Exploring the extremes

The exploration of extremes is one of the standard tools of the physicist. It exposes them to what lies beyond our intuitions; conditions not previously observed. Newton's assumption of instantaneous propagation of gravitational fields worked just fine in daily life, but it broke near massive objects. We can't go back to the moments of the early universe, but we can mimick its conditions by building a 27km long tunnel under Switzerland.

Reductio ad absurdum

Philosophers have been using the trick of using extremes for ages and we still use "reductio ad absurdum" to disprove our opponent's arguments by taking their premises and deducing something absurd from it.

He can't catch that bus, he'd need to fly!

Galileo famously disproved that "heavier objects fall faster than lighter ones" using a thought experiment. He considered two objects connected by a string. One object was heavier than the other one. Now, let's also assume that the heavier object would fall faster than the lighter one — what we'd like to disprove. Upon dropping the composite object, the heavier one would fall faster and start pulling on the lighter one, acting like a brake on the heavier object. The heavier object would therefore reach the ground slower than if it wasn't connected by the lighter object, but the composite object is even heavier than the singular heavy object. Reductio ad absurdum!

The magic wand number

Nobody can fly and there's no such thing as a magical wand — everybody knows that. But how do we know something, say a new technology, is actually impossible? Because we haven't seen it before? If we apply this reasoning to any new technology in the past, the argument breaks down. If everybody reasoned like that, the new thing would never get invented …

Nobody wants a car, because horses are great and we’re used to them and they can eat grass and there’s lots of grass all over the place. There’s no gasoline that people can buy. So … people are never going to get cars.

— People, end of 19th century

Electric cars are a fantasy because battery packs are really expensive and that’s just the way they’ll always be, because that’s the way they’ve been in the past. Historically, it has cost $600 per kWh and so … it’s not going to be much better in the future.

— People, not that long ago

First-principles reasoning and exploring the extremes is a more solid approach than thinking from analogy — what if the magic wand were real?

What are the material constituents of the batteries? What is the spot market value of the material constituents? Ok, It’s got cobalt, nickel, aluminum, carbon and some polymers for separation and a steel can. So break that down on a material basis. If we bought that on the London Metal Exchange, what would each of those things cost? Oh geez, it’s like $80 per kWh! So clearly, you just need to think of clever ways to take those materials and combine them into the shape of a battery cell and you can have batteries that are much — much — cheaper than anyone realises …

— Elon Musk, not that long ago