Mathematical model shows how the Nazis could have won WWII's Battle of Britain

With just a few strategical tweaks, the Nazis could have won one of World War II's most decisive battles.

Mathematical model shows how the Nazis could have won WWII's Battle of Britain
Photo: Heinrich Hoffmann/ullstein bild via Getty Images
  • The Battle of Britain is widely recognized as one of the most significant battles that occurred during World War II. It marked the first major victory of the Allied forces and shifted the tide of the war.
  • Historians, however, have long debated the deciding factor in the British victory and German defeat.
  • A new mathematical model took into account numerous alternative tactics that the German's could have made and found that just two tweaks stood between them and victory over Britain.


Soon after the Nazis took control of France in June 1940 they began a military campaign against Britain. For three months, the Luftwaffe bombed targets in Britain, countered by the Royal Air Force (RAF). Their targets were sporadic: First, the Luftwaffe attacked ports and shipping centers, then RAF bases, then strategic infrastructure, and finally, civilians and politically significant sites. This military campaign was known as the Battle of Britain, which included the series of high-intensity night bombings known as the Blitz.

Defeating the RAF was crucial before the German army could launch a land invasion of Britain, but ultimately, the military campaign became too costly for the German forces to sustain. The planned invasion was called off, and the campaign against Britain shifted its focus to blockading the island nation's access to the sea. This would become the German's first major defeat in the war and form a crucial turning point that would define its remainder.

In part, the British victory was won by the German's lack of preparation. Hitler never expected to need to invade Britain; after France fell, he expected Britain would recognize "her hopeless military situation" and agree to the favorable terms of surrender he had put forth. Historians have long debated what the Luftwaffe could have accomplished had the Germans developed a more comprehensive strategy.

Two strategic blunders

Now, historians and mathematicians from York St. John University have collaborated to produce a statistical model (docx download) capable of calculating what the likely outcomes of the Battle of Britain would have been had the circumstances been different.

Would the German war effort have fared better had they not bombed Britain at all? What if Hitler had begun his bombing campaign earlier, even by just a few weeks? What if they had focused their targets on RAF airfields for the entire course of the battle? Using a statistical technique called weighted bootstrapping, the researchers studied these and other alternatives.

"The weighted bootstrap technique allowed us to model alternative campaigns in which the Luftwaffe prolongs or contracts the different phases of the battle and varies its targets," said co-author Dr. Jaime Wood in a statement. Based on the different strategic decisions that the German forces could have made, the researchers' model enabled them to predict the likelihood that the events of a given day of fighting would or would not occur.

"The Luftwaffe would only have been able to make the necessary bases in France available to launch an air attack on Britain in June at the earliest, so our alternative campaign brings forward the air campaign by three weeks," continued Wood. "We tested the impact of this and the other counterfactuals by varying the probabilities with which we choose individual days."

Ultimately, two strategic tweaks shifted the odds significantly towards the Germans' favor. Had the German forces started their campaign earlier in the year and had they consistently targeted RAF airfields, an Allied victory would have been extremely unlikely.

Say the odds of a British victory in the real-world Battle of Britain stood at 50-50 (there's no real way of knowing what the actual odds are, so we'll just have to select an arbitrary figure). If this were the case, changing the start date of the campaign and focusing only on airfields would have reduced British chances at victory to just 10 percent. Even if a British victory stood at 98 percent, these changes would have cut them down to just 34 percent.

A tool for understanding history

This technique, said co-author Niall Mackay, "demonstrates just how finely-balanced the outcomes of some of the biggest moments of history were. Even when we use the actual days' events of the battle, make a small change of timing or emphasis to the arrangement of those days and things might have turned out very differently."

The researchers also claimed that their technique could be applied to other uncertain historical events. "Weighted bootstrapping can provide a natural and intuitive tool for historians to investigate unrealized possibilities, informing historical controversies and debates," said Mackay.

Using this technique, researchers can evaluate other what-ifs and gain insight into how differently influential events could have turned out if only the slightest things had changed. For now, at least, we can all be thankful that Hitler underestimated Britain's grit.

This is what aliens would 'hear' if they flew by Earth

A Mercury-bound spacecraft's noisy flyby of our home planet.

Image source: sdecoret on Shutterstock/ESA/Big Think
Surprising Science
  • There is no sound in space, but if there was, this is what it might sound like passing by Earth.
  • A spacecraft bound for Mercury recorded data while swinging around our planet, and that data was converted into sound.
  • Yes, in space no one can hear you scream, but this is still some chill stuff.

First off, let's be clear what we mean by "hear" here. (Here, here!)

Sound, as we know it, requires air. What our ears capture is actually oscillating waves of fluctuating air pressure. Cilia, fibers in our ears, respond to these fluctuations by firing off corresponding clusters of tones at different pitches to our brains. This is what we perceive as sound.

All of which is to say, sound requires air, and space is notoriously void of that. So, in terms of human-perceivable sound, it's silent out there. Nonetheless, there can be cyclical events in space — such as oscillating values in streams of captured data — that can be mapped to pitches, and thus made audible.

BepiColombo

Image source: European Space Agency

The European Space Agency's BepiColombo spacecraft took off from Kourou, French Guyana on October 20, 2019, on its way to Mercury. To reduce its speed for the proper trajectory to Mercury, BepiColombo executed a "gravity-assist flyby," slinging itself around the Earth before leaving home. Over the course of its 34-minute flyby, its two data recorders captured five data sets that Italy's National Institute for Astrophysics (INAF) enhanced and converted into sound waves.

Into and out of Earth's shadow

In April, BepiColombo began its closest approach to Earth, ranging from 256,393 kilometers (159,315 miles) to 129,488 kilometers (80,460 miles) away. The audio above starts as BepiColombo begins to sneak into the Earth's shadow facing away from the sun.

The data was captured by BepiColombo's Italian Spring Accelerometer (ISA) instrument. Says Carmelo Magnafico of the ISA team, "When the spacecraft enters the shadow and the force of the Sun disappears, we can hear a slight vibration. The solar panels, previously flexed by the Sun, then find a new balance. Upon exiting the shadow, we can hear the effect again."

In addition to making for some cool sounds, the phenomenon allowed the ISA team to confirm just how sensitive their instrument is. "This is an extraordinary situation," says Carmelo. "Since we started the cruise, we have only been in direct sunshine, so we did not have the possibility to check effectively whether our instrument is measuring the variations of the force of the sunlight."

When the craft arrives at Mercury, the ISA will be tasked with studying the planets gravity.

Magentosphere melody

The second clip is derived from data captured by BepiColombo's MPO-MAG magnetometer, AKA MERMAG, as the craft traveled through Earth's magnetosphere, the area surrounding the planet that's determined by the its magnetic field.

BepiColombo eventually entered the hellish mangentosheath, the region battered by cosmic plasma from the sun before the craft passed into the relatively peaceful magentopause that marks the transition between the magnetosphere and Earth's own magnetic field.

MERMAG will map Mercury's magnetosphere, as well as the magnetic state of the planet's interior. As a secondary objective, it will assess the interaction of the solar wind, Mercury's magnetic field, and the planet, analyzing the dynamics of the magnetosphere and its interaction with Mercury.

Recording session over, BepiColombo is now slipping through space silently with its arrival at Mercury planned for 2025.

Study helps explain why motivation to learn declines with age

Research suggests that aging affects a brain circuit critical for learning and decision-making.

Photo by Reinhart Julian on Unsplash
Mind & Brain

As people age, they often lose their motivation to learn new things or engage in everyday activities. In a study of mice, MIT neuroscientists have now identified a brain circuit that is critical for maintaining this kind of motivation.

Keep reading Show less

New brain scan analysis tool can detect early signs of dementia

Researchers develop the first objective tool for assessing the onset of cognitive decline through the measurement of white spots in the brain.

Credit: Gorodenkoff/Shutterstock
Mind & Brain
  • MRI brain scans may show white spots that scientists believe are linked to cognitive decline.
  • Experts have had no objective means of counting and measuring these lesions.
  • A new tool counts white spots and also cleverly measures their volumes.
Keep reading Show less
Strange Maps

End gerrymandering? Here’s a radical solution

Why not just divide the United States in slices of equal population?

Scroll down to load more…
Quantcast