91av

ULTIMATELY, the jumbo shrimp tells us why we are doomed to never fully understand reality.

But let’s back up a bit first. We know we live in a universe where there are hard physical limits to what we can know. Light’s finite speed restricts our ability to see in time and space, quantum uncertainty our understanding of subatomic particles.

So what? Our largest telescopes look back to a few hundred million years after the big bang, while our sharpest microscopes can spy on individual photons escaping from atoms. The universe is as it is, and we work quite well within its limits. True, we can’t explain what happens at the big bang, or inside a black hole – but that’s just a matter of devising better theories of nature and ways to test them.

So to know more we need to compute better. Easier said than done. Were we able to simulate the fine-grained movements of all the universe’s matter, we might predict its evolution and fate. But with current computing power, that would take more time than the universe has to offer.

Computational power is a practical limitation we can blame for everything from unreliable weather forecasts to shoddy logistics: once you try to optimise an itinerary linking more than a few thousand destinations, it becomes impossible to compute. “There are so many parts to it it’s simply improbable that we can work it out,” says , an information scientist at the City University of New York.

But ultimately, that’s just a fig leaf for a mega-sized limitation. However powerful we make them, computers ultimately rely on human input to program them – and human thought is a glorious, uproarious, complex mess. Statements like “this statement is false”, hating someone yet loving them and yes, that small-yet-large jumbo shrimp, both compute and do not compute. “Language is an expression of the mind, and my mind and language is full of contradictions,” says Yanofsky.

Can’t compute

That flexibility allows us to think outside the box, while remaining firmly inside it. Because we are predicated on contradiction, we see contradiction everywhere. The defining feature of reality, however, is that it admits no contradiction. Take the way quantum objects apparently act as waves or as particles according to how we choose to measure them, a confusing duality physicist Richard Feynman called “the only mystery” of the quantum world. In all probability, the basic building blocks of reality are neither wave nor particle, but something else entirely. It’s just something that we lack the experience or cognitive ability to express.

Logic, and the mathematics that builds on it, is supposedly our way out: a cleaner, neutral language for a trained brain to describe in abstract terms what it cannot visualise. That’s all very well – until you encounter the logical limitations of mathematics itself.

These start with well-known injunctions such as never to divide a number by zero. Why not? Because if you do, you can begin to do things like . If maths is the language of a flawless universe, we can’t allow that – so we don’t. “If you want mathematics to continue without contradictions then you have to somehow restrict yourself,” says Yanofsky.

And sooner or later, we come to the end of the road. As Austrian mathematician Kurt Gödel showed in the 1930s, any system of logic containing the rules of arithmetic is bound to contain statements that can be neither proved nor disproved. It will remain “incomplete”, trapped in the same inconsistency as we are (see “An unknowable problem“). Gödel incompleteness is a mathematical expression of the logical-illogical statement “this statement is false”. The fundamental truth is there is no way for anything, be it a simple sentence, a system of logic or a human being, to express the full truth about itself (see “Knowledge: Why knowing thyself is the hardest thing“).

This problem of self-reference is endemic. Gödel’s contemporary Alan Turing showed that you cannot ask a computer program in advance whether it will run successfully. Quantum mechanics sprouts paradoxes because we are part of the universe we are trying to measure (see “Knowledge: Is information the only thing that exists?“).

So the sobering truth is that we can build the most powerful telescopes, microscopes and computers we want, but we will never overcome the limitations of our minds. Our perspective on reality will always be skewed because we – and the jumbo shrimp – are part of it.

This article appeared in print under the headline “How much can we ever know?”