Most of us think of time as something that divides neatly into seconds, minutes and hours, in a way that’s as regular and predictable at the farthest reaches of the cosmos as it is in our kitchens. But scientists and philosophers have discovered that time has some weird tricks up its sleeve. This week we’re talking about twins who grow older at different rates, broken vases that jump off the floor to reassemble themselves on the bench, and why quantum physicists are learning to do without time altogether.

In July 1656, the young philosopher Baruch Spinoza was cast out of his Jewish community for "abominable heresies". We don't know what those crimes were, but we do know that Spinoza has remained a polarising figure within Judaism ever since.

Insect farming, we’re told by its proponents, is the next big thing in edible protein production, and it may just save the environment. But an insect “farm” is more like a manufacturing plant, where tiny organisms are frozen, boiled, baked, crushed or shredded alive in their billions. What is the moral status of these living things? Can we be sure they’re not sentient beings, capable of experiencing pain and suffering? And if we can’t be sure, how should we treat them?

Today, market capitalism is so deeply woven into the fabric of everyday existence that it seems as natural and inevitable as the movement of the planets. But in fact, there was a moment in the early 20th century when an alternative economic philosophy – one of planned economies oriented toward community wellbeing – gave the free market model a run for its money. What happened, and how might things have been different?

Who is responsible for structural injustice? The answer is “practically everybody” - but that can be just another way of saying “effectively nobody”. So what responsibility do individuals bear for structural injustice? And how can this responsibility be acted upon, without falling into practices of blaming and shaming?

Why do women join white nationalist and other far-right movements? Misogyny is rampant on the alt-right, along with the notion that women's primary role is to be wives and child-bearers. But the liberal centre can be an ambivalent place for women too. Feminism was founded on the ideal of equality, and on the belief that women should be treated as individuals rather than undifferentiated members of a subordinate class. But have these liberal humanist ideals of of equality and individual autonomy outgrown their usefulness?

Friedrich Nietzsche engaged closely with Christian themes and concepts, re-casting them for a secular age. One of these was transfiguration, the strange alchemical process by which human brokenness and misfortune can be turned into a kind of redemption. For Nietzsche, this was an aesthetic process, and it made an art form of philosophy.

Public trust in experts is on the wane. And when we consider that a key role of experts is the assessment and management of risk, this mistrust becomes worrying, given that life in an industrialised technology-driven world keeps getting riskier by the day. How should experts communicate risk? and what kind of trust should we place in them?

We all use numbers every day of our lives, and most of us fail to appreciate how mysterious they are. What exactly is a number? You can't trip over the number 4, it has no physical properties, so in what sense can it be said to exist? If it's just a symbolic representation, then why are numbers and other mathematical objects so effective in the real world - in solving scientific problems, in helping cicadas to evade predators, and so on?

It's strange to think that in a supposedly egalitarian democracy like Australia, we could have a misogyny problem. But the never-ending toll of intimate partner violence, sexual assault and casual workplace sexism confirms it, as does the growing "men's rights" backlash against any attempt to foreground the problem. What light can philosophy - a notoriously male dominated profession - throw on the issue?