Why did Winston Churchill say "perverted science" in his Finest Hour speech?

I can't speak for sure, but I'm pretty confident he didn't mean using scientific advances for evil (as so many in this thread presume). He's referring to people performing evil actions and justifying them, or completely failing to recognize them as evil because it's "just science". For example; creating a genetically similar culture, experimenting on humans, performing abortions, eliminating persons who only drag a society down- all just part of the evolutionary process.

The strong survive, the weak fade away, the human race continues to advance. This is all "science" - that is "Nazi science". In reality, science has nothing to do with it. It's a perverted philosophy that claims science as its source - hence Churchill's term "perverted science". A philosophy still relevant in Western culture today.

Elements of "perverted science" that were in use, or being explored in the 1930s and 1940s included the following:

1) Poison gas, e.g. mustard gas, as used in World War I.
2) Poison gas, e.g. Cyklon B, as used in Nazi concentration camps.
3) "Medical experiments," on twins, and other types of people, conducted by "doctors" like Joseph Mengele, that were both horrifying in themselves, and also supported "skewed" Nazi theories of genetics.
4) Many people would consider nuclear weapons, researched by both the Allies and the Nazis, as "perverted science."
5) Then there was the "Sun gun", researched only by the Nazis, a space station to launch the sun's rays onto enemy cities, that fortunately never got off the drawing board.

Basically, the world wars featured a number of "horror weapons," (not to mention the horrors of conventional weapons) used mainly by the Germans.

There is nothing mysterious about this.

Churchill is comparing the previous "Dark Age" which was made possible by the techniques and knowledge of the medieval world, with what might have been possible in a "new Dark Age" guided by the light and understanding of modern science. He is not obliquely or covertly referring to any specific horror beyond what the human mind was capable of conceiving. He is also, of course, implying that the Nazis had demonstrated that they possessed minds with such a level of evil intent.

What Churchill is referring to were various German scientific inventions which confounded the British and at the time seemed miraculous and terrifying, at least to the military analysts that knew about them. Since Churchill was privy to secret briefings describing these technologies, so far as they were known, he had been exposed to these fears. His remark in his speech is a nod to the advanced developments of German scientists which were being put to military use.

Germany has been safely defeated now, so noone now gives these things a second thought anymore, but at the time there was a tremendous fear in the higher circles of government that the Germans might invent some critical new device that would turn the war in their favor. Every month new reports of some new German technology was coming from intelligence analysts and this "perverted science" Churchill found very threatening.

Two key examples of the technology are what we now know as "radar" and "proximity fuses". In history books you will read that the British invented radar, but this is completely false. The first radar system was Seektat, a German naval radar that used an amplification tube of a type completely unknown to the British. All they knew at the time was that the Germans could detect their ships at long ranges. This was a key factor in the Norway War. The British fleet could not stop the Germans from invading Norway in part because of long range radar detections. The basis for this technology was a special kind of vacuum tube developed by Manfred Von Ardenne, now known as a travelling wave tube. This type of radar amplifier was vastly more powerful than any amplifier the British ever had or would develop. In fact, even today, the most modern radars such as the SPY-1 still use this kind of tube which is exactly of Ardenne's design. We only gained access to this technology after the war was over.

Another technology was the proximity fuse. This is miniature radar which is fitted to the fuse of an artillery shell. It allows the shell to explode at exactly a certain height above the ground. It makes the shells much, much, much more deadly and effective. When the Germans started using these shells on the French it was terrifying. The German shells were simply vastly more lethal and destructive than the British and French could even imagine. Eventually they figured out the cause and made their own proximity fuses, but at the time it was occurring, it was mysterious and frightening. Even long after that in the 1950s, the American army considered proximity fuzes to be critical "top secret" technology.

Semaphore pointed out historical examples. I believe the context (thank you for providing the link) also helps. The following are all quotes from that same speech.

The disastrous military events which have happened during the past fortnight have not come to me with any sense of surprise.

The Admiralty had confidence at that time in their ability to prevent a mass invasion even though at that time the Germans had a magnificent battle fleet in the proportion of 10 to 16....

Now, the Navy have never pretended to be able to prevent raids by bodies of 5,000 or 10,000 men flung suddenly across and thrown ashore at several points on the coast some dark night or foggy morning.

Some people will ask why, then, was it that the British Navy was not able to prevent the movement of a large army from Germany into Norway across the Skagerrak?

Can we break Hitler's air weapon?

There remains, of course, the danger of bombing attacks, which will certainly be made very soon upon us by the bomber forces of the enemy. It is true that the German bomber force is superior in numbers to ours; but we have a very large bomber force also, which we shall use to strike at military targets in Germany without intermission.

In what way has our position worsened since the beginning of the war? It has worsened by the fact that the Germans have conquered a large part of the coast line of Western Europe, and many small countries have been overrun by them.

If Hitler can bring under his despotic control the industries of the countries he has conquered, this will add greatly to his already vast armament output.

We must not forget that from the moment when we declared war on the 3rd September it was always possible for Germany to turn all her Air Force upon this country, together with any other devices of invasion she might conceive, and that France could have done little or nothing to prevent her doing so.

Over and over again, Churchill addresses the losses they have suffered and the dangers they face from Germany's military might. These losses would not be so severe if German technology were not on par with that of the Allied powers.

What General Weygand called the Battle of France is over. I expect that the Battle of Britain is about to begin. Upon this battle depends the survival of Christian civilization.

Being caught in a terrible war, the enemy is evil (even if he also claims to be Christian) and any technology or science he uses is considered a perversion of that technology and science.

In the original speech, Churchill said "by the lights of a perverted science". He may perhaps have been speaking about Hitler's pure-bred Aryan superbeings, and the now discredited but then accepted science or pseudo-science of eugenics - the creation of an improved human race through select breeding of the finest specimens. The "lights" of this perverted science were the best and most able superbeings the Nazis might have been able to create.

I'd like to add some second-hand context to Paul Rowe's first-hand context.

England of the early 20th Century had a very different perspective about technology than we do today. Our most recent innovations have brought the public things like the Internet and ubiquitous cheap connectivity. Theirs had most recently brought mustard gas and automatic weaponry, resulting in the bloodiest war in human history. Before that was industrialization, which brought about great social disruption, along with pollution and unremitting toil and poverty to the masses, and was thus not viewed as an unalloyed good.

An exemplar of this attitude is the German movie Metropolis, which was a big deal in Europe in the late 20's. It depicted a dystopian future where an authoritarian society used machines reminiscent of high-tech mills to isolate and control people. Among the movie's fans was Joseph Goebbels (to the despair of the movie's creators).

Also, since this is Churchill and wartime England, we should mention the unofficial English national anthem, Jerusalem, with its reference to "dark satanic mills" and the duty of Englishmen to take up their weapons and fight for a better world. It was originally written by William Blake, and is thought to have been meant in part to show his disapproval of the effects of the relatively new Industrial Revolution. These words could not possibly have been far from Churchill's mind, as he'd been periodically singing them.