This is a hat problem. The participants are supposed to be infinitely clever Mensa members, each wearing a hat bearing a number, such that they can see each other’s numbers but not their own. The hat numbers are integers, greater than zero. There are 3 participants (A, B and C, or Albert, Brian and Clarence if you prefer), and the number on one of the hats is the sum of the numbers on the other two. They take turns as follows:

A: I don’t know my number.

B: I don’t know my number.

C: I don’t know my number.

A: My number is 25.

What are the numbers on the other two hats?


Sometimes people ask me this question, and this is the answer I give. Obviously I’m not going to do the whole topic justice, but here is my simplistic way of looking at the question.

First: what do you mean by “god”?

If you mean “god” as a concept, obviously it exists. Virtually everyone on the planet has some kind of concept of a god, and it is possible to have a conversation with references to a god and be confident of some meaningful exchanges of information.

If you mean “god” as a physical entity that currently exists then the relevant facts are all the scientific information we have gathered about the physical world. None of those facts indicate the existence of a physical god, so we can be exactly as certain that there is no god as we can be that there is no unicorn, no Easter Bunny, no Santa Claus etc. In my view that is a high level of certainty, but whether it leaves room for doubt could be a matter of opinion.

If you mean “god” as something else eg a non-physical entity, or an entity that existed in the past but no longer, then the burden of definition is yours to bear. If you can’t define what you mean, then you can’t expect me to argue whether it exists or not. That is “agnostic by definition”.

In my view of the world, “god” exists as a concept of human invention and does not exist as a real, physical entity. I think the facts available are sufficient to reach that conclusion with a high degree of certainty, and that the process of getting to that point is highly rational. Regarding other kinds of god, I deal with those on a case by case basis as anyone offers a definition of what “god” means.

Aren’t you glad you asked?

I personally know a handful of OA or similar award recipients, and in many cases what I see is the effectiveness of the networks they belong to in rewarding their own, rather than any intrinsic worth. Is it enough if their peers think it’s enough?

I am directly involved in the awarding process in two organisations, and I have to say it’s not easy to do. No-one wants to give an award for “just doing your job”, but if you have a candidate for recognition within their chosen profession or speciality, what exactly is it that they should have done to justify that award? Not an easy question.

The guidelines used for some the awards I am involved in include:
1. “Took a risk, made a difference; encouragement in mid-career ”
2. “Distinguished contribution to the field of …”
3. “Outstanding and distinguished lifetime achievement in and contribution to the field of …”
4. “Very significant lifetime achievement in and contribution to the field of …”
5. “Extraordinary and long-term contribution to the … organisation”

They all imply something more than just “doing your job” but how much more?

Another question: in many cases we look to a recipient as a role model, for the young to emulate. What if you have someone who makes a truly outstanding contribution, recognised by everyone, but cheats on the tax? Or perhaps molests little girls? Where do you draw that line?

Let me know if you find some easy answers. I don’t know any.

Laws generally fall into 3 categories: (a) protecting the rights of individuals or minorities (b) regulating conduct (c) operating the state.

Type (a) laws only limit freedom to the extent that rights are in conflict: the protection of the rights of the victim restricts the rights of the perpetrator. Most laws in this category are a net positive for personal freedoms, and laws such as those in a Bill of Rights are entirely about freedoms.

Type (c) laws are relatively neutral on freedoms. The laws that set up the parliament, the police force, courts, ATO, banks, industry, contracts, public transport, infrastructure, corporations, etc have little impact on personal freedom. The agencies they create may have an impact, but not the laws themselves.

Type (b) laws are the ones we should worry about. They include laws on topics like public drunkenness, affray, most traffic laws, public nuisance, censorship, etc, etc. These are the “do-good” laws that sound great in theory but add up to the nanny state.

So what about banning the burqa?

I don’t favour a ban, because I see it as type (b), regulating conduct with no great contribution to the protection of rights. However, there are some undesirable aspects and it would be relatively easy to introduce 2 specific laws, to make it:

  1. A criminal offence for a person to engage or attempt to engage in any commercial, contractual or regulated transaction or activity, or the creation, signing, production of any document related to personal identity, without exposing one’s full face, except with the prior express and written permission of the other part(ies) or the relevant regulating organisation as the case may be;
  2. A criminal offence for a person to impose or attempt to impose any obligation or demand or exemption on any other person or organisation on the grounds of any religious belief, principle or claim.

The rationale is that you are personally free to do what you like but transactions with other people give them the right to know who they are dealing with, and you can hold what beliefs you like but not impose them on others.

So, you can wear your burqa, but you cannot buy or use a ticket for a train, tram or bus; cannot drive a car; cannot go shopping; cannot buy food etc unless you are willing to remove it whenever you interact with anyone; and you cannot use “freedom of religion” as an excuse to force your requirements onto others.

These are type (a) laws that protect the freedoms and rights of the people and organisations you interact with against unwelcome religion-based demands and obligations. I would like them to extend to a number of other religious groups, but we won’t go into that now.

As a youngster, a friend of mine owned a Datsun 240K automatic. Some of his friends had V8s. He discovered however that he could do some impressive burnouts by selecting reverse at highway speed & flooring it!

The argument is over the relative speed of one back tire spinning, compared to the road below.

The following are given:
1. Vehicle speed 120 km/h.
2. Engine at redline, consulting gearbox ratios extrapolates this to 100 km/h in reverse.
3. Open diff, so one tire does not slip at all, but remains in contact with the road while the other spins backwards.

So, does anyone have an idea what the relative speed difference was under those conditions?

His view, by assuming the same ratios as when driving at slow speed in reverse, results in a rear wheel speed equivalent to something over 400 km/h.

My view goes something like this. First, it seems inescapable that if the gearbox engages immediately and if there is no slippage in the torque converter, then the instantaneous situation would be that the engine must be rotating backwards. That simply isn’t possible, so we have to assume major slippage in the transmission.

Assuming there is slippage even for a brief period, then where is it? The torque converter is by far the best candidate. We know that a heavy load can switch a torque converter out of coupling mode (that happens if you tow something too heavy in too high a gear). So we get the following sequence of events.

1. Reverse gear engaged in gearbox.
2. Front shaft of gearbox reverses, breaks torque converter out of coupling mode (stator locks).
3. Engine goes to full power, peak revs.
4. Torque converter passes magnified engine torque back to gearbox.
5. Gearbox passes torque (reverse direction) back to diff and to wheels.
6. Torque exceeds limiting friction of one tyre, wheel slows down and may reverse.
7. Steady state is reached when torque transmitted by the engine is equal to torque transmitted from two wheels, one slipping.

If this is the situation, then it’s not possible to predict exactly what the slipping wheel is doing, but I would guess rotating slowly forwards (same direction as road).

Google was not my friend.

Just ran across these incredibly useful words that English lacks.

Utepils (Norwegian) means “outside beer”. It refers to the highly pleasurable activity of sitting outside enjoying a beer, especially the first warm day of spring.

Drachenfutter (German) means “dragon fodder”. This is the gift a husband gives his wife when he’s been a naughty boy, in the hope of not having to sleep on the sofa.

Attaccabottoni (Italian) means “button attacker”. Someone who starts conversations and won’t let you get away.

Saudade (Portuguese) means “sadness”, but really refers to an intense nostalgia for the past or missing friends or anything really.

I’m sure these are all words we could use from time to time.

Here are two puzzles, superficially similar, but different answers.

A. Alf meets Bert, and asks him how many children he has, and of what sex.
The puzzle: if Bert has two children and at least one of them is a boy, what are the odds that he actually has two boys?

B. Alf now asks the same questions of several more people, until he gets to Charlie.
The puzzle: if Charlie has two children and at least one of them is a boy, what are the odds that he actually has two boys?

C. Alf goes back to Bert, and asks him what days any boys were born on.
The puzzle: if Bert has two children and at least one of them is a boy born on a Tuesday, what are the odds that he actually has two boys?

D. Alf now asks the same questions of several more people, until he gets to Dave.
The puzzle: if Dave has two children and at least one of them is a boy born on a Tuesday, what are the odds that he actually has two boys?

This strange puzzle and/or variants of it was originally set by Martin Gardner. The surprising thing is that the exact same question can have two different answers depending on the assumed context from which the odds should be calculated. There are enough clues here to make the answers fairly obvious.


Anyone fancy a logic puzzle/game? I just ran across this one.

It’s a download, text-based propositional logic with a cute back story. Only 10 questions, but it certainly made me think.


Multiple Choice Question:
If you choose an answer to this question at random, what is the chance you will be correct?
A: 25%
B: 50%
C: 0%
D: 25%


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