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As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.

How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.

Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.

Find out why the formula we use to work out conditional probabilities is true!

- We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.

There is intuitive time and there is physical time. Intuitive time is our own sense of time, which results from the rhythmic activity of our brains and body. I doubt it's a coincidence that one heartbeat of the average person is about a second long. It may even be that the duration of a second was based on the heart rate of some important individual (king, emperor, revered philosopher, etc). Virtually every animal, especially predators, must have an intuitive sense of time because a lung needs to be timed, a pursuit trajectory has to be timed in order to meet the prey in its trajectory. Our intuitive sense of time is also dependent upon memory. The charging predator has to remember what it felt and saw a split second prior to now in order make a correction in its trajectory. We are most aware of time when we remember past events. Because of this, we are seduced into thinking that time has an objective reality. It does not.

What we would call physical time is the time we think we are measuring with our clocks. But all we are really doing is substituting a more consistent device for our heart, our firing neurons, our memory, the movement of the sun's shadow on a sundial, the cycles of the moon, etc. All we are doing with clocks is establishing what we believe is a cyclical device that is highly consistent--a standard. And then we measure all other movements of matter and energy in space as a ratio of the object's distance traveled to the "distance" traveled by the clock, i.e., velocity. I say "distance" because many clocks we have developed have no moving parts.

But how did we establish a system for determining, to a high probability, that a particular device or process is highly consistent? There are at least two ways: By converting its cyclical output into a linear form that can be measured with a "yardstick"--a measuring device that is consistent and objective. A cyclical output can be fed into an electronic oscilloscope which would display it as a sign wave. Observation and measurement of many cycle lengths can establish its consistency. Another way is to make a large number of physically identical devices which, when operated, would be initially synchronized, then observed over many cycles and note taken of how much a-synchronicity develops among them. None of these processes are dependent upon a preconceived standard of time. In fact, what we have developed are highly consistent standards of movement to which all other movement are compared.