The original version of this story appeared in Quanta Magazine.

If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost. You may end up spending too much time putting the pieces in order.

This dilemma is especially relevant to one of the most iconic problems in computer science: finding the shortest path from a specific starting point in a network to every other point. It’s like a souped-up version of a problem you need to solve each time you move: learning the best route from your new home to work, the gym, and the supermarket.

“Shortest paths is a beautiful problem that anyone in the world can relate to,” said Mikkel Thorup, a computer scientist at the University of Copenhagen.

Intuitively, it should be easiest to find the shortest path to nearby destinations. So if you want to design the fastest possible algorithm for the shortest-paths problem, it seems reasonable to start by finding the closest point, then the next-closest, and so on. But to do that, you need to repeatedly figure out which point is closest. You’ll sort the points by distance as you go. There’s a fundamental speed limit for any algorithm that follows this approach: You can’t go any faster than the time it takes to sort.

Forty years ago, researchers designing shortest-paths algorithms ran up against this “sorting barrier.” Now, a team of researchers has devised a new algorithm that breaks it. It doesn’t sort, and it runs faster than any algorithm that does.

“The authors were audacious in thinking they could break this barrier,” said Robert Tarjan, a computer scientist at Princeton University. “It’s an amazing result.”

The Frontier of Knowledge

To analyze the shortest-paths problem mathematically, researchers use the language of graphs—networks of points, or nodes, connected by lines. Each link between nodes is labeled with a number called its weight, which can represent the length of that segment or the time needed to traverse it. There are usually many routes between any two nodes, and the shortest is the one whose weights add up to the smallest number. Given a graph and a specific “source” node, an algorithm’s goal is to find the shortest path to every other node.

The most famous shortest-paths algorithm, devised by the pioneering computer scientist Edsger Dijkstra in 1956, starts at the source and works outward step by step. It’s an effective approach, because knowing the shortest path to nearby nodes can help you find the shortest paths to more distant ones. But because the end result is a sorted list of shortest paths, the sorting barrier sets a fundamental limit on how fast the algorithm can run.

A proposed constellation of satellites has astronomers very worried. Unlike satellites that reflect sunlight and produce light pollution as an unfortunate byproduct, the ones by US startup Reflect Orbital would produce light pollution by design.

The company promises to produce “sunlight on demand” with mirrors that beam sunlight down to Earth so solar farms can operate after sunset.

It plans to start with an 18-meter test satellite named Earendil-1 which the company has applied to launch in 2026. It would eventually be followed by about 4,000 satellites in orbit by 2030, according to the latest reports.

So how bad would the light pollution be? And perhaps more importantly, can Reflect Orbital’s satellites even work as advertised?

Bouncing sunlight

In the same way you can bounce sunlight off a watch face to produce a spot of light, Reflect Orbital’s satellites would use mirrors to beam light onto a patch of Earth.

But the scale involved is vastly different. Reflect Orbital’s satellites would orbit about 625km above the ground, and would eventually have mirrors 54 meters across.

When you bounce light off your watch onto a nearby wall, the spot of light can be very bright. But if you bounce it onto a distant wall, the spot becomes larger—and dimmer.

This is because the sun is not a point of light, but spans half a degree in angle in the sky. This means that at large distances, a beam of sunlight reflected off a flat mirror spreads out with an angle of half a degree.

What does that mean in practice? Let’s take a satellite reflecting sunlight over a distance of roughly 800km—because a 625km-high satellite won’t always be directly overhead, but beaming the sunlight at an angle. The illuminated patch of ground would be at least 7km across.

Even a curved mirror or a lens can’t focus the sunlight into a tighter spot due to the distance and the half-degree angle of the sun in the sky.

Would this reflected sunlight be bright or dim? Well, for a single 54 meter satellite it will be 15,000 times fainter than the midday sun, but this is still far brighter than the full moon.

The balloon test

Last year, Reflect Orbital’s founder Ben Nowack posted a short video which summarized a test with the “last thing to build before moving into space”. It was a reflector carried on a hot air balloon.

In the test, a flat, square mirror roughly 2.5 meters across directs a beam of light down to solar panels and sensors. In one instance the team measures 516 watts of light per square meter while the balloon is at a distance of 242 meters.

For comparison, the midday sun produces roughly 1,000 watts per square meter. So 516 watts per square meter is about half of that, which is enough to be useful.

However, let’s scale the balloon test to space. As we noted earlier, if the satellites were 800km from the area of interest, the reflector would need to be 6.5km by 6.5km—42 square kilometers. It’s not practical to build such a giant reflector, so the balloon test has some limitations.

So what is Reflect Orbital planning to do?

Reflect Orbital’s plan is “simple satellites in the right constellation shining on existing solar farms”. And their goal is only 200 watts per square meter—20% of the midday sun.

Can smaller satellites deliver? If a single 54 meter satellite is 15,000 times fainter than the midday sun, you would need 3,000 of them to achieve 20% of the midday sun. That’s a lot of satellites to illuminate one region.

Another issue: satellites at a 625km altitude move at 7.5 kilometers per second. So a satellite will be within 1,000km of a given location for no more than 3.5 minutes.

This means 3,000 satellites would give you a few minutes of illumination. To provide even an hour, you’d need thousands more.

Reflect Orbital isn’t lacking ambition. In one interview, Nowack suggested 250,000 satellites in 600km high orbits. That’s more than all the currently catalogued satellites and large pieces of space junk put together.

And yet, that vast constellation would deliver only 20% of the midday sun to no more than 80 locations at once, based on our calculations above. In practice, even fewer locations would be illuminated due to cloudy weather.

Additionally, given their altitude, the satellites could only deliver illumination to most locations near dusk and dawn, when the mirrors in low Earth orbit would be bathed in sunlight. Aware of this, Reflect Orbital plan for their constellation to encircle Earth above the day-night line in sun-synchronous orbits to keep them continuously in sunlight.

Bright lights

So, are mirrored satellites a practical means to produce affordable solar power at night? Probably not. Could they produce devastating light pollution? Absolutely.

In the early evening it doesn’t take long to spot satellites and space junk—and they’re not deliberately designed to be bright. With Reflect Orbital’s plan, even if just the test satellite works as planned, it will sometimes appear far brighter than the full moon.

A constellation of such mirrors would be devastating to astronomy and dangerous to astronomers. To anyone looking through a telescope the surface of each mirror could be almost as bright as the surface of the sun, risking permanent eye damage.

The light pollution will hinder everyone’s ability to see the cosmos and light pollution is known to impact the daily rhythms of animals as well.

Although Reflect Orbital aims to illuminate specific locations, the satellites’ beams would also sweep across Earth when moving from one location to the next. The night sky could be lit up with flashes of light brighter than the moon.

The company did not reply to The Conversation about these concerns within deadline. However, it told Bloomberg this week it plans to redirect sunlight in ways that are “brief, predictable and targeted”, avoiding observatories and sharing the locations of the satellites so scientists can plan their work.

The consequences would be dire

It remains to be seen whether Reflect Orbital’s project will get off the ground. The company may launch a test satellite, but it’s a long way from that to getting 250,000 enormous mirrors constantly circling Earth to keep some solar farms ticking over for a few extra hours a day.

Still, it’s a project to watch. The consequences of success for astronomers—and anyone else who likes the night sky dark—would be dire.

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Some of the world’s biggest tech firms have soared in value over the last year. As AI evolves at pace, there are hopes that it will improve lives in ways that people could never have imagined a decade ago—in sectors as diverse as health care, employment and scientific discovery.

OpenAI is now worth US$500 billion (£373 billion), compared with US$157 billion last October. Another firm, Anthropic, has almost trebled its valuation. But the Bank of England has now warned of a possible rapid “correction” due to its concerns about these staggering valuation rises.

The question is whether these values are realistic—or based on hype, excitement and unfounded optimism for the potential of AI. Put simply, is AI’s value today a product of what AI will do in future or what people hope it may do? Ultimately, we will only really know if it’s a bubble if it bursts—though the warning signs are evident today.

With hindsight, many things that happen in a bubble may sound exceedingly optimistic. If you take many headlines and replace the word AI with the word computers it often sounds a lot more naive.

But, predicting the path of technological change is hard. Back in 2000, the Daily Mail declared the internet could be a passing fad. Just a few months earlier the dotcom boom had peaked.

A burst bubble may not change the end of the journey. The internet was not a passing fad. However, bubbles are extremely disruptive and affect people in very real ways. Stocks fall, pensions suffer, unemployment rises and investment is wasted. Real potential is crowded out in the hype and mania to focus all investment in a small number of stocks and firms.

Right now, we have the first sign of a bubble—a rapid rise in valuations. If these correct and fall we will have a bubble. If these valuations continue to rise we could be seeing a new sustained market that is focused on the technology of the future.

Of course, it might be that these valuations plateau. What happens then depends on whether people have invested in the belief that prices will always rise.

Consider a situation where people believe—as the Bank of England does—that AI firms’ valuations may be “stretched.” It’s helpful to consider what these valuations are based on. Investment is simply a bet that AI increases profitability for the firms involved. These massive valuations are bets that AI will hugely increase future profitability.

In some cases, these are bets that AI will improve in capabilities towards some kind of “artificial superintelligence” that can do everything a human can do—or more. This could raise the living standards of everyone on Earth. Leading computer scientist Stuart Russell estimates the value of that at US$14 quadrillion—investors are buying a claim on that outcome too.

If investors begin to fear that AI profits won’t materialize, then they will try to get their money back. This realization can appear quite suddenly and can be prompted by seemingly minor events. It doesn’t require a big needle to pop a bubble.

A US article published in March 2000 warned that internet companies were fast running out of money. This caused many people to rethink their investments

At this stage of the bubble, investment excitement had spread to everyday investors. These regular people balanced their fear of missing out with a fear that they were investing in something new that they didn’t know much about. For many, an article in a popular magazine suggesting they may have made a mistake tipped the scales towards caution. They began to sell their dotcom stocks.

In search of profit

It may come as a surprise to some that, despite its increasing valuations, OpenAI does not yet make a profit. It may require ten times more revenue to do so.

A US$500 billion valuation is quite something for a company that reportedly lost US$7.8 billion in the first half of this year. Some of this value appears to flow from a new deal between OpenAI and Nvidia where Nvidia will invest in OpenAI and OpenAI will buy Nvidia chips. This circular financing keeps everything afloat for now, but at some point investors will need to see returns.

AI firms more generally do not appear to be profitable at the moment. Investors are not putting their money into today’s losses—they are betting on an AI future.

It is of course perfectly feasible that AI firms will develop business models to increase their profitability. OpenAI is exploring advertising options and allowing chatbots to recommend products.

Using AI to deliver these messages is a viable option, though they will have to avoid the tricks and manipulations associated with online platforms, such as when hotel websites announce that rooms are about to sell out. We believe that AI can increase the power of these manipulations and we wonder how persuasive chatbots may be in their recommendations.

However, the big four—Meta, Alphabet, Microsoft and Amazon—are this year spending the equivalent of the GDP of Portugal on AI infrastructure. This is not investment in new targeted ads, it is investment in an AI future. The bubble will burst if and when this future is in doubt.

This article is republished from The Conversation under a Creative Commons license. Read the original article.