Free web hosting and "new" website

I had a small website up for a while, but Geocities and my ISP have both discontinued their web hosting services. As an experiment I was looking for a new host that was a completely free replacement. The best thing I found so far is:

http://www.awardspace.com

The basic features in a nutshell are:

Total file space: 250 MB

Maximum file size: 2 MB

Monthly Bandwidth: 5 GB

FTP/PHP/MySql included

No Ads.

I had actually registered an account with them several years ago when it was all still in beta, and the test page I made was still working as I left it. So, I was pleasantly surprised to see they have their act together (so far) and have improved the service since I last saw it.

Here's a couple limitations I ran into and work-around's:

1. Some files types are restricted. Though I can see the point of restricting high bandwidth file types like .mov, as well as files with security issues like .exe. They don't want to become the next Napster and get shut down.

• mp3 file types are not allowed. I used the open source alternative "ogg." In Linux, I found a free program called "soundconverter" that made it easy to do a batch conversion from mp3 to ogg. (The program did pop up an error when first lauching, but worked perfectly otherwise).
• zip files are not allowed. I used the .bz2 compression format instead. Or you can drop the .zip extension from the file.

2. The marketing about domains is a bit misleading I think. It says it the free package has "1 domain" included and I initially thought "wow, they throw in a free domain name?!" The answer: no. You either have to pay for a domain name, or piggy back off a handful of generic domains like atwebpages.com.

3. If using FTP, probably using a FTP client like "filezilla" would probably work better. On a large batch of file transfers I hit a couple times where the FTP stream was cut off. This is not a big deal though if you have an FTP client that will automatically reconnect and retry the file transfers.

Still this host is a big improvement from what I had been using. On both my previous free hosts, I used to be bound by a 10 MB limit, which is hard to do much with. :)

My website is now at:

http://kevinsstuff.atwebpages.com

Growing Peppers, and a spicy treat

Well, I grew a few different kind of peppers this year, and will miss them during the winter. The plants are winding down now that fall is here.

The jalapeño is a great pepper. It's moderately spicy with a great flavor for pizzas, and mexican food. It's about 2,500 - 8,000 on the scoville heat scale.

The habanero, extremely spicy with a sweet "fruity" flavor. You don't want to eat these things straight, or you will be in pain. They are 100,000-350,000 on the scoville scale. But they are great mixed with other foods:

And the hottest chili in the world, the naga jolokia. I will probably dry these, and use crushed, since they are about 1,000,000 on the scoville scale. That's approaching pepper-spray strength.

I have found a great use for the habaneros. If you like Indian food or spicy food, you might like this recipe. It's a bit like a crunchy popcorn snack but would also be a great side dish.

Roasted Chick Peas

Drain 1 can of chick peas (garbonzo beans) and rinse in a large bowl. You can roll the beans against each other, and all the skins will come off. These float to the top and can be poured off through a strainer. You don't have to remove the skins, but I think they cook up a bit crunchier without them.

Put the chickpeas in a small dish. Mix with 1-2 tablespoons of olive oil, then sprinkle with:

Curry

Salt

Black Pepper

Cinnamon

1-2 chopped Habanero peppers

Cook at 450 F, for 25 minutes.

Origami in 3D

I while back I was thinking about Origami, and the limits of working in three dimensions.

I realized that if you start with a rigid piece of paper, and fold it back on itself, this can create a layered buffer of paper that can be tapped or stored. So, a rigid sheet can be converted into one of virtually limitless elasticity. That means any form that is possible within traditional sculpture (clay, metal, etc) can be built from a single sheet of uncut lamina.

I ran across work by origami artist Joel Cooper that demonstrates this potential on an amazing level.

From Joel Cooper:
http://joelcooper.wordpress.com/2008/08/19/faq/

From Joel Cooper: http://www.flickr.com/photos/origamijoel/sets/72157606262466165/

Robert Lang explains origami

Robert Lang explains the principles behind origami, origami design software, along with practical applications in space, medicine, and auto industries (18 min).

One thing that is not covered, is that origami folding can construct the same point sets that can be constructed with a marked-ruler and compass. For example, how to trisect an angle:

http://www.sciencenews.org/view/generic/id/8567/title/Math_Trek__Trisecting_an_Angle_with_Origami

Pythagorean Puzzle

I like wooden toys, puzzles, and mechanical devices. The other day, I was looking at a simple proof of the Pythagorean Theorem. The idea behind the proof was incredibly simple, but the simplicity was obscured with the mathematical notation and formalism. But I noticed it could be directly translated into a mechanical device. So, I thought I'd make a toy out of it. The idea is it might make the concepts a little more clear, without the clutter of notation.

The general idea behind the proof is this:

Suppose I have a rug and place it flat on the floor of an empty room. If the rug is too small for my tastes, can I cover more of the floor by moving the rug around (on the floor)? Not really. Regardless of where I put the rug, the same total area of floor will be covered, the same total area will be uncovered.

So, imagine four rugs that are all the same size, and shaped like right triangles. The black space is the uncovered floor:

Now, I can rearrange the rugs, in another pattern:



But either way, the same area of floor is uncovered, regardless of how I move the rugs. So, the black area a² + b² has the exact same area as black area c². So,

a² + b² = c²

But also, the axa, bxb, cxc squares are formed directly with the sides of the triangles. In other words, a and b are the length of the triangle's legs, and c is the length of the hypotenuse.

So, this is a visual, mechanical demonstration of the Pythagorean Theorem, for an arbitrary right triangle. :)

Below are the steps I used in making the prototype:

First I started with a large sheet of 1/8" hardboard, and cut a 1" strip. Though, in hindsight, it would have been easier to just find a precut, plained 1" x 1/4" strip.

Now, there will be three basic layers: top middle and bottom.

The top layer can all be cut from the long 1" strip. I used 2"x1" triangles. So the inside of the frame will be 3" and the outside 5". The four small 1"x1" squares will be corner supports between the bottom and top layers. The three small 1/2" x 1" rectangles will be used for sliding tabs (handles).

The middle layer (left bottom) will need to be slightly thinner so that it can slide freely between the corner supports. I just took off a hair with a flat file. The bottom layer (right bottom) will need a slot cut that intersects points (0,0) and (2,1), if the origin is at the lower left. I just used a drill and coping saw. Any thickness for the bottom is fine.

Roughly assembled:

The yellow triangle will slide along the slot in the bottom layer. The back tab will connect to the yellow triangle with screws (passing through the slot). These will need to be attached at the same angle as the triangles:



Glue the green and yellow triangles to their middle layer supports. Use two small screws to prevent rotation. It's probably best to drill pilot holes for these small pieces.:

Also, I cut a thin strip of felt, and glued to the insides of the slot. This smooths the slide mechanism, and looks a little better. After dry, then cut flush with a razor blade.

The sliding yellow triangle can be attached first. This will determine the position of the frame and other pieces. (backside)


Then add corner supports (which will be cut to size at the end). The only thickness that really matters, is that the middle layer is slightly thinner than the corner supports.

The side tabs and red blue triangles will sit on top of the middle layer, and allow the pieces to slide vertically and horizontally. Glue both tabs and triangles to the middle layers.

Personally, I like the natural wood toys better. But, since this is a wooden toy for kids, I picked bright simple colors. :)

For a children's toy, I think the squares should have been purple, and the frame should have been black. Since I think it's easier to focus on purple than black (a void), and is often a favorite color. But I didn't have any purple felt on hand. Though, black doubles as a chalk board.

(I actually painted everything at the first step, but had to touch up scratches afterwards.)

After painting everything, use a flat bastard file so that edges are clean and sharp.

Then, apply drips of glue to the corner supports, and adjust the frame so that both triangle positions are flush. Cut excess off when dry. I rounded the tabs off with a Dremel tool, and painted the white labels on the black background. These labels are obscured by the resting position of the triangles. A hole can be drilled in the back for hanging somewhere.

And that's it. Now, even a five year old can demonstrate this fundamental theorem of mathematics. :)

File Encryption on the Command Line and a Secure Text Editor

Update: I added this script to github at:
https://github.com/sevkeifert/text-utils/blob/master/svi


A while back I needed a really simple way to encrypt a password file on the command line. I wanted to be able to write quick, simple scripts, with no more than one line of code handling the file encryption part. So, in Linux or Windows (using cygwin), I used these aliases:

# for simple encryption methods, use:
#     echo "text" | encrypt
#     echo "U8askj123lkjasdflkjasdlkjargoi+/==" | decrypt

alias encrypt="openssl aes-256-cbc -a -salt"
alias decrypt="openssl aes-256-cbc -d -a -salt"

Then other quick shell scripts can easily encrypt/decrypt files as needed.

However, while this works, it was still a nuisance to actually edit and maintain the encrypted files. Here's an alternate approach that will work under Linux or Windows (using cygwin). It wraps the classic vi text editor, or any editor for that matter, in a shell script that opens and saves files in any standard encryption format (like aes 256), which can then be decrypted by other script utilities. Also, it will save an encrypted snapshot of the file every day it's updated in case you mangle the password or file.

Here's the bash script, which can be saved to /usr/local/bin/svi

#!/bin/bash
# A simple secure vi editor, for aes encrypted files
# file name passed in as argument, for example
#     svi FILENAME
# to open file as read only
#     ln -s svi sview
#     sview FILENAME
# GPL

# type of encryption
cipher=aes-256-cbc

# where temp files will be decrypted
tmp=/tmp/


# create tmp dir/file
me=`basename $0`
dir=`dirname "$tmp$1.tmp"`
mkdir -p "$dir"
touch "$tmp$1.tmp"
chmod 600 "$tmp$1.tmp"

# decrypt to tmp
if [[ -e "$1" ]]
then

 if openssl $cipher -d -a -salt -in "$1"  > "$tmp$1.tmp"
 then
   if [[ ! -s "$tmp$1.tmp" ]]
   then
     echo "WARNING: decrypted an empty file, exiting."
     exit
   fi
 else
   echo "WARNING: bad password, exiting."
   exit
 fi

fi


if [[ $me == 'sview' ]]
then
 # open file read only
 vi -n -R "$tmp$1.tmp"

else
 # open file for editing
 vi -n "$tmp$1.tmp"

 # re-encrypt after exiting vi
 if [[ -s "$tmp$1.tmp" ]]
 then
   touch "$tmp$1.aes"
   chmod 600 "$tmp$1.aes"
   while [[ ! -s "$tmp$1.aes" ]]
   do
     openssl $cipher -a -salt -in "$tmp$1.tmp" > "$tmp$1.aes"
   done

   # make backup, replace old
   if [[ -s "$tmp$1.aes" ]]
   then
     if [[ -s "$1" ]]
     then
       cp -pf "$1" $1.$(date "+%Y-%m-%d").bac
     fi
     mv -f "$tmp$1.aes" "$1"
   fi
 fi

fi

# cleanup
shred -z -u "$tmp$1.tmp"
rm -f "$tmp$1.aes"

Then for example, to open or create a new encrypted text file, use:

svi  YOUR_FILE

Disclaimer

Overall, this is a reasonably simple and secure method for protecting files, in the case a laptop is lost or stolen. The strength is that these files can be transferred across or stored on insecure media.

As for weaknesses though, this does create a decrypted copy of the file on the local computer while it is being edited. And the temp file, even if deleted (unlinked), may leave an image on the local disk. Another weak point is that insecure memory could be flushed to swap space on the hard disk.

And, as with any encryption cipher, it can be always broken with the old "wrench" method.... :)



(comic courtesy of xkcd)

Does 1=.999...?

I heard a joke about logic a while back:

One man's modus ponens is another man's modus tollens

Though, I am hesitant to tell such a joke, for fear it will injure someone through uncontrollable side-splitting laughter. I am not responsible for burst spleens! ;)

It basically means any valid chain of reasoning can be run in two directions. For example:

Here's one proof for 1 = .999...


In Axiomatic System 1

(1) Assume: 1/3 = .333...
(2) Then adding this equation to itself three times results in:

1/3 = .333...
+ 1/3 = .333...
+ 1/3 = .333...
-------------------
1 = .999...

(3) Therefore 1 = .999...

However, this result seems a bit counter-intuitive.

There is however an equally valid argument that can be constructed by running this same chain of reasoning in reverse:


In Axiomatic System 2

(1) Assume: 1/3 = .333...
(2) Then adding this equation to itself three times results in:

1/3 = .333...
+ 1/3 = .333...
+ 1/3 = .333...
-------------------
1 = .999...

(3) Therefore, 1 = .999...
(4) However, clearly this conclusion is absurd. There is one point of difference, if we define the set of real numbers by repeatedly dividing a line into ten parts. The coordinate .999... would describe the next-to-last point in the line.
(5) Therefore we can conclude that the assumption (1) was false (by reductio ad absurdum).
(6) And since 1 > .999... by one point,

1/3 > .333...

Just like that we get a completely different conclusion.


Point Schmoint

Generally both axiomatic systems coincide on calculations, literally, 99.9... % of the time. Does a difference of a point or two matter? Who would notice the error in a calculation off by such a small amount?

The practical significance will emerge in a calculation that amplifies the difference, such as:

(1 - .999...) * (the number of points in a line of length 1)

This infinite summation is an indeterminate form, roughly:

0 * oo

In the first axiomatic system we may take this product to be 0. Since if the difference is truly zero, zero times anything must be zero.

In the second axiomatic system we may take this product to be equal to 1. Since if N represents the non-finite number of points in the line, 1/N * N = 1.

Neither 0 or 1 is "the" correct answer, any more than saying Checkers is "more correct" than Othello. Different ground rules will lead to different results in different games. A chain of reasoning only establishes a connection between a set of assumptions and the conclusion. It does not establish a direction the reasoning must travel along that chain. Just as we can accept the conclusion, we may equally reject both the conclusion and at least one assumption which led to it.

We might even imagine a system in which 1=0 (mod 1, for example), and both answers are correct. :)

So overall, we may take these numbers '1/3' and '.333...' to be infinitely close together on the number line, but not exactly equal. Or we may take them to be *exactly* equal -- the exact same point. Both systems can be consistent. But whether or not they are equal really depends on what our definition of "is equal" is.