Hash Functions With The Golden Ratio

April 25, 2025 by Bryan Cockfield 6 Comments

In the realm of computer science, it’s hard to go too far without encountering hashing or hash functions. The concept appears throughout security, from encryption to password storage to crypto, and more generally whenever large or complex data must be efficiently mapped to a smaller, fixed-size set. Hashing makes the process of looking for data much faster for a computer than performing a search and can be incredibly powerful when mastered. [Malte] did some investigation into hash functions and seems to have found a method called Fibonacci hashing that not only seems to have been largely forgotten but which speeds up this lookup process even further.

In a typical hashing operation, the data is transformed in some way, with part of this new value used to store it in a specific location. That second step is often done with an integer modulo function. But the problem with any hashing operation is that two different pieces of data end up with the same value after the modulo operation is performed, resulting in these two different pieces of data being placed at the same point. The Fibonacci hash, on the other hand, uses the golden ratio rather than the modulo function to map the final location of the data, resulting in many fewer instances of collisions like these while also being much faster. It also appears to do a better job of using the smaller fixed-size set more evenly as a consequence of being based around Fibonacci numbers, just as long as the input data doesn’t have a large number of Fibonacci numbers themselves.

Going through the math that [Malte] goes over in his paper shows that, at least as far as performing the mapping part of a hash function, the Fibonacci hash performs much better than integer modulo. Some of the comments mention that it’s a specific type of a more general method called multiplicative hashing. For those using hash functions in their code it might be worth taking a look at either way, and [Malte] admits to not knowing everything about this branch of computer science as well but still goes into an incredible amount of depth about this specific method. If you’re more of a newcomer to this topic, take a look at this person who put an enormous bounty on a bitcoin wallet which shows why reverse-hashing is so hard.

Revivification: a Room with cymbals and plinth

Posthumous Composition Being Performed By The Composer

April 25, 2025 by Seth Mabbott 13 Comments

Alvin Lucier was an American experimental composer whose compositions were arguably as much science experiments as they were music. The piece he is best known for, I Am Sitting in a Room, explored the acoustics of a room and what happens when you amplify the characteristics that are imparted on sound in that space by repeatedly recording and playing back the sound from one tape machine to another. Other works have employed galvanic skin response sensors, electromagnetically activated piano strings and other components that are not conventionally used in music composition.

Undoubtedly the most unconventional thing he’s done (so far) is to perform in an exhibit at The Art Gallery of Western Australia in Perth which opened earlier this month. That in itself would not be so unconventional if it weren’t for the fact that he passed away in 2021. Let us explain.

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A false colour image of the region of sky containing the CMZ.

Unsolved Questions In Astronomy? Try Dark Matter!

April 23, 2025 by Tyler August 21 Comments

Sometimes in fantasy fiction, you don’t want to explain something that seems inexplicable, so you throw your hands up and say, “A wizard did it.” Sometimes in astronomy, instead of a wizard, the answer is dark matter (DM). If you are interested in astronomy, you’ve probably heard that dark matter solves the problem of the “missing mass” to explain galactic light curves, and the motion of galaxies in clusters.

Now [Pedro De la Torre Luque] and others are proposing that DM can solve another pair of long-standing galactic mysteries: ionization of the central molecular zone (CMZ) in our galaxy, and mysterious 511 keV gamma-rays.

The Central Molecular Zone is a region near the heart of the Milky Way that has a very high density of interstellar gases– around sixty million times the mass of our sun, in a volume 1600 to 1900 light years across. It happens to be more ionized than it ought to be, and ionized in a very even manner across its volume. As astronomers cannot identify (or at least agree on) the mechanism to explain this ionization, the CMZ ionization is mystery number one.

Feynman diagram: Space-time vectors for electron-positron annihilation — Feynman diagram of electron-positron annihilation, showing the characteristic gamma-ray emission.

Mystery number two is a diffuse glow of gamma rays seen in the same part of the sky as the CMZ, which we know as the constellation Sagittarius. The emissions correspond to an energy of 515 keV, which is a very interesting number– it’s what you get when an electron annihilates with the antimatter version of itself. Again, there’s no universally accepted explanation for these emissions.

So [Pedro De la Torre Luque] and team asked themselves: “What if a wizard did it?” And set about trying to solve the mystery using dark matter. As it turns out, computer models including a form of light dark matter (called sub-GeV DM in the paper, for the particle’s rest masses) can explain both phenomena within the bounds of error.

In the model, the DM particles annihilate to form electron-positron pairs. In the dense interstellar gas of the CMZ, those positrons quickly form electrons to produce the 511 keV gamma rays observed. The energy released from this annihilation results in enough energy to produce the observed ionization, and even replicate the very flat ionization profile seen across the CMZ. (Any other proposed ionization source tends to radiate out from its source, producing an uneven profile.) Even better, this sort of light dark matter is consistent with cosmological observations and has not been ruled out by Earth-side dark matter detectors, unlike some heavier particles.

Further observations will help confirm or deny these findings, but it seems dark matter is truly the gift that keeps on giving for astrophysicists. We eagerly await what other unsolved questions in astronomy can be answered by it next, but it leaves us wondering how lazy the universe’s game master is if the answer to all our questions is: “A wizard did it.”

We can’t talk about dark matter without remembering [Vera Rubin].

Virtual Nodes, Real Waves: A Colpitts Walkthrough

April 22, 2025 by Heidi Ulrich 14 Comments

If you’ve ever fumbled through circuit simulation and ended up with a flatline instead of a sine wave, this video from [saisri] might just be the fix. In this walkthrough she demonstrates simulating a Colpitts oscillator using NI Multisim 14.3 – a deceptively simple analog circuit known for generating stable sine waves. Her video not only shows how to place and wire components, but it demonstrates why precision matters, even in virtual space.

You’ll notice the emphasis on wiring accuracy at multi-node junctions, something many tutorials skim over. [saisri] points out that a single misconnected node in Multisim can cause the circuit to output zilch. She guides viewers step-by-step, starting with component selection via the “Place > Components” dialog, through to running the simulation and interpreting the sine wave output on Channel A. The manual included at the end of the video is a neat bonus, bundling theory, waveform visuals, and circuit diagrams into one handy PDF.

If you’re into precision hacking, retro analogue joy, or just love watching a sine wave bloom onscreen, this is worth your time. You can watch the original video here.

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Multi-stage steam turbine with turbo generator (rear, in red) at the German lignite plant Boxberg (Credit: Siemens AG)

How Supercritical CO2 Working Fluid Can Increase Power Plant Efficiency

April 22, 2025 by Maya Posch 42 Comments

Using steam to produce electricity or perform work via steam turbines has been a thing for a very long time. Today it is still exceedingly common to use steam in this manner, with said steam generated either by burning something (e.g. coal, wood), by using spicy rocks (nuclear fission) or from stored thermal energy (e.g. molten salt). That said, today we don’t use steam in the same way any more as in the 19th century, with e.g. supercritical and pressurized loops allowing for far higher efficiencies. As covered in a recent video by [Ryan Inis], a more recent alternative to using water is supercritical carbon dioxide (CO₂), which could boost the thermal efficiency even further.

In the video [Ryan Inis] goes over the basics of what the supercritical fluid state of CO2 is, which occurs once the critical point is reached at 31°C and 83.8 bar (8.38 MPa). When used as a working fluid in a thermal power plant, this offers a number of potential advantages, such as the higher density requiring smaller turbine blades, and the potential for higher heat extraction. This is also seen with e.g. the shift from boiling to pressurized water loops in BWR & PWR nuclear plants, and in gas- and salt-cooled reactors that can reach far higher efficiencies, as in e.g. the HTR-PM and MSRs.

In a 2019 article in Power the author goes over some of the details, including the different power cycles using this supercritical fluid, such as various Brayton cycles (some with extra energy recovery) and the Allam cycle. Of course, there is no such thing as a free lunch, with corrosion issues still being worked out, and despite the claims made in the video, erosion is also an issue with supercritical CO₂ as working fluid. That said, it’s in many ways less of an engineering issue than supercritical steam generators due to the far more extreme critical point parameters of water.

If these issues can be overcome, it could provide some interesting efficiency boosts for thermal plants, with the caveat that likely nobody is going to retrofit existing plants, supercritical steam (coal) plants already exist and new nuclear plant designs are increasingly moving towards gas, salt and even liquid metal coolants, though secondary coolant loops (following the typical steam generator) could conceivably use CO₂ instead of water where appropriate.

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The central solenoid taking shape in the ITER assembly hall.

What’s Sixty Feet Across And Superconducting?

April 22, 2025 by Tyler August 54 Comments

What’s sixty feet (18.29 meters for the rest of the world) across and superconducting? The International Thermonuclear Experimental Reactor (ITER), and probably not much else.

The last parts of the central solenoid assembly have finally made their way to France from the United States, making both a milestone in the slow development of the world’s largest tokamak, and a reminder that despite the current international turmoil, we really can work together, even if we can’t agree on the units to do it in.

A cutaway diagram of the ITER tokamak showing the central solenoid — The central solenoid is in the “doughnut hole” of the tokamak in this cutaway diagram. Image: US ITER.

The central solenoid is 4.13 m across (that’s 13′ 7″ for burger enthusiasts) sits at the hole of the “doughnut” of the toroidal reactor. It is made up of six modules, each weighing 110 t (the weight of 44 Ford F-150 pickup trucks), stacked to a total height of 59 ft (that’s 18 m, if you prefer). Four of the six modules have been installed on-site, and the other two will be in place by the end of this year.

Each module was produced ITER by US, using superconducting material produced by ITER Japan, before being shipped for installation at the main ITER site in France — all to build a reactor based on a design from the Soviet Union. It doesn’t get much more international than this!

This magnet is, well, central to the functioning of a tokamak. Indeed, the presence of a central solenoid is one of the defining features of this type, compared to other toroidal rectors (like the earlier stellarator or spheromak). The central solenoid provides a strong magnetic field (in ITER, 13.1 T) that is key to confining and stabilizing the plasma in a tokamak, and inducing the 15 MA current that keeps the plasma going.

When it is eventually finished (now scheduled for initial operations in 2035) ITER aims to produce 500 MW of thermal power from 50 MW of input heating power via a deuterium-tritium fusion reaction. You can follow all news about the project here.

While a tokamak isn’t likely something you can hack together in your back yard, there’s always the Farnsworth Fusor, which you can even built to fit on your desk.

PoX: Super-Fast Graphene-Based Flash Memory

April 21, 2025 by Maya Posch 15 Comments

Recently a team at Fudan University claimed to have developed a picosecond-level Flash memory device (called ‘PoX’) that has an access time of a mere 400 picoseconds. This is significantly faster than the millisecond level access times of NAND Flash memory, and more in the ballpark of DRAM, while still being non-volatile. Details on the device technology were published in Nature.

In the paper by [Yutong Xing] et al. they describe the memory device as using a two-dimensional Dirac graphene-channel Flash memory structure, with hot carrier injection for both electron and hole injection, meaning that it is capable of both writing and erasing. Dirac graphene refers to the unusual electron transport properties of typical monolayer graphene sheets.

Demonstrated was a write speed of 400 picoseconds, non-volatile storage and a 5.5 × 10⁶ cycle endurance with a programming voltage of 5 V. It are the unique properties of a Dirac material like graphene that allow these writes to occur significantly faster than in a typical silicon transistor device.

What is still unknown is how well this technology scales, its power usage, durability and manufacturability.