I also watched a Minute Physics talk where it explains that Neutrinos that they are all left handed and there isn't a corresponding right hand version.
Monday 19 December 2011
A little bit of physics
It's been a day of videos. I watched the BBC program A Night with the Stars with Brian Cox talking about quantum physics. (http://www.bbc.co.uk/iplayer/episode/b018nn7l/A_Night_with_the_Stars/) He explains why there is so much space in matter, the bonding of atoms and dying stars forming diamond planets. I think this link to a clip may be available outside the UK: http://www.bbc.co.uk/news/science-environment-16200089.
I also watched a Minute Physics talk where it explains that Neutrinos that they are all left handed and there isn't a corresponding right hand version.
I also watched a Minute Physics talk where it explains that Neutrinos that they are all left handed and there isn't a corresponding right hand version.
Sunday 18 December 2011
Microbes
Between thinking about the AI exam, shopping and java exercises, I've been watching the following video by the Open University about the wonders of the microbe world.
It briefly covers
It briefly covers
- yeast in beer making in ancient Egypt
- the Black Death
- preserving food
- microbes fixing nitrogen in the soil by combining it with hydrogen or oxygen
- microbes helping digest food
- antibiotics produced by one microbe to kill other microbes
- using e. coli to produce, for example, insulin and treatments for AIDS
Friday 16 December 2011
End of a Chapter
This year has certainly brought about a lot of changes for me. Today was another one. The end of a chapter.
From September 2003 I've taught a craft class every Friday morning from September until somewhere around April. Today was the last one. There have been ups and downs, and quite a few people have come and gone as circumstances changed. I've learnt a lot and developed my skills as the people in the class have developed theirs. I've been pushed to be creative and come up with new ideas for cards, and sometimes other projects, every week. It's been challenging but I'm now ready to move on to other things. I don't know quite what but I'm sure time will tell. From a craft point of view, I want to go in a slightly different direction and look into fabric and fibres instead of paper which is the medium I've mostly worked with.
From September 2003 I've taught a craft class every Friday morning from September until somewhere around April. Today was the last one. There have been ups and downs, and quite a few people have come and gone as circumstances changed. I've learnt a lot and developed my skills as the people in the class have developed theirs. I've been pushed to be creative and come up with new ideas for cards, and sometimes other projects, every week. It's been challenging but I'm now ready to move on to other things. I don't know quite what but I'm sure time will tell. From a craft point of view, I want to go in a slightly different direction and look into fabric and fibres instead of paper which is the medium I've mostly worked with.
Not so much learnt today
So these are the things I learnt today.
Natural Language Processes
Java
Progress is slow, but at least I'm picking up bits and pieces. Today, I tried to write a loop using
for(int item:nums)
{
item=5;
}
to change the values in the nums array. This doesn't work. It does the equivalent to
for(int i=0;i <nums.length;i++)
{
item=nums[i];
item=5;
}
So it was back to the normal for loop
So it was back to the normal for loop
for(int i=0;i <nums.length;i++)
{
nums[i]=5;
}
to do what I wanted to do.
to do what I wanted to do.
Wednesday 14 December 2011
The end draws near
Today, it's a bit harder to summarise exactly what I've learnt as it consisted of the material from 2 hours of lectures on machine learning and about an hour on language processing. I also learnt about how == works in Java between Strings and objects compared with primitive types. It might be a slow process, but hopefully I'm improving.
I feel a mixture of sadness and relief today as I've finished the second of the three free Stanford courses running this term. It's been interesting looking behind the scenes at how machine learning is being used all around us from news sites recommending news we might be interested in to variable pricing on websites depending on acceptance or rejection of previous offers to predicting whether a tumour might be cancer or not. The course was quite mathematical and the programming involved a high level of vectorisation so that built in algebra libraries could be used. Today I finally understood why we used the summation sign rather than just working with the vectorised version all the time. It's because in order to split the work over multiple computers or cores, we give each computer/core part of the summation to do, then combine the results.
It's really quite amazing what can be done, and is being done in this field. The course has given me quite a few "so that's how they do it" moments.
The course runs again from January for about 10 weeks. For details see http://jan2012.ml-class.org/. From looking at the other course dates, my guess is it will start around the last week in January.
I feel a mixture of sadness and relief today as I've finished the second of the three free Stanford courses running this term. It's been interesting looking behind the scenes at how machine learning is being used all around us from news sites recommending news we might be interested in to variable pricing on websites depending on acceptance or rejection of previous offers to predicting whether a tumour might be cancer or not. The course was quite mathematical and the programming involved a high level of vectorisation so that built in algebra libraries could be used. Today I finally understood why we used the summation sign rather than just working with the vectorised version all the time. It's because in order to split the work over multiple computers or cores, we give each computer/core part of the summation to do, then combine the results.
It's really quite amazing what can be done, and is being done in this field. The course has given me quite a few "so that's how they do it" moments.
The course runs again from January for about 10 weeks. For details see http://jan2012.ml-class.org/. From looking at the other course dates, my guess is it will start around the last week in January.
Three things for today
- Today I learnt that not only can you use compression to determine the language of a passage, but you can also use it to tell which of a series of photographs is the sharpest. A blurry image will compress more than a sharp one.
- In java, StringBuilder can be used instead of, and if preferable to StringBuffer if not using multiple threads.
- We have brains, first and foremost to control movement. There is a creature called a sea quirt which as a juvenille swims around but then finds a place to anchor itself. Once it has done this, it digests its own brain and nervous system for food. A brain isn't needed when you're not going to move.
 |
| Photo Wikipedia Commons: Nhobgood |
Tuesday 13 December 2011
Gzip and Determining Language
While watching the last set of videos for the free Stanford Artificial Intelligence course, the following video completely blew me out of the water. It was so completely unexpected.
This is my third thing I learnt on Monday. The unix command gzip can be used to recognise which language a passage is written in. Suppose you have passages in different languages, and want to know which language a new passage is written in. What you can do is concatenate the passage onto each of the other passages, compress and check which one has compressed the best. The reason this method works is because compression works by shortening the representation of common language patterns, such as "is " in English, by a single byte. This compression will be different for each language and thus the best compression should be achieved for the concatenation with the same language.
This is my third thing I learnt on Monday. The unix command gzip can be used to recognise which language a passage is written in. Suppose you have passages in different languages, and want to know which language a new passage is written in. What you can do is concatenate the passage onto each of the other passages, compress and check which one has compressed the best. The reason this method works is because compression works by shortening the representation of common language patterns, such as "is " in English, by a single byte. This compression will be different for each language and thus the best compression should be achieved for the concatenation with the same language.
Finding Components in a Directed Graph
The second thing I've learnt today is about finding strongly connected components in a directed graph. A strongly connected component is one in which there exists a directed path between every pair of vertices in each direction.
The algorithm in involves starting with an ordering (any ordering) of the vertices, running a depth first search on the graph with all arcs reversed, while keeping note of position the vertices are removed from the stack. This position is then used to order the vertices in the original graph. A second depth first search is run, this time on the original graph with the new ordering of the vertices from largest to smallest. Whichever vertices are generated from the same leader are in the same component.
Example
For the directed graph above, I'll run through the algorithm. First we reverse all the arcs like this:
Starting at 1, we do a depth first search on the graph. From 1 we can go to 2 or 4, and we arbitarily pick 4. From 4 we can go to 10 or 6 so we'll go for 10. From 10 we have no choice but to go to 7, then 8 and from there to 9 and then 3. From 3 we have no unvisited vertex to add so 3 pops off the stack and gets new label 1. I'll use f(3)=1 to denote the new label of vertex 3.
1-> 4 -> 10 ->7-> 8->9->3 dead end so f(3)=1.
1->4->10->7->8->9 dead end so 9 pops off next giving vertex 9 the new label 2, that is, f(9)=2.
1->4->10->7->8 dead end so 8 pops off giving f(8)=3.
1->4->10->7 dead end so 7 pops off giving f(7)=4.
1->4->10 dead end so 10 pops off giving f(10)=5.
1->4 this time it isn't a dead end so we take the other option at 4 which is 6, then 5.
1->4->6 ->5 dead end since 1 has already been visited so 5 pops off giving f(5)=6.
1->4->6 dead end so f(6)=7.
1->4 dead end so f(4)=8.
1 not a dead end as we haven't yet visited 2.
1->2 but since 10 has already been visited this is a dead end. Thus f(2)=9.
1 dead end and finally 1 pops off giving f(1)=10.
Since all vertices have been visited, we're done with the first DFS. The original graph with the new ordering of vertices is shown below.
Starting at 10, we do a depth first search again, taking note of the leader vertex for each vertex, that is, the vertex which starts the path containing that vertex.
10-> 6->7->8. Now 8 pops off then 7 then 6 and finally 10. All of these have leader vertex 10 and thus are in the same strongly connected component as 10.
The next unvisited vertex is 9, so we start the next path with 9. There is no unvisited vertex accessible from 9 so it's in a component on its own.
Now we move on to 5.
5->1->2->3->4. Each of these vertices pops off, 4 then 3, 2, 1, 5. All of them have lead vertex 5 so are in the same strongly connected component..
All vertices have been visited so we are done with the second DFS. This leaves us with the following three components. Note that vertex 9 is in a component on its own and not the same component as 1,2,3,4,5.
Source
CS 161 - Design and Analysis of Algorithms Lectures 6
The algorithm in involves starting with an ordering (any ordering) of the vertices, running a depth first search on the graph with all arcs reversed, while keeping note of position the vertices are removed from the stack. This position is then used to order the vertices in the original graph. A second depth first search is run, this time on the original graph with the new ordering of the vertices from largest to smallest. Whichever vertices are generated from the same leader are in the same component.
Example
Starting at 1, we do a depth first search on the graph. From 1 we can go to 2 or 4, and we arbitarily pick 4. From 4 we can go to 10 or 6 so we'll go for 10. From 10 we have no choice but to go to 7, then 8 and from there to 9 and then 3. From 3 we have no unvisited vertex to add so 3 pops off the stack and gets new label 1. I'll use f(3)=1 to denote the new label of vertex 3.
1-> 4 -> 10 ->7-> 8->9->3 dead end so f(3)=1.
1->4->10->7->8->9 dead end so 9 pops off next giving vertex 9 the new label 2, that is, f(9)=2.
1->4->10->7->8 dead end so 8 pops off giving f(8)=3.
1->4->10->7 dead end so 7 pops off giving f(7)=4.
1->4->10 dead end so 10 pops off giving f(10)=5.
1->4 this time it isn't a dead end so we take the other option at 4 which is 6, then 5.
1->4->6 ->5 dead end since 1 has already been visited so 5 pops off giving f(5)=6.
1->4->6 dead end so f(6)=7.
1->4 dead end so f(4)=8.
1 not a dead end as we haven't yet visited 2.
1->2 but since 10 has already been visited this is a dead end. Thus f(2)=9.
1 dead end and finally 1 pops off giving f(1)=10.
Since all vertices have been visited, we're done with the first DFS. The original graph with the new ordering of vertices is shown below.
Starting at 10, we do a depth first search again, taking note of the leader vertex for each vertex, that is, the vertex which starts the path containing that vertex.
10-> 6->7->8. Now 8 pops off then 7 then 6 and finally 10. All of these have leader vertex 10 and thus are in the same strongly connected component as 10.
The next unvisited vertex is 9, so we start the next path with 9. There is no unvisited vertex accessible from 9 so it's in a component on its own.
Now we move on to 5.
5->1->2->3->4. Each of these vertices pops off, 4 then 3, 2, 1, 5. All of them have lead vertex 5 so are in the same strongly connected component..
All vertices have been visited so we are done with the second DFS. This leaves us with the following three components. Note that vertex 9 is in a component on its own and not the same component as 1,2,3,4,5.
Source
CS 161 - Design and Analysis of Algorithms Lectures 6
Monday 12 December 2011
Kaprekar's Constant
I've been watching the University of Nottingham videos by Brady Haran on physics and chemistry for a while now but I hadn't come across this channel, numberphile before which is, rather unsurprisingly, about numbers.
So for the first thing I've learnt today, it's Kaprekar's constant. Take any four digit number, excluding numbers where all the digits are the same (0000, 1111, 2222, etc). Make the largest number and the smallest number out of these digits. Subtract them and repeat the process until it converges, that is you get the same number again. That number will always be 6174.
For example, take 2395. Rearrange the digits to make 9532 and 2359.
9532-2359 = 7173, and repeat
7731-1377 = 6354
6543-3456 = 3087
8730-0378 = 8352
8532-2358 = 6174
7641-1467 = 6174, and as we had this on the line above, we'll always get 6174 so the process has converged.
For more details, and an expansion to numbers with a different number of digits, see http://plus.maths.org/content/mysterious-number-6174.
So for the first thing I've learnt today, it's Kaprekar's constant. Take any four digit number, excluding numbers where all the digits are the same (0000, 1111, 2222, etc). Make the largest number and the smallest number out of these digits. Subtract them and repeat the process until it converges, that is you get the same number again. That number will always be 6174.
For example, take 2395. Rearrange the digits to make 9532 and 2359.
9532-2359 = 7173, and repeat
7731-1377 = 6354
6543-3456 = 3087
8730-0378 = 8352
8532-2358 = 6174
7641-1467 = 6174, and as we had this on the line above, we'll always get 6174 so the process has converged.
For more details, and an expansion to numbers with a different number of digits, see http://plus.maths.org/content/mysterious-number-6174.
Sunday 11 December 2011
It's been a while...
The last three months have been quite busy for me with three online courses to study. I've had a wonderful time learning lots of new things. When I started I thought I was going to struggle and not really be able to manage them. I've found that I could do more than I expected. I've found the three courses quite different.
Introduction to Databases
When I watched the first lecture on databases I thought I was crazy and didn't know what was going on. I had to pause and rewind the video multiple times. I felt completely in over my head. After a very shaky start, it became my favourite of the three courses. There were many additional exercises that meant I could really get my teeth into the material. I did everything. It brought back the joy and excitement of learning which made university such a wonderful time for me. I've missed the intellectual challenge.Machine Learning
This was by far the most mathematical of the courses which meant that I could follow fairly easily. The programming exercises in Octave were frustrating at times as I seem to have a great ability to make the program crash. My poor laptop found it a little tough at times to process everything such as a load of spam emails to predict whether another one was spam or not. It's been great to see the sort of techniques used behind the scenes to analyse spam, categorise news or predict whether someone has a tumour or not.Artificial Intelligence
This has been the most frustrating and yet most interesting course. I think if I'd watched the course from a casual point of view, I would have loved it. There have been hiccups over precision in asking questions which have lead to confusion. The lecturers are enthusiastic and you can really see how keen they are to explain their subject. It's a shame about the problems but the potential for a great course is there.What's Next?
I'm trying to learn Java over Christmas so that I can take part in some more courses from January to April. A list of the available courses can be found at the bottom of this page: http://www.anatomy-class.org/. There are 16 courses at the moment, one of which is the machine learning course mentioned above. I don't know which ones I will do yet as they all sound interesting. I think I might just watch some of the courses without being active since I am sure my coding will not be good enough by then and it's also impossible for me to do 15 courses at once.Java
So, in order to do these courses I've been working my way through http://codingbat.com/java which I'm finding quite helpful. It's a basic enough level that I can work quite quickly while learning some of the classes. I'll need to find something else later on to drag myself up to a higher level but I'll look for that later. I did start off with http://docs.oracle.com/javase/tutorial/java/TOC.html but it went too fast for me so I've paused that for a while and will come back to it later.Regex
I've started reading one of the recommended books for Natural Language Processes and it looks like I need to get to grips with regular expressions. I've been intending learning this for several years so finally I'm going to do it.Other Aims
I have quite a few other things I want to get done next year, and I've started to collect them together at a new site called Schemer. The following link is an invitation to the site: http://schemer.com/invite/9vidub2r7rqn6 (It's good for 20 invitations.) You can see other people's goals as well so there is lots of inspiration. Some of the things I'm hoping to do are- become proficient at sewing - I have a sewing machine (well several) but I am not really confident in using it. I'd like to be able to alter clothes, make clothes and do patchwork on it.
- make a patchwork quilt
- finish some of the many half done projects I have
- learn some yoga
- learn three new things a day
- learn some more Dutch
- learn to recognise the constellations of the stars
- improve my knowledge of physics
- cook my way through a cookery book
- walk a few miles every week
- grow some vegetables
I'd rather have too many aims than too few - more chances to succeed! I don't know how I'm going to fit everything in but it going to be fun anyway.
Sunday 2 October 2011
1st October 2011 Things I Want to Accomplish This Month
These are my aims for October.
This month I want to continue to work on those words, and further increase my vocabulary by at least 200 words.
I've signed up for the basic track for AI and ML, but will be doing the full DB course. So far I've complete the first week of lectures and exercises for DB. It feels so good to be studying again in a structured way. I hope I will be able to allocate sufficient time to all of this as each is supposed to require approximately 10 hours per week. I'm not actually sure I have that much time but I will give it my best shot and I will know more than I would have if I had not attempted this.
A couple of days ago, Christine Cantow Smith on Google+ posted a picture of a collage she is working on. When I saw it, I misread the word collage as college. Her collage contains lots of words and I thought, "Words, things to do at college, learning" and something clicked connecting it to the 12 things in a year.
What I'm going to do this month is collect together pictures and words connected to things I want to do and make a visual representation of what I want to do. I'm not sure whether it will turn out to be 12 things over the year, or some things spread out over a longer period. I'm swinging back and forth over that and over Yanik Falardeau's 30 changes in 30 days experiment which she carried out in August.
(*Added following section on 2011-10-02)
Dutch
I've been learning Dutch on and off for a couple of years, but not getting very far. Last month I came across a program memrise linked to by someone on Google+. I started using it at the beginning of September and since then I've learn about 500 words. I enjoy it and find it a fun way to learn the vocabulary without getting stressed or frustrated. Learning spellings in any language has always been something I'm quite bad at so this progress is quite significant for me.This month I want to continue to work on those words, and further increase my vocabulary by at least 200 words.
Stanford Free Courses
I think I'm somewhat crazy to have signed up to all three of the Stanford free online courses for this autumn. They officially run from 10th October to 12 th December. The courses are- http://www.db-class.org/ Introduction to Databases
- http://www.ml-class.org/ Machine Learning
- http://www.ai-class.com/ Artificial Intelligence
I've signed up for the basic track for AI and ML, but will be doing the full DB course. So far I've complete the first week of lectures and exercises for DB. It feels so good to be studying again in a structured way. I hope I will be able to allocate sufficient time to all of this as each is supposed to require approximately 10 hours per week. I'm not actually sure I have that much time but I will give it my best shot and I will know more than I would have if I had not attempted this.
Putting Together Ideas for 2012
A few years ago a friend of a friend decided to do 12 things, one per month over the course of the year. I tried it in a sort of messy, disorganised way and I accomplished some things but I didn't really have clear goals or really know what I wanted to do. It has been a positive experience, even though I didn't manage everything because it meant that I could look back over the year and say, "Yes, I did do something this year."A couple of days ago, Christine Cantow Smith on Google+ posted a picture of a collage she is working on. When I saw it, I misread the word collage as college. Her collage contains lots of words and I thought, "Words, things to do at college, learning" and something clicked connecting it to the 12 things in a year.
What I'm going to do this month is collect together pictures and words connected to things I want to do and make a visual representation of what I want to do. I'm not sure whether it will turn out to be 12 things over the year, or some things spread out over a longer period. I'm swinging back and forth over that and over Yanik Falardeau's 30 changes in 30 days experiment which she carried out in August.
Exercise
I want to work exercise into my daily routine. I have EA sport active 2 which I set up today, so that is what I will be using, at least in part. I have leaves to clear in the garden and so I will use activities like that as well.Craft
I would like to get at least two weeks ahead in my craft class preparation so that if I find I have too much to do with the courses, I have some flexibility.Quests
I will continue to do the leaving the house quests. I am going to go to Cafe Scientifique on Tuesday for the first time. This time I will not have a preliminary test run to check I know where it is before hand, like I did with Skeptics in the Pub. I'm going to just find my way there somehow from looking at Google maps.(*Added following section on 2011-10-02)
Clear Out
I have quite a lot of clothes and other things in the house that need to be thrown out. I'm going to try to do 15 minutes per day to make a dent in it.Thursday 29 September 2011
29th September 2011 An Optimist's Tour of the Future
Last night I went to another Skeptics in the Pub talk. This talk should have occurred 6 weeks ago, but because of the riots, it was delayed which was good for me as I would have missed it otherwise.
It was a very different talk from the first one I went to on lucid dreaming which was packed full of so much information that my head was reeling afterwards. Who needs drugs when you can get an intellectual high from a talk like that? Whee!
The speaker was Mark Stevenson, and the title "An Optimist's Tour of the Future." It was about changing from looking at the future from a negative point of view to a 'Yes, there is a problem but there are also solutions.' The problem with the doom and gloom is that if we can't see hope, we just give up. What's the point of trying when we're going to fail anyway? Fear is a terrible motivator as it can also paralyse and cause us to give up.
Having a more optimistic view of the future isn't about denying there is a problem, but looking for solutions. Not the cynical 'No, can't solve that, impossible, wont work' but finding a vision and striving for it. There is no way I can express the hope the talk gave to me. The future could be better. It might not be, but that possibility, that glimmer of hope, exists and it's that we need to focus on and make happen.
The population is increasing but wont the world become full? The rate of increase of population is slowing and in some countries, the population is decreasing. ;A best guess estimate is that the world population will reach about 10 billion and then start to decrease. There is the capacity to feed that many people.
There's too much carbon dioxide. What can we do? There are materials being produced, and made into something that looks like a brush (http://knowledge.allianz.com/?1580/carbon-capture-artificial-trees-suck-co2-from-air) which captures carbon dioxide from the air and holds on to it. To release this carbon dioxide, just put the brush in water. Ok, so now we have a heap of carbon dioxide and what are we going to do with that? Make it into fuel! (http://www.brightgreencities.com/v1/en/bright-green-book/estados-unidos/conversao-direta-de-dioxide-de-carbon-e-agua-diretamente-em-combustivel/) The aim is carbon neutral fuel stations in 10 years.
The usual way to farm is to split animals into smaller groups and have them in different fields, but this isn't how animals behave in nature. What do zebras do? They graze in tight groups for a few days in one area and then move on. Mimicking this by making fields into smaller sections, allowing the animals to graze for a couple of days and then moving them on leads to
The video shows Luke, who had his bladder replaced by a new one grown in the lab 10 years ago.
At the moment about 1 in 5000 drugs are accepted for use so the drug companies have to absorb the cost of the others making the cost of drugs rocket. If this cost did not have to be absorbed, then the cost of drugs could drop dramatically.
It was a very different talk from the first one I went to on lucid dreaming which was packed full of so much information that my head was reeling afterwards. Who needs drugs when you can get an intellectual high from a talk like that? Whee!
The speaker was Mark Stevenson, and the title "An Optimist's Tour of the Future." It was about changing from looking at the future from a negative point of view to a 'Yes, there is a problem but there are also solutions.' The problem with the doom and gloom is that if we can't see hope, we just give up. What's the point of trying when we're going to fail anyway? Fear is a terrible motivator as it can also paralyse and cause us to give up.
Having a more optimistic view of the future isn't about denying there is a problem, but looking for solutions. Not the cynical 'No, can't solve that, impossible, wont work' but finding a vision and striving for it. There is no way I can express the hope the talk gave to me. The future could be better. It might not be, but that possibility, that glimmer of hope, exists and it's that we need to focus on and make happen.
Look how far we've come.
The amount of change over the last century has been incredible. Here are a few of the things that have been achieved, and are already being achieved.Life Expectancy
The minimum life expectancy in any country in 1909 was 22 in Bangladesh. Now (2009 figures), the worst is in war torn Afghanistan at double that.World Population and Food Production
Since 1950, even though the world population has increased from 2.6 billion to 6.9 billion (http://www.npg.org/facts/world_pop_year.htm), the per capita amount of food produced has also increased. There are two and a half times the number of people and we're producing more food per person? Remarkable. So why is there starvation? We've got the food but we're failing on the distribution.The population is increasing but wont the world become full? The rate of increase of population is slowing and in some countries, the population is decreasing. ;A best guess estimate is that the world population will reach about 10 billion and then start to decrease. There is the capacity to feed that many people.
There's too much carbon dioxide. What can we do? There are materials being produced, and made into something that looks like a brush (http://knowledge.allianz.com/?1580/carbon-capture-artificial-trees-suck-co2-from-air) which captures carbon dioxide from the air and holds on to it. To release this carbon dioxide, just put the brush in water. Ok, so now we have a heap of carbon dioxide and what are we going to do with that? Make it into fuel! (http://www.brightgreencities.com/v1/en/bright-green-book/estados-unidos/conversao-direta-de-dioxide-de-carbon-e-agua-diretamente-em-combustivel/) The aim is carbon neutral fuel stations in 10 years.
Nanotechnology
Nanotechnology is enabling cheaper solutions - reducing the cost of desalination of sea water. How about something that looks like a teabag for less the 0.5 cents to filter water? (http://inhabitat.com/nanotech-tea-bag-purifies-drinking-water-for-less-than-a-penny/)Agricultural Waste
Plants capture carbon, but then they die and rot and release it again. Turning agricultural waste into charcoal retains the captured carbon. Why would farmers do this? Two reasons.- The right sort of charcoal can be used to improve the soil and increase yields by up to 50%. (The wrong sort can decrease it.) More carbon in the soil makes it retain more water, and the soil is more open so after a dry period, the rain doesn't just run off.
- It can be turned into a revenue stream, since agricultural waste can be turned into high quality activated carbon. Activated carbon is used in filtration systems.
Grazing Animals
In Australia, there are area where on one side of the fence the grass is overgrazed and the other it is long and dying. The growing part of grass is at the base, so if the base is blocked, then photosynthesis is restricted and the grass doesn't grow. When grass is eaten by animals, some of the roots are lost to the soil, which puts more carbon back into the soil. It's only a small amount, but a small amount repeated over and over leads to a large amount. (I don't know why this rotting doesn't release carbon dioxide into the atmosphere though.)The usual way to farm is to split animals into smaller groups and have them in different fields, but this isn't how animals behave in nature. What do zebras do? They graze in tight groups for a few days in one area and then move on. Mimicking this by making fields into smaller sections, allowing the animals to graze for a couple of days and then moving them on leads to
- no need for fertilisers to make the grass grow
- increased biodiversity
- no need to buy food since the grass is growing
Medicine
We have the skills to transplant organs, but there aren't enough donors. How can this be solved? Printing organs!The video shows Luke, who had his bladder replaced by a new one grown in the lab 10 years ago.
Drugs
Many drugs are rejected because some people have negative reactions to them. What if the genomes of those people could be sequences and the gene causing the problem be isolated so that drug could be used for the ninety-nine people who could benefit from it and the one person who would have an adverse reaction could be given something else? Sequencing someone's genome is getting cheaper and cheaper, and it's claimed it can currently be done for $30.At the moment about 1 in 5000 drugs are accepted for use so the drug companies have to absorb the cost of the others making the cost of drugs rocket. If this cost did not have to be absorbed, then the cost of drugs could drop dramatically.
Barriers to Change
What is it that stops this exciting future from becoming a reality, and from problems being solved?- Waiting for the government to act - governments are slow and if we wait for them to do something it will be too late. They need to see something being done so they can jump on the bandwagon.
- Cynicism. It's seen as cool and wise to be cynical but it blocks progress and is filled with negativity. It's bad for you and bad for the people around you. It's not about finding a way past problems, but just focusing on them. We need to take responsibility to keep our own cynicism in check.
Now what?
A few things- The future is here already, it's just not evenly distributed.
- If you can imagine a better future, you can aim for it.
- Keep cynicism in check.
- Never look at limitations as anything you ever comply with. (Cosmic speed limit? Let's wait and see.)
For further information, the speaker has written a book, An Optimist's Tour of the Future which I haven't read yet. (I ordered it when I got home last night.) If it's half as good as the talk, it's going to be well worth reading. The book is going to be turned into a film, which is definitely something I want to see even though I dislike cinemas intensely.
Mark is also starting a "meeting place for people and organisations who want to make the world better". For further information see http://leagueofpragmaticoptimists.com/.
At the moment, I don't know what I can do except live with an attitude of hope and a vision of better things to come. That's a start, isn't it?
Mark is also starting a "meeting place for people and organisations who want to make the world better". For further information see http://leagueofpragmaticoptimists.com/.
At the moment, I don't know what I can do except live with an attitude of hope and a vision of better things to come. That's a start, isn't it?
Thursday 15 September 2011
14th September 2011 Life as an RPG
Life as an RPG
A few weeks ago, I saw a t-shirt with the slogan "Achievement Unlocked: Left the House". Around the same time, I started to read posts by +Aristotle Bancale about life as an rpg. I love rpg, whether pen and paper adventures or computer games. I met my husband through a text based rpg, a MUD. Doing quests and levelling up in games is fun. I get it. I can do it. Dealing with real life - no, really not my thing. Was there something in the idea of making life into an rpg that could help me to deal with the anxiety of real life and dealing with new situations?The Aim
I'd heard about meetings of skeptics in America, and wondered if there was anything similar in my area over here in the UK. I googled and found a local group. I thought that I'd like to go and meet some intelligent, thoughtful people in real life instead of just online. I wasn't particularly interested in the topic, but that didn't seem so important. I wanted to go to this meeting, but I was scared.Quests and Achievements
So, how was I going to overcome the fear and panic and manage to do this? It started as just joking around about quests. Oh, do I get the 'Leave the house achievement for going to the doctors?' Yay! "How about the touring Europe quest since I've visited seven different countries?" "Let's make it level 2 for seven, with five countries for level 1."The First Quest
Two weeks ago, a friend was visiting, and we went into Birmingham. Was I going to manage any quests? Could I find my way anywhere? I have no sense of direction at all, but with a lot of standing and looking around and thinking, I managed the "find my way to the bus stop from the market" quest. In the process of working out where I was, I drew a rough map to a shop I wanted to be able to find again. When I was doing this, with the thought of rpgs on my mind, I suddenly realised that I can't find my way in games either but I've developed a way of dealing with that. Why on earth was I not applying this to real life too? DOH!Mapping the Route
A week later, it was time to try again, but this time going to the location of the meeting. The day before, I looked at google street view and travelled the route as I mapped it out in the same way as I map for games. Was this going to work?The Second Quest
Saturday arrived, and my husband and I caught the bus into Birmingham. I started off, remembering the map but then I had to check it. One quick glance and I knew where I was going. I found the pub where the meeting would be held quite easily. It felt good! Going back to the bus stop? No problem. Finding the chocolate shop (with amazing 100% dark chocolate)? Easy peasy! The market? It's that way (pointing) but we'll go this way instead. That's four quests right there!The Main Quest
So, tonight arrived. I was panicking. I wanted to go but I didn't want to go. I wasn't sure whether to just call it off but after dragging my husband into Birmingham on Saturday, it didn't seem fair not to try. I caught the bus to Birmingham. There was a girl and her friend sitting behind me on the bus and she wasn't feeling well. The poor lass was sick which took my mind completely off the meeting. I had some wet wipes and a plastic bag in my bag so was able to help out. I got off the bus with plenty of time to spare and wandered in the direction of the pub. I don't know what I was doing as I just turned right at a random place and walked on. After a minute or two, I thought, "Where on earth am I going?", turned around, went back the way I'd come and continued the right way.Side Quest
Going home, I was going to need to catch the train. I hadn't practised this. The route to the pub passed the station so I thought I'd buy a ticket home so that if the talk finished late, I wouldn't have to mess around but could go straight to the train. What a silly station Birmingham New Street is. You go in the entrance, can get straight to the platform but there is nowhere to buy a ticket! Fortunately, I found someone to ask and was told I had to go down to the platform to get to the main part of the station. It certainly wasn't obvious where I was supposed to get a ticket but I found it and then went back the way I'd come. Now I knew how I was going to get home. Phew!The Main Quest Continued
I was about half an hour early when I arrived at the pub. I find pubs rather daunting places so I didn't really want to go in. There were a couple of people outside so even though I really wanted to walk around the block and come back later, I thought I'd just look weird so I plunged in hoping to find the stairs down to where the meeting was. There were no stairs down. Utoh! I did a quick circuit of the room and dived into the ladies!Now what should I do? I'm definitely in the right place, but which of these people are here for the meeting? No idea. I know, I'll buy a drink. That must be a quest. I know going to a pub was. I'm sure we talked about that one before. At least I'll have done some quests even if I don't stay for the meeting. When I got my drink, I asked where the meeting was. "Upstairs." I'm sure the notice said downstairs, but no matter.
I went upstairs to a room which was filling up rather quickly. I found a spot in the corner to perch and settled in. I was there. I'd done it! Achievement unlocked. Quest completed!
Conclusion
So did thinking of life as an rpg help? Most certainly. It gave me another perspective on how to do things. It enabled me to break down a problem into steps which were worth achieving on their own. It showed me how I could apply skills from gaming in everyday life. It felt empowering and I feel successful. I feel much more confident and able to do the next quest now, whatever that quest may be.Monday 5 September 2011
5th September 2011 Little Things Make a Difference: Just a Smile
About 3 weeks ago, as I was walking to a doctor's appointment, I smiled at a lady as I walked past and she smiled back. It brightened up my day and mood. It made a difference to me. It also set me thinking about how differently people interact on a day to day basis in a city compared with a day out in the countryside, and how different those two experiences feel.
When walking in the countryside, almost everyone makes eye contact with the people they meet on the way and exchanges a cheery good morning or afternoon. They may even stop for a chat. I love the sense of connection with others this gives, even though we will probably never meet again. It's good to take time to interact.
On the other hand, in the city, it's often hard to even get a smile from anyone. People rushing all the time with no time for connection, locked in their own private little worlds. Are we really too busy to smile?
I wonder how much less stressed and more connected we would feel if we just took a moment to smile at someone. Would other people would find their day brightened by that smile, or just find it weird? Maybe that person you smiled at lives alone and hasn't spoken to anyone all week. Would people feel threatened by the smile? Could it be a dangerous in some situations?
Link to discussion on G+.
When walking in the countryside, almost everyone makes eye contact with the people they meet on the way and exchanges a cheery good morning or afternoon. They may even stop for a chat. I love the sense of connection with others this gives, even though we will probably never meet again. It's good to take time to interact.
On the other hand, in the city, it's often hard to even get a smile from anyone. People rushing all the time with no time for connection, locked in their own private little worlds. Are we really too busy to smile?
I wonder how much less stressed and more connected we would feel if we just took a moment to smile at someone. Would other people would find their day brightened by that smile, or just find it weird? Maybe that person you smiled at lives alone and hasn't spoken to anyone all week. Would people feel threatened by the smile? Could it be a dangerous in some situations?
Link to discussion on G+.
Monday 22 August 2011
22nd August 2011 - How Infinity Messes Up Stuff
I just love this video. It's caused me much amusement for me in tormenting my friends so I thought maybe I should write about it.
On Minute Physics, Henry Reich 'proves' that
On Minute Physics, Henry Reich 'proves' that
1+ 2 + 4 + 8 + 16+... = -1.
You can see how in the video so I'll just let you watch it before proceeding.
Now, according to the mathematics you're taught at school, every step is correct yet something seems terribly wrong here. How can you be adding positive numbers and end up with a negative number?
Let's look at what he does.
- He multiplies by 1 which doesn't change anything.
- He rewrites 1 as (2 - 1) which is also fine since 2 - 1 = 1.
- He applies the distributive law. The distributive law says that (a + b)c = ac + bc and a(b + c) = ab + bc). For example, (3+5)x2 = 3x2 + 5x2. If you check this, you will see that (3 + 5)2 = 8 x 2 =16 and also 3x2 + 5x2 = 6 + 10 = 16. To apply this to the example, he does 2(1+2+4+8+...) - 1(1+2+4+8+...) and then applies it again to multiply each number inside the bracket by the number outside to get 2 + 4 + 8 + 16 + ... - 1 - 2 - 4 - 8 - 16 - ...
- He cancels all the terms and is left with -1.
So where is the flaw? It's in step 4 because when we deal with infinity strange things happen, and the distributive law doesn't work. The method in itself is a useful mathematical tool, as we'll see below, but unfortunately it doesn't work when we are dealing with infinite series.
Let's look at how it should work. What we will do is use another mathematical trick, and by trick I don't mean something bad or deceitful, but something clever. We will look at a finite series which has N+1 terms, and then we will let N get as big as we want, infinite in fact, and see what happens. This will show us how infinity is confusing us in the video above. We're going to follow the Minute Physics method
Now, as we're doubling each time, so we have
1st Term: 1 = 20
2nd Term: 2 = 21
3rd Term: 4 = 2x2=22
4th Term: 8 = 2x2x2=23
5th Term: 16 =2x2x2x2=24
Notice that the power of 2 for each term is one less than its position in the series. This means for the N th term, where N is some number (we don't care what number it is at the moment, just some large positive whole number.)
N th Term: 2x2x2x..x2=2N-1.
Right, back to the method given in the video, but this time for a finite series.
1 + 2 + 4 + 8 + ...+2N-1 = 1(1 + 2 + 4 + 8 + ...+2N-1)
= (2-1)(1 + 2 + 4 + 8 + ...+2N-1)
= 2(1 + 2 + 4 + 8 + ...+2N-1)-1(1 + 2 + 4 + 8 + ...+2N-1)
= 2 + 4 + 8 + ...+ 2N-1+2N - 1 - 2 - 4 - 8 - ...- 2N-1
= 2N - 1.
Well, that means that 1 + 2 + 4 + 8 + ...+2N-1= 2N - 1, which is quite a nice formula but how does it help us with the infinite series in the video?
What we'll do now we've got this nicely written down is make N get bigger and bigger so it tends to infinity. That means the left hand side becomes 1 + 2 + 4+ 8 + ... where the dots mean carry on forever. What happens to the right hand side? Since N tends to infinite, then 2N tends to infinity even more quickly, so the right hand side tends to infinity. This means that the sum 1+2+ 4+ 8 + ... tends to infinity too, and most definitely not -1.
Friday 19 August 2011
19th August 2011 Fact or Fiction? The Importance of Looking More Closely
Today I came across the following article being shared on Google+. The headline is "Science Reveals Women Who Wear Less Clothing Live Longer". The article claims the following.
A prominent British anthropologist has completed a ground-breaking, 10-year study proving that women who wear less clothing live up to 20 years longer. And the fewer clothes they wear, the longer they live. Writing in the Royal Journal of Social Anthropology, Sir Edwin Burkhart presents the results of over 5,000 interviews with women ages 70 to 120. It's clear from the interviews and graphs shown that those women at the older end of the spectrum consistently wore either fewer clothes throughout their lifetime -- or no clothing at all!It goes on to further discuss the topic, giving examples and possible explanations.
Copies of this article have spread all over the place. Do people believe the content? Should they? Is it a case of confirmation biased in that people want it to be true?
There are no links to the source, nor is it referenced properly. Sadly, this is often the case in journalism and in itself doesn't mean the information is incorrect. In this case, however, I can find no evidence for the existence of the Royal Journal of Social Anthropology, nor for the 'prominent' anthropologist Sir Edwin Burkhart.
The design of the study seems strange. A 10 year study which doesn't appear to have any follow-up? Why would it take 10 years and how could it be extrapolated to mean 20 extra years' life? Where is the proof of causation and not just correlation (not that any evidence for that is presented here)?
Let's look at some of the information given: "... 5,000 interviews with women ages 70 to 120." Where did the researcher find this 120 year old? According to the Guinness Book of Records,
[t]he oldest person living is Maria Gomes Valentim (Brazil), of Carangola, Brazil, who was 114 years 313 days old as of 18 May 2011. [1]The quotations from the supposed research subjects are somewhat ridiculous.
Philomena Bushfield, 120, is a life-long nudist who hasn't "worn more than a pair of socks since I was 7." She is rarely sick, still runs in marathons, and has the energy and enthusiasm of a woman half her age. "It also made it much easier to meet men," says Bushfield, who currently has three different boyfriends.Could someone who was born in 1891 really have lived her life from 1898 without clothes? Wouldn't we all know about her is she had, especially if she were running marathons while wearing nothing more than a pair of socks!
Now, apart from looking at the content, and there is more that could be said about it, if we look at the author of the article it is Mark C. Miller, humorist. Surely that is sufficient evidence to take this all with a pinch of salt?
Much as I can see that this is meant as a humorist piece, I find it worrying that people seem to believe it, or to take it at face value. The subject concerns me in that I wonder if it could be used as a weapon against women and their right to dress as they wish. Maybe that is taking it too seriously, but seeing how subtle pressure can be applied to people 'for their own good', I don't really like to see something that could potentially be used like this.
Although this doesn't seem to have been picked up by any newspapers, a recent incident with an article by the BBC on the IQ of Internet Explorer users highlights the danger of not checking our facts and believing everything we read without a critical thought.
Wednesday 17 August 2011
17th August 2011 Overcoming a Problem by Making it a Game
Today I read about the actions of a father whose daughter was struggling to cope with the breathing exercises she had to do to clear her lungs because she has cystic fibrosis. Instead of just battling on with the problem and forcing her to go through the necessary steps every night he turned it into fun. He made use of his contacts to develop a game which is controlled by the puffs on the breathing machine.
What I like about this story is that someone looked beyond the problem and traditional way of doing things to find a new and innovative solution. It's a story of one person making a difference with an idea and then pushing it through to development.
If something as onerous and painful can be made fun by making it into a game, what other things can be made more fun in some way? We might not all be able to come up with something that will have an effect on many other people, but how can we use our own creativity to make life easier and more enjoyable for ourselves and those around us?
What I like about this story is that someone looked beyond the problem and traditional way of doing things to find a new and innovative solution. It's a story of one person making a difference with an idea and then pushing it through to development.
If something as onerous and painful can be made fun by making it into a game, what other things can be made more fun in some way? We might not all be able to come up with something that will have an effect on many other people, but how can we use our own creativity to make life easier and more enjoyable for ourselves and those around us?
Tuesday 16 August 2011
15 August 2011 - 1 Multiplying Numbers When the First Digits are the Same & the Last Sum to Ten
Continuing the theme of multiplying various numbers, we come to some which satisfy a particular condition as explained in the examples below.
Hence 26 x 24 = 624. The method also works for larger numbers.
Hence 113 x 117 = 13221.
We'll now check to see if the method gives the same result.
Hence the method gives 10c2 + 10c + d2 - 10d which is ab so it works for numbers of the prescribed form.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Example 1
We'll multiply 26 by 24. The method we'll use requires the first digits to be the same, here 2, and the last digit from each number sums to ten, here 6 + 4 = 10.| 1. Take the first digit | 2 |
| 2. Add one | 2 + 1 = 3 |
| 3. Multiply the numbers from step 1 and 2. | 2 x 3 = 6 |
| 4. Multiply the last 2 digits of the original numbers | 6 x 4 = 24 |
| 5. Write the answer to step 4 after step 3. | 624 |
Hence 26 x 24 = 624. The method also works for larger numbers.
Example 2
We'll multiply 113 by 117. We'll check the numbers satisfy the conditions for the method. The first digits are the same, both 11, and the last two digits sum to ten: 3 + 7 = 10.| 1. Take the first digit | 11 |
| 2. Add one | 11 + 1 = 12 |
| 3. Multiply the numbers from step 1 and 2. | 11 x 12 = 132 |
| 4. Multiply the last 2 digits of the original numbers | 3x7=21 |
| 5. Write the answer to step 4 after step 3. | 13221 |
Proof
Again, let's check that the examples above weren't just flukes. Let's multiply two numbers a and b which both start with c which could be a single digit or several digits, and end in d and (10 - d) respectively. Hence
a = 10c + d and b = 10c + (10-d).
Multiplying a and b, we get
ab = (10c + d)(10c + (10-d))
= 100c2+ 100c -10cd + 10cd + 10d - d2
= 100c2+ 100c -10cd + 10cd + 10d - d2
= 100c2+ 100c + 10d - d2.
| 1. Take the first digit | c |
| 2. Add one | c + 1 |
| 3. Multiply the numbers from step 1 and 2. | c(c + 1) = c2 + c |
| 4. Multiply the last 2 digits of the original numbers | d(d-10) = d2 - 10d |
| 5. Write the answer to step 4 after step 3. This is the equivalent to multiplying the answer to step 3 by 10 and then adding the answer to step 4. | 10(c2 + c)+d2 - 10d = 10c2 + 10c + d2 - 10d |
Hence the method gives 10c2 + 10c + d2 - 10d which is ab so it works for numbers of the prescribed form.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Sunday 14 August 2011
14 August 2011 - 1 Sea Pen Video
A couple of days ago, I wrote about sea pens. Today, youtube suggested the following video which shows sea pens contracting to bury themselves under the sand over a four hour period. It's a clip taken from the BBC's Ocean series, so I hope it's visible outside the UK.
13th August 2011 -1 Squaring Two Digit Numbers Ending in 5
I saw this method in a GCSE foundation paper, as well as here.
Squaring a number is simply multiplying it by itself, so 3 squared, written as 32 means 3 x 3 = 9. That is 32=9.
Does this method really work?
Squaring a gives
Now we'll apply the method to a and see if we get the same result. First we write down the tens figure b and then add one to it, giving b + 1. These are then multiplied to give
Method
This method works for numbers ending in 5. As an example, we'll square 35.| Example | Method |
|---|---|
| 3 | 1) Write down the tens figure. |
| 3 + 1 = 4 | 2) Add 1 to it. |
| 3 x 4 = 12 | 3) Multiply the numbers from steps 1 and 2. |
| 1225 | 4) Write 25 after the number obtained in step 3. This is the original number squared. |
Does this method really work?
Proof
Let the number to be squared be a where a is a number ending in 5. Let the tens digit be b. Then we can write
a = 10b + 5.
Squaring a gives
a2 = (10b + 5)2
= 100b2 + 100b + 25. (1)
Now we'll apply the method to a and see if we get the same result. First we write down the tens figure b and then add one to it, giving b + 1. These are then multiplied to give
b(b + 1) = b2 + b.
which is what we obtained when we multiplied a by itself in (1). Hence the method gives us a2, that is, it works.
Note that this proof can be adapted for any number ending in 5 as we never use that b is a single digit. For instance 1152 is found as follows:
11 x 12 = 132 (since 12 = 11+1)
so 1152 = 13225 (putting 25 after the number above).
Since, we write 25 immediately after this number, we are actually multiplying by 100, which shifts the 12 in the example above to 1200, and then adding 25.
100(b2 + b) + 25 = 100b2 + 100b + 25,
which is what we obtained when we multiplied a by itself in (1). Hence the method gives us a2, that is, it works.
Note that this proof can be adapted for any number ending in 5 as we never use that b is a single digit. For instance 1152 is found as follows:
11 x 12 = 132 (since 12 = 11+1)
so 1152 = 13225 (putting 25 after the number above).
Friday 12 August 2011
12th August 2011 - 1 Can Leaf Veins Be Used To Predict Climate?
Benjamin Blonder, an ecology graduate student, working with his advisor Brian Enquist at the University of Arizona in Tucson is examining the connection between the veins in leaves and climate. Preliminary results from his models predict temperature and precipitation. I'll be very interested to see if these preliminary results hold up when tested more widely and whether they can be extrapolated to accurately determine climate from fossil records, as he suggests.
His website has some useful resources including details on making leaf skeleton, and his blog has fascinating articles about leaves from the cost of producing veins and their function to colour change to how plants survive with only the occasional flash of sunlight through the dense canopy above.
His website has some useful resources including details on making leaf skeleton, and his blog has fascinating articles about leaves from the cost of producing veins and their function to colour change to how plants survive with only the occasional flash of sunlight through the dense canopy above.
Source
11th August 2011 - 2 Jigsaw Pieces Everywhere
I read a lot of articles and blogs every day, along with my Google+ stream, books and conversations with friends. I'm very hungry-for-knowledge but then some days it feels like there is too much, and that nothing fits together. It's as if each piece of knowledge is a jigsaw piece and they are strewn all over the place.
How can I ever make sense of all these pieces? Nothing ties up. Such small snippets but surely they go together somehow? I jump from one thing to another, wondering what is going on and then suddenly I get a feeling that something is familiar. Just a moment, didn't I hear something about that a few days ago? Then it dawns on me. I did! I love that AHA moment when things link up.
I had that feeling today when I was reading up on sea pens. A predator of the sea pen is the nudibranch. Nudibranch, nudibranch, oooh, wasn't that something someone posted a picture of on Google+? I checked back and sure enough, +Kjetil Greger Pedersen had posted a photograph of one which eats anemones and uses their poison to protect itself. Great feeling.
11th August 2011 - 1 First Pencils, Now Pens - Pen Urchins
Back in April, I wrote about the beautiful pencil urchins. Today, I came across this lovely collection of photographs of sea pens, so I thought I'd carry on with the stationary theme.
The visible part of the sea pen can be up to 2 m in some species, such as the tall sea pen which can be found off the west coast of Scotland.
Some species reproduce by releasing eggs and sperm into the water, whereas in others the female retains the eggs and fertilisation is internal. The developing embryos are brooded until they have reached an advanced larval stage when they are released into the water, where they root to form new pens.
Name
The sea pens are types of soft coral of the order Pennatulacea, sub order Subselliflorae. The name 'sea pen' arises from their feather-like appearance which resembles a quill pen. |
| Photo by fiveinchpixie |
Life Cycle
A sea pen is a colonial animal, which means it is made up of individual polyps which together function as a whole animal. It begins life as a larva which roots itself and then develops into a stalk. This stalk is called a rachis. It has a root-like structure at its base which anchors it to the sea floor. Both this and this stalk are strengthened by calcium carbonate. The feather-like protrusions are made up of two new types of polyps formed through asexual reproduction. These polyps are responsible for feeding (gastrozoids) and respiration (siphonozoids). The gastrozoids capture food while the siphonozoids move water around to allow for gas exchange.Some species reproduce by releasing eggs and sperm into the water, whereas in others the female retains the eggs and fertilisation is internal. The developing embryos are brooded until they have reached an advanced larval stage when they are released into the water, where they root to form new pens.
Habitat
Sea pens prefer deeper water, from 10 m to 2 km deep, where they are less likely to be uprooted. They tend to stay in one place but can re-establish themselves if necessary. They position themselves so currents ensure a steady flow of plankton, their main source of food.Threats and Defences
Unfortunately, sea pens are often destroyed by prawn trawlers and dredgers as well as being prey for sea stars and nudibranchs. In defence, a sea pen may luminesce or deflate and retreat completely underground.Sources
- http://en.wikipedia.org/wiki/Sea_pen
- http://www.bbc.co.uk/nature/blueplanet/factfiles/jellies/seapen_bg.shtml
- http://www.naturalengland.org.uk/ourwork/marine/protectandmanage/mpa/mcz/features/habitats/seapen.aspx
- http://www.marlin.ac.uk/speciesfullreview.php?speciesID=3353#
- http://www.advancedaquarist.com/2003/10/inverts
- http://www.ehow.com/about_6418563_sea-pens.html
Thursday 11 August 2011
10th August 2011 - 1 Multiplying Numbers just over 100
Today, we're going to look at extending the methods discussed earlier this week to numbers just above 100.
Again, we'll look first at the method, then its feasibility and finally a proof.
Example 1
For instance, 102 x 145 since 2 x 45 = 90 is easy if you're comfortable with doubling. Once you've multiplied those, all that is left to do is add 102 and 45 which is 147, put a couple of zeroes on the end and add the 90 you got earlier. That is,
Example 2
Similarly, 120 x 145 is as follows. Do 20 x 45, which is just 2 x 45 = 90 with a zero on the end, that is
and so
We will multiply a and b, which are numbers greater than 100. Next we subtract 100 from each of them to give a - 100 and b - 100, and then multiply them together.
Moving on to the other part of the calculation, we add a - 100 to b to get a + b - 100. Next we multiply by 100 which gives
Adding (1) and (2), we obtain
again showing that our method does indeed multiply a and b together.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Method
We'll multiply 105 by 107. How does the method differ from earlier methods? Instead of subtracting the numbers from 100, we subtract 100 from then, and instead of subtracting diagonally, we add. (See table below.)| Numbers to Multiply | Left hand column minus 100 |
|---|---|
105
|
5
|
107
|
7
|
ADD the number diagonally opposite. It doesn't matter which pair we use as we get the same answer. The pairs are shown in red and blue.
|
Multiply the numbers in this column
|
105 + 7 or 107 + 5 = 112
|
5 x 7 = 35
|
Multiply this by 100
| |
112 x 100 = 11200
|
35
|
Finally, we add the two numbers.
| |
11200 + 35 = 11235
| |
When is it useful?
If you can multiply the two digits after 100 by each other, then this method works.Example 1
For instance, 102 x 145 since 2 x 45 = 90 is easy if you're comfortable with doubling. Once you've multiplied those, all that is left to do is add 102 and 45 which is 147, put a couple of zeroes on the end and add the 90 you got earlier. That is,
147 x 100 = 14700,
14700 + 90 = 14790,
and so
102 x 145 = 14790.
Example 2
Similarly, 120 x 145 is as follows. Do 20 x 45, which is just 2 x 45 = 90 with a zero on the end, that is
20 x 45 = 900.
Then
120 + 45 = 165,
165 x 100 = 16500,
16500 + 900 = 17400,
and so
120 x 145 = 17400.
Proof
The proof is similar to those I've given for the last three posts on this topic.We will multiply a and b, which are numbers greater than 100. Next we subtract 100 from each of them to give a - 100 and b - 100, and then multiply them together.
(a - 100)(b - 100) = ab - 100a - 100b + 10000. (1)
Moving on to the other part of the calculation, we add a - 100 to b to get a + b - 100. Next we multiply by 100 which gives
100(a + b - 100) = 100a + 100b - 10000. (2)
Adding (1) and (2), we obtain
ab - 100a - 100b + 10000 + 100a + 100b - 10000 = ab,
again showing that our method does indeed multiply a and b together.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Tuesday 9 August 2011
9th August 2011 - 1 Moeraki Boulders in New Zealand
Inspiration
A photograph that caught my eye this morning on Google+ was a picture by . My initial reaction was "Whoa, that's amazing!" It's a lovely image in soft pastels of something I've never seen before. Fortunately Mr Sojka gives some background to his shots and explains that this is a broken Moeraki boulder on the Otago coast of New Zealand. I don't know the scale of the boulder from the shot, but it looks quite large to me. Quite how such large boulders could be just sitting there on the beach puzzled me so to google I went.Description
The picture below shows unbroken boulders. Moeraki boulders are roughly spherical and up to 3m in diameter. They are covered in cracks called septaria. |
| Moeraki Boulders at Sunrise by Karsten Sperling via Wikipedia Commons |
Formation
 |
| Not to scale! |
The cracks which taper off from the centre to the outer layer are taken as evidence that the surface was more rigid than the softer inside and so could not shrink as much. This is attributed to the differing amounts of calcite in the different layers.
There are several suggestions as to why the cracks formed:
- dehydration of clay rich, gel rich or organic rich cores,
- shrinkage of the boulder's cenre,
- expansion of gases produced by decaying organic matter,
- brittle fracturing or shrinkage of the interior by earthquake or compaction.
They are exposed when the softer surrounding mudstone is eroded by the elements.
Sources
Monday 8 August 2011
8th August 2011 - 1 Multiplying Numbers Just Below 100
The underlying method I talked about two days ago can be extended so you can multiply numbers just below 100. What do we need to do to adjust it? Wherever we used 10, we replace it by 100. Let's try 96 x 91.
If you know your tables up to 10 x 10, then any two numbers in the 90s will be easy to multiply together because the differences will be at most 10.
Multiplying 98 by any number is going to be fairly straightforwards if doubling is something you can do easily. For example 98 x 46.
If you're happy to double and double again, you'll find you can multiply by 96 as that is 4 less than 100. Similarly, 80 and 60 aren't too bad since then you're just multiplying by 20 (double and put a 0 on the end) or 40 (double, double again and put a 0 on the end).
And just to make sure, let's check the proof still works out ok.
We subtract them from 100 to get 100-a and 100-b. We multiply these (right hand column in the table) to get
(100 - a)(100 - b) = 10000 - 100a - 100b + ab. (1)
Next we subtract to get a - (100 - b) = a + b - 100 and then multiply by 100,
100(a + b - 100) = 100a + 100b -10000. (2)
Finally we add (1) and (2) to get
10000 - 100a - 100b + ab+100a + 100b -10000 = ab.
This means that applying the method does indeed multiply a and b as claimed.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Edit: Corrected two typos where I put 10 instead of 100.
Method
| Numbers to Multiply | 100 minus left hand column |
|---|---|
96
|
4
|
91
|
9
|
Subtract the number diagonally opposite. It doesn't matter which pair we use as we get the same answer. The pairs are shown in red and blue.
|
Multiply the numbers in this column
|
96 - 9 or 91 - 4 = 87
|
4 x 9 = 36
|
Multiply this by 100
| |
87 x 100 = 8700
|
36
|
Finally, we add the two numbers.
| |
8700 + 36 = 8736
| |
When is it Useful?
So let's consider when this method might be useful. Personally, I think the method for small numbers is interesting but too time consuming compared with the benefit of learning tables up to at least 10 x 10. When the maths gets more advanced, to have to resort to fingers to do 8 x 7 is slow compared with recalling from memory. Small numbers are multiplied fairly often so the investment of time is worth it, even if you struggle to learn things by rote, like I do.If you know your tables up to 10 x 10, then any two numbers in the 90s will be easy to multiply together because the differences will be at most 10.
Multiplying 98 by any number is going to be fairly straightforwards if doubling is something you can do easily. For example 98 x 46.
| Numbers to Multiply | 100 minus left hand column |
|---|---|
98
|
2
|
46
|
54
|
Subtract the number diagonally opposite. It doesn't matter which pair we use as we get the same answer. The pairs are shown in red and blue.
|
Multiply the numbers in this column
|
98-54 or I prefer 46 - 2 = 44
|
2 x 54 = 108
|
Multiply this by 100
| |
44 x 100 = 4400
|
108
|
Finally, we add the two numbers.
| |
4400 + 108 = 4508
| |
If you're happy to double and double again, you'll find you can multiply by 96 as that is 4 less than 100. Similarly, 80 and 60 aren't too bad since then you're just multiplying by 20 (double and put a 0 on the end) or 40 (double, double again and put a 0 on the end).
And just to make sure, let's check the proof still works out ok.
Proof
Let's apply this method to a and b which are two whole numbers less than 100.We subtract them from 100 to get 100-a and 100-b. We multiply these (right hand column in the table) to get
(100 - a)(100 - b) = 10000 - 100a - 100b + ab. (1)
Next we subtract to get a - (100 - b) = a + b - 100 and then multiply by 100,
100(a + b - 100) = 100a + 100b -10000. (2)
Finally we add (1) and (2) to get
10000 - 100a - 100b + ab+100a + 100b -10000 = ab.
This means that applying the method does indeed multiply a and b as claimed.
Source: http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
Edit: Corrected two typos where I put 10 instead of 100.
Sunday 7 August 2011
7th August 2011 - 1 Multiplying Single Digits Part 2 - Using Fingers
The Method
Using the principle covered in yesterday's post, here are two videos showing how to use your fingers to apply it. The first touches fingers togetherand the second folds some down.
I think the videos explains the methods clearly, but I do have one minor issue with the second and that is the comment "To show it's no fluke, let's try another multiplication." Unfortunately, two examples do not show it is not a fluke. Checking all possibilities would, or a proof such as the one I gave yesterday. The proof needs a slight change from yesterday's to apply to this method.
The Proof
Let's look at what is happening with the numbers first, and then generalise to show how the method works for any two numbers a and b, between 5 and 10 inclusive.
The circled fingers in the first picture correspond to the fingers in both circles in the second picture.
Circled Fingers
On my left hand I have 3 fingers folded down because 8 - 5 = 3. On the right hand it's 7 - 5 = 2. These are added, 3 + 2 = 5. This corresponds to the number of fingers circled in the first picture. This number is multiplied by 10 to give 50. In general, on the left hand there are a - 5 fingers circled, and on the right b - 5. Summing these gives
(a - 5) + (b - 5) = a - 5 + b - 5 = a + b - 10.
This is multiplied by 10 to give
10(a + b - 10) = 10a + 10b - 100,
which is the same as we had yesterday. We need to work out the value obtained from the non-circled fingers and then add that to this value.
Non-circled Fingers
The number of non-circled fingers is 10 - 8 = 2 on the left hand and 10 - 7 = 3 on the right hand. We multiply these two numbers together to give 6 and add it to the answer from the circled fingers, calculated above.On the left hand we have 10 - a non-circled fingers, and on the right 10 - b. Multiplying these together gives
(10 - a)(10 - b) = 100 -10a - 10b + ab.
Finally, adding this to the circled fingers answer, and simplifying, gives
10a + 10b - 100 + 100 -10a - 10b + ab = ab,
showing that both methods do correctly multiply a and b together.
6th August 2011 - 1 Multiplying Single Digits Part 1
There are many methods for multiplying numbers together.
The first method I'm going to look at is for single digits which are both 5 or above. If one of the digits is below 5, you gain nothing over just multiplying them together, or at best, very little. If both digits are 5 or above, all you need to know is how to subtract and times tables up to 5 x 5.
So when we multiply 8 and 6 we get 48.
Sometimes when you multiply the two new numbers together, we get a number which is two digits, as shown in the example below where we multiply 6 by 6. This doesn't make any difference to the method.
So 6 x 6 = 36.
The first method I'm going to look at is for single digits which are both 5 or above. If one of the digits is below 5, you gain nothing over just multiplying them together, or at best, very little. If both digits are 5 or above, all you need to know is how to subtract and times tables up to 5 x 5.
The Method
As an example, we'll multiply 8 and 6.
First we subtract both numbers from 10 to get 2 and 4, and write the answer in the corresponding right hand column below.
| Numbers to Multiply | 10 minus left hand column |
|---|---|
8
|
2
|
6
|
4
|
Subtract the number diagonally opposite. It doesn't matter which pair we use as we get the same answer. The pairs are shown in red and blue.
|
Multiply the numbers in this column
|
8-4 or 6-2 = 4
|
2 x 4 = 8
|
Multiply this by 10
| |
4 x 10 = 40
|
8
|
Finally, we add the two numbers.
| |
40 + 8 = 48
| |
So when we multiply 8 and 6 we get 48.
Sometimes when you multiply the two new numbers together, we get a number which is two digits, as shown in the example below where we multiply 6 by 6. This doesn't make any difference to the method.
| Numbers to Multiply | 10 minus left hand column |
|---|---|
6
|
4
|
6
|
4
|
6 - 4 or 6 - 4 = 2
|
4 x 4 = 16
|
2 x 10 = 20
|
16
|
| 20 + 16 = 36 | |
So 6 x 6 = 36.
How does it work?
With some algebra, we can see that the method above really does give the right answer.
Let the two numbers to be multiplied be a and b.
Let the two numbers to be multiplied be a and b.
| Numbers to Multiply | 10 minus left hand column |
|---|---|
a
|
10-a
|
b
|
10-b
|
a - (10 - b) = a -10 + b
= a + b -10 |
(10 - a)(10 - b)
|
Multiply by 10.
|
Multiply out the brackets.
|
10(a + b -10)=10a + 10b -100
|
(10 - a)(10 - b) = 100 - 10a - 10b + ab
|
We now add the two expression above.
| |
10a + 10b -100 + 100 - 10a - 10b + ab = (-100 + 100) + (10a - 10a) + (10b - 10b) +ab = ab
| |
As we get ab, this means the method does indeed give us the correct answer when we multiply a and b.
| |
Saturday 6 August 2011
5th August 2011 - 3 Correlation but is it causation?
Ben Goldacre posted an interesting illustration of how data can mislead and needs to be analysed before posting. His example shows a correlation between lung cancer and drinking, that is, if you drink you are more likely to get lung cancer than if you don't drink. Does that really mean that drinking causes lung cancer or is there another factor in play?
When the figures are split into smokers and non-smokers, the smoker who drink and the smokers who don't drink have the same occurrence of lung cancer. Similarly, for non-smokers, drinker and non-drinkers have the same occurrence of lung cancer. This shows that the occurrence of lung cancer is explained by smoking versus not smoking rather than drinking versus not drinking.
When the figures are split into smokers and non-smokers, the smoker who drink and the smokers who don't drink have the same occurrence of lung cancer. Similarly, for non-smokers, drinker and non-drinkers have the same occurrence of lung cancer. This shows that the occurrence of lung cancer is explained by smoking versus not smoking rather than drinking versus not drinking.
5th August 2011 - 2 Bad Maths
I noticed as my twitter feed flew past today the following link which amused me in a strange sort of way. It's an image of a poster claiming to solve the world financial crisis along with some conspiracy claims. In the middle of the poster they make the following claim.
Suppose an item costs $10. From the first sentence, we have that 51% of this price is interest on the National Debt. That would be $10 x 0.51 = $5.10, so without this interest on the item, it would cost $10 - $5.10 = $4.90.
The claim in the second sentence claims that everything in stores is 51% than it would be without the National Debt, as the poster claims that the United States Note will solve this. This 51% is now referring to the 51% of $4.90 (the price without debt) which is $4.90 * 0.51 which is about $2.50. If the second sentence were true, the item would cost $4.90+2.50=$7.40 which it doesn't. So how much more is being paid as the 51% is clearly wrong and not enough.
As we want the percentage to be compared to the price without the debt, we write the extra paid, $5.10, as a fraction of the price without debt and multiply by 100 to turn it into a percentage.
5.10/4.90 * 100 = 104% (to nearest percent)
What this tells us is that instead of paying about half extra as the poster claims, people are paying more than double what the price would be without the debt payments!
This illustrates how important it is to know what any percentage is of so that mistakes like this do not occur.
*An estimated 51% of retail prices are a result of interest on the National debt. This means that as of right now, everything in stores is 51% more than it would be if we used a national currency like the United States Note.What amused me was that someone claiming to solve the monetary crisis doesn't understand basic percentages.
Suppose an item costs $10. From the first sentence, we have that 51% of this price is interest on the National Debt. That would be $10 x 0.51 = $5.10, so without this interest on the item, it would cost $10 - $5.10 = $4.90.
The claim in the second sentence claims that everything in stores is 51% than it would be without the National Debt, as the poster claims that the United States Note will solve this. This 51% is now referring to the 51% of $4.90 (the price without debt) which is $4.90 * 0.51 which is about $2.50. If the second sentence were true, the item would cost $4.90+2.50=$7.40 which it doesn't. So how much more is being paid as the 51% is clearly wrong and not enough.
As we want the percentage to be compared to the price without the debt, we write the extra paid, $5.10, as a fraction of the price without debt and multiply by 100 to turn it into a percentage.
5.10/4.90 * 100 = 104% (to nearest percent)
What this tells us is that instead of paying about half extra as the poster claims, people are paying more than double what the price would be without the debt payments!
This illustrates how important it is to know what any percentage is of so that mistakes like this do not occur.
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