Theodor Benfey’s periodic table (1964) [image Wikimedia Commons].
Archive for the 'Irish Times' Category
The Potency of Pattern: Mind the Gap
Published May 18, 2023 Irish Times Leave a CommentTags: Group Theory, Physics
DLWP: A New Age of Weather Forecasting
Published April 20, 2023 Irish Times ClosedTags: Climate Modelling, Numerical Weather Prediction
Hurricane Frances
Before the age of computers, weather forecasters analysed observations plotted on paper charts, drew isobars and other features and — based on their previous knowledge and experience — constructed charts of conditions at a future time, often one day ahead. They combined observational data and rules of thumb based on physical principles to predict what would follow from a given state. The results were undependable for two main reasons: the data were sparse, and the empirical rules were unreliable [TM244 or search for “thatsmaths” at irishtimes.com].
For the past sixty years or so, forecasts have been based on computer models that numerically solve the mathematical equations expressing the physical laws. This approach is radically different but, after a shaky start, the numerical weather prediction (NWP) models have become remarkably accurate, with forecasting skill increasing by about one day each decade. Now there are signs of a return to the analogue, data-driven methods.
Weather Warnings in Glorious Technicolor
Published February 16, 2023 Irish Times ClosedTags: Algorithms, Geophysics
Severe weather affects us all and we need to know when to take action to protect ourselves and our property. We have become familiar with the colourful spectrum of warnings issued by Met Éireann.
For several years, Met Éireann has issued warnings of extreme weather. These depend on the severity of the meteorological event and the level of confidence in the forecast. They are formulated using forecasts produced by computer, algorithms that determine the likely impacts of extreme weather, and the expertise of the forecasters [TM242 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Weather Warnings in Glorious Technicolor’
The Cosmology of the Divine Comedy
Published January 19, 2023 Irish Times ClosedTags: Astronomy, Cosmology, Topology
Divina Commedia: Online at Columbia University.
If you think poetry and maths are poles apart, think again. Around the sixth century, Indian poet and mathematician Virahanka codified the structure of Sanskrit poetry, formulating rules for the patterns of long and short syllables. In this process, a sequence emerged in which each term is the sum of the preceding two. This is precisely the sequence studied centuries later by Leonardo Bonacci of Pisa, which we now call the Fibonacci sequence [TM241 or search for “thatsmaths” at irishtimes.com].
Convergence of mathematics and physics
Published December 15, 2022 Irish Times ClosedTags: Applied Maths, Physics
The connexions between mathematics and physics are manifold, and each enriches the other. But the relationship between the disciplines fluctuates between intimate harmony and cool indifference. Numerous examples show how mathematics, developed for its inherent interest in beauty, later played a central role in physical theory.
A well-known case is the multi-dimensional geometry formulated by Bernhard Riemann in the mid 19th century, which was exactly what Albert Einstein needed 50 years later for his relativity theory [TM240 or search for “thatsmaths” at irishtimes.com].
The Rich Legacy of Indian Mathematics
Published November 17, 2022 Irish Times ClosedTags: History, Ramanujan
Jeremy Irons and Dev Patel in The Man Who Knew Infinity, a film about the life of Srinivasa Ramanujan.
For more than three thousand years, mathematics has played an important role in Indian culture. Sometimes it was studied for practical reasons and sometimes for pure intellectual delight. The earliest traces of mathematics are found in the Indus Valley, around 3000 BC. There is clear evidence of a structured system of weights and measures and samples of decimal-based numeration [TM239 or search for “thatsmaths” at irishtimes.com].
From Sub-atomic to Cosmic Strings
Published October 20, 2022 Irish Times , Occasional ClosedTags: Astronomy, Physics
The two great pillars of modern physics are quantum mechanics and general relativity. These theories describe small-scale and large-scale phenomena, respectively. While quantum mechanics predicts the shape of a hydrogen atom, general relativity explains the properties of the visible universe on the largest scales.
Making Sound Pictures to Identify Bird Songs
Published September 15, 2022 Irish Times ClosedTags: Algorithms, Fourier analysis
Top: Audio signal with three chirps. Bottom: Time-Frequency spectrogram of signal.
A trained musician can look at a musical score and imagine the sound of an entire orchestra. The score is a visual representation of the sounds. In an analogous way, we can represent birdsong by an image, and analysis of the image can tell us the species of bird singing. This is what happens with Merlin Bird ID. In a recent episode of Mooney Goes Wild, Niall Hatch of Birdwatch Ireland interviewed Drew Weber of the Cornell Lab of Ornithology, a developer of Merlin Bird ID. This phone app enables a large number of birds to be identified [TM237 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Making Sound Pictures to Identify Bird Songs’
The Navigational Skills of the Marshall Islanders
Published August 18, 2022 Irish Times ClosedTags: Navigation, Wave Motion
Marshallese canoe sailing on Majuro Lagoon. Image from: www.canoesmarshallislands.com
For thousands of years, the Marshall Islanders of Micronesia have been finding their way around a broadly dispersed group of low-lying islands, navigating apparently without effort from one atoll to another one far beyond the horizon. They had no maps or magnetic compass, no clocks, no weather forecasts and certainly no GPS or SatNav equipment [TM236 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘The Navigational Skills of the Marshall Islanders’
In just three weeks the largest global mathematical get-together will be under way. The opening ceremony of the 2022 International Congress of Mathematicians (ICM) opens on Wednesday 6 July and continues for nine days. Prior to the ICM, the International Mathematical Union (IMU) will host its 19th General Assembly in Helsinki on 3–4 July [TM234 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘ICM 2022 — Plans Disrupted but not Derailed’
Image Processing Emerges from the Shadows
Published May 19, 2022 Irish Times ClosedTags: Astronomy, Trigonometry
Satellite images are of enormous importance in military contexts. A battery of mathematical and image-processing techniques allows us to extract information that can play a critical role in tactical planning and operations. The information in an image may not be immediately evident. For example, an overhead image gives no direct information about the height of buildings or industrial installations, but shadows, together with the time, date and basic trigonometry, enable heights to be determined [TM233 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Image Processing Emerges from the Shadows’
The Whole is Greater than the Part — Or is it?
Published April 21, 2022 Irish Times ClosedTags: Cantor, Geometry, Set Theory
Euclid flourished about fifty years after Aristotle and was certainly familiar with Aristotle’s Logic. Euclid’s organization of the work of earlier geometers was truly innovative. His results depended upon basic assumptions, called axioms and “common notions”. There are in total 23 definitions, five axioms and five common notions in The Elements. The axioms, or postulates, are specific assumptions that may be considered as self-evident, for example “the whole is greater than the part” [TM232 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘The Whole is Greater than the Part — Or is it?’
The Improbability Principle and the Seanad Election
Published March 17, 2022 Irish Times ClosedTags: Social attitudes, Statistics
A by-election for the Seanad Éireann Dublin University constituency, arising from the election of Ivana Bacik to Dáil Éireann, is in progress. There are seventeen candidates, eight men and nine women. Examining the ballot paper, I immediately noticed an imbalance: the top three candidates, and seven of the top ten, are men. The last six candidates listed are all women. Is there a conspiracy, or could such a lopsided distribution be a matter of pure chance?
To avoid bias, the names on the ballot paper are always listed in alphabetical order. We may assume that the name of a randomly chosen candidate is equally likely to appear at any of the positions on the list; with 17 candidates, there about 6% chance for each of the 17 positions; the distribution for a single candidate is uniform. However, when several candidates are grouped, the distribution is more complicated [TM231 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘The Improbability Principle and the Seanad Election’
A Prescient Vision of Modern Weather Forecasting
Published March 3, 2022 Irish Times ClosedTags: Numerical Weather Prediction
Lewis Fry Richardson in 1931.
One hundred years ago, a remarkable book was published by Cambridge University Press. It was a commercial flop: although the print run was just 750 copies, it was still in print thirty years later. Yet, it held the key to forecasting the weather by scientific means. The book, Weather Prediction by Numerical Process, was written by Lewis Fry Richardson, a brilliant, eccentric mathematician. He described in detail how the mathematical equations that govern the evolution of the atmosphere could be solved by numerical means to deduce future weather conditions from a set of observations [TM230 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘A Prescient Vision of Modern Weather Forecasting’
Henri Poincaré
Where does new mathematics come from? The great French mathematician Henri Poincaré, a brilliant expositor of the scientific method, described how he grappled for months with an arcane problem in function theory. Exasperated by lack of progress, he went on vacation and forgot about the problem. But, as he was boarding a bus in Caen, the answer came to him in a flash. He was later able to return to his office and complete a proof of the result [TM229 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Sources and Scenes of Mathematical Inspiration’
In his scientific best-seller, A Brief History of Time, Stephen Hawking remarked that every equation he included would halve sales of the book, so he put only one in it, Einstein’s equation relating mass and energy, E = mc2. This cynical view is a disservice to science; we should realize that, far from being inimical, equations are our friends [TM228 or search for “thatsmaths” at irishtimes.com].
Letters to a German Princess: Euler’s Blockbuster Lives On
Published January 20, 2022 Irish Times , Occasional ClosedTags: Euler, History
The great Swiss mathematician Leonhard Euler produced profound and abundant mathematical works. Publication of his Opera Omnia began in 1911 and, with close to 100 volumes in print, it is nearing completion. Although he published several successful mathematical textbooks, the book that attracted the widest readership was not a mathematical work, but a collection of letters [TM227 or search for “thatsmaths” at irishtimes.com].
For several years, starting in 1760, Euler wrote a series of letters to Friederike Charlotte, Princess of Brandenburg-Schwedt, a niece of Frederick the Great of Prussia. The collection of 234 letters was first published in French, the language of the nobility, as Lettres à une Princesse d’Allemagne. This remarkably successful popularisation of science appeared in many editions, in several languages, and was widely read. Subtitled “On various subjects in physics and philosophy”, the first two of three volumes were published in 1768 by the Imperial Academy of Sciences in St. Petersburg, with the support of the empress, Catherine II.
Continue reading ‘Letters to a German Princess: Euler’s Blockbuster Lives On’
Some Characteristics of the Mathematical Psyche
Published January 6, 2022 Irish Times ClosedTags: Social attitudes
What are mathematicians really like? What are the characteristics or traits of personality typical amongst them? Mathematicians are rarely the heroes of novels, so we have little to learn from literature. A few films have featured mathematicians, but most give little insight into the personalities of their subjects [TM226 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Some Characteristics of the Mathematical Psyche’
Bernoulli’s Golden Theorem and the Law of Large Numbers
Published December 16, 2021 Irish Times ClosedTags: History, Probability
Swiss postage stamp, issued in 1994 for the International Congress of Mathematicians in Zurich, featuring Jakob Bernoulli and illustrating his “golden theorem”.
Jakob Bernoulli, head of a dynasty of brilliant scholars, was one of the world’s leading mathematicians. Bernoulli’s great work, Ars Conjectandi, published in 1713, included a profound result that he established “after having meditated on it for twenty years”. He called it his “golden theorem”. It is known today as the law of large numbers, and it was the first limit theorem in probability, and the first attempt to apply probability outside the realm of games of chance [TM225 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Bernoulli’s Golden Theorem and the Law of Large Numbers’
Buffon’s Noodle and the Mathematics of Hillwalking
Published December 2, 2021 Irish Times ClosedTags: Geometry, Geophysics
In addition to some beautiful photos and maps and descriptions of upland challenges in Ireland and abroad, the November issue of The Summit, the Mountain Views Quarterly Newsletter for hikers and hillwalkers, describes a method to find the length of a walk based on ideas originating with the French naturalist and mathematician George-Louis Leclerc, Comte de Buffon [TM224 or search for “thatsmaths” at irishtimes.com].
[Image from November issue of The Summit, the Mountain Views Quarterly Newsletter.]
Émilie Du Châtelet and the Conservation of Energy
Published November 18, 2021 Irish Times ClosedTags: History, Mechanics
A remarkable French natural philosopher and mathematician who lived in the early eighteenth century, Émilie Du Châtalet, is generally remembered for her translation of Isaac Newton’s Principia Mathematica, but her work was much more than a simple translation: she added an extensive commentary in which she included new developments in mechanics, the most important being her formulation of the principle of conservation of energy [TM223 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Émilie Du Châtelet and the Conservation of Energy’
Topsy-turvy Maths: Proving Axioms from Theorems
Published November 4, 2021 Irish Times ClosedTags: Logic, Philosophy
Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic assumptions axioms and the consequent results theorems. But can things be done the other way around, using theorems to prove axioms? This is a central question of reverse mathematics [TM222 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Topsy-turvy Maths: Proving Axioms from Theorems’
Edna St Vincent Millay’s sonnet “Euclid alone has looked on beauty bare” evokes the ethereal, otherworldly quality of mathematics. Scandalous behaviour is not usually associated with mathematicians, but they are human: pride, overblown ego and thirst for fame have led to skulduggery, plagiarism and even murder. Some of the more egregious scandals are reviewed here [TM221 or search for “thatsmaths” at irishtimes.com].
French postage stamp issued in 1984.
A Grand Unification of Mathematics
Published October 7, 2021 Irish Times ClosedTags: Algebra, Analysis, Group Theory, Number Theory
Rene Descartes
There are numerous branches of mathematics, from arithmetic, geometry and algebra at an elementary level to more advanced fields like number theory, topology and complex analysis. Each branch has its own distinct set of axioms, or fundamental assumptions, from which theorems are derived by logical processes. While each branch has its own flavour, character and methods, there are also strong overlaps and interdependencies. Several attempts have been made to construct a grand unified theory that embraces the entire field of maths [TM220 or search for “thatsmaths” at irishtimes.com].
Earth System Models simulate the changing climate
Published September 16, 2021 Irish Times ClosedTags: biology, Climate Modelling, Geophysics
Image credit: NASA.
The climate is changing, and we need to know what changes to expect and how soon to expect them. Earth system models, which simulate all relevant components of the Earth system, are the primary means of anticipating future changes of our climate [TM219 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Earth System Models simulate the changing climate’
The Social Side of Mathematics
Published September 2, 2021 Irish Times ClosedTags: Education, Ireland
On a cold December night in 1976, a group of mathematicians assembled in a room in Trinity College Dublin for the inaugural meeting of the Irish Mathematical Society (IMS). Most European countries already had such societies, several going back hundreds of years, and it was felt that the establishment of an Irish society to promote the subject, foster research and support teaching of mathematics was timely [TM218 or search for “thatsmaths” at irishtimes.com].
Changing Views on the Age of the Earth
Published August 19, 2021 Irish Times ClosedTags: Geophysics, History, Ireland
[Image credit: NASA]
Driving along the motorway on a busy day, you see brake-lights ahead and slow down until the flow grinds to a halt. The traffic stutters forward for five minutes or so until, mysteriously, the way ahead is clear again. But, before long, you arrive at the back of another stagnant queue. Hold-ups like this, with no apparent cause, are known as phantom traffic jams and you may experience several such delays on a journey of a few hours [TM216 or search for “thatsmaths” at irishtimes.com].
Traffic jams can have many causes [Image © Susanneiles.com. JPEG]
Is space continuous or discrete? Is it smooth, without gaps or discontinuities, or granular with a limit on how small a distance can be? What about time? Can time be repeatedly divided into smaller periods without any limit, or is there a shortest interval of time? We don’t know the answers. There is much we do not know about physical reality: is the universe finite or infinite? Are space and time arbitrarily divisible? Does our number system represent physical space and time? [TM215 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘All Numbers Great and Small’
Kalman Filters: from the Moon to the Motorway
Published July 1, 2021 Irish Times ClosedTags: Algorithms
Before too long, we will be relieved of the burden of long-distance driving. Given the desired destination and access to a mapping system, electronic algorithms will select the best route and control the autonomous vehicle, constantly monitoring and adjusting its direction and speed of travel. The origins of the methods used for autonomous navigation lie in the early 1960s, when the space race triggered by the Russian launch of Sputnik I was raging [TM214 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Kalman Filters: from the Moon to the Motorway’
From a hilltop, the horizon lies below the horizontal level at an angle called the “dip”. Around AD 1020, the brilliant Persian scholar al-Biruni used a measurement of the dip, from a mountain of known height, to get an accurate estimate of the size of the Earth. It is claimed that his estimate was within 1% of the true value but, since he was not aware of atmospheric refraction and made no allowance for it, this high precision must have been fortuitous [TM213 or search for “thatsmaths” at irishtimes.com].
Snowdonia photographed from the Ben of Howth, 12 January 2021. Photo: Niall O’Carroll (Instagram).
The Simple Arithmetic Triangle is full of Surprises
Published June 3, 2021 Irish Times ClosedTags: Arithmetic, Number Theory
Pascal’s triangle is one of the most famous of all mathematical diagrams, simple to construct and yet rich in mathematical patterns. These can be found by a web search, but their discovery by study of the diagram is vastly more satisfying, and there is always a chance of finding something never seen before [TM212 or search for “thatsmaths” at irishtimes.com].
Pascal’s triangle as found in Zhu Shiji’s treatise The Precious Mirror of the Four Elements (1303).
Continue reading ‘The Simple Arithmetic Triangle is full of Surprises’
A truncated octahedron within the coronavirus [image from Cosico et al, 2020].
Improving Weather Forecasts by Reducing Precision
Published May 6, 2021 Irish Times ClosedTags: Numerical Weather Prediction
Weather forecasting relies on supercomputers, used to solve the mathematical equations that describe atmospheric flow. The accuracy of the forecasts is constrained by available computing power. Processor speeds have not increased much in recent years and speed-ups are achieved by running many processes in parallel. Energy costs have risen rapidly: there is a multimillion Euro annual power bill to run a supercomputer, which may consume something like 10 megawatts [TM210 or search for “thatsmaths” at irishtimes.com].
The characteristic butterfly pattern for solutions of Lorenz’s equations [Image credit: source unknown].
Entropy and the Relentless Drift from Order to Chaos
Published April 15, 2021 Irish Times ClosedTags: History, Physics
In a famous lecture in 1959, scientist and author C P Snow spoke of a gulf of comprehension between science and the humanities, which had become split into “two cultures”. Many people in each group had a lack of appreciation of the concerns of the other group, causing grave misunderstandings and making the world’s problems more difficult to solve. Snow compared ignorance of the Second Law of Thermodynamics to ignorance of Shakespeare [TM209 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Entropy and the Relentless Drift from Order to Chaos’
Queueing system with several queues, one for each serving point [Wikimedia Commons].
Queueing is a bore and waiting to be served is one of life’s unavoidable irritants. Whether we are hanging onto a phone, waiting for response from a web server or seeking a medical procedure, we have little choice but to join the queue and wait. It may surprise readers that there is a well-developed mathematical theory of queues. It covers several stages of the process, from patterns of arrival, through moving gradually towards the front, being served and departing [TM207 or search for “thatsmaths” at irishtimes.com].
Goldbach’s Conjecture: if it’s Unprovable, it must be True
Published March 4, 2021 Irish Times ClosedTags: Euler, Logic, Number Theory
Image © easycalculation.com
The starting point for rigorous reasoning in maths is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. The Greek mathematician Thales is credited with introducing the axiomatic method, in which each statement is deduced either from axioms or from previously proven statements, using the laws of logic. The axiomatic method has dominated mathematics ever since [TM206 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Goldbach’s Conjecture: if it’s Unprovable, it must be True’
Machine Learning and Climate Change Prediction
Published February 18, 2021 Irish Times ClosedTags: Climate Modelling
Current climate prediction models are markedly defective, even in reproducing the changes that have already occurred. Given the great importance of climate change, we must identify the causes of model errors and reduce the uncertainty of climate predictions [TM205 or search for “thatsmaths” at irishtimes.com].
Schematic diagram of some key physical processes in the climate system.
Continue reading ‘Machine Learning and Climate Change Prediction’
Complexity: are easily-checked problems also easily solved?
Published February 4, 2021 Irish Times ClosedTags: Algorithms, Computer Science
From the name of the Persian polymath Al Khwarizmi, who flourished in the early ninth century, comes the term algorithm. An algorithm is a set of simple steps that lead to the solution of a problem. An everyday example is a baking recipe, with instructions on what to do with ingredients (input) to produce a cake (output). For a computer algorithm, the inputs are the known numerical quantities and the output is the required solution [TM204 or search for “thatsmaths” at irishtimes.com].
Al Khwarizmi, Persian polymath (c. 780 – 850) [image, courtesy of Prof. Irfan Shahid].
Continue reading ‘Complexity: are easily-checked problems also easily solved?’
Euler: a mathematician without equal and an overall nice guy
Published January 21, 2021 Irish Times ClosedTags: Euler
Mathematicians are an odd bunch. Isaac Newton was decidedly unpleasant, secretive and resentful while Carl Friedrich Gauss, according to several biographies, was cold and austere, more likely to criticize than to praise. It is frequently claimed that a disproportionate number of mathematicians exhibit signs of autism and have significant difficulties with social interaction and everyday communication [TM203 or search for “thatsmaths” at irishtimes.com].
It is true that some of the greatest fit this stereotype, but the incomparable Leonhard Euler is a refreshing counter-example. He was described by his contemporaries as a generous man, kind and loving to his 13 children and maintaining his good-natured disposition even after he became completely blind. He is comforting proof that a neurotic personality is not essential for mathematical prowess.
Continue reading ‘Euler: a mathematician without equal and an overall nice guy’
We are living at the bottom of an ocean
Published January 7, 2021 Irish Times ClosedTags: Geophysics
Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides have been known for more than two thousand years, the discovery of tides in the atmosphere had to await the invention of the barometer [TM202 or search for “thatsmaths” at irishtimes.com].
Arrangements and Derangements
Published December 24, 2020 Irish Times ClosedTags: Combinatorics, Number Theory
Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer — about 37% whatever the number of students — emerges from the theory of derangements.
On what Weekday is Christmas? Use the Doomsday Rule
Published December 17, 2020 Irish Times ClosedTags: Algorithms
An old nursery rhyme begins “Monday’s child is fair of face / Tuesday’s child is full of grace”. Perhaps character and personality were determined by the weekday of birth. More likely, the rhyme was to help children learn the days of the week. But how can we determine the day on which we were born without the aid of computers or calendars? Is there an algorithm – a recipe or rule – giving the answer? [TM201 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘On what Weekday is Christmas? Use the Doomsday Rule’
Decorating Christmas Trees with the Four Colour Theorem
Published December 3, 2020 Irish Times ClosedTags: Geometry, Topology
When decorating our Christmas trees, we aim to achieve an aesthetic balance. Let’s suppose that there is a plenitude of baubles, but that their colour range is limited. We could cover the tree with bright shiny balls, but to have two baubles of the same colour touching might be considered garish. How many colours are required to avoid such a catastrophe? [TM200 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Decorating Christmas Trees with the Four Colour Theorem’
Ireland’s Mapping Grid in Harmony with GPS
Published November 19, 2020 Irish Times ClosedTags: Geophysics, Maps, Spherical Trigonometry
The earthly globe is spherical; more precisely, it is an oblate spheroid, like a ball slightly flattened at the poles. More precisely still, it is a triaxial ellipsoid that closely approximates a “geoid”, a surface of constant gravitational potential [TM199 or search for “thatsmaths” at irishtimes.com].
Transverse Mercator projection with central meridian at Greenwich.
Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’
Weather Forecasts get Better and Better
Published November 5, 2020 Irish Times ClosedTags: Geophysics, Numerical Weather Prediction
Weather forecasts are getting better. Fifty years ago, predictions beyond one day ahead were of dubious utility. Now, forecasts out to a week ahead are generally reliable [TM198 or search for “thatsmaths” at irishtimes.com].
Anomaly correlation of ECMWF 500 hPa height forecasts over three decades [Image from ECMWF].
Terence Tao to deliver the Hamilton Lecture
Published October 15, 2020 Irish Times ClosedTags: Hamilton
Pick a number; if it is even, divide it by 2; if odd, triple it and add 1. Now repeat the process, each time halving or else tripling and adding 1. Here is a surprise: no matter what number you pick, you will eventually arrive at 1. Let’s try 6: it is even, so we halve it to get 3, which is odd so we triple and add 1 to get 10. Thereafter, we have 5, 16, 8, 4, 2 and 1. From then on, the value cycles from 1 to 4 to 2 and back to 1 again, forever. Numerical checks have shown that all numbers up to one hundred million million million reach the 1–4–2–1 cycle [TM197 or search for “thatsmaths” at irishtimes.com].
Fields Medalist Professor Terence Tao.
Continue reading ‘Terence Tao to deliver the Hamilton Lecture’
Mathematics and the Nature of Physical Reality
Published October 1, 2020 Irish Times ClosedTags: Logic, Philosophy
Applied mathematics is the use of maths to address questions and solve problems outside maths itself. Counting money, designing rockets and vaccines, analysing internet traffic and predicting the weather all involve maths. But why does this work? Why is maths so successful in describing physical reality? How is it that the world can be understood mathematically? [TM196, or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Mathematics and the Nature of Physical Reality’
Will mathematicians be replaced by computers?
Published September 17, 2020 Irish Times ClosedTags: Computer Science
There are ongoing rapid advances in the power and versatility of AI or artificial intelligence. Computers are now producing results in several fields that are far beyond human capability. The trend is unstoppable, and is having profound effects in many areas of our lives. Will mathematicians be replaced by computers? [TM195 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Will mathematicians be replaced by computers?’
One year ago, there were just two centibillionaires, Jeff Bezos and Bill Gates. Recently, Facebook’s Mark Zuckerberg has joined the Amazon and Microsoft founders. Elon Musk, CEO of Tesla and SpaceX, is tipped to be next to join this exclusive club [TM194 or search for “thatsmaths” at irishtimes.com].
ThatsMaths 
