## Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...## A Star for Everyone Who Ever Lived

Behind every man now alive stand thirty ghosts, for that is the ratio by which the dead outnumber the living. Since the dawn of time, roughly a hundred billion human beings have walked the planet Earth. Now this is an interesting number, for by a curious coincidence there are approximately a hundred billion stars in our local universe, the Milky Way. So for every man who has ever lived, in this Universe there shines a star. But every one of those stars is a sun, often far more brilliant and...In just our own galaxy.

## 1847 Speculation About Extraterrestrials

In general I would be cautious against … plays of fancy and would not make way for their reception into scientific astronomy, which must have quite a different character. Laplace's cosmogenic hypotheses belong in that class. Indeed, I do not deny that I sometimes amuse myself in a similar manner, only I would never publish the stuff. My thoughts about the inhabitants of celestial bodies, for example, belong in that category. For my part, I am (contrary to the usual opinion) convinced ... th...**Folksonomies:**xenobiology

**Folksonomies:**xenobiology

On the sun trees would be larger, but would break apart if made of the same material as those on Earth.

## Copernicus' Hypothesis

After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formally used, if some assumptions (which are called axioms) were granted me. They follow in this order. There is no one center of all the celestial circles or spheres. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. All the spheres revolve about...That the Earth revolves around the Sun.

## Naming the Science of Probability

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability,...A definition of the early field of mathematics.

## How Euclid Became a Physician

Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid...Bolzano reads a mathematical doctrine by Euclid when he is ill and immediately feels better.

## Marijuana Use is Self-Regulating

There is a very nice self-titering aspect to cannabis. Each puff is a very small dose; the time lag between inhaling a puff and sensing its effect is small; and there is no desire for more after the high is there. I think the ratio, R, of the time to sense the dose taken to the time required to take an excessive dose is an important quantity. R is very large for LSD (which I've never taken) and reasonably short for cannabis. Small values of R should be one measure of the safety of psychedelic...Because the period of time between the puff of smoke and its effect on the user, it is easy to regulate how high you want to get when smoking it.

## Predators Prevent Their Prey from Suffering

The appointment of death by the agency of carnivora, as the ordinary termination of animal existence, appears therefore in its main results to be a dispensation of benevolence; it deducts much from the aggregate amount of the pain of universal death; it abridges, and almost annihilates, throughout the brute creation, the misery of disease, and accidental injuries, and lingering decay; and imposes such salutary restraint upon excessive increase of numbers, that the supply of food maintains per...Stephen Jay Gould quoting the Reverend William Buckland.

## We Exaggerate the Magnitude of Ice Ages

The history of Earth's climate is one of the more compelling arguments in favour of Gaia's existence. We know from the record of the sedimentary rocks that for the pst three and a half aeons the climate has never been, even for a short period, wholly unfavorable for life. Because of the unbroken record of life, we also know that the oceans can never have either frozen or boiled. Indeed, subtle evidence from the ratio of the different forms of oxygen atoms laid down in the rocks over the cours...Ice Ages did not encroach on over 70 percent of the Earth's surface, meaning they were not as significant of an event as we tend to imagine them.

## How Much Would a Heavier Helium Atom Affect the Pitch of ...

Cyko_01: does it make your voice go higher or lower when inhaled? Menkhaf: I guess it was a joke, but it should be rather simple to determine: if the gas if lighter than the atmosphere you're breathing, your voice will be lighter if you inhale this. sploxx: To be more specific, the molecular weight of normal He to He with one muon attached is roughly 4.1/4.0. The change in pitch relative to breathing He should be the square root of that ratio, which is a change of about 1.2%. For someone wi...If inhaled, how much would a helium atom altered to have a heavier muon substituted in place of an electron to resemble hydrogen affect the pitch of your voice?