My Apology

May 4th, 2008 RaVPup | Bookmark

She resides where Erin is free
Amongst roué of din and glee
A life coloured by bigotry of men
Insanity kisses to her from me

Anothers cage is Erins den
Through his folly he did descend
Into an ailment that hath no relief
Only hope and fickle mend

They both smoked the amber leaf
Her with joy and him with grief
The difference was their frame of mind
He was ratiocinative

Told the locus was undefined
She captures light, he studies sine
In the garden he plants a tree
He studies it to remind her of me

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Gods Art

April 15th, 2008 RaVPup | Bookmark

I thought I would take a little bit of time out from my schedule to write about Jennifer and her trip abroad. There have been many things happening in my life, all of them quite positive. That’s not to say that a week without Jennifer is positive, but that I have been directed by a sense of purpose about the things that I am doing.

I have been giving some thought to languages. One of the things that draw me to Jennifer is the fact that she speaks a few Germanic languages. I myself speak two languages with complete native fluency and have always wanted to develop that further. I had the opportunity in my teenage years to study Arabic, so I have some command of the alphabet, words and even a few phrases. I would have liked to have become natively fluent in the language by this point in my life, but unfortunately that was not to be.

One of the reasons that I could not complete my study of Arabic was that it was delivered by a person that was full of bias and he wasn’t in synergy with my learning style. I believe the pursuit of knowledge should be directed in a calm and relaxed way so that memories of the experience invoke pleasant feelings. I am not sure what school of thought most people are from, but a majority of those I have met seem to view it as a chore rather than a personality building experience. This is not a belief that I share in any away because I feel the wide and varied learning experiences that I’ve had in my life have made it all the richer.

Jennifer seems to me a very mature and deep woman, one that I can relate to on some level that I have yet to explain. It is not really of consequence however, as my goal is not to explain it but to experience it on that level. I can tell that she had a wonderful time during her trip abroad because she is in high spirits and much more expressive. Stress changes people in ways that haven’t been fully understood. It changes their psyche and their physiology. I recount the experience of a childhood friend who grew up to become a bitter adult because of the environment that he was exposed to.

I have read about the theories of Freud and their interpretations in modern psychology. They are quite balanced and well structured, although there are many schools of thought in psychology that I have not explored. I was speaking to a friend of mine that I bumped into by chance and he was telling me of his lack of success with his psychologist. Upon further discussion, he revealed that he did not really believe in the efficacy of psychology and I explained to him that his problem lay there. The first stage that must be achieved if one is to have success with any method is to approach it with an open mind, free from bias and ill informed notions. With psychology, you cannot really begin to function as a patient without first gaining psychological awareness. If there is no interest in psychology itself, and a magic bullet is desired, then the results will not be optimal.

I had Jennifer in my thoughts while she was away and I imagined the things that she would be doing, the sights that she would be seeing and the people that she would be meeting. I really wanted her to unwind and take a break from it all, because it seems to me that she is under some stress. I can sense that she is dealing with some pressures in her life, ones that she does not really share with me. I’m not sure what it is that worries her but I am sure that when the time is right, she will share her thoughts with me. I didn’t miss her so much as I acknowledged that she was not with me for the duration of the week. It is a feeling that is hard to explain, and perhaps it is representative of the altered state of consciousness from my earlier years. I feel a lot closer to people that I keep company with, without the need to constantly remind them of my presence or be reminded of theirs. I am glad that Jennifer is back and I look forward to talking with her when she has recovered from her trip.

When I look at Jennifer, I am still captivated by her beauty. It hasn’t worn thin on me yet and is something that I hope will stay with me for a long time. I have been making an effort to return to the more virtuous values that I held firm in my younger years with the insight that I have now in my older years. I appreciate Jennifer more because I have had my own experiences to draw from and I know that she does not lead a shallow life that is focused simply on the pursuit of power and wealth. There are other things that build a person’s character and I am of the view that there are parts to her personality that I have yet to explore.

I have been conversing with various people all over the world and I have been able to share some of their insights about the places that they live and the lives that they lead. After some consideration, I consider myself quite lucky in that I have managed to lead a life that has been relatively varied and interesting, and that I wake up every morning wanting to learn more about myself and others. The reason that I enjoy mathematics and computing is that they are two fields in which I can express ideas in a rigorous and concrete manner, and communicate those ideas to others without much loss of information. It is not that I don’t have an appreciation for other forms of expression, but to me they are ambiguous and open to interpretation. I remember discussing with students of the humanities about the role of engineering as a creative outlet. They seemed to disagree that something so functional could be artistic. I believe their ideas about art were malformed in that they believe that art is a means to provide entertainment or to relax. By their definition, and the definitions of others that are of the same mindset, the analytical person is not capable of producing art. I disagree with this wholeheartedly. I believe that both the analytical and the creative mind are capable of producing art. The difference lies in the assumption that the analytical minds art will be of the same form as the creative person’s art.

I will end this with a note about Jennifer. I appreciate her in all her forms. To me she is Gods art.

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Analysis of Key Spaces

April 2nd, 2008 RaVPup | Bookmark

I have been entertained by the brute force attempts on this server since I deployed it and have been meticulously reading the logs. The reason I have been paying so much attention to them is because there was a noticeable absence of a firewall or any other mechanism of protecting the ports from enumeration. The occurrences of brute force attacks conducted by robots or very bored people with programs are quite common on the Internet. There are myriads of infected machines out there that can be dedicated to finding more vulnerable hosts. This is the currency of the hacker world. I do not mind the attempts so much as I mind the principle of them. Brute forcing passwords over an Internet connection is the last resort of the least intelligent.

There is a common misconception among Information Technology professionals without a thorough grounding in permutations and combinations to misquote the difficulty of brute forcing a password from the length of their key. The length of the key is important, what it defines is the key space of the cryptanalysis problem. Where your key lies in that key space is another matter altogether. Let’s consider the case where there is a key of length nine, in the set of all Unicode characters. Say we are given a key which is ‘aaaaaaaaa’ and another key which is ‘zzzzzzzzz’. The key space of both these keys is the same. That is to say from elementary combinatorics that each character has 1114112 states, and each of the states are not mutually exclusive. This can be generally represented as –

For any Q which represents the events that your machine can represent and the integer n which represents the number of these events. For keys that have events which are mutually exclusive, a minor modification to the general equation yields –

We can compute the key space for both our very simple keys to be

The magnitude of the key space is 10⁵⁴ and from some rough references, the fastest supercomputer available today, the Blue Gene/P which is operating at 360×10¹² flops, would take 7.3×10³⁹ seconds to brute force the entire key space, assuming an ideal efficiency of one key per flop.

That is the ideal scenario. Let’s consider a practical application, the web application. Firstly, we can eliminate the Unicode superset because most people only use one, or in the case of Jennifer, a handful of the subsets. A cursory look at the web application will usually yield the information that is required in terms of linguistics. This has already eliminated the majority of the sample space and we are now left with the problem in the target subset. Let us use the ASCII subset as an example. We can reduce the sample space further by eliminating the non-printable characters, yielding only a sample space of 5.7×10¹⁷. To gain some perspective, this would take Blue Gene/P 1.6×10³ seconds to compute. It is time to make some intelligent guesses about the passwords. Determining the sample space of the web application is a key priority, as this yields the information that we would need to determine if we can reduce this key space even further. I have found several, perhaps more web applications where the passwords are limited to the alphanumeric key space. This is only a total of 36⁹ events, or a sample space of 1.0×10¹⁴, for a nine character password. If the designers of the web application are astute, they have hashed the passwords to prevent accidental disclosure using SQL injection. This is rarely the problem it might seem at first. To give you a real world situation, an eight character MD5 hashed key was successfully brute forced on a Pentium III in under a week.

What make attacks like these possible are two factors, both generalising to hash functions. I have discussed these attacks with a few people only to receive the response that the passwords are encrypted and there is no way to recover them. Technically, this is true. They are encrypted with a cryptographic hash which differs from a normal hash in that some of the original information is lost in the hashing process. What they have failed to consider is that because the algorithm is known, we can generate our own hashes and use a known plain text attack on the hash. This is done by generating random sets of characters that match the maximum possible key space of the target and encoding each one in turn to yield a hash. The hash is then compared to the recovered target and if they are the same, the original set is the key that we are after.

Another problem that plagues hashes is that they are susceptible to collision. For any hash that can be computed from any combination of input events, there exists another set of input events that can generate the same hash. This is known as the birthday paradox and it can be combined with a reduction in sample space to yield working input sets more quickly. Web applications hash the password before storing it in a database and a successful authentication is registered when an input password hashes to the same password recorded for the account that is being enumerated. It is now possible to generate a collision with MD5 in one minute on a laptop computer, leading to the conclusion that MD5 is no longer a cryptographically secure hashing algorithm.

There are another class of problems that all hashes are susceptible to known as the time-memory problem. If we were to set aside dedicated resources computing hashes and store them in a look aside table, we would be able to save the time required to compute the hash by trading memory to store the computed hashes. The second, not so obvious way to exploit this issue is when combined with the reuse of account passwords. The problem I faced in 2001 was that someone had created another user account on a forum and was masquerading as a legitimate user. Once it became obvious that the user was an interloper, the problem of how to locate the user was presented. With some improvised thinking, I decided to compare the hash of the interloper to all hashes in the database. I first retrieved the offenders hash and then used an SQL query to locate any legitimate accounts with the same hash. The method was successful and I saw the results immediately because the responsible party changed their password while sitting right next to me. I didn’t have to wait for the results of the query. I don’t know if they realise that they disclosed themselves but I continued the ruse to give them an easy exit.

Returning to our sample keys, if the attacker were to start brute forcing at the least significant portion of the key space, with some intelligent guesses for the key space domain, they would have to compute 26⁸+1 hashes. With the second password they would have to compute 26⁹ hashes. This translates to 2.1×10¹¹ operations versus  5.4×10¹² operations. If however, the attacker computed the hashes from the high order of the space to the low order, the situation would be reversed. Therefore, it is important to note that without knowledge of the algorithm that the attacker is using to compute the sample space, we cannot say anything about the security of the key. This is especially true for dedicated hardware and advanced methods that are used by sophisticated attackers. There are many optimisations that can be performed based on the weakness of algorithm implementations or based on dedicated hardware such as FPGAs. The NSA has made an art of it.

We can make the hash more resistant to a birthday attack by the use of salts which are added to the hash in some way, rendering the hash a non-linear transformation of the input set. That is to say, the salt must be non-computable from the input set. In practical terms, this requires that the application compute a salt and store it internally without disclosure to the legitimate user or otherwise. The security of the hash then depends to some extent on the security of the salt. Therefore, any disclosure of the salts of the hashes by means of SQL injection, XSS or inspection of the internal state of the machine will compromise the hashes. Due to the fact the salts are added to the input before the hashing function, an input set that is equivalent to the original input set plus the salt will yield a successful attack.

In real terms, brute forcing of passwords on servers is not a serious problem unless the algorithms are highly targeted. What I mean by that is, for an attacker hoping to break short passwords, the algorithm will generally tend to start from the lowest order of the key space that is to be computed. This may be optimised with current knowledge about password selection by starting computation from an input set that is a reasonable estimation of the target input set. If the attacker knows that the administrator of the system uses the maximum possible key length, they can start their attack from that specific key length and save the computation time it would require to trial suboptimal sets. On my terms, I have eliminated the mechanisms by which they can trial input sets. If nothing else, it will push them to think outside the box and use innovative methods.

Errata 03/04/08 - It seems that after working 24:07 hours in a row, fatigue has gotten the better of me and caused me to publish the wrong equation for an exclusive set of events. The error has been fixed.

Addendum 06/04/08 - Cleared the ambiguity with regard to salts.

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Earth Hour, 2008

March 29th, 2008 RaVPup | Bookmark

I’ve switched on my computer after the power hiatus that it took at 8:00pm. For those of you who haven’t caught on yet, it’s Earth Hour. Earth Hour started in Sydney in 2007 with two million participants and had a significant impact on the energy throughput of the city. Integral Energy estimated that we reduced our power usage by 10.2% last year. The first city to switch their lights off this year was Tel Aviv, followed by Suva and Christchurch. I’ve lived in both Fiji and New Zealand and can visualise those cities without power.

There wasn’t much publicity leading up to the event in Sydney and I could see how some people may have missed it. I turned on the television at 9:00pm but there weren’t any pictures being televised. I did manage to catch the city lights circling the night sky as the event was about to start and I also managed to catch the fireworks that were displayed at 12:00pm. The internet provided the information that I needed however, and it was easy to see that people on the grid were connecting from all around the globe and raising awareness of the event.

I was pleased to see that Google contributed by blackening their homepage because they can raise awareness across a large demographic. The Opera House lights were dimmed. The Harbour Bridge didn’t escape the symbolism either as I can see from the pictures that were taken. For my part, I switched off all the computers and lights that I own and plunged the house into total darkness. I used the time to message some people around Sydney on my PDA to see what they were doing. Awareness of Earth Hour in Sydney is not as high as I thought it was, it could be higher. There were still people having engagement parties and using computers at that time.

I consider myself to have a high carbon footprint. I have seven computers, two switches, two routers, two printers a PDA and two internet connections in my house. In addition to that I have servers that are across the globe in other countries doing my bidding. The amount of power I use in a year is probably enough to satisfy the needs of 10 people with moderate technology needs. In that sense, I felt I had to make a contribution to reducing carbon emissions.

Christchurch reported a Watt reduction of 12.8% during Earth Hour and I’m waiting for the official figures to be published on Sunday to see how Sydney fared against the rest of the world. Although it is touted as being a symbolic event, the reductions are an important way to measure how many people are aware of the conservation issues surrounding our planet. I have some friends that are environmentally conscious and do their best to raise awareness of these issues around the world and I have friends that are not concerned about environmental issues. The economic downturn we would face as a result of the energy crisis is quite disastrous and many people stand to lose everything because of retrenchment and market crashes. Add to this the horrific environmental conditions we would face if we continue generating emissions at the rate we are now and the future doesn’t look too bright at all.

However, things are improving. We have reduced the amount of power that a computer uses while increasing its processing capability. These advances were made possible by architectural and fabrication innovations brought in by the major manufactures due to the diminishing gains given by raising clock cycles. We have more efficient consumer devices, for instance mobile phones which come in a smaller form factor and use less battery power. The amount of energy that can be stored in a battery has an upper limit which has more or less been reached. Therefore a reduction in battery size is a good indication that your mobile phone is using less power. Whitegoods are also coming in reduced footprints due to consumer pressure for more economical running costs.  California, under the guidance of Arnold Schwarzenegger, has spearheaded the campaign to become an energy efficient city. The reforms that have taken place there are quite revolutionary and timely given the large carbon footprint of the state. You only have to see a satellite photo of the Earth during night to realise that California uses massive amounts of electricity.

Clean and efficient energy is the prime goal of the planet. There are a number of areas of research dedicated to this problem including fusion, bio-fuels and natural energy. Fusion reactors are a long term goal and there is a significant investment in the research because ideal fusion would be the ideal solution to our problems. The problem with building a fusion reactor is that, from a materials science standpoint, the amount of neutron flux present in a helium isotope reaction is quite large and under constant bombardment from these neutrons the materials weaken and become brittle. This particular sub-problem is the domain of the ITER reactor being built in France. When the reactor is built, scientists will use it to conduct tests on materials to determine the behaviour of these materials under neutron flux.

Bio-fuels are another interesting area, but in my view they are not the solution. The issue that faces bio-fuels is that it requires the dedication of vast areas of land to grow the crops that are necessary to harvest the fuel. In addition to this, the fuel that is harvested is of low energy density which means we require more of the fuel then we would of a comparable mass of fossil fuel. There have been recent revelations that bio-fuels will affect the nitrogen balance of the atmosphere. Lower nitrogen fuels can be used but they have lower energy densities.

Natural energy is abundant, does not carry the same scientific problems as fusion and does not require the same amount of resources as a bio-fuel. Although the energy density is low, the abundance of the energy enables us to harness more of it by the combination of solar, wind and wave power. It is also the cleanest form of energy available because it requires a minimal amount of processing to reach a useable state. The problems that I can see with natural energy are to do with the balance of life on the planet. To be more precise, consider a large scale deployment of wave farms. The energy generated by the wave farm comes from the wave, thereby reducing the amount of energy in the wave and changing the wave in some way. If the deployment of wave farms was large enough they might change wave patterns significantly. This may result in more catastrophic weather, reduction in food supplies for communities which are dependent on fishing and other problems of that nature. It is not only wave power, but wind power that could affect these changes in the environment.

The largest solar farm can generate 80MW of power, the largest wind farm can generate 700MW of power and the largest wave farm can generate 20MW of power. By comparison, Earth Hour saved 1000MW of power in Sydney alone. Toronto followed closely behind saving 900MW of power and Bangkok was reporting a 73MW saving. A very successful effort by Sydney and the rest of the world.

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Cryptic Love

March 27th, 2008 RaVPup | Bookmark

I have been keeping myself immersed in life over the last few weeks, with the last three days being the busiest of them all. I seem to be in overdrive trying to catch up on all the things that I wanted to accomplish a while ago but never had the energy to do. I have many ideas and I’ve been discussing some of them with people and putting them into practise.

I started coding some basic cryptanalysis software to help me analyse a cipher that I haven’t been able to break. The first version of the cipher was susceptible to frequency analysis and during the process of breaking it, I discovered that it was a dual round substitution cipher. The newer cipher seems to be a poly-alphabetic one, though I haven’t yet figured out if there is any transposition involved. What I am trying to do is convert the techniques that I’m using into software so that at some stage I will be able to automatically recover the cipher text. This process essentially involves applying the inverse algorithm to the cipher text and by extension I would have the original algorithm as well. It’s an interesting project for me in two ways, one that it is an application of principles that I learned at a very early age and two because it holds information that I actually want to recover. More on the second point later.

The other project I have been working on over the last day is a project that I started last year. It was a very interesting project to me at the time but I was side tracked with University and work and could not really focus my full attention on it. The project involves some quite difficult problems in computing and I can see that it will be a real test of my ability to develop it to the extent that I want to. The reason that the project has had new life breathed into it is because someone else has voiced an interest in a similar sort of project and I can see the parallels between the problems we are trying to solve. What I envisage is that we combine the ideas from both our projects and develop a truly fantastic project that is bigger than the union of the ideas alone. I haven’t really indicated what the project is of course, because it is a little too early to be counting my chickens, but expect more on that in another post.

Finally, the last slice of the time pie is the Sudoku solver that I had up on my projects page a while ago. I’ve taken that project off the projects page because I wasn’t really that happy with the way the problem was solved. To be forthcoming, I wrote the project to try and impress Jennifer but she was not impressed at all. The solver uses a brute force algorithm with a trivial hit cache to compute the solution to a nine by nine square. The software is successful at what it was designed to do but there are better and more efficient ways to solve the problem. To that end I am rewriting the Sudoku solver to use a binary algorithm, which based on my research is the most efficient algorithm to use to compute the Latin square problem. It is worth noting that the Latin square problem is NP-Complete in that it cannot be solved for arbitrarily sized squares with any degree of timeliness. I plan to keep the project restricted to a nine by nine Latin square and improve the algorithm to solve it faster. I am hoping for a completion time of 7.0×10^-3s to compete with the best solvers out there but a lot of research into the algorithm is required on my part.

The cipher text I’m trying to recover has a message in it from Jennifer. You might notice that two of the three projects that I am working on are directly focused on Jennifer. She is always in my thoughts it seems. She read the post that I made last time and things have progressed a little further with us. I know she cares about me but she has her own problems to deal with. I wish I could help her with her problems but she doesn’t really let me in. When I bring them up she shuts the conversation down. It’s not to say that we don’t talk about things, we do. She told me that she is not sure if she sees me as a friend or a lover and I am not sure about that either. Our relationship is a complex adult relationship and it will take a lot of time to develop. I can say for my part there was instant attraction but I’m not sure if it was as instant for her.

The problems she is dealing with are problems that I have also dealt with. I don’t feel that I can divulge the true nature of her problem on a public blog and still maintain my self-respect so I am not going into the details here. I know that I have been in a similar situation and it is really difficult when you are in this situation to fully appreciate the love that someone else has for you.

I keep asking myself if we’re right for each other. I have gone so far as to think about what our children would be like given both of our genetics. I know what I had to go through to pull myself out of the abyss that I was in and I don’t wish that on my children, but at the same time I don’t want to give up on her because of something of that nature. I am of Aramaic descent and our custom is to marry someone that is chosen and meets the approval of our families. However, I know that I could not live with a woman that I did not get the chance to know and fall in love with. This is the reason I haven’t married yet.

Marriages are based in both the realistic and the emotional. My view of a wife is someone that is realistic enough to meet the expectations of the world she is living in and emotional enough to have a rewarding relationship with. These demands are high I know, but I don’t feel the need to marry for the sake of marriage as most people do. If I never find the sort of partner that I want, I am quite content to never marry at all. It would be a lonely life but a productive one. I have talked about Jennifer and marriage in the same paragraph so I assume you’ve already made the connection. I am not one to have meaningless relationships with women and I think that there is something about Jennifer that attracts me to her and makes me think that there could be something worthwhile to come from it.

She doesn’t know if I’m the sort of person she wants to be with and I don’t know if she is going to be as I imagine her to be. It’s really too soon for either of us to decide one way or the other. I know that I have feelings for her that could well mature into love but I don’t know if that love will go so far as to result in marriage. I know that what I feel for her is more then what I’ve felt for a woman in a long time. It’s a mix of empathy, respect and desire in just the right proportions to be healthy for me. I think that Jennifer has a good value system, one that I could merge into my own and still be true to myself. I don’t know if she feels the same way about me but only time will tell.

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Lady Katrana

March 21st, 2008 RaVPup | Bookmark

This is a personal blog, so I guess I should write something personal. She, who must be obeyed, has also indicated that I am not forthcoming in public displays of my affection. The reason that I don’t post about things of a personal nature here anymore is that I regard it as an invasion of my privacy.

So, where did it all start? I met Jen by pure coincidence on an IRC channel that was dedicated to computer security. All this came about because I mentioned to a colleague of mine that there was a lack of women in the computing sciences. It must have been that I bent Minkowski space in some way because at the next instant, she joined our channel. So we conversed for a while and then at some point I saw her. She was beautiful, so beautiful that I remember the photo etched at the back of my mind to this day.

I was a little bit sceptical of the internet dating phenomenon due to the logistical problems and the emotional load of maintaining a relationship with someone who you’ve never shared Euclidean 3 space with. I was myself, not in the most fruitful part of my life and career at that point so, as chauvinist as this sounds, she was just some internet flirt candy.

We exchanged MSN contact details and chatted for what would now be three years. I don’t keep track of it, she does. Whenever I need to put our relationship in perspective I seek her advice. As to that relationship, it is complex in the sense that we are not dating each other, or even have any commitment for each other.

I guess what started out as a joke between me and someone else has led me down this path. That is to say, when I first met her I was in a dark time, and I was later to find out that she was as well. I myself don’t know quite what happened between now and then but I can make some guesses. When we first started chatting to each other it was superficial conversation. I was driven by my lust, I don’t know what she was driven by. My advances were quite crude and not really aimed at producing the result of a relationship. I was on some level trying to get rid of her, or to keep her as a trophy internet girl.

Gradually, I started finding about who she was inside. I started learning about the real Jen. I learned that she had suffered a loss and that she has carried that ever since. She has told me that she is still in love with the person that she lost and for that reason I keep my emotions in check. I guess the relationship has developed to the point that we discuss issues of a personal nature with each other, so we know where we stand. I class myself as single and she does too. There is no commitment between us other than some understanding of a sliver of attraction. The fact that we are both guarded to this degree would indicate an abortive relationship but that has not been the case so far.

I know that from my perspective, there are so many things that I still want to accomplish and I don’t really have time for a woman that cannot understand my ambition. To that end I have pushed myself to overcome the hurdles that I face, whereas it is my perception that she is still stuck in the past. I cannot love a woman that doesn’t love me and the first step to that is building trust. I would like to be able to send her gifts on her birthday to show that I am thinking about her but she does not trust me with her address. Two birthdays have come and gone, and on each birthday I religiously seek out a gift that I would like to send her, and on that same day I ask her to give me her address so that I can send it to her, but she refuses. For me to fall in love with her at this point would mean to give up my own dignity. I refuse to let myself waste away pining for woman that is still grieving for someone that she lost many years ago. I understand her position, and I believe that she understands mine. It is very painful for me to watch her waste away in this manner because I feel that she has so much more capability then she is displaying right now. I want her to wake up one morning, shake off the shackles of the past and grab hold of life with both hands. Whether it is the case that we live our lives together is not really that important to me at this stage. I have regained my focus and my motivation and I wish her to do the same.

I get the feeling that deep down she doesn’t really care about me. Whether it is because she doesn’t want to or she is not able to, I’m not sure. She hasn’t displayed an interest in my life to any great degree. At a low point in my life she told me that to marry her I would have to be someone special. She places a great value on herself in this way and that is something that reflects a healthy self esteem to some extent. To get to know her better, I resorted to playing online games with her. We didn’t really converse at all and instead, I spent a large amount of time interacting with others and building my character. Somehow this helped rebuild my motivation. When realised how much time I was wasting looking in reverse instead of focusing on the future, I quit WoW and started living life. On some level, I feel I’m indebted to her for helping me realise the nature of my predicament and I wish that I could do the same for her.

I find it hard though, to communicate with her. For a long time I thought this was some failing on my part but I realise that we are equally at fault. I cannot get through to her until she trusts me and she cannot reach into my soul until I trust her. I haven’t given up on her though, as it is plain to see. I still hold out that there will be in future, some open line of communication between us and that we can build on that. There are many things for me to consider in my present situation, now that things are finally converging to some positive end. In my view, I have successfully collected all the pieces of my past and painstakingly glued them back together. I can see myself progressing forward and if the people that share my company cannot move forward at the same rate then I have no option but to sweep them by the wayside and carry on. My future plans involve her, but there is no certainty in it, therefore I can only commit myself up to a certain point, after which it would be an error on my part to make any assumptions. She could change that if she wanted to and I think that she knows that. Whether I am to wait for her or not, I don’t really know. I cannot say at this stage if things will work out for the best but I hope they do.

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Mathematical Musings

March 19th, 2008 RaVPup | Bookmark

My interests have diversified somewhat since I began learning the theory of computers. Through introduction to mathematical concepts behind computing science, I gained an appreciation for mathematical science. These fields are related to each other in that computing science deals with the subset of maths problems that are computable.

In my early years I was very confident in mathematics. I had a good pool of teachers to draw from and we were always pushed far in the accelerated streams. This changed when we moved to another suburb where the teachers spent less time focusing on maths and more time focusing on the other areas. It is said that maths is not studied well in Western societies because the teachers themselves are not confident with maths. This anxiety is passed on to children through subtle cues which propagate the cycle of maths incompetence. Most students find that success in science and engineering fields requires remedial work at the University level, by which time they have already developed an anxiety about the subject matter.

My troubles with maths started in elementary trigonometry but since then I have progressed onto higher level maths without any problems. I managed to do this with self revision, after a few years of struggling with trigonometric functions. The process I went through was to first find an online site that had maths problems and practised those from the very beginning. I started with elementary arithmetic and learned things that I had never encountered before such as the divisibility tests. When I felt confident enough with my basics, I went to the University book store and purchased my old high school texts and started working my way through them. I found that there were a lot of concepts that I had forgotten or hadn’t really grasped in full context with the knowledge I had back then. I even found a few errors in the books which aided my misconceptions. There were two sets of books that I used during high school, one set was of a very high standard and the other set was of such a low standard that any competent student exposed to them would yield negative gains in mathematical knowledge.

I find that most people that are not confident in maths feel the same way. They blame their failures on themselves rather than taking the time to understand what factors led to those failures in the first place. If you are living in Australia and want your child to have the best education that money can buy, I suggest sending your children to Newington Boys. It is located in NSW and is one of the best schools that I have had the pleasure of learning from. I can appreciate the knowledge I gained from there simply by comparing the standard of the text books to the ones used by others.

One thing I realised is that you must have the very best textbooks from which to learn mathematics. It is not worth the trouble learning something in error and then undoing your error later with more work. The fundamental error will stay with you for a very long time, dare I say the rest of your life if you never correct it. It is helpful to me to review my old texts and find the errors that lead me to erroneous ways of thinking and pondering why the writer made that error. I have found numerous errors in the texts, some of typesetting, some of opposite meanings and a few on the actual logic itself. These errors have led me to the practise of cross-checking everything that I’m unsure about in mathematics. If there is something that intuitively doesn’t make sense to me, I will check it with a number of different texts and reference materials before I commit it to memory. I don’t gloss over equations, I study them until I fully understand the transformations that are taking place and the reasons behind them. Stephen Wolframs Mathworld has been a valuable resource for me, as has the MIT OpenCourseWare notes that are provided free of charge. If you want to learn to be good at something, learn from the best.

I have, after a long journey through computers, come to realise that mathematics is just as fun as computers. The combination of the two disciplines is where the most interest lies for me. I have decided that in my future academic endeavours I would like to pursue pure mathematics for a while. I feel confident enough to take it as far as it will go.

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Hacker Philosophy

December 25th, 2007 RaVPup | Bookmark

I’ve spent the best part of three days setting up servers for the company. It’s the first time I’ve used my UNIX skills in a production environment for some time and I wasn’t really prepared for the amount of debugging I would have to do with the whole thing. There is a lot of extra care exercised when you are working for a company that you own. To this end, I made sure the email setup was nothing short of perfect with spam filtering, virus scanning, web mail, full SSL enabled POP3, IMAP and SMTP. I couldn’t have set up a more bulletproof email solution without coding it myself.

I’m using Debian Etch as the operating system, in the first place because I’ve heard good things about it and in the second because I had experience with very reliable servers being run on the distribution. My initial thoughts are that it is a very easy system to administer, especially in regards to package management. When I first started using Linux, almost 10 years ago, everything was very time consuming because the operating system was in its infancy and held together by rickety bridges of code. It seemed that way to me when I was running a bleeding edge early Slackware distribution. I set this up on the recommendation of hackers.

Hackers are a curious breed of people, preferring to do everything in minutia. If you are ever going to ask a hacker for operating system recommendations, be prepared for a whole spectrum of opinions. Hacker philosophy is distributed along a continuum from sinister to dexter, and their recommendations follow the same distribution. The attitude of the extreme left is puritanical while the attitude of the extreme right is corporate. It is my opinion that every hacker starts black, on the left of the spectrum. White hats are a later stage of development.

The early hacker, invariably black, is in a state of pure intellectual pursuit. He reverse engineers, re-engineers, disassembles and re-assembles in a constant flux of achieving some state of hacker Zen. He derives great satisfaction from learning the most intricate detail of a complex system. The satisfaction is proportionally related to the obscurity of the system and the intricacy of the detail. The hacker exists in this state for some time, up to a decade in some cases, but eventually the pressures of the external world enter his life. This usually manifests itself in the monetary form, resulting in the hacker seeking employment in a profession where the secondary benefits of his skills can be utilised. At some point in time after entering into his first career-focused position, the hacker enters a state of internal conflict. This conflict is between two paradigms, the paradigm of the hacker where time pressure is not an issue and the paradigm of the corporate employee where the focus shifts towards getting things accomplished quickly and with a certain level of robustness. The outcome of this conflict is usually a victory for the corporate way of thought because the pressures of society are great. To quote Buddy Ackerman, “Look, it’s like they say, if you’re not a rebel by the age of 20, you got no heart, but if you haven’t turned establishment by 30, you’ve got no brains.”

In my experience, people tend to trade innovation for experience. What I mean is that as a person matures they are more likely to act in ways that satisfy social norms. This may work in your favour if your role in society is one of rationality. However, we need innovation and innovation comes from great necessity combined with the ability to think outside the bounds of social normality. One thing to note is that most of our great ideas have come from minds that many psychologists consider neurotic. The hacker psyche is just such a neurotic one. It is free to visualise an idea in its very embryonic stage and develop that idea into a proof that can be demonstrated to a world outside his own head. In very rare cases, the hacker also recognises the worth of his creation to others but in reality he lacks the ability develop his proof into a product that can earn him revenue. The reason for this is that hackers are interested in technology, not the management of technology.

There is a great blog post on the Development Abstraction Layer by Joel Spolsky, an ex-employee of Microsoft. He describes the culture that they have created, allowing programmers to focus on their core business of creating code. This principle is echoed in the more traditional realm of academia where researchers are separated from the final incarnation of their ideas by a series of stages. Universities have started recognising this and collaborating with industry to develop products that contribute directly to their revenue. However, climbing the academic ladder to the point where you are able to conduct your own meaningful research is itself a process of normalisation disguised as academic rigour. Innovators have rarely been academic. The normalisation process is precisely the mechanism by which the hacker loses his ability to innovate, and the art of hacking is innovation.

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The Dichotomy Paradox

June 11th, 2006 RaVPup | Bookmark

We represent the paradox as an infinite series as such -

First we have to test for convergence of this series. We apply the ratio test to the series -

The absolute value of the ratio is less then 1 so this series converges. For any x, where x is the distance to be travelled in the paradox, we have -

The limit of this sum is x, which is the original distance, thereby disproving the Dichotomy Paradox.

Addendum 25/03/08 - The proof presented before was the specific case of x=1. The proof has been generalised.

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