throwawaymath

Not bothering me in the first place, or maybe taking a hint.

If I didn’t reply to your first or second emails, assume I don’t want to. A motivating example: the only people who have ever emailed me repeatedly and used language like, “one last time” are cold calling salespeople and recruiters. I do nothing when they initially reach out, but when they start using tactics like this I send them directly to spam. I get that they have to sing for their supper, but I won’t respond to synthetic overtures of familiarity or urgency.

Toilets are also a "near requirement" in any meaningful sense that phones are a near requirement. But toilets (and sewage more generally) are obviously quality of life improvements over what humans had in previous epochs of history.

Stated more succinctly: hasn't it always been common for major improvements in quality of life to eventually become the default, rather than the exception? Or am I misunderstanding your point?

To be fair this is mathematical pedantry when we're talking about trivial objects. But in principle it's meaningful because every field you can construct will lose critical properties if you allow one element to be both the additive and multiplicative identity. Unfortunately authors don't always make it clear that you need both existence and uniqueness when they state the field axioms.

To illustrate this for you, let me turn it around a bit. Is it security by obscurity if the only thing stopping someone from logging into your account is knowing your password?

Security by obscurity is when you (for example) roll your own cryptosystem and rely (in whole or part) on the secrecy of your new-fangled algorithm to save you. That is unsafe. But if you're saying high-entropy strings shouldn't be the only barrier to authentication, you're throwing out half a century of complexity theoretic cryptography.

That being said I'm a little surprised to hear about the complexity. Are you able to share which DB/stack you were using? This functionality should be natively supported at two distinct abstractions: your programming language and your database.

The other commenter's point about leaking information is also correct. In the finance industry one of the basic tricks to obtaining alternative data is to scrape it from private APIs which expose sequential IDs corresponding to a source of revenue. For example, a publicly traded car company might have its revenue extrapolated from an open API which sequentially increments an ID every time a vehicle is sold. Research groups will reverse engineer mobile apps from companies with only one or two dimensions of revenue, find the private API endpoints (reversing request signing as needed), and then look for object IDs which can be thrown into a timeseries on a quarterly basis.

Generally speaking the risk and compliance department of a hedge fund disallows this kind of data if it's gathered from an actual security vulnerability (e.g. leaks PII). It needs to be "only" a neutral information side channel without sensitive data, so that doesn't really apply in this specific scenario. But it does apply for people considering using integer IDs for user-facing APIs.

1. Using sequentially incremented integer sequences as object IDs, and

2. Failing to protect sensitive data using some kind of authentication and authorization check.

This is becoming a trend with data breaches. Several of Krebs' other reports on behalf of security researchers were originally identified by (trivially) walking across object IDs on public URLs.

My cynical take is that Krebs couldn't go public before this afternoon because First American wanted it to hit the news at an opportune time, then get ahead of it with their own messaging. Krebs got in touch with First American on Monday May 19th. The story is only just breaking now on a Friday afternoon at 5 pm; markets are conveniently closed for the weekend.

I expect them to issue a hollow PR statement about valuing security despite being unable to act on security reports until an investigative journalist threatens to go public.

That being said, it would be kind of narratively satisfying if Riemann is undecidable. There are many novel theorems from the past two decades which are conditionally true assuming Riemann is true. Riemann itself has become a useful technique for conditionally proving new theorem. If Riemann is undecidable, it would imply a great deal of mathematics has been developed which compartmentalizes the undecidability of other theorems. ______________________

1. https://mathoverflow.net/questions/79685/can-the-riemann-hyp...

True, and that's why we like to generalize things. It's usually easier to prove a mathematical object belongs to another class of structure which has certain properties than to prove the object itself has all those properties.

Of course as you've noted it's not always like that at all. It's significantly easier to prove many things about finite-dimensional vector spaces over fields versus infinite-dimensional modules over rings.

Solving mathematical problems is a lot like working a sponge. It's often useful to alternate between expanding and contracting the scope of your problem.

Code is available for most of these proposals because NIST is currently running a PQCrypto Standardization CFP[1]. However I strongly recommend against deploying your own post-quantum cryptosystem for a few reasons:

1. As I've cited elsewhere in this thread, this paper notwithstanding, most leading researchers in the field are frankly bearish about the prospects of 2048-bit RSA being broken in the next 20 years or so.[2] This can obviously change, which leads me to the next few points of consideration.

2. Most of the post-quantum cryptosystems are not well-studied, relatively speaking. They are fundamentally unproven compared to classical systems - we just haven't had enough academic scrutiny yet. It's still premature to say which post-quantum cryptosystems will remain secure under academic scrutiny over the next few years. Many were dropped from consideration after Round 1 of the NIST standardization review.

3. Most (perhaps all) of the implementations are immature and not well-supported. The majority of them are proofs of concept for NIST, not production-ready code. Authors themselves will caution you against using them. We don't have a libnacl for post-quantum public-key cryptography right now, which means that you'd be substantially rolling your own interfaces to underlying primitive implementations. It's hard enough maintaining secure cryptography in production when everything has been done to keep you from footgunning yourself - you won't have such guardrails for post-quantum cryptosystems.

4. Unfortunately, all post-quantum cryptosystems are grievously inefficient in either time or spatial performance compared to classical cryptosystems. As a general rule of thumb, lattice and error-correcting code based cryptography tends to be on the faster side with very large key requirements, and isogeny-based cryptography tends to be on the slower side with lower key size requirements. But all are noticeably slower than classical systems across both dimensions.

You should wait until these cryptosystems have been proven out by academic and industrial research. Google[3] began implementing lattice-based cryptography for TLS in Google Chrome in 2016. Adam Langley has a nice writeup[4] which also includes a few performance concerns. He's also written a blog post to talk about the next round of implementations they'll start experimenting with[5].

_______________________

1. https://csrc.nist.gov/Projects/Post-Quantum-Cryptography/Pos...

2. https://www.nap.edu/catalog/25196/quantum-computing-progress...

3. https://security.googleblog.com/2016/07/experimenting-with-p...

4. https://www.imperialviolet.org/2018/04/11/pqconftls.html

5. https://www.imperialviolet.org/2018/12/12/cecpq2.html

1. A secret key as long as the plaintext.

2. A consistent source of true randomness and a way of sampling it such that your secret key is truly random.

3. To never reuse a key once it's been used once.

Imagine the ramifications of retrofitting servers to use one-time pads for TLS. Moreover, essentially everything we take for granted in cryptography relies on constructions which use pseudorandom permutations and generators. Even if we resolved all these problems and forged ahead in a brave new world using stream cipher-like constructions based on one-time pads, we'd still have to rethink all of public-key cryptography.

This impracticality is one of the major reasons we moved on from information theoretic security to complexity theoretic security by the mid 20th century.

The reason you get pushback is because Moore's Law exists within a historical context in which it was actually plausible for exponential increases to occur each year, year after year. The field of quantum computing is so nascent that such a context is utterly alien to it. We simply don't have the economies of scale, engineering capabilities nor even theoretical groundwork required to achieve and sustain those kinds of improvements. The other reason is because transistors and qubits are not directly comparable, and you shouldn't try to infer the growth trajectory of one from the other's.

So to answer your question directly - it's not nonsensical at all to measure and forecast the rate of physical qubit capacity increase. The report I cited in another comment does exactly that, which is how you can derive that 20 year estimate I made. But we don't have any evidence those kinds of annual doublings will be achievable anytime soon, so most of it comes down to educated guessing.

We are several theoretical and engineering breakthroughs away from a scalable quantum computer with sufficiently many error-corrected, logical qubits to do something useful with Shor's algorithm. The current rate of error-correction needs to decrease by a factor of 10 - 100. The current state of the art in physical qubits needs to increase by a factor of at least 10,000.

If we assume the number of usable physical qubits doubles every year while the decoherence rate halves every year, it's plausible a quantum computer could be designed to break 2048-bit RSA in slightly under 20 years.[1] To be generous, we'll also assume the implementation and engineering work doesn't meaningfully increase that estimate once the design is finished.

This is an optimistic forecast, to put it mildly. There are credible arguments from skeptics[2][3] in the academic community that it's not actually possible to build a quantum computer capable of breaking RSA in practice. Likewise, everything I've mentioned is only in regard to the known unknowns we need to resolve. It's very probable there are a variety of unknown unknowns to contend with as well.

This is also all aside from the possibility (emphasized by the first report I cited) of a looming winter in quantum computing research. In order to actually reach a point where RSA can be broken, the field needs to start paying out the checks it's been writing. This means actually achieving quantum supremacy and developing legitimately useful quantum computers - scalable or otherwise - for industry applications.

Finally, D-Wave's progress isn't relevant here. They're building a quantum annealer, not a general-purpose quantum computer. All the foregoing is based on the idea of building a general-purpose quantum computer to implement Shor's algorithm. Annealing methods aren't applicable.

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1. https://www.nap.edu/catalog/25196/quantum-computing-progress...

2. https://spectrum.ieee.org/computing/hardware/the-case-agains...

3. https://gilkalai.wordpress.com/2017/10/16/if-quantum-compute...

If you literally mean infinite memory, your claim is trivially correct regardless of whether we postulate a team of 100 Elon Musks or a team of any 100 replicated adult humans in the world. Even a modest human intelligence with access to infinite memory can eventually do anything possible in a computational sense. So let's pare that back a bit, because infinities break thought experiments.

Do you mean something like 100 Elon Musks, each with a datacenter's worth of GPUs? Is that sufficiently many to conquer the Earth and do what they wish? If so, why? How would they do it? If you don't have a realistic example for how they'd do it, why are you confident they can?

If you want to counter the arguments that AGI will be capable of exponential self-improvement, you need to use an analogue other than humans. Humans categorically lack the capability to exponentially self-improve. Likewise human intelligence is definitionally non-alien, which is not something we can say a priori about any successful AGI we create.

Why? What makes you confident in this assertion?

To whoever has downvoted: I doubt it. Surely if you think this is so obvious that my question seems disingenuous, you can clearly articulate why the claim has substantial credibility?

1. Deutsche Bank facilitated a basket option trading strategy used by Renaissance Technologies, which has since earned the latter an investigation from the IRS for aggressive tax avoidance. RenTech is (unfortunately) synonymous with Robert Mercer's political activity in the eyes of many because he was a major partner and CEO of the hedge fund before he stepped down last year. This leads to my second point.

2. Deutsche Bank is (separately from RenTech) involved with Donald Trump in a number of real estate dealings, which other commenters have already cited. Regardless of your personal stance on the president, the NYT is going to spend time investigating any areas of financial misconduct it can find which may be directly or indirectly related to the president.

Does that mean he wouldn't be saying anything about it if it were 11 instead? That seems like just as subjective an assessment as the one he's currently making. A seemingly "random" looking number can be just as arbitrarily chosen as a neat looking one.

It wouldn't surprise me to know analysts like to slightly round up or down a valuation target to hit a neat number like 10. But that seems like human nature to me, not a lack of integrity or critical analysis. I don't think this is a very critical heuristic to use...

1. It is arguably the most sophisticated CAS available. Open source tooling has crept up in performance and completeness in recent years, but Mathematica still dwarfs every open source system in performance and feature availability. Competing proprietary systems like Maple are capable of beating Mathematica in certain specific domains (like PDEs), but that leads me to my second point.

2. Mathematica isn't just a CAS. It also supports sophisticated data analysis and ingestion, visualization, (some) machine learning, natural language processing, speech recognition, signal processing, climatology, meteorology, geography, financial analysis, and limited forms of convex optimization.