trompete

Definition given by Wikipedia:

A modulator-demodulator, commonly referred to as a modem, is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by modulating one or more carrier wave signals to encode digital information, while the receiver demodulates the signal to recreate the original digital information.

So fiber optics are not analog, but then again, neither are modern phone lines that use VoIP. No analog (as in analogous to sound waves) signal goes over them, both ends are permanently connected to modems. Yet it's still called a modem.

I think that turning a laser on and off can technically be described as modulating a carrier wave, so that part of the definition fits.

The ONT is fulfilling the same function as a modem, except the medium is a fiber optic cable instead of a copper one, so that makes me want to call it a modem by analogy. An electric burner doesn't burn anything either.

Thoughts?

Wim Wenders: "We have to stay out of politics"

https://www.jungewelt.de/artikel/517070.ukraine-krieg-der-algorithmus-des-krieges.html

DeepL machine translation:

Western analysts measure the war in Ukraine in meters per day. According to new calculations by the Center for Strategic and International Studies, Russian forces have been advancing at an average rate of 15 to 70 meters per day since the beginning of 2024.¹ This is slower than the Battle of the Somme in 1916, according to the analysis. The British Telegraph concurs: “Russia's forces are advancing more slowly than any other army in the last century.” (January 30, 2026) The Washington think tank concludes that Russia is paying an extraordinary price for minimal territorial gains and is therefore becoming a second- or third-rate power. These results fall far short of Moscow's goal of conquering Ukraine militarily.

However, this finding is based on a categorical error. Since spring 2023, there has been no documented Russian attempt anywhere on the front to achieve a classic breakthrough into the depths of enemy territory. Neither massed tank movements nor an operational phase of exploiting successes have been observed. The system is apparently not geared toward offense in the Western sense, but rather toward controlling the balance of power and creating areas of attrition.

What Western observers interpret as a lack of offensive action may in fact be a different understanding of efficiency: there is no “winter offensive,” but rather a continuous regulation of one's own impact. Russia does not view front lines as targets, but rather as measures of a process of attrition. The war is being waged as a continuous, cybernetic control loop in which loss and impact curves are more important than territorial gains.

If this interpretation is correct, the war is not designed to achieve victory through conquest, but rather through systemic resilience: it is not about seizing territory, but about which system can hold out longer. Russia is keeping its own pressure below the tipping point at which its own system would become unstable, while attempting to systematically overload the enemy's system—until its logistics, recruitment, economy, or command structure collapse. The war will not end with a breakthrough, but with the failure of one side's system.

The fog is lifting

This form of warfare can be described as cybernetic warfare: a self-regulating system that learns and adapts through feedback. The conceptual basis for this type of warfare can be traced back to Soviet military theorist Aleksandr Svechin. For Svetchin, strategy was not a plan, but a constant response to changes in the overall situation. Whereas Clausewitz focused on the decisive battle, Svetchin developed the concept of an adaptation system. War as a continuous process of strategic adaptation. In this sense, Russian warfare today is more Svetchinian than Clausewitzian – Svetchin plus digitalization.

Norbert Wiener, the founder of cybernetics, provides the theoretical bridge to this concept. Wiener defined cybernetics as the science of control and regulation through feedback: a system observes its environment, evaluates data, and adapts its behavior. Cybernetic warfare means that war is conducted on the basis of control loops in order to cause maximum damage to the enemy's systems with minimum effort on one's own part.

The difference to previous attempts to rationalize war is fundamental. While former US Secretary of Defense Robert McNamara attempted to mathematize military success retrospectively during the Vietnam War—for example, through body count statistics—Russia has algorithmized warfare operationally. From statistical body counts to real-time data feedback. This form of warfare can be described as a digitized, industrial process of destruction: Russia wages war like a factory—standardized, data-driven, serial. The primary goal is not territory, but the predictable exhaustion of enemy systems. This form of warfare is abstract and procedural, which is why it is often incomprehensible to Western observers who measure success in kilometers. Russian warfare operates on a different level of abstraction: the West focuses on stock variables – such as the concretion of territorial control – while Russia focuses on flow variables, i.e., the ratio of effort to effect over time.

The technical backbone is ESU-TZ, a Russian network-based command and control system that brings together units, reconnaissance assets, and firepower in a shared information field—comparable to Western C2 systems, but optimized for feedback and real-time adaptation. Sensors feed a unified information field, algorithms and models support the prioritization of targets, and firepower is deployed with significantly reduced latency. It forms the computer-based heart of cybernetic warfare.

One of the most accurate self-descriptions of this new form of warfare comes from Russia itself. Yuri Baluyevsky, former Chief of the General Staff of the Russian Armed Forces (2004–2008), and Ruslan Pukhov, Director of the Center for Analysis of Strategies and Technologies, published an essay in December 2025 entitled “Digital War – New Reality.” In it, they describe what is happening in Ukraine.

The most important change is the complete transparency of the battlefield. The “fog of war” has lifted. Ubiquitous drones, satellite communications, and networked sensors have created a unified information environment that functionally merges tactical, operational, and strategic levels. The boundaries between these levels are becoming blurred. The second fundamental change: the tactical battlefield and the depths of space up to many dozens of kilometers are transforming into “zones of total destruction.” In these zones, every movement, every concentration of forces is immediately visible and vulnerable to attack. The result: extreme dispersion and very low density of combat units.

Balujewski cites the introduction of globally available satellite networks such as Starlink as the catalyst for this development. For the first time, there is a continuous, scalable information infrastructure that enables feedback down to the lowest tactical level. The cybernetic logic of this warfare is not a theoretical construct, but can be observed empirically. Three elements can be cited as examples here: the mass use of Geran drones, the industrialized deployment of glide bombs, and the organizational structure of the Russian drone unit Rubicon.

New type of drone

The organizational embodiment of cyber warfare is the “Rubicon” drone unit. It was founded in August 2024 on the instructions of Defense Minister Andrei Belousov and, unlike the units responsible for conventional drones, reports directly to him. “Rubicon” combines combat operations, development, production, and testing in an integrated model with feedback loops. The unit's headquarters has its own development department, training center, analytics department, and independent combat units. A significant part of the technological developments originate from the so-called people's defense industry – individuals or small companies that develop technology for the Russian army on their own initiative. Rubicon provides these developers with direct feedback on current needs and problems. Proven solutions are scaled up and transferred to mass production.

The most striking example is fiber optic drones, which are immune to electronic jamming. These systems were first tested in Kursk and deployed across the front within a few weeks. The key difference to traditional military structures is that Rubicon experiments like a start-up—rapid testing, direct feedback loops from the front to development—but can immediately scale successful solutions across the entire military with state authority. While Ukraine is working innovatively from the bottom up but appears to have difficulty systematizing innovations, Russia can quickly expand proven solutions across the entire military and defense industry. Rubicon bridges the gap between the two approaches.

Old technology further developed

However, this organizational innovation only becomes effective through concrete weapon systems that are embedded in cybernetic logic. The mass deployment of Russian glide bombs, for example, is a functional refinement of an old weapon. At their core, these are still classic Soviet-style aerial bombs equipped with relatively simple glide and control systems. Their industrial manufacture is straightforward, the production lines have been in place for decades, and the unit costs are significantly lower than those of modern cruise missiles. The decisive factor, however, is that the precision of these weapons has increased significantly in recent months. The impact patterns show that the glide bombs are being used in a targeted manner along defined defensive structures. Impacts follow trench lines, shelters, known assembly points, and rear connection axes. Entire sections of the front are being systematically worked through – not indiscriminately, but in a structured manner.

This precision does not come solely from the technology of the bomb, but from its integration into an overall sensory system. Drone reconnaissance, battlefield surveillance, and feedback from previous strikes enable continuous adjustment of the target parameters.

The functional role of glide bombs is clearly defined. They are used to target and destroy deeply staggered, fortified defensive positions. In many places, Ukrainian defenses have been built up over many years – with trench systems, concrete shelters, covered roads, and rear bases. It is precisely these structures that are systematically destroyed or rendered inoperable by precise series of glide bombs.

The result is a devaluation of the position, not necessarily its immediate abandonment. Cover disappears, shelters become unusable, and logistics routes collapse. The attacking infantry is thus confronted with a qualitatively changed combat zone: advances are made into a defense that has already been gutted, with significantly reduced losses on their own side.

In the logic of cybernetic warfare, the glide bomb is therefore not a crude instrument, but a precise control element. It combines low costs, high frequency of use, and increasing accuracy with rapid feedback from combat. Its effect is not achieved once, but is optimized step by step. The glide bomb exemplifies the character of this war: old in its basic form, highly precise in its application, embedded in a continuous, data-driven process of attrition. It is not a sign of technological backwardness, but rather an expression of warfare that prioritizes efficiency over technical perfection.

Collapse as the goal

While the glide bomb targets fortified structures, a second system targets the infrastructure behind them. The Geran drone—the Russian variant of the Iranian Shahed-136—embodies the principle of industrial warfare. According to Ukrainian sources, up to 120,000 of these systems have been deployed since 2022. Over the course of 2025, the Geran underwent several stages of technological evolution. Since the summer, Russia has been equipping the drones with Chinese mesh network modems and front cameras as standard. This technology enables attacks on moving targets – such as locomotives and trains – for the first time. What was originally designed as a strategic weapon for static targets is evolving into a versatile weapons platform.

Even more revealing is its tactical use. In June 2025, Russia fundamentally changed its attack strategy. Instead of irregular waves, Moscow established a continuous background noise of 50 to 100 Geran drone flights per day, supplemented by weekly mass waves of over 500, sometimes over 800 combined attacks from drones, missiles, and cruise missiles. This combination of constant pressure and periodic saturation attacks is not an improvised tactic, but controlled system management.

The drastic effect of this serial destruction was particularly evident in early February 2026. After months of systematic attacks on its energy infrastructure, Ukraine experienced a nationwide power outage that even paralyzed parts of neighboring Moldova. Even the Kiev metro came to a standstill. The situation was described as “apocalyptic.”

The collapse is no coincidence, but the predictable result of industrial warfare. Ukraine now has only 11 gigawatts of electricity capacity, but needs 16 to 18 gigawatts in winter. Between 70 and 90 percent of the remaining energy comes from nuclear power plants, some of which had to be shut down during the blackout.

The “Geran” is therefore not a space weapon. It is not used to conquer territory, but to generate a series of scalable effects against enemy systems until they collapse. This is cybernetic warfare in its purest form: constant pressure, controlled intensity, measurable attrition, systemic failure. However, the “Geran” operates primarily in strategic space – against industrial facilities, power plants and power grids, urban infrastructure. For a long time, there was a gap between the immediate battlefield and this strategic depth. Moscow now wants to close this gap.

“Zones of total destruction”

The introduction of a new category of medium-range drones is fundamentally changing the geometry of the battlefield. The Russian “Shahed-107” with a range of 300 kilometers fills the gap between tactical FPV drones (FPV stands for First Person View, drones with cameras that are controlled from a first-person perspective, jW) and strategic long-range weapons. It is extremely simple in design, costs probably well under €10,000, and targets supply depots, command posts, and moving targets at a depth of 100 to 300 kilometers behind the front lines.

This allows Baluyevsky's “zones of total destruction” to be shifted far into the former hinterland. To understand what this means, one must distinguish between two forms of military force: shock waves and pressure waves. A shock wave is a short-term, concentrated impulse of force. High use of firepower in a short time, focus on local breakthrough, significantly increased self-exposure. The goals are rapid change of the situation, gain of space, and exploitation. This is classic maneuver warfare. A pressure wave, on the other hand, acts over a longer period of time and a large area. Instead of a concentrated explosion, a permanent, controllable pressure is created. The attacks are spread over a wide area, each individual strike remains measured, is repeated and modulated. Large formations do not expose themselves. The goal is not breakthrough, but attrition: the enemy's resources are depleted step by step, its responsiveness tested and exhausted.

The “total destruction zones” are not caused by shock waves, but by pressure waves.

The battlefield can now be divided into concentric rings of constant pressure. The innermost ring, zero to 30 kilometers from the front line, has become an absolute death zone. Vehicle movement is virtually impossible in this area. The middle ring, 30 to 300 kilometers deep, is dominated by systems such as “Shahed-107,” “Molnija,” and “Italmas.” This zone was previously considered a safe rear area for command posts, logistics centers, and troop gatherings. The outer ring is covered by strategic weapons such as the “Geran-2,” which can reach targets well over 1,000 kilometers away.

The crucial point is that these zones do not create additional space. They create systemic pressure. The classic principle that leadership can be protected by physical distance no longer works. The concept of rear space is dissolving. This means that the entire area up to 300 kilometers behind the front line becomes a continuous pressure zone—it is not conquered, but functionally controlled by permanent threat.

Strength through decoupling

This spatial penetration of the battlefield has consequences for conventional military concepts. The dissolution of classic combined arms warfare is one of the least understood consequences of cybernetic drone warfare. This is exemplified by a statement made by British military analyst Jack Watling of the Royal United Services Institute. Last year, Watling wrote in a study: “FPVs are particularly effective when combined with other types of weapons.”³

However, the Russian elite unit “Rubicon” shows how drones are actually most effective: not in combination, but independently. ‘Rubicon’ operates autonomously, conducts its own reconnaissance, and selects its own targets—without any tactical ties to a brigade, without maneuver targets, without connection to “combined arms.” The effect comes precisely from decoupling, not integration. Decentralization, mass instead of coordination, permanent threat 24 hours a day, seven days a week. “Rubicon” is an autonomous cluster of destruction.

Combined arms combat is based on prioritization, movement, surprise, timing, and mutual cover. Tanks protect the infantry, the infantry secures the tanks, the artillery prepares the way, and all elements work in sync. But these principles no longer work on the transparent battlefield, because every priority is immediately detected. Movement of any kind attracts drones, and the element of surprise no longer exists. Coordination means mass accumulation, and mass accumulation becomes a target for FPV cluster attacks. Tanks are the primary hunting target, and infantry can hardly move. Combined arms combat breaks down into its individual components because the prerequisite—limited visibility—no longer exists.

Watling's mistake is symptomatic of Western thinking: he tries to squeeze new technology into old concepts. But drones do not function as a supplement to combined arms combat. They replace it.

Are tanks obsolete?

In the West, the crisis facing tanks is also generally interpreted as a problem of inadequate protection. This is incorrect. The problem is structural in nature. Tanks were developed as protected platforms for “direct fire.” The tank must see the target in order to engage it. Drones, on the other hand, no longer need direct sight – they operate at a distance, controlled from dozens of kilometers away, against targets that the operator can only see via a video feed. This asymmetry is crucial: on the transparent battlefield, the tank is seen and attacked before it is even within firing range.

In August 2025, Ukrainian reconnaissance discovered only 23 Russian tanks within 70 kilometers of the front line, compared to 470 tanks on the southern axis in May 2023 alone. Tanks have not disappeared because they are vulnerable—they have largely disappeared because they are too expensive and too exposed for an industrial process of destruction. The same effect—wearing down enemy forces—can be achieved with smaller, more controllable means. Tanks are primarily tools of maneuver warfare. They are unsuitable for cybernetic warfare.

The obsolescence of tanks is only the most obvious symptom of a broader paradigm shift. Western military thinkers do not understand this change because it challenges their fundamental categories. Cybernetic warfare, molecular battlefields, autonomous destruction clusters, the dissolution of operational depth, and sensor-effector networks as primary weapons are concepts and terms that are not understood in the West.

The war in Ukraine is no longer a battlefield in the traditional sense. It is a rule-based process in which intensity, frequency, and impact are continuously adjusted. The decisive factor is not the maximum use of force, but its controllability. The fighting in Ukraine could be part of a longer-term learning and adaptation process for the Russian military. The real break with previous warfare therefore lies not only in individual branches of the armed forces or tactics, but in the transition from battle-focused warfare to process-focused warfare. Anyone who continues to measure the war in Ukraine in kilometers is missing its logic.

https://www.jungewelt.de/artikel/516792.kriegspropaganda-verst%C3%A4ndnis-f%C3%BCr-faschisten.html

Machine translation (DeepL):

Sympathy for fascists

With the support of the Rosa Luxemburg Foundation [me: foundation of the party "Die Linke" ("The Left")], an activist wants to break down "prejudices" against Ukrainian Azov fascists.

Evelyn Deller wants to counteract the glaring lack of “left-wing solidarity with Ukraine.” Since 2025, the Ukrainian living in Germany has been touring left-wing gatherings with lectures to correct images of “military resistance” against the Russian invaders and to “sharpen them with a historical outline.” At the “anti-German” pub Bajszel in Berlin, she spoke about the “anti-imperialist character and continuity of Ukrainian anti-fascist self-defense,” among other things. That she is not referring to the Ukrainians who fought against Nazi Germany in the Red Army during World War II or who follow in their tradition is revealed by Deller's accusation against the Soviet Union as a colonialist state in which “Jewish and Ukrainian people were deliberately murdered – Holodomor.” But who is she talking about then?

Further insight may be provided by another lecture by Deller entitled “Why we on the left must support Ukraine” this coming Friday in Trier, which addresses the following concern: “The German left either speaks about this war without being informed or not at all. We want to counter this and break down prejudices (for example, about what the ominous Azov Battalion is all about),” the announcement states. The text does not reveal the extent to which the armed wing of Ukraine's most powerful Nazi movement, which expanded into a regiment in 2014 and into a brigade in the National Guard and the army in 2023, and whose founder Andriy Biletsky (nicknamed “White Leader”) is being touted as the successor to the commander-in-chief of the Ukrainian armed forces, Olexander Sirskij, is a victim of left-wing bias – the text does not reveal anything about this.

Deller is deputy chairwoman of the Jewish Student Association of North Rhine-Westphalia and is committed not only to fighting “anti-Semitic” solidarity with Palestine, such as “anti-Coca-Cola BDS campaigns,” as she reported in an interview with “Mena-Watch” published on December 21, 2025, and against “anti-Semitic” Jewish leftists such as Norman Finkelstein, but also against “anti-Semitic projections onto Ukraine.” Deller, who considers Ukraine a “country affected by genocide,” ends her speeches with the salute of the fascist Banderists, who participated in the Holocaust as Hitler's collaborators.

Deller presents Radical Aid Force (RAF) as a model for left-wing solidarity with Ukraine. The anarchist group organizes donations for humanitarian aid as well as for the purchase of military equipment, such as combat robots, for “anti-authoritarian fighters” – here and there also fascists, as shown by a photo published by the RAF of a member of the drone unit “Eyes of God” supplied by them, wearing the badge of the Banderist party and militia UNA-UNSO. A second pillar of RAF activities is agitation for “arming Ukraine to the teeth,” including deliveries of ‘Taurus’ cruise missiles, as well as hate propaganda against the Russian “Orcs.” A video on the RAF Instagram channel shows footage of Russian soldiers being torn apart by grenades, set to the beach party hit “Samba de Janeiro.”

Such misguided worldviews fit into the hothouses of “anti-German” [Antideutsche] sectarianism such as “Conne Island” in Leipzig, where one of Deller's next performances will take place. However, supporters can also be found in the right wing of the Left Party: RAF has already received funds from the solidarity fund of Saxony state parliament representative Juliane Nagel in 2024. The Rosa Luxemburg Foundation (RLS) Rhineland-Palatinate has agreed to cooperate as a partner for Deller's lecture in Trier, which is being organized by the “Rosa Salon,” which calls for a critical examination of “left-wing dogmas,” and the RLS Thuringia has agreed to cooperate for another event in Erfurt. “Parts of the German left are reproducing Russian propaganda and delegitimizing the self-defense of the Ukrainian population,” reads the RLS website. “The lecture places these distortions in their historical context and analyzes the foundations of Russian imperial ideology in order to raise awareness of disinformation.”

Scaling up a recipe for a massive gathering is a common holiday practice in my Italian American family. I tried showing Copilot a recipe for stuffed mushrooms from Sip and Feast. It acknowledged that to go from a serving size of six to 14 would require multiplying each ingredient by about 2.3 times, but it usually only did a couple calculations before expecting me to do the rest or trying to move on to another topic by asking me a question. When it noticed the site had options for scaling up the recipe, it mistook the “2x” and “3x” buttons for plus and minus ones that would let me dial in exactly 14 servings, and kept insisting that’s what those buttons are for. They aren’t. Then, as a last-ditch effort, I asked it to just calculate each ingredient and spell it out for me in a document. Copilot told me it would, and then did nothing.

I sometimes accidentally drag tabs rather than click them (touchpad sucks). I already have an extension that prevents them opening as separate windows. But recently new interesting things started happening: Sometimes they "group" together, I have no idea what the point of it is or how to undo that. Just now one of my tabs turned into a mini icon version???

Can't find the bloody thing.

It's just a line, black on white, segmented by round checkpoints. The line does a little angle at the checkpoints, but that's purely a visual thing. You can move left or right on it, that's all the possible inputs. You got HP and XP and levels. Totally automatic "random encounter" battles occur. There is no actual battle. When you run into a random encounter, the only thing that happens is that your XP gets higher, and your HP gets lower; there's not even an animation, just the XP and HP bars on screen change randomly.

The strategy of the game is to "grind" around the checkpoints, by moving left and right across them repeatedly, until you have leveled up enough to be able to make it to the next checkpoint.

It's some (J)RPG parody, making fun of the exponential XP grind mechanics of those games. I cannot remember what it's called and I'd like to show it to someone.

I probably spent somewhere between 100-200€ on EU4 back in the day over a couple of years. Still missing half the DLC. Still can't play any African nation without all my troops and advisors looking like Prussians. Still don't have access to some of the special mission trees and mechanics needed to do an interesting playthrough of many nations.

They apparently want another 212€ for me to get the full game, or pay a subscription of 8€/month.

Fuck them please pirate their games or don't play them at all.

I'm not high right now I swear I just had this thought going through my head for a while.

Imagine you had an Eve online (never played) style space game. There are 1000 servers, organized in a grid 10x10x10. Each server is simulating a region of space corresponding to their grid position, and connected via a network link only to the servers right next to it, so as to facilitate traveling between them.

The game is populated by a bunch of bots flying around shooting each other or whatever they're doing. If too many bots happen to be on the same server, it gets overwhelmed, everything on this one specific server slows down to slideshow levels.

I posit that, over time, the bots would tend to get stuck in this laggy region of space. If they fly around randomly, they'd encounter the laggy region of space eventually, and it would take them a lot longer to get out again.

Furthermore, the neighboring servers might also slow down, to a lesser degree, because they have to wait for the laggy server which is unable to respond quickly when handing over bots.

The observable result would be (a) clumping, like how matter clumps together in the universe due to gravity, and (b) time would seem to slow down in the clumped up area, like it does in the theory of relativity.

(a) At a sufficiently large scale, like trillions of servers and bots, this might look like a large scale attracting force. I can even imagine that two large bots swarms, flying past each other, might get stuck more towards their common center point, effectively creating a kind of orbital mechanic. Though maybe not, you'd have to simulate this to see if you could make this happen.

(b) The bots in the clumped up area, being bots simulated by the overwhelmed server, would not notice that time has slowed locally. But if you had two bots, one flies around the empty parts of space, while the other flies into the clump and then comes back out, it would seem like more time has passed for the bot that was in empty space the whole time.

I just bought an ice cream machine with a compressor for half price. I thought it would be easy (it isn't) but I am nerding out.

I will explain to you all, to my best understanding, some theory about frozen deserts.

First, about ice formation: Imagine some water-ice mixture. Liquid H₂O molecules will, with some probability pertaining to their low kinetic energy and being next an ice crystal, join the ice crystals, making the ice crystal grow. At the same time, water molecules on the surface of the ice crystal, will, with some probability related to their kinetic energy, break loose of the crystal structure and join the liquid water.

If more molecules go from liquid to ice, more ice will form. If more molecules go from ice to liquid, the ice melts. What effect dominates depends on the average kinetic energy of the water molecules aka the temperature. Above 0 °C, more ice melts than freezes onto crystals; below, more freezes than melts.

Now, if, instead of pure water, you dissolve sugar (or salt or ethanol or whatever) into the water, that will make it less likely for liquid water molecules to join the ice crystals, because the sugar is in the way of the water molecules wanting to join the ice. It makes the liquid-to-solid transition less common, less probable, because there are just less liquid water molecules next to the ice surface. Because the sugar doesn't join the ice crystals itself, the ice is is just pure water, and the opposite ice-to-liquid transition is not affected by the sugar.

So, in a sugar-in-water solution, for the same temperature, less H₂O molecules will join the ice, while the same amount will melt as in the pure water case. This effectively depresses the freezing point. You now will need a lower temperature than 0 °C to form ice in order to make up for this. You can approximately calculate this temperature quite easily because the drop in freezing point is proportional to the amount of sugar (or salt ...) molecules in the solution.

Interestingly, the mass of the sugar doesn't matter, only the number of molecules does: If you dissolve a certain amount of sucrose (a double sugar) molecules, it will affect the freezing point the same way as adding the same amount of glucose molecules, even though glucose is half the mass. The same goes for salt: One NaCl, because it splits up when dissolved in water, will depress the freezing point approximately like two sugar molecules.

The second important point: The concentration of sugar in the water increases as ice forms. The sugar stays in the liquid solution; the ice is pure water. So more ice means a higher sugar concentration in the liquid that remains, depressing the freezing point of the remaining liquid. This means that for any specific temperature, sugar-water will freeze only partially to a certain percentage. You can calculate (for example), if you have 500 g of sucrose dissolved in 1 l of water, and you freeze that to -18 °C, about 79% of the water will be in ice form.