Month: October 2000

For all the students wondering why they would ever need to use the Pythagorean theorem, Katie Steckles is delighted to report on a real-world encounter.

Recently, I was building a flat-pack wardrobe when I noticed something odd in the instructions. Before you assembled the wardrobe, they said, you needed to measure the height of the ceiling in the room you were going to put it in. If it was less than 244 centimetres high, there was a different set of directions to follow.

These separate instructions asked you to build the wardrobe in a vertical orientation, holding the side panels upright while you attached them to the base. The first set of directions gave you a much easier job, building the wardrobe flat on the floor before lifting it up into place. I was intrigued by the value of 244 cm: this wasn’t the same as the height of the wardrobe, or any other dimension on the package, and I briefly wondered where that number had come from. Then I realised: Pythagoras.

The wardrobe was 236 cm high and 60 cm deep. Looking at it side-on, the length of the diagonal line from corner to corner can be calculated using Pythagoras’s theorem. The vertical and horizontal sides meet at a right angle, meaning if we square the length of each then add them together, we get the well-known “square of the hypotenuse”. Taking the square root of this number gives the length of the diagonal.

In this case, we get a diagonal length a shade under 244 cm. If you wanted to build the wardrobe flat and then stand it up, you would need that full diagonal length to fit between the floor and the ceiling to make sure it wouldn’t crash into the ceiling as it swung past – so 244 cm is the safe ceiling height. It is a victory for maths in the real world, and vindication for maths teachers everywhere being asked, “When am I going to use this?”

This isn’t the only way we can connect Pythagoras to daily tasks. If you have ever needed to construct something that is a right angle – like a corner in joinery, or when laying out cones to delineate the boundaries of a sports pitch – you can use the Pythagorean theorem in reverse. This takes advantage of the fact that a right-angled triangle with sides of length 3 and 4 has a hypotenuse of 5 – a so-called 3-4-5 triangle.

If you measure 3 units along one side from the corner, and 4 along the other, and join them with a diagonal, the diagonal’s length will be precisely 5 units, if the corner is an exact right angle. Ancient cultures used loops of string with knots spaced 3, 4 and 5 units apart – when held out in a triangle shape, with a knot at each vertex, they would have a right angle at one corner. This technique is still used as a spot check by builders today.

Engineers, artists and scientists might use geometrical thinking all the time, but my satisfaction in building a wardrobe, and finding the maths checked out perfectly, is hard to beat.

Katie Steckles is a mathematician, lecturer, YouTuber and author based in Manchester, UK. She is also puzzle adviser for New Scientist’s puzzle column, BrainTwister. Follow her @stecks

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*Credit for article given to Peter Rowlett*

In the quest to unravel the underlying mechanisms of natural systems, accurately identifying causal interactions is of paramount importance. Leveraging the advancements in time-series data collection through cutting-edge technologies, computational methods have emerged as powerful tools for inferring causality.

However, existing model-free methods have struggled to differentiate between generalized synchrony and causality, leading to false predictions. On the other hand, model-based methods, while accurate, have been limited by their dependence on specific models, hindering their widespread applicability.

Addressing these challenges head-on, a team of researchers from the Biomedical Mathematics Group within the Institute for Basic Science (IBS) has developed a computational package called General Ode Based Inference (GOBI). This innovative tool overcomes the limitations of both model-free and model-based inference methods by introducing an easily testable condition for a general monotonic ODE (Ordinary Differential Equation) model to reproduce time-series data. The work is published in the journal Nature Communications.

Dr. Kim Jae Kyoung, the lead researcher behind GOBI, explains, “Our goal was to create an accurate and broadly applicable inference method that could unlock insights into complex dynamical systems. We recognized the limitations of existing approaches and set out to develop a solution that could overcome these challenges.”

GOBI goes beyond the capabilities of traditional model-free methods, such as Granger Causality, by successfully inferring positive and negative regulations in various networks at both the molecular and population levels. Unlike its predecessors, GOBI can distinguish between direct and indirect causation, even in the presence of noisy time-series data.

Park Seho, the first author of the paper, said, “GOBI’s strength lies in its ability to infer causal relationships in systems described by nearly any monotonic system with positive and negative regulations, as captured by the general monotonic ODE model. By eliminating the dependence on a specific model choice, GOBI significantly expands the scope of inference methods in complex systems.”

In addition to its powerful inferential capabilities, GOBI offers user-friendly features that simplify the computational process. The researchers have designed the package to be accessible to a wide range of users, including those without extensive computational expertise. Through GOBI, scientists and researchers can gain deeper insights into gene regulatory networks, ecological systems, and even understand the impact of air pollution on cardiovascular diseases.

The researchers have validated the effectiveness of GOBI by successfully inferring causal relationships from synchronous time-series data, where popular model-free methods have faltered. By providing accurate and reliable inference in a variety of scenarios, GOBI paves the way for a more comprehensive understanding of complex dynamical systems.

With its groundbreaking capabilities, GOBI promises to revolutionize the field of computational causal inference, empowering researchers to unlock the secrets hidden within complex systems. As the scientific community embraces this powerful tool, we can anticipate unprecedented advancements in various domains, including biology, ecology, and epidemiology.

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Credit of the article given to Institute for Basic Science