Happy Christmas

Sunday, December 19th, 2010 | Author:

e^{2\pi i}=1

I wish you all a very happy Christmas time and some delicious cookies like these:
$e^{2\pi i}=1$
Frohe Weihnachten!

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Froyo (and root) on Samsung Galaxy I9000 with Linux only

Friday, December 03rd, 2010 | Author:

Phone

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.

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Questions in Information Theory V: Life and Metaphysics

Saturday, November 27th, 2010 | Author:

Entropy

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

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Questions in Information Theory IV: Philosophy of Science

Friday, November 12th, 2010 | Author:

Entropy

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?

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Some old talk notes

Wednesday, November 03rd, 2010 | Author:

Something written

I just re-discovered some notes (in german) for expository talks I gave at the University of Freiburg in student's seminars.

Here they are:

For the sake of completeness, here are links to blog posts discussing other old (german) expository talks:

And soon you might see some notes on the Weil conjectures on elliptic curves (I'm still preparing this..)

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Flat modules

Saturday, October 30th, 2010 | Author:

Flat Module

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!

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