Wei-rd joke

A: What's four, plus FOUR!?

B: Eight?

A: Nope, twenty-eight.

Tort law perverse incentive

Even if not paid to the claimant, the very threat of punitive damages may pressure a defendant into an out of court settlement unjustly excessive of any compensatory damages that would have been awarded otherwise, creating another perverse incentive in tort law.

Informed consent

Wei Hong commented on CN’s link:

The Age

Doctor says he sucked nipple to diagnose problem

8 September 2010

That the patient “consented” is not a defence. Consent is meaningless unless informed, with accurate representation of facts (there is no such taste test in evidence-based medicine) and alternative courses of action (for example, the doctor could have obtained a taste via a swab or gauze). 

Iced coffee the Wei way

In Hong Kong, I order an "Iceberg Coffee." I am served a shot-jug of liquid and a glass of coffee sitting in a bowl of ice:

The liquid turns out to be sugar syrup, while the coffee is unsweetened. My course of action becomes clear; I take the sugar syrup and pour a little into the bowl of ice. The waiter probably thinks I’m stupid because the syrup was supposed to go into the coffee, but the thing is:

0. After the ice leaves the freezer, it absorbs heat from the environment until it reaches 0 °C, the freezing point (T) of water. Any further heat goes into enthalpy of fusion (∆H) needed to melt the ice, so the temperature stays at 0 °C until all the ice is melted.

1. Via Raoult’s law, the freezing point of a solvent is changed by –RMT²/∆H per molal of dissolved particles, so for water:

–8.31 J/(K mol) × 0.0180 kg/mol × 273² K² ÷ 6010.0 J/mol = –1.86 °C kg/mol

▪ For each 10 g of ice, each gram of dissolved sucrose changes the freezing point by:

0.1 × –1.86 °C kg/mol ÷ 0.342 kg/mol = –0.543 °C
to a limit of –9.5 °C at the eutectic point.

2. The 0 °C ice is now hotter than its lowered freezing point so it melts. The enthalpy of fusion (∆H = 334000 J/kg) needed is absorbed from any surrounding heat; liquid water has a specific heat capacity of 4220 J/(kg K) at STP: 

–334000 J/kg ÷ 4220 J/(kg K) = –79.1 °C

▪ Each 10 g of ice that melts from the sugar removes enough heat to chill 100 mL of water by 7.91 °C until the new lowered freezing point is reached.

I feel the spot where I poured the sugar. It seems slightly colder, but sugar syrup isn’t going to cut it. I ask the waiter for a salt shaker:

3. Salt dissolves more easily than sugar. It also dissociates into Na⁺ and Cl^– so that’s double the molal.
▪ For 10 g of ice, each gram of dissolved NaCl changes the freezing point by:

0.1 × –1.86 °C kg/mol × 2 ÷ 0.0584 kg/mol = –6.36 °C
to a limit of –21.1 °C at the eutectic point

I pour in the salt. The outside of the bowl frosts over from the extra coldness. I like my iced coffee unsweetened and below freezing.

Scale invariance

People often refer to how ants can life many times their body weight as though this were somehow remarkable. The greater the size difference between the objects compared, the less meaningful a concept "strength-to-weight ratio" becomes. The strength of an object scales with the square of its length, while the weight scales with the cube of its length. Therefore, I propose "√strength-to-³√weight ratio" as a more suitable measure.