Category: Mathematics

Domains of Conception
The Borders of Understanding My molecular biologist friend, Barry Bowman, brewed up this stimulating thought: One can understand much about nature without mathematics. Can one understand quantum mechanics only through its arcane mathematics? Can one not comprehend quantum physics other than through its mathematical expression? To explore the thought some agreement is needed on the…

Meaning from Data
Intelligence: Artificial vs. Real Here is the problem David Cope solved many years ago Given the enormous musical library of compositions left to us by the venerable Johann Sebastian Bach, can new compositions be manufactured as if his signature were upon them? As if they were long lost Bach musical manuscripts only recently discovered? Cope…

Exponential Growth
Living cells multiply. Their number grows exponentially. The more there are the faster they increase. An exponentially growing population has a doubling time: the time it takes for the population to double. Having a doubling time is a characteristic of exponential growth. In the time it takes each individual cell to divide into two cells,…

The Equation
An equation is a statement that says ‘this equals that’. It’s hard to imagine, from that raw and basic idea, that something called an equation could be of any use. Whether ‘this equals that’ or not seems a matter of little consequence! But, in fact, we know that to state what things are equal can…