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...basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large…
In my view, what's most outmoded within science, most badly in need of retirement, is the way we structure and organize scientific knowledge itself. Academic literature, even as it moves online, is a relic of the era of typesetting, modeled on static, irrevocable, toothpaste-out-of-the-tube publication. Just as the…
A child stacks and packs all kinds of blocks and boxes, lines them up, and knocks them down. What is that all about? Clearly, the child is learning about space! But how on earth does one learn about time? Can one time fit inside another? Can two of them go side by side? In music, we find out! It is often said that…
The main difference between an instructional system and a selectional system is that the instructional system uses information from the environment to change the properties of the object in question, but a selectional system has a large and varied population of objects, and the ones that are most fit for the…
One may picture, then, these beings, nuclearly resident, so to speak, in a relatively small set of mental units, each utilizing the bare minimum of energy, connected together by a complex of etherial intercommunication, and spreading themselves over immense areas and periods of time by means of inert sense organs…
Piet Hut, another Dutch astronomer fifty years younger than Jan Oort, decided to take seriously the possibility that comet showers are periodic. If they are periodic, the theory that they are caused by the random passing-by of alien stars cannot be right. If showers are periodic, they must be explained by a different…
Sure there is music even in the beauty, and the silent note which Cupid Strikes, far sweeter than the sound of an instrument. For there is music wherever there is harmony, order and proportion; and thus far we may maintain the music of the spheres; for those well ordered motions, and regular paces, though they give no…
Music Theory. You will forgive me for turning, as I always do in moments of intellectual want, to my Webster's Collegiate Dictionary, which defines the word "theory" as, and we quote, "The analysis of a set of facts in their relation to one another." My friends, few words offer as much rational solace as does the word…
Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the…
All good intellects have repeated, since Bacon's time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true…
10 years of music lessons There’s another powerful way to fine-tune a child’s hearing for the emotional aspects of speech: musical training. Researchers in the Chicago area showed that musically experienced kids—those who studied any instrument for at least 10 years, starting before age 7—responded with…