that the number of odd rooms is not smaller than the number of even + odd rooms. Both sets have the same cardinality.
Figure 1
As an aside, there are sets with a different cardinality to the integers. Consider, for example, the set of infinite binary sequences; 0000000000…, 1111111111…, 0101010101… and so on. Cantor imagined laying these out in a vertical table, just as we did for our sets S and S/2, against the column of integers. Now imagine constructing a new binary sequence by changing all the digits in a diagonal line down the table; when there is a 1, swap it for a 0, and when there is a 0, swap it for a 1 (see Figure 1). The resulting sequence is not in the table; it can’t be the same as the sequence in the first row because the first digit has been flipped. It can’t be the same as the sequence in the second row because the second digit has been flipped, and so on. Every row will differ from the new sequence by at least one digit, claimed Cantor, because there are more infinite sequences of 1s and 0s than there are integers. A mathematician would say that the infinite set of binary sequences has a cardinality greater than the set of integers.
Infinity exists in mathematics, and as we have seen there are different sorts of infinity. We might ask whether there are infinities in the real world, and the answer is that we don’t know. The Universe may or may not be infinite in extent. The part of the Universe we can observe is certainly finite, and cosmologists refer to this as the Observable Universe. The most distant objects we can see are objects from which light has been able to travel during 13.8 billion years, which is the age of the Universe. You might be tempted to say that the Observable Universe is 27.6 billion light years across, but this is not correct because the Universe has been expanding throughout this time, and the objects have receded from us. Because we know how much the Universe has expanded, we can calculate the diameter of the Observable Universe today; it is just over 93 billion light years.
There are around 2 trillion galaxies in this observable sphere centred on the Earth, but this is very likely to be a small fraction of the entire Monkey Cage. Whether it is a finite subset of an infinite cage is an open question.
DEATH, WHERE IS THY PUDDING?
‘In many ways, Schrödinger’s Strawberry changed my life. Or death. Or whichever – it’s so hard to tell these days. All I know is the episode which featured that singular fruit gave me and my career a new lease of life. Or death. Oh god…’
Katy Brand, comedian
In the history of human thought, there are a few philosophical questions that become eternal.
Can we ever truly experience reality?
Why is there something rather than nothing?
When is a strawberry dead?
For some reason, neither Plato nor Nietzsche took time to consider the strawberry. Nietzsche’s madman ran into the town square declaring that God was dead, but made no mention of the strawberry – and what of the plum, peach and gooseberry?
It took Professor Cox to contemplate the strawberry.
In a rare moment when he was distracted from thinking about subatomic particles and Hawking radiation, Brian’s brain accidentally allowed a thought about strawberries on a level above muon and lepton.
Could it be that his jam was in a superposition?
Schrödinger’s Compote?
And if there is Schrödinger’s strawberry compote, does that also mean we should be investigating Planck’s raspberries and Heisenberg’s goji berries?
Should market gardeners be looking at their fruit at a quantum rather than molecular level?
We were discussing levitating frogs. Andre Geim is a rarity in the scientific world, being a winner of both the Nobel and Ignoble Prizes. His Nobel Prize in Physics was awarded for discovering a method to isolate a single layer of graphite atoms and thus create graphene, the thinnest and strongest material in the world. His frog levitation took place a decade before. Geim levitated frogs to demonstrate diamagnetism. Biologist and maggot expert Matthew Cobb explained the experiment. He told us it wasn’t really about the frog, though don’t tell that to the frog, they are very egotistical, especially the Poison Dart frog, which does not take criticism well. The experiment was about quantum mechanical effects; Geim also used water and ‘dead strawberries’.
Brian’s Vulcan ears pricked up like those of a German Shepherd. He was perplexed. ‘What qualifies a strawberry as being dead?’
It is here that the potential melancholy of jelly and the funereal possibilities of the trifle began.
What pathologist has the correct qualifications to declare a strawberry dead?
Animals are much easier than fruit to pronounce dead. The clues seem simpler: no heartbeat, no breathing, no eating, no movement. Even that may not offer certainty though.
Rana sylvatica is a species of wood frog (two frog mentions already, this should keep the frogs on side) that has ‘extreme freeze tolerance’. Species with this attribute can survive when two-thirds of their body water is frozen. Rana sylvatica also stops breathing and has no heartbeat for days at a time.
Life is notoriously hard to define. Every time you think you’ve come to a neat definition, some philosopher or other will pipe up, ‘ah, but isn’t that also the property of fire?’ Then, when you redefine, they’ll say, ‘ah, but isn’t that the property of crystals?’ Eventually, rather than define life, you want to take one.
Death must be easier to define.
Questions of life and death, whether on the scale of amoeba, strawberries or physicists demonstrates the complexity of living things and the difficulty of defining what it is to be alive.
For the physicist, the question becomes ‘how do you write the wave function of strawberry?’
According to the work of the French, Nobel Prize-winning physicist Louis De Broglie, it will have a wave length.
The definition of a dead strawberry became slippery. In the simplest terms, Professor Nick Lane stated that if it’s not continually harnessing energy to maintain being alive, it’s dead. The ability to harness energy seems to offer one of the most rewarding views of defining what is alive.
Professor Nick Lane: We need an enormous amount of energy to live… if you put a plastic bag over your head you’ll be dead in a minute and a half.
Brian:
