# A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

## A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

I haven't read this book fully and it is kind of "old" but worth a look when creating interactive programs to demonstrate the "Charge Field".

Author Stephen Wolfram

https://www.wolframscience.com/nks/

https://www.wolframscience.com/nks/p51--the-search-for-general-features/

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In order to study simple rules and their often complex behaviour, Wolfram argues that it is necessary to systematically explore all of these computational systems and document what they do. He further argues that this study should become a new branch of science, like physics or chemistry. The basic goal of this field is to understand and characterize the computational universe using experimental methods.

The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible. There are also some forms of production that are in some ways unique to this field of study. For example, the discovery of computational mechanisms that emerge in different systems but in bizarrely different forms.

Another kind of production involves the creation of programs for the analysis of computational systems. In the NKS framework, these themselves should be simple programs, and subject to the same goals and methodology. An extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. Wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. However, in general Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.

Wolfram has since expressed "A central lesson of A New Kind of Science is that there’s a lot of incredible richness out there in the computational universe. And one reason that’s important is that it means that there’s a lot of incredible stuff out there for us to 'mine' and harness for our purposes."[5]

While Wolfram advocates simple programs as a scientific discipline, he also argues that its methodology will revolutionize other fields of science. The basis of his argument is that the study of simple programs is the minimal possible form of science, grounded equally in both abstraction and empirical experimentation. Every aspect of the methodology advocated in NKS is optimized to make experimentation as direct, easy, and meaningful as possible while maximizing the chances that the experiment will do something unexpected. Just as this methodology allows computational mechanisms to be studied in their simplest forms, Wolfram argues that the process of doing so engages with the mathematical basis of the physical world, and therefore has much to offer the sciences.

Wolfram argues that the computational realities of the universe make science hard for fundamental reasons. But he also argues that by understanding the importance of these realities, we can learn to use them in our favor. For instance, instead of reverse engineering our theories from observation, we can enumerate systems and then try to match them to the behaviors we observe. A major theme of NKS is investigating the structure of the possibility space. Wolfram argues that science is far too ad hoc, in part because the models used are too complicated and unnecessarily organized around the limited primitives of traditional mathematics. Wolfram advocates using models whose variations are enumerable and whose consequences are straightforward to compute and analyze.

Wolfram argues that one of his achievements is in providing a coherent system of ideas that justifies computation as an organizing principle of science. For instance, he argues that the concept of computational irreducibility (that some complex computations are not amenable to short-cuts and cannot be "reduced"), is ultimately the reason why computational models of nature must be considered in addition to traditional mathematical models. Likewise, his idea of intrinsic randomness generation—that natural systems can generate their own randomness, rather than using chaos theory or stochastic perturbations—implies that computational models do not need to include explicit randomness.

Based on his experimental results, Wolfram developed the principle of computational equivalence (PCE): the principle states that systems found in the natural world can perform computations up to a maximal ("universal") level of computational power. Most systems can attain this level. Systems, in principle, compute the same things as a computer. Computation is therefore simply a question of translating input and outputs from one system to another. Consequently, most systems are computationally equivalent. Proposed examples of such systems are the workings of the human brain and the evolution of weather systems.

The principle can be restated as follows: almost all processes that are not obviously simple are of equivalent sophistication. From this principle, Wolfram draws an array of concrete deductions which he argues reinforce his theory. Possibly the most important among these is an explanation as to why we experience randomness and complexity: often, the systems we analyze are just as sophisticated as we are. Thus, complexity is not a special quality of systems, like for instance the concept of "heat," but simply a label for all systems whose computations are sophisticated. Wolfram argues that understanding this makes possible the "normal science" of the NKS paradigm.

At the deepest level, Wolfram argues that—like many of the most important scientific ideas—the principle of computational equivalence allows science to be more general by pointing out new ways in which humans are not "special"; that is, it has been claimed that the complexity of human intelligence makes us special, but the Principle asserts otherwise. In a sense, many of Wolfram's ideas are based on understanding the scientific process—including the human mind—as operating within the same universe it studies, rather than being outside it.

https://en.wikipedia.org/wiki/A_New_Kind_of_Science

Reviews:

http://shell.cas.usf.edu/~wclark/ANKOS_reviews.html

**A New Kind of Science**Author Stephen Wolfram

https://www.wolframscience.com/nks/

https://www.wolframscience.com/nks/p51--the-search-for-general-features/

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**Mapping and mining the computational universe**In order to study simple rules and their often complex behaviour, Wolfram argues that it is necessary to systematically explore all of these computational systems and document what they do. He further argues that this study should become a new branch of science, like physics or chemistry. The basic goal of this field is to understand and characterize the computational universe using experimental methods.

The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible. There are also some forms of production that are in some ways unique to this field of study. For example, the discovery of computational mechanisms that emerge in different systems but in bizarrely different forms.

Another kind of production involves the creation of programs for the analysis of computational systems. In the NKS framework, these themselves should be simple programs, and subject to the same goals and methodology. An extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. Wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. However, in general Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.

Wolfram has since expressed "A central lesson of A New Kind of Science is that there’s a lot of incredible richness out there in the computational universe. And one reason that’s important is that it means that there’s a lot of incredible stuff out there for us to 'mine' and harness for our purposes."[5]

**Systematic abstract science**While Wolfram advocates simple programs as a scientific discipline, he also argues that its methodology will revolutionize other fields of science. The basis of his argument is that the study of simple programs is the minimal possible form of science, grounded equally in both abstraction and empirical experimentation. Every aspect of the methodology advocated in NKS is optimized to make experimentation as direct, easy, and meaningful as possible while maximizing the chances that the experiment will do something unexpected. Just as this methodology allows computational mechanisms to be studied in their simplest forms, Wolfram argues that the process of doing so engages with the mathematical basis of the physical world, and therefore has much to offer the sciences.

Wolfram argues that the computational realities of the universe make science hard for fundamental reasons. But he also argues that by understanding the importance of these realities, we can learn to use them in our favor. For instance, instead of reverse engineering our theories from observation, we can enumerate systems and then try to match them to the behaviors we observe. A major theme of NKS is investigating the structure of the possibility space. Wolfram argues that science is far too ad hoc, in part because the models used are too complicated and unnecessarily organized around the limited primitives of traditional mathematics. Wolfram advocates using models whose variations are enumerable and whose consequences are straightforward to compute and analyze.

**Philosophical underpinnings****Computational irreducibility**Wolfram argues that one of his achievements is in providing a coherent system of ideas that justifies computation as an organizing principle of science. For instance, he argues that the concept of computational irreducibility (that some complex computations are not amenable to short-cuts and cannot be "reduced"), is ultimately the reason why computational models of nature must be considered in addition to traditional mathematical models. Likewise, his idea of intrinsic randomness generation—that natural systems can generate their own randomness, rather than using chaos theory or stochastic perturbations—implies that computational models do not need to include explicit randomness.

Principle of computational equivalencePrinciple of computational equivalence

Based on his experimental results, Wolfram developed the principle of computational equivalence (PCE): the principle states that systems found in the natural world can perform computations up to a maximal ("universal") level of computational power. Most systems can attain this level. Systems, in principle, compute the same things as a computer. Computation is therefore simply a question of translating input and outputs from one system to another. Consequently, most systems are computationally equivalent. Proposed examples of such systems are the workings of the human brain and the evolution of weather systems.

The principle can be restated as follows: almost all processes that are not obviously simple are of equivalent sophistication. From this principle, Wolfram draws an array of concrete deductions which he argues reinforce his theory. Possibly the most important among these is an explanation as to why we experience randomness and complexity: often, the systems we analyze are just as sophisticated as we are. Thus, complexity is not a special quality of systems, like for instance the concept of "heat," but simply a label for all systems whose computations are sophisticated. Wolfram argues that understanding this makes possible the "normal science" of the NKS paradigm.

At the deepest level, Wolfram argues that—like many of the most important scientific ideas—the principle of computational equivalence allows science to be more general by pointing out new ways in which humans are not "special"; that is, it has been claimed that the complexity of human intelligence makes us special, but the Principle asserts otherwise. In a sense, many of Wolfram's ideas are based on understanding the scientific process—including the human mind—as operating within the same universe it studies, rather than being outside it.

https://en.wikipedia.org/wiki/A_New_Kind_of_Science

Reviews:

http://shell.cas.usf.edu/~wclark/ANKOS_reviews.html

Last edited by Cr6 on Sun Feb 18, 2018 2:09 am; edited 1 time in total

**Cr6**- Admin
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## Re: A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

Found this quote interesting:

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And indeed Immanuel Kant wrote in 1790 that "it is absurd to hope that another Newton will arise in the future who will make comprehensible to us the production of a blade of grass according to natural laws". In the late 1700s and early 1800s mathematical methods began to be used in economics and later in studying populations. And partly influenced by results from this, Charles Darwin in 1859 suggested natural selection as the basis for many phenomena in biology, including complexity.

https://www.wolframscience.com/nks/notes-1-1--complexity-and-science/

---------

And indeed Immanuel Kant wrote in 1790 that "it is absurd to hope that another Newton will arise in the future who will make comprehensible to us the production of a blade of grass according to natural laws". In the late 1700s and early 1800s mathematical methods began to be used in economics and later in studying populations. And partly influenced by results from this, Charles Darwin in 1859 suggested natural selection as the basis for many phenomena in biology, including complexity.

https://www.wolframscience.com/nks/notes-1-1--complexity-and-science/

**Cr6**- Admin
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## Re: A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

How is this not an immediate contradiction?

Wolfram says "If theoretical science is to be possible at all, then at some level the systems must follow definite rules." He then asserts that these rules can be likened to the processed dictated by a computer program. How exactly can a computer be told to doing something that is completely different from the mathematical principles that guided it's construction?

He admits that he used to think a simple set of rules must give equally simple behavior. But why would a mathematician think that after Mandelbrot? I'll just quote the Jonathan Coulton song: "He saw that infinite complexity could be described by simple rules." He even uses a fractal pattern on his cover so I'd guess he must be aware of this on some level, yet he is pretending like he discovered this. I really feel like this is a tome for the worship of modern technology.

Mathis' work has shone that the universe is elegant and self-similar. The primary motion is spin and the primary particle the photon. From those simple rules we have nigh infinite complexity. We didn't need a computer model to discover that. We just had to pay attention and look for a theory that didn't contradict itself.

Edit: I'm addressing his physical/philosophical basis for writing as outlined here and in his preface. But certainly the charge field will make much better computer models possible, especially in molecular chemistry.

Wolfram says "If theoretical science is to be possible at all, then at some level the systems must follow definite rules." He then asserts that these rules can be likened to the processed dictated by a computer program. How exactly can a computer be told to doing something that is completely different from the mathematical principles that guided it's construction?

He admits that he used to think a simple set of rules must give equally simple behavior. But why would a mathematician think that after Mandelbrot? I'll just quote the Jonathan Coulton song: "He saw that infinite complexity could be described by simple rules." He even uses a fractal pattern on his cover so I'd guess he must be aware of this on some level, yet he is pretending like he discovered this. I really feel like this is a tome for the worship of modern technology.

Mathis' work has shone that the universe is elegant and self-similar. The primary motion is spin and the primary particle the photon. From those simple rules we have nigh infinite complexity. We didn't need a computer model to discover that. We just had to pay attention and look for a theory that didn't contradict itself.

Edit: I'm addressing his physical/philosophical basis for writing as outlined here and in his preface. But certainly the charge field will make much better computer models possible, especially in molecular chemistry.

Last edited by DavidBehlman on Sun Feb 18, 2018 6:29 pm; edited 2 times in total

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## Re: A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

What he means is that a computer program is a set of defined rules and a scientific model is a set of defined rules so they can be likened to each other. From that, we may be able to see new ways of creating theories based on things we learn from analyzing programs. It isn't so much about needing computers to make theories, but about learning from both to see how they might effect each other.

Of course, this is a very mathematical way of looking at them both. What else would we expect from a mathematician? However, Miles has shown that it is not the math we need more of but the mechanics.

Of course, this is a very mathematical way of looking at them both. What else would we expect from a mathematician? However, Miles has shown that it is not the math we need more of but the mechanics.

**Nevyn**- Admin
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## Re: A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

Oh, and welcome to the forum!

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## Re: A New Kind of Science (Wolfram 2002)-- Systematically "Mathematizing" Computational Reality

Thanks! Glad to be here!

Yes, I guess the tenor of Wolfram's writing struck an ill chord in me. He's really overselling his "discovery". As a huge part of it seems to be having a plethora of programs that exist simply because they

I think I'll read more of this book soon as I mainly studied math and physics, but never got too to programming.

Yes, I guess the tenor of Wolfram's writing struck an ill chord in me. He's really overselling his "discovery". As a huge part of it seems to be having a plethora of programs that exist simply because they

*might*have application eventually. That's a set-up to get lost in a forest of extraneous programs, seems par for mainstream theorists. Of course programs based on logical mechanics like the Charge Field will help us to know which ones to create or study.I think I'll read more of this book soon as I mainly studied math and physics, but never got too to programming.

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