This paper presents a study on digitization of Traditional Chinese Medicine diagnosis. The research consists of two aspects: a) algorithms for blood vessels extraction in sclera-conjunctiva images, which can be applie...This paper presents a study on digitization of Traditional Chinese Medicine diagnosis. The research consists of two aspects: a) algorithms for blood vessels extraction in sclera-conjunctiva images, which can be applied in syndrome differentiation by observing human eyes (named Ocular Diagnostic in Traditional Chinese Medicine);b) digitization of extracted vessels. First, sclera-conjunctiva region is isolated by optimal threshold segmentation and mathematical operation;Scanning and edge detection methods are used to gain the edge of the blood vessels. Moreover, the edge feature parameters are gained, which can be used to reconstruct the blood vessels. Experimental results show that blood vessels information can be obtained fast and accurately for the further TCM diagnosis by artificial system.展开更多
The beneficial acclimation hypothesis (BAH) predicts that animals acclimated to a particular temperature have enhanced performance or fitness at that temperature in comparison with animals acclimated to other temperat...The beneficial acclimation hypothesis (BAH) predicts that animals acclimated to a particular temperature have enhanced performance or fitness at that temperature in comparison with animals acclimated to other temperatures. The BAH has been tested by a variety of empirical examinations, and was rejected by some of them. In order to provide new evidences for the BAH, the effects of acute and acclimation temperature (AT) on locomotor performance of Macrobiotus hufelandi (Tardigrada: Macrobiotidae) were investigated. The tardigrades were collected from Nanwutai, Qinling Mountains which traverse from west to east in central China. The subjects were acclimated to either 2℃ or 22℃ for 2 weeks. The animal was transferred onto a frosted slide and allowed to walk freely at the performance temperature (PT) 2℃ or 22℃. Only one individual was tested per test bout, which lasted from three to five minutes. To avoid occurrence of thermal acclimation effect, the standard adaptation time was limited to 1.5 min. Each subject was tested for once at the same PT, and was tested only at one PT. A total of 25 individuals were tested and measured at the same PT. The locomotor performance of the animals was recorded with a digital video camera mounted on a microscope at 4×10 amplification and replayed on a PC. Every subject was identified. Walking speed (WS) and percentage of time moving (PTM) at both PTs (2℃ or 22℃) were selected as the rate parameters of locomotor performance. The two-way repeated measures ANOVA with a significance level of α= 0.05 and Duncan multiple range test were used to analyze the data. WS of the animals acclimated to and tested at the same temperatures was significantly faster than that for animals acclimated to and tested at the different temperatures, similarly, PTM of the animals acclimated to 22℃ and tested at 22℃ was significantly greater than PTM of animals acclimated to 22℃ and tested at 2℃, which indicated that the animals acclimated to a particular temperature have enhanced locomotor performance in that temperature relative to the animals acclimated to that temperature in other thermal environment. WS of the animals acclimated to 22℃ and tested at 22℃ was significantly faster than WS of animals acclimated to 2℃ and tested at 22℃, PTM of the animals acclimated to 22℃ and tested at 22℃ was significantly greater than PTM of animals acclimated to 2℃ and tested at 22℃. These results supported the BAH. It could be concluded that the PT and thermal acclimation as well as the interaction between the PT and AT significantly influence the locomotor performance of M.hufelandi, and that, despite the existence of a few results of this study that don’t support the BAH, some results of this study support for this hypothesis, and that the animals acclimated to a particular temperature have enhanced locomotor performance in that temperature relative to the animals acclimated to that temperature in other thermal environment, implying that any performance temperature that deviates from the acclimation temperature could cause the reduction of the walking speed which is closely related to the fitness of the M.hufelandi.展开更多
High-strength steels are mainly composed of medium-or low-temperature microstructures,such as bainite or martensite,with coherent transformation characteristics.This type of microstructure has a high density of disloc...High-strength steels are mainly composed of medium-or low-temperature microstructures,such as bainite or martensite,with coherent transformation characteristics.This type of microstructure has a high density of dislocations and fine crystallographic structural units,which ease the coordinated matching of high strength,toughness,and plasticity.Meanwhile,given its excellent welding perform-ance,high-strength steel has been widely used in major engineering constructions,such as pipelines,ships,and bridges.However,visual-ization and digitization of the effective units of these coherent transformation structures using traditional methods(optical microscopy and scanning electron microscopy)is difficult due to their complex morphology.Moreover,the establishment of quantitative relationships with macroscopic mechanical properties and key process parameters presents additional difficulty.This article reviews the latest progress in microstructural visualization and digitization of high-strength steel,with a focus on the application of crystallographic methods in the development of high-strength steel plates and welding.We obtained the crystallographic data(Euler angle)of the transformed microstruc-tures through electron back-scattering diffraction and combined them with the calculation of inverse transformation from bainite or martensite to austenite to determine the reconstruction of high-temperature parent austenite and orientation relationship(OR)during con-tinuous cooling transformation.Furthermore,visualization of crystallographic packets,blocks,and variants based on actual OR and digit-ization of various grain boundaries can be effectively completed to establish quantitative relationships with alloy composition and key process parameters,thereby providing reverse design guidance for the development of high-strength steel.展开更多
The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is stric...The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.)展开更多
In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped i...In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.展开更多
In recent years, some governments have been working on solutions to transform public administrations and provide high-quality services to users. The United Nations has recommended integrating digital technology into v...In recent years, some governments have been working on solutions to transform public administrations and provide high-quality services to users. The United Nations has recommended integrating digital technology into various aspects of life, including public services. The objective is to offer real-time, high-quality digital services, improve the delivery of public services, enhance their effectiveness and efficiency, while achieving objectives such as transparency, interoperability and citizen satisfaction. However, most governments in developing countries are unable to keep up with this trend. As a result, they often create digital public services that fall short of users’ expectations. This study aims to identify the fundamental factors influencing the quality of service in relation to user satisfaction and to explore the relevance of digital technology in implementing this quality within Cameroon public administrations. To achieve this, we used a qualimetric research method, which included non-directive interviews, questionnaires, and structured observations. The results showed that the public services offered in our study environment did not meet users’ expectations. However, the study identified the fundamental aspects to be considered in providing quality public services connected to user satisfaction, as well as the strengths of digitization in achieving this quality.展开更多
Compared with traditional waveform digitization with flash-ADCs, waveform digitization with switched-capacitor arrays (SCAs) is able to achieve the sampling speed above 1 GS/s without degrading the analog to digital c...Compared with traditional waveform digitization with flash-ADCs, waveform digitization with switched-capacitor arrays (SCAs) is able to achieve the sampling speed above 1 GS/s without degrading the analog to digital conversion precision significantly. In this paper, we present the implementation of a fast waveform digitization system with the use of SCAs, and evaluate its performance of waveform digitization and the waveform timing. At about 5 GS/s, the dynamic input range of the digitizer is about 66 dB, and its timing precision is about 20 ps (RMS).展开更多
In a short time, during the early phases of the COVID-19 pandemic outbreak, we managed to shift rapidly to use digital technologies and replace some of our daily operations with virtual modes. This shift happened so i...In a short time, during the early phases of the COVID-19 pandemic outbreak, we managed to shift rapidly to use digital technologies and replace some of our daily operations with virtual modes. This shift happened so instantly and widely that it enables us to argue that the COVID-19 became a valid reason to boost some of the gradual and ongoing transitions towards faster transformations. In this study, we use gray literature to delve into arguments around the boost for digitization, digitalization, and systems thinking in the development of the built environment. This is mostly discussed from the influence of COVID-19 on some of the existing practices or the business-as-usual of the built environment sector. From technological advancement to technology use, these arguments are put forward to discuss what is likely to be the major driver of technological adoption and the shifting paradigms that are yet to be revealed. The study concludes that the current push towards new directions and development pathways are likely to be widely accepted in a shorter time. The findings of this brief study feed into existing arguments on transformative pathways due to the COVID-19 pandemic.展开更多
The article shows that the foundation of the digital economy can be a new paradigm for predicting the future from the future,i.e.from the future in which the development goal has already been achieved.This allows to m...The article shows that the foundation of the digital economy can be a new paradigm for predicting the future from the future,i.e.from the future in which the development goal has already been achieved.This allows to minimize all costs and completely avoid incorrect system solutions of the existing trial-and-error approach.Using the achievements of the technological revolution of Industry 4.0,an effective digital economy can be formed only when it is seen as an economy of coordinated interests between the state,business,society and the interests of each individual in real time at every local level.This will make it possible to solve the problem of ensuring the high quality of life not of citizens in general,but of each individual.展开更多
The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approach...The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.展开更多
文摘This paper presents a study on digitization of Traditional Chinese Medicine diagnosis. The research consists of two aspects: a) algorithms for blood vessels extraction in sclera-conjunctiva images, which can be applied in syndrome differentiation by observing human eyes (named Ocular Diagnostic in Traditional Chinese Medicine);b) digitization of extracted vessels. First, sclera-conjunctiva region is isolated by optimal threshold segmentation and mathematical operation;Scanning and edge detection methods are used to gain the edge of the blood vessels. Moreover, the edge feature parameters are gained, which can be used to reconstruct the blood vessels. Experimental results show that blood vessels information can be obtained fast and accurately for the further TCM diagnosis by artificial system.
文摘The beneficial acclimation hypothesis (BAH) predicts that animals acclimated to a particular temperature have enhanced performance or fitness at that temperature in comparison with animals acclimated to other temperatures. The BAH has been tested by a variety of empirical examinations, and was rejected by some of them. In order to provide new evidences for the BAH, the effects of acute and acclimation temperature (AT) on locomotor performance of Macrobiotus hufelandi (Tardigrada: Macrobiotidae) were investigated. The tardigrades were collected from Nanwutai, Qinling Mountains which traverse from west to east in central China. The subjects were acclimated to either 2℃ or 22℃ for 2 weeks. The animal was transferred onto a frosted slide and allowed to walk freely at the performance temperature (PT) 2℃ or 22℃. Only one individual was tested per test bout, which lasted from three to five minutes. To avoid occurrence of thermal acclimation effect, the standard adaptation time was limited to 1.5 min. Each subject was tested for once at the same PT, and was tested only at one PT. A total of 25 individuals were tested and measured at the same PT. The locomotor performance of the animals was recorded with a digital video camera mounted on a microscope at 4×10 amplification and replayed on a PC. Every subject was identified. Walking speed (WS) and percentage of time moving (PTM) at both PTs (2℃ or 22℃) were selected as the rate parameters of locomotor performance. The two-way repeated measures ANOVA with a significance level of α= 0.05 and Duncan multiple range test were used to analyze the data. WS of the animals acclimated to and tested at the same temperatures was significantly faster than that for animals acclimated to and tested at the different temperatures, similarly, PTM of the animals acclimated to 22℃ and tested at 22℃ was significantly greater than PTM of animals acclimated to 22℃ and tested at 2℃, which indicated that the animals acclimated to a particular temperature have enhanced locomotor performance in that temperature relative to the animals acclimated to that temperature in other thermal environment. WS of the animals acclimated to 22℃ and tested at 22℃ was significantly faster than WS of animals acclimated to 2℃ and tested at 22℃, PTM of the animals acclimated to 22℃ and tested at 22℃ was significantly greater than PTM of animals acclimated to 2℃ and tested at 22℃. These results supported the BAH. It could be concluded that the PT and thermal acclimation as well as the interaction between the PT and AT significantly influence the locomotor performance of M.hufelandi, and that, despite the existence of a few results of this study that don’t support the BAH, some results of this study support for this hypothesis, and that the animals acclimated to a particular temperature have enhanced locomotor performance in that temperature relative to the animals acclimated to that temperature in other thermal environment, implying that any performance temperature that deviates from the acclimation temperature could cause the reduction of the walking speed which is closely related to the fitness of the M.hufelandi.
基金supported by the National Key Research and Development Project of China(Nos.2022YFB3708200 and 2021YFB3703500)the National Natural Science Foundation of China(Nos.52271089 and 52001023).
文摘High-strength steels are mainly composed of medium-or low-temperature microstructures,such as bainite or martensite,with coherent transformation characteristics.This type of microstructure has a high density of dislocations and fine crystallographic structural units,which ease the coordinated matching of high strength,toughness,and plasticity.Meanwhile,given its excellent welding perform-ance,high-strength steel has been widely used in major engineering constructions,such as pipelines,ships,and bridges.However,visual-ization and digitization of the effective units of these coherent transformation structures using traditional methods(optical microscopy and scanning electron microscopy)is difficult due to their complex morphology.Moreover,the establishment of quantitative relationships with macroscopic mechanical properties and key process parameters presents additional difficulty.This article reviews the latest progress in microstructural visualization and digitization of high-strength steel,with a focus on the application of crystallographic methods in the development of high-strength steel plates and welding.We obtained the crystallographic data(Euler angle)of the transformed microstruc-tures through electron back-scattering diffraction and combined them with the calculation of inverse transformation from bainite or martensite to austenite to determine the reconstruction of high-temperature parent austenite and orientation relationship(OR)during con-tinuous cooling transformation.Furthermore,visualization of crystallographic packets,blocks,and variants based on actual OR and digit-ization of various grain boundaries can be effectively completed to establish quantitative relationships with alloy composition and key process parameters,thereby providing reverse design guidance for the development of high-strength steel.
文摘The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.)
文摘In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.
文摘In recent years, some governments have been working on solutions to transform public administrations and provide high-quality services to users. The United Nations has recommended integrating digital technology into various aspects of life, including public services. The objective is to offer real-time, high-quality digital services, improve the delivery of public services, enhance their effectiveness and efficiency, while achieving objectives such as transparency, interoperability and citizen satisfaction. However, most governments in developing countries are unable to keep up with this trend. As a result, they often create digital public services that fall short of users’ expectations. This study aims to identify the fundamental factors influencing the quality of service in relation to user satisfaction and to explore the relevance of digital technology in implementing this quality within Cameroon public administrations. To achieve this, we used a qualimetric research method, which included non-directive interviews, questionnaires, and structured observations. The results showed that the public services offered in our study environment did not meet users’ expectations. However, the study identified the fundamental aspects to be considered in providing quality public services connected to user satisfaction, as well as the strengths of digitization in achieving this quality.
基金Supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX2-YW-N27)the National Natural Science Foundation of China (No. 11175176)
文摘Compared with traditional waveform digitization with flash-ADCs, waveform digitization with switched-capacitor arrays (SCAs) is able to achieve the sampling speed above 1 GS/s without degrading the analog to digital conversion precision significantly. In this paper, we present the implementation of a fast waveform digitization system with the use of SCAs, and evaluate its performance of waveform digitization and the waveform timing. At about 5 GS/s, the dynamic input range of the digitizer is about 66 dB, and its timing precision is about 20 ps (RMS).
文摘In a short time, during the early phases of the COVID-19 pandemic outbreak, we managed to shift rapidly to use digital technologies and replace some of our daily operations with virtual modes. This shift happened so instantly and widely that it enables us to argue that the COVID-19 became a valid reason to boost some of the gradual and ongoing transitions towards faster transformations. In this study, we use gray literature to delve into arguments around the boost for digitization, digitalization, and systems thinking in the development of the built environment. This is mostly discussed from the influence of COVID-19 on some of the existing practices or the business-as-usual of the built environment sector. From technological advancement to technology use, these arguments are put forward to discuss what is likely to be the major driver of technological adoption and the shifting paradigms that are yet to be revealed. The study concludes that the current push towards new directions and development pathways are likely to be widely accepted in a shorter time. The findings of this brief study feed into existing arguments on transformative pathways due to the COVID-19 pandemic.
基金RFBR according to the research project(No:19-010-00809)。
文摘The article shows that the foundation of the digital economy can be a new paradigm for predicting the future from the future,i.e.from the future in which the development goal has already been achieved.This allows to minimize all costs and completely avoid incorrect system solutions of the existing trial-and-error approach.Using the achievements of the technological revolution of Industry 4.0,an effective digital economy can be formed only when it is seen as an economy of coordinated interests between the state,business,society and the interests of each individual in real time at every local level.This will make it possible to solve the problem of ensuring the high quality of life not of citizens in general,but of each individual.
文摘The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.