As I've written in another comment here, a great example of a number-y field which is not totally ordered is Games ⊂ Surreal Numbers ⊂ ℝ.
There you have certain "numbers" which can can confused with (read incomparable) whole intervals of numbers. Games are really cool :)
You've got the subset relationships backwards: Reals are a subset of the field of Surreal Numbers which is a subset of the group of Games. (Probably better phrased as embeddings, rather than subsets, but the point remains...)
Note that Games do _not_ form a field: there is no general multiplication operation between arbitrary games.
Reminds me of the concept of games in combinatorial game theory, they are a superset of surreal numbers (which are themselves a superset of the real numbers) in which the definition of the surreal numbers is loosened in a way which looses the property of they being totally ordered. This creates games (read weird numbers) which can be "confused with" or "fuzzy" with other numbers, the simplest example is * (star) which is confused with 0, i.e. not bigger or smaller than it, it's a fuzzy cloud around zero (notated 0║*). More complex games called switches can be confused with bigger intervals of numbers and are considered "hot". By creating numbers from switches you can create even more interesting hot games.
Exactly this video made me read more into this topic, I'm currently reading winning ways and lessons in play simultaneously. It's quite fun!
I've just gotten started and am looking forward for what's left.
Thanks for sharing this. I just discovered it now and I love it too.
The space of possible abstractions for any given phenomenon is vast, yet we almost always just assume that real numbers will do the trick and then begrudgingly allow complex ones when that doesn't work. If we're not lucky we end up with the wrong tool for the job, and we haven't equipped people to continue the exploration. It's a bias with some pretty serious consequences (thanks... Newton?).
I don't think I've seen the inadequacy of number-systems-you've-heard-of demonstrated so clearly as it is done here.
I'm just starting to learn about all this stuff, but iirc thr game of Go is famously "hot". Also I will emphasize thats when talking about "games", usually what is meant is a game position. What spe cific game you are playing isn't too important as it can be shown that some positions in different games are equivalent.
Actually it seems according to the issue that TigerBeetle (one of the bigger zig projects out there) noticed this issue [1]. It's also on their issue tracker [2].
When you use a language that's in alpha- (maybe beta- now?) stage, this kind of thing should be expected.
Even with the latest version of Zig, perfectly correct programs can segfault due to miscompilation, so performance issues are not even the biggest worry you should have.
One thing I really don't unserstand is how bun already reached stability with it's 1.0 release (https://bun.sh/blog/bun-v1.0) while being written in Zig, which still hasn't reached it's 1.0 release.
If you test your software built on Zig close to 100% then you can be pretty confident you didn't run into any of the Zig compiler bugs. Bun has certainly run into them but they can almost always be worked around... if you work around all problems and manage to catch everything then yeah, you can have an application that's production worthy while being built on a compiler that's not quite there yet.
The problem is, of course, you almost certainly didn't test anything near 100% and probably not even everything users may do with your software, so it's a risky bet.
That’s the point OP is making, even if the program is bug-free, given the compiler’s current state there’s a chance the compiled binary has bugs (due to miscompilation).
Now that can happen with every compiler but using one in still in alpha significantly increases the risk.
If we're talking SemVer then 1.0 only means a commitment to a public interface. It doesn't mean the code has no more bugs and ready for use in a spaceship.
Conversely, taking on a dependency prior to its 1.0 just means you're on the hook for dealing with API changes as they come up. But as long as the API you expose doesn't change, it's fine to be on 1.0 yourself.
First of all, I am biased to my opinions so take everything I say eith a grain of salt.
Now, you need to divide your concept of thr Palestinian people to (at least) 2 groups or factions, those that live in Gaza and those that live in the west bank. The major difference between these groups is that Israel is the sovereign over the West Bank but disengaged from Gaza about 18 years ago and since it's disengagement, terrorist groups like Hamas have taken control of the Gaza strip[1]. One could have a long conversation about human rights issues in the West Bank but what is happening in Gaza right now isn't oppression, it's a war. You could point out Israel's blockade of Gaza as a form of oppression but it's just a way for Israel to prevent Hamas from accumulating massive amounts of weapons from certain foreign actors[2]. The really terrible thing ia that Hamas's infrastructure is so deeply linked and interleaved with civilian life it's impossible to fight them effectively without hurting civilians (Israel has some measures to attempt to do that[3] but everything has it's limits). Hamas isn't interested in peace and will slaighter their way to victory whatever happens, they are actively hurting both Gaza and Israeli civilians as we recently observed with the cruel massacre. The world will be better without Hamas, it's heartbreaking it has to happen this way.
In my opinion you shouldn't be worried about that possibility, the presence of the US in the middle east right now is probably just to deter other parties from escalating the conflict. The US has no interest and no intent for entering Gaza, Israel has the resources to deal with Hamas on it's own.
One of the most important parts of this conflict I think which most people here aren't talking about ia the geopolitics in the middle east. Most of this is still just a big old proxy war spear-headed by Iran. All the big terrorist groups and actors in the region wheather it be Gaza-based terror groups like Hamas or Lebanon's Hezbollah are funded and controlled by Iran.
Israel has bombed airports in Syria only a few days ago. They seem willing to strain the American protection and could little by little provoke an escalation involving regional powers, leading to our involvement. The one thing that could make this catastrophe worse is if America is drawn in.
Not only a few days ago, they do that on a regular basis by now because there are regular shipments of weapons by Iran. Syria in its state of civil war doesn't have much influence in the northern regions, where Iran tried to deploy the weapons against Israel.
One need not forget that Israel too has no interest in an all out conflict. Also the syrian attack iirc was to prevent Iran's foreign minister from landing there.
Everyone's (except maybe Iran's) hope is that this conflict does not escalate any more.
