Interesting ideas in CACM (Vol.55, No.9)

I found two interesting ideas in CACM, Vol.55, No.9.

1. DieHard

Many C++ program's crash bugs are caused by small out of bound access. So, if a memory allocator gives a slightly large memory chunk, also randomize the heap allocation. Then many bugs become non-deterministic, Heisenberg bug.

This is a nightmare for developers who should fix this kind of bugs. Because, it is hard to catch the bug.

However, for some users, this might be better. If one just restarts the program, the crash may be gone if they are lucky.

You can find this idea entitled DieHard from Microsoft research. Although, I don't think randomly hiding bugs are analogy of Seat belts or Airbags. I found this idea interesting, but I prefer deterministic bugs as a developer. Also I prefer to fix the bugs rather than hiding them.

http://queue.acm.org/detail.cfm?id=2333133

2. CriptDB

I heard some methods that you can search encrypted data without decrypt it or search a compressed data without decompress it. I don't understand the details, but the basic idea is having a kind of data onto map function. For example, I have a database which contains English text. I encrypt this database by translating German. So if anyone who don't know German can not read the database. If I want to search a word ``mountain'', then ``mountain'' is encrypted as ``Berg'', the I search the word ``Berg''. The story is also not so simple, however, the basic idea seems like this.

http://dl.acm.org/citation.cfm?doid=2330667.2330691

Comments

Why parallelogram area is |ad-bc|?

Here is my question. The area of parallelogram is the difference of these two rectangles (red rectangle - blue rectangle). This is not intuitive for me. If you also think it is not so intuitive, you might interested in my slides. I try to explain this for hight school students. Slides: A bit intuitive (for me) explanation of area of parallelogram (to my site, external link) .

Geometric Multiplicity: eignvectors (2)

If eigenvectors of a matrix A are independent, it is a happy property. Because the matrix A can be diagonalized with a matrix S that column vectors are eigenvectors of A . For example, Why this is a happy property of A? Because I can find A's power easily. A^{10} is not a big deal. Because Λ is a diagonal matrix and power of a diagonal matrix is quite simple. A^{10} = SΛ^{10} S^{-1} Then, why if I want to compute power of A ? That is the same reason to find eigenvectors. Eigenvectors are a basis of a matrix. A matrix can be represented by a single scalar. I repeat this again. This is the happy point, a matrix becomes a scalar. What can be simpler than a scalar value. But, this is only possible when the matrix S's columns are independent. Because S^{-1} must be exist. Now I come back to my first question. Is the λ's multiplicity related with the number of eigenvectors? This time I found this has the name. Geometric multiplicity (GM): the number of in...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

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