A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure�...

 The Increasing Chemical Complexity of the Cosmos

The ancient origins of stars, planets and life may be viewed as a sequence of emergent events, each of which added to the chemical complexity of the cosmos. Stars, which formed from the primordial hydrogen of the Big Bang, underwent nucleosynthesis to produce all the elements of the Periodic Table. Those elements were dispersed during supernova events and provided the raw materials for planets and all their mineralogical diversity. Chemical evolution on Earth (and perhaps countless other plan...

 Learning Strengths: Map Readers and Explorers

I recognize Map Readers because they often like to work independently, but they are most comfortable when they have specifi c instructions or procedures to follow. Th ey often take more time and work deliberately, showing all their steps on homework or taking detailed notes in class or during group work. Explorers are the students who want to skip the detailed instructions and jump right into fi guring things out by trial and error. Th ese students are not likely to use estimation, even when ...

 We Are Living in a Science Fictional Age

1) We’re living in a science fictional era, thanks to all the incredible technological and scientific discoveries we’ve made. (At the time, we were just starting to discover exoplanets and sequence the DNA of individual people.) In some sense, science fiction has “come true.” 2) This means science fiction is uniquely qualified to comment on the era we’re living in, and is the only pop culture that accurately reflects the world around us. 3) Meanwhile, science fiction itself has cl...

 An Eloquent Description of Science and Wonder

As I gathered information for this book, I was continually reminded of the reality that science, rooted as it is in the certainties of the physical world, is a process that necessarily unfolds over time. In school, science classes tend to work according to this linear model; there's a “beginning, middle, and end” to science investigations, no matter how hard teachers may fight the “cookbook” reductionism that threatens true scientific inquiry. Yet, in probing further, I came to unders...

 Nature Works in Increments

Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse's structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in a...

 Better to be a Perfected Ape than Degraded Adam

As for me ... I would much rather be a perfected ape than a degraded Adam. Yes, if it is shown to me that my humble ancestors were quadrupedal animals, arboreal herbivores, brothers or cousins of those who were also the ancestors of monkeys and apes, far from blushing in shame for my species because of its genealogy and parentage, I will be proud of all that evolution has accomplished, of the continuous improvement which takes us up to the highest order, of the successive triumphs that have m...

 Vonnegut on Fiction vs. Journalism - Noise and Melody

I am reminded now, as I think about news and fiction, of a demonstration of the difference between noise and melody which I saw and heard in a freshman physics lecture at Cornell University so long ago. (Freshman physics is invariably the most satisfying course offered by any American university.) The professor threw a narrow board, which was about the length of a bayonet, at the wall of the room, which was cinder block. "That's noise," he said. Then he picked up seven more boards, and he...

 Ontogeny Recapitulates Phylogeny

Now, we’re not absolutely sure why some species retain much of their evolutionary history during development. The “adding new stuff onto old” principle is just a hypothesis—an explanation for the facts of embryology. It’s hard to prove that it was easier for a developmental program to evolve one way rather than another. But the facts of embryology remain, and make sense only in light of evolution. All vertebrates begin development looking like embryonic fish because we all descended...

 The Train of Thought to Equality

Since then society has evolved a sequence of ci central con¬ cepts each of which was at one time thought to make it work of itself, and each of which has had to be corrected to the next. There was the early eighteenth-century concept of selfinterest, in Mandeville and others; then came enlightened self-interest; then the greatest happiness of the greatest num¬ bet; utility; the labor theory of valueie; and thence its expression either in the welfare state or in the clasassless society. Men ...