Aristotle's Wheel Paradox - To Infinity and Beyond

I love Paradoxes, and I recently accidentally stumbled upon a new one (which is actually really old, so, actually only new for me) on the youtubes.

References

Wikipedia - Artistle's wheel paradox

https://en.wikipedia.org/wiki/Aristotle%27s_wheel_paradox

Youtube - Aristotle's Wheel Paradox - To Infinity and Beyond

https://youtu.be/mrVg9GM5h7Q

Simpson's paradox

“There are three kinds of lies: lies, damned lies, and statistics.”

During my travels across the Internet, I recently stumbled upon a paradox that exemplifies the quote¹ above.

It is called the Simpson's Paradox² and I had never heard of it before.

From what I can gather, it means that data that is aggregated might point in the exact opposite direction compared to the same data partitioned by a certain type/relation.

It depends on the situation which of the two should be preferred, in order to extract proper conclusions from the data.

The Wikipedia entry in the references has some very good examples of Simpson's Paradox and should be required reading for any budding statistician.

References

Wikipedia - Lies, Damned lies and statistics

https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics

wikipedia - Simpson's Paradox

https://en.wikipedia.org/wiki/Simpson%27s_paradox

Logic in Epimenides Paradox

The Epimenides paradox reveals a problem with self-reference in logic¹.

Epimenides was a Cretan who made one immortal statement:

“All Cretans are liars.”

Now then, there are two statements that are part of the paradox:

• Epimenides was a Cretan.
  
• All Cretans are liars.

If we assume that Epimenides said "All Cretans are liars.", there are exactly four possible outcomes:

Epimenides was a Cretan	All Cretans are liars
False	False
False	True
True	False
True	True

The Paradox is only visible if both statements be true. In all other cases, there is no paradox, and things go merrily on their way.

Thomas Fowler (1869) made a major mistake in determining the logic negation of the statement "All Cretans are liars.".

He assumed that the opposite of "All Cretans are liars." is "All Cretans speak the truth.". We, hardcore software designers, of course, do not fall for this trap.

The logical negation of "All Cretans are liars." is "Not all Cretans are liars." This, consequently, can be rewritten as "There is at least one Cretan who speaks the truth."

References

[1] Wikipedia - Epimenides Paradox

https://en.wikipedia.org/wiki/Epimenides_paradox

The Clothesline Paradox and the Sharing Economy

“If you put your clothes in the dryer, the energy you use is measured and counted, but if you hang them on the clothesline to be dried in the sun, the energy saved disappears from our accounting.”

I found out about this talk of Tim O'Reilly on YouTube. I thought it was worth a reference in one of my little blogposts.

References

The Clothesline Paradox

http://www.wholeearth.com/issue/2008/article/358/the.clothesline.paradox

Building a Paradox

According to Wikipedia^[1]:

“A paradox is an argument that produces an inconsistency, typically within logic or common sense.”

Every once in a while, it helps to do something that is totally unrelated to the field of Software Design. In my case I like to make the occasional wooden thing. In this case, I decided to build a wooden paradox.

Just to elaborate, I wished to make a wooden version of Curry's Paradox^[2]. If you wish to know how the trick works, youtube^[3] has some very good explanations.

This little project is one of the easiest I've made. (Quickest too)

Ingredients

• some wood, 1 cm thickness, made of glued-together-layers of wood
• different colour paints
• varnish
• magnets

Utensils:

• a fretsaw (I used an iron saw, because I'm short a fretsaw)
• glue
• sandpaper
• tapemeasure (essential)
• pencil
• paper (I used cm² paper)
• scissors
• eraser
• brushes

The Making Of

Cut the shapes out of paper.

Mark the shapes on the wood.

Saw the shapes using the fretsaw.

Use sandpaper on the pieces.

Paint them.

Varnish them.

After drying, apply glue to the magnets and glue them to the shapes.

Done.

It's not rocket science!

Notes

I managed to make something appropriate using an iron saw instead of a fretsaw, and I do not recommend it. It's a pain to create 90 degrees corners.

Next time need to sandpaper more, as the edges were quite rough.

References

[1] Paradox - Wikipedia

http://en.wikipedia.org/wiki/Paradox

[2] Missing square puzzle

http://en.wikipedia.org/wiki/Missing_square_puzzle

[3] Curry's Paradox and the Notion of Area: Part I (Tanton)

http://youtu.be/eFw0878Ig-A

Curry's Paradox