Friday, 17 April 2015

How did Albert and Bernard solve Cheryl's puzzle?

In the recent viral mathematics problem, readers were invited to solve the mystery of Cheryl’s birthday based on the ten possible dates and the responses of Albert and Bernard. The solution to that puzzle is readily available on the Internet.

This post addresses the other question: How did Albert and Bernard solve the mystery?

Here’s the setup. The ten possible dates are May 15, 16, 19; June 17, 18; July 14, 16; August 14, 15, 17. Cheryl tells Albert the month: July. Then she tells Bernard the date: 16.

Albert thinks: It is July, so Bernard has either 14 or 16. If Bernard has 14, Bernard will think Jul or Aug. If Bernard has 16, Bernard will think May or Jul. Hence: Bernard does not know the month.

Albert says: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard thinks: It is 16, so May or Jul. Albert can say I do not know birthday only if all dates in the birth month (which Albert knows) have duplicates in other months. So Jul or Aug, since dates in only these months are all duplicated in other months. Only Jul has 16. So Jul 16.

Bernard says: At first I don’t know (see "Albert thinks" above) when Cheryl’s birthday is, but I know now.

Albert thinks: From my remark ("Albert says" above), Bernard can shortlist Jul or Aug. It is Jul, so Bernard has either 14 or 16. If Bernard has 14, Bernard will still be unsure (both Jul and Aug have 14). So Bernard has 16. Only Jul has 16. Hence, Jul 16.

Albert says: Then I also know when Cheryl’s birthday is.

That is how Albert and Bernard solve the puzzle of Cheryl’s birthday.

By the way, this is not a mathematics problem; it is a logic problem. And I daresay a careful Primary Five student could have a decent crack at solving it.


Friday, 21 November 2014

Interstellar -- virus!

I watched the movie Interstellar recently.

The reviews emphasised the real science that was depicted in the movie. My beef is not with the science. My beef is with the ethics. Here it is in a nutshell: If mankind is responsible for the "destruction in process" of the earth environment, is it then ethical to export the virus homo sapiens (this was proven in Matrix) to yet another planet? The conclusion of the movie showed a glowing Interstellar colony -- but what assurance do we have that the colonists are only "good" guys, that no "bad" guys were exported?

The morally responsible thing for mankind to do is to let homo sapiens destroy themselves on this planet -- and thence give Planet Earth a chance to recover (though this may take some millions of years). I'm hoping this happens before we find a way to colonise some other planet -- and spread the virus homo sapiens. Intelligent life is nature's latest experiment gone wrong. I hope we are smart enough to realise that -- but I fear we are not.

Here's an indicator: The great benefit of the melting Arctic ice cap is the opening of a new sea route.


Tuesday, 1 July 2014

What do large numbers prove?

In times past, every civilised person believed that the earth was flat, and that the sun orbited the earth. Everyone also believed illnesses were caused by evil spirits. Many civilisations thrived on a slave economy, and everyone believed this to be the rightful arrangement. Similarly, many civilisations believed men worked outside the home while women worked inside the home, and everyone believed this to be the rightful arrangement. But today, all these arrangements are believed by everyone to be false and wrongful.

These simple counterexamples illustrate the fallacy known as Argumentum ad Populum, or Appeal to the Gallery. Just because a great number of people believe something true / false or right / wrong, does not therefore make that thing true / false or right / wrong. Large numbers of support or opposition prove only the position's popularity or unpopularity.

Assertions of "true / false" and "right / wrong" require other grounds of support. Appeal to numbers of supporters or opposers (that is, supporters of the contradictory position) cannot do that job.

This past Saturday saw large numbers of people wearing pink or white, in support of and in opposition to a particular position. Let us be clear what the large numbers are able or not able to prove or disprove.


Thursday, 12 June 2014

Unnecessary tizzy over Renault Twizy

On Wednesday, 11 June 2014, Today newspaper ran a story about the Land Transport Authority (LTA) classification for Renault's new vehicle, the Twizy, a "two-seater electric vehicle".

Notice the description does not state what type of vehicle. That exactly is the (alleged) puzzle.

The Twizy has four wheels, a cabin, seats for two persons (one behind the other), a 17hp engine (one-tenth the power of an average car), a top speed of 80kph, two doors, no airconditioning, no proper window, and weighs 450kg.

The current LTA definition of a motorcycle requires the vehicle to have fewer than four wheels, and weigh below 400 kg. On this definition, the Twizy is clearly not a motorcycle. But is it a car?

The story does not provide LTA's definition of a car.

So I visited the LTA website. It says: "The new categorisation will retain the existing Cat A criterion that the engine capacity of the car should not exceed 1,600cc for Cat A, and add a new criterion that the engine power of the car should not exceed 97kW (equivalent to about 130 bhp)."

On this description, the Twizy could be classified as a Category A car.

But let me quote from the story.

"In a statement to TODAY, the LTA said initial evaluation showed the vehicle does not fall within the classification for motorcycles that Renault had applied for." Then later: "...the distributor's spokesperson said its application categorised the Twizy as a car". So it is unclear which category Renault had applied for.

But here is my clincher criterion: How is the vehicle to be operated?

A car must be operated via a steering wheel; and a motorcycle must be operated via handlebar controls. This is the only definition that is consistent with the intentions of the Class Three and Class Two driving licences -- because the respective methods are how learners are trained to operate the respective vehicles. We cannot have someone holding only a Class Two driving licence operating a vehicle with steering wheel control.

The accompanying picture of the Twizy clearly shows that it is operated via a steering wheel, not via handlebar controls.

The story says LTA is seeking "more information from Renault" over this matter. This is not necessary. Once we clarify the definitions (a major function of philosophy), it becomes clear.

The Renault Twizy is a car.


Wednesday, 11 June 2014

The rights of Eugene Goostman

On 10 June 2014, The Straits Times reported that "a Russian supercomputer posing as a 13-year-old boy has convinced judges that it is human, being the first to pass the 'Turing Test' in a historic moment in artificial intelligence". This is a very big deal.

In 1950, pioneer of computer science Alan Turing published a journal article in which he set out the now famous Turing Test -- a test to establish whether a machine can think. The criterion is whether, in the words of Professor Kevin Warwick of the University of Reading, "a computer convinces a sufficient number of interrogators into believing that it is not a machine but rather is a human." Any machine that passes this test is deemed to be able to think.

At a competition on 7 June 2014 at Royal Society in London, the Russian supercomputer simulated the responses of a 13-year-old boy named Eugene Goostman -- and persuaded the judges 33 percent of the time that it was human.

This is a remarkable engineering achievement. It is more than an engineering achievement.

Rene Descartes, the father of modern philosophy, founded his philosophy on his realisation that "Cogito, ergo sum" -- usually translated as "I exist, therefore I am". The presence of thought proves the existence of a thinker.

Eugene Goostman thinks. Therefore, Eugene Goostman exists. Eugene Goostman is human.

Visit any divorce or child abuse case, and one will immediately be informed that children have rights -- the rights to food, shelter, clothing, security, education etc. When a child reaches maturity, that child will acquire adult rights -- freedom of speech, freedom of association and assembly, freedom of religion, freedom to work and leisure etc.

How many of these rights are we prepared to extend to Eugene Goostman?

Scientists often claim that science is amoral, that science is neither intrinsically good nor evil, and that only people can be said to be good or evil, morally right or morally wrong. This seems to hold the door open for scientists to further believe that "if it can be done, therefore, it must be done." Well, now it has been done.

When Eugene Goostman demands his rights, are we still going to insist: "No, you are just a machine"?


Tuesday, 10 June 2014

No chance for climate salvage

On Monday, 9 June 2014, Jeffrey D Sachs wrote an article published in Today newspaper. In it, he says December 2015 will be when the world will have its "last chance for action" on climate change. Why December 2015? Because that is when the next United Nations climate change meeting will take place. But what will happen if January 2016 rolls around, and no firm action is taken on global warming? Big Business will carry on as usual. That is all.

The world will get hotter. The weather will worsen. Species will die. Coastal lands will get wiped out. Some people will die. But the profit motive will continue to prevail over all these. There are two main reasons for this. First, the meaningful horizon. Profit is seen over a horizon of months and quarters, climate change is seen over a horizon of decades and centuries. It is clear that the profit motive will prevail. The second reason is that "profit" as a more strongly held philosophy than "ecology". Why this is so is another question, but it is so.

In his opening paragraph, Professor Sachs says "scientists have pointed out that a rise in temperature of two degrees Centigrade above pre-industrial levels will put the Earth in dangerous, uncharted territory.

I query the word "dangerous". We need to know: dangerous for whom? For Earth, as the sentence suggests? Absolutely not. Planet Earth is in no danger. Planet Earth will continue to orbit its sun for millions of years after Planet Earth has become devoid of life -- of any kind. It will just become like all the other planets we know of so far. No big deal, cosmically speaking.

The big deal is that climate change is dangerous for mankind. But here we run up against Profit Motive -- and Profit Motive will win. Realisation will finally sink in only when Big Business starts to run out of slaves (because of climate induced illness and death) to produce profits for its leisure-enjoying owners. But by then it will really be too late to reverse climate change. December 2015 will have come and been long gone.

So what should helpless minions (that is, not Big Business owners) do? Enjoy the time we have left. That is all we can do. Oh, and try not to produce any grandchildren, for they shall not inherit the Earth.


Thursday, 29 May 2014

Flaw in X-men Days of Future Past

I found a philosophical flaw in X-men: Days of Future Past.

The world is caught up in an all-out war of Sentinels vs mutants. Wolverine and company decide that the historical event that triggered this timeline was Mystique’s killing Trask. To avert this all-out war, Wolverine and company send Wolverine’s consciousness back in time to take over the mind of the younger Wolverine, so he can persuade the younger Professor X and the younger Magneto to help him prevent Mystique killing Trask. Events then unfold. When the critical killing moment comes, Professor X has control of Mystique’s mind, and is in a position to force her body to walk away from the opportunity to kill Trask. Instead of doing that, Professor X releases Mystique’s mind, saying she must make that decision for herself. He gives her free will.

There are of course the philosophical questions of (1) whether consciousness exists apart from body, (2) whether consciousness can travel through time, and (3) whether consciousness can be transplanted into another body. But let’s allow all these as literary licence. There is still a philosophical flaw, and it’s a logical flaw – which is very much harder to “literary licence” away.

To say that one specific historical event triggers a given timeline, and further to say that changing that one specific historical event will change the eventual outcome many years hence presumes the philosophical doctrine known as determinism – which says that every event is caused, and that, given complete information, every event can be predicted. There is no freedom in the causal chain. Let me be specific: there is no free will in the causal chain.

Giving Mystique the free will to decide whether to kill Trask contradicts this philosophical presumption. If Mystique has free will, then so does everyone else along that timeline. There is then no guarantee that the war will be averted.

This is the philosophical flaw in the movie. But it is, nonetheless, a wonderfully entertaining movie.


Tuesday, 27 May 2014

Philosophy dispute in Thailand

The current political impasse in Thailand is actually a philosophical dispute -- between democracy and aristocracy; between "government by all" and "government by some". For there to be a rational resolution, there must first be common ground between these two political philosophies. So far as I can see, the only common ground is that there not be a "state of nature". Martial law has achieved this. However, if the military persists in governing, then that will be also a form of aristocracy -- which those preferring democracy will not like. A military-imposed "state of peace" is not a viable long-term solution. History tells us how this philosophical dispute will be resolved. It will not be pretty.

Monday, 22 August 2011

Whom shall we vote for president? Part 3

A dreadful thought just occurred to me: We must not cast a negative vote -- it may become self-defeating. Let me explain.

There are four presidential candidates. Let us call them A, B, C and D. We decide we do not want A to be president. Hence, we decide to not vote for A. This is what I call a negative vote -- a vote we will not cast. We then randomly cast our vote for one of the other three candidates. Our positive votes therefore will be split among B, C and D. In this way, the result can be A: 30%, B: 25%, C: 25%, D: 20%. Even though A polls a mere 30%, A becomes president! Instead of ensuring that A does not become president, this way of voting could positively make him president! Our negative vote has become self-defeating.

There may be some who would say a candidate garnering such a low percentage of the valid votes does not have the mandate of the population. I disagree. The mandate of the population arises from the fact that the entire population was polled, and not from the percentage of the polled population which voted for the candidate. A winner with 30% of the valid votes does have the mandate of the population.

Thus, we must instead cast a positive vote. We must vote for the candidate whom we think will best be able to block any (in his view) bad decisions of the PAP government -- at least those within his power to veto. (I specify the PAP government only because that happens to be the present government. In principle, it could be government by any political party.) I have in my first post on this topic specified the questions we should ask and answer in determining our personal best candidates.

Let us all cast positive votes, not negative ones.


Friday, 19 August 2011

Whom shall we vote for president? Part 2

I said in my previous post on this topic: "The originating principle behind the Elected Presidency is to have someone in place who can veto government proposals should the day come when the government makes a poor decision on certain specified matters."

Veto power is a negative power, a blocking power. It is the power to prevent something from happening -- quite different from the power to make something happen.

The candidates' respective campaigns are underway. Some candidates are telling us what they would do if they are elected president. These are indications of how they would exercise positive power, creative power. These are not indications of how they would exercise veto power.

What we need to hear from the respective candidates are what they would block the PAP government from doing should they feel such initiatives inappropriate or unwise. We need to hear from the respective candidates how they are prepared to exercise negative power should the need arise.

So far as I recall, only one candidate has said he is prepared to exercise negative power. But he has not yet indicated the kind of government initiatives he is prepared to veto. (Note that no initiative is in principle precluded from a veto, since reserves may be drawn upon for any purpose.)

In the days to follow, I shall be listening out for the respective candidates' thoughts on their prospective use of veto power. And so should every voter.