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Posted by O3marchnative 15 hours ago

Missile defense is NP-complete(smu160.github.io)
281 points | 288 commentspage 3
zabzonk 15 hours ago|
Oh, I thought this was going to be about the old trackball arcade game. Or perhaps it is? Same sort of rules? The maths is going so far over my head I can't hear the whoosh.
gs17 10 hours ago|
I expected that too, but it's about the inspiration for the game, I guess. I was trying to figure out how you encode computation in the game.
dboreham 15 hours ago||
It's been known since the 1960s that effective anti ballistic missile defense is impossible.
cpgxiii 15 hours ago||
There are several different levels of ballistic missiles.

ICBMs, for which the GBI is intended, are the most challenging to defend against and show the least interceptor success.

In contrast, we do have some pretty definitive evidence that theater and "lower" MRBM/IRMB ballistic missiles can be intercepted successfully. If you define "effective defense" as "most missiles that would cause damage are intercepted", then it is clearly possible with current technology. If you define "effective defense" as "all missiles are intercepted", then it remains beyond the current technology.

hedora 13 hours ago||
If you define "effective" in terms of cost ratios: R = (cost of defense system + cost from failed intercepts) / (cost of attack system)

then N < 100 is well beyond current technology, regardless of whether the defense system is perfect or non-existent.

There's no magic Pareto-optimal point where investing the right amount in missile defense means that starting a war against a medium-sized country makes economic sense. Russia figured this out in Ukraine, and the US figured it out in Iran.

Israel's genocide worked pretty well tactically, but is a long-term strategic disaster. If the US continues to be a democracy, polls say that it will cause us to withdraw support sometime this decade. Also, it only works if you have an incredibly asymmetric fight.

trollbridge 15 hours ago||
A lot of things involving rockets and putting things in space have changed since the 1960s.
BoredPositron 15 hours ago|||
Observability has changed in most other ways we have regressed.
XorNot 14 hours ago||||
That's true. And while I disagree with the parent comment, ICBM interception remains enormously problematic and likely will remain so until directed energy weapons get really cheap.

Fundamentally the rocket equation and orbital dynamics really fight you on this.

It's a lot less "can't be done" versus "would be financially untenable to build and maintain even when the objective is nuclear defense".

skywhopper 15 hours ago|||
Have they, really?

* Small rockets can now land themselves.

Anything else?

sumtechguy 15 hours ago||
Computer guidance? Better materials? Better telemetry?
pwndByDeath 13 hours ago||
Still short amount of time to make a decision based on very messy data
OrangePilled 13 hours ago||
If you're looking for a job and are still squeamish about working in the defense industry...I'm sorry to hear about that.

Because, boy, do I think you'll be missing out.

sgtsteaks 14 hours ago||
What are you gonna do when Iran destroys the missile defense system itself, oops already happened
jmyeet 14 hours ago||
Pardon the pun but this is an arms race and the defenders are going to lose. There are broadly five classes of missiles (one isn't a missile per se):

1. Ballistic. These are traditional rockets, basically. While rockets are designed to reach orbit or leave the Earth, a ballistic missile basically goes straight up and comes down. The higher it goes, the further away it can get because of the ballistic trajectory and the rotation of the Earth.

Ballistic missiles are most vulnerable in the boost phase ie when they're just launched. Since you have little to no warning of that, that's not really helpful.

But one weakness of ballistic missiles is you pretty much know the target within a fairly narrow range as soon as they launch. That's the point of early-warning radar: to determine if a launch is a threat so defenses can be prepared.

Attackers can confuse or defeat defenses in multiple ways such as making small course corrections on approach, splitting into multiple warheads, using decoys for some of these warheads, deploying anti-radar or anti-heat seeking defenses at key points and breaking into many small munitions, sometimes called cluster munitions on the news but traditionally that's not what a cluster bomb is or was. In more sophisticated launch vehicles, the multiple warheads can be independently targeted. These are called MIRVs (multiple independently targetable reentry vehicles).

Economicallky, depending on range and capability, a ballistic missile might cost anywhere from $100k+ to $10M+.

2. Rockets. Militarily this is different to a rocket in a civilian context. It's not much different to a hobby rocket, actually. Often these are "dumb" but some have sensors and guidance capability or might be heat-seeking.

These tend to be incredibly cheap to produce and not terribly accurate but that's not really the point. The point is they're cheap and easy to produce and the interceptors are much more expensive.

3. Cruise missiles. Rather than a ballistic trajectory, these have more sophisticated guidance and travel much closer to the ground, usually to avoid radar. The Tomahawk missile is a prime example of this. These tend to be relatively expensive and much slower than ballistic missiles.

4. Hypersonic missiles. This is a relatively new invention that's kind of like a cruise-ballistic hybrid. It flies in the atmosphere for part or all of the time and, unlike cruise missiles, will fly faster than the speed of sound, usually significantly so (eg Mach 4-10). Such high speed makes interception near-impossible currently.

The big advantage of a hypersonic missile is that it has the speed of a ballistic missiles without the predictability of the target area. Plus it can be retargeted in-flight.

5. Drones (honorable mention). Not technically a missile but they fit in this space regardless. This is basically a scaled up commercial drone with an explosive payload. These are significantly slower than cruise missiles or rockets but can be live-targeted, re-targeted and have a variety of types ranging from dropping hand grenades from a height (eg as has happened in Ukraine) to suicide-type drones that explode on impact.

Drones are typically so slow that you could shoot them down with an shotgun in some cases. But they're incredibly cheap and easy to produce.

sgtsteaks 14 hours ago||
You cannot shoot a drone down with a shotgun. The range on a shotgun is nothing.

Do you know that it actually fires bb's out in a cone shape? If you aim a shotgun up in the air, you are not taking out any drones.

Look up the video of the drone hitting the hotel in Bahrain to get an idea of the speed and altitude.

ultimafan 7 hours ago||
I think you and the previous comment are talking about different types of drones- the smaller commercial quadcopters used in the Russia-Ukraine conflict can be shot down with shotguns fairly effectively.

Both sides have been seen with one member of a squad carrying around an issued shotgun in an anti-drone role- the fact that it shoots pellets in a cone is precisely why it's so effective. Skeet shooting is a great example of how relatively small fast moving targets can be hit consistently at range with a shotgun and they are usually using much smaller/lighter pellets with poorer velocity/range, I would assume the loads used in an anti-drone role are bigger.

chasd00 6 hours ago|||
Maybe the winning strategy is always attack and never be the one defending. That’s unfortunate.
Noumenon72 14 hours ago||
[flagged]
inaros 13 hours ago||
I spent some time reconstructing the current US missile defense interceptor numbers. This was done from open source DoD data, CSIS P-21 procurement exhibits, and CRS reports, that are are in depth, non partisan, objective policy analyses written by experts at the Congressional Research Service (CRS) specifically for U.S. Congress members. Also used Lockheed/RTX financial disclosures.

The numbers are pretty bad… Way worse than the headlines suggest. But anyway nowadays, investigative journalism has been decimated....For example experts like Kelly Grieco at Stimson estimated that at 12 day war consumption rates, the entire US interceptor stockpile depletes in 4 to 5 weeks. We are now in week 4...

As of December 2025, CSIS documented delivery of 534 THAAD interceptors and 414 SM-3. The 12 day War burned through around 150 THAADs (that is 28% of inventory) and about 80 SM-3s. The current war has been drawing down from that already depleted starting point for 25 days straight...

Gulf states reportedly expended around 600 to 800 PAC-3 MSE interceptors in the first 72 hours of Epic Fury alone, and that is more than the entire global 2025 production ( about 620 units).

Meanwhile THAAD production is 96 per year….with a recent Lockheed commitment to quadruple to 400 per year, but that will only deliver these additional missiles after 2027 or later. For example the sole ammonium perchlorate supplier for every US solid rocket motor runs one plant in Utah, and the sole HMX/RDX source is a WWII facility in Tennessee…

The US has procured roughly 270 PAC-3 MSE ( the Patriots ) per year since 2015, but has diverted around 600 to Ukraine over four years. The exact remaining US stockpile is not known with the same precision as THAAD/SM-3, so they could not have more than 3000 before Epic Fury...

But it is known as I said above, Gulf allies burned through 600 to 800 or more PAC-3 MSE in the first 72 hours of Epic Fury alone from their own stocks. Since they have zero domestic production capacity, and will be competing with the US for the same Lockheed production line that only makes about 600 per year, Iran really has them by the balls.

By the way, the cost so far in munitions is 20 billion ( check references…).

Then on Intelligence...

Iran has 13 satellites of their own, and it is known to be receiving intelligence from the Russians. This data allows them to know exactly how many Patriots or THAAD were fired so far. They are also probably customers of MizarVision, a Chinese AI startup, that has been cataloguing every significant American military asset in the Middle East. Every base, every carrier strike group, every F-22 deployment, every THAAD battery, every Patriot missile position, tracked, labeled, analyzed, and posted publicly.

So...

Unless the US escalates to a Ground Invasion (most likely scenario…), or negotiates a deal with Iran, if Iran can keep their industrial production of missiles, or maybe move them far up and inside tunnels in its Northern Mountains, and...if the USA does not escalate to a ground invasion due to the political risks, they can actually win this war both from the political and strategic aspects, as incredible as that might seem.

Who is truly screwed are the Gulf countries, as their stocks of US missiles get progressively depleted… And they wont get a refill soon.

Russia strategic interests are in helping Iran, since it weakens the US and strengthens their hand in Ukraine.

What might make it worst for the Iranians is the Chinese view of this. I speculate they will prefer to help the US and its economy, by forcing the US to do a great commercial interesting deal for them, then using their strong leverage on Iran to come to an agreement.

Strategically, over the next four to six months: Russian wins, Iran wins (despite all the destruction), China wins, Israel loses, the US loses. Trump truly is the biggest loser...

"Are We Running Out of Missile Defense Interceptors?" - https://www.csis.org/events/are-we-running-out-missile-defen...

"‘Race of attrition’: US military’s finite interceptor stockpile is being tested" - https://www.defensenews.com/news/your-military/2026/03/06/ra...

"The Depleting Missile Defense Interceptor Inventory" - https://www.csis.org/analysis/depleting-missile-defense-inte...

"Over 5,000 Munitions Shot in the First 96 Hours" - https://www.fpri.org/article/2026/03/over-5000-munitions-sho...

"A Chinese AI Startup With 200 Employees Is Mapping Every US Military Asset in the Middle East — In Real Time" - https://breached.company/mizarvision-chinese-ai-satellite-us...

https://www.mizarvision.com/

aftbit 7 hours ago||
How does this guarantee a political and strategic win for Iran?

Iran was already teetering on the edge of being a failed state: socially, economically, environmentally, and agriculturally. Iran is expending expensive ballistic missiles to force those THAAD and Arrow shoot-downs. Yes, they're winning the shot exchange ratio, but their economy is orders of magnitude smaller than the US. Besides, unlike the Gulf states, the US and Israel are not just sitting around playing defense. They are systematically destroying substantial fractions of the Iranian war machine and have both threatened and attacked domestic and international energy production, the lifeblood of the Iranian economy.

The only true winner of this war, however it shakes out in the end, is Russia. All of the Middle Eastern powers aligned with the US are going to be desperate to rebuild their interceptor stockpiles and will surely get priority over Ukraine, likely for a very long time as the production rates are very low as you've pointed out. Plus, Russian gas and oil are worth a lot more than they were prior to this war, and are being allowed to trade more openly as well.

maxglute 53 minutes ago||
Iran already bled enough high end regional interceptors, the strategic balance is if they can build enough moped shaheeds that can be assembled in garages to overwhelm whatever comes in theatre. And we know upper limit of US+co interceptor production for next 3-4 years. Economic size =/= productive capability. Ultimately Iran with survivable regional strike complex can existentially threaten gulf state adversaries who are all dependent on desalination while Iran, as shit as their water crisis is, is not. UAE, Qatar Saudi and Israel are like 70-90% desalination. They can threaten Iran economic lifeblood, Iran can literally end their lifeblood. Iran simply has massively more lethal/credible escalation dominance vs GCC. Iran already being failed state ironically allows them to escalate harder - they have much less economy to lose, vs GCC losing economy and biology.

Ultimately if Iran locks down Hormuz long term they can transit tax their way to prosperity, and if they can convince PRC to be enforcer of petro-yuan (big if), they'll basically get unlimited hardware to do so. Not that burning bridges with GCC is PRC first choice, but if Iran can lock down Hormuz, they have leverage to compel PRC to accept arrangement because it's worse than no Hormuz energy. The spoiler obviously is US who would rather toast GCC oil than lose petro dollar. Or Israel being nuke happy.

ifwinterco 7 hours ago|||
The democratisation (if that's the right word) of high quality satellite imagery is really something.

Of course top military powers will have even better images, but there are random Twitter users and YouTubers commissioning imagery of Russian tank bases and as long as there's no clouds on the day in question the quality is pretty good.

Things that move (ships) are still very hard to find and that's where the top powers still have a real advantage, but military bases, storage depots etc. are all impossible to hide in 2026. Even your local ragtag jihadist group can get coordinates for all your bases with a small amount of money and effort if they need them.

Making missiles that are accurate enough to take advantage of all the targeting data is still quite hard though

granoIacowboy 6 hours ago|||
Not necessarily disagreeing with your conclusions, but you aren’t factoring in other European or Korean interceptors the GC have been using. Israeli production. Fighters and other systems can be used for drone defense - lasers, AA guns, Manpads, EW, microwaves - Ukraine’s drone on drone defense and other solutions will be implemented asap.

The math is still brutal

keybored 11 hours ago||
[flagged]
inaros 11 hours ago||
A wonderfully ambiguous and diplomatic statement...
keybored 6 hours ago||
[flagged]
EGreg 13 hours ago||
What happened to Iron Beam / lasers and those vaunted "space lasers" dubbed "star wars"?
hedora 13 hours ago||
Apparently, Iron Beam still exists (or at least was demoed in 2024).

Originally, the lasers were going to be mobile, but now they have to be stationary, so it will work like the game Missile Command, except you have unlimited ammo, but no concurrent shots, and the missiles can't be rotating (like a rifled bullet would).

That's much more feasible-sounding that I'd assumed (coming from low expectations).

https://en.wikipedia.org/wiki/Iron_Beam

EGreg 12 hours ago||
I seriously can't wait for this technology.

It can be purely defensive, and shoot down all aerial attacks - drones, etc. over your country's airspace.

So... no wild weasel, no successful air raids, etc. We're back to ground invasions, and frankly, a country can defend against those a lot easier.

And it also means countries not lobbing missiles at each other, and at oil fields and igniting them, or destroying shipping etc.

jandrewrogers 13 hours ago||
The US has deployed operational anti-drone lasers for a few years now, though not widely. They are still quite new but they have several kills. This is probably operational field testing for fine-tuning the design prior to producing them at scale though.
koakuma-chan 14 hours ago||
Why does a ground based interceptor cost $75M? High idiot index?
hedora 13 hours ago||
$1M, but we can only make 600 / year, globally.
koakuma-chan 13 hours ago||
From the article,

"Each GBI costs approximately $75 million, and as of 2024, 44 are deployed across Alaska and California [3]."

hedora 13 hours ago||
I'm quoting the missile cost. I think they're quoting the launchers + a few missiles.

(Also, lower bounding the cost improves the argument that they're too expensive to be practical.)

O3marchnative 12 hours ago||
Author here. The $75M is specifically for Ground Based Interceptors (GBIs). This is the U.S.'s ICBM mid-course interceptor. There are other interceptor types in the current U.S. arsenal:

Patriot PAC-3 (~$4M): Nations burnt through 600-800 in the first few days of Operation Epic Fury. There are reports that they're being used for drone defense.

SM-3 (~$10-30M): Ship-launched

SM-6 (~$4-5M): Ship-launched

THAAD (~$12-15M): Terminal phase, high altitude

GBI (~$75M): intended for interception of ICBMs (reported as the hardest type of missile to intercept)

Each type of interceptor is optimal for certain type of threats, which is yet another constraint on the optimization problem.

mrguyorama 11 hours ago||
In what world would a specialized, niche, high precision, high readiness rocket meant to loft a very advanced interceptor munition into an extremely high velocity interception ever be cheap?

These things are closing at like mach 20. Physics says that's hard to do. That means it's expensive.

For reference, $75 million is in the realm of a Falcon 9 launch, which is a very cost optimized platform that doesn't have to place a very very precision instrument payload in a very very specific point in space to prepare it for a high energy, extremely difficult interception.

koakuma-chan 11 hours ago||
Does it being very high precision or whatever mean that it must cost $75M per unit? Is it made of gold?
echoangle 11 hours ago|||
The cost primarily comes from the work needed to be done to make sure it works, not the raw materials. But there probably are some pretty expensive materials in it too.
mrguyorama 9 hours ago|||
https://en.wikipedia.org/wiki/Advanced_Inertial_Reference_Sp...

This is what we had to build in the 60s to allow a missile to know where it physically existed precisely enough to allow it to 50% of the time hit within a circle of ~50 meters.

When you get to certain points in physics, certain energy regimes, you no longer are building machines or tools or something mass market. You are building artisan scientific instruments, and then sometimes gluing explosives to them.

Even modern laser ring gyros do not even share a dinner table with the precision and accuracy of the above singular component of the Peacekeeper ICBMs, and that was a long time ago.

"Tech" and some of the developments of the past few decades have really confused people. The miniaturization of the transistor, and building billions of transistors on a small slice of silicon is an aberration, an anomaly. Most things don't get "Better and better and cheaper and cheaper" like that because shit just doesn't scale infinitely and in general materials science isn't that precise.

For these ground based midcourse interceptors, they have to precisely loft the interceptor package at an incoming projectile. They have to shoot a bullet with a bullet, except the target bullet might even be moving around a bit, and your ability to precisely quantify the exact parameters of it's position and velocity is already limited. Is your position and velocity measurement an inch off? Two inches? Is that too much?

How well have you quantified the thrust of your rocket engine? THIS specific rocket engine, not a random one from the batch. Will you be off in a direction by a few meters per second? That might be enough to scuttle your interception.

IIRC this is the interception payload, a kinetic kill vehicle:

https://www.youtube.com/watch?v=KBMU6l6GsdM

Then, are any of those nozzles slightly less smooth than they should be? That's a miss. Did propellant slosh in an unexpected way? That's a miss, Chicago is now a smoldering crater. Incoming round bounce your rader signal in just a slightly different way than you had the data to know about? Miss, San Fransisco now has significantly cheaper real estate. Chaotic properties of hot expanding gas slightly different than your simulation in the unluckiest way? Miss.

You have to exhaustively inspect, reinspect, quality control, test, simulate, retest, catalogue, document, every single component. You have to be able to predict, almost perfectly, how every single component will act and perform in a situation you will never get a test for.

High energy physics is always going to be hard, never cheap, because high concentrations of energy are literally what the universe itself is trying to reduce. The rules of reality itself are against you.

A creator on youtube named Alexander the Ok has done wonderful videos on a lot of the technology that goes into these systems, especially older, less classified systems.

metaphor 1 hour ago||
> This is what we had to build in the 60s...

>> drift less than 1.5×10−5 °/h

Wow...just wow. Not a GNC engineer, but that drift spec strikes me as exceptionally good today, let alone the 60s.

EDIT:

> Even modern laser ring gyros do not even share a dinner table with the precision and accuracy of the above singular component of the Peacekeeper ICBMs, and that was a long time ago.

No kidding; full transparency, that was my basis of comparison.

quotemstr 15 hours ago||
The sole mention of directed energy:

> Directed energy has been proposed as a cost-effective alternative, but introduces its own scheduling constraints — dwell time, platform coverage, atmospheric degradation — with similar scaling issues

The author is doing the thing where a writer tries to bamboozle the reader into a conclusion without having to prove it by overwhelming the reader with nouns. Life is too short for shitty gosh gallops.

myrmidon 14 hours ago||
You are basically complaining that the article is not about a your preferred, different topic.

Directed energy defense does not really compete with a system like GMD at all, because the range is extremely limited by comparison.

The US might be able to justify throwing a few billion at a few dozens of ICBM interceptors stationed in a handful of sites, but protecting every potential target (city, military base) with some kind of laser array is obviously unrealistic.

tonnydourado 14 hours ago||
Gotta say, did not know direct energy weapons were actually leaving science fiction and entering the real world yet, but it seems they're. It's obviously not star trek level, but it's way more advanced than I expected
hedora 13 hours ago||
They are, but only have a range of 1.2 miles in earth's atmosphere. Since they're on the ground, and presumably near the target (not the launcher), that means they're aimed at the warhead just before it hits the ground.

I looked up the numbers, and, interestingly, ICBMs have to slow down before they hit their target. In the midrange flight, they travel at 15,000 mph, but at re-entry the warheads are only traveling at 1900 mph, or 0.58 miles per second.

So, in the best case (the warhead is headed to the laser), the laser only gets 2.5 seconds of dwell time to intercept it. This rapidly decreases as the distance from the laser to the target increases (to 0 seconds of dwell time at 1.2 miles). Also, if the ICBM fires multiple warheads, or chaff, then you'd need to scale up the number of lasers or scale down the dwell time linearly, assuming they're all conveniently aimed within a small fraction of a mile of the laser (again, I'm assuming best-case).

Current direct energy weapons have only been demoed against UAVs, probably for this reason.

edit: my math is completely wrong: Modern nukes are optimally detonated at about 5000 ft above ground level. So, you get about 0.33 seconds of dwell time, assuming the attacker doesn't just set the warhead to detonate at a non-optimal (but still devastating) 1.2 mile altitude.

https://remm.hhs.gov/zones_nucleardetonation.htm

OrangePilled 13 hours ago||
Bearing in mind the three constraints quoted, which of these do you think a country's deployed directed-energy weapons (e.g., US, Israel, Russia) would be useful against:

https://missilethreat.csis.org/country/iran/

hedora 13 hours ago||
You don't really have to guess. None of those countries are using directed energy weapons, and they're all repeatedly getting hit by Iranian technology (so they have an incentive to test whatever they have).
OrangePilled 12 hours ago||
> None of those countries are using directed energy weapons

The USS Preble is equipped with HELIOS and is in Iran. [0] The US has also used "dazzlers" there too (as mentioned in the linked X thread). [1]

Israel's Iron Beam was used against Hezbollah's drones (Iranian tech), with apparently limited return for it, this could explain why it won't be seeing action in Iran. [3][4]

The only alleged case of Russia using DEWs was in August 2025. [5] Admittedly, it was a reach for me to even name them.

As cost-effective (and cool-sounding) as DEWs are meant to be, there's a reason the US and Gulf states are beckoning Ukraine for help. At the same time, the Pentagon want's to ramp up development with 3 years and the US military at large seems to be bullish on lasers...[6]

[0]: https://xcancel.com/sebastienroblin/status/20361510681621877...

[1]: https://www.armyrecognition.com/news/navy-news/2026/u-s-navy...

[3]: https://www.jpost.com/defense-and-tech/article-889677

[4]: https://www.jpost.com/defense-and-tech/article-889701

[5]: https://t.me/milinfolive/154597?single/

[6]: https://www.defensenews.com/industry/techwatch/2026/03/18/th...

MoonWalk 6 hours ago|
Whatever that means.
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