A mathematical model of innovation

Posted by $ CBJ 7 years, 3 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.


All Comments

  • Posted by $ Thoritsu 7 years, 3 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 $ 7 years, 3 months ago in reply to this comment.
    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 chad 7 years, 3 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 Seer 7 years, 3 months ago in reply to this comment.
    It's always good to know the alternative viewpoints, real or not. RE: your reference to dobrien and another.
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  • Posted by Seer 7 years, 3 months ago in reply to this comment.
    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 $ allosaur 7 years, 3 months ago in reply to this comment.
    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 7 years, 3 months ago in reply to this comment.
    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 Dobrien 7 years, 3 months ago in reply to this comment.
    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 7 years, 3 months ago in reply to this comment.
    Frankly, though, I'm more interested in Insull and pyramidization at the moment. Control without ownership.
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  • Posted by Seer 7 years, 3 months ago in reply to this comment.
    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 Seer 7 years, 3 months ago in reply to this comment.
    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 Seer 7 years, 3 months ago in reply to this comment.
    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 7 years, 3 months ago in reply to this comment.
    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 dbhalling 7 years, 3 months ago in reply to this comment.
    Nothing in the article logically applies to technology. I am sorry if innovations applies to any change then the word becomes meaningless.
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  • Posted by $ 7 years, 3 months ago in reply to this comment.
    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 Seer 7 years, 3 months ago in reply to this comment.
    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 dbhalling 7 years, 3 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 $ 7 years, 3 months ago in reply to this comment.
    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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