timelets: (Default)
Maldacena discovered that the boundary and the bulk are completely equivalent.... the relatively simple, gravity-free equations that prevail on the boundary contain the same information and describe the same physics as the more complex equations that rule the bulk.

“It’s kind of a miraculous thing,” says Van Raamsdonk. Suddenly, he says, Maldacena’s duality gave physicists a way to think about quantum gravity in the bulk without thinking about gravity at all: they just had to look at the equivalent quantum state on the boundary.



http://www.nature.com/news/the-quantum-source-of-space-time-1.18797


== link thanks to lxe

As a side note, I never thought about the equivalence of information and energy wrt entropy. There's a vague analogy here with Hayek's idea that prices convey information. Moreover, we can think about Arrow's technical change hypothesis as two stage process: productive absorption of information (learning curve) and productive absorption of capital (cumulative investment).
timelets: (Default)
(via Vlad) An instructive interview that shows how people make mental mistakes by extrapolating technology solutions with "more-of-the-same" thinking:
http://archive.is/6M8mg#selection-1375.7-1381.541

We spend our time looking for threats against a company. We look for things that might be active inside the company that would cause us concern, and then of course we look to respond—detecting, containing, and deflecting those threats as much as possible while at the same time keeping in mind that our executives and board of directors always want to know what's going on with security in the company.

Generically, every breach has the big data problem. For example, in a malware incident that results in a breach, the malware comes in and spreads across the environment.

When that scope [of investigation] expands, the security team typically has to deal with a sudden increase in big data -- logs, alerts, etc. -- making budget planning critical. Right now I'm planning my budget for next year, and I hope I ask for enough disk space and computing power so that the infrastructure is prepared for future attacks. ... Burst capacity is really critical for the security team who needs to find answers quickly.


Basically, she assumes that data security and hardware capacity/budget are "entangled" linear orders.

also see https://timelets.dreamwidth.org/682944.html

upd: the alleged exploit https://qz.com/1073221/the-hackers-who-broke-into-equifax-exploited-a-nine-year-old-security-flaw/
timelets: (Default)
There seems to be a direct connection between Born's argument and CT.
This root of the matter is a very simple logical distinction which seems to be
obvious to anybody not biased by a solipsistic metaphysics; namely this : that often a measurable quantity is not a property of a thing, but a property of its relation to other things.

In every physical theory there is a rule which connects the projections of the same object
on different systems of reference, called a law of transformation, and all these transformations have the property of forming a group, i.e. the sequence of two consecutive transformations is a transformation of the same kind.

DOI 10.2307/2216882

Developing a new paradigm necessarily involves construction of a new frame of reference. For example, Newton was highly successful at creating new frames of reference for time and space. Born notes it in his Nobel speech.

Newtonian mechanics is deterministic in the following sense: If the initial state (positions and velocities of all particles) of a system is accurately given, then the state at any other time (earlier or later) can be calculated from the laws of mechanics. All the other branches of classical physics have been built up according to this model. Mechanical determinism gradually became a kind of article of faith: the world as a machine, an automaton. As far as I can see, this idea has no forerunners in ancient and medieval philosophy.* The idea is a product of the immense success of Newtonian mechanics, particularly in astronomy. In the 19th century it became a basic philosophical principle for the whole of exact science. I asked myself whether this was really justified. Can absolute predictions really be made for all time on the basis of the classical equations of motion?

* A new default worldview.
timelets: (Default)
They [gods] emerge always with a certain mystery; for they conduct the mind beyond objective experience into a symbolic realm where duality is left behind.
...
"So God created man in his own image, in the image of God created he him; male and female created he them." The question may arise in the mind as to the nature of the image of God; but the answer is already given in the text, and is clear enough. "When the Holy One, Blessed be He, created the first man, He created him androgynous.'
The removal of the feminine into another form symbolizes the beginning of the fall from perfection into duality; and it was naturally followed by the discovery of the duality of good and evil, exile from the garden where God walks on earth, and thereupon the building of the wall of Paradise, constituted of the "coincidence of opposites," by which Man (now man and woman) is cut off from not only the vision but even the recollection of the image of God.
...
... symbolizing the mystery of creation: the devolvement of eternity into time, the breaking of the one into the two and then the many, as well as the generation of new life through the reconjunction of the two.

--- The Hero with a Thousand Faces.
timelets: (Default)
Reminds me of adjunction in Category Theory.



quote from The Hero with a Thousand Faces, by Joseph Campbell.


timelets: (Default)
http://www.economicsonline.co.uk/Competitive_markets/Production_possibility_frontiers.html



D and D-op are linear orders.


Production possibility frontiers

An opportunity cost will usually arise whenever an economic agent chooses between alternative ways of allocating scarce resources. The opportunity cost of such a decision is the value of the next best alternative use of scarce resources. Opportunity cost can be illustrated by using production possibility frontiers (PPFs) which provide a simple, yet powerful tool to illustrate the effects of making an economic choice.

A PPF shows all the possible combinations of two goods, or two options available at one point in time.

Production possibilities

Mythica, which is a hypothetical economy, produces only two goods - textbooks and computers. When it uses all of its resources, it can produce five million computers and fifty five million textbooks. In fact, it can produce all the following combinations of computers and books.

COMPUTERS (m)TEXTBOOKS (m)
070
169
268
365
460
555
648
739
824
90

timelets: (Default)
Here's two categories: Technology and Business

Technology is represented by a product of desires DxD. Desires conflict; therefore, one desire D is a PreOrder, while another is a PreoOrder Op. That is, improving our position on one desire makes another one worse off. Each desire has a terminal object 1, which is the lowest performance threshold, respectively. The thresholds form technical specification 2.

Business is represented by a Utility Monoid, e.g. a combination of Revenues (or expenses). Business has a terminal object 1, which represents profitability requirements, i.e. "the bottom line." The business would like to increase Utility, but it is constrained by the conflict of desires in Technology.

We can probably build adjoints, but I don't know how to specify them.

timelets: (Default)
Empirical data shows that new technologies succeed in combination with new markets only. I have a gut feeling that we can prove it theoretically using adjoint functors.
timelets: (Default)
It seems like effect (F) and understanding (U) are adjoint functors.

upd.

Learning/Sci -> Technology -> Business

Business -> Technology -> Learning/Sci

Beautiful!

Jul. 30th, 2017 01:36 pm
timelets: (Default)
A poset A is often said to arise concretely if we are given a large category E of
structured spaces, choose an object X in E, and define A to be a category of parts of X (in the sense of E) with inclusions as maps.
 
timelets: (Default)
Жизнь прекрасна. Я сегодня применил элементы теории категорий, чтобы помочь двум врачам придумать новую систему для лечения переломов. Это выглядело вот так:
A -> B -> C -> D (wherein *: C->D is monic)

or

A -> D

Проблема в том, что сегодня все строят свободные моноиды на А, и это очень долго, дорого и вызывает осложнения. А мои новые друзья будут строить свободные моноиды на D. Забавно, что один из врачей вот-вот станет son-in-law моего бывшего начальника и разговорились о переломах мы совершенно случайно.

Leverage

Jul. 28th, 2017 07:48 pm
timelets: (Default)


In the structure on the left, f represents a constraint.

In the structure on the right, f represents a multiplier.
timelets: (Default)
A possible reason why CT works for developing new ideas:
“the words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined.”

- Albert Einstein, quoted from Herbert A. Simon. Models of my life. p 375.


upd. Another possible related concept is "problem isomorphs."

Simon defined problem isomorphs as problems whose solutions and moves can be placed in one-to-one relation with the solutions and moves of the given problem [17]. The key to isomorphism is that even when two representations contain the same information, they can still provide very different sets of operations for accessing and inferring about that information, which can make a given problem easier or harder to solve [13]

Dou, Wenwen, et al. "Comparing different levels of interaction constraints for deriving visual problem isomorphs." Visual Analytics Science and Technology (VAST), 2010 IEEE Symposium on. IEEE, 2010.
timelets: (Default)

As it happened, one of Hall's contemporaries, Jacques Plante of the Montreal Canadiens, began getting the notion that being playing goal without a mask was a bad idea. Ever creative, even as a junior player, Plante began experimenting with the idea of a face protector.

https://www.nhl.com/news/jacques-plante-becomes-first-goalie-to-wear-mask/c-290431748




Now, all hockey goalies wear masks. Moreover, all college hockey players wear masks and the vast majority of professional players wear visors. How would we predict that Jacques Plante's idea would become the initial object? Also, is it a terminal object too? How should we construct a meaningful category to model that?
timelets: (Default)
It seems like Paul Romer makes a certain mistake in his approach to the theory of innovation. He assumes that characteristic function ("the recipe") is given, while it has to be discovered. In short, the set of elements is the initial object, not the terminal one.
Maybe we can think of the set of elements as the initial object, while the free group generated by it represents the terminal object.

E.g. printed book vs handwritten book (different terminal objects built using different initial objects.)

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