[ad_1]
Posted on 15 Apr 2019
It turns out that any biological or physical system that "calculates" input outputs, such as a cell processing energy or an evolving ecosystem, conceals hidden variables. "This type of model is really natural," observes physicist Jeremy A. Owen of MIT, "based on assumptions that the weather is continuous and that the state you are in determines your destination." . following."
"A surprising thing, which makes this more general and more surprising to us, is that all these results are valid even without thermodynamic considerations," recalls David Wolpert at the Santa Fe Institute. "This is a very pure example of Phil Anderson's mantra "More is different" because all these low-level details [hidden states and hidden timesteps] are invisible for top-level details [map from visible input state to visible output state]. "
"Warp Bubbles" – NASA handles space-time for faster travel than light
"In a very minor way, it looks like the limit of the speed of light," says Wolpert, "the fact that systems can not exceed the speed of light is not immediately a consequence for the vast majority of scientists . But this is a restriction of allowed processes that applies everywhere and must always be kept in mind. "
Gumball warning … the following is a little complex
Scientists believe that time is continuous and not unobtrusive. Basically, they think that it does not progress in pieces, but rather in flow, smoothly and continuously. Thus, they often model the dynamics of physical systems in the form of "Markov processes", named after the mathematician Andrey Markov. Scientists have used these processes to study a series of real-world processes, from protein folding to changing ecosystems, to financial markets, with incredible success.
However, invariably, a scientist can observe the state of a system only at discrete moments, separated by an interval rather than continuously. For example, a stock market analyst may repeatedly observe how the market condition at the beginning of a day is tied to the market at the beginning of the following day, creating a conditional probability distribution of the market condition. second day is given the state to the first day.
From the Dark Side – "The Milky Way could be a huge wormhole in space-time"
In two articles, one in Nature Communications this week and the other in the New Journal of Physics, physicists from the Santa Fe Institute and MIT have shown that for such a dynamic two time on a set of "visible states" "To result from a continuous time Markov process, this Markov process must actually take place over a larger space, which includes hidden states in addition to visible states. They further prove that the evolution between such a pair of times must take place in a finite number of "hidden timesteps", dividing the interval between these two times. (Strictly speaking, this proof is valid whenever the evolution between the beginning and the end is noiseless – see the paper for more details.)
"We say that there are hidden variables in dynamic systems, implicit in the tools that scientists use to study such systems," says co-author Wolpert. "In addition, in a very limited sense, we say that time advances in discrete stages, even if the scientist models time as he continued. Scientists may not have paid attention to these hidden variables and these hidden time steps, but they are there and play a key behind-the-scenes role in most of the documents they read, and surely also papers that these scientists have written.
Space-time bubble – "A" time machine "that moves more than the speed of light, allowing it to travel back and forth"
In addition to discovering hidden states and time steps, scientists have also discovered a compromise between the two; the more hidden states there are, the lower the minimum number of hidden time steps required. According to coauthor Artemy Kolchinsky (Santa Fe Institute), "these results surprisingly demonstrate that Markov processes present a kind of trade-off between time and memory, which often occurs in the mathematical domain separated from the memory." analysis of computer algorithms.
The minimum configuration to switch an information bit from 1 to 0 requires three states and three sequential time steps. (David Wolpert)
To illustrate the role of these hidden states, the co-author, Owen, gives the example of a biomolecular process, observed at one-hour intervals: If you start with a protein in the 39; state & # 39; a & # 39; and over an hour, it usually turns into a state. b, and then, after one hour, it usually returns to "a", there must be at least one other state "c" – a hidden state – that influences the dynamics of the protein. "It's there in your biomolecular process," he says. "If you have not seen it yet, you can go get it."
The authors came across the need for states and no hidden time while looking for the most energy efficient way to return some information to a computer. As part of this investigation, which is part of a broader effort to understand the thermodynamics of computation, they discovered that there was no direct way to implement a map that sends both responses 1 At 0 and the answers 0 to 1. information, the bit must go through at least one hidden state and involve at least three hidden time steps.
The Daily Galaxy via Santa Fe Institute
Credit image back to top: Thanks to Magazynbieganie
[ad_2]
Source link