Science

1250 Articles

Treating Functions As Vectors In Hilbert Space

December 25, 2025 by 2 Comments

Perhaps the most beautiful aspect of mathematics is that it applies to literally everything, even things that do not exist in this Universe. In addition to this there are a number of alternative ways to represent reality, with Fourier space and its related transforms being one of the most well-known examples. An alternative to Euclidian vector space is called Hilbert space, as a real or complex inner product space, which is used in e.g. mathematical proofs. In relation to this, [Eli Bendersky] came up with the idea of treating programming language functions as vectors of a sort, so that linear algebra methods can be applied to them.

Of course, to get really nitpicky, by the time you take a function with its arguments and produce an output, it is no longer a vector, but a scalar of some description. Using real numbers as indices also somewhat defeats the whole point and claim of working in a vector space, never mind Hilbert space.

As with anything that touches upon mathematics there are sure to be many highly divisive views, so we’ll leave it at this and allow our esteemed readers to flex their intellectual muscles on this topic. Do you think that the claims made hold water? Does applying linear algebra to every day functions make sense in this manner, perhaps even hold some kind of benefit?

Roll Your Own Hall Effect Sensor

December 24, 2025 by 8 Comments

If you read about Hall effect sensors — the usual way to detect and measure magnetic fields these days — it sounds deceptively simple. There’s a metal plate with current flowing across it in one direction, and sensors at right angles to the current flow. Can it really be that simple? According to a recent article in Elektor, [Burkhard Kainka] says yes.

The circuit uses a dual op amp with very high gain, which is necessary because the Hall voltage with 1 A through a 35 micron copper layer (the thickness on 1 oz copper boards) is on the order of 1.5 microvolts per Tesla. Of course, when dealing with tiny voltages like that, noise can be a problem, and you’ll need to zero the amplifier circuit before each use.

The metal surface? A piece of blank PCB. Copper isn’t the best material for a Hall sensor, but it is readily available, and it does work. Of course, moving the magnet can cause changes, and the whole thing is temperature sensitive. You wouldn’t want to use this setup for a precision measurement. But for an experimental look at the Hall effect, it is a great project.

Today, these sensors usually come in a package. If you want to know more about the Hall effect, including who Edwin Hall was, we can help with that, too.

The Music Of The Sea

December 22, 2025 by 8 Comments

For how crucial whales have been for humanity, from their harvest for meat and oil to their future use of saving the world from a space probe, humans knew very little about them until surprisingly recently. Most people, even in Herman Melville’s time, considered whales to be fish, and it wasn’t until humans went looking for submarines in the mid-1900s that we started to understand the complexities of their songs. And you don’t have to be a submarine pilot to listen now, either; all you need is something like these homemade hydraphones.

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Why Chopped Carbon Fiber In FDM Prints Is A Contaminant

December 21, 2025 by 36 Comments

A lot of claims have been made about the purported benefits of adding chopped carbon fiber to FDM filaments, but how many of these claims are actually true? In the case of PLA at least, the [I built a thing] channel on YouTube makes a convincing case that for PLA filament, the presence of chopped CF can be considered a contaminant that weakens the part.

Using the facilities of the University of Basel for its advanced imaging gear, the PLA-CF parts were subjected to both scanning electron microscope (SEM) and Micro CT imaging. The SEM images were performed on the fracture surfaces of parts that were snapped to see what this revealed about the internal structure. From this, it becomes apparent that the chopped fibers distribute themselves both inside and between the layers, with no significant adherence between the PLA polymer and the CF. There is also evidence for voids created by the presence of the CF.

To confirm this, an intact PLA-CF print was scanned using a Micro CT scanner over 13 hours. This confirmed the SEM findings, in that the voids were clearly visible, as was the lack of integration of the CF into the polymer. This latter point shouldn’t be surprising, as the thermal coefficient of PLA is much higher than that of the roughly zero-to-negative of CF. This translates into a cooling PLA part shrinking around the CF, thus creating the voids.

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A device within a vertical rectangular frame is shown, with a control box on the front and an LCD display. Within the frame, a grid of syringes is seen held upright beneath two parallel plates.

Building A Multi-Channel Pipette For Parallel Experimentation

December 20, 2025 by 6 Comments

One major reason for the high cost of developing new drugs and other chemicals is the sheer number of experiments involved; designing a single new drug can require synthesizing and testing hundreds or thousands of chemicals, and a promising compound will go through many stages of testing. At this scale, simply performing sequential experiments is wasteful, and it’s better to run tens or hundreds of experiments in parallel. A multi-channel pipette makes this significantly simpler by collecting and dispensing liquid into many vessels at once, but they’re, unfortunately, expensive. [Triggy], however, wanted to run his own experiments, so he built his own 96-channel multi-pipette for a fiftieth of the professional price.

The dispensing mechanism is built around an eight-by-twelve grid of syringes, which are held in place by one plate and have their plungers mounted to another plate, which is actuated by four stepper motors. The whole syringe mechanism needed to move vertically to let a multi-well plate be placed under the tips, so the lower plate is mounted to a set of parallel levers and gears. When [Triggy] manually lifts the lever, it raises the syringes and lets him insert or remove the multi-well. An aluminium extrusion frame encloses the entire mechanism, and some heat-shrink tubing lets pipette tips fit on the syringes.

[Triggy] had no particularly good way to test the multi-pipette’s accuracy, but the tests he could run indicated no problems. As a demonstration, he 3D-printed two plates with parallel channels, then filled the channels with different concentrations of watercolors. When the multi-pipette picked up water from each channel plate and combined them in the multi-well, it produced a smooth color gradient between the different wells. Similarly, the multi-pipette could let someone test 96 small variations on a single experiment at once. [Triggy]’s final cost was about $300, compared to $18,000 for a professional machine, though it’s worth considering the other reason medical development is expensive: precision and certifications. This machine was designed for home experiments and would require extensive testing before relying on it for anything critical.

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Improving The Cloud Chamber

December 19, 2025 by 8 Comments

Want to visualize radioactive particles? You don’t need a boatload of lab equipment. Just a cloud chamber. And [Curious Scientist] is showing off an improved miniature cloud chamber that is easy to replicate using a 3D printer and common components.

The build uses a Peltier module, a CPU cooler, an aluminum plate, thermal paste, and headlight film. The high voltage comes from a sacrificed mosquito swatter. The power input for the whole system is any 12V supply.

The cloud chamber was high tech back in 1911 when physicist Charles T. R. Wilson made ionizing radiation visible by creating trails of tiny liquid droplets in a supersaturated vapor of alcohol or water. Charged particles pass through, leaving visible condensation trails.

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Neutrino Transmutation Observed For The First Time

December 18, 2025 by 27 Comments

Once upon a time, transmutation of the elements was a really big deal. Alchemists drove their patrons near to bankruptcy chasing the philosopher’s stone to no avail, but at least we got chemistry out of it. Nowadays, anyone with a neutron source can do some spicy transmutation. Or, if you happen to have a twelve meter sphere of liquid scintillator two kilometers underground, you can just wait a few years and let neutrinos do it for you. That’s what apparently happened at SNO+, the experiment formally known as Sudbury Neutrino Observatory, as announced recently.

The scinillator already lights up when struck by neutrinos, much as the heavy water in the original SNO experiment did. It will also light up, with a different energy peak, if a nitrogen-13 atom happens to decay. Except there’s no nitrogen-13 in that tank — it has a half life of about 10 minutes. So whenever a the characteristic scintillation of a neutrino event is followed shortly by a N-13 decay flash, the logical conclusion is that some of the carbon-13 in the liquid scintillator has been transmuted to that particular isotope of nitrogen.

That’s not unexpected; it’s an interaction that’s accounted for in the models. We’ve just never seen it before, because, well. Neutrinos. They’re called “ghost particles” for a reason. Their interaction cross-section is absurdly low, so they are able to pass through matter completely unimpeded most of the time. That’s why the SNO was built 2 KM underground in Sudbury’s Creighton Mine: the neutrinos could reach it, but very few cosmic rays and no surface-level radiation can.  “Most of the time” is key here, though: with enough liquid scintillator — SNO+ has 780 tonnes of the stuff — eventually you’re bound to have some collisions.

Capturing this interaction was made even more difficult considering that it requires C-13, not the regular C-12 that the vast majority of the carbon in the scintillator fluid is made of. The abundance of carbon-13 is about 1%, which should hold for the stuff in SNO+ as well since no effort was made to enrich the detector. It’s no wonder that this discovery has taken a few years since SNO+ started in 2022 to gain statistical significance.

The full paper is on ArXiv, if you care to take a gander. We’ve reported on SNO+ before, like when they used pure water to detect reactor neutrinos while they were waiting for the scintillator to be ready. As impressive as it may be, it’s worth noting that SNO is no longer the largest neutrino detector of its kind.