lack of a shared global clock that would impose a total ordering [1] on events/reads/writes/etc. Instead, events in both situations are only ordered partially [2]. In relativity the ordering is determined by the speed of light, in distributed systems the ordering is determined by what messages have been exchanged by two nodes and in concurrent programming reads and writes are ordered by synchronization actions such as lock acquisition and release, memory barriers etc (c.f. the happens-before relationship in JMM [3] and other memory models).

See for example [4] and [5].

[1]: https://en.wikipedia.org/wiki/Total_order

[2]: https://en.wikipedia.org/wiki/Partially_ordered_set

[3]: https://en.wikipedia.org/wiki/Java_memory_model

[4]: https://www.youtube.com/watch?v=UYZIHP120go

[5]: https://www.microsoft.com/en-us/research/publication/time-cl...

I don't find the argument that distances are too great for intelligence to meet particularly convincing. At its core lies unjustified extrapolation that the ratio of average lifespan to typical interstellar distance - a pure accident of Earthly biology - somehow extends to the whole universe.

The key quantity on which the argument hinges is

    T * c / D

where T is the average lifespan of the intelligent being in question, c is the speed of light and D is a typical separation between stars in a region of interest.

In our stellar neighborhood there are about 0.004 stars per cubic light year [1], so if we choose to measure D as the reciprocal of the cubic root of stellar density then D is about 6.3 light years which is of the same order of magnitude as the distance to Proxima Centauri (~4.2 ly). This quantity varies somewhat, e.g. global clusters have about 0.4 stars per cubic parsec [2] which is more than 0.01 stars per cubic light year for D of 4.4 ly.

In case of humans, T is about 79 years. We don't know anything about any alien lifeforms, but even among lifeforms on Earth T varies significantly. For example, Bowhead whales can live more than 200 years [3]. Traveling 4 ly at 5% of the speed of light is a possibility for such creatures. Moreover, entities with artificial intelligence could live (function?) significantly longer. Possibly forever.

[1]: https://en.wikipedia.org/wiki/Stellar_density

[2]: https://en.wikipedia.org/wiki/Globular_cluster

[3]: https://en.wikipedia.org/wiki/Bowhead_whale

> Can a person live a decent life without working?

Here is how I read this:

"Can I live a decent life?" - > Can other people make sure I have what I need when and where I need it?

"...without working?" -> ...without me doing anything for them in return?

Sounds awesome. For me.

Returns on investment in automation increase with the scale of the system being automated. Therefore, automation promotes centralization of control.

Be careful what you wish for.

VLBI arrays [1] are networks of radio telescopes that combine data from multiple instruments spread out over a continent or the whole planet. A network like this emulates a continent-size or a planet-size radio telescope and produces radioastronomy's highest resolution images.

The most sensitive VLBI array is the European VLBI network [2] which spans the sort of scales you have in mind.

A VLBI array can also incorporate space-based nodes, see e.g. [3].

[1] https://en.wikipedia.org/wiki/Very-long-baseline_interferome...

[2] https://en.wikipedia.org/wiki/European_VLBI_Network

[3] https://en.wikipedia.org/wiki/HALCA

Can an employee on EB green card leave their sponsoring employer to start a PhD in the US and keep the GC?

> and if black holes really do explode at the end of evaporation, then maybe that is also observable

I suppose her reason to assume we can't observe this is that evaporation takes extremely long time. For example, a solar mass black hole will take about 10^64 years to evaporate [1] (this is approximately 7 * 10^54 times the age of the universe). Note that astronomical black holes are heavier than the Sun, so take even longer to evaporate.

I suppose the micro black holes [2] might offer a glimmer of hope, but these objects are entirely hypothetical.

[1] https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_e... [2] https://en.wikipedia.org/wiki/Micro_black_hole

Not the OP, but I suppose one can read their comment as referring to the original colonizers who crossed the Bering strait, not those who crossed the Atlantic.

Earth is a graveyard of species. Looking at the geological record, more than 99% of species that ever existed here have gone extinct [1]. Overwhelming majority of them long before we showed up. And in any case, this planet will not support life forever [2].

Believing we have no destiny outside Earth is believing we have no destiny at all.

[1] https://en.wikipedia.org/wiki/Extinction [2] https://en.wikipedia.org/wiki/Future_of_Earth

> How could you upload just your brain and be the same person? Need your whole body, surely?

In practice, people who received heart transplants are generally considered to be the same person as they had been before the transplantation, so it seems most of us have already accepted that you don't need the whole body.

I think the history of physics does not support this view. New theories that explain a wider range of phenomena tend to be harder to understand than their predecessors that explain a narrower range of observations. For example, Newtonian mechanics is simpler than relativistic mechanics which is simpler than quantum field theories.

Also, I see nothing that would make fundamental aspects of nature comprehensible for humans. Our cognition evolved to handle classical mechanics without the relativistic or quantum effects that we find bizarre and indeed classical mechanics is roughly where average person's understanding of nature ends.

An alternative view is that there is a survivorship bias at play: we tend to understand the things about the universe that are simple enough for a human mind and remain oblivious to the ones that are too complicated for it.