# 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/

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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

**DavidBehlman**- Posts : 8

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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.

**DavidBehlman**- Posts : 8

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

I don't think he is actually talking about programs in the normal sense of the word. He is talking about algorithms and software design principles, sometimes called design patterns. These are generic ways of solving certain problems which a developer then implements into their specific solution. So in a way they are programming structures and patterns that might have some application eventually, but that is also what they are meant to be. They are just tools for developers much like Pythagoras Theorem is a tool for a mathematician. It isn't always useful but it is there waiting for the moment that it is.

I haven't actually read his work, but being a Software Engineer I can see what he is talking about. At least, what I think he is talking about.

I haven't actually read his work, but being a Software Engineer I can see what he is talking about. At least, what I think he is talking about.

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

DavidBehlman wrote: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.

Nice to see another face (name!) around here, hello David! A very succinct and definitive summary of Mathisian theory.

Glad you're here and your input is sound and profound. So my only dissension would be purely semantical, and in no way a jab at you.

We don't have "nigh infinite complexity" with Mathis's additions and corrections, we have

*far less complexity*. And that's a good thing, since the Universe is far less complex than it's often (always) sold to us in the mainstream. He's dismembering mysteries, not adding more. And sure, there are many factors and variables involved still - but far less than the douchebag fake physicists we all grew up learning.

*No*variables multiply up to infinity unless one of them contains infinity already.

For example, we don't have to worry about string theory, chaos theory, quarks, dark matter, singularities, and all manner of other silliness anymore. We discard the strong and weak nuclear "forces" as well, so two more variables down.

Mathis has cleaned things up tremendously, or at least given us a focus that eliminates a lot of fluff. So to say "nigh infinite" is kinda just sensationalism. Nothing can be "nigh infinite" to begin with, by definition of infinite!

And that's my warm welcome. Just laugh, it's just for fun.

**Jared Magneson**- Posts : 440

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

I interpreted 'nigh infinite complexity' to be referring to the complexity of the universe. That Miles has given us some simple, low level concepts that then produce the complexity that is our world. Just take our own bodies as an example. The complexity is perplexing but it all happens as a result of many, many, little interactions that aren't necessarily that complex. Cr6 has just posted about using violet lasers to treat cancer and various other things. Such a simple thing like light at a certain wavelength (or should I say spin frequency) can cause dramatic effects in cancers that have had trillions and trillions of dollars spent on it with little to no outcome.

I think scientists (and most other fields) race towards complexity because it looks intelligent, but the irony is that real progress is made by simplification and transparency.

I think scientists (and most other fields) race towards complexity because it looks intelligent, but the irony is that real progress is made by simplification and transparency.

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

Nevyn wrote:I interpreted 'nigh infinite complexity' to be referring to the complexity of the universe.

Thank you, that is what I meant!

**DavidBehlman**- Posts : 8

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

DavidBehlman wrote:Nevyn wrote:I interpreted 'nigh infinite complexity' to be referring to the complexity of the universe.

Thank you, that is what I meant!

Totally understand! I'm just picking on the semantics, in much the same way that Miles does. Infinity has a definition and most people don't use it anywhere close to properly. Kinda like "literally" or "exponentially" or many other words, I suppose.

**Jared Magneson**- Posts : 440

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

Jared Magneson wrote:DavidBehlman wrote:Nevyn wrote:I interpreted 'nigh infinite complexity' to be referring to the complexity of the universe.

Thank you, that is what I meant!

Totally understand! I'm just picking on the semantics, in much the same way that Miles does. Infinity has a definition and most people don't use it anywhere close to properly. Kinda like "literally" or "exponentially" or many other words, I suppose.

Yes, I could have been more careful with that. Infinity is unfathomably huge and can be understood to contain a lot of junk as well as the good stuff.

Though the human creature is pretty sweet, to defend my use of 'infinity' I would have to step into less scientific sources... Ancient King Solomon wrote: "He has made everything beautiful in its time. He has even put eternity in their heart; yet mankind will never find out the work that the true God has made from start to finish." Assuming humans weren't made to die, it makes sense that we could learn and learn forever. Shedding the nonsense interpretations of Christendom's churches, I am finding the old Good Book a lot more logical and encouraging. But this isn't what I came here to talk about!

So, to you programmers here, how does this hardware evolution compare or fit in with what Wolfram is talking about? I guess there's two questions here, about the hardware evolution itself and then program that guides it.

[Also notice that the Charge Field perfectly explains the seemingly unconnected logic gates they get in the end.]

**DavidBehlman**- Posts : 8

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

I see these as two opposite paths to the same thing. Wolfram is taking the more usual path of analyzing everything and try to find patterns and then apply them to other fields. Thompson is taking the opposite path of letting the system figure it out itself. Wolfram's path is decisive: we know everything about it. Thompson's is fuzzy: we not only don't know, but can't even figure it out. Wolfram requires great amounts of human work. Thompson only needs humans to set the goal and the system then takes great amounts of time to find the solution.

Maybe we need to combine both of them so that Thompson's FPGA's can figure out the patterns in Wolfram's algorithms.

Maybe we need to combine both of them so that Thompson's FPGA's can figure out the patterns in Wolfram's algorithms.

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