In a similar vein, this is an encoding I designed specifically for 256 bit keys; my design includes checksumming and some consideration to consistent verbalization:
I have been using a technique that's almost identical to this for years, based simply on observing that the roots are symmetric around the min/maximum: differentiate, set to zero, then difference of squares.
This doesn't invalidate the point you're making, but saying that it's 'basically impossible to play a wrong note on a diatonic harmonica' is simply false, as anyone hearing me play one will attest to.
> I don’t think the government did anything wrong.
I think that rather depends on whether you regard the role of government here to assist its (future) citizens, or censure them (narrowly avoiding arrest and detention in this case) for what appear to be minor violations of immigration law.
> For AR though we need multiple apps to share the same 3D space all running at the same time
This is something that I've given some practical thought to. The approach that I considered was to treat each application process as a client to a '3D space' service through which it could add and modify defined geometry.
Failure/slowness of any given application would leave the existing application geometry in-situ within the 3D environment and avoid the most jarring extremes of user experience. I imagined that the service interface itself would mandate the availability of simplified geometries together with meta information. This would allow the service to appropriately degrade the 3D rendered environment to maintain high framerates.
I think this approach could be effective and would not require a new OS.
I had a similar thought a few weeks ago, but for smartphone camera and mapping apps (and the intersection of the two when it comes to world-based AR). Rather than every new app out there having to implement their own camera and map view, have them provide an extension that can be called by the native camera/map apps (providing the view bounds/coordinates/etc), that returns a rendered layer that gets overlaid on the view.
Examples:
In my state we have a govt funded web/native app that provides the fuel prices at all the service stations around you. If there was a mapping extension you could turn on, it would show this directly within the mapping app, and also an indicator "cheapest fuel within X km is at Y location" when you're in navigation mode.
In camera view with an extension turned on, provide object detection similar to how QR codes are recognised.
SteamVR basically does this - it is a very evolved implementation of a VR OS.
Apps which crash or otherwise stop rendering trigger a fade out to the white-room VR space, whereas frame-skips are handled by hard drops (so the effect is like a teleport to avoid motion sickness).
Like, Valve have really done an incredible job on the user application interface there.
> Failure/slowness of any given application would leave the existing application geometry in-situ within the 3D environment and avoid the most jarring extremes of user experience.
This is already true with even the oldest and most rudimentary AR/VR systems, eg, Gear VR. The interface and head tracking is 90fps all the time. If the app is slow, the viewport will not freeze. Just it will be stuck on one frame.
> Perhaps, but if anything the UK's own government and press were major offenders in this regard.
It's quite possible that this behaviour by the UK political classes is what hastened to movement towards Brexit. I personally think that many people in the UK were aware of the behaviour, by both major parties, of using the EU to impose laws for which they lacked democratic support technocratically. Since there was no electable party that stood in contrast to this, the electorate took its opportunity by evicting the EU instead. Seen in this light, Brexit is as much a reflection of a failure of national politics, as it is of continental politics.
The mantra 'taking back control' of many Brexit supporters is perhaps better seen as citizens wanting to stop their government from acting in ways they don't vote for, than as the government taking back control from the EU.
The dissembling (as I see it) of politicians from across the EU on this law (and others before it) indicates that this is not a problem that is restricted to the UK.
Brexit was about immigration. Nothing else comes close. I think you're right that this was in the mix, but so were a hundred other factors that might have got raised here or there, but they're all dwarfed by immigration.
Britain more than any other member has managed to get exclusion clauses from any EU regulations or rules we didn't want, so the argument that we couldn't do anything about rules imposed by Brussels is obviously untrue. We opted out of stuff all the time, it was routine. The irony is that if we end up in a soft Brexit situation with an open trade deal with the EU, we won't be able to negotiate any opt-outs anymore because we won't have any representation in Brussels. We'll have to take everything Brussels serves up, or crash out hard.
Not to deny that immigration was a major part, but the belief is more important than reality for both that and sovereignty. Yes, the UK had a great deal with loads of opt-outs, but that didn’t stop the papers blaming the EU for everything — including immigration, which was mostly non-EU.
I'm not sure I understand this, and I'm genuinely interested in why it would be.
I find zero indexing logical: zero is the first natural number and is thus a fine candidate for being the first ordinal.
In my experience most mathematical series lose nothing in terms of elegance or readability by being indexed from zero instead of using more traditional indexing from one.
Generally I've found you carry around fewer n +/- 1 type expressions when you index from 1. Also, most applied math papers I've read index from 1 and that makes implementing them a lot easier.
Generally 1 is considered the first natural number, except bourbaki.
The reason for this is the set {1...n} has order n, but the set {0...n} has order n+1, so you get lots of off by n+1 inelegancies or errors when order is important. It's better to be explicit at the set level when you need an {0...n-1} set, because usually the order gets passed around to later expressions and not the set element, so there's less algebra.
Zero indexing is great when your index is an offset, as it is for true arrays.
You find zero indexing logical most likely because you learned programming on languages which are zero-based. But most of the rest of the population, including statisticians, for which R is the intended audience, likely start at one and aren't used to OB1 errors.
It seems needlessly confusing to me to refer to the first number in a series as the 0th number. 0-based indexing is only good for offset counting, which is very much based on having a mental model based on pointer arithmetic for a number sequence.
Yeah years start at 0. But that's because it measures the offset from the beginning of the calendar. You can similarly expand this to all distance based measurements. But that is completely different from counting, which shouldn't be conflated with distances. People always say the first of some sequence and only people who care about 0-based indexing tries to spread the 0th of some sequence meme.
My ideal calendar has 12 30 day months, days 0 to 29.
If it's 10th June and you have an appointment for 0 August, that's 50 days from now.
At the end of the year, a 5 or 6 day 'month' called Holiday. 30th December becomes Christmas Day (observed) and 0 January is still New Years. New Years Eve is either 5 or 6 Holiday.
I have to concede that I still talk in this now outmoded manner. I have to make a conscious effort to switch to modern gender neutral language (eg. they) when speaking or writing to anyone outside my family and friends.
> English language changed to expunge the ambiguity.
I think it's more accurate to say it adopted different ambiguities. The use of 'they' can create ambiguities of number, and just switching between he/she leaves the same ambiguity (is the gendering intentional or not?) albeit in a gender balanced way.
As a side-note, 'he' was used to refer to people, who could be regarded as interchangeable (man or woman) and 'she' was reserved for 'uniquely individual' things, which is why countries and ships (as two examples) are referred to as such. At least, this was may understanding when growing up and I've never lost this habit.
> The solution to this paradox was to use a set of axioms (most commonly the Zermelo-Fraenkel axioms) which do not allow the construction of such a contradictory set ...
Or one can adopt a non-well-founded set theory that admits such a set.
Those who want the UK to remain in the EU will see this as just one damaging consequence of the UK's decision to leave. Conversely, Brexiteers will see this as an example of maladministration by an EU bureaucracy, and another demonstration of why the UK needs to exit. Sadly, there will be no consensus.
Putting aside the politics, this seems like a very poor decision. Historically, I believe most registering authorities have made great efforts to grandfather-in prior domains, for practical reasons apparent to most visitors of this site.
Additionally, shoddy treatment of 10% of current registrees will do nothing to increase the perceived value of an .eu domain. I also note that it appears the EU commission didn't even discuss the policy with the company that manages the .eu domain:
That's a fair comment. I hadn't considered that perspective.
I'm aware of several TLDs that require evidence of residency/trade within the geographic region for the purpose of registration, but I don't think any of them require it in perpetuity for renewals; it's this that seems problematic to me. In principle, URLs are based on a degree of immutability: saying that a domain name must change when circumstances change seems at odds with the architectural fundamentals of the web, in which case I question the value of establishing a .eu domain at all.
This doesn't seem to immediately affect existing registrations, so they can renew for up to ten years before the withdrawal date, and start redirecting people to some other domain.
... as of the withdrawal date ... the Registry for .eu will be entitled to revoke such domain name on its own initiative and without submitting the dispute to any extrajudicial settlement of conflicts ...
https://github.com/tomgibara/keycode