Blockchains

Ownership on the Bitcoin blockchain is determined by a pair of cryptographic keys. The first, called the public key, resides in the blockchain for anyone to see. The second is called the private key, and its owner keeps it safe from view. The two keys have a special mathematical relationship that makes them useful for signing digital messages. Here’s how that happens: Helmut takes a message, combines it with his private key, does some calculations, and ends up with a long number. Anyone who...

 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 ...

 Energy Needed to Power Civilization

The numerical results of my calculations show that the quantities of energy required for permanent survival and communication are surprisingly modest. For a society with the same complexity as the present human society on Earth, starting from the present time and continuing forever, the total reserve of energy required is about equal to the energy now radiated by the Sun in eight hours. The total energy reserve contained in the Sun would be sufficient to support forever a society with a compl...

 Science is Monism

Monism is the default worldview of natural science. In science, an explanation has to be grounded in empirical evidence. In a slightly different take, for a statement to be considered a scientific explanation, it must be falsifiable—there has to be some kind of test that could be applied to the statement to prove it wrong. For example, the statement that the moon is made of cheese is a scientific statement because it can be falsified. Facts can be brought to bear on the claim (such as the d...

 Argument for Decimal Currency

[Decimal currency is desirable because] by that means all calculations of interest, exchange, insurance, and the like are rendered much more simple and accurate, and, of course, more within the power of the great mass of people. Whenever such things require much labor, time, and reflection, the greater number who do not know, are made the dupes of the lesser number who do.

 Dissecting Crystals

A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one's ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop th...

 Biology is Too complex for Mathematical Explanation

There is a strange disparity between the sciences of inert matter and those of life. Astronomy, mechanics, and physics are based on concepts which can be expressed, tersely and elegantly, in mathematical language. They have built up a universe as harmonious as the monuments of ancient Greece. They weave about it a magnificent texture of calculations and hypotheses. They search for reality beyond the realm of common thought up to unutterable abstractions consisting only of equations of symbols...