“Divide each difficulty into as many parts as necessary to solve it”

Honesty above all. What I had in my hands last Sunday afternoon while reading on the balcony of my house was not the ‘Discourse on method’ of Rene Descartesbut ‘Jotadé’a (highly recommended) novel by Santiago Díaz. At a given moment in the story, however, one of its characters quotes one of the French philosopher’s maxims. He does not do so by sticking to literality or with the high epistemological purpose that his author wanted to give him in the 17th century, but there were Descartes’ words with all their burden of common sense: “Divide each difficulty into as many parts as necessary to solve it”. In the novel, the protagonist’s father, a troubled police officer, shares this reflection with his son at a time when everything seems to be going uphill for him. It is unlikely that when Descartes he wrote itfour centuries ago, did it thinking about life advice or bestsellers police, but the truth is that it fits into the novel just as well as it does into his philosophical treatise. Doubting everything Back in 1637, Descartes asked himself one of those impossible questions that seem condemned to dead ends: How can I be sure of the certainty of what I consider ‘true’? Are we humans doomed surrounded by doubts, without reliable handholds to lean on? How do I know that what I judge ‘real’ is not a deception of my senses, an erroneous idea that I have assumed to be true? To get out of such epistemological quagmire the philosopher made a curious movement. He used doubt against doubt itself. He assumed that he only had access to his own mind and confirmed the obvious: that he was in doubt. Then he pulled the thread to formulate what is probably his most famous phrase: “Cogito ergo sum”which is usually translated as “I think, therefore I am” or “I am because I think.” Another way of putting it is that if there is anything undoubtable, it is the act of doubting itself. In words from Descartes himself: “Considering that the same thoughts that we have when awake can come to us when we sleep, without there being any true ones in that state, I pretended that all the things that had entered my spirit were no truer than the illusions of my dreams.” “But I realized that, while I wanted to think in this way that everything is false, it was necessary that I, who thought it, be something. And observing that this truth ‘I think, therefore I am’ was so firm and so certain that the most extravagant assumptions of the skeptics were not capable of undermining it, I judged that I could admit it as the first principle of the philosophy I sought.” At that point, how to move forward? How to continue collecting valid knowledge? To get out of this new quagmire, Descartes, philosopher, mathematician and physicist, had a bigger idea: he developed the so-called ‘Cartesian method’. His system encourages us to carry skepticism as our flag and proposes a series of steps that are as valid for working in a laboratory as they are for facing personal problems such as those that concern Jotadé in Díaz’s novel. What steps are those? We quote back to Descartes. “The first consisted of not admitting anything as true without having known with evidence that it was so. That is to say, to avoid haste and to admit nothing more than what presented itself so clearly and distinctly to my mind that I had no reason to doubt it.“. “The second, to divide each of the difficulties to be examined into as many parts as possible and necessary for its best solution.“. “The third, in conducting my thoughts in order, starting with the simplest and easiest to know objects, to ascend little by little, gradually, to the knowledge of the most complex and even assuming an order among those that do not precede each other.” “And the last, to make in everything such complete enumerations and such extensive revisions, that one would be sure of not having omitted anything.“. Descartes basically encourages relying only on logical analysis or (even worse) relying on authority as an infallible source. What it invites us to do is to resort to observation and experimentation, to cultivate the methodical doubt and be thorough in pursuing knowledge. Its four rules are a valuable guide to develop critical thinking, but its application is not limited there. This was claimed a few years ago by the writer and professor Shaunta Grimes in an article published in Mediumin which he focuses precisely on the second step of Descartes’ method, the one that encourages us to divide problems. “The phrase alludes to his method of evaluating the logic of a statement, but its applications are much broader,” clarify Grimes. In his opinion, Descartes also offers a guide for facing problems that seem unsolvable. The tactic is very simple: think of a problem that worries you. Then think about how you can solve it. Complicated, right? But… What if you cut it apart? The challenge as a whole may seem insurmountable, but it is likely that it is actually a sum of smaller problems. If we can divide it into as many parts as possible, just like a big puzzlewe will surely find a first piece that will no longer seem so complicated. We exchange a seemingly unsolvable whole for manageable parts. Grimes illustrates it with an example. Imagine that a friend confesses to you that he is not feeling well. The logical thing would be to ask: “Why?” He may respond that he misses a family member, that he hasn’t played sports for a while, that he hasn’t slept much in recent weeks, or that he feels frustrated at work. Among these ‘pieces’ there are some that are relatively easy to deal with (if you sleep little you can go to bed earlier), others may not be so easy, but even in those cases they can break … Read more

Apple completely changes the architecture of its chips with a textbook “divide and conquer”

The week started with a flurry of news from Apple, something we already expected after Tim Cook’s words stating that it was going to be a “great week.” And in addition to the new iPhone 17e and iPad Airtoday it was the MacBook’s turn. In this article we wanted to focus on explaining what is special about the new M5 Pro and M5 Max processors, chips that land at the latest MacBook Pro. The company follows the same pattern as always. First comes the base chip, the M5, which we already saw in the 14-inch MacBook Prohe iPad Pro and Apple Vision Proalong with the new MacBook Air, and then, they take advantage of their most capable equipment to welcome the most powerful variants. But this year there is something different, and that is that the company uses a new manufacturing architecture internal that Apple had not used until now in its Mac chips. We will tell you all the details. Apple’s M4 Pro and M4 Max SoCs, in numbers m5 pro m5 max M5 m4 photolithography 3nm (3rd gen) 3nm (2nd generation) 3nm (2nd generation) 3nm architecture Fusion Fusion A single die A single die CPU cores Up to 18 18 Up to 10 Up to 10 Supercores 6 6 4 4 performance cores 12 12 6 6 GPU cores Up to 20 Up to 40 Up to 10 Up to 10 neural engine 16 16 16 16 maximum unified memory 64 128 32 32 bandwidth 307GB/s 614 GB/s 153GB/s 120GB/s ray tracing Yes (3rd gen.) Yes (3rd gen.) Yes (3rd gen.) Yeah neural accelerator on GPU Yes (per core) Yes (per core) Yes (per core) No connectivity Thunderbolt 5 Thunderbolt 5 Thunderbolt 4 Thunderbolt 4 / USB 4 codecs H.264, HEVC, ProRes, AV1 H.264, HEVC, ProRes, AV1 H.264, HEVC, ProRes, AV1 H.264, HEVC, ProRes, AV1 memory integrity enforcement Yeah Yeah No No The big news: the Fusion architecture Perhaps one of the most striking aspects of these new chips is the call ‘Fusion’ architecture. Apple has designed this SoC (system on a chip) by combining two other chips manufactured in TSMC’s third-generation 3-nanometer node. The signature promise that the chips communicate with each other through very high bandwidth and minimal latency. Why this approach? As chips grow in number of cores and memory needs, Putting everything on a single piece of silicon becomes increasingly complicated and expensive. The solution of dividing it into two interconnected chips allows its capabilities to be scaled without sacrificing efficiency. Each of these chips integrates CPU, GPU, neural engine, unified memory controller, Media Engine (which are the cores dedicated to processing multimedia codecs) and controllers. Thunderbolt 5. It is, in essence, the basis that makes it possible for the M5 Max to reach figures that we previously only saw in desktop chips. A new CPU from top to bottom Both the M5 Pro and M5 Max share the same CPU design: 18 cores organized into two very different types. On the one hand there are the so-called super cores: six high-performance cores which Apple also incorporated into the standard M5. The company assures which are “the world’s fastest CPU cores in single-thread performance”thanks to the fact that they handle greater bandwidth, and have a new cache hierarchy and better branch prediction. On the other hand, the chip incorporates 12 performance cores completely new, different from the efficiency cores we have seen in previous generations. They are optimized specifically for multi-threaded workloads that require sustained power without skyrocketing consumption. The combination of both groups of cores allows, according to Apple, a jump of up to 30% in performance for professional tasks regarding M4 Pro and M4 Maxand up to 2.5 times more multi-threaded performance compared to M1 Pro and M1 Max. It will be interesting to see this performance improvement in action when we test the devices in depth. What the M5 Pro promises Your GPU scales up to 20 cores next generation, each with an integrated neural accelerator. Memory bandwidth goes up to 307GB/sand the chip can manage up to 64 GB of unified memory. Apple promises up to 20% more graphics performance compared to the M4 Pro, and up to 35% improvement in applications that use ray tracing, thanks to its dedicated third-generation engine included in the chip. The shading engine is also updated, incorporating second-generation dynamic caching technology and hardware-accelerated mesh shading. What this technology basically does is simplify complex geometries into more manageable meshes for when it’s time to render. In terms of AI, Apple claims that the M5 Pro offers more than four times the GPU performance for artificial intelligence compared to the M4 Pro, and more than six times compared to the M1 Pro. M5 Max: the ceiling of Apple laptops The M5 Max shares the same 18-core CPU as the M5 Pro, but doubles the graphics and memory resources. Your GPU reaches 40 coresthe unified memory bandwidth reaches 614 GB/s (twice as much as the M5 Pro) and can hold up to 128 GB of unified memory. In graphic performance, Apple assures an improvement of up to 20% compared to the M4 Maxand up to 30% in ray tracing applications. For AI tasks, the chip promises more than four times the peak GPU performance compared to its direct predecessor and more than six times compared to the M1 Max. With these astronomical figures, Apple puts on the table a tremendously capable chip for all types of professionals, from 3D artists to app developers, AI, etc. And in the end, having such an amount of bandwidth on a laptop makes tasks with large volumes of data much easier to digest. We will see in practice how they perform. The rest of the package: Neural Engine, Thunderbolt 5 and security Beyond the CPU and GPU, both chips incorporate a 16-core Neural Engine renewed, which promises a higher bandwidth connection to memory, ideal for functions of Apple Intelligence and other local AI applications. In connectivity, the M5 Pro and … Read more

Nothing has done with CMF what OnePlus and Xiaomi did not know: divide before betraying each other

Carl Pei released Nothing in 2022 with the classic manual of technological ‘covering’: A distinctive design. An aggressive price. An anti-narrativeestablishment. But some time later he did something that no brand in his position had attempted: he cloned himself before he grew up. ‘CMF by Nothing‘is not just any sub-brand. It’s an insurance policy against the cycle that killed OnePlus’ mystique and tamed Xiaomi. Let’s go in parts. The pattern is known: A brand emerges promising “more for less” and building a tribe with early adopters that they feel part of something exclusive. The forums are burning, unboxings They go viral, people practically tattoo the logo. But commercial success eventually requires betraying that promise: you raise prices, chase better margins, and normalize. We have seen the same process in two brands dominating that space in two stages: OnePlus went from “flagship killer” in 2014 to sell mobiles indistinguishable from Oppo around 2018. Xiaomi went from being the Robin Hood of telephony in 2017 to having 1,200 euro models in 2021. In 2025 it’s already going for 1,500. It’s not that they are hypocrites, it’s that that position cultural requires smallness. As soon as you grow big enough to matter, you’re no longer credible as an alternative. Xiaomi tried it with POCO and Redmi, but without all the conviction. POCO was born in 2018 with the F1 as flagship killer perfect, direct heir to the original Xiaomi mystique, and this year it has given a brutal terminal like the F8. But instead of keeping the brand as a permanent outlet for purists, they let it languish with erratic launches, confusing positioning and some constant cannibalization with Redmi. And Redmi, although successful in volume, never had its own narrative beyond ‘Xiaomi, but cheaper’. They were functional subbrands, but not cultural. And CMF is the opposite: it has a recognizable design from fifteen meters, and most importantly, explicit permission not to last. Xiaomi wanted POCO to grow and mature. Nothing knows that CMF must burn bright and short, and when it goes out, they will light another match. CMF breaks this logic because it externalizes the growth hacking to a separate entity. Nothing can chase premium (and is doing so, Their prices rise discreetly every year) without contaminating the narrative indie. Meanwhile, CMF inherits the role of “brand of the enthusiast who knows”: singular design, brutal prices, no pretense of long-term sustainability. It is disposable by design, but consciously so. When CMF burns or has to raise prices, Nothing can launch another sub-brand and repeat the trick. They have turned the inevitable betrayal into a rotation maneuver. The interesting thing is that this can work precisely because Nothing does not pretend. OnePlus promised not to change and it changed. Xiaomi built an incredible base of Mi Fans and then the phenomenon faded away. Nothing from the beginning structures its growth as a fork: If you want to continue being early adopterhere you have CMF. If you want to join us in the premium life, here is Nothing. There is no betrayal because there was never a promise of immutability. It is a brand that understands that maturing means disappointing, so it institutionalizes disappointment in its brand architecture. Possibly the genius is not in CMF, but in having understood that the “enthusiast’s position”, the brand that “those in the know buy”, is not a long-term sustainable brand identity, but rather a industrializable growth phase. Just like adolescence: you can go through it just once, or you can design a system where there is always someone in your business family as a teenager while you mature and start coming home whenever you want, earn your own money and stop hiding your tobacco. OnePlus and Xiaomi played Peter Pan and that stage is over. Nothing has built a nursery. In Xataka | Nothing Phone (3a) Lite, analysis: it seems like black magic that a mobile like this costs less than 250 euros Featured image | Shawn Rain

They exist, offers them lunagets in Spain and allow to divide the cost

A private flight from Madrid to Mallorca for seven people for 3,000 euros. From Andalusia to the capital for four friends for about 2,000 euros. These figures would be exorbitant if we think of commercial flights. But if we take into account that we talk about private jets and at the time/day of preference of the client, the thing changes. Lunagets, the Swiss executive aviation broker that arrived in Spain two years ago, has brought the experience of flying in private jet without ruined. The business behind luxury. The key is in the model: lunajets does not have airplanes, but connects aircraft owners With passengers. They have access to 4,800 aircraft of 350 operators worldwide, from small four -seater jets to Boeing Business Jet. Its specialty is the “empty flights”, planes that move without passengers to reposition themselves, and that can offer discounts of up to 75%. With 17 years of experience and billing of 200 million euros, they have converted private aviation into a more accessible customer service. Closer to what it seems. Carlos Matallana, director of Lunajets Spain since 2023, was blunt in Your interview For the country: “You don’t have to be onassis to fly privately.” The problem, according to him, is knowledge and culture. Spain has less tradition in executive aviation than neighboring countries, partly due to social prejudices and ignorance. “There is an incredible amount of accommodated middle class people who can occasionally allow these flights and do not know it,” he says in Another interview For the world. His team responds in maximum 10 minutes and has three hours to find the perfect solution, whether Kilimanjaro is flying over at sunset or transporting a pet in cabin. Reality after glamor. “Hollywood has done a lot of damage,” Matallana admits. 99% of flights are “absolutely disappointing” compared to films. For Matallana, true value is not in luxury, but in efficiency: avoid safety tails, control schedules, travel comfortably. Matallana account That the client profile has “informal” a lot in the last decade, moving away from the stereotype of the powerful banker. The numbers in Spain. The Spanish market is yet to explode. Lunagets manages about 220 annual flights Here, in front of the more than 15,000 of the global group. The margins are adjusted, between 4% and 5% in Europe, but the volume compensates. The company aspires to double its Spanish turnover this year, taking advantage of the fact that more and more people discover that flying in private does not require an account in Switzerland. And the environmental controversy. Critics for CO2 emissions They do not go unnoticed. It is not for less, since we are talking about flying a plane without practically passengers. France has uploaded taxes To discourage these flights. Matallana recognizes responsibility: “We emit less than people think, but that does not exempt us from having to reduce what we emit to the minimum.” And it is that while the industry seeks more sustainable alternatives lunasts is firm in what gives value to the service it proposes: save time. Cover image | Lunagets In Xataka | Amancio Ortega: the billionaire who lives as one more neighbor (except for private jets and superyates)

divide Spain into three price areas for light

It has been a month since a mass blackout left millions without electricity on the peninsula. What caused it It is not yet clear. What has emerged again is an uncomfortable question for the electrical system: should you continue working with a single price zone? The current model. The blackout made it clear that the current model of a single price zone does not always conform to how electricity is generated, transported and consumed. Following this, proposals have sounded again They ask to review the price fixing system. Among them, a strength gains: divide the territory into several areas with differentiated prices, as already do other European countries. The Nord Pool case. One of the most cited examples, the electrical market of the Nordic and Baltic countries. This system divide its territory In offer areas (Bidding Zones), which may have different prices based on local generation availability, demand and capacity limitations in the transport network. In other words, if there is abundant renewable generation in an area (for example, in northern Norway) and very remote demand (for example, in southern Sweden), but the transport network between the two is congested, the price of electricity will be lower in the generating and higher area in the consumer. This difference pushes batteries where it is already consumed to improve the network where it collapses. According to Nord Pool’s own official siteprices are calculated every day depending on the balance of supply and demand in each area, taking into account the physical restrictions of the system. The result is a more realistic market, where prices are not artificially uniform and bottlenecks are directly reflected in the price. And is it possible in Spain? The proposal to divide in several areas has not been officially raised by the Government or by Red Electric (REE). Even so, the imbalance is evident: Much of the renewable generation is concentrated in rural areas of the southern and interior (such as Andalusia, Castilla-La Mancha or Aragon), while consumption triggers mostly on the Mediterranean axis and in Madrid. This asymmetry generates bottlenecks, cost overruns and, as has been seen in the blackout, critical vulnerabilities. In fact, Spain could be pressed to change its model if these structural limitations persist. Besides, Ree report data On the electrical system they show that only in 2024, the cost of adjustment services – which include redisarking and other measures to balance the network – amounted to 2,668 million euros. These costs represented 15 % of the final average price of energy, with an impact of € 11.43/MWh. That is, they are invisible cost overruns for the consumer, but that could be reduced if the system offered more realistic and differentiated price signals. Future scenarios. The recent electrical crisis has only underlined a reality that many experts have not been warning: the Spanish electrical system, as designed, is not able to absorb renewable growth No structural adjustments. The question about whether we must move from a single price zone to a zonal model is not only technical, but deeply political and territorial. Faced with a model that artificially uniforms prices and hides network imbalances, a well -designed zoning could become a useful tool to direct investments, reduce system costs and increase their resilience. But it also raises a complex political challenge: how to explain to a community that its electricity will be more expensive than that of another region? How to guarantee that the transition is fair and that does not increase territorial inequalities? Image | Pexels Xataka | The more you know about the blackout in Spain, the less guilty the lack of inertia seems to be renewable

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