Tag Archives: Mathematics

Logic gates and neurons

At their most abstract level, the logic gates that make up a digital computer are machines for destroying information. That might not be immediately apparent, but take a look at this (image from Wikipedia):

AND symbol

Two inputs; one output. At every operation, one bit of information is lost forever in an irreversible process. Continue reading

Happy birthday to me!

happybirthdayToday is my birthday, and at this age, I am three times as old as my elder son, and four times the age of my younger. My elder son is four years older than his younger brother. Can you tell how old I am? Continue reading

Newton vs Einstein

newtonMy all-time favourite scientist was Isaac Newton. Newton was very clever. In fact he was a genius. He discovered lots of interesting and important things. Unfortunately, most of them turned out to be wrong. That doesn’t make him a bad scientist, of course. Finding wrong answers is an important way that science makes progress.

One of the reasons we know that Newton was a genius is that it took a very long time before anyone proved that he was wrong. Around 200 years, in fact. Then Albert Einstein (my second favourite scientist) showed that Newton was wrong, by coming up with some better explanations. Continue reading

Alien mathematics class

Indulge me in a little thought experiment. Imagine a rocky planet a long way from here, orbiting a star rather similar to our own sun, at just the right distance for water to remain liquid. Let this planet have an atmosphere containing all the elements needed for interesting biochemistry to take place – carbon, hydrogen, oxygen, nitrogen, phosphorus, sulphur and so on. Now imagine that on this planet lives a single lifeform – one composed of trillions of tiny plant-like organisms amassed in one huge layer that covers the entire planet. This lifeform quietly converts the sun’s energy into food, and while it does so, it thinks. What kinds of thoughts might it ponder? Continue reading

Counting on my fingers

The iPhone is perhaps the ultimate symbol of 21st-century technology. How peculiar then, that the Apple website gives its size in inches and its weight in ounces – units of measurement that the Victorians would have heartily approved of, over a century ago. How odd too, that in the United States, oil is measured in barrels, land in acres and temperature in Fahrenheit. Continue reading

Opinions, facts and theories

megaphoneWe start out in life without any knowledge, but it’s not long before we start forming simple opinions about the world we find ourselves in. We might call these preferences (I like milk). These probably change over time (I like beer) but they are inherently subjective and cannot be exposed to objective scrutiny (my daddy is better than yours), at least not in a meaningful way (no he isn’t.) We think of these preferences as conscious choices, but we are really just observing what we like and don’t like. Continue reading

An infinite number of monkeys with typewriters

This is how I plan to write my blog in future. I will keep this little guy in my basement and supply him with bananas until he produces an article I’m happy with. It’s a great method if you’re lazy but patient.

But how patient would I have to be? How long would it actually take? Continue reading

Physics, information, patterns, consciousness and God

thematrixLevel 1 of the universe is matter, energy, forces, space-time – the physical world. It follows rules, although precisely what those rules are and why they are like that, we aren’t yet certain. But we know enough about it to measure it and explain much of what it does.

The level 1 universe does something else too. It encodes information. Matter exists in different states, and the more physically-distinct states there are, the more information that can be encoded. For example, if an atom can exist in one of two energy states, then it encodes one binary bit of information (0 or 1). Information is not a subjective human thing. It’s an objective property of the physical universe and can be measured. The total amount of information encoded in the whole universe is mind-bogglingly vast. Continue reading

Perfect imperfect

I’m not a perfectionist. I never finish jobs properly. This is not laziness, but efficient time management. I never complete a task 100% perfectly. I stop at 90%, or sometimes 70%, then move on to the next job. That means I complete more jobs. Does this bother you? It shouldn’t. It’s not necessary to complete jobs perfectly. To prove this, I won’t even bother to finish this … Continue reading

Science, philosophy, and the Mountain of Ignorance

mountainofignoranceThere’s been a lot of debate online recently (like here and here) about whether philosophy is a waste of time. Here’s my metaphor for thinking about this question.

Imagine that ignorance is represented by a mountain. The mountain is big and in plain view of everyone. Even small children can see it clearly, and love to ask questions about it that their parents can’t answer. You know the kinds of questions I mean. Continue reading