jwtadvice

While I can not claim to have made any imporant progress on the sorts of toy problems I like to work on (e.g. counting/bounding the number of strings two regular expressions both accept, counting the number of ways to represent integers using polynomials), I find the mere process of working on them, inventing new notation to succinctly express ideas and read relevant (and completely irrelevant) mathematical textbooks and articles a way to keep an "active brain" but relax: probably because nobody expects me to produce anything and my career doesn't depend on it.

I feel like CNBC did it particularly well [1].

> "Our understanding is that this is not the start of sanctions easing," said Ian Bremmer, a widely respected political scientist and president of consulting firm Eurasia Group.

> "It's a rule change clearing up a problem with the sanctions regime that prevented U.S. exporters of non-sanctioned electronic devices from complying with both U.S. and Russian law. The problem was identified by the Obama administration, and this appears to be the response to address it."

> Sen. John McCain, R-Ariz., a Russia hawk who has called for more sanctions on Moscow, told NBC News that Thursday's move looks like "largely a technical fix."

The sanctions brought against Russia for the proxy war in Ukraine and secondarily the sanctions for information war between the two countries specifically target particular people (individual officials enumerated by the Department of Treasury, under so called "smart sanctions") and particular sectors of the Russian economy (military moderization and acquisition sectors as well as parts of Russia's Defense Industrial Base).

The restrictions eased on software transfers were not a lifting of sanctions in any meaningful way. Unfortunately the way these headlines are being written is causing a public panic.

[1] http://www.cnbc.com/2017/02/02/us-treasury-eases-some-sancti...

Similarly if you click on one point continuously it creates "non-physical" topologies and overlapping blocks.

But seriously, really cool work. Excited about the future of CSS with VR, 3D displays, etc.

The way this is layed out in a table and suddenly properties line up in rows and columns reminds me of the Periodic Table in Chemistry.

Obviously it shows how the ASCII committee used the first two bits as control bits and the remaining bits as a mixture of control and data bits, but I’d never seen it displayed this way.

Really neat.

Thanks. I'm aware of this! I just used Xi a bunch and didn't want to keep typing Xi Jinping either so I used Jinping. Changed up the pronoun for readability and variety.

Is it culturally unacceptable to refer to Xi Jinping as Jinping?

Thanks for your informed and interesting comment!

This is an interesting position, though I think it suffers from the same shortcuts that much US thinking does when it tries to grapple with prior arrangements that seem inconvenient today because of changing strategic context.

To what extent did it contribute to the fall of the Soviet Union? An incredible amount. China blocked the Soviet Union in all of South Asia, it abstained from diplomatic support - it wielded both its position on the UNSC and it's nuclear capability to check USSR. Then, it challenged the central tenets of Communism specifying that it had a different interpretation closer to the original theory - thus challenging the centrality of Russia ideologically. China's withdrawl represented approximately a third of the world population removing itself from the union: the concept of "domino theory" at the time described - in a certain pop science way - how states arriving into and dropping out of the union had a chain reaction effect. Since the alliance with China, the Cold War no longer was fought in the Asian theatre - closing down an entire continent of front to the war. The rest of the Cold War would be fought in Central Asia (and eventually in the Middle East), and in Europe.

Of course, the United States knew from very early that it was going to lose in Vietnam: the Pentagon Papers discussed this in great detail. The United States was there on a cost imposition exercise. The result it found in the alliance with China was a mutually satisfactory way to close the conflict. In this regard China didn't win the Vietnam war either.

> The various potential military hotspots – Vietnam, the Korean peninsula, the South China Sea – would probably be in much the same state if the US-China deal never happened.

I have no idea. That's 60 years of alternative history to imagine. Fascinating, but not clear.

> Many people say that Nixon's decision was a great strategic move, but I am unconvinced – the US got some short-term assistance against the Soviets which it didn't really need and didn't make much difference anyway; in exchange, the US put itself in a weaker strategic position vis-à-vis China for many decades to come.

This seems to be a rising opinion in the National Security Core of the United States, and also seems to be the take of the new Trump Administration.

Personally I see this as historical revisionism, contextualized by modern concerns over historical accuracy.

I fully agree that China and it's potential rise are considered by the National Security State of the American Government to be a dark horse scenario, and a greater potential spoiler to American hegemony than Russia (a waning power) today.

I understand how someone could mistake the situation we are in today with a security outlook at China's rise and want to throw out some of the alliance concessions because in this day and age they are inconvenient. We've seen that before in history (indeed, in American history) and so it's congruent with the kind of behavior we would expect.

> China's economic development since the 1980s has provided many economic benefits to the US and its allies. But, that still could have happened even if there was a more assertive US policy towards PRC

I think all of this is very accurate, provided there was _some_ deal to get an alliance. Had it been possible for the United States to do that without recognizing PRC, I serious doubt. But yeah, if that had been possible, I think much of the geoeconomic situation would have looked the same.

China needed strong assurances from the US and UK that formally splitting from the Soviet Union wouldn't see the American alliance then turn against China in a divide-and-conquer strategy.

Could we have gotten a better deal? I'm not sure. Given the earlier incursion into Vietnam and Korea, the military support of the ROC and the militarization of the First Island Chain, I can't imagine that anything short of the very strong reassurance the alliance pursued with the "One China Policy" would have been acceptable.

The move is one of the only things heralded of the scandal-plagued Nixon Administration as a wild success for the United States, and is even often credited for being the key diplomatic victory that ultimately won America the Cold War.

The quick response to these concerns is that they very highly speculative. They are the sort of thing that - like medieval models of the solar system - seem to predict the the movement of the planets, except that you keep needing to explain away all the inconsistencies and that there are much simpler explanations available, which don't suffer from the exhaustion of the requirement to constantly tweak and reinterpret.

If Xi Jinping were to try to purge the Chinese Government (a highly paranoid organization, with military, intelligence and national security communities that far outlast his particular inter-party alignment) that would be incredible, shocking and enormous news.

> If Mr. Xi's goal were to stay on past the customary 10-year term, wouldn't he need to discredit the current institutions of government and portray himself as the antidote?

Maybe? Generally, the party is the face (you used the word veneer) of the government and its institutions. Weakening public opinion of the party only makes sense if Xi Jinping were pushing to replace the party system with a cult of personality. In the mind of the Chinese, Xi merely runs the party, and any damaged public opinion about the party reflects directly on public opinion about how Jinping is running it.

The kind of steps to become a cult of personality necessary to replace the party system just aren't being seen. You aren't seeing the government under Jinping trying to mass mobilize a change of public opinion to value his leadership over and above the party system.

Rather than discredit the current institutions of government he'd need to purge the institutions and norms which facilitate the cap on leadership and the interior modes for leadership to be replaced, as well as top brass in the People's Army that would enforce that - while pushing for the citizens of China to support such a transition. I have yet to read anything that makes a case that that's happening (much less a compelling one).

> Just out of curiosity, have we seen any such documents or communications (on any subject) that weren't intended for public consumption? That seems like important context as to whether absence of evidence can realistically be considered evidence of absence.

Yup. Take "Document Number 9" or the leaks regarding Ling Jihua or the leaks from the public diplomacy and strategic communication (propaganda) centers in China or the so called "50 Cent Party" - their version of the US's "Global Engagement Center".

Documents are leaked in China the same as they are leaked anywhere else. In any case, I'm just suggesting the type of really strong evidence you'd want to be able to reference to support a really strong claim. Unfortunately not enough leaks from any government are available to always have a "smoking gun" (though incredibly in the case of Brazil we got them, not that it mattered). I agree with you that absence of a leaked smoking gun is not evidence that it doesn't exist. My point was that there's nothing even close - so either the conspiracy is incredibly underground, has thought 15 moves ahead, and is going to manage to capture a government with a billion people even without taking the steps you'd expect to see - or it's a rumor similar to those about President Trump's, President Obama's, and President Putin's ambitions to overthrow their governments that were/are popular during their respective eras.

Color me really skeptical. I'm willing to believe it though - I would just need to see the right set of circumstances or the right set of leaked documents for it to make enough sense. Overall I'm much more interested in current affairs, geopolitics, and the potential ouster of Najib Razak in Malaysia and the workings of the next China party congress than these kinds of highly speculative and underevidenced theories.

To consolidate the similar threads of discussion, another comment mentioned this here: https://news.ycombinator.com/item?id=13533864

To consolidate the similar threads of discussion, another comment mentioned this here: https://news.ycombinator.com/item?id=13533864

It seems to me that it's an actual genuine effort, given that the publicity of the drive has damaged Chinese public confidence in their institutions of government (high profile corruption is often featured in the news) and because many of the people taken to court have been in Xi Jinpeng's own circle and have represented for him a loss of personal power in the party. I haven't read much about Xi's personal power growing all particularly much during the anti-corruption drive, and there is a legitimate question whether he will be revoted to lead the party during the congress next year (though it is expected to continue).

Definitely this angle on understanding the drive should not be ignored. An attempt to corroborate it - to unpick the knot - would require a great amount of study of the Chinese People's Party, of Xi Jinping's constituency, and both the consistency of and the timing of charges brought to bring in the high level fraud. Documents and communications from Jinping or his circle discussing "who to go after" would represent a smoking gun (of course we haven't even smelled anything like this).

I read an expose from Foreign Policy where they tried to build a case that Xi Jinping has been using it to consolidate power, but it was very clumsy and as its predictions and information came into question the investigative direction taken by the expose has been abandoned (as far as I can tell).

The way the anti-corruption drive has proceeded, as I understand, has been in tracking how government finances are being used and that the Chinese Government tends to find - using traditional accounting audits - rings of people who are enriching themselves using various schemes (though many times really obvious transfers into personal accounts). So far it has appeared that the anti-corruption effort has both been making an actual positive effect on government efficiency and that it has been primarily non-political and untargetted, focusing more on finding abuse of public funds than in chasing after any officials in particular.

This appears to be an aspect of the anti-corruption drive that has been holding billionaires and politically connected people high up in the Chinese government to account of the law, with Xiao Jianhua caught in financial fraud.

The controversy here isn't that China took Xiao Jianhua in to face the law, but that he was taken from Hong Kong, where an agreement with Britain gives its former colony de facto autonomy within its small borders until 2047 - which disallows Chinese police from entering there on their own until that time.

I haven't seen any reports yet about whether there has been cooperation with the Hong Kong provisional government (which would make his capture legal). Then, it's hard to determine exactly what happened as the source linked here hasn't done that investigation yet - and is reporting on rumors that there was a small (but notable if true) sovereignty violation.

Acknowledgement that I've received the file.

I'm very impressed by the level of effort that has gone into curating this information.

I will get back to you (I'll find you on HN) after digesting this information.

It's my understanding that it doesn't store a file, it just sychronizes a transfer. You have to trust that this is the case, but you can look at the source code that it's based on (on Github).

So I think we both need to be online at the same time for it to work...

The documentation states: "FileTea does not store any file in the server. It just synchronizes and bridges an upload from the seeder with a download to the leacher."

Huh looks like I need to do a lot more reading to understand all of this! :)

I'm still trying to understand what the Probablistic Method looks like as a program. Any thoughts on that?

Gotcha. So basically the "axiom" of the law of excluded middle would become an oracle, and then with a call to that oracle a problem requiring the law of excluded middle becomes a proof. Basically - the axiomatic decisions made by mathematicians can be represented as programs by turning them into oracles.

In this case, with the axiom of choice implemented as an oracle, the program for Cantor's Diagonalization can be written.

This makes a kind of ultimate sense. Rice's Theorem shows how a program with an oracle about the behavior of a Turing Machine is contradictory, and this implies that "even with a finite set of axioms" there are no proofs about general classes of Turing Machines and thus there are statements independent of mathematics (a kind of Godelian statement).

Is that right?

If so, that's profoundly simple and also incredible to me. (Hopefully I haven't excited myself into thinking I "got it".)

Could you help me understand what Erdo's Probablistic Method looks like as a program? Which oracles might be required and how you would call them?

Anyone really familiar with this: are non-constructive proofs, things like Cantor Diagonalization or Erdos's Probabilistic Method, programs? Are they just non-terminating programs?

I can see Cantor Diagonalization as a non-terminating program really easily, but I don't understand what the Probabilistic Method looks like as a program.

No problem. Looking forward. :)

In my opinion the way to stage these technologies is not to blitz toward a fully cyborg doctor replacement, but to bolster the capabilities of the doctor with new technology - similar to how calculators did not replace mathematicians (despite historical headlines suggesting this would happen).

Giving a doctor the ability to get a "second opinion" fast and cheaply to a patient is a large boon to medicine, and shouldn't be underestimated. It allows the doctor to deal with all the nuance limited automated tools can not, and gives the MD the ability to check themselves against the computer. If the MD finds themselves disagreeing on something like a skin condition, the feedback can both improve the doctor's service and provide bug information for the code and databases used to train the AI.

Firefox remains one of the browsers I use.

I sideload Chrome, Safari and Firefox on my work machine because we work with mTLS with smartcards and honestly none of the browsers work reliably (it's not a very high use case).

The biggest difference I notice to my browsing experience is when I switch over to Safari (Webkit). It's not that it's slow - it just renders pages slightly differently, whereas Firefox and Chrome seem to have aligned over the years very well on how to interpret stylesheets.

I'm never doing anything intense enough in the browser (besides maybe streaming a single video?) to notice significant performance differences.

How do you feel about base64 encoding it and putting it on something like pastebin?

If you want to keep the link secret, here's a public key you can encrypt the link to:

-----BEGIN PUBLIC KEY----- MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAs+Zefow5vk22331dfQD/ VB/l8CbDNx+fo3r4MUGuOSVBnq2U2mEE0Q91oGSeSluuq7OHRuaZ0O3fKi793+ne LH41NNH8Yn9Dn6dyvyxyM2+mXa7g6pxhb2fjhUl2Sp8DhcaxKlpHSGY0B9sJGu7H oBiFzO3wd/GO0mI0wdW+/7SpqaidjrLiyA2Lftdo3IrVqHCQL0CqbmFC1xK3kAKE xIgWTA07HG3AyJpyUp1tRNP70czWn6Pl9pIufjalgZPjeNNej+R6q7WKLfH8gBZR lWEtsQnag53fyjrn2LySAbXrdRNTXoGecAliONSV6atmiqr1pa6iH6xfPFH+ebON vwIDAQAB -----END PUBLIC KEY-----

Or, if all of that is too complicated how do you feel about https://filetea.me/?

Yes. I would love to see your spreadsheet.

Some sources that may interest you: The Federation of American Scientists (fas.org), the Strategic Studies Institute (strategicstudiesinstitute.army.mil), OpenCourseWare (ocw.mit.edu/courses/political-science/), the Center for Strategic and International Studies (csis.org).

Reddit /r/geopolitics maintains a wiki with a list of open source references that you may find interesting: https://www.reddit.com/r/geopolitics/wiki/index

There's too many things to recommend: foreign news outlets, official press briefings, leaked documents, academic and military history, think tanks and their analysis.

Basic advice: read everything and don't believe any of it.

Absolutely. Shared respect.

1) Yes agreed here. The investments/loans aren't gifts. They are expected back - with interest - and there is real risk that insolvency and default will stall the investments. This gives China leverage, it develops regions that create the possibility of alternative trade routes and supply chains from the US system, and ultimately China expects their investments not only to produce growth but also pay back into the Bank of China.

2) The 25 year forecast is for regional military parity. Economic parity is on a similar timeline, but I don't know offhand what the most recent projections are. If you look at the strategic literature, many analysts (even journalists) focus on China's ascention in 2040-2050: 25-35 years. (25 years is the smaller number of the projections.) You will have difficulty finding analysts discussing Chinese ascension in 2030 or 2020. I would be interested, of course, in any such literature.

3) "their Communist economic system was fatally flawed, would inevitably collapse, and all the West had to do was wait" - this was Cold War propaganda, which reinforced the message that "The USSR is the wrong trade network to be in" ("Our trade network is the one to be in ;)"). The strategic thinkings from the National Security core of the United States was focused on economic warfare of all kinds that would put pressure on the USSR to collapse. The USSR had attempted to organize strategic resources across nations. When these states were flipped, either by "accidents to their leadership", economic pressure from the US trade network, diplomatic pressure, or internal instability, the USSR needed to reallocate and adjust its system. Twenty five years of unconventional warfare intended to cut the Soviet Union from strategic resources in key areas (Middle East and Central Asia), raise its costs with proxy wars and arms races, containment strategies that limited its options for economic flexibility, and pressure on China to pry the Soviet Union apart from the inside ultimately thwarted the attempt to foment the Eurasian free trade network. The Security State in America was _not_ resting on their laurels, waiting for the USSR to "just collapse". The actions of the United States were meant to put as much pressure toward insolvency and inflexibility in the Union as possible.

> From what I've read many times from foreign policy insiders, such a thing doesn't exist. The foreign policy institutions are so massive and complex, from Dept of State to Dept of Defense to the National Security Advisor and staff, to all the large subcomponents of each, to Congress, to all the career bureaucrats that outlast any President, that getting them all moving in the same direction is impossible.

No, the US has Grand Stategies. You can download, for example, the once-leaked copy of the Bush Administration era "Wolfowitz Doctrine".

Now the interagency process of getting a giant organization like the United States government and private sector to act together in coordinated concert? That's another problem entirely, and something that -rightfully- foreign (and domestic) policy insiders complain about. The difficulty of administering a giant bureaucracy is not the same as there being no Grand Strategy: indeed you can find declassified documents, leaked copies (as mentioned), strategic advice for modernization of Grand Strategy and the like.

Thanks, I'll read this later! FP is... okay. It's just so full of childish references ("pee"-otus), quips and nationalist gilding it's hard to read some times. Though some of their authors are very nice when the editing isn't heavy handed and there's not much competition on the subject (incredibly).

> As I understand it (I'm no expert in the field), U.S. policy in regard to China is that its rise to superpower status is inevitable

Interesting. My understanding is quite the opposite: that the U.S. policy in regard to China is that its rise to superpower status is in question.

China is 25 years or more from being on par with the United States in terms of military projection in its own region (much less power projection in distant lands and seas). China has legitimate issues with all of its territories that have strategic resources: its water is in Tibet, its minerals and oil is in its Uyghur region. The United States today has China surrounded by the "first island chain." China's economy is robust, but has inherent weaknesses that could cause it to fracture as it tries to jump the 'middle income gap'. Indeed out of several dozens of states that have attempted jumping the gap, only a couple have succeeded. Ongoing sovereignty disputes in Hong Kong and Taiwan keep the Chinese mainland divided and focused in on its own territory. Japan today could match Chinese military might, and with the right trajectories could maintain an upper hand in the future. America has tried to block Chinese multilateral/international banking efforts (AIIB, ADB, etc) and it's admission into the Special Economic Basket of currencies at the IMF. Today the United States (well, under the prior administration...) is trying to prevent full membership of China inside the WTO, and it's membership isn't guaranteed. India forms a natural check on Chinese regional power as its population is larger than China and its economy is growing at even faster rates. Russia (which shares a huge and important border with China) and America both eye China and it's ambitions and could individually or together align to snuff Chinese expansion where they to find a good justification. China's international investments are questionable, as much of them are in countries with poor histories of solvency (this is a strategic bet on the part of China). It's One Belt One Road infrastructure project is vulnerable to stability issues in Central Asia (of which there is a long history). The people's party in China also (rightly) fears regime change operations in their country - this remains a real possibility. China has a burgeoning nuclear power (DPRK) on its border, a nation in dispute with a long time American military protectorate.

The United States has a lot of issues it can make with China, from internation trade, currency practices, South China Sea settlement, Taiwan and recognition of independence, Japanese security (look at their reform of National Security legislation), Indian bolstering, Korean Unification, Russia's far east, Central Asian proxies, etc.

The United States is hoping that, with containment pressure on all of China's strategic bets that it won't be able to realize its ambitions to greatness - and will fizzle. This is a practiced playbook: it's how the United States prevented the Soviet Union from realizing super power parity. Curiously, the timeline originally predicted by strategic thinkers for the Soviet Union for parity was also "25 years."

Including China into the "rules-based international order" isn't code for "we want a nation as powerful as our own to also rule the international order." The United States Grand Stategy toward China - indeed toward any and every potential adversary - is to prevent their rise by raising obstacles and costs to its succession.

The insanity here (for me) is that I spent years trying to communicate the containment strategy aspect to TPP, even linking to public officials and defense documents specifying that this was the purpose. Ultimately I think I found some small measure success, but for the most part it was unwelcome news that the United States was trying to apply coercive statecraft on a competitor. For the most part the entire political spectrum didn't want to hear what I had to say. What's more those discussions often got hit hard by downvote brigading, trolling and moderator bans.

I never very much liked the TPP as it very clearly represented not only unwelcome international competition and power projection, but also because its chapters (first leaked and then eventually published) very clearly benefit large multinational businesses that lord over the United States' strategic resources, exacerbating issues of economic equality on the homeland. The benefit to the American people was that it made problems for the Rise of China - the real possibility of which could see my generations' children and grandchildren in an America that doesn't dominate the world like we do today.

I always felt like there was a better way: a way to both build America so that it is happy and safe, and create deals that benefit all social classes in the homeland.

I'm fairly certain that the Trump Administrations' instincts here will be to replace economic coercion with military coercion and I'm fairly certain that the administration's replacement deals will just as unequally favor those in America who already wield an outsized share of power.

In this regard I'm glad to see TPP go but I would much rather have seen a more creative administration holding the reins.

If I’m hiring for a candidate that has expressed a need to work remotely, I interview them very differently. First, I give extra importance to the communication with the candidate over email/LinkedIn to set up the phone screen, and also the phone screen itself. I know that I will be interacting with the person primarily this way. It’s extremely helpful to obtain referrals from people who have worked with the person remotely before, so they can provide feedback about how frequently and engaged that person has been with the on-site team in the past. I also look for and ask questions probing the persons communication skills more than my usually technically-focused interviews.

The reason for this is that I’ve experienced different results working with the same people from remote than when they are on-site. For that reason I don’t think it’s enough to assume that because a developer is a good remote worker they will work well in an office setting or that if they are a productive office worker they will function highly from remote.

Basically, people are hired into specific roles. If you’ve hired someone for an open space agile environment and the role/work dramatically changes (going remote, acquired by “waterfall method inc”, etc) the hiring decision very well may no longer be informative.

Thank you! Very keen.

To add to this comment, there’s more nuance when speaking less generally:

* In cases where there is competition between powerful nations, weaker nations can and do gain advantage by playing the interests of one country off of one another. For instance, during the Cold War the United States and Soviet Union would engage in trade, weapons, and security deals. States caught in the middle understood that both empires were competing with one another to either expand their network outward or prevent the other from doing so (America often included “and you may not trade with the Soviet Union” as an aspect of its bilateral negotiations) would try to internalize the security/strategic value that the empires sought - rather than the pure quid-pro-quo of markets.

* The United States effort with both NAFTA and the TPP were to contain Russia and China, respectively, by building a coalition of countries with trade that excludes each specific United States adversary. This strategically weaponizes the second point above: coalitions of nations together banded together against a more powerful economic force. Similarly, the Chinese RCEP agreement bands together trade centered around the Chinese economy, and excludes the United States. Indeed, the Soviet Union was, as a security/power concept, an idea that a trade network on the Eurasian Supercontinent would be able to outperform and outcompete other continental sized trade networks (the United States), which led the United States to disrupt the trade framework with proxy war, etc.

* Similar episodes are common throughout history: Nasser’s Egypt had tried, unsuccessfully, to create a Republic of Arab nations in the Middle East, so that they could collectively bargain and negotiate with external powers such as Europe and the United States. This was considered a security threat to these powers, because the West much preferred strong-on-weak bilateral agreements, protectorates and mandates.

From the security side of the coin, great nations including China, Russia (now the Eurasian Union), and the United States strategically try to build coalitions of small nations against their powerful adversaries in an attempt to disrupt their ability to successfully compete.

The Trump Administration decision to abandon this represents an idea that the United States will be able to “out-deal” regional competitors (primarily China but also Japan, South Korea) on a one-for-one basis. My guess is that the diplomacy will get very nasty - even if its all in the back room.

Another advantage to paper is that you can invent your own notation (this seems to be the primary innovation of "bullet journaling).

The full 2D space and the relationship of symbols is available to you on paper, whereas on the computer we are still struggling to enable this type of expression.

There's some question about whether Feynman would have invented Feynman diagrams had he been restricted to Latex.

Interestingly at today's White House Press Briefing, a reporter asked the Press Secretary whether the Trump Administration thought that it could surround/contain China with bilateral trade agreements the way that the TPP had intended to do on a multilateral basis.

China has a couple of free trade deals in the region. It has a multilateral effort (RCEP) which is somewhat stalled and primarily pursued bilateral trade agreements.

This may put American and China toe-to-toe in reaching agreements with Asian Pacific states. There’s a question about the quality of the trade deals that can be reached, if the target nations are clever enough to play Beijing and Washington off against one another.

The Trump Administration has suggested that bilateral agreements are better because they don’t devolve into “least common denominator” the way multilateral deals do; and that they also allow the deals to be quickly withdrawn from or renegotiated to account for new realities.

At my office we lost a lot of time because someone put up a challenge to represent all the numbers 0-99 with algebriac expressions containing exactly four digits '4'. The use of powers and radicals was allowed.

I myself solved several numbers before exhausting the tricks I could think of, and reverted to brute force/search with Polish/prefix notation, then realizing how massive the search space was for even just a few operators. Adding parentheses ordering further explodes the search space.

Finally, while this kind of concrete and explicit expression is "toy math", it is related to Godel Sentences and lexigraphic ordering of proofs used through much of the establishment of logic, the foundations of proof systems, and computer science.