Monthly Archives: July 2013

Fish ladders

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A fish ladder is a structure designed to enable migratory fish (in particular diadromous fish that migrate between salt and freshwater) to bypass barriers such as dams and locks that humans have created.

fish-ladder

A permanent fish ladder at the John Day Dam.

Diadromous fish migrate against the current when returning to freshwater so most ladders are constructed from a series of low steps constructed so that water pours over them fast enough to attract migrating fish, but not so fast that the fish cannot swim upstream.

fish-ladder-plastic

A temporary removable fish ladder on the Little Sur river.

For fish moving downstream in the other direction, a combination of a spillway and gravity usually does the trick.

Types of typefaces

First off, an important note: the terms typeface and font are not synonymous. The typeface Raleway is available in a variety of styles (italic, condensed, etc.) and weights (light, book, bold, etc.) but only becomes a font when the typeface, size, style and weight are all specified simultaneously.

text2985-91

A sample of the styles and weights available for the Raleway typeface.

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Mathematics as the language of physics

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It is often said that “mathematics is the language of physics“. But what does this mean? In this post I’m going to try to explain, by using one of my favourite proofs as an example.

The Problem

The problem is this:

A ball is placed atop a sphere and released. At what angle to the vertical does the ball lose contact with the sphere?

You would be excused for thinking that the answer is 45° or 90°, but the correct answer is more complicated than that.

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Eigengrau

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Close your eyes. What colour do you see? Black? Look again.

eigengrau

Eigengrau (“intrinsic grey”), also called “dark light” or “brain grey” is the dark grey colour “seen” in the absence of light. Eigengrau appears lighter than a black object viewed in normal light because the brain prioritises contrast over true colour representation. For example, in the diagram below the two circular dots are the same colour, but appear to be different because of the way that they contrast with their backgrounds.

contrast-illusion

Eigengrau is produced when rhodopsin molecules undergoing a process of spontaneous isomerisation, indistinguishable from the process that would occur if the rhodopsin molecule had been struck by an incoming photon of light. In individual rod cells these events occur only about once every 100 seconds, but as there are about 125 million rod cells in each human eye this level of background signal is enough to produce eigengrau.

Galileo thermometer

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Like most physicists, I have a soft spot for Galileo thermometers.

galileo-thermometer

A Galileo thermometer* works because the density of water changes as its temperature changes. The mass of a substance remains constant as it is heated (because the number of atoms doesn’t change) but because those atoms move faster the volume increases and therefore the density decreases, as shown in the graph for water below.

water-density-graph

As the water inside the thermometer is heated by its environment its density decreases and the more dense bubbles, that represent lower temperatures, are then more dense than the surrounding fluid and therefore sink. The Galileo thermometer is read by reading the temperature tag of the bubble closest to the middle of the cylinder.

The density of the bubbles inside the thermometer is set by altering the size of the metal tags attached to them: the bubbles that represent higher temperatures have smaller tags and therefore lower densities. (The overall density of the bubble does not change as it is heated because the overall density of the bubble depends only on its overall mass and overall volume, and as the liquid inside a bubble expands it merely compresses the air inside that bubble.)

* Not actually invented by Galileo, but by a group that included one of his students.