Saturday, November 15, 2014

Minimalist Four Stroke Engine (codename: Batwing)

A while back I built a four-stroke engine kit for fun.  I had a few thoughts ...
  1. Hmm, so that's how they work  :-)
  2. That's how it works ?!
  3. All the circular to linear conversion of motion seems inefficient to me.
  4. The whole design seems to have too many parts for what it needs to do.
So, I started thinking about how I'd like to see a four stroke engine designed (in theory).  A couple design goals were:
  1. minimize the number of parts
  2. avoid the circular to linear conversion of motion
  3. increase the symmetry of design
So, to start, I wanted to use both ends of a piston for combustion.   This immediately cuts the components in half.  Also, this way the engine could reuse momentum for compression in the next cycle.

Though it can do better.  The whole mechanism can be reduced to use only one irregularly shaped piston.

Here's a rough sketch of the idea.  Suppose the piston and case are both circular (like a torus).  The piston nests inside the case.    Since both are circular, the piston can move freely inside the case, but create a seal.  The piston could oscillate in a clockwise and counter-clockwise motion inside the case.

While I sketched the piston as having flat sides, the original thought was more of a torus shape.  I thought a flat design would be simpler to machine though.   

Compression occurs between the end of the piston and the points A B C D.

Ignition occurs in the cycle:

    A  B  C  D

Vent and fuel lines are between B and C.  Also, between A and D.   If cams are used, they can be driven directly from the rotations off the piston axle (no need for timing belt).

Example of operation, focusing on A:
  1. Piston rotates clockwise compressing the fuel at A, igniting A
  2. Piston rotates counter-clockwise (away from A).  Fuel at B compresses and ignites
  3. Piston rotates clockwise (away from B) compressing A.   The spent fuel at A vents out.  C ignites.
  4. Piston rotates counter-clockwise (away from C and A, and towards B and D).  Fuel is injected into A as the space opens up.  It's ready for re-compression.  Goto 1
The other cases follow the same pattern (just re-label A B C D).

Since all the motion is circular, this simplifies the cams needed to control the vent valves.  Everything is moving around the same point of symmetry.

Power is tapped from the piston's axle as it rotates.

Possible issues I see would be:
  1. The compression force would want to bend the piston slightly, causing possible wear on the inside of the case.
  2. The piston would fire like a bullet into the next compression cycle  (diesel fuel might make more sense in this case).  The power would have to be tapped in a very controlled fashion, otherwise you don't want excess force slamming the piston into the other side.  
  3. It may be difficult to get a tight 3D seal.

Let me know if you see any issues with the concept/design.  I don't plan on building it... but the fun part for me is in the design part.

I call this thing a "Batwing Engine," named after that weirdly shaped piston.  :-)

Origami Puppet

Here's another attempt at creating a simple Origami toy puppet (well, it's not pure Origami if you cut the hair).   

The design is based off a shallow box like:

You'll need a long piece of paper (around 3x1).  Start by folding a long shallow box, but allow a bit extra paper on one end for hair.  

Then just fold the box over on itself.

Draw a face, and you have a kids toy :-)

Friday, November 14, 2014

Chocolate Sniffer

Each bar of Lindt & Sprüngli chocolate is personally sniffed by the master chef  :-)

Batman Safety Mask

Here's batman mask that cracks me up:

especially with the warning label on the inside:

"Caution: For costume only.  Not to be used as a safety mask."

Oh noooooo ... now what I going to use to to weld with?!    ;-)

Wednesday, November 12, 2014

A Short Analysis of Gödel's Ontological Argument

Kurt Gödel developed a thought provoking axiomatic version of the Ontological argument. Here is a short summary:  

I like analyzing abstract philosophical/logical arguments.  I do see a few potential issues with Gödel's Ontological proof. Here is a short analysis of the proof :)

1. For the backbone of Gödel's Ontological argument, it looks like Gödel constructs a set of 'positive' attributes, and then includes the concept of  existence in the set (with the assumption that necessary existence is a positive attribute).  For example, he constructs a set like: 

G1 = { p1, p2, p3, ... , E }

In this case, p1, p2, p3 are 'positive' essential attributes, and E is the idea of existence. 

If I try to imagine the specifics of what the set contains, a random set of ‘postive’ things might look something like this to me:

G2 = { 'shoes', 'chewing gum', 'paper  clips', 'x-ray vision', 'invisibility', ..., 'the idea of existence' }.  

Here's the issue.  If a set contains 'the idea of existence' as a member, it doesn't imply the entire set of attributes exists, or even that each member of the set  exists or interacts with other members of the set.  

Otherwise, consider applying a similar argument to a subset.  

Define: Superman is a man, such that no greater man can be conceived. He’s basically a watered-down version of all essential attributes in set G1, except as applied to a flesh-and-blood two-legged man with a weakness to Kryptonite.

Such a set of essential attributes may include:

S1 = { 'super strength', ‘wisdom’, 'two legs', 'cape', 'great smile', 'laser vision', 'can fly', ...  }.  

However we can add the idea of 'exists' to the set, where 

S2 = { S1, E }

Then, S2 is greater and more powerful than S1.  So, by similar reasoning, Superman exists.  

Because, between the two, “real Superman” would win any fight, because “fake Superman” can never show up. Superman's existence is an essential attribute to the concept of superman. If he didn't exist in the comic books, he would not be Superman. :)

2. A potential issue is the subjective notion of 'positive'.  Gödel seems to view this as a binary property (something is either positive or not positive).  But in reality, this is usually quite a bit messier.  Positive and negative attributes  are often two sides of the same coin, and they cannot always be separated. 

For example is 'knowledge' intrinsically good?  What is better, an evil genius, or someone who wants to cause harm but lacks knowledge to do so? (imma looking at the "underwear bomber")  

Similarly, 'existence' in itself is neither good or bad intrinsically (consider the idea of ebola in one's mind, vs real ebola virus in one's mind). :)  

In general, I think when assigning 'positive' or 'negative' values, usually some thing or action must be combined with intent, and then potential   effects are weighed as 'desirable' or 'not desirable' by those affected.  For example, people might even view ebola as a ‘good’ thing if it produced effects that people liked and could control (like curing cancer).

3. A more general issue with an Ontological-style proof is 'greater' is a comparison operator applied to an ordered set.  But for example, consider defining N to be the largest number, such that no larger number can be conceived.  For an infinite (unbounded) set,  this definition itself may not be consistent.  We can always add 'one' to make the number larger.  Similarly, we can always form composite sets to create a larger set, or add new attributes.  Or simply double the measure of all attributes. While Gödel's version avoids the direct issue, it is still present.  It’s not enough to say an attribute is included in a set, the attribute will have a measure.  For example, regarding an attribute like 'knowledge', how many primes can be known, if there cannot be a largest prime?

4. The notion of 'necessary existence' is a bit puzzling.  Clearly one may imagine a possible world in which no life at all exists.  As a quick proof, consider a possible world that consisted of nothing but a null set.  To understand existence in modal logic then, we may treat each axiom introduced as excluding the set of possible worlds where such an axiom is false.  For example, if we introduce an axiom, ‘the sun is necessarily yellow’, then the sun is necessarily yellow in all possible worlds (as we exclude possible worlds where the sun is blue by assumption).  By the same token, if we introduce an axiom `the sun is necessarily blue’ then the sun is blue in all possible worlds.  Therefore the subtle point here is that with modal logic, the actual world does not necessarily belong to the set of possible worlds that survive the cut by the axioms introduced. This probably should be added as a disclaimer.

5. However, what is very interesting about Gödel's argument is it brings out a point about broader limitations of math and logic.  Math is the study of patterns. Logic is the method by which information can be rearranged, cross-checked, and discarded.  Math/logic in itself cannot produce apriori truths about reality.  Conclusions in pure logic can only rearrange the information already contained in the premises.