Accurately And Rapidly Predicting Next-Generation Product Breakthroughs In The Medical-Devices, Disposable Shaving Systems, And Cosmetic Industries
Editor | On 08, Mar 1999
Gernot Mueller, M.D., President, BioFutures Incorporated930 Tahoe Blvd.#802, Suite 461 Incline Village, Nevada 89451(530) 692-1945 ~ email: firstname.lastname@example.org
BioFutures Inc. partners with management and professional staffs from companies in the medical devices, pharmaceutical and cosmetic industries, forecasting next-generation products in design detail. This capability allows BFI – and their partnering companies – to do the impossible: field breakthrough products of the future – now. Behind this capability lies a creative approach that is both rapid and highly accurate.
THE EVOLUTION OF PRODUCTS All products are “technical systems,” evolving over time. What evolves is the performance of technical systems,as may be discerned from the following seven examples representing different productareas:
- Transdermal Patches If the technical system is a transdermal patch for delivering therapeutic agents through the skin, and into the blood stream, “evolution” refers to the system’s increased capability for delivering drugs of ever-increasing molecular size (e.g., insulin and large protein molecules).
- Shaving System If the technical system is a disposable shaving system for “cutting” whiskers or hairs growing out of the skin, “evolution” refers to the system’s increased capability to deliver closer shaves without cutting or injuring the skin, with manufacturing costs being only a fraction of the manufacturing cost of existing razors.
- Inhalers If the technical system is an inhaler for delivering a therapeutic agent to the lungs, “evolution” refers to the system’s increased capability for delivering larger fractions of the quantity dispensed to the lungs, while not causing other problems on the way to the lungs.
- Defibrillators If the technical system is a defibrillator, “evolution” refers to the system’s increased probability of reviving heart attack victims without also causing harmful effects (body burns, tissue damage, etc.) to the patient. Related goals are to achieve miniaturization and significant cost reduction.
- Pacemakers If the technical system is a pacemaker-like device – e.g., for treating
epilepsy – “evolution” refers to the system’s increased ability to delive intermittent signals to the brain to control seizures – or even to allow patients to activate signals if they sense an oncoming seizure – without causing adverse effects of any kind, and at a reduced (pacemaker) unit manufacturing cost.
- Non-invasive Instruments If the technical system is a non-invasive instrument for measuring, e.g., elasticity of large and small arteries (to assist physicians in assessing patients’ risk for cardiovascular disease), “evolution” refers to the system’s increased accuracy, and to its increased ability to penetrate bodily tissues to the targeted areas of interest.
- Cosmetics If the technical system involves the timed delivery of cosmetics over a selected portion of the face, neck, etc., “evolution” refers to the system’s increased ability to dispense cosmetic ingredients of ever-increasing molecular size – according to predetermined time-release profiles – to and into the skin.
S-CURVES DEPICT MARKET EXPANSION FOR PRODUCT FAMILIES All product families – including medical devices, drug delivery systems, shaving systems, and cosmetic products – follow certain patterns as they evolve. The first point on an “evolutionary time-scale curve” for a product is discovery – marking the “invention” of an entirely new – or significantly improved – product family.
For various reasons (lack of adequate investment capital, formidable technical challenges, apparent market disinterest, etc.), it normally takes years or even decades before the chief problems associated with a new product family are resolved. Only then is the product ready for the marketplace. The performance progress of a typical product family can be depicted by S-curves(1).
Such curves have been collected for many industries and are available in the book(2), Predictions : Society’s Telltale Signature Reveals the Past and Forecasts the Future, by Theodore Modis (further remarks on Modis’ book are presented as an Appendix to this paper). The uniqueness of these product family curves is that they all follow the “S ” shape – in spite of the fact that certain industries are affected by the war-torn years, by politics, by natural disasters, or by other major events.
Oral delivery is the primary form of drug delivery used today. It represents a multi-billion dollar industry. The performance of the industry as a whole can be measured by the total number of units (tablets, etc.) produced. This performance is illustrated below on a cost-independent S-curve.
Oral-medication drugs represent a rather mature family. As indicated by this generalized curve, at one point the industry went through a period of time during which little progress occurred, then reached a point where production began to rise rapidly, and finally approached a limiting level of production – which is the current state of the oral drug industry, as measured by this performance index.
A linearized version of an S-Curve plot shows that oral drugs (i.e., powders, tinctures and tablets) initially went through an “infancy” stage (discussed above), where little apparent progress occurred (behind the scenes, there was a sporadic, if ill-funded, effort to resolve the problems associated with this mode of drug delivery). After these problems were resolved, production rose rapidly.
During the “rapid growth” stage, competitors began producing similar products. Competition guaranteed a high rate of improvement. The product family (tablets) flourished in the marketplace. Significant technical strides were made, including “time released capsules,” “low-friction coatings,” and “sublingual and liquefied drugs.” Manufacturing production methods were
improved. Ultimately a “saturation” limit was reached, which fixed the market possibilities for oral medicines.
At this stage of the S-curve, drug manufacturers wanted to assure that their “cash cow” products would continue. This goal drove all further technical efforts associated with oral medications. The product had reached a certain “maturity” level. All truly innovative efforts are downplayed at this stage, or even halted. This is essentially the point that the oral-medications industry is at today.
Some small, new company (or perhaps the research department of an existing large company already in the business) may – at this stage – achieve a breakthrough that makes it possible to deliver literally all (formerly orally delivered) drugs in a non-invasive way that is “other than oral,” and which is cost effective. Such a breakthrough will make orally delivered drugs (pills, etc.) relatively obsolete. This breakthrough initiates a new S-Curve. A brand new industry is born –
perhaps with new corporate players. If existing pharmaceutical companies are not a part of the new breakthrough, they may not be among the new players.
S-CURVES DESCRIBE THE EVOLUTION OF PRODUCT PERFORMANCE As discussed above, the performance of an entire industry is measured in terms of the number of product
units produced by that industry. However, the functional performance of an individual product is measured in units that are more “technical.” Some of these “technical performance indices” are mentioned for products 1 through 7 above.
For example, transdermal drug delivery systems are technically limited to the range of molecular sizes of drugs capable of permeating the skin. The skin will not admit most larger-molecules. Therefore transdermal delivery systems can be “rated” in terms of the “limiting” (i.e., maximum) molecular weight that can be successfully delivered. This rating is the performance index of the system, which, when plotted historically against time, should yield an S-curve shape. As
transdermal systems evolve, it is expected that they will become capable of delivering drug molecules of ever-increasing size and complexity.
The S-curve for transdermal drug delivery systems is shown below. The “X” point on the curve indicates that today’s transdermal systems are in the “infancy” stage of their possible evolution. Designers, scientists and researchers have been working to discover how to deliver an entire range of larger-molecule therapeutic agents through the skin, in a way that does not increase costs to producers of transdermal patches and similar devices.
BioFutures has already discovered how to do this, using the Triads(3)
and TRIZ approaches, as well as their own, proprietary, technology-forecasting algorithms, developed for the pharmaceutical and allied industries.
This same technology forecasting capability has also been applied to the cosmetics industry. The cosmetics industry enjoys an advantage that pharmaceutical companies making prescription drugs does not have. Over-the-counter cosmetic substances are not subject to the same, rigorous, time-consuming requirements imposed by outside agencies on prescription drug companies.
BioFutures is actively engaged in applying lessons learned in transdermal delivery technology to cosmetics.
PREDICTING NEXT-GENERATION PRODUCT BREAKTHROUGHS
DISPOSABLE RAZORS Disposable razor blades for shaving represent a huge world-wide marketplace. A real driver in this industry is cost-reduction. Some producers of disposable razors believe that significant cost reduction is not possible without compromising technical performance features of their products. Others believe that further breakthrough-level performance increases are not possible. BioFutures’ next-generation, product-forecasting algorithm predicts that both are possible: significant cost reductions and next-generation, disposable shaving systems.
BioFutures applied its proprietary technology-forecasting algorithms to disposable razor blade design and manufacturing. Results indicate that unit manufacturing costs can be significantly reduced, while also conceiving next-generation design breakthroughs in performance.
BioFutures’ algorithms make use of the “Triads” and TRIZ creativity approaches. These approaches assist designers in eliminating or reducing habitual barriers to creating breakthrough designs. Altshuller(4) calls these barriers “psychological inertia.” One form of psychological inertia is the belief that “the current design has already been optimized, and is close to the ideal design.”
For a typical disposable razor sold on the shelves, this belief is not true. BioFutures’ design and cost algorithms demonstrate that the efficiency of the main performance function for this system – “cutting” – is still quite low, and can be significantly improved. It has also been demonstrated that unit manufacturing costs of most disposable razors currently on store shelves can be reduced by a minimum of ten to forty percent.
BioFutures has already conducted a cost and performance analysis of disposable razors, and is now planning to ally with a major disposable razor producer in order to field next-generation disposable razor designs, while simultaneously achieving significant cost reductions. The analysis was conducted by using invention software produced by the Invention Machine Corporation. This software is called TechOptimizer 3.0, and it contains several very useful problem-solving and invention modules. Three modules employed by BioFutures on disposable shavers are called (1) “Effects,” (2) “Product Functional Analysis,” and (2) Feature Transfer.
CASE STUDY: USING TRIADS TO PREDICT
AND CONCEIVE NEXT-GENERATION PRODUCTS
For proprietary reasons it is not possible to disclose further information about next-generation razor blade systems. However, the following case study example on defibrillation systems serves as an example of how BioFutures uses the Triad Approach for the prediction of next-generation designs(5).
NEXT-GENERATION DEFIBRILLATORS The main function of a defibrillator is to re-start the heartbeat of a heart-attack victim through the application of an electrical shock. The passive object is the heart. The active object is the defibrillator system. The enabling object is an emergency team member. The essential functions are:
DEFIBRILLATOR ELECTRICALLY SHOCKSHEART.
EMERGENCY TEAM MEMBER ACTIVATES DEFIBRILLATOR.
- EMERGENCY TEAM MEMBER OBSERVES & ASSESSES STATE OF HEART.
These three objects (heart; defibrillator; and emergency team member), and their interactions, form the triad shown below.
If one of the objects of the triad are pruned (i.e., eliminated), then that object’s functions need to be considered.
For example, suppose we decide to “prune” the emergency team member.
Eight key questions emerge from this decision:
- Is the defibrillator really necessary from the point of view that it needs to be activated by an emergency team member? Under what circumstances would the defibrillator not be necessary?
- Is it necessary for the defibrillator to be activated? Under what circumstances might it not have to be activated?
- Can the patient himself, or his own heart, activate the defibrillator? What could this mean in terms of a new design?
- Can the defibrillator activate itself? What could this mean in terms of a new design?
- Is the heart really necessary – from the point of view that it’s state (or the patient’s state) needs to be observed and assessed? Under what circumstances would the heart or patient not be necessary from this point of view?
- Is it necessary for the state of the heart or patient to be observed and assessed by the emergency team member? Under what circumstances would that not be necessary?
- Can the patient, or the patient’s heart, observe and assess its/his own state? What could this mean in terms of a new design?
- Can the defibrillator observe and assess the state of the heart or patient? What could this mean in terms of a new design?
The answers to these eight questions are not easy. Some of them may appear to be ridiculous. Others may in fact actually be ridiculous. Nevertheless, as a collection, they lead to next-generation revival systems – in a manner that also leads to the ideal final system.
Eight more questions arise if we decide to prune the defibrillator:
- Is the heart really necessary from a “providing an electrical shock to the heart” point of view? Under what circumstances would the heart not be necessary from this point of view?
- Is it necessary for the heart to be electrically shocked? Under what circumstances might
it not have to be electrically shocked?
- Can the emergency team member, in the absence of a defibrillator, somehow electrically
shock the heart? What could this mean in terms of a new design?
- Can the heart (or the patient), in the absence of a defibrillator, electrically shock itself (himself)? What could this mean in terms of a new design?
- Is the emergency team member really necessary if the defibrillator is pruned? Under what circumstances would the emergency team member not be necessary?
- Is it necessary for the defibrillator to be activated at all? Under what circumstances would that not be necessary?
- Can the emergency team member, in the absence of a defibrillator, somehow activate an electrical shock to the heart of the patient? What could this mean in terms of a new design?
- Can the heart itself (or the patient), in the absence of a defibrillator, somehow activate an electrical shock to itself/himself? What could this mean in terms of a new design?
If we consider the 16 questions listed above as a whole, certain creative paths – and features of creative solutions – come to mind. The following is a list of potential solution features (along with the question number above that stimulated each solution feature):
- (1) The defibrillator can be activated remotely by a third party, of from an auxiliary device. Design this feature in.
- (2) When there is a patient heartbeat, the defibrillator will not deliver an electrical shock, but it will deliver an electrical shock when it is attached to the patient, and when there is no heartbeat. This feature should be designed into the defibrillator.
- (3) The patient sends out a signal to the defibrillator to activate an electrical shock. This signal decision may come directly from the patient’s heart, or from a device that is monitoring the patient’s heart. The defibrillator is designed to receive such a signal, and to automatically deliver an electrical shock when signaled.
- (4) Design a defibrillator that is self-activating. When an electrical shock is required for the patient, the defibrillator itself activates that requirement. No human being (i.e., emergency team member) is necessary to activate it.
- (5) Some other part of the patient (i.e., other than the heart) is assessed/observed to determine the patient’s state of health. This observation/assessment does not require an emergency team member.
- (6) The state of the heart (patient) can be observed/assessed by other means than by the emergency team member (i.e., by a sensor/monitor worn by the patient, which is programmed to determine the need for an electrical shock).
- (7) The heart/patient has its own “micro” version of an emergency team member, attached to it. This device is electro-sensory, recording one or more of the patient’s vital signs or signals, and transposing them into a signal, which is transmitted to a miniaturized defibrillator also attached to the patient.
- (8) The defibrillator is equipped with a receiver that senses the patient’s state, and determines appropriate action.
- (9) Start the heartbeat in the heart by doing something to another organ, to the nervous system, etc., via another medical device system.
- (10) Find/design another way to re-instate a heartbeat, other than through an electrical shock, or other than from a defibrillator.
- (11) Use the emergency team member’s vehicle, electrically equipped to deliver the required power-time profile, to the patient.
- (12) The patient wears an electrical shock device that also senses the patient’s state and decides if the patient needs the shock.
- (13) The defibrillator is self-activating (see D above).
- (14) The defibrillator is always activated, and therefore never needs to re-activated, as long as the patient has no heartbeat.
- (15) The emergency team member has an alternative way of reviving the patient.
- (16) See G above.
STEP-BY-STEP PROCEDURE: DISCUSSION AND RESULTS It’s easy to miss important results that can be gathered by the steps that we just went through – even though we have not yet completed the entire procedure. I want to stop at this point, therefore, and review – from a generic point of view – what we just did, and also review some of the conclusions and results that have come from what we just did. We’ll start with a generic description of the procedure used, referring to the defibrillation system case study for clarification.
- We began with the selection of an actual system for accomplishing some performance function. The specific system chosen was the defibrillation system. It’s used to re-start the heart of a heart attack victim.
- The next step we took was to construct the triad of three objects that describes the function – that triad actually is the function, because without any one of the three objects in a triad, there would be no function. Therefore the objects in the triad are essential parts of the selected “system” called “re-starting the heart of a heart-attack victim.”
- There are always three objects in a triad. One of the objects is the passive object, and it is the object to which something is being “done” or “accomplished.”
- A second object is the active object, and it is the object that does something to the passive object – it’s also the object that accomplishes what is being accomplished.
- The third object is not always easy to identify. That is the enabling object, and it is the object, without which, the active and passive objects would not interact in the desired way.
- Once we have the triad in place, we examine the interactions in the triad to determine the functional relationships between the objects. Generally speaking, the functional relationship between the active and passive object is easy to understand. The relationships between the enabling object and the other two objects, however, are not always easy to understand.
COMMENTARY If we have gone this far in analyzing a problem situation, then we are already pretty far along. We usually have three interactions to examine. Each of these can be improved in various ways, and there are several tools of the TRIZ approach that can assist us in improving these interactions. For example, we could apply the laws of development of technical systems to the objects and actions in this triad. Or, we could look at the interactions between any two objects and further develop the problem in terms of a conflict, and use Altshuller’s conflict matrix to locate inventive principles that we can apply to the objects and actions of the interaction. Or,
we can follow the entire ARIZ procedure for a particular interaction in the triad – usually ARIZ is to an interaction between the active and passive object.
All of these “ways leading to creative solutions” are admissible, but there is a way that leads us to the ideal final result not only “ultimately” – but quite rapidly. This way involves “pruning” (i.e., removing) a part, or the whole, of one of the objects in the triad.
The step called “pruning” rapidly leads us towards the ideal final result. The system also becomes simplified (not made more complex). By pruning a system, one or more measures of “ideality” of the system are increased.
If one of the objects in a triad is pruned, then we have a problem: we no longer have a function, because there is no triad. The minimum requirement for any function to exist is that there have to be three objects (active, passive and enabling).
So after pruning occurs, we truly have a conflict:
The object must be pruned, in order to simplify the system and
move towards ideality, and the object must not be pruned, so that we retain the function.
We’ll continue the “Triads plus Pruning” procedure with step 4 below.
- Choose one of the objects for pruning, using your intuition and knowledge of the constraints on the system. It may be good not to choose the passive object first, although it is probably a good idea to explore the ramifications of pruning each of the three objects in the system – one at a time. For the defibrillator system, we decided to prune the operator – the emergency team member who applies the defibrillator to the heart attack victim.
- Examining the remaining parts of the triad, ask the following question: “When the object chosen is pruned, what interactions are affected?” Identify the interaction – or interactions – that are affected. For example, if we prune the emergency team member,two interactions are affected:
- “Emergency team member activates defibrillator,” and
- “Emergency team member observes and assesses the state of the patient’s heart.”
- Identify the interactions in which the object being pruned is the “active” object. For each interaction where the object being pruned is the active object, consider the following questions:
- Is it possible that some other object in the system (including any parts remaining from the object being pruned) can assume the functions of the object being pruned? What design configurations will make this happen? Identify those design configurations.
- Are there design configurations where – for the sake of the interaction under consideration – the passive object (or the part or parts of it that are involved in the interaction) is not required? Identify those design configurations (keeping in mind that the active object – or certain parts of it – has been pruned).
- Are there design configurations where the interaction or action itself is not required? Identify those design configurations, keeping in mind that the active object of that interaction has been pruned.
COMMENTARY This is about as far as we have gone in the process of “Forming a triad and then pruning,” with the defibrillator example. If you recall, we generated sixteen generic solutions – some of which appeared to be very similar to each other. Then we considered each generic solution, and through the application of “abstract thinking,” generated specific solutions (A through P). Let’s attempt to summarize the features of specific designs that are generated by our procedure:
FEATURES OF NEXT-GENERATION “REVIVING” SYSTEMS
- ELIMINATION OF HUMAN INVOLVEMENT The system under consideration involves human beings other than the heart attack victim, for two purposes: assessing the victim’s state of health, and activating the defibrillator. Inventive prompts from the “triads plus pruning” process suggest that designs of the future will eliminate these aspects of human involvement. Instead, the “defibrillator itself” will assess the victim and decide to deliver what is necessary to the victim. This requires sensory, feedback, decision-making, and activating features on new “defibrillator” designs. Implied with these features are “connections” between the new “defibrillator” and the victim.
- REMOTE, THIRD-PARTY, OR AUTOMATIC INVOLVEMENT Intelligent sensing, decision-making and activation can be provided remotely at any time, around the clock. This implies an intimate connection between the next-generation “defibrillator” and the victim, as well as sensory, feedback, decision-making, and activation features “at a distance” from the victim.
- INTELLIGENT SENSING AND DECISION-MAKING Next-generation designs will have some sort of programmed intelligence concerning the information communicated from intelligent sensors already in touch with (i.e., monitoring) the victim’s body (perhaps before the oncoming of a heart attack). These intelligent sensors may be monitoring the victim’s heart directly, or they may be indirectly monitoring other patient characteristics (i.e., other vital signs of the patient) – which may be able to be monitored more remotely (and with less invasiveness or patient inconvenience).
Sensing devices can be described as being “electro-sensory,” recording one or more of the patient’s vital signs or signals, and transposing them into a signal, which is transmitted to a miniaturized defibrillator also attached to the patient (see Feature 4, next).
- PATIENT “WEARS” CERTAIN SYSTEM PARTS Sensors with feedback capability, and means of delivering shocks or signals, can be worn in advance by the patient (or, implanted in advance in the patient). The implication is there that advance “shocks” could be far less mild than the conventional defibrillator shock – e.g., more like a pacemaker. In the case of a conventional defibrillator, future design requirements call for far lighter and far more intelligent defibrillators – capable of being worn by patients who might require defibrillation sometime in the future (as determined by their physicians).
- REVIVING VICTIMS THROUGH OTHER-THAN-ELECTRIC-SHOCK MEANS Next-Generation designs
will feature means to revive heart attack victims other than through the conventional
method of delivering an electrical shock with a fixed, power-time profile. A next-step
design configuration will probably include a pulsed, power-time profile – delivering the
same profile shape, but significantly less energy. Then new revivification techniques will
follow. These may involve organs and bodily systems other than just the heart – or,
instead of the heart.
- MODIFICATIONS TO THE “ENGINE” OF CURRENT DEFIBRILLATORS In the near term, we can expect to see some system merging, involving the use of other available systems to be the source of power for defibrillators – thereby allowing defibrillators to be lighter and more effective. For example, motorized vehicle power units can be equipped to provide defibrillator power to victims reached by mobile emergency teams.
The above characteristics of next-generation defibrillator devices are only a few, among many, that can be realized by using all the tools of TRIZ. They are, however, major characteristics and features that move current defibrillators closer to “the ideal design.”
TRIADS AND PRUNING ON A MICRO-LEVEL
It is also possible to apply the “Triads and Pruning” procedure to defibrillators (or to any product or process) on a micro-level. For example, one of the problems associated with defibrillators is “chest area burns” associated with the energy absorbed during shock delivery. Medical research dictates that the shape of the electrical Power-Time profile delivered has to have a certain shape for maximizing the probability of reviving the patient. The area under the power-time curve is energy, and unfortunately, this excessive energy causes the harmful side effects mentioned
The passive object of this triad is the heart. The active object is an electrical shock having a certain power-time profile shape. The enabling object is an electrical power supply system. Let us divide the electrical power-time profile into two “parts” – a useful one and a harmful one. If the harmful part of the electrical shock profile (the one that contributes to patient burns) is pruned, we are left with the useful part (the essential part of the electrical shock profile that revives the patient).
This is where the tools of TRIZ can be used. Let’s express the physical contradiction:
The profile shape of the electrical shock has to be unchanged, to maximize the probability of reviving the victim, and the profile shape of the electrical
shock has to be changed, to reduce the area (energy) under the power-time curve.
This conflict can be resolved in several ways, including the following:
- Deliver a rapid burst of many, shorter-in-time, power-time profiles – each having the required shape.
- Deliver the same profile shape, except that the power is “pulsed.” That is, the overall shape looks the same in time and in power, but on a more microscopic scale, the shock is delivered in short pulses with no electrical delivery in between the pulses.
In this way the power-time profile shape is the same, but the total energy delivered is only a fraction of what was previously delivered to the victim. Drawings of the problem and the solution (i.e., before and after Triads was applied) are shown below.
Let’s discuss what was accomplished. We first formed a Triad.Then, the original power-time profile was pruned, and replaced by a pulsed
power-time profile having the same shape. A modification of existing system resources was used to solve the problem.
CURRENT PROJECT ACTIVITY
BioFutures’ application of “Triads + Pruning” to disposable razor blades has resulted in a project to build disposable razor prototypes that have both superior performance as well as significantly lower unit-manufacturing-costs. This project is already in the testing stage and the results are very promising. BioFutures plans to form a strategic alliance with a major disposable
razor producer to manufacture the new disposable razor systems in the near future.
I hope that this brief introduction to Triads and Pruning has helped you to understand more about the Triads approach. The Triads approach is particularly useful for predicting – with high accuracy – next-generation design configurations for any product family you choose. At BioFutures we welcome inquiries from medical-device, shaving system and cosmetic companies seeking to conceive and produce next-generation products of the future – now.
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APPENDIX. S-CURVE COMMENTARIES
Predictions : Society’s Telltale Signature Reveals the Past and Forecasts the Future, by Theodore Modis
Citing experts at the International Institute of Advanced Systems Analysis as the source of the information he presents, Theodore Modis, a physicist formerly from the Digital Equipment Corporation), examines technical, economic, and social trends. He describes growth curves that predict how competing animal species survive in the face of competition for limited resources. Modis goes on to explain how these same curves – and the equations upon which they are based – can be applied to
nonbiological phenomena – inventions, sources of energy, and human activities, ranging from an artist’s productivity to the spread of diseases.
Modis explores two types of curves that the above-mentioned systems and their associated phenomena follow:
- The well known bell-shaped, “normal distribution” curve.
- The curve of its integral: the S-curve.
The plots presented in Modis’ book address motor-vehicle deaths, world-wide energy-source competition and substitution, the output of geniuses, economic cycles, and innovation.
Some readers might view what Modis has to offer with so much skepticism, that they are likely to miss the key points of this book. Nature follows certain laws. Human beings – and their output and results – are a part of nature. Humans too, are subject to these same laws. Knowing the laws means being able to predict phenomena associated with nature and human beings. The phenomena of specific interest to this audience include inventing (product and process conception), problem-solving, product and process improvement, technical forecasting and anticipatory failure analysis.
Modis’ laws and equations apply to these phenomena.