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Athabasca University

Mathematics Applied

How a Mathematical Model Solved the Mystery of an Underground Subway Fire

A small fire was detected beneath a wooden stairwell in the Kings Cross Underground Station in London. Fire safety staff were alerted and thought it could be easily contained. However, within minutes, it erupted into a raging inferno which ultimately killed 31 people and injured dozens more. Arson investigators were able to pinpoint the cause of the fire but were puzzled because the dynamics of the blaze contravened all known laws of flame spread. It would take a mathematical model, state-of-the-art computer technology and experts in the field of fluid dynamics to explain why it developed into such a deadly inferno.

See “Flashover"
(Published on Mar 24, 2016 by FilmRise)

Can Mathematical Models Predict Climate Change Accurately?

The short answer is: That will depend on the mathematical model chosen, the relevance of its parameters (explanatory variables) and the accuracy of the data used in the prediction.

Lord Christopher Monckton, Third Viscount Monckton of Brenchley and Chief Policy Advisor of the Science and Public Policy Institute, has challenged the model currently accepted for such predictions that was proposed by the United Nations Intergovernmental Panel on Climate Change (IPCC).

Monckton’s keynote presentation on March 24, 2017 at the 12th International Conference on Climate Change (ICCC), hosted by The Heartland Institute in Washington, DC, justifies and details (23:52 – 48:00)  another possible model involving the parameter “time,” in picoseconds, which was not used in previous scientific studies on the environment.

As might be expected, the complex nature of global climate changes necessitates an equally sophisticated, scientifically-based mathematical model which, at this juncture in time, includes:

  • optical physics equations (involving CO2 radioactive forcing and absorption bands),
  • graphs of estimated global mean surface temperatures dating back 810,000 years using measures of atmospheric carbon trapped in ice cores taken from the Antarctica,
  • the asymptotic behavior of how temperature responds to the feedback sum factor in the climate model,
  • a commentary on the large statistical variances of temperature feedbacks from a number of different climate change models,
  • a deeper look into the subject of Network Analysis and Feedback Amplifier Design ……. because the mathematics behind the feedback in all dynamical systems, including climate, is derived from electronic circuitry,
  • the conclusions of an electronics engineer who built an electronic feedback circuit to test the validity of Monckton’s climate change model, and finally
  • what the model implies in terms of the “social cost of carbon.”

See “END OF THE SCARE - Lord Christopher Monckton
(published on September 1, 2017 by the Oppenheimer Ranch Project)
Politics aside, view this talk as a mathematical argument against the prevailing conjectures on climate change – in particular, global warming. Valid mathematical proofs, as was pointed out by Lord Monckton during his lecture, have no political stripes.

Research Which Modifies the Social and Scientific Narrative on Global Climate Change
Watch One Man’s Discovery Sinks Major Climate Change Study
(published on November 15, 2018 by Bill Whittle)

"Nicholas Lewis, who blogs at Climate Etc. ( questioned the data in a major study claiming oceans are warming much fast than previously thought. He was right, and the journal Nature had to admit it. Bill Whittle Now talks about how politics has ruined science."

(There is an anecdotal aside not associated with Climate Science between 1:39 – 3:23 minutes.)

"For those of you who are interested in learning more about the dynamics of weather and climate, check out our geography course: GEOG 365 Atmosphere Weather and Climate"

ARCTIC ICE EBB and FLOW: the Science and Mathematics of Observable Climate Change

Professor Willie Soon, Physicist at the Harvard-Smithsonian Center for Astrophysics, poses the question:  "Is Human Activity Primarily Responsible for Global Climate Change?"

For his response, watch his lecture presented at the Heartland Institute 12th International Conference on Climate Change (ICCC) on March 23, 2017, Washington D.C. In it, he details the independent research done by him, Ronan Connolly and Michael Connolly on Arctic Sea Ice History. Dr. Soon claims that this research was not funded by any local, national or international interest group.

Arctic Sea Ice History - Solar Cycles - The Sun Drives Climate Not Man(published August 26, 2017 by the Oppenheimer Ranch Project)

Research Which Modifies the Scientific Narrative on Arctic Sea Ice
Check out the article Wintertime Arctic Sea Ice Growth Slows Long-term Decline
(published on December 6, 2018 by NASA)

The Mathematics of Optical Reflections

Quite a Spectacle (published on July 18, 2016 by Filmrise)

“Police in Canada received a chilling 911 call from a woman who was just attacked in her apartment, but by the time they arrived she was dead. Little evidence remained at the scene, except for a pair of eyeglasses and a shoeprint in a squished tomato. With the help of Canada's only forensic optometrist, police put away a killer who is larger than life.”

Knowledge of the mathematics of geometrical optics helped solve this case.

A New Modeling Challenge : an intricate blend of geography, oceanography, meteorology, physics and mathematics

Excessive wind speeds, inordinately high temperatures of the ocean waters, rotation of the earth, no significant wind shear (cross winds), low atmospheric pressure, the path of the storm, and the geography of the U-shaped coastline all colluded together to make up the intensity of the strongest storm surge to hit land in recorded history. Meteorologists tracking the Pacific storm and a disbelieving public could not have predicted the intensity of the tropical depression turned killer typhoon, Haiyan, as it plowed into the Philippines’ provincial capital, Tacloban, that fateful November day in 2013. The typhoon’s penultimate, 20-foot, storm surge went off the charts with sustained wind speeds of 200 mph as it met the coastline. It was classified as an 8.08 (170 Knots or 195 mi/hr wind speed with gusts up to 240 mi/hr) storm on the Dvorak scale, a number which exceeded the scale’s maximum value of 8.

With world-wide climate changes and rising sea temperatures and levels, scientists and mathematicians are challenged to create a predictive model of tropical storm surges which can help us prepare for future monster storms so as to save lives and create more protective landscapes along the coastal waters of the planet.

For a scientific account and very human story of this storm, see:  One of the Deadliest Typhoons published by Geographic TV on January 20, 2017.

The Illusion of Certainty: Risk, Probability and Chance

(published by the World Science Festival on January 7, 2015)

Is our intuition or extra sensory perception a reasonably reliable source for decision making? How well do our “gut feelings” measure up to the cold reality of factual information? Do our innate, mental patterns of processing information emulate statistical Bayesian processes?

Find out the opinions of a panel of five academic experts who regularly grapple with the complexities of statistical information and how to interpret data properly, who critically examine how decisions are made in the public arenas of medicine and law, and who analyze the neurological, cognitive processes of the human mind.

MODERATOR:    Marcus du Sautoy, Professor of Mathematics at the University of Oxford, England


Gerd Gigerenzer, Director of the Max Plank Institute for Human Development in Berlin, Germany

Leonard Mlodinow, physicist and author of a number of books including The Drunkard’s Walk: how randomness rules our lives, which has been described as a readable course in randomness and statistics

Josh Tenenbaum, Professor of Computational Cognitive Science in the Department of Brain and Cognitive Sciences at MIT (Massachusetts Institute of Technology)

Amir Aczel, a mathematician and science writer, one of whose books is entitled, Chance, and is described by the New York Times as an edifying and amusing  guide to the basic elements of probability theory.

Mathematics and Forensic Science

Since the time of  Joseph Bell (1837 – 1911), forensic science began to be instrumental in the solving of numerous crimes, including murder cases. Dr. Bell, both a lecturer at the medical school of the University of Edinburgh and a surgeon at the Royal Infirmary of Edinburgh, is considered to be a pioneer in the subject of forensic pathology. Also of interest is that Arthur Conan Doyle, creator of the Sherlock Holmes series of detective stores, had worked for Bell as a clerk during his student days. It is widely believed that Dr. Bell was the prototype for Doyle’s  famous fictional sleuth.

Today, over a century later, finger prints, blood spatter patterns, ballistics, residual drug levels in body tissues, and DNA are most often the techniques which collude to glue together a crime scene into an indictable offense with the sole purpose of bringing the perpetrator(s) to justice.

However, have you ever heard of using mathematics and astronomy in a court room to tear apart a killer’s seemly rock solid alibi at the time of the murder? Check out the following true crime story:  Solved: Truth in Shadows   to uncover the hidden reality behind a murder mystery where there were no eye witnesses except the killer ....... and the sun.

For six years a serial killer prowled the streets of New York City shooting his victims with a zip gun but eluding capture. His pattern of attacks followed the Zodiac calendar. In the end, a group of New York City Police detectives were able to track him down by using forensic astronomy, hand writing analysis, DNA samples, finger print images, tool mark analysis and a World War II code breaker. Watch the Forensic Files season 8 documentary, Sign of the Zodiac, to find out how.

A woman was shot to death while walking her dogs in a relatively remote wooded area. Police initially suspected that the killing had been an accident. There were no witnesses, no weapon, no bullet, no DNA and the dogs had all run home. Find out how the “accident” was re-classified to a “homicide,” which ultimately led to the conviction of the actual murderer through applying the Laws of Physics to an experiment with a slingshot and some marbles.

Watch the Forensic Files season 9 documentary, Hunter or Hunted?
(published on May 30, 2014 by FilmRise)

Fuzzy Sets and Systems

by Peter Crickmore

This is an introduction to fuzzy sets, fuzzy functions, fuzzy arithmetic, and fuzzy logic with fuzzy applications towards environmental concerns. Moreover, these concepts and ideas lead to Possibility Theory instead of Probability Theory and how they are related.

For those who think this is a piece of someone's fuzzy imagination, take a look and judge for yourself.

Experimental Design

by Peter Crickmore

A presentation on how to design field experiments to yield the most information from the fewest runs. Prediction variances and confidence intervals come into play in the analysis of the experiments.

Presentation on Significance and Confidence

by Peter Crickmore

A discussion on confidence intervals and what is considered to be 'significant' in the oil patch.

Updated December 07 2018 by Student & Academic Services

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