A mathematical model of innovation

Posted by $ CBJ 5 years, 6 months ago to Science
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The article describes a new mathematical model of innovation patterns. The model accounts for unexpected breakthroughs as well as anticipated developments, a feature not seen in previous ones.

This model ties in with the Objectivist view of conceptualizing, which Ayn Rand describes as “an actively sustained process of identifying one’s impressions in conceptual terms, of integrating every event and every observation into a conceptual context, of grasping relationships, differences, similarities in one’s perceptual material and of abstracting them into new concepts, of drawing inferences, of making deductions, of reaching conclusions, of asking new questions and discovering new answers and expanding one’s knowledge into an ever-growing sum.” –Ayn Rand, The Objectivist Ethics.

According to the authors, their model applies both to novelties - “they are new to an individual” – and to innovations - “they are new to the world.” Conceptualizing can lead to either outcome. The model builds on an earlier theory of the “adjacent possible”, defined in the article as “all those things—ideas, words, songs, molecules, genomes, technologies and so on—that are one step away from what actually exists.” This ties in with the Objectivist view that integration of existing conceptual and perceptual data occurs in discrete steps.

Although this model neither contradicts nor extends the Objectivist theory of concept formation, it sheds light on the actual process by which new concepts and ideas originate and propagate within a society or culture.
SOURCE URL: https://www.technologyreview.com/s/603366/mathematical-model-reveals-the-patterns-of-how-innovations-arise/


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  • Posted by dbhalling 5 years, 6 months ago
    The article starts off interesting and reasonable and then deteriorates. I think it is more a PR piece than a real article and the title is misleading as I will show below.


    "One of these is Heaps’ law, which states that the number of new things increases at a rate that is sublinear"
    -This is clearly wrong when it comes to inventions. First of all the rate is not constant through out history. Second the rate of potential inventions grows combinatorially with respect to new inventions.

    Heap's and Zipf’s law are about words not new technologies and I think they are stretching to suggest that they apply outside of language.

    "he model accurately predicts how edit events occur on Wikipedia pages, the emergence of tags in social annotation systems, the sequence of words in texts, and how humans discover new songs in online music catalogues"
    -what does this have to do with innovation? Another poor use of language. People love to throw around the word innovation, but, as this article shows, it has become almost meaningless. Discovering new songs in online music catalogs is innovation??????
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    • Posted by $ 5 years, 6 months ago
      Here is the original paper:
      https://arxiv.org/pdf/1701.00994.pdf
      The actual title of the paper described in the article is Dynamics on expanding spaces: modeling the emergence of novelties. The authors use the terms “novelty” and “innovation” somewhat interchangeably, and in a manner that encompasses more than technological breakthroughs and inventions. “Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction . . . “
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  • Posted by $ Thoritsu 5 years, 6 months ago
    I tend to agree with elements of this article. Most innovations I see are not fundamental science. These take years of concentrated study. Innovations tend to arise when someone looks at a problem differently and applies solutions or just options from other fields. I see these as the "possibilities" described in the article.
    The reason this is valuable is that once a solution is developed, it is optimized by the industry. As the optimal solution is developed, narrower and narrower views are taken and the risk is driven out of that local minima solution to minimize cost, a process capitalistic industry is excellent at. People fail to look at alternates because it is disruptive, just like people never look up when walking around.

    An interesting company tried to develop a semantic engine and logical process to reduce the basic process being worked to the fundamentals, and then match it against wide ranging alternatives. Goldfire Innovator by Invention Machines did this. I thought it was great, but we did not invest in it (boo hoo). It also contained an excellent natural language interface around this semantic engine that could search in a contextually relevant manner (vs keywords). For example it could distinguish between a hydrogen environment for annealing and hydrogen in an annealing process. Very powerful. I forget who bought these guys, but they did good work.
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  • Posted by chad 5 years, 6 months ago
    It might be interesting to study how living free of tyrannical encumbrances has affected innovation. As far as coming up with a mathematical model to predict when more might arrive depends on predicting when someone might see a problem differently and then want to act on discovering a different solution. It would be difficult to predict the drive of human behavior down to a sum that says; space travel will begin . . . . . . . Now!
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    • Posted by $ 5 years, 6 months ago
      True. The models are more about estimating the overall rate of innovation rather than predicting when a particular innovation will arise.
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  • Posted by andrewtroy 5 years, 6 months ago
    A very interesting article indeed. Thank you. It seems the math calculates the what, and the how, but not the why. Why do some ideas change the world? Why do others lay forgotten on the cutting room floor? Why do some innovations grow into novelties and then grow into commonplace? Can and why are some innovations suppressed for the wrong reasons? Can novelties become commonplace through means of deception?

    I am not a mathematician, do not fully understand the given formula, and I am very interested in this concept from a non-math perspective.
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    • Posted by Seer 5 years, 6 months ago
      I had to get B.F.Skinner in there. "Conditioning" and mathematical models of human behavior, and how that induces conformity and stifles creativity.
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    • Posted by Seer 5 years, 6 months ago
      You are asking good questions. Asking good questions is the beginning of "innovation". As the saying goes, "To find the answer, ask the question."

      I may have a partial answer to your question "why are some innovations suppressed..." I think it lies in the concept of "conditioning." That is probably also a partial answer to the next question: "Can novelties become commonplace through means of deception?"
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    • Posted by $ 5 years, 6 months ago
      Re: “It seems the math calculates the what, and the how, but not the why.” Exactly. The modeling provides a sense of “here’s what’s going on,” contributing to our understanding of innovation as an overall process rather than a series of random events. Understanding the what and the how brings us closer to comprehending the why.
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      • Posted by Seer 5 years, 6 months ago
        How does that compare with "The Great Man Theory", as far as "...rather than a series of random events."
        Are you one of the MIT professors who developed the model?
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  • Posted by Seer 5 years, 6 months ago
    Just thought of something else. Hope you don't get too tired of this.

    When I took logic and scientific method, we studied creativity. A little of it, anyway. Kekule, Darwin, Einstein. What I remember is that in most cases, each scientist studied a problem, then underwent a period of "relaxation" of getting away from the problem. They then found that the solution seemed to come a later time; Kekule as he was staring at his hearthfire, saw the molecules of carbon, hydrogen and oxygen form themselves into a ring.
    Darwin was riding in a carriage when the "solution" of natural selection came to him.
    Einstein has said, when he was an adolescent, he imagined riding on a photon and wondered what that would be like.

    I had a calculus professor tell me once not to work on a problem for longer than 20 minutes. If you haven't solved it in that time, let it go, try a different problem, and let your subconscious work on the original problem. And who knows what goes on in your subconscious.
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    • Posted by $ Dobrien 5 years, 6 months ago
      +1 , Tesla also.
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      • Posted by Seer 5 years, 6 months ago
        Actually, I'm still up in the air about Tesla. Don't know enough about him. But I'd hardly put him in the same class as the other three.
        And if you do that, you would need to add Edison, who was simply an inventor, more than a thinker. He had a sign in his lab: "There's a better way; find it!!"
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        • Posted by $ Dobrien 5 years, 6 months ago
          I suggest before you classify him you learn of his accomplishments .
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          • Posted by Seer 5 years, 6 months ago
            I SAID I'm still up in the air about him. Need to find a good biography. But compared to Faraday and Maxwell's influence, from my studies in electricity, he isn't mentioned.
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            • Posted by $ Dobrien 5 years, 6 months ago
              Nikola Tesla was a multi-disciplinary genius. His discovery of the rotating magnetic field in 1882 led to a series of US Patents in 1888, which gave us the AC electric power system still in use today. This one achievement earned him the honor of being called “The Man Who Invented the 20th Century”.

              But his research went way beyond what has found its way into everyday use. He is the recognized inventor of the brushless AC induction motor, radio, remote control by radio, super-conductivity, fluorescent lighting, the bladeless turbine engine and pump, the capacitor discharge ignition system for automobile engines, the mechanical oscillator, and dozens of other inventions. But he also discovered that useful energy could be extracted from the heat of the ambient air, and that electric power in the form of Radiant Energy could be broadcast to everyone in the world through the ground.
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              • Posted by Seer 5 years, 6 months ago
                I wonder if he has been made into a folk hero. Don't know, will check it out someday.
                Like I said, I'm more concerned with Insull and pyramidazition, the early power companies, and control without ownership.
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    • Posted by Seer 5 years, 6 months ago
      How can you not like my comment?
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      • Posted by $ 5 years, 6 months ago
        The downvote was not by me.
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        • Posted by Seer 5 years, 6 months ago
          Or, I could have an enemy. That would certainly not be unusual. I tell people, I don't have a lot of friends. I have a lot of enemies, though, does that count?
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        • Posted by Seer 5 years, 6 months ago
          I wonder who it was. There's only 4 posting on this thread: me, you, db and andrew.
          If someone disagrees with me, that's fine, he/she can always post his criticism. If he/she disagrees with SCIENCE, that would make it very hard to refute my comments. Another thing altogether.
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          • Posted by $ allosaur 5 years, 6 months ago
            Me dino gave you a point for the subconscious hell of it. Sometimes I come to solutions for sleeping on it.
            Looks like Dobrein did too before someone else came along.
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            • Posted by Seer 5 years, 6 months ago
              I took a test in my Logic course and ran out of time trying to solve the last logic problem---almost got the solution, but not quite. Turned in the test, went home and the next morning the answer was in my head. Unfortunately, the test was over. I did tell the instructor, though, and figured I learned something from my subconscious.
              Funny you should bring that up.
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    • Posted by Seer 5 years, 6 months ago
      That same professor told us that solving integrations and differentiating were completely different. To differentiate, one had only to follow a set of rules. To integrate, one had to employ creativity; all the rules in the world could not always help you solve an integration problem.
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  • Posted by Seer 5 years, 6 months ago
    Just thought of something else. Some might say that geometry is a "mathematical model". It is not. It is an abstraction from reality. (I never thought of it as that, though.Just as those lines of force were never abstract to Faraday).
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  • Posted by Seer 5 years, 6 months ago
    It just occurred to me that risk-taking presupposes the notion of failure. Unless failure is a possible outcome, there is no risk.
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  • Posted by Seer 5 years, 6 months ago
    Trying to mathematically model innovation will only help extinguish it.
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    • Posted by $ 5 years, 6 months ago
      Evidence?
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      • Posted by Seer 5 years, 6 months ago
        Human nature.
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        • Posted by Seer 5 years, 6 months ago
          Innovation abhors conformity. The very "concept" mathematical model invites conformity.
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          • Posted by $ 5 years, 6 months ago
            Innovation and scientific advancement require conformity with the laws of nature. Try forecasting the weather or calculating a path to Mars without mathematical modeling.

            Your statements will carry more weight if you give examples.
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            • Posted by Seer 5 years, 6 months ago
              Well, here's an example. One mathematical discipline I love, and am pretty good at and which has somewhat gone out of fashion with the abstracted math of today, is geometry. I will sit and draw circles, sine waves, hyperbolas, etc. And once in a while I'll get an idea, and I'll think: I wonder what would happen if I (for instance) draw circles intersecting hyperbolas. What would the resulting constellation of geometric figures look like, and what could I do with them?
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            • Posted by Seer 5 years, 6 months ago
              I'm talking human nature, here. The Leyden scientists were able to understand the "laws of nature" (and by the way, I dislike the term laws used to describe natural phenomena) only after they got a idea..

              Remember what I said about the early Gothic cathedrals in Europe? Guess that was on a different forum.

              Anyway, I said I wonder how many cathedrals actually collapsed before they got that flying buttress idea down right.

              How many years did it take Reardon to fashion his metal, once he got the idea? Ten, I think.

              Failure is as important as success. Risk takers are not afraid to fail. As I said, human nature.
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  • Posted by Seer 5 years, 6 months ago
    Along this same line, businessmen are inherently risk-takers. I think it is one reason Rand wished to exalt the human soul.

    It is precisely for actions such as the Leyden scientists that give ME some hope for mankind.
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  • Posted by Seer 5 years, 6 months ago
    There were some scientists in Leyden around the 18th century (and I read this in a Physics text) that "got the idea"---the very words used in that text--to see what would happen if they filled a huge glass jar with water, then charged it up and stuck their hand in it. Well you know what happened!
    But they didn't stop there. Then they "got the idea" to have an entire line of scientists holding hands, and then the initial man stuck his hand in the charged-up water.
    And voila! The study of electricity was begun!
    It had nothing to do with concept formation. I give you Benjamin Franklin as another example of getting an idea. Or Newton sticking his finger in his eye to see how much of man's perception of light was internally generated.
    Europeans are risk-takers. Not good at introspection, but definitely risk-takers. And sometimes fatally so.
    I always laugh when I think of that initial Leyden Jar. I got an idea!
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  • Posted by Seer 5 years, 6 months ago
    “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.”

    Albert Einstein. QED.
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  • Posted by Seer 5 years, 6 months ago
    It's very simple, it simply boils down to:

    I got an idea!

    Or: I just want to see what would happen!

    Why waste time on how and why? I don't believe it can be taught. It is however, directly related to risk-taking behavior, more than any type of conceptual reasoning.

    Also, don't forget, the study of psychology, neurology and motivation has come a long way since Rand's philosophical exegesis of the subject and topic of "concept". I doubt that the concept of concept is even similar to what it once was.
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    • Posted by $ 5 years, 6 months ago
      Concept [kon-sept] - an idea of something formed by mentally combining all its characteristics or particulars; a construct. Dictionary . com The definition hasn’t changed since I first read Ayn Rand in the 1960s.

      How is it possible to come up with an idea without the building blocks of previous concepts and perceptions? And for anyone seriously interested in philosophy, how can the study of the source and characteristics of ideas be a waste of time?
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      • Posted by Seer 5 years, 6 months ago
        The MIT professors are not interested in philosophy. They are interested in modeling human behavior. A sure road to disaster.
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      • Posted by Seer 5 years, 6 months ago
        How is it possible? Simply like this: I wonder what would happen if...

        Innovation is a LEAP. Perhaps without prior "knowledge" one could not make another leap, but it is a risk, first and foremost.
        Newton did say he "stood on the shoulders of giants." He also said he wasn't any smarter than others, he just thought about things more.

        And it is that leap that is the risk.
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      • Posted by Seer 5 years, 6 months ago
        Some people are so averse to risk-taking behavior that they refuse to even think in terms different from their peers.

        I was thinking of Archimedes and Galileo. They didn't, as far as I know, come up with ideas (notions) in the same way as the later Europeans or others, but they did take a risk in that they chose to think "differently" than others of their time. Galileo for sure.
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      • Posted by Seer 5 years, 6 months ago
        Idea has more than one conceptual definition.

        You are using a definition based on a philosophical considerations.
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      • Posted by Seer 5 years, 6 months ago
        Perhaps concept formation is only the means of carrying out the risk-taking behavior?

        You are talking apples; I am talking oranges.

        The primitive African cultures were very un-innovative. It has to do with their avoidance of risk-taking behaviors. As is their continued matriarchal cultural habits.
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