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Pedant’s Paradox: Gallows Humour

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The Problem: A man is told that he will be hung one day next week, but that he will not know until the day. He works out that he can’t be hung on Friday as he would know after noon on Thursday that only Friday 12:00pm remained. Likewise on Wednesday, he can rule out Thursday because he can rule out Friday, and so on through the week, so he can rule out being hung.

At this point the logic paradox stops, but the version I originally heard included a caveat missing here:

On Monday at 12:00 pm he is very surprised. Why?

The Answer: If you stop with the proof by induction, then he is correct: he cannot be hung by surprise. If you take the logic one step further however, the prisoner has just stated that he cannot be hung without knowing the day before and therefore cannot be hung. So, since he thinks he can’t be hung, whenever he is hung it will be a surprise.

The problem is that it assumes the prisoner can rule out each day in succession because he has ruled it out before – so on Thursday afternoon, he would know he was to be hung on Friday, on Wednesday afternoon it would have to be Thursday (because otherwise he would know on Thursday that it would be Friday) and so on.

He can be hung on:

He thinks:It is actually:
Mondayt+1t+4
Tuesdayt+1t+3
Wednesdayt+1t+2
Thursdayt+1t+1
Fridaytt

On any day but Friday and Thursday there are multiple options so he cannot know for sure that he will be hung on the following day.

There is also the alternative, where he can be hung, but insists he cannot be hung by surprise. Again, he cannot know for sure which day he will be hung on until Thursday (because until Thursday pm he is not in possession of the certain knowledge that he has not been hung previously).

 

Posted by on July 27, 2015 in AuthorBlog

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Blackberry Memopad to PC Word

Without the Blackberry desktop software, I had been told it would be difficult to get the data off. I love a challenge. The problem with the desktop is that there doesn’t seem to be a build for one of my OS’s. Also, when I checked, Memopad files can’t be opened even if you do back it up. They are stored in a database, not as text files, and though you can download third party software to crack backups I prefer not to.

Now, I’m no Blackberry expert, but there is a workaround, and putting it here might save someone a few hours googling:

You will need:
  • PC Software to create Word files (e.g. LibraOffice or Word)
  • A micro-SD card
  • A micro-USB cable
  • A Blackberry
Instructions:

Step 1: Plug SD card into PC.

Step 2: Create a blank Word file for every memo you want to save.

Step 3: Install SD card into BlackBerry

Step 4: Open Memopad and copy a Memo’s contents

Step 5: Go to Applications/Docs to Go/Docs

Step 6: Find the Word Docs you created under Storage. Open one of the Word docs, paste the content in and save.

Step 7: Using Steps 4-6, paste each memo into its own word doc.

Step 8: Plug the Blackberry into the PC

Step 9: Enter Mass Storage mode

Step 10: Copy data onto PC

It may sound like a kludge, but it is easier then the Kobo / Linux custom build I was using which can only be detected over USB by devices running Puppy Linux.

Also, once the SD Card is in the Blackberry, you can create new word docs without uninstalling it. Plug it in through USB, enter mass storage mode and then access it as you would a USB drive to create or delete files as needed.

It works well enough to get this post off!

 

Posted by on July 2, 2015 in AuthorBlog

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Upgrading to a handheld

Well, today I decided to join the hand-held revolution; or truthfully to rejoin it after the death of my dearly beloved Psion Revo a few years ago. Being a classic early adopter I went for not an iPhone, nor a tablet…but a Blackberry 8900. (I thought they’d had a few years to get the bugs out).

Lovely bit of kit: palm sized, real keyboard, easy access through USB, previous user’s data all over it… No, the last one wasn’t expected or wanted.

I’d bought it at CEX for 20 pounds, so I disconnected it from the computer and dived back down to town. CEX weren’t happy, and to their credit immediately performed another factory reset and told me I could take it home while it completed. I hung around in-store just in case, checking messages as it reset. One did make me raise an eyebrow. Sure enough, after the reset I rebooted. All the old data reappeared.

I took it back up to the counter and showed them. The assistant looked a bit baffled, and paged through again so I asked:

“Could there be a storage card in this?”

Yep, when it rebooted, the screen had flashed up ‘storage media detected’. They cracked the case, fiddled with the insides and sure enough, there was a very old, green, and wonky looking micro-SD hidden in it. Every time they reset it, the Blackberry was restoring the data from back-up.

So, to make a long story short, SD out, contacts cleaned, factory reset again and this time it worked perfectly. How perfectly? I’ve written two short stories and this blog post on it.

I’ve even fixed the camera.

Next: A Challenge! How to get data off Memopad and onto a PC without Blackberry desktop.

 

Posted by on June 24, 2015 in AuthorBlog

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Pedant’s Paradox: Buridan’s ass

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The Problem: An Ass is at equal points between two plates of equally delicious food. Unable to choose between the, it starves to death rather than eat either.

The Answer: For the really literal-minded, the food will have rotted long before the ass starves, and as food breaks down at different rates, one plate will at certain times be less appealing than the other breaking the paradox. However, rather than break the paradox, let’s assuming they break down at equal rates.

In its literal form the problem still fails because the choice is not between two plates of food, it is between eating and not eating. At a certain point, eating must rationally take priority since the ass presumably does not want to die. It also forgets option D – the ass decides to eat the grass it is standing on while it decides which plate to eat or E it wanders off. Walking away from a problem can be the easiest solution.

However, this isn’t a literal paradox as much as a commentary on human behaviour. If you have ever watched a politician trying to avoid making a choice, you will know just how accurate this can be.

 

Posted by on June 22, 2015 in AuthorBlog

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Pedant’s Paradox: Kavka’s Toxin

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The Problem: A billionaire will give you £1 Million if the next day at noon you take a pill that will make you violently ill for 24 hours, after which you will recover fully with no side effects. However, to earn the money, you must form the intention of taking the pill at midnight the night before. After midnight you can back out of taking the pill with no penalty and still receive the money.

The Answer: Gregory Kavka who created the problem stated it was impossible to form the intention at midnight as everyone would undoubtedly back out rather than be sick the next day.

This is provably false just by the existence of drug testers, live organ donors etc.

It is possible to form and hold the intention to do something even if you know it will be unpleasant if the incentive is high enough. Many generation of people have gritted their teeth through family gatherings for less incentive than $1 million.

How many people have agreed to do something they don’t like, despite knowing they could back out with no consequences? Seeing that awkward relative is normally arranged in advance, but you can phone and plead illness or cancel at any point with no issues – and yet some people carry it through.

Kavka assumes it is impossible to form the intention because obviously you will back out rather than get sick. The problem is that for anyone whose word is their bond, once they have agreed to the billionaire’s deal to take the toxin it is binding and therefore if they agree the day before they will, at midnight that night, have a sincere intention of taking the toxin. A problem that fails if the individual is honourable is not a very good problem.

 

 

Posted by on May 25, 2015 in AuthorBlog

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Pedant’s Paradox: Chrysppus’ Crocodile.

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic). This month we are moving onto a traditional Egyptian puzzle.

The Problem: A woman is walking by a river with her child when her child is snatched from her by a crocodile. The crocodile tells her that it will return the child if she can correctly answer the question “What do you intend to do with the child?”

The Answer: The mother is traditionally supposed to reply “You intend to keep it.” to guarantee the return of her child.

 With this one it is not the problem that breaks, it is the solution. The crocodile could equally well answer false, and eat the child on the spot. Eating something is not the same as keeping it. It could also drop the child in the river so neither of them have it. The error is in that assuming the crocodile has only two options – to keep the child or hand it back. It also has options to destroy the child or dispose of it so no one has it.

Even “You intend to keep it” does not guarantee the return of the child or its condition when it is returned. Worse if the crocodile is, as many in myth were, a sage akin to an Eastern Dragon, the answer might actually be false. Its intent may be simply to test the mother’s intelligence.

So what could she say? The actual answer could be a negative. “You do not intend to return the child safely to me.” However there is no room in the question for a negative. Likewise the conditional, “You intend to return it if I can answer your riddle” may be disqualified although it is undoubtedly true.

Or as a mathematician friend put it: “You intend to use it to make me answer a stupid bloody question.”

 

Posted by on April 27, 2015 in AuthorBlog

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Pedant’s Paradox: The Balding Man

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The problem: If a man has a full head of hair, removing one hair will not make him bald. Therefore the act of removing one hair cannot make a man bald.

The Answer:
This is a well-known paradox by Eubulides, a greek philosopher.
However the standard answer is incorrect. The definition of bald is “possessing no hair on the scalp”. If hair still remains, the individual is balding – that is, in the process of going bald. Therefore if there is no more hair to remove, the individual is bald.

This type of problem is the sort of thing programmers have to solve all the time, and if it was a true paradox then most coding would be impossible. Viewed programmatically, the paradox fails very easily:

$h = 100,000; //total amount of hair on head
$bald = false; //person is not bald
for (h, h=0, h–) {
   //remove one hair at a time until none remain.
If h ==0 {
bald = true;// person is now bald.
}
}

 

You could even take this a stage further. “Balding” is described as in the process of going bald – having lost the majority of hair. Majority is defined as more than 50% – so…

$h = 100,000; //total amount of hair on head
$total-hair = //original amount of hair on head
$status = “not bald”; //person is not bald
for (h, h=0, h–) {
  //removes one hair at a time until none remain.
If (h ==0) {
$status = “bald”;// person is now bald.
}
elseif (h<=( ($total-hair/2)-1) ){
$status = “balding”; //person is balding
}
}

Ignoring my rather pedantic programming digression, the correct answer is simple.

When no further hair remains to be removed, the individual is bald.

 

Posted by on March 23, 2015 in AuthorBlog

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Pedant’s Paradox: Theseus’ ship

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The Problem: The Athenians preserved Theseus’ ship for posterity. This meant replacing damaged parts as they wore out over time – the sails, the timbers, the decorations. At what point is it no longer Theseus ship?

The Answer: This is a curious one because there isn’t any true answer, but it is an interesting debate.

Some people would argue that it stops being Theseus’ ship when the last original part is replaced. This overlooks one thing – that the ship is not just its physical existence, it is its design. A question that must be asked is whether the original sailors would recognise it. If Theseus could see it today and immediately identified it as his ship, would anyone have the right to gainsay him even if all the timbers had been replaced?

I’ll go back to programming for an example. In Object Oriented Programming you have a class, which is a type of object and an instance, which is a specific member of that class. In this case we have a class: Ship and an instance: Theseus’ ship.

To make it easier to understand, let’s take a more radical change. Suppose we had class Password and an instance Mary’s password. Mary forgets her password, so she changes it to something completely new with no link to the old one. The new password is still Mary’s password. It still does everything the old password did, it unlocks the account, it needs to be remembered etc.

It isn’t Mary’s password any less because the letters have changed. It had better not be, since if it isn’t Mary’s password the login program won’t work and Mary’s locked out!

So going back to class: Ship and instance: Theseus’ ship, is changing the timber enough to make it not his ship? Or is it the point where the program – in this case the population of Athens – no longer recognises that instance as Theseus’ ship no matter how much it may have changed?

There is an extended problem, where the rotting planks are used to construct a vessel at another location so there are now two Ships of Theseus, and the issue is determining which is the true ship. This is more easily disposed of by anyone familiar with how quickly wood rots and sails break down. The second constructed ship will never at any one time have the entire body of Theseus’ ship present at its location. The fact the ship may have timbers from the original does not make it the original.

As a side note, this issue has actually been encountered in aircraft restoration – if parts of two spitfires are used to restore a third, which aircraft does the restoration count as in terms of flying hours, etc? It counts as the aircraft originally registered, not the ones used to restore it regardless of parts. The Iron Duke steam engine was broken down to save space in 1919 only to have a replica rebuilt at a new location using many of the salvaged parts less than a year later. The new engine still counts as a replica, not the original.
 

Posted by on February 23, 2015 in AuthorBlog

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Pedant’s Paradox: Lightning Strikes Twice?

Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The problem: If the chance of someone in the population being hit by lightning is 650,000 a year, and Kelly is hit by lightning in 2009 what are the chances she will be hit by lightning again in 2010?

The Answer: The standard answer is one in 650,000 as years do not affect each other. However this is incorrect. Kelly is no longer only part of the group “general population”, she is also part of a smaller group: people who have already been hit by lightning. The chances of that group being hit may not be the same as the general population.

This is because people who have already been hit by lightning include a subset, and in some years a majority, of people who engage in behaviours more likely to get them struck by lightning – e.g. steeplejacks, deep sea anglers, high altitude construction workers, mountaineers, and depending on your definition of lightning, electricians who immediately skew the odds.

Their chances of being struck by lightning are higher. The average (mean) chance across a group is the total number of probabilities divided by the number of members in the group. As there are more people in the group with higher risks, the average chance of being struck by lightning again is higher. By being struck by lightning, Kelly therefore enters a higher risk group.

However, even this is incorrect. What we do not know is how Kelly reacted to the first strike. If she changed jobs, decided she was not at risk, or even if she survived the strike. This is why mathematical models must be treated with caution.

The correct answer is two-part:

  1. i) given no changes in circumstance (ceteris paribus – all things being equal) her chance of being struck by lightning should be the same as the year before.
  2. ii) without knowing more about her behaviour and circumstances, that probability is impossible to determine.
 

Posted by on January 26, 2015 in AuthorBlog

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A new series of posts for 2015

To replace the videos, which I proved to be dreadful at keeping up with, I’m starting a new series for 2015.

Pedants Paradox was inspired by a christmas gift that had me tearing my hair out: a book of paradoxes. The problem is that most of them aren’t paradoxes, those that are are presented badly, and a statistician of my acquaintance did not think much of the math. Therefore, I’m picking them apart in the hope it will provoke a bit of a debate on the blog.

I’ve got one a month coming out on the fourth Monday of each month, and several already written and queued up. Feel free to argue it out in the comments or message board.

(I’ve also finally figured out how to syndicate this, so tumblr can start getting some traffic.)
 

Posted by on January 12, 2015 in AuthorBlog

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