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I think this figure is going to be important for many fields outside of quantum physics because it models a system's capacity to accommodate additional energy/information.

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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.


== 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).
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В ЖЖ очень хороший физик показал, что неплохой (регулярно хохмящий) математик -
мудак; причем физик сделал это деликатно, чтобы поняли только те, кто в теме.

Тут, как минимум, три learning moments: 1) как не стать мудаком, совершив мудацкий поступок; 2) какой правильный поступок нужно совершить, чтобы не стать мудаком в потенциально мудацкой ситуации; 3) как деликатно указать на мудачество, а не мудака, чтобы у окружающих появился шанс чему-то научиться.
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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.
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Age is probably a more important factor than gender. Moreover, lab vs life discrepancy appears to be a big issue in cognitive abilities research.

Abstract: Adult age differences in a variety of cognitive abilities are well documented, and many of those abilities have been found to be related to success in the workplace and in everyday life. However, increased age is seldom associated with lower levels of real-world functioning, and the reasons for this lab-life discrepancy are not well understood.

Source: doi: 10.1146/annurev-psych-120710-100328

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And the reason for Purdue [offering a masters program on semiconductors in 1960] is most people don’t know that the transistor effect was found at Crane Naval Air Development Center three weeks after Shockley. And it’s the tragedy of being second.

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У bamalip недавно был пост про математику, об отношении логики и абстракции. Поскольку я не математик, а пользователь, то отношение к предмету у меня чисто потребительское. То есть мне скорее интересно, почему математика, включая логику и абстракцию, полезна в человеческом сообществе (а в сообществе дельфинов - нет).

По-моему, дело в том, что в отличии от естественных наук (natural sciences), разнообразные искусственные науки (artificial sciences - computer science, engineering, finance, architecture, etc.) занимаются конструированием новой реальности. Использование математики позволяет быстро создавать сложные непротиворечивые (consistent) штуки, причем делать это с применением принципа разделения труда. Здесь логика работает на непротиворечивость, а абстракция на специализацию.

Для сравнения, в естественных биологических системах непротиворечивая сложность достигается путем эволюции в течение многих миллионов лет.

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Within the next 10-15 years the situation with Climate Change science will resolve itself through massive satellite data collection. Thanks to Elon Musk and others, people will be launching satellites and getting plenty of data to prove or disprove the hypothesis. Most likely, it'll be cheaper to get data from space than from a drone. A global science problem will be solved by a true global data data collection system plus DL.

I can probably describe the solution in terms of Category Theory through two categories: climate events C and data collection (D). Right now, implementation of the functor F: C->D is sufficient for localized weather-related conclusions, but not sufficient for climate ones.
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The only genuine access to them (entities) lies in knowing [Erkennen], intellectio, in the sense of the kind of knowledge [Erkenntnis] we get in mathematics and physics. Mathematical knowledge is regarded by Descartes as the one manner of apprehending entities which can always give assurance that their Being has been securely grasped. If anything measures up in its own kind of Being to the Being that is accessible in mathematical knowledge, then it is in the authentic sense.
That which enduringly remains, really is. This is the sort of thing which mathematics knows.
his ontology of the world is not primarily determined by his leaning towards mathematics, a science which he chances to esteem very highly, but rather by his ontological orientation in principle towards Being as constant presence-at-hand, which mathematical knowledge is exceptionally well suited to grasp.

--- Martin Heidegger. Being and Time, p. 96.
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It cannot be overemphasized that System A had no analogous precursor, and thus that – unlike virtually all succeeding scientific theories – its invention was a radical departure from anything which preceded it. Consequently, we can say almost nothing with confidence about its motivation, which cannot have been directed at the shortcomings of a (non-existent) prevailing theory, nor seemingly at any urgent practical need, since we have still no evidence of how it was employed. Indeed, how little we know of the circumstances of its origin is reflected in the fact that we do not even know for certain its author’s name.
The crucial step – apart from conceiving the desirability and imagining the feasibility of constructing a comprehensive mathematical model of this complex set of variable phenomena – was the separation and successful modeling of the effects of lunar and solar anomaly on the intervals between syzygies. The crux of this development was the initial construction of a model depicting the variations due to lunar anomaly of the intervals between syzygies.
One of the fundamental tools of Babylonian astronomy was the concept of period relation which equated Π phenomena of one sort with Z of another.
In each case the period relation implied that variations associated with the second phenomenon recurred after Π instances of the first phenomenon, and thus that Π phenomena = Z cycles of variation.
* the Substitute King ritual, practiced extensively during the reigns of Esarhaddon and Ashurbanipal, in which a substitute “king” (and queen) would be appointed to absorb the unfavorable effects of an adverse eclipse, which would be expunged from the kingdom by their subsequent deaths.

Source: John P. Britton. Studies in Babylonian Lunar Theory: Part I. Empirical Elements for Modeling Lunar and Solar Anomalies.

Arch. Hist. Exact Sci. 61 (2007) 83–145. Digital Object Identifier (DOI) 10.1007/s00407-006-0121-9
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Proclus believed that mathematics was intrinsic to the fabric of things, and that its language enabled one to articulate the knowledge of reality: the relation between whole and parts could be expressed in terms of divisibility; the bonds between disparate parts of the same universe could be seen as proportions; the generation of beings from the divine Monad, the One which is the principle of everything, was a sort of multiplication, and so on. Mathematical objects themselves are intermediate between the intelligibles and the sensibles and consequently reflect the human condition....

S.Cuomo. Ancient Math.
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Source: Serafina Cuomo, Ancient Mathematics.
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...nothing in the universe
Is born unique and grows unique, alone,
But all belong to a species, very many
Of the same kind.
Therefore one must accept that sky
And earth and sun, moon, sea and all else that exists
Are not unique, but in number numberless.

- Lucretius, Trans. Melville, On the Nature of the Universe. Book 2, line 1077.



Nov. 23rd, 2016 01:07 pm
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Arguably, ageing population doesn't necessarily make the world wiser, but it definitely makes it less open to new experiences.

Wisdom and Mental Health Across the Lifespan Webster 2012

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Вероятность - это предел для частоты благоприятных исходов на большом массиве однотипных событий. Т.е. метода подсчета всегда одна:
1) задается пространство независимых элементарных событий
2) вычисляется общее число возможных событий (комбинаций)
3) вычисляется число благоприятных исходов.
4) второе делится на первое - всё! Это и есть вероятность, и ничего другого нет и не надо.

It looks like the probability space (p.1) is always a discrete category.
p.3 presupposes a value judgement.
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How a "magnificently" wrong science theory developed by Max van Pettenkofer helped solve the cholera problem and stimulated development of modern sanitation systems in the 19th century Europe.

Contagionism vs Anticontagionism


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