Postagens
The Simulated Binary Crossover (SBX) is a well known variation operator for genetic real-valued optimization. It's surprising that I never came to implement this before, since I've been working with GAs for three years.
This is a remarkably elegant operator which was specifically designed to preserve the properties of the one-point crossover used for binary-coded GA optimization:
1) The average of the generated values is approximately the same of the original values before crossover; and
2) The probability of a spread factor value of betha = 1 is higher than for other spread factor values, what yeilds a stationary crossover operator.
That's such a great thing that I'm finally merging it into my NSGA2 implementation for numerical optimization benchmark. To find out more, go through the following slides:
Mostrando postagens com marcador computação. Mostrar todas as postagens
Mostrando postagens com marcador computação. Mostrar todas as postagens
domingo, 25 de abril de 2010
sexta-feira, 26 de fevereiro de 2010
My contribution to "Is Computer Science a Misguided Field?"
This is my answer to Amir Michail recent inquiries in Google Buzz. Amir has posted a nice set of questions that make us stop to wonder whether we're on the right track in terms of CS education. In his original post, he wrote (originally posted on http://bit.ly/dp8WKW):
Here it is my follow-up on this thread:
On what Computer Science (CS) is about (and what it isn't)
Interesting discussion. CS is about complexity theory, computability, algorithms, data structures, automata theory, quantum computation science, formal languages and much more. There's a whole theoretical background that is unique to CS.
Definitely, there should be separated majors, such as Software Engineering or Data and Information Management, in order to avoid misconceptions and to address industry's specific needs.
In short, CS is a basic science in wich we can learn about modelling the complex processes that occur in Nature by using abstract mathematical tools. The models we construct in CS (basically, algorithms) have to (i) be given formal descriptions and proofs; (ii) have its fundamental properties investigated (complexity bounds, completeness, etc.); and much more.
So, CS is a basic science and other sciences can benefit from it by using its outocomes. An example of this is Artificial Intelligence. Although it first got inspiration from early mathematical models of the brain (neuroscience), it became clear thereafter that the 'algorithimic' way of modelling natural processess would be fundamental to AI. Today, AI is commonly regarded as a standard discipline in CS, though still multidisciplinary.
Why not segregate the lots of teaching contents flooding CS students minds into separate majors?
Furthermore, let's not forget the revealing quote of a prominient computer scientist:
"Computer Science is no more about computers than Astronomy is about telescopes" Edsger Dijkstra
That summarizes well what CS is definitely not about.
I believe that multidisciplinarity should raise from a well planned reform in the graduate educational system, instead of requiring that a CS major covers every single topic from software engenieering to computation theory. Both are, separetedly, deep and complex enough disciplines to be studied in their own terms.
See: http://en.wikipedia.
On Creativity
With regard to creativity, well, I'd say that computer scientists need to be creative as much as mathematicians and physicists do. There's no difference in coming up with a novel algorithm and discovering a fundamental power law in a complex system.
So, yes, you need much creativity to work on CS, no more nor less then in other related areas.
On the role of Game Design and related areas on CS
Now, why do I think game design (GD) does not play a significant role in CS? Because game design is an application of CS. Although there are many CS researchers who focus in GD, they are just aplying the standard tools of CS to modelling new useful algorithms for the problems they are working on in the area. So, again, GD 'uses' the 'know-how' and tools provided by CS.
As a perhaps useful analogy, think about CS as the 'Kernel' of an operating system (OS), which provides all the basic functioning to the system, and GD as one of the many 'services' provided by that OS which uses the basic kernel units. That is, GD is closely related to CS, but there is much more about it than just CS and, thus, I'd say that there's no need to consider studying GD in a basic CS curriculum, though it might be interesting to CS practicioneers, just like other disciplines.
In short: I'd say that GD is on the same level of AI, Database Management, Programming Languages and so on... that is, all those disciplines are 'users' of the core knowledge that exists on CS.
Computers are interesting because you get to invent new applications that change the world.
By focusing on efficiency and correctness of programs, doesn't computer science completely miss the point as to what is interesting about computers?
By contrast, consider the field of computer games where game design is a key aspect of study. Why isn't there something like that in the more general field of computer science?
Where's the application level creativity? Why focus only on implementation issues?
What do you think?
Here it is my follow-up on this thread:
On what Computer Science (CS) is about (and what it isn't)
Interesting discussion. CS is about complexity theory, computability, algorithms, data structures, automata theory, quantum computation science, formal languages and much more. There's a whole theoretical background that is unique to CS.
Definitely, there should be separated majors, such as Software Engineering or Data and Information Management, in order to avoid misconceptions and to address industry's specific needs.
In short, CS is a basic science in wich we can learn about modelling the complex processes that occur in Nature by using abstract mathematical tools. The models we construct in CS (basically, algorithms) have to (i) be given formal descriptions and proofs; (ii) have its fundamental properties investigated (complexity bounds, completeness, etc.); and much more.
So, CS is a basic science and other sciences can benefit from it by using its outocomes. An example of this is Artificial Intelligence. Although it first got inspiration from early mathematical models of the brain (neuroscience), it became clear thereafter that the 'algorithimic' way of modelling natural processess would be fundamental to AI. Today, AI is commonly regarded as a standard discipline in CS, though still multidisciplinary.
Why not segregate the lots of teaching contents flooding CS students minds into separate majors?
Furthermore, let's not forget the revealing quote of a prominient computer scientist:
"Computer Science is no more about computers than Astronomy is about telescopes" Edsger Dijkstra
That summarizes well what CS is definitely not about.
I believe that multidisciplinarity should raise from a well planned reform in the graduate educational system, instead of requiring that a CS major covers every single topic from software engenieering to computation theory. Both are, separetedly, deep and complex enough disciplines to be studied in their own terms.
See: http://en.wikipedia.
On Creativity
With regard to creativity, well, I'd say that computer scientists need to be creative as much as mathematicians and physicists do. There's no difference in coming up with a novel algorithm and discovering a fundamental power law in a complex system.
So, yes, you need much creativity to work on CS, no more nor less then in other related areas.
On the role of Game Design and related areas on CS
Now, why do I think game design (GD) does not play a significant role in CS? Because game design is an application of CS. Although there are many CS researchers who focus in GD, they are just aplying the standard tools of CS to modelling new useful algorithms for the problems they are working on in the area. So, again, GD 'uses' the 'know-how' and tools provided by CS.
As a perhaps useful analogy, think about CS as the 'Kernel' of an operating system (OS), which provides all the basic functioning to the system, and GD as one of the many 'services' provided by that OS which uses the basic kernel units. That is, GD is closely related to CS, but there is much more about it than just CS and, thus, I'd say that there's no need to consider studying GD in a basic CS curriculum, though it might be interesting to CS practicioneers, just like other disciplines.
In short: I'd say that GD is on the same level of AI, Database Management, Programming Languages and so on... that is, all those disciplines are 'users' of the core knowledge that exists on CS.
sexta-feira, 27 de novembro de 2009
The Intelligent Quotient (IQ) of Evolution
I'm going through the first three chapters of the excellent 1999's "The Age of Spiritual Machines" by Ray Kurzweil. So far, it has been a mix of everything: from cosmology, biology and information theory to computer science, nanoengineering and philosophy. I'm quite amazed on the way Ray was able to deliver all of those breathtaking subjects in less then one hundred pages without making things obscure or even scary to the non-initiated.
Take for instance the discussion going on chapter 2 about the IQ of evolution. He concludes that it should be no better than an infinitesimal quantity greater than zero, given the great lenght of time (in a scale of billions of years) that was needed to evolve some remarkable things such as the human brain. Of course, Ray is agreeing whith many psychologists who evaluate an intelligent process in terms of the elapsed time to reach a solution, i.e., the quicker the better.
The most interesting conclusion drawn here, though, is that all the astonishing complexity observed in Nature is a byproduct of only a slight amount of order encompassed by the emergence of extraordinarily intricate chemical and biological patterns formed apparently by chance.
I'm enjoying it so much!
Take for instance the discussion going on chapter 2 about the IQ of evolution. He concludes that it should be no better than an infinitesimal quantity greater than zero, given the great lenght of time (in a scale of billions of years) that was needed to evolve some remarkable things such as the human brain. Of course, Ray is agreeing whith many psychologists who evaluate an intelligent process in terms of the elapsed time to reach a solution, i.e., the quicker the better.
The most interesting conclusion drawn here, though, is that all the astonishing complexity observed in Nature is a byproduct of only a slight amount of order encompassed by the emergence of extraordinarily intricate chemical and biological patterns formed apparently by chance.
I'm enjoying it so much!
quinta-feira, 26 de novembro de 2009
Conferences vs. Journal publications in CS
This was originally posted as a comment in the GPEMJournal blog:
http://gpemjournal.blogspot.com/2009/08/journal-publication-versus-conference.html
While deadlines, as well as all the follow-up review process which is needed to have a work considered for publication in journals, might directly affect the publishing preferences of many computer scientists towards conferences and workshops, these factors alone don't help me to understand why the same effect does not occur in other related areas. In other words, if these were two of the primary causes behind, we would see the same happening among, say, physicists and mathematicians. Yet this does not seem to be the case.
I sincerely believe that there is one simpler factor that could also be considered in the specific case of CS: the relative lack of maturity of the field regarding consolidated research methodologies and data analysis. Of course, working in a scientific field with less than 60 years do not help us much. We're often borrowing ideas and methodologies from other areas and, still, there's no concensus on, say, which statistical tests are more appropriate.
So, this may perhaps explain why someone in the CS field might think that it's no use considering to fufill journal reviewers and editors' requests - who are mainly (and correctly) concerned with methodological issues - when one can bypass this process and have his/her results published immediately in somewhat respectful and prestigious conferences.
http://gpemjournal.blogspot.com/2009/08/journal-publication-versus-conference.html
While deadlines, as well as all the follow-up review process which is needed to have a work considered for publication in journals, might directly affect the publishing preferences of many computer scientists towards conferences and workshops, these factors alone don't help me to understand why the same effect does not occur in other related areas. In other words, if these were two of the primary causes behind, we would see the same happening among, say, physicists and mathematicians. Yet this does not seem to be the case.
I sincerely believe that there is one simpler factor that could also be considered in the specific case of CS: the relative lack of maturity of the field regarding consolidated research methodologies and data analysis. Of course, working in a scientific field with less than 60 years do not help us much. We're often borrowing ideas and methodologies from other areas and, still, there's no concensus on, say, which statistical tests are more appropriate.
So, this may perhaps explain why someone in the CS field might think that it's no use considering to fufill journal reviewers and editors' requests - who are mainly (and correctly) concerned with methodological issues - when one can bypass this process and have his/her results published immediately in somewhat respectful and prestigious conferences.
quinta-feira, 12 de novembro de 2009
Smart Dust
I've transcribed today a short video about Smart Dust technology. It was quite difficult, given some rapid passages. The accent of Dr. Kris Pisters from Berkeley didn't help much too. I found at least two passages which were challenging to understand.
Anyway, even not being a native speaker, I think I did a good job on this one. The translation to brazilian Portuguese is also done.
I'm enjoying the dotSub transcipt/translation interface very much.
Here it goes:
Anyway, even not being a native speaker, I think I did a good job on this one. The translation to brazilian Portuguese is also done.
I'm enjoying the dotSub transcipt/translation interface very much.
Here it goes:
The biological and cultural ethereal conflict
To the extent Nature is conceived, marriage should never stand against our intrinsic polygamic instincts driven by our biologically pre-programmed ultimate goal of self-reproducing. Hence, it's not surprising that both men and women are following their basic instincts in the grounds of divorce, since no single life-form on Earth has been ever evolved to establish long-term matrimonial unions. However, it's well known that Humans, as highly susceptible to culture and morality, are being pushed towards the establishment of solid relationships, which in turn have been proved to play an important role in social mobility.
Based on these assumptions, it seems clear to me that there's a conflict of interests between our biological and social goals. On one hand, there's the need for each human of serving as generators of genetic diversity for the sake of continuous biological evolution, which is still happening among the human race. It's interesting to note, though, that our needs as social beings go straight in the opposite direction: we don't want to change our sexual partners all the time (at least when it comes to kinship descending) and, therefore, we end up by slowing down the diversity generation process in human race by preferring stable matrimonial engagements under social standards.
It turns out that there is a noticeable and complex interaction between genes and memes. This has been already observed by many researchers, including those working on memetic computing field. Since it seems that social evolution is surpassing biological evolution in terms of how much they affect human development (just look at how technology and culture are rapidly changing human behavior under a much higher pace than genes have done before the last decades), it's reasonable to imagine that there will come the day when the human race will transcend from its old-fashioned biological prision (i.e., the carbon-based "survival machines" of Richard Dawkins) to perpetuate itself through cultural and technological meanings.
Again, nothing new here, yet another appealing topic which should be more often discussed by academics.
Based on these assumptions, it seems clear to me that there's a conflict of interests between our biological and social goals. On one hand, there's the need for each human of serving as generators of genetic diversity for the sake of continuous biological evolution, which is still happening among the human race. It's interesting to note, though, that our needs as social beings go straight in the opposite direction: we don't want to change our sexual partners all the time (at least when it comes to kinship descending) and, therefore, we end up by slowing down the diversity generation process in human race by preferring stable matrimonial engagements under social standards.
It turns out that there is a noticeable and complex interaction between genes and memes. This has been already observed by many researchers, including those working on memetic computing field. Since it seems that social evolution is surpassing biological evolution in terms of how much they affect human development (just look at how technology and culture are rapidly changing human behavior under a much higher pace than genes have done before the last decades), it's reasonable to imagine that there will come the day when the human race will transcend from its old-fashioned biological prision (i.e., the carbon-based "survival machines" of Richard Dawkins) to perpetuate itself through cultural and technological meanings.
Again, nothing new here, yet another appealing topic which should be more often discussed by academics.
sábado, 26 de setembro de 2009
Lições aprendidas do resultado individual do ENADE
O boletim está estruturado com as notas em escala de zero à 100 por componente (i.e., formação geral e específica) e tipo das questões (i.e., objetivas e discursivas), ou seja, há quatro notas individuais disponíveis que são utilizadas para o cálculo da média final.
Após conhecer a minha média individual, a qual não me atreverei em aqui divulgar (mas que pode ser facilmente deduzida) pois, no email enviado com a senha gerada há um breve informe sobre a existência de uma lei que proíbe a associação de resultados individuais à identificação do aluno, constatei nas estatísticas contidas no boletim que obtive a melhor média individual entre os alunos concluintes de Ciência da Computação em Pernambuco.
Obviamente, fiquei muito feliz em saber que estou em uma boa posição para alçar grandes vôos. Mas tudo o que consigo pensar no momento é que o significado desse resultado claramente contradiz algumas "verdades" adotadas institucionalmente em diversos lugares. A começar no meu querido e estimado Centro de Informática (CIn) da UFPE. É de meu parcial conhecimento que a "qualidade" da instituição de origem do candidato no processo seletivo para o mestrado (i.e., conceito do ENADE), por exemplo, é levada em consideração no ranqueamento final dos candidatos, o que acaba por influenciar certas decisões (e.g., a alocação de bolsas institucionais para os novos ingressantes).
Por que esse cenário é preocupante?
Porque eu, por exemplo, realizei a minha graduação em um curso que, apesar de oferecido por uma instituição tradicional e respeitada no Estado, não vem obtendo resultados, digamos, "excepcionais" nas últimas avaliações do ENADE. Então, como pode um aluno advindo dos quadros desse curso obter o melhor desempenho entre os concluintes do estado, acima, inclusive, daqueles que representaram um amostra significativa dos concluintes de cursos considerados de "excelência" em Pernambuco? Claramente esse fato constitui-se em uma contradição. Isto é, como se justifica a prática de influenciar negativamente o escore final de um candidato que cometeu o "pecado" de ter estudado em um curso de qualidade "inferior"?
Apesar dessa questão ter me incomodado desde a época em que procurei me informar acerca dos critérios de classificação das instituições para as quais pretendia enviar inscrições, apenas agora me veio a certeza de quão absurdo são certas "generalizações institucionalizadas". Afinal, um dos fatores aos quais eu atribuo o meu bom desempenho como estudante de graduação foi a qualidade da proposta curricular que me foi oferecida, para não mencionar os excelentes professores, as muito bem estruturadas disciplinas e os eficientes programas de monitoria e iniciação científica. Ou seja, considero-me um produto do Departamento de Estatística e Informática da Universidade Católica de Pernambuco.
Em qual outro lugar um aluno de Ciência da Computação poderia cursar disciplinas como Computação Evolucionária, Processamento Digital de Imagem, Técnicas de Simulação Estocástica e Criptografia, no âmbito da graduação, todas lecionadas por professores acima da média? Em qual instituição você pode cursar uma cadeira como Humanismo e Cidadania e, além de discutir vários problemas relevantes existentes na sociedade contemporânea brasileira, ter a oportunidade de ler e discutir objetivamente em sala o clássico "A Vingança da Tecnologia" de Edward Tenner? (E todas essas com cargas horárias de 60 horas).
Pouquíssimas, aposto eu.
Então, como é possível a disparidade entre o meu desempenho individual e aquele encapsulado em um pobre e inexpressivo indicador que, erroneamente, representa a "qualidade" do meu ex-curso?
Simples: várias instituições particulares tornaram-se reféns da necessidade de sobrevivência. Afinal, na condição de empresas privadas, precisam sustentar-se mediante a manutenção de um bom número de estudantes matriculados em todos os períodos de seus cursos. O caminho encontrado por muitas? Moderar os requisitos de aprovação entre disciplinas (e.g. aproveitamento de 50 ou 60%) ou aceitar pessoas despreparadas no vestibular - afinal, os alunos "preparados" acabam sendo aprovados nas universidades públicas ou preferindo esperar mais um ou dois anos em preparatórios até conseguirem o tão almejado objetivo. Infelizmente, muitos dos alunos que entram não conseguem se dedicar o suficiente ao curso, seja por conta da necessidade de trabalhar 8 horas e cursar as cadeiras à noite, ou por mero comodismo e falta de interesse.
Mas sejamos conscientes e objetivos:
Tal fato não está de forma alguma correlacionado com fatores como o nível da estrutura (e.g., laboratórios, bibliotecas, etc.), o nível dos professores (i.e., a habilidade didática e graus de conhecimento da matéria) ou a qualidade da proposta pedagógica (i.e, matrizes curriculares, ementas de disciplinas, etc.).
Inconcebível é, para mim, tudo isso!
Já perdi as contas de quantos colegas conheci no mestrado do CIn que não se graduaram na UFPE ou em outras instituições federais com conceitos 4 ou 5 no ENADE e se destacam positivamente nas disciplinas, seja pela qualidade nas implementações e discussões de projetos e seminários ou pelo conhecimento demonstrado através dos instrumentos de avaliação tradicionais (i.e., provas). Aliás, muitos desses colegas vêm de curso particulares e não estiveram exatamente bem classificados no processo seletivo.
Para muitas instituições bem ranqueadas, é relativamente fácil obter indicadores favoráveis, dado a enorme pressão seletiva no tocante ao ingresso nos cursos de graduação (em bom português, o vestibular), o qual resulta em ingressantes com enorme potencial de se tornarem "bons" concluintes. Para que uma interpretação mais justa dos resultados seja realizada, além do conceito final do ENADE, é imperativo que se observe o índice IDD (Indicador de Diferença entre os Desempenhos observado e esperado), o qual fornece uma medida mais objetiva do quanto a instituição contribui para o resultado obtido pelos concluintes na prova do ENADE. Em outras palavras, o IDD mostra o quão o desempenho do curso se afasta (ou adere) da média de todos os demais cursos cujo o perfil dos ingressantes possui forte grau de similaridade.
Soluções?
Extinguir de vez o (pré) conceito institucional para fins de avaliação e ranqueamento individuais e passar a considerar com maior (ou, quiçá, total) ênfase os índices de desempenho individuais (i.e., coeficiente de rendimento e nota do POSCOMP). Apenas dessa forma teremos um processo justo e sem viés institucional.
Espero sinceramente que nós alunos advindos de instituições não "mainstream" [hahaha] tenhamos o tratamento digno que merecemos, afinal, possuímos a mesma capacidade cognitiva para o aprendizado acadêmico dos demais alunos que vieram de cursos com indicadores "mais favoráveis".
Espero nunca mais ouvir estórias de colegas que foram sutilmente humilhados nas entrevistas informais com seus futuros orientadores, quando alguns desses senhores e senhoras costumam torcer o nariz ao ouvirem de nós os nomes das instituições nas quais obtivemos o nosso (santo) grau [hahaha].
Amém.
sexta-feira, 25 de setembro de 2009
Keystroke dynamics
Assisti essa semana a uma apresentação de um colega meu, Roberto Pinheiro, bem interessante sobre um tipo de biometria comportamental que reconhece o usuário através da dinâmica de digitação.
Procurando mais a respeito do tema, encontrei uma empresa que fornece uma demo bem legal (com interface web) em que é requerido do usuário a digitação de uma frase em inglês por 8 vezes para registrar o template na base.
Após isso, tudo o que se tem a fazer é testar se sistema irá reconhecê-lo ou não ao digitar a frase novamente.
Funcionou muito bem aqui para mim, especialmente se considerarmos que eu registrei algumas dinâmicas de digitação diferentes para tentar ver se dava algum falso positivo. E de fato, não aconteceu.
Tudo o que se precisa fazer é cadastrar um email válido para testar o sistema.
Segue o link: http://www.psylock.com
sexta-feira, 28 de agosto de 2009
Yes, You Can Change the World From Your Bedroom
There are many ways to change the world from your bedroom. One of them is to subscribe to the World Community Grid (WCG) and donate some of the idle time of your PC and/or Laptop to process valuable scientific data. For instance, you can help researchers to discover new drugs and treatments for Cancer, Dengue Fever, Yellow Fever, Hepatitis C and AIDS, only to name a few serious human diseases.
The idea behind WCG is to execute in a few months important research projects, as demanded by leading research institutions, that would take thousands of years to finish with the available computational resources in universities and research centers. Therefore, whenever someone decide to participate in such a project, this person will join the efforts of hundreds or maybe hundreds of thousands other users that have done the same, composing a huge network of computers (i.e., a grid) which provides the necessary processing power to do the hard job within the strict time constraints required by the urgent nature of the projects.
All of these is done without any interference in the way you use your PC. The only thing that is needed is to download the program which will be running on the background as a screensaver, only when you are not interacting with your desktop.
Some people complain they would like to help the world to be a better place but they don't know how, or worse, they don't have the necessary time. These must not serve as excuses anymore. Stand up now and help to change the world from your bedroom.
Learn how to help on: http://www.worldcommunitygrid.org
sábado, 13 de outubro de 2007
O tamanho do universo te deprime?
Sou um grande fã do senhor David Deutsch - físico israelense considerado o "papa" da computação quântica. Não somente pela sua geniosidade, mas também pela forma simples, descontraída e otimista de enxergar o mundo.
Faz tempo que esse grande homem, considerado por muitos como um futuro ganhador do Nobel de física, não atualiza o seu blog. Mesmo assim, vale a pena passar por lá e desfrutar algums de seus pensamentos irreverentes, como esse breve post que tomei a liberdade de traduzir:
"Algumas pessoas ficam deprimidas quando descobrem o quão grande é o universo. Elas se sentem pequenas e insignificantes e pensam que nada mais importa nesse mundo.
Isso é tão sem sentido quanto deprimir-se quando você descobre que as vacas são maiores que você. Qual é o problema com a 'grandeza' das coisas? Uma vaca é muito maior que você, mas é um animal ridículo e você é uma pessoa valiosa. Você sabe que é só uma vaca. Ela não sabe de nada. [Ela] Apenas permanece lá comendo grama (grama!) e hibernando. E se ela fosse ainda maior, isso somente a faria ainda mais ridícula.
Eu acho que [isso] é uma completa refutação da idéia de que o tamanho do universo nos torne insignificantes, ou que [saber o tamaho do universo] seja deprimente."
por David Deutsch.
Texto em inglês:
http://www.qubit.org/people/david/index.php?blog=20050309193428
Faz tempo que esse grande homem, considerado por muitos como um futuro ganhador do Nobel de física, não atualiza o seu blog. Mesmo assim, vale a pena passar por lá e desfrutar algums de seus pensamentos irreverentes, como esse breve post que tomei a liberdade de traduzir:
"Algumas pessoas ficam deprimidas quando descobrem o quão grande é o universo. Elas se sentem pequenas e insignificantes e pensam que nada mais importa nesse mundo.
Isso é tão sem sentido quanto deprimir-se quando você descobre que as vacas são maiores que você. Qual é o problema com a 'grandeza' das coisas? Uma vaca é muito maior que você, mas é um animal ridículo e você é uma pessoa valiosa. Você sabe que é só uma vaca. Ela não sabe de nada. [Ela] Apenas permanece lá comendo grama (grama!) e hibernando. E se ela fosse ainda maior, isso somente a faria ainda mais ridícula.
Eu acho que [isso] é uma completa refutação da idéia de que o tamanho do universo nos torne insignificantes, ou que [saber o tamaho do universo] seja deprimente."
por David Deutsch.
Texto em inglês:
http://www.qubit.org/people/david/index.php?blog=20050309193428
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