**3. The innovation Turing Machine**

The innovation process can be described via a generic machine. Its operation is designed to express any innovation sequence. The machine is dubbed The Innovation Turing machine, citing its analogy to the famous Turing Machine that became the generic framework for all computers (up to the emerging quantum computers). The Innovation Turing Machine, ITM, operates on the fundamental innovation object: the innovation challenge, IC. The innovation challenge may be viewed as the gap between two states: a desired state, and an existing state. The states define a technological situation. The fundamental dilemma of innovation is the mystery of that gap, the difficulty to measure it, and to eliminate it. Measuring the gap constitutes a quantitative definition of the effort to close it, where effort is measured in time, cost or any individual or combinations of resources. To resolve, or to solve an IC is to eliminate its gap. The fundamental rhythm of the ITM is a combination of foretracking and backtracking, defined as follows: If an IC is too difficult to resolve, then advance (foretrack) to another, −- hopefully, but not necessarily -- simpler IC, and when it is resolved, backtrack to the former IC, and try again. Repeat and re-apply the sequence of foretracking-backtracking. By reapplying the foretracking-backtracking sequence to each IC that was defined to help out with a former IC, one generates an indefinite sequence of ICs -- an IC track. And since every IC may have more than one simpler IC associated with it, these tracks expand into a tree structure. And, since some of the ICs so defined may be identical, the tree structure transforms into a network, referred to as the ITM-WEB.

According to the ITM model there are only three types of "simpler ICs": those that may be defined as components of the IC, those that may be defined as an abstraction of the IC, and those that may be defined as an extension of the IC. By way of convention, the number of components may be two or more, while all possible extensions are summarized into a single "master extension challenge," and similarly all possible abstractions are summarized into a single "master abstraction challenge". Hence, every innovation challenge gives rise to m + 2 next generation of challenges, where m is the number of components.

One's attention is focused on a single challenge. If that challenge is not the very original one then, following the attempt to resolve it, one's attention moves to another; either to the "next" challenge or to the "before" challenge. This is analogous to the motion of the tape under the read/write head in the original Turing machine. This process continues until the original challenge is resolved, or the system halts. Like with the original Turing machine the single read/write head may be expanded to two or more heads working in parallel. This expansion will reflect the work of a large R&D team working in parallel. See ahead a sample of the IC map:

**THE TRIANGULAR OPTIONS:** The three triangular options B-X-A (Breakdown, Extension, and Abstraction), along with the nominal (direct solution) option, represent the full spectrum available for the innovator wrestling with an innovation challenge. This is essentially a dialectic range: If you cannot solve a problem directly, you can opt downward -- breaking the problem down to smaller parts, or upward -- considering a 'higher' problem where insight may be easier to come by. The 'higher' option divides to abstraction and extension, while the 'lower option' divides to at least two parts. The nature of these options is explained below.

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**Figure 4.**

*IC serial breakdown.*

*Artificial Intelligence Assisted Innovation DOI: http://dx.doi.org/10.5772/intechopen.96112*

• serial breakdown configuration

• parallel breakdown configuration

**Figure 4**.

ding constricting assumptions.

• concentric breakdown configuration

**BREAKDOWN CONFIGURATION**: We distinguish between three types of configurations, which can be pieced together to form a complex configuration:

**SERIAL BREAKDOWN CONFIGURATION:** An innovation challenge (problem), IC, may be broken into n serial breakdown units: S1, S2, S3, .....Sn, such that a sequential solution of these units, constitutes a solution to the former challenge, IC.

If any one of the n serial units remained unsolved, then IC remains unsolved.

**PARALLEL BREAKDOWN CONFIGURATION:** An innovation challenge (problem) IC, may be broken down into n distinct parallel breakdown units: L1, L2, L3, .....Ln, such that solution to any one of the parallel breakdown units would constitute a solution to the former problem, P. In order to insure completeness, one of the n solution options (solution scenarios) would have to be: "a solution different from the other (n-1) scenarios". This implicit scenario would be associated with a

**CONCENTRIC BREAKDOWN CONFIGURATION:** An innovation challenge (problem), IC, may be broken down to n concentric breakdown units: C1, C2, C3, .....Cn, such that the first unit provides a solution to IC1 a simplified model of IC, the second unit provides a solution to IC 2, a bit less simplified solution to IC, and in general C i provides a solution to ICi, a simplified model of IC. For all j > i ICi is more simplified than ICj and ICn = IC. For each IC, it may be that Ci i = 1,2,...(n-1) would be practically sufficient for the purpose at hand. There are several typical formats for concentric breakdown. For instance: theory-practice sequence, shed-

It's quite common to formulate an IC as 'build contraption X'. One could then define the following children challenges: (1) prove or disprove theoretical feasibility; (2) find a practical feasibility. (If the IC is not zero-generation then the first and second consecutive steps may be sufficient); (3) develop a construction option. There are circumstances when an innovation objective cannot be carried out under a set of some constricting assumptions. In that case, one might break down that challenge into concentric components. The first component is comprised of parallel

probability rating, and treated computationally as the others. **Figure 5**.

IC S S S .....S<sup>=</sup> { 123 n ®®® } (1)

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innovation challenge. Once this challenge is negotiated (resolved), the innovator's attention shifts back to its parent challenge. Applied repetitively, this "Innovation Machine" ends up with a resolved original challenge. Check out an evolved map in

The innovation process can be described via a generic machine. Its operation is designed to express any innovation sequence. The machine is dubbed The Innovation Turing machine, citing its analogy to the famous Turing Machine that became the generic framework for all computers (up to the emerging quantum computers). The Innovation Turing Machine, ITM, operates on the fundamental innovation object: the innovation challenge, IC. The innovation challenge may be viewed as the gap between two states: a desired state, and an existing state. The states define a technological situation. The fundamental dilemma of innovation is the mystery of that gap, the difficulty to measure it, and to eliminate it. Measuring the gap constitutes a quantitative definition of the effort to close it, where effort is measured in time, cost or any individual or combinations of resources. To resolve, or to solve an IC is to eliminate its gap. The fundamental rhythm of the ITM is a combination of foretracking and backtracking, defined as follows: If an IC is too difficult to resolve, then advance (foretrack) to another, −- hopefully, but not necessarily -- simpler IC, and when it is resolved, backtrack to the former IC, and try again. Repeat and re-apply the sequence of foretracking-backtracking. By reapplying the foretracking-backtracking sequence to each IC that was defined to help out with a former IC, one generates an indefinite sequence of ICs -- an IC track. And since every IC may have more than one simpler IC associated with it, these tracks expand into a tree structure. And, since some of the ICs so defined may be identical,

the tree structure transforms into a network, referred to as the ITM-WEB.

challenges, where m is the number of components.

According to the ITM model there are only three types of "simpler ICs": those that may be defined as components of the IC, those that may be defined as an abstraction of the IC, and those that may be defined as an extension of the IC. By way of convention, the number of components may be two or more, while all possible extensions are summarized into a single "master extension challenge," and similarly all possible abstractions are summarized into a single "master abstraction challenge". Hence, every innovation challenge gives rise to m + 2 next generation of

One's attention is focused on a single challenge. If that challenge is not the very

original one then, following the attempt to resolve it, one's attention moves to another; either to the "next" challenge or to the "before" challenge. This is analogous to the motion of the tape under the read/write head in the original Turing machine. This process continues until the original challenge is resolved, or the system halts. Like with the original Turing machine the single read/write head may be expanded to two or more heads working in parallel. This expansion will reflect the work of a large R&D team working in parallel. See ahead a sample of the IC map: **THE TRIANGULAR OPTIONS:** The three triangular options B-X-A (Breakdown, Extension, and Abstraction), along with the nominal (direct solution) option, represent the full spectrum available for the innovator wrestling with an innovation challenge. This is essentially a dialectic range: If you cannot solve a problem directly, you can opt downward -- breaking the problem down to smaller parts, or upward -- considering a 'higher' problem where insight may be easier to come by. The 'higher' option divides to abstraction and extension, while the 'lower option' divides to at least two parts. The nature of these options is explained below.

**110**

**Figure 3**.

**3. The innovation Turing Machine**

**BREAKDOWN CONFIGURATION**: We distinguish between three types of configurations, which can be pieced together to form a complex configuration:


**SERIAL BREAKDOWN CONFIGURATION:** An innovation challenge (problem), IC, may be broken into n serial breakdown units: S1, S2, S3, .....Sn, such that a sequential solution of these units, constitutes a solution to the former challenge, IC.

$$\text{IC} = \left\{ \mathbf{S}\_1 \to \mathbf{S}\_2 \to \mathbf{S}\_3 \to \dots \to \mathbf{S}\_n \right\} \tag{1}$$

If any one of the n serial units remained unsolved, then IC remains unsolved. **Figure 4**.

**PARALLEL BREAKDOWN CONFIGURATION:** An innovation challenge (problem) IC, may be broken down into n distinct parallel breakdown units: L1, L2, L3, .....Ln, such that solution to any one of the parallel breakdown units would constitute a solution to the former problem, P. In order to insure completeness, one of the n solution options (solution scenarios) would have to be: "a solution different from the other (n-1) scenarios". This implicit scenario would be associated with a probability rating, and treated computationally as the others. **Figure 5**.

**CONCENTRIC BREAKDOWN CONFIGURATION:** An innovation challenge (problem), IC, may be broken down to n concentric breakdown units: C1, C2, C3, .....Cn, such that the first unit provides a solution to IC1 a simplified model of IC, the second unit provides a solution to IC 2, a bit less simplified solution to IC, and in general C i provides a solution to ICi, a simplified model of IC. For all j > i ICi is more simplified than ICj and ICn = IC. For each IC, it may be that Ci i = 1,2,...(n-1) would be practically sufficient for the purpose at hand. There are several typical formats for concentric breakdown. For instance: theory-practice sequence, shedding constricting assumptions.

It's quite common to formulate an IC as 'build contraption X'. One could then define the following children challenges: (1) prove or disprove theoretical feasibility; (2) find a practical feasibility. (If the IC is not zero-generation then the first and second consecutive steps may be sufficient); (3) develop a construction option. There are circumstances when an innovation objective cannot be carried out under a set of some constricting assumptions. In that case, one might break down that challenge into concentric components. The first component is comprised of parallel

**Figure 4.** *IC serial breakdown.*

#### **Figure 6.** *Concentric breakdown.*

ICs, each defined as accomplishing the parent IC by circumventing one assumption. The second concentric component would be to accomplish the same circumventing two assumptions, etc. It would be the same if the assumptions are worded to alleviate the construction: the first component would assume all these relaxing

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solvers.

scientists Altshuller [10–12].

• Any-Fit/Best-Fit

• Grouping

• Bayesian

• Needle in a Haystack

*Artificial Intelligence Assisted Innovation DOI: http://dx.doi.org/10.5772/intechopen.96112*

minus two assumptions, etc. **Figure 6.**

assumptions; the second would assume the same minus one assumption, then

**ABSTRACTION:** This R&D route amounts to an effort to redefine the challenge at hand with fewer confusing details, and more fundamental principles, with the hope that the new view would bring to the fore some insight that was hidden when the issue was presented with all its "gory details". Filtering out less important particulars might be helpful by reducing the emotional impact of those details. **ENLARGING THE CIRCLE OF PROBLEM SOLVERS:** Abstraction has the inherent benefit of allowing for a larger number of people to think of a solution to the R&D challenge. By stripping the former challenge to its essence, its difficulty can be appreciated by intelligent people who are not necessarily versed with the particular discipline of knowledge of the formal R&D. They may offer a solution that escapes the narrow professional. The more readily communicated abstracted version of the problem, also allows for the challenge to be considered by people who are not cleared to know the details of the original problem. It's a confidentiality issue. For so many cases this aspect severely limits the number of potential problem

**EXTENSION:** This option amounts to identifying related challenges, and defining a master challenge that would encompass them all. The underlying idea is that every challenge at hand has some "neighbors" -- challenges that bear certain similarities with it. Some of these challenges are associated with a solution or a partial solution, and this can inspire or suggest a solution to the former problem. The pioneer of the extension approach to innovation practice is the Russian

**IDENTIFYING RELATED CHALLENGES:** The quality of this step determines the prospects of the extension route. Some similar challenges are obvious, and read-

A search may be conducted to find one fit instance among many, and it matters not which. Alternatively, the case may be where one is searching for the best fit, and second best will not do. This is a critical search parameter. When a search is characterized as a needle in a haystack, it implies that both the needle and the haystack are well defined. Once the needle is found, there is no confusion about it being the needle and not a strand of hay. The challenge here is simply the size of the stack compared to the size of the needle. Some search cases may be conducted by grouping individual instances into a single group and somehow concluding whether the target is, or is not, in that group. Such searches share a strategy for how to define the most efficient groups. Some searches develop new information as the search goes on. Even failed searches are thus helpful. This is expressed through the revised probability profile for the unchecked instances based on the search so far (Bayesian probabilities). In attempting to diagnose a disease, generally the results from failed tests help reshape the probabilities for the remaining options. By contrast, searching for the right cryptographic key is a case where all the futile searches are probably unhelpful in terms of better searching the remaining

ily listed. Others need a more formal effort to be flushed out. SEARCH STATUS: The search parameters are generally:

#### *Artificial Intelligence Assisted Innovation DOI: http://dx.doi.org/10.5772/intechopen.96112*

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ICs, each defined as accomplishing the parent IC by circumventing one assumption. The second concentric component would be to accomplish the same circumventing two assumptions, etc. It would be the same if the assumptions are worded to alleviate the construction: the first component would assume all these relaxing

**112**

**Figure 6.**

*Concentric breakdown.*

**Figure 5.**

*IC parallel breakdown.*

assumptions; the second would assume the same minus one assumption, then minus two assumptions, etc. **Figure 6.**

**ABSTRACTION:** This R&D route amounts to an effort to redefine the challenge at hand with fewer confusing details, and more fundamental principles, with the hope that the new view would bring to the fore some insight that was hidden when the issue was presented with all its "gory details". Filtering out less important particulars might be helpful by reducing the emotional impact of those details.

**ENLARGING THE CIRCLE OF PROBLEM SOLVERS:** Abstraction has the inherent benefit of allowing for a larger number of people to think of a solution to the R&D challenge. By stripping the former challenge to its essence, its difficulty can be appreciated by intelligent people who are not necessarily versed with the particular discipline of knowledge of the formal R&D. They may offer a solution that escapes the narrow professional. The more readily communicated abstracted version of the problem, also allows for the challenge to be considered by people who are not cleared to know the details of the original problem. It's a confidentiality issue. For so many cases this aspect severely limits the number of potential problem solvers.

**EXTENSION:** This option amounts to identifying related challenges, and defining a master challenge that would encompass them all. The underlying idea is that every challenge at hand has some "neighbors" -- challenges that bear certain similarities with it. Some of these challenges are associated with a solution or a partial solution, and this can inspire or suggest a solution to the former problem. The pioneer of the extension approach to innovation practice is the Russian scientists Altshuller [10–12].

**IDENTIFYING RELATED CHALLENGES:** The quality of this step determines the prospects of the extension route. Some similar challenges are obvious, and readily listed. Others need a more formal effort to be flushed out.

SEARCH STATUS: The search parameters are generally:


A search may be conducted to find one fit instance among many, and it matters not which. Alternatively, the case may be where one is searching for the best fit, and second best will not do. This is a critical search parameter. When a search is characterized as a needle in a haystack, it implies that both the needle and the haystack are well defined. Once the needle is found, there is no confusion about it being the needle and not a strand of hay. The challenge here is simply the size of the stack compared to the size of the needle. Some search cases may be conducted by grouping individual instances into a single group and somehow concluding whether the target is, or is not, in that group. Such searches share a strategy for how to define the most efficient groups. Some searches develop new information as the search goes on. Even failed searches are thus helpful. This is expressed through the revised probability profile for the unchecked instances based on the search so far (Bayesian probabilities). In attempting to diagnose a disease, generally the results from failed tests help reshape the probabilities for the remaining options. By contrast, searching for the right cryptographic key is a case where all the futile searches are probably unhelpful in terms of better searching the remaining

options. These search parameters will help identify similar ICs to exercise the extension step with the IC at hand.

**SYMMETRY:** Symmetry refers to the relationship of an innovation challenge towards its counter-challenge (a precise definition of counter challenge is given ahead). In the symmetric case both challenges are difficult, in the a-symmetric case the counter-challenge is easy, or no challenge at all. To suppress some gene expression may be as difficult as it would be to express the same (symmetry), but to construct a gene sequence from inorganic building blocks is infinitely more difficult than the opposite job (a-symmetry). A-symmetric challenges enjoy some similarities that may be exploited in the extension step. Generally the counter-challenge of an a-symmetric challenge represents a verification metrics for performance or even progress of the original challenge. Also, a-symmetric challenges may allow for incremental R&D work. Trying to cure an ailment, one may wonder if some measures taken have been helpful or not. Since it is generally easy to induce a disease, it opens the possibility for some animal trials where infected specimens are compared (statistically) as to any distinction between treated and untreated cases. It is therefore that the symmetry status of an IC is an important factor in trying to round up similar challenges for the extension step.

**METRIC DEVELOPMENT:** Challenges can be sorted out based on how easy it would be to measure success and progress towards success. Consider a researcher trying to develop a dye that would not be shaded or faded for one hundred years. How would one measure a successful accomplishment of that challenge (without waiting one hundred years)? Challenges that face such metric difficulty have some attributes in common. They all have to come up with some metric-substitute. Such substitutes have innate similarities. They may be mathematical models, some indirect metric, or extrapolated incremental measurements. By reviewing such similar challenges together, these similarities are likely to generate resolution ideas for the challenge at hand. Progress metric is also an important parameter. In a search challenge suppose one tries to find a single target within a field of search candidates. If the number of candidates is not known, then one lacks any measure of progress after having checked (and not found) m candidates. However if the number of search candidates, n, is known, then the ratio m/n represents progress rating [0:1]. If the search is also Bayesian, then the information skimmed from the m tests would change the probability profile for the remaining (n-m) candidates, and potentially accelerate the R&D progress. For that reason, it is generally helpful to identify the metric status of the IC at hand, and to identify similar ones to help develop solution ideas.

**COUNTER-RESEARCH:** Generally, an IC may be matched with a counter-IC, IC\*, such that the two ICs in a series void each other:

$$\text{IC} + \text{IC}^\* = \mathbf{0} \text{ [the null IC]}.\tag{2}$$

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**Figure 7.** *ITM-web.*

*Artificial Intelligence Assisted Innovation DOI: http://dx.doi.org/10.5772/intechopen.96112*

and n steps would lead to (m + 2)<sup>n</sup>

challenge with its counter.

from each other. It is therefore a recommended extension option to match a given

number of challenges to consider becomes astronomical and impractical. It is necessary then, at some point, to rank-order the three branching options to limit the number of attacked challenges. An innovator may pick one of the three options at a given challenge, and proceed accordingly, chaining more triangles to the web. At some point, the innovator would conclude that this route is futile, and s\he might return to the original challenge and pick a different branching option. Since this can happen at every challenge, the actual "travel route" of the innovator over this so called Turing Web may be quite complicated. Complicated or not,

**TRIANGULAR CHAINING:** Any challenge that is not resolved directly is eventually being replaced by one or more different (but related) challenges, taking one of the three routes: breakdown, extension, or abstraction. The new challenge or challenges may be solved in a direct manner or may opt again to one of the three replacement routes, and so on. An innovator unable to find a direct solution to the problem at hand may choose to bet all his time and resources on one of the three replacement options. The new challenge may be solved directly, or branch out again in one and only one direction. In the simplest version the innovator would branch out n times, and face (n + 1) challenges. When the (n + 1)-th challenge is eventually resolved in a direct manner, the process returns, and after n back-branching (backtracking) the innovator is facing the original challenge. If one of the branching is a breakdown, then the number of challenges is larger. If the innovator, considering a given challenge is unsure about which is the best branching option, and thus he divides his resources to two or three options in parallel, then the number of challenges becomes much larger yet. If we assume that every breakdown step produces m subdivision challenges, then a single branch option would lead to (m + 2) new challenges,

challenges. Even for modest values of n, the

If the IC under consideration is to find something, then IC\* is to lose the same. Configured in a series, they pose no challenge at all. Same for reduction and increase, mixing, and separation, etc. Recalling the symmetry attribute, an IC would be either a "one way" or a "zero way" case where the former is defined as an IC where the counter-IC is an easy one, not really much of a challenge, while a zeroway challenge is one where the counter challenge is also intractable. While it may be difficult to separate two similar liquids, it's rather easy to mix them (one-way). While it is difficult to increase the amount of rain in a given area, it is also difficult to decrease the same (zero-way). In either way it may be very helpful to define the counter-IC for the IC at hand, and handle the two challenges together, learning

#### *Artificial Intelligence Assisted Innovation DOI: http://dx.doi.org/10.5772/intechopen.96112*

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extension step with the IC at hand.

round up similar challenges for the extension step.

IC\*, such that the two ICs in a series void each other:

options. These search parameters will help identify similar ICs to exercise the

**SYMMETRY:** Symmetry refers to the relationship of an innovation challenge towards its counter-challenge (a precise definition of counter challenge is given ahead). In the symmetric case both challenges are difficult, in the a-symmetric case the counter-challenge is easy, or no challenge at all. To suppress some gene expression may be as difficult as it would be to express the same (symmetry), but to construct a gene sequence from inorganic building blocks is infinitely more difficult than the opposite job (a-symmetry). A-symmetric challenges enjoy some similarities that may be exploited in the extension step. Generally the counter-challenge of an a-symmetric challenge represents a verification metrics for performance or even progress of the original challenge. Also, a-symmetric challenges may allow for incremental R&D work. Trying to cure an ailment, one may wonder if some measures taken have been helpful or not. Since it is generally easy to induce a disease, it opens the possibility for some animal trials where infected specimens are compared (statistically) as to any distinction between treated and untreated cases. It is therefore that the symmetry status of an IC is an important factor in trying to

**METRIC DEVELOPMENT:** Challenges can be sorted out based on how easy it would be to measure success and progress towards success. Consider a researcher trying to develop a dye that would not be shaded or faded for one hundred years. How would one measure a successful accomplishment of that challenge (without waiting one hundred years)? Challenges that face such metric difficulty have some attributes in common. They all have to come up with some metric-substitute. Such substitutes have innate similarities. They may be mathematical models, some indirect metric, or extrapolated incremental measurements. By reviewing such similar challenges together, these similarities are likely to generate resolution ideas for the challenge at hand. Progress metric is also an important parameter. In a search challenge suppose one tries to find a single target within a field of search candidates. If the number of candidates is not known, then one lacks any measure of progress after having checked (and not found) m candidates. However if the number of search candidates, n, is known, then the ratio m/n represents progress rating [0:1]. If the search is also Bayesian, then the information skimmed from the m tests would change the probability profile for the remaining (n-m) candidates, and potentially accelerate the R&D progress. For that reason, it is generally helpful to identify the metric status of the IC at hand, and to identify similar ones to help develop

**COUNTER-RESEARCH:** Generally, an IC may be matched with a counter-IC,

IC IC\* 0 [the null IC . **]** + =

If the IC under consideration is to find something, then IC\* is to lose the same.

Configured in a series, they pose no challenge at all. Same for reduction and increase, mixing, and separation, etc. Recalling the symmetry attribute, an IC would be either a "one way" or a "zero way" case where the former is defined as an IC where the counter-IC is an easy one, not really much of a challenge, while a zeroway challenge is one where the counter challenge is also intractable. While it may be difficult to separate two similar liquids, it's rather easy to mix them (one-way). While it is difficult to increase the amount of rain in a given area, it is also difficult to decrease the same (zero-way). In either way it may be very helpful to define the counter-IC for the IC at hand, and handle the two challenges together, learning

(2)

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solution ideas.

from each other. It is therefore a recommended extension option to match a given challenge with its counter.

**TRIANGULAR CHAINING:** Any challenge that is not resolved directly is eventually being replaced by one or more different (but related) challenges, taking one of the three routes: breakdown, extension, or abstraction. The new challenge or challenges may be solved in a direct manner or may opt again to one of the three replacement routes, and so on. An innovator unable to find a direct solution to the problem at hand may choose to bet all his time and resources on one of the three replacement options. The new challenge may be solved directly, or branch out again in one and only one direction. In the simplest version the innovator would branch out n times, and face (n + 1) challenges. When the (n + 1)-th challenge is eventually resolved in a direct manner, the process returns, and after n back-branching (backtracking) the innovator is facing the original challenge. If one of the branching is a breakdown, then the number of challenges is larger. If the innovator, considering a given challenge is unsure about which is the best branching option, and thus he divides his resources to two or three options in parallel, then the number of challenges becomes much larger yet. If we assume that every breakdown step produces m subdivision challenges, then a single branch option would lead to (m + 2) new challenges, and n steps would lead to (m + 2)<sup>n</sup> challenges. Even for modest values of n, the number of challenges to consider becomes astronomical and impractical. It is necessary then, at some point, to rank-order the three branching options to limit the number of attacked challenges. An innovator may pick one of the three options at a given challenge, and proceed accordingly, chaining more triangles to the web. At some point, the innovator would conclude that this route is futile, and s\he might return to the original challenge and pick a different branching option. Since this can happen at every challenge, the actual "travel route" of the innovator over this so called Turing Web may be quite complicated. Complicated or not,

**Figure 7.** *ITM-web.* the travel route of the innovation process over the Turing web of triangles is a formal codification of the innovation process. It can be documented, analyzed, compared, and learned-from for the benefit of future innovative processes. The accumulating history of innovation processes mapped on the Turing web leads to the identification of innovation invariants that would be helpful for future R&D.

**UNIVERSALITY:** Is the Innovation Turing Machine universal? That is, is it possible to map every innovation process onto the Turing web? Historic innovation processes, to the extent they were tested, could all be mapped onto the web. It serves as no proof with respect to future innovation tasks, but at least this is a positive indication. The generality of the model can be argued from the following analysis: The three triangular options to handle a challenge that cannot be solved directly are well defined, distinct and thus valid. However, these options may not be complete. In other words, a technological challenge may be faced with the three options: A (abstraction), B (breakdown), and X (extension), plus a forth one, Y, not recognized by the model. To be distinct, Y must not be a component of the current challenge, and may not be an abstraction thereto. It may not be some reverse-abstraction challenge, which means it is a breakdown component. It may be a different description of the current problem, at the same level of abstraction. In such case, the Y option would qualify as a challenge to be listed abreast of the current one by selecting the extension option. See **Figure 7**.
