New number line

Could you invent a number system which has zero and pi as fundamental integers instead of zero and one?

What is the difference between 'identical' and 'indistinguishable'?

Here are some identical things:
• Fundamental particles of the same type (eg 2 electrons).
• Perfectly replicated DNA molecules
• A digital image (before it is printed or displayed on a screen)
• A poem  remembered accurately by 2 people.
• Two identical numbers

Here are some indistinguishable things (or are they?):
• Copies of the same book - or any mass-produced product.
• 'Identical' twins
• Peas in the same pod

Listen to the birds

We're all gonna die

Imagination will save us

I watched the brilliant Argentinean film La Antena last night. A picture like this appears briefly towards the end and inspired me to draw this - and make a series for this blog.

Problems with infinity

Considering all the difficult problems which the concept of infinity poses, Aristotle suggested separating the idea of ‘actual infinite’ from ‘potential infinite’.

If you add all the terms in the series: ‘a half plus a quarter plus an eighth plus a sixteenth … and so on’ you get closer and closer to One the more terms you add, but you never quite get there unless you have an ‘infinite number’ of terms.

But suppose we ban the idea of an actually infinite number and put in its place a very big (but real) number (L). Then, considered in this way as a sum of fractions, the number One would be ‘imperfect’ since it could never quite be really one! Of course, all the other natural numbers would be ‘tarnished’ in the same way.

How could this very big number L be defined?

Here are two suggestions for what L could be:

L₁ The total number of particles in the universe. (about 10⁸⁷)

L₂ The biggest number anyone has ever thought of. (apparently there are lots of ways to generate huge numbers, but at any given time, one of them would be the biggest).

If it was, L₂ this would be dependant on human (or perhaps computer) interaction – is this the first time that a mathematical quantity depends on human behaviour?

According to the Associated Press:

“If all Americans between 10 and 74 walked just half an hour a day instead of driving, they would cut the annual U.S. emissions of carbon dioxide, the chief greenhouse gas, by 64 million tons. That would save about 6.5 billion gallons of gasoline …and Americans would also shed more than 3 billion pounds (flesh) overall, according to these calculations.”