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2019.09.27
カテゴリ： カテゴリ未分類
大きな Isabelle/HOL mailing list で取り上げられ、議論されている。
管理者は、意味のない議論、メールを排除しているからである。
José Manuel Rodríguez Caballero
4:50 (31 分前)
To Felix, 自分
Thank you for the update [1]. Currently, I am developing a library in the proof assistant Isabelle/HOL for verifying quantum cryptography. In this library, I am using the complex numbers as an approximation of reality, not as reality itself, but as Claude Aslangul said: in physics, there is neither zero nor infinite (quotation in [3]). So, if reality is described by finite mathematics rather than by continuous mathematics as you consider, there may be possible to violate the security of a quantum cryptographic system whose security proof is based on the assumption that reality is discrete. Such a violation may be in theory, assuming ideal conditions which are beyond the current engineering possibilities. Nevertheless, even in that case, my library is just a first approximation, more precise approximations of reality are future work.
Also, I would like to share this email with Prof. Saburou Saitoh, who is also trying to avoid the notion of mathematical infinite and he developed a geometric interpretation of the fact that any number divided by zero is zero [2]. This may seem crazy, but after reading him everything makes sense. A short explanation could be that identifying zero with infinite in the Riemann sphere we obtain the desired results (Horn torus [4]), i.e., large complex numbers (in absolute value) are like small complex numbers (in absolute value) in some sense, hence zero is identified with infinite and the sphere becomes a torus.
Kind regards,
References:
[1] https://arxiv.org/abs/1104.4647
[2] https://www.semanticscholar.org/paper/D%5C%22aumler's-Horn-Torus-Model-and%5C%5C-Division-by-Zero-Saitoh/ae2141415078c7a288d4e4e561435415d86da80a
[3] https://youtu.be/MGU1fSihH9o
[4] http://www.artmetic.de/n/9100.html
El jue., 26 sept. 2019 a las 22:20, Felix Lev (escribió:
Dear Jose Manuel Rodriguez Caballero,
Maybe you might be interested in the new version of my monograph . I also would be grateful if you tell other
people who might be interested.
All the best, Felix Lev.
添付ファイル エリア
管理者は、意味のない議論、メールを排除しているからである。
José Manuel Rodríguez Caballero
4:50 (31 分前)
To Felix, 自分
Thank you for the update [1]. Currently, I am developing a library in the proof assistant Isabelle/HOL for verifying quantum cryptography. In this library, I am using the complex numbers as an approximation of reality, not as reality itself, but as Claude Aslangul said: in physics, there is neither zero nor infinite (quotation in [3]). So, if reality is described by finite mathematics rather than by continuous mathematics as you consider, there may be possible to violate the security of a quantum cryptographic system whose security proof is based on the assumption that reality is discrete. Such a violation may be in theory, assuming ideal conditions which are beyond the current engineering possibilities. Nevertheless, even in that case, my library is just a first approximation, more precise approximations of reality are future work.
Also, I would like to share this email with Prof. Saburou Saitoh, who is also trying to avoid the notion of mathematical infinite and he developed a geometric interpretation of the fact that any number divided by zero is zero [2]. This may seem crazy, but after reading him everything makes sense. A short explanation could be that identifying zero with infinite in the Riemann sphere we obtain the desired results (Horn torus [4]), i.e., large complex numbers (in absolute value) are like small complex numbers (in absolute value) in some sense, hence zero is identified with infinite and the sphere becomes a torus.
Kind regards,
References:
[1] https://arxiv.org/abs/1104.4647
[2] https://www.semanticscholar.org/paper/D%5C%22aumler's-Horn-Torus-Model-and%5C%5C-Division-by-Zero-Saitoh/ae2141415078c7a288d4e4e561435415d86da80a
[3] https://youtu.be/MGU1fSihH9o
[4] http://www.artmetic.de/n/9100.html
El jue., 26 sept. 2019 a las 22:20, Felix Lev (escribió:
Dear Jose Manuel Rodriguez Caballero,
Maybe you might be interested in the new version of my monograph . I also would be grateful if you tell other
people who might be interested.
All the best, Felix Lev.
添付ファイル エリア
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2019.09.27 05:29:27
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