## Saturday, April 3, 2010

## Thursday, March 11, 2010

### The Golden Ratio and Understanding the Universe

When you stop and think about it, it is truly astonishing how well we can describe the universe around us using mathematics. That equations as simple as F=ma and E=mc^2 can describe so much of what we observe is really amazing.

The Golden Ratio by Mario Livio is essentially an examination of one of the most remarkable numbers to be discovered as a pretext for ultimately exploring the question why do mathematics work so well. The golden ratio, known from the time of the ancient Greeks, is a pretty simple concept: take a line (defined by points A and B) and divide it (at point C) such that the length of the entire line over the length of the longer portion of the division is the same as the length of this longer portion over the shorter portion. That is, if the longer portion is CB and the shorter is AC, then AB/CB=CB/AC. A pretty simple concept and definition. It turns out, this has many profound consequences. This golden ratio, normally dubbed phi by mathematicians, is one of the first irrational numbers discovered and is, in some sense, the most irrational of all. It shows up in many branches of math, especially geometry, and has been observed in nature in the patterns formed by petals on flowers, the seeds in sunflowers, the shape of certain seashells, and the shape of galaxies. It is ubiquitous in nature. Why should that be so? That is the real point of Livio’s book.

Livio spends a lot of time on the history of phi, how it was discovered, how it was understood, and what it means to math and science. When he is focusing on the role of phi in science, the book is wonderful. There were many very interesting insights that I was unaware of that were real gems to discover. Livio also spends a lot of time on the supposed role the golden ratio played in art, poetry, music, and architecture, including the constrution of the pyramids of Egypt. His goal is to debunk those who claim that the golden ratio was an instrumental part in many such works, and he does so convincingly. Unfortunately, I found this a huge distraction and very uninteresting. I would much rather that he had filled those pages with more discussion of how the golden ratio is found in nature and science. I understand that he felt a need to determine where the golden ratio is really to be found, but I felt it was over done.

Ultimately, the fact that the golden ratio, and by extension math as a whole, figures in so much of what we see around us leads Livio to examine why that is so. He describes two alternative views. First, that the universe is objectively Platonic; that humans are discovering the laws of the universe and those are written in the language of math. Any civilization in the universe would uncover the same mathematical laws. The second view is that math is a human language, a human construct, and we are using it to interpret our observations of the universe. Civilizations with different formulations of mathematics would have a different view of how the universe works. Livio falls somewhere in the middle, and, to be honest, I did not overly understand his reasoning for his position.

It is an interesting question. I guess I would tend a bit more towards the Platonic view. I think that it is just too striking that our math and physics can not only describe but predict what is happening around us so well. I once had a chat with a fellow grad student at the UW physics department that was about this. His point, as far as I could understand, is that maybe we create the reality around us via our investigations and our interpretations of our observations. Essentially, that there is no objective reality, that reality is created by the observer. Thus, as we develop our math, we view the universe through that math and thus shape it to conform to our math. This “the observer shapes reality” perspective seems like an extreme view of the Copenhagen interpretation of quantum mechanics. I definitely wouldn’t go so far as this. But, it is an interesting question.

The Golden Ratio by Mario Livio is essentially an examination of one of the most remarkable numbers to be discovered as a pretext for ultimately exploring the question why do mathematics work so well. The golden ratio, known from the time of the ancient Greeks, is a pretty simple concept: take a line (defined by points A and B) and divide it (at point C) such that the length of the entire line over the length of the longer portion of the division is the same as the length of this longer portion over the shorter portion. That is, if the longer portion is CB and the shorter is AC, then AB/CB=CB/AC. A pretty simple concept and definition. It turns out, this has many profound consequences. This golden ratio, normally dubbed phi by mathematicians, is one of the first irrational numbers discovered and is, in some sense, the most irrational of all. It shows up in many branches of math, especially geometry, and has been observed in nature in the patterns formed by petals on flowers, the seeds in sunflowers, the shape of certain seashells, and the shape of galaxies. It is ubiquitous in nature. Why should that be so? That is the real point of Livio’s book.

Livio spends a lot of time on the history of phi, how it was discovered, how it was understood, and what it means to math and science. When he is focusing on the role of phi in science, the book is wonderful. There were many very interesting insights that I was unaware of that were real gems to discover. Livio also spends a lot of time on the supposed role the golden ratio played in art, poetry, music, and architecture, including the constrution of the pyramids of Egypt. His goal is to debunk those who claim that the golden ratio was an instrumental part in many such works, and he does so convincingly. Unfortunately, I found this a huge distraction and very uninteresting. I would much rather that he had filled those pages with more discussion of how the golden ratio is found in nature and science. I understand that he felt a need to determine where the golden ratio is really to be found, but I felt it was over done.

Ultimately, the fact that the golden ratio, and by extension math as a whole, figures in so much of what we see around us leads Livio to examine why that is so. He describes two alternative views. First, that the universe is objectively Platonic; that humans are discovering the laws of the universe and those are written in the language of math. Any civilization in the universe would uncover the same mathematical laws. The second view is that math is a human language, a human construct, and we are using it to interpret our observations of the universe. Civilizations with different formulations of mathematics would have a different view of how the universe works. Livio falls somewhere in the middle, and, to be honest, I did not overly understand his reasoning for his position.

It is an interesting question. I guess I would tend a bit more towards the Platonic view. I think that it is just too striking that our math and physics can not only describe but predict what is happening around us so well. I once had a chat with a fellow grad student at the UW physics department that was about this. His point, as far as I could understand, is that maybe we create the reality around us via our investigations and our interpretations of our observations. Essentially, that there is no objective reality, that reality is created by the observer. Thus, as we develop our math, we view the universe through that math and thus shape it to conform to our math. This “the observer shapes reality” perspective seems like an extreme view of the Copenhagen interpretation of quantum mechanics. I definitely wouldn’t go so far as this. But, it is an interesting question.

## Friday, February 26, 2010

### المقطع الذهبى ونظرية زمان المكان الكنتورى للعالم الدكتور محمد النشائى

المقطع الذهبى اساس العلوم الا خطية و الفوضى المحددة ( علم الشواش) و بالتالى ميكانيكا الكم و هذا ما اثبته العالم المصرى الدكتور محمد النشائى فى نظريتة عن زمان المكان الكنتورى . ومن ثم يمكننا ان نجزم بانه كان رائدا وبنظريته استطاع ان يوحد القوى الاساسية فى الطبيعة واوجد الحل المثالى للمعضلة التى طالما احتار فيها العلماء فى مجال الطبيعة والان وبعد ثبات نجاحها فى المعمل من قبل علماء من معهد بالمانيا

Helmholz

يمكننا ان نفخر بان نظرية النشائى كانت سباقه فى ان المقطع الذهبى الذى استخدمه القدماء المصريون فى بناء الاهرام هو من الناحية العلمية حسب نظريته اساس توحيد القوى الاساسية فى الطبيعة .

Helmholz

يمكننا ان نفخر بان نظرية النشائى كانت سباقه فى ان المقطع الذهبى الذى استخدمه القدماء المصريون فى بناء الاهرام هو من الناحية العلمية حسب نظريته اساس توحيد القوى الاساسية فى الطبيعة .

للاطلاع على ابحاث الدكتور محمد النشائى المتعلقة بالمقطع الذهبى الرجاء تحميل تلك الملفات :

1. الملف الاول

2. الملف الثانى

3 . الملف الثالث

و للاطلاع على ابحاث اخرى للدكتور النشائى تتعلق بنظريته عن المقطع الذهبى فى ميكانيكا الكم و الطاقات العليا برجاء زيارة الموقع التالى htttp://www.siencedirect.com

فى مجلة Chaos, Solitons and Fractals التى قام بتاسيسها منذ اكثر من سبعة عشر عاما

تاكيدا لما سبق يمكنكم الاطلاع على المقالة التالية و التى تفيد بان عدد من الباحثين فى مركز هلم هولز للطاقة و المواد ببرلين, ألمانيا و بالتعاون مع زملائهم من جامعات اكسفورد و برستول و معمل روزر فورد ابلتون بالمملكة المتحددة استطاعوا لاول مرة ان يروا فى المعمل تماثل جزئى النانو فى المواد الصلبة و ذلك عن طريق قياسه ووجدوه مطابقاً للمقطع الذهبى الذى سبق استخدامه فى الفن و العمارة .

Public release date: 7-Jan-2010

**Golden ratio discovered in a quantum world**

Hidden symmetry observed for the first time in solid state matter

This release is available in German

Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture. The research team is publishing these findings in Science on the 8. January.

On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.

When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain – or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."

By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture." Radu Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system – a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material", he explains.

The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology. Prof. Tennant remarks on the perfect harmony found in quantum uncertainty instead of disorder. "Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state."

The researchers achieved these results by using a special probe - neutron scattering. It allows physicists to see the actual atomic scale vibrations of a system. Dr. Elisa Wheeler, who has worked at both Oxford University and Berlin on the project, explains "using neutron scattering gives us unrivalled insight into how different the quantum world can be from the every day". However, "the conflicting difficulties of a highly complex neutron experiment integrated with low temperature equipment and precision high field apparatus make this a very challenging undertaking indeed." In order to achieve success "in such challenging experiments under extreme conditions" the HZB in Berlin has brought together world leaders in this field. By combining the special expertise in Berlin whilst taking advantage of the pulsed neutrons at ISIS, near Oxford, permitted a perfect combination of measurements to be made.

### رؤية لميكانيكا الكم من خلال نظرية الفراغ الكنتورى و اتجاه الزمن للعالم المصرى محمد النشائى

## Thursday, February 25, 2010

### المقطع الذهبى و فيزيا الطاقات العاليا

فى هذا البحث يتعرض الدكتور جيرالدو ايوفانى الذى يجرى ابحاثه فى جامعة سارينو فى ايطاليا الى اهمية المقطع الذهبى فى فيزياء الطاقات العاليا و نظرية

E-infinity

للدكتور محمد النشائى

E-infinity

للدكتور محمد النشائى

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