I've just realised that I have forgotten to put "Read Choas" in my new GANTT chart. I am already fully aware of the fact that I may not have enough time to read all of the books. I have decided that, because I have so many quantum books to read, I will not read the second Quantum book (by Manjit Kumar) and that slot on my GANTT chart will be dedicated to reading Chaos.
Next week is half term and so hopefully I will have a lot of time to do extended project work. However, my Oxford maths admissions test is on November the 3rd (2 weeks time) so I will be doing a lot of preparation for that next week. Luckily I dont't have too much school work to do so I will make extended project a main priority.
Thursday, 21 October 2010
Tuesday, 19 October 2010
Probability section
I have begun collecting all sources and quotes in preparation for writing the Probability section of my dissertation.
Evaluation of Randomness
Deborah J. Bennett is assistant professor of mathematics at Jersey City State College, New Jersey. This shows that she is definitely a reliable source. Reading this book has helped me with my project in many ways.
Firstly, before reading the book I did not know much about the history of randomness, but now I do. This encouraged me to do more research on the history of the deabte of randomness, which I did not think of doing before.
Bennett made all the mathematical concepts (probabilities) very easy to understand and quite enjoyable. I liked how Bennett investigated a wide range of ideas about randomness. There were quotes about probability, random number generators and other topics that will be extremely useful to me when writing my dissertation.
"In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed." - J.A.Rial, American Scientist
"Deborah J. Bennett's book is a useful survey of an often misunderstood topic. Randomness is deceptively complex -- in particular, as Bennett points out, because aspects of it are counterintuitive. " www.complete-review.com
I will definitely be using quotes for this book in my dissertation.
Firstly, before reading the book I did not know much about the history of randomness, but now I do. This encouraged me to do more research on the history of the deabte of randomness, which I did not think of doing before.
Bennett made all the mathematical concepts (probabilities) very easy to understand and quite enjoyable. I liked how Bennett investigated a wide range of ideas about randomness. There were quotes about probability, random number generators and other topics that will be extremely useful to me when writing my dissertation.
"In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed." - J.A.Rial, American Scientist
"Deborah J. Bennett's book is a useful survey of an often misunderstood topic. Randomness is deceptively complex -- in particular, as Bennett points out, because aspects of it are counterintuitive. " www.complete-review.com
I will definitely be using quotes for this book in my dissertation.
Sunday, 17 October 2010
More from Quantum
"Consider a million identical radioactive nuclei that are unstable and will, sooner or later, spontaneously 'decay' by emitting a particle and changing into a more stable form. While quantum mechanics enables us to calculate something called the half-life (the time after which half of the nucleus will have decayed)it cannot tell us when any particular nucleus will decay. [...] We can calculate the probability that a nucleus will have decayed after any given time, but the fact that we cannot do any better that this is not due to our ignorance.[...] What we are lacking is a deeper understanding of Nature whereby we are able to predict exactly when any given nucleus might decay, just a fuller knowledge of all the forces involved in a toss of a coin would allow us to predict its outcome."
This is an example of quantum mechanics. This implies that although theoretically, if we knew everything about the conditions of the atom, we could predict when it would decay, it is impossible for us to actually know the conditions. It could then be argued that randomness does exist.
This is an example of quantum mechanics. This implies that although theoretically, if we knew everything about the conditions of the atom, we could predict when it would decay, it is impossible for us to actually know the conditions. It could then be argued that randomness does exist.
What am I doing right now?
At the moment, I am reading Quantum by Jim Al-Khalili. I am also writing the Random Number Generators section of my dissertation. I don't seem to have much to really say about number generators, despite the research I have done on them. I have typed up roughly 300 words, and don't really know where to go with it. I think I will leave this section for a while and begin another part, because it is stopping me from progressing.
I was just about to update my GANTT chart when I realised that I have nothing to add to it. I want to redo my GANTT chart again, but I feel as though I shouldn't keep doing this. The wholepoint of a GANTT chart is that it is there for you to stick by it, but if I keep changing it whenever I fall behind, I'm not really progressing, am I?
Having said that, I really think that a new GANTT chart is what I need right now. But I promise that this will be the last GANTT chart that I make!!
I am fully aware that I have a lot of books to read in a short amount of time. I will aim to always be ahead of this GANTT chart.
Things I need to do this week:
Evaluate Randomness
Finish reading Quantum - Jim Al-Khalili
I was just about to update my GANTT chart when I realised that I have nothing to add to it. I want to redo my GANTT chart again, but I feel as though I shouldn't keep doing this. The wholepoint of a GANTT chart is that it is there for you to stick by it, but if I keep changing it whenever I fall behind, I'm not really progressing, am I?
Having said that, I really think that a new GANTT chart is what I need right now. But I promise that this will be the last GANTT chart that I make!!
I am fully aware that I have a lot of books to read in a short amount of time. I will aim to always be ahead of this GANTT chart.
Things I need to do this week:
Evaluate Randomness
Finish reading Quantum - Jim Al-Khalili
Saturday, 16 October 2010
"Isaac Newton believes that every particle in the Universe should obey simple laws of motion subject to well-defined forces. This mechanistic view - one that was still shared universally by scientists and philosophers more than two centuries later - states that no matter how complex the workings of nature are, everything should be ultimately reducible to interactions between the fundamental building blocks of matter. [...] if we could know the precise position and state of motion of every particle in a given system, no matter how many are involved, then we should be able to predict, through Newton's laws, how these particles will interact and move, and hence how a system will look at any given time in the future. [...]
Of course in practice such determinism is impossible for all but the simplest systems."
This is similar to what I have researched previously; randomness may just be a lack of knowledge. It could be a pattern that is just too complex for us to be able to understand right now.
Of course in practice such determinism is impossible for all but the simplest systems."
This is similar to what I have researched previously; randomness may just be a lack of knowledge. It could be a pattern that is just too complex for us to be able to understand right now.
Really interesting example of quantum mechanics from the book
This is quite a long extract so I'll try to cut it down to the most relevant parts. There are some really useful diagrams that I may take pictures of and blog them because they explain this very well. I cannot upload photos onto this blog via my mobile though, so will have to do it another time.
"First, a beam if light is shone on a screen with two narrow slits in it that allow some light to pass through to a second screen where an interference pattern is seen. This is a sequence of light and dark bands that are due to the way the separate light waves emerging from the two slits spread out, overlap and merge before hitting the back screen."
I remember being shown this experiment in a gcse science lesson.
"Next, a similar experiment is carried out using sand. This time the second screen is placed below the one with the slits and gravity does the work. As the sand falls onto the first screen, separate piles gradually build up on the lower one beneath the two slits. This is not surprising since each grain of sand must pass through one or the other of the two slits; we are not dealing with waxes now and there is no interference. The two piles if sand will be if the same height provided the two slits are of the same size and the sand is poured from a position above their mid-point."
"Now for the interesting part: repeating the trick with atoms. A special apparatus - let us call it an atomic gun for want of a better name - fires a beam if atoms at a screen with two appropriately narrow slits. On the other side, the second screen is treated with coating that shows up a tiny bright spot wherever a single atom hits it. [...] First, we run the experiment with just one slit open. Not surprisingly, we get a spread of light spots on the back screen behind the open slit. [...] Next, we open the second slit and wait for the spots to appear on the screen. If I asked you now to predict the distribution if the bright spots that build up you would naturally guess that it would look like the two piles on sand. [...]
Instead, we see an interference pattern of light and dark fringes just as we did with light. [...]
With a detector in place that records which slit each atom passes through, the interference pattern disappears. It is as though the atoms do not wish to be caught in the act of going both ways at once, and only travel through one slit of the other. Two bands form on the screen adjacent to the slits as a result of particle-like behaviour, similar to what happens with the sand.
With the detector turned off we now have no knowledge of the route taken by each atom. Now that their secret is safe, the atoms revert to their mysterious wave-like behaviour and the interference pattern comes back!"
I find this so fascinating! I dont even know what to say in order to evaluate this extract.
"How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome. [...] Physicists have been forces to admit that, in the case of the double slit trick, there is no rational way out. We can explain what we see but not why. However strange you may find the predictions of quantum mechanics, it must be emphasized that it is not the theory - mankind's invention - that is strange, but rather Nature herself that insists on such a strange kind of reality on the microscopic scale".
"First, a beam if light is shone on a screen with two narrow slits in it that allow some light to pass through to a second screen where an interference pattern is seen. This is a sequence of light and dark bands that are due to the way the separate light waves emerging from the two slits spread out, overlap and merge before hitting the back screen."
I remember being shown this experiment in a gcse science lesson.
"Next, a similar experiment is carried out using sand. This time the second screen is placed below the one with the slits and gravity does the work. As the sand falls onto the first screen, separate piles gradually build up on the lower one beneath the two slits. This is not surprising since each grain of sand must pass through one or the other of the two slits; we are not dealing with waxes now and there is no interference. The two piles if sand will be if the same height provided the two slits are of the same size and the sand is poured from a position above their mid-point."
"Now for the interesting part: repeating the trick with atoms. A special apparatus - let us call it an atomic gun for want of a better name - fires a beam if atoms at a screen with two appropriately narrow slits. On the other side, the second screen is treated with coating that shows up a tiny bright spot wherever a single atom hits it. [...] First, we run the experiment with just one slit open. Not surprisingly, we get a spread of light spots on the back screen behind the open slit. [...] Next, we open the second slit and wait for the spots to appear on the screen. If I asked you now to predict the distribution if the bright spots that build up you would naturally guess that it would look like the two piles on sand. [...]
Instead, we see an interference pattern of light and dark fringes just as we did with light. [...]
With a detector in place that records which slit each atom passes through, the interference pattern disappears. It is as though the atoms do not wish to be caught in the act of going both ways at once, and only travel through one slit of the other. Two bands form on the screen adjacent to the slits as a result of particle-like behaviour, similar to what happens with the sand.
With the detector turned off we now have no knowledge of the route taken by each atom. Now that their secret is safe, the atoms revert to their mysterious wave-like behaviour and the interference pattern comes back!"
I find this so fascinating! I dont even know what to say in order to evaluate this extract.
"How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome. [...] Physicists have been forces to admit that, in the case of the double slit trick, there is no rational way out. We can explain what we see but not why. However strange you may find the predictions of quantum mechanics, it must be emphasized that it is not the theory - mankind's invention - that is strange, but rather Nature herself that insists on such a strange kind of reality on the microscopic scale".
My laptop has been sent off to get fixed and hopefully will be back on Monday. I need it back as soon as possible because although I can blog through my mobile, I haven't been able to finish the "random number generators" section, which is on word. Also, I've just realised that there could be a chance that the people who are fixing the laptop may have to reboot it. If this happens, I will lose a lot of my extended project work such as my GANTT charts. Virtually all of my research and work is in this blog but I need to GANTT charts in excel form, not just a print screen which is what they are in this blog. Anyway, hopefully this isn't going to happen.
I am reading through "Quantum" but Jim Al-Khalili.
"Quantum mechanics is remarkable for two seemingly contradictory reasons. On the one hand, it is so fundamental to our understanding of the workings if our world that it lies at the very heart of moat of the technological advances made in the last half a century. On the other hand, no one seems to know exactly what it means!"
"Quantum mechanics accurately predicts and explains the behaviour of the very building blocks of matter - not just the atoms, but the particles that make up the atoms - with incredible accuracy. It has led us to a very precise and almost complete understanding of how subatomic particles interact with each other and connect up to form the world we see around us, and of which we are of course a part."
Jim Al-Khalili is a physicist and has been studying quantum mechanics for over twenty years. The quotes that I find in this book should therefore be very reliable.
I am reading through "Quantum" but Jim Al-Khalili.
"Quantum mechanics is remarkable for two seemingly contradictory reasons. On the one hand, it is so fundamental to our understanding of the workings if our world that it lies at the very heart of moat of the technological advances made in the last half a century. On the other hand, no one seems to know exactly what it means!"
"Quantum mechanics accurately predicts and explains the behaviour of the very building blocks of matter - not just the atoms, but the particles that make up the atoms - with incredible accuracy. It has led us to a very precise and almost complete understanding of how subatomic particles interact with each other and connect up to form the world we see around us, and of which we are of course a part."
Jim Al-Khalili is a physicist and has been studying quantum mechanics for over twenty years. The quotes that I find in this book should therefore be very reliable.
Tuesday, 12 October 2010
Supervision
I had a meeting with my supervisor a couple of hours ago. I discussed where I am in terms of my GANTT chart. I have now completed my ucas application and although I will be preparing for the Oxford maths admissions test, I should still be able to get some extended project work done. My supervisor said that I have an impressive range of sources but I need to make sure that I evaluate all of them and talk about how they all relate to each other. In order to fulfil the criteria for the assessment objectives, I need evidence to show that I have used technology. This could mean using Microsoft excel for my GANTT chart, using the Internet and discussing how a website works, for example RANDOM.ORG, the random number generator.
From this supervision, I learnt that I am on the right track at the moment and just need to make sure that I motivate myself to read all the books and write my dissertation.
From this supervision, I learnt that I am on the right track at the moment and just need to make sure that I motivate myself to read all the books and write my dissertation.
Saturday, 9 October 2010
I have begun reading "quantum theory: a very short introduction"
I doubt that I will be making much progress in my project during the next few weeks because I will be preparing for the maths admissions test for Oxford university. Doing this and also keeping on top of school work may mean that I will have to not do as much extended project work as I would like to. I'll jus have to see how it goes. I need to arrange another meeting with my supervisor because the last meeting did not take place.
I doubt that I will be making much progress in my project during the next few weeks because I will be preparing for the maths admissions test for Oxford university. Doing this and also keeping on top of school work may mean that I will have to not do as much extended project work as I would like to. I'll jus have to see how it goes. I need to arrange another meeting with my supervisor because the last meeting did not take place.
Tuesday, 5 October 2010
Half way through Random Number Generators
Here is what I have so far:
"One day, I was sitting in my maths class fiddling with my calculator when I came across a button called Ran#. I realised that if I typed in a number and pressed this button, the calculator would randomly produce a number between zero and the number that I typed. But how could this be? Calculators use algorithms to perform functions so does this mean that there is an algorithm to produce random numbers? If so, random must not exists because the fact that there is an algorithm to produce a random sequence completely undermines the concept of randomness.
After some research, I came across a website called Random.org which claimed to be a “True Random Number Service”. The website discussed how computer and calculator programs use “pseudorandom number generators” which is less effective than this website because they use the randomness from “atmospheric noise”. Wikipedia defines atmospheric noise as “radio noise caused by natural atmospheric processes, primarily lightning discharges in thunderstorms”. Pseudorandom number generators are algorithms that are not entirely random but produce a set of numbers that pass all tests for randomness. So, there are certain properties that a sequence must have for it to be random. The fact that people are aware of this and it is possible to create sequences that could be classed as random shows that although one cannot predict a random sequence, a sequence can be made that is identified as random.
American mathematician Robert R. Coveyou stated that “The generation of random numbers is too important to be left to chance.” This is an incredibly intriguing quote. "
I'm finding it very difficult to word things well in this section. Also, I'm not too sure of the message that I actually what to get across in this section. I have all the quotes and sources but what do I actually want to acheive?
Anyway, as I keep saying, HOPEFULLY this will be finished soon. I have a meeting with my supervisor in about half an hour so will blog about how that goes soon.
"One day, I was sitting in my maths class fiddling with my calculator when I came across a button called Ran#. I realised that if I typed in a number and pressed this button, the calculator would randomly produce a number between zero and the number that I typed. But how could this be? Calculators use algorithms to perform functions so does this mean that there is an algorithm to produce random numbers? If so, random must not exists because the fact that there is an algorithm to produce a random sequence completely undermines the concept of randomness.
After some research, I came across a website called Random.org which claimed to be a “True Random Number Service”. The website discussed how computer and calculator programs use “pseudorandom number generators” which is less effective than this website because they use the randomness from “atmospheric noise”. Wikipedia defines atmospheric noise as “radio noise caused by natural atmospheric processes, primarily lightning discharges in thunderstorms”. Pseudorandom number generators are algorithms that are not entirely random but produce a set of numbers that pass all tests for randomness. So, there are certain properties that a sequence must have for it to be random. The fact that people are aware of this and it is possible to create sequences that could be classed as random shows that although one cannot predict a random sequence, a sequence can be made that is identified as random.
American mathematician Robert R. Coveyou stated that “The generation of random numbers is too important to be left to chance.” This is an incredibly intriguing quote. "
I'm finding it very difficult to word things well in this section. Also, I'm not too sure of the message that I actually what to get across in this section. I have all the quotes and sources but what do I actually want to acheive?
Anyway, as I keep saying, HOPEFULLY this will be finished soon. I have a meeting with my supervisor in about half an hour so will blog about how that goes soon.
Writing "Random Number Generators"
I am just writing about algorithms and came across a relevant quote that I found a while ago. The quote itself doesn't matter at the moment, but the website that it is from is called scholarpedia.org.uk. I decided to Google the website just to see if it had any connection to wikipedia and the actual description for scholarpedia is:
"Scholarpedia feels and looks like Wikipedia -- the free encyclopedia that anyone can edit. Indeed, both are powered by the same program -- MediaWiki. Both allow visitors to review and modify articles simply by clicking on the edit this article link.
However, Scholarpedia differs from Wikipedia in some very important ways:
Each article is written by an expert (elected by the public or invited by Scholarpedia editors).
Each article is anonymously peer reviewed to ensure accurate and reliable information.
Each article has a curator -- typically its author -- who is responsible for its content.
Any modification of the article needs to be approved by the curator before it appears in the final, approved version."
This implies that scholarpedia is a more accurate and reliable version of wikipedia. For future references, I will be using scholarpedia rather than wikipedia to look up things.
"Scholarpedia feels and looks like Wikipedia -- the free encyclopedia that anyone can edit. Indeed, both are powered by the same program -- MediaWiki. Both allow visitors to review and modify articles simply by clicking on the edit this article link.
However, Scholarpedia differs from Wikipedia in some very important ways:
Each article is written by an expert (elected by the public or invited by Scholarpedia editors).
Each article is anonymously peer reviewed to ensure accurate and reliable information.
Each article has a curator -- typically its author -- who is responsible for its content.
Any modification of the article needs to be approved by the curator before it appears in the final, approved version."
This implies that scholarpedia is a more accurate and reliable version of wikipedia. For future references, I will be using scholarpedia rather than wikipedia to look up things.
Monday, 4 October 2010
Atmospheric Noise (a method of generating random numbers)
http://en.wikipedia.org/wiki/Atmospheric_noise
"Atmospheric noise is radio noise caused by natural atmospheric processes, primarily lightning discharges in thunderstorms.
Atmospheric noise is mainly caused by cloud-to-ground flashes as the current is much stronger than for cloud-to-cloud flashes. On a worldwide scale, eight million lightning flashes occur daily. This is about 100 lightning flashes per second.
The sum of all these lightning flashes results in atmospheric noise. It can be observed[1] with a radio receiver in the form of a combination of white noise (coming from distant thunderstorms) and impulse noise (coming from a near thunderstorm). The power-sum varies with seasons and nearness of thunderstorm centers.
Atmospheric noise and variation is also used to generate high quality random numbers. Random numbers have interesting applications in the security domain."
"Atmospheric noise is radio noise caused by natural atmospheric processes, primarily lightning discharges in thunderstorms.
Atmospheric noise is mainly caused by cloud-to-ground flashes as the current is much stronger than for cloud-to-cloud flashes. On a worldwide scale, eight million lightning flashes occur daily. This is about 100 lightning flashes per second.
The sum of all these lightning flashes results in atmospheric noise. It can be observed[1] with a radio receiver in the form of a combination of white noise (coming from distant thunderstorms) and impulse noise (coming from a near thunderstorm). The power-sum varies with seasons and nearness of thunderstorm centers.
Atmospheric noise and variation is also used to generate high quality random numbers. Random numbers have interesting applications in the security domain."
I have just borrowed the remaining three books from the school library! They have allowed to to keep them until December (when the Extended Project will end). Hopefully I have everything I need to just work and work on my project and finish everything.
I am in the school library right now, and my lesson starts in 10 minutes but I will try and write more of the Random Number Generator section now.
HOPEFULLY I will be able to get it finished soon!
I am in the school library right now, and my lesson starts in 10 minutes but I will try and write more of the Random Number Generator section now.
HOPEFULLY I will be able to get it finished soon!
Saturday, 2 October 2010
Right...
Up to date GANTT chart:
OKAY.
Tasks for this week:
1) Write Random Number Generators section.
2) Don't read the quantum physics books just yet - focus on starting to read Chaos again (as I stopped reading this over the summer so I could get other tasks done).
3) Take out Does God Play Dice?, Quantum Theory and Introduction to random time and quantum randomness from the school library.
OKAY.
Tasks for this week:
1) Write Random Number Generators section.
2) Don't read the quantum physics books just yet - focus on starting to read Chaos again (as I stopped reading this over the summer so I could get other tasks done).
3) Take out Does God Play Dice?, Quantum Theory and Introduction to random time and quantum randomness from the school library.
Friday, 1 October 2010
So I haven't managed to get much done this week, which is extremely disappointing. My laptop is still not working and it seems as though I haven't had time to anything other than schoolwork. On top of that, I've been doing my university application that needs to be submitted in a couple of weeks. As a result of this, my extended project has not been high in my list of priorities. I have begun reading Quantum (well, the chapter that seems most relevant) but there's my much to comment on right now. On a brighter note, my school library have bought the remaining books that I need.
Tomorrow, my plan is to go to muswell hill library and use their computer to write the random number generators section and update my GANTT chart (which I am definitely behind on). I hope to get this project back on track and really work hard to get all the research done.
Tomorrow, my plan is to go to muswell hill library and use their computer to write the random number generators section and update my GANTT chart (which I am definitely behind on). I hope to get this project back on track and really work hard to get all the research done.
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