I wish you all a very happy Christmas time and some delicious cookies like these:

Frohe Weihnachten!

So I just updated my Samsung Galaxy GT-i9000 Android phone from Android 2.1 to Android 2.2 "Froyo", using a Linux system only (no Samsung Kies or Odin required). Here is my HOWTO:

DISCLAIMER: Everything described here can "brick" your phone, which means UNUSABLE and somewhat DESTROYED FOREVER.
It hasn't done any harm to my phone, but every phone is different (mine is an unbranded european model). For example, the "download mode" you get into when pushing the "volume down"+"home button"+"power on" combo doesn't work on some phones. You absolutely NEED to fix this if you have the so-called "3-button-problem". If you get a yellow sign with "Downloading..." after using the combo on booting, everything should be fine.

Continue reading «Froyo (and root) on Samsung Galaxy I9000 with Linux only»

See also: Questions part I - Information and Entropy
Questions part II - Complexity and Algorithmic Complexity
Questions part III - Statistical Physics, Quantum Physics and Thermodynamics
Questions part IV - Philosophy of Science

Questions part V - Life and Metaphysics [Sch68]

1. Is nature deterministic?
2. Can causality be defined without reference to time? [BLMS87] [Sua01]
3. How is it possible that semantic information emerges from purely syntactic information? [BLHL+ 01]
4. Is there an inherent tendency in evolution to accumulate relevant information on the real world?
   Is there an inherent tendency in evolution to increase the complexity of organisms and the biosphere as a whole?

   “Humanity is now experiencing history’s most difficult evolutionary transformation.” – Buckminster Fuller, 1983

5. Why are robustness and simplicity good and applicable criteria to describe nature (with causal networks)? [Jen03]
6. Should we re-define “life”, using information-theoretic terms?
7. What do Gödel’s theorems imply for information and complexity theory? [Cha82]
   Is there an analogy between emergence and true but unprovable statements? [Bin08]
8. Are there limits of self-prediction in individuals and societies?
   

   “The human brain is incapable of creating anything which is really complex.” – Andrey Nikolaevich Kolmogorov 1990

9. What is the answer to life, the universe and everything?
   

   “There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another which states that this has already happened.” – Douglas Adams, 1980

References

• [Bin08] P.M. Binder, Theories of almost everything, Nature 455 (2008), 884–885.
• [BLHL+ 01] T. Berners-Lee, J. Hendler, O. Lassila, et al., The semantic web, Scientific american 284 (2001), no. 5, 28–37.
• [BLMS87] Bombelli, Lee, Meyer, and Sorkin, space-time as a causal set, Physical Review Letters 59 (1987).
• [Cha82] Gregory J. Chaitin, Gödel’s theorem and information, International Journal of Theoretical Physics 21 (1982), 941–954, 10.1007/BF02084159.
• [Jen03] Erica Jen, Essays & commentaries: stable or robust? what’s the difference?, Complex. 8 (2003), no. 3, 12–18.
• [Sch68] E. Schrödinger, What is life?, Cambridge University Press Cambridge, 1968.
• [Sua01] A. Suarez, Is there a real time ordering behind the nonlocal correlations?, 2001.

See also: Questions part I - Information and Entropy
Questions part II - Complexity and Algorithmic Complexity
Questions part III - Statistical Physics, Quantum Physics and Thermodynamics

Questions part IV - Philosophy of Science [Pop34] [Kuh62] [Fey75] [Mil09]

1. Does the point of view of information theory provide anything new in the sciences? [GM94]
   Does information theory provide a new paradigm in the sciences? [Sei07]
2. Is quantum information the key to unify general relativity and quantum theory?
   Is information theory a guiding principle for a “theory of everything”?

   “I think there is a need for something completely new. Something that is too different, too unexpected, to be accepted as yet.” – Anton Zeilinger, 2004

3. (Why) are real discoveries possible in mathematics and other structural/formal sciences? [Bor07]
4. Can we create or measure truly random numbers in nature?
   How would we recognize random numbers?
   What is a random number (or a random string of digits)?

   “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.” – John von
   Neumann, 1951

5. What is semantic information, what is meaning in science?
   What do we expect from an “explanation”?

   “The Tao that can be told is not the eternal Tao.” – Lăozı, 4th century B.C.

6. How do the concepts “truth” and “laws of nature” fit together? [Dav01] [Car94]
7. Does is make sense to use linguistic terminology in natural sciences? [Gad75]
8. Should physicists try to interpret quantum physics at all? [Dir42]
9. Would it make sense to adapt the notion of real numbers to a limited amount of memory?
   Can we build a theory of physics upon intuitionist logics?

References

• [Bor07] Borovik, Mathematics under the microscope, 2007.
• [Car94] J.W. Carroll, Laws of nature, Cambridge Univ Pr, 1994.
• [Dav01] D. Davidson, Inquiries into truth and interpretation, Oxford University Press, USA, 2001.
• [Dir42] PAM Dirac, Bakerian lecture. the physical interpretation of quantum mechanics, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 180 (1942), no. 980, 1–40.
• [Fey75] Paul Feyerabend, Against method, 1975.
• [Gad75] H.G. Gadamer, Truth and method (g. barden & j. cumming, trans.), 1975.
• [GM94] M. Gell-Mann, The quark and the jaguar, Freeman New York, 1994.
• [Kuh62] Thomas Kuhn, The structure of scientific revolutions, 1962.
• [Mil09] David Miller, Hard questions for critical rationalism, 2009.
• [Pop34] Karl Popper, The logic of scientific discovery, 1934.
• [Sei07] C. Seife, Decoding the universe: how the new science of information is explaining everything in the cosmos, from our brains to black holes, Penguin Group USA, 2007.

What is a flat module? How should I think of it?

To answer that question, I will provide some background, then define what a flat module is, clarify the definition by means of example and counter-example and finally show some nice and useful properties which you can memorize later by doing exercises. If you're lost, take a look at the references below.

Some far-fetched motivation to understand flat modules:

Flat modules are the "local" model for flat morphisms of schemes. Flatness is an essential part of the definition of étale morphisms. Etale morphisms are used in the definition of étale cohomology, which was used by Deligne 1974 to prove an analogue of the Riemann hypothesis over finite fields. The proof of the Riemann hypothesis over finite fields finished the proof of the Weil conjectures, some of the most influential conjectures in algebraic geometry.

You think you already know flat modules are? Then look if you can do all the exercises!

Continue reading «Flat modules»

See also: Questions part I - Information and Entropy
Questions part II - Complexity and Algorithmic Complexity

Questions part III - Statistical Physics, Quantum Physics and Thermodynamics [GM94] [Pen05]

1. Can there be some kind of Maxwell’s daemon, and why (not)?
2. Can all analog information be transformed to digital information losslessly?
   Is physical information always digital (digital philosophy)?
3. Does the second law of thermodynamics depend on a human observer?
4. Can quantum mechanical entanglement be reduced to mutual information? [NC00] [DH00] [PV06] [BP07]
5. What is the mathematical, what is the physical content of Heisenberg’s uncertainty relation?
   

   “I think I can safely say that nobody understands quantum mechanics.” – Richard Phillips Feynman, 1965

6. Is there a method to denote and calculate, for an open physical system, how the information content changes in time when the system’s dynamics are known?
7. Is there an important difference between information loss into small scales and information loss into microscopic freedoms?
8. Where do (thermal, quantum, vacuum, ?) fluctuations come from? [Lam97] [Lam98]
   What do they change on the macroscopic scale?
   Are gravitational fluctuations possible?
9. According to Einstein’s fluctuation-dissipation-theorem, do thermal fluctuations compensate exactly for information loss through dissipation? [CW51]
10. Is probability theory powerful enough to capture any micro-physical phenomena?
    Is mathematical probability theory the correct language for modern physics? [Mil04]

    “In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.” – Werner Heisenberg, 1992

11. How is Zeilinger’s concept of elementary systems generalizable to general state spaces?
12. Given the fact that every system is continually measured, is the concept of a closed quantum system (with unitary time evolution) relevant for real physics? [And97]
    Does decoherence by interference with the background universe render the concept of closed quantum systems obsolete? [BTV09]
13. How does randomness in quantum measurement emerge from unitary evolution?
    Is quantum physics truly information-preserving?
14. How relevant is the classical concept of degree of freedom for quantum mechanics?

References

• [And97] Philip W. Anderson, Is measurement itself an emergent property?, Complex. 3 (1997), no. 1, 14–16.
• [BP07] S.L. Braunstein and A.K. Pati, Quantum information cannot be completely hidden in correlations: Implications for the black-hole information paradox, Physical Review Letters 98 (2007).
• [BTV09] Buchleitner, Tiersch, and Viviescas, Entanglement and decoherence, Lecture Notes in Physics, Springer, 2009.
• [CW51] Herbert B. Callen and Theodore A. Welton, Irreversibility and generalized noise, Phys. Rev. 83 (1951), no. 1, 34–40.
• [DH00] D. Deutsch and P. Hayden, Information flow in entangled quantum systems, Proceedings: Mathematics, Physical and Engineering Sciences 456 (2000), no. 1999, 1759–1774.
• [GM94] M. Gell-Mann, The quark and the jaguar, Freeman New York, 1994.
• [Lam97] SK Lamoreaux, Demonstration of the casimir force in the 0.6 to 6 µm range, Physical Review Letters 78 (1997), no. 1, 5–8.
• [Lam98] S. K. Lamoreaux, Erratum: Demonstration of the casimir force in the 0.6 to 6 µm range [phys. rev. lett. 78, 5 (1997)], Phys. Rev. Lett. 81 (1998), no. 24, 5475–5476.
• [Mil04] David Miller, Probability generalizes logic, 2004.
• [NC00] Nielsen and Chuang, Quantum computation and quantum information, 2000.
• [Pen05] Roger Penrose, The road to reality: A complete guide to the laws of the universe, 3 ed., Knopf, 2005.
• [PV06] Martin B. Plenio and S. Virmani, An introduction to entanglement measures, arXiv, Jun 2006.