## Tuesday, April 28, 2009

### Blind Rubik's Cube 2

I decided after getting slagged for my incredibly girly last cube to do something a bit less pink. So I went to the craft shop. Where I did not look in anyway out of place amongst all the girls buying glitter and sparkles.

The materials I had to choose from were clockwise from top left

Tire Rubber, paper, foam, felt,velcro hooks, velcro, canvas, ribbon and mesh. I also got black sandpaper later.

I removed the stickers. I then washed off the residual stickiness with glue. I sandpapered 5 of the faces. After some thought I went for foam, velcro hooks, canvas, sandpaper, mesh and clear.

## Sunday, April 26, 2009

### Swine Flu

There has been a worrying outbreak of swine flu. there is a good description of it here. The new scientist has another article on the issue here.

The pandemic ventilator project here says

So what do we know? First the people that are dying are not the typical elderly and very young. They are mainly healthy young and middle aged adults. The death rate seems fairly high, perhaps as great as 10%. Death rates early on in a pandemic however are very difficult to pin down, as we really do not know how many people were infected but in fact had very mild symptoms and were not counted. The virus is spreading to many geographical locations quickly. The WHO has already stated that it’s first line defense against pandemic outbreaks, which is containment, is no longer possible. The reason that there are no major travel restrictions imposed by governments is not that they think the threat is too minor, but that it is past the point where travel restrictions will help. What is still unknown is how severe it will eventually be, and how readily it will spread.

There is not much information in this post. All I am trying to do is point out some sources of useful information on this new flu outbreak.

## Sunday, April 19, 2009

### Blind Rubik's Cube

I saw this and thought a tactile rubik's cube was a good idea.

So I made one. Anyone need a cube they won't look at? Id love to send one to Bernard Morin the blind topologist.

1. Peel off the stickers

2. Get rid of crud left using white spirit

3. Scour the cube and the buttons with a stanley knife

4. Glue buttons onto cube

5. Wait

The result looks a bit like the Borg assimilated hello kitty.

I am going to do up another but this time with different textures instead of shapes. This gets over the symmetry problems. What substances should I use? I want to use felt and thinking of it reminded me of fuzzy felt

I dont want to get all Angela's Ashes here but really was fuzzy felt the best toy ever?

## Friday, April 10, 2009

### Shannon limit progress

Shannon was the guy who came up with much of the theory of digital computers but is mostly famous for creating information theory. I found out today invented the worlds first wearable computer to cheat at roullette in Vegas here. This is pretty similar to finding out Einstein invented a time machine to grift rubes in three card monte.

He also developed a motorised pogo-stick and flame throwing trumpet. A picture of Shannon using these or even just juggling on his unicycle would finally prove the internet was useful.

So how has attempts to get a code that approaches the Shannon limit progressed? "The Shannon limit or Shannon capacity of a communications channel is the theoretical maximum information transfer rate of the channel, for a particular noise level."

It is really important because it controls how much information a device can transmit. Which is important if you make phone calls or communicate with a satellite.

So in 1948 Shannon put a limit on how much information can be transferred. Mathematicians (and engineers) devise ways to encode information to make communications close to this limit. As maths progresses you would expect the codes to get closer to this limit.

I have taken this first picture from this very good article. You can see how codes improve over time

In this picture you can see new codes moving closer to 0 on the y-axis showing improvements in the coding schemes. I'm having trouble getting the world record closeness to the Shannon limit for particular dates. When I do I'll add them.

What I have so far is

Year Power Who

1977 2.1 dB Reed–Solomon code(now 1–1.5db)

1997 .27 db hamming code

2009 0.0045 dB LDPC codes

Sometimes codes have been invented before they were practical, but even then people tend not to have known how good they were.

"LDPC codes were invented by Robert Gallager in 1962! However, LDPC codes were largely forgotten until their rediscovery by David Mackay in 1998, who not only rediscovered them but used powerful modern computers (which were not available to

Gallager) to simulate their performance and thereby demonstrate their astonishing power"

The importance of this progress has been summed up by suggesting future historians will write

"Claude Shannon formulated the notion of channel capacity in 1948 A.D. Within several decades, mathematicians and engineers had devised practical ways to communicate reliably at data rates within 1 percent of the Shannon limit...."

Coding theory is one where we can see practical applied progress in mathematics over the last 60 years.

## Thursday, April 09, 2009

### Rubik's Progress

How quickly is maths improving? Say you look at how good your best solution to certain problems is over time. You can estimate how much improvement there is in maths over this time. Most of maths is based around proofs which are pretty hard to measure the quality of. But by looking at applied results you might get evidence to how much the pure maths knowledge has improved also.

So take the example of optimal algorithms for Rubik's cubes (most of this data taken from here).

Start 1974 until now how many face turns are needed to solve the Rubik's cube in the worst case?

52 moves 1981 using Thistlethwaite's Algorithm

42 moves 1990 Kloosterman (doc)

39 moves Mike Reid (i'm trying to get a date for this)

29 moves 1995."In 1995 Michael Reid proved that using these two groups every position can be solved in at most 29 face turns"

27 moves 2006, Silviu Radu

26 moves August 2007, Daniel Kunkle and Gene Cooperman

25 Moves Mar 2008 Tomas Rokicki

23 moves Jun 2008 Tomas Rokicki

22 moves August 2008 Tomas Rokicki

This implies 20 moves are enough using the given algorithm but it has not been proved

Now the best possible solution is at least 20 moves (known as gods algorithm). This number used to be 18 but was improved in 1995 by Michael Reid. The bounds on solutions to the Rubik's cube is improving from two sides. The ability to solve a Rubiks cube going from 52 to 22 moves does not seem earth shattering. There are probably more important maths calculations that have improved over time though. Can you think of any? As usual if you have any more information or corrections I will add them.

So take the example of optimal algorithms for Rubik's cubes (most of this data taken from here).

Start 1974 until now how many face turns are needed to solve the Rubik's cube in the worst case?

52 moves 1981 using Thistlethwaite's Algorithm

42 moves 1990 Kloosterman (doc)

39 moves Mike Reid (i'm trying to get a date for this)

29 moves 1995."In 1995 Michael Reid proved that using these two groups every position can be solved in at most 29 face turns"

27 moves 2006, Silviu Radu

26 moves August 2007, Daniel Kunkle and Gene Cooperman

25 Moves Mar 2008 Tomas Rokicki

23 moves Jun 2008 Tomas Rokicki

22 moves August 2008 Tomas Rokicki

This implies 20 moves are enough using the given algorithm but it has not been proved

Now the best possible solution is at least 20 moves (known as gods algorithm). This number used to be 18 but was improved in 1995 by Michael Reid. The bounds on solutions to the Rubik's cube is improving from two sides. The ability to solve a Rubiks cube going from 52 to 22 moves does not seem earth shattering. There are probably more important maths calculations that have improved over time though. Can you think of any? As usual if you have any more information or corrections I will add them.

## Wednesday, April 08, 2009

### Timing Accuracy

As technological improves you would expect that our ability to measure things would improve. So if we take the accuracy of measurements as a crude gauge of technological progress can we graph how quickly we are progressing?

So take time. How quickly is our ability to measure time accurately improving?

I'm going to have a look at how accurately people have been able to measure time since the start of the modern world (about the time Newton got hit by an apple) till now. I take accuracy to mean how many seconds you could count before you would be out by one on average.

1656, Dutch astronomer Christian Huygens. It had an error of less than one minute a day according to here

1721, George Graham improved the pendulum clock’s accuracy to within a second a day

1761 John Harrison, half a second a day

1889 to Siegmund Riefler's clock with a nearly free pendulum, which attained an accuracy of a hundredth of a second a day

1952 Quartz clock at accuracy of 1 in 10^8 seconds.

Modern times are graphed here

For the atomic age I got the figures from here

So that gives the data

year accuracy

1650 10E+03

1721 10E+05

1889 10E+07

1952 10E+08

1955 10E+10

1970 10E+13

1989 10E+16

2008 10E+17

One problem with this line of thought is that exponential increases tend to stop. Otherwise we would be up to our ears in Fibonacci's rabbits. The problem with this exponential reasoning is described here

There are all sorts of other things whose accuracy have improved over time. Has temperature and mass measurement accuracy increased at the same rate?

So take time. How quickly is our ability to measure time accurately improving?

I'm going to have a look at how accurately people have been able to measure time since the start of the modern world (about the time Newton got hit by an apple) till now. I take accuracy to mean how many seconds you could count before you would be out by one on average.

1656, Dutch astronomer Christian Huygens. It had an error of less than one minute a day according to here

1721, George Graham improved the pendulum clock’s accuracy to within a second a day

1761 John Harrison, half a second a day

1889 to Siegmund Riefler's clock with a nearly free pendulum, which attained an accuracy of a hundredth of a second a day

1952 Quartz clock at accuracy of 1 in 10^8 seconds.

Modern times are graphed here

For the atomic age I got the figures from here

So that gives the data

year accuracy

1650 10E+03

1721 10E+05

1889 10E+07

1952 10E+08

1955 10E+10

1970 10E+13

1989 10E+16

2008 10E+17

One problem with this line of thought is that exponential increases tend to stop. Otherwise we would be up to our ears in Fibonacci's rabbits. The problem with this exponential reasoning is described here

There are all sorts of other things whose accuracy have improved over time. Has temperature and mass measurement accuracy increased at the same rate?

## Monday, April 06, 2009

### Turkeys Voting for Christmas

Surely this expression should mean that things should not engage in acts they don't have the cognitive capacity needed to do. A bit like saying dogs should not do quantum theory. Taleb has a theory of turkey philosophy here.

But that is not the excepted meaning which is

Other then the obvious practical difficulties of running meleagrine elections Christmas has to be the best thing that has ever happened to turkeys. I remember a talk on the long now that the best way to ensure your species survival is to be really tasty.

Without Christmas we would have no reason to have such large numbers of turkeys. People don't keep skunks because they serve no useful purpose. Numbers would be vastly reduced. If only wild turkeys survived and they were not farmed for food their numbers would be orders of magnitude less.

Of course there is the question of whether it is a good idea for turkeys to put all their eggs in one basket Christmas wise. They have intelligently diversified in the American market into thanksgiving. Some sort of Summer festival in Asia would be where they should concentrate their marketing on next I would think.

But that is not the excepted meaning which is

like turkeys voting for (an early) Christmas (British & Australian humorous)

if people are like turkeys voting for Christmas, they choose to accept a situation which will have very bad results for them

Usage notes: Turkeys are large birds which are often eaten on Christmas Day.

Other then the obvious practical difficulties of running meleagrine elections Christmas has to be the best thing that has ever happened to turkeys. I remember a talk on the long now that the best way to ensure your species survival is to be really tasty.

Without Christmas we would have no reason to have such large numbers of turkeys. People don't keep skunks because they serve no useful purpose. Numbers would be vastly reduced. If only wild turkeys survived and they were not farmed for food their numbers would be orders of magnitude less.

Of course there is the question of whether it is a good idea for turkeys to put all their eggs in one basket Christmas wise. They have intelligently diversified in the American market into thanksgiving. Some sort of Summer festival in Asia would be where they should concentrate their marketing on next I would think.

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