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The Rolf Nevanlinna Prize

A few days ago I read that Constantinos Daskalakis got the Rolf Nevanlinna Prize for
 For transforming our understanding of the computational complexity of fundamental problems in markets, auctions, equilibria, and other economic structures. His work provides both efficient algorithms and limits on what can be performed efficiently in these domains. Thus, according to this, we now can somehow compute economies. However, even economists have started to realize that economies cannot be described with  mathematics only. In fact,  Why economists need to expand their knowledge to include the humanities is a recent article that discusses exactly this problem. Daskalakis's approach is based on the assumption that humans are Turing machines. Unfortunately, they are not and this is the reason why economists fail so miserably in their predictions. Furthermore, there are some other things that people who work in computational economics "fail" to realize. For example, even if…

Everything is computable...

Recently I read an article that presented a novel idea by  Nicolas Gisin. In a nutshell, Gisin says that
 only a certain number of digits of real numbers have physical meaning. After some number of digits, for example, the thousandth digit, or maybe even the billionth digit, their values are essentially random. This is very interesting because it means that there are no noncomputable numbers. Provided this idea is correct, we can easily decide if for example there are three 4s in the decimal expansion of π! The real problem of course is to agree on the number of significant digits. Once this problem is settled, then we can answer any question about physical real numbers. Another consequence of this idea would be that real numbers might be directly representable in even present computer hardware. What is left is to examine deeply this idea and see if it is actually valid.

A "Solution" to Riemann Hypothesis

Riemann hypothesis is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12". The Riemann zeta function is conventionally represented as the sum:
ζ(z)=∑k=1∞1kz
Recently, I read in Peter Woit's blog that some researchers have published a paper that describes a  Hamiltonian operator H that can be used to possibly solve this problem. This operator has the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function! The paper is also available as a preprint. In a sense, this paper says that one can set up a quantum system whose evolution "solves" Riemann hypothesis. To me this is a reasonable approach to the solution of the problem. And it reminds me of the work of  Leonard Adlemam.

Multiverse and Computation

The idea that quantum computation is a manifestation of the multiverse is not new. For example, David Deutsch believes that quantum computers can be used to test its existence. Personally I believe that the multiverse is good for scripts of scifi series (e.g., the Fringer) but that's all. But I think that something is also logically wrong with this idea.

Roughly, the multiverse is the idea that there many copies of our universe (or some universe) and each evolves differently, yet in each one of them there is a copy of me but all these copies are different pairwise. Obviously, at each moment many things happen that can have different outcomes so in one universe a spermatozoon fuses with an ovum while in another this never happens but in another universe a different spermatozoon fuses with it. Practically, this means that in the first universe person A will be born, in the second nothing will happen while in the third person B will be born. If all these things are quite possible (!…

Memcomputing

Εικόνα
Memcomputing is a new computing paradigm that is based on the idea that the memory can and should be used to compute. The idea is based on the functionality of the brain where neurons are used to both store information and process it.  In particular the following drawing shows the way a memecomputer operates. The zigzag arrow specifies that  a signal is sent.  All other arrows designate flow of information.


Now compare this architecture with the "traditional" von Neumann architecture:

I think the difference is obvious. The interesting thing with me memcomputing is that the people who designed this computer architecture published a paper where they claim that memcomputers can solve NP-complete problems. In particular, they claim that their machine can solve instances of the subset sum problem. This problem can be phrased as follows:  Consider a finite set G of integers  having n elements, is there a non-empty subset K of G whose elements sum up to s? As happens in this and ot…

Creator of EAC implementation passed away

Today I was informed that  Jonathan Wayne Mills, the creator of an implementation of the Extended Analog Machine passed away on January 27, 2016 at the age pf 64 after a six month fight against cancer. I am really saddened when I hear such tragic news.
on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf JonathanWayneMillsJonathanWayneMills Jonathan Wayne Mills Jonathan Wayne Mills

A solution to Thomson’s Lamp?

Today I discovered a paper that claims to offer a solution to Thomson’s Lamp.The paper is entitled Hypercomputation, Frege, Deleuze: Solving Thomson's Lamp. Right now I have no time to read it and offer comments on it.