Mixed-initiative interaction is the idea of organizing interaction in dialogue where both the computer and the human can take initiative.

Code-switching refers to a switch in language to match the capabilities of the communication partner.

According to Suchman, robustness is a key consideration in the design of dialogue.

A mode refers to the variation in the interpretation of a user's input according to an internal state.

Norman offered two central concepts to help us understand these cognitive efforts: the gulf of execution and the gulf of evaluation.

A significant early theory of dialogue interaction is the seven-stage model of Norman [600].

Fourth, both the computer and the user may have initiative.

Third, in dialogue, both the computer and the human participate in establishing a shared context.

In one turn, an appropriate communication act is made by one partner based on the communication context.

The key idea in the dialogue view of interaction is the organization of communication as a series of turns.

The dialogue view of interaction evolved early in the history of computing.

In human–computer interaction (HCI), the communication partners are an interactive system and the user of such a system.

Formal models of computation are suitable for describing discrete, moded dialogues. A mode refers to the variation in the interpretation of a user's input according to an internal state. In a modeless dialogue, all inputs are possible in all states and their interpretation is always the same.

prompt engineering—the search for prompts that give the output the user finds adequate for the task.

Mapping requires the user to figure out how to accomplish a goal with an interface.

An FSM is a model of discrete computation applicable to dialogues. In computer science, an FSM is a special case of a Turing machine that reads but does not write on the tape.

Communication repair refers to the "work of restoring shared understanding" when conversational partners misunderstand each other.

Kirsh argued that the discoverability of such options is as important as their visibility; however, discoverability is not covered well by Norman's theory.

Communication repair refers to the "work of restoring shared understanding" when conversational partners misunderstand each other.

Employing dialogue to resolve key uncertainties: If the system is uncertain about the user's intent, the system should ask the user after having considered the cost of interrupting the user. While ambiguities can be resolved via dialogue, this principle warns against always asking the user: Every interaction bears a cost (e.g., time and effort) that should be factored in when deciding whether and when to engage in dialogue.

The paradoxical effect of hyperarticulation is that despite trying to improve understanding, it can make speech recognition worse.

Users are 'architects' of their environments, as Kirsh put it. For example, users may change the settings to turn on or off a function or change the way it behaves. They also choose the applications they use. Such tailoring behaviors are not explained by Norman's intention–action–response–interpretation–evaluation cycle.

Fourth, both the computer and the user may have initiative. For example, a pop-up window can be presented to confirm a risky selection.

Therefore, the design of feedback, affordances, and cues is central to dialogue-based interaction.

Third, in dialogue, both the computer and the human participate in establishing a shared context. The computer does not simply receive a message; it also communicates the effects of that message.

Context, as we will see, can be understood through the concept of a state: The feasible communication acts and their effects are conditioned by the state of the partner.

In other words, in dialogue, acts of communication are conditional: The meaning of a turn depends on the communication context.

Siri's reply and the selection of "compose" would make no sense without the context provided by the preceding exchange.

Second, both dialogues in Figure 18.1 evolve in a turn-based manner. Each turn redefines the communication context.

For instance, the seven-stage model of interaction proposed by Norman [600] applies to all modalities of interaction; Section 18.1 explains this model in detail.

In Figure 18.1, two nominally different types of interaction are shown: speech-based and graphical. Both are forms of dialogue. This means that the concepts of dialogue are applicable across modalities.

This broad definition has several immediate and important consequences for HCI. First, dialogue, as a form of interaction, is not limited to speech and language even though this is often our first interpretation of the term "dialogue."

Initially, text consoles were used to provide access to programs running on mainframe computers.

This made it possible to structure interaction in the form of a dialogue, freeing the user from having to memorize commands, as required in command-based interfaces.

Kirsh argued that we are not just passively reacting to computer-generated options. If we look at interaction at a higher level, beyond a single action, we see that users are also actively influencing their environments. Users are "architects" of their environments, as Kirsh put it. For example, users may change the settings to turn on or off a function or change the way it behaves. They also choose the applications they use. Such tailoring behaviors are not explained by Norman's intention–action–response–interpretation–evaluation cycle.

From the 1960s to the 1980s, rapid advances in computer displays made it possible to present much richer information to users.

Kirsh points out that Norman's model makes an unrealistic assumption: The user is assumed to know the environment and its options and is merely picking an option. In practice, we do not always know what the options mean or even what options are available. Kirsh argued that users need to actively explore interfaces to become aware of the available functions and how they work. Via exploration, they also learn about their own abilities in using them. Consider the first time you launch an application; you probably try out various actions to see what happens. Kirsh argued that the discoverability of such options is as important as their visibility; however, discoverability is not covered well by Norman's theory.

The modelling subscribes to a linear account of the cognitive mechanism, going from goals to actions and back. However, according to current understanding in cognitive sciences, the picture is more complicated. One thing that is missing is an account of how beliefs about the computer are formed and updated and how they drive action specification. The current understanding is that users form internal models that predict how their actions produce perceived outputs, and they learn to minimize prediction errors. This explains why people explore interfaces (to develop better internal models) and why, eventually, they no longer need to compare outcomes against goals. Moreover, the model was initially used in a weak, heuristic sense and did not converge with efforts to implement interactive systems.

The dialogue view of interaction evolved early in the history of computing.

These theories also have implications for how we design interaction.

These theories explain what happens in dialogue and how it shapes the relationship between the partners.

HCI researchers have developed a rich palette of theories to understand such dialogues.

In human–computer interaction (HCI), the communication partners are an interactive system and the user of such a system.

This view draws on what we know about human–human communication and, in particular, how conversations are structured; see Chapter 9 for a summary.

Interaction may be viewed as a dialogue, that is, a conversation that occurs between two partners in a context for some purpose.

One thing that is missing is an account of how beliefs about the computer are formed and updated and how they drive action specification. The current understanding is that users form internal models that predict how their actions produce perceived outputs, and they learn to minimize prediction errors.

The core elements of dialogue are communication turns, the communication context, and turn interpretation.

Dialogue is about the organization of communication as a series of turns between communication partners.

A mode refers to the variation in the interpretation of a user's input according to an internal state.

Code-switching refers to a switch in language to match the capabilities of the communication partner.

Communication repair refers to the "work of restoring shared understanding" when conversational partners misunderstand each other.

Robustness refers to the communication partners' ability to achieve shared understanding even in light of misunderstandings and other unanticipated troubles.

Mixed-initiative interaction is the idea of organizing interaction in dialogue where both the computer and the human can take initiative.

Norman offered two central concepts to help us understand these cognitive efforts: the gulf of execution and the gulf of evaluation.

A significant early theory of dialogue interaction is the seven-stage model of Norman.

This understanding then forms the context within which the other partner takes their turn.

The act aims to get the other partner to do or understand something.

In one turn, an appropriate communication act is made by one partner based on the communication context.

The key idea in the dialogue view of interaction is the organization of communication as a series of turns.

both the computer and the human participate in establishing a shared context. The computer does not simply receive a message; it also communicates the effects of that message.

Robustness refers to the communication partners' ability to achieve shared understanding even in light of misunderstandings and other unanticipated troubles.

Communication repair refers to the "work of restoring shared understanding" when conversational partners misunderstand each other.

Employing socially appropriate behaviors for agent–user interaction: Any interruptions by a system should be compatible with the social expectations of the user being interrupted and offered automated services. For example, social media feeds may integrate AI-generated and human-generated content without disclosing the source.

A mixed-initiative interface needs to infer the user's goals so that it can act upon them. Several machine learning techniques are potentially suitable depending on the specific AI problem.

Mixed-initiative interaction is the idea of organizing interaction in dialogue where both the computer and the human can take initiative. Unlike in the case of an FSM, the computing system can take action without a command from the user; the initiative is mixed.

Liu and Chilton [488] studied prompt engineering for text-to-image generation

Liu and Chilton [488] noted that interaction with such models faces a dilemma. While it is possible to input anything as a prompt to such models, users must "engage in bruteforce trial and error with the text prompt when the result quality is poor." The challenge here is sometimes described as prompt engineering—the search for prompts that give the output the user finds adequate for the task.

New ways of interacting that rely on dialogue keep emerging; at the time of writing this book (early 2020s), large language models such as ChatGPT and Google Bard are making the headlines daily. The interaction with such models is primarily done through text prompts to which the model replies.

In interaction with interactive systems based on artificial intelligence, mixed-initiative dialogue is crucial. We discuss mixed-initiative interfaces in Section 18.4.

Mixed-initiative interaction is the idea of organizing interaction in dialogue where both the computer and the human can take initiative.

Code-switching refers to a switch in language to match the capabilities of the communication partner... Such differences are important because depending on the communication context, people will have different expectations and styles they use in dialogue with a computer.

Consistency: Are the same actions available, and do they have the same consequences across similar states? Dialogue length: How many turns are needed to get from the initial state to the end state? Number of choices: The number of options available to the user is a predictor of choice reaction time. Error recovery cost: If an error is made, how many turns are needed to recover from it? Connectedness: Can final states be reached from all initial states? Strong connectedness: Can final states be reached from all initial states via a particular action? Reversibility: Can the effect of a given action be reversed in one action?

An FSM is a tuple (Σ, S,s0, δ, F), where: • Σ is the input, that is, a finite set of symbols; • S is a finite set of states or modes; • s0 ∈ S is the initial state; • δ is the state transition function δ : S × Σ→S; • F is the set of final states, that is, a subset of S.

Gulf of evaluation: This gulf refers to knowing how a perceived change in the computer has moved it closer to the intended goal state.

Gulf of execution: This gulf is about knowing what to do to bring about a desired state change in the computer.

Code-switching refers to a switch in language to match the capabilities of the communication partner.

An FSM is a model of discrete computation applicable to dialogues. In computer science, an FSM is a special case of a Turing machine that reads but does not write on the tape.

A mode refers to the variation in the interpretation of a user's input according to an internal state. In a modeless dialogue, all inputs are possible in all states and their interpretation is always the same.

The key idea in the dialogue view of interaction is the organization of communication as a series of turns. Dialogue evolves through communication turns between two or more partners. In one turn, an appropriate communication act is made by one partner based on the communication context. The act aims to get the other partner to do or understand something. This understanding then forms the context within which the other partner takes their turn.

Dialogue is about the organization of communication as a series of turns between communication partners. The core elements of dialogue are communication turns, the communication context, and turn interpretation. Dialogue interaction includes speech-based and graphical interactions. Dialogue can be understood as computation, goal-directed action, communication, or embodied action.

Kirsh argued that we are not just passively reacting to computer-generated options. If we look at interaction at a higher level, beyond a single action, we see that users are also actively influencing their environments. Users are 'architects' of their environments, as Kirsh put it.

Kirsh points out that Norman's model makes an unrealistic assumption: The user is assumed to know the environment and its options and is merely picking an option. In practice, we do not always know what the options mean or even what options are available. Kirsh argued that users need to actively explore interfaces to become aware of the available functions and how they work.

Mixed-initiative interaction is the idea of organizing interaction in dialogue where both the computer and the human can take initiative. Unlike in the case of an FSM, the computing system can take action without a command from the user; the initiative is mixed.

Code-switching refers to a switch in language to match the capabilities of the communication partner.

Communication repair refers to the 'work of restoring shared understanding' when conversational partners misunderstand each other.

Robustness refers to the communication partners' ability to achieve shared understanding even in light of misunderstandings and other unanticipated troubles.

Human–machine interaction, according to Suchman, is similar to but different from human–human dialogue. It is similar in the sense that people pursue a shared understanding: They actively work to make themselves understood. It is different in the sense that the communication abilities of computers are limited, which requires humans to adapt.

FSMs are an effective way to describe how dialogue is structured; however, they are limited to memory-free dialogue.

An FSM is a model of discrete computation applicable to dialogues.

A mode refers to the variation in the interpretation of a user's input according to an internal state. In a modeless dialogue, all inputs are possible in all states and their interpretation is always the same.

Dialogue can be described using models of computation from computer science. Such models include finite state machines (FSMs), pushdown automata, and Petri nets.

Affordance, which we discussed in Chapter 3, refers to how well users can interpret what actions are possible with a widget. Visibility is a handy related concept in design that underlies direct manipulation interfaces.

Mapping and feedback are crucial concepts for understanding a computer's turn.

Gulf of evaluation: This gulf refers to knowing how a perceived change in the computer has moved it closer to the intended goal state.

Gulf of execution: This gulf is about knowing what to do to bring about a desired state change in the computer.

Norman offered two central concepts to help us understand these cognitive efforts: the gulf of execution and the gulf of evaluation. These two concepts describe inferential breakpoints for users seeking to express their intentions and interpret feedback from the system, respectively.

A significant early theory of dialogue interaction is the seven-stage model of Norman [600]. It considers interaction as goal-directed, turn-based dialogue.

both the computer and the user may have initiative. For example, a pop-up window can be presented to confirm a risky selection. When there is a misunderstanding about the context of the dialogue, errors may happen, and the partners must recover from them.

both the computer and the human participate in establishing a shared context. The computer does not simply receive a message; it also communicates the effects of that message. Therefore, the design of feedback, affordances, and cues is central to dialogue-based interaction.

in dialogue, acts of communication are conditional: The meaning of a turn depends on the communication context.

the concepts of dialogue are applicable across modalities.

The key idea in the dialogue view of interaction is the organization of communication as a series of turns. Dialogue evolves through communication turns between two or more partners. In one turn, an appropriate communication act is made by one partner based on the communication context.

Dialogue can be understood as computation, goal-directed action, communication, or embodied action. Each perspective provides specific methods for the analysis and design of dialogue.

Dialogue interaction includes speech-based and graphical interactions.

The core elements of dialogue are communication turns, the communication context, and turn interpretation.

Dialogue is about the organization of communication as a series of turns between communication partners.

The key idea in the dialogue view of interaction is the organization of communication as a series of turns. Dialogue evolves through communication turns between two or more partners. In one turn, an appropriate communication act is made by one partner based on the communication context. The act aims to get the other partner to do or understand something. This understanding then forms the context within which the other partner takes their turn.

Interaction may be viewed as a dialogue, that is, a conversation that occurs between two partners in a context for some purpose.

TAM posits that the intention to adopt a particular technology is driven by two kinds of perceptions: (1) how easy it is to use a system and (2) how useful it will be to use it [180]. Furthermore, the perceived ease of use affects the perceived usefulness: If technology is hard to use, it is less useful.

The theory of task–technology fit (TTF) can illuminate what users consider useful and how this affects their decision to adopt a particular technology. TTF refers to the ability of technology to support a task [197]. The capabilities of the technology should match the demands of the task and the skills of the individual; in this case, the fit is perfect.

One prominent definition of accessibility is given by ISO 9241-171, which defines it as 'the usability of a product, service, environment or facility by people with the widest range of capabilities.'

The second dimension, social acceptability, concerns whether interactions map well to the social norms and roles in the settings where they occur.

Acceptability has two main dimensions [591]. The first dimension, practical acceptability, includes costs, the reliability of the interactive system, and its compatibility with other systems. The perceptions of utility and usability may also influence the judgment of practical acceptability.

ISO 9241-11 definition... defines usability as the 'extent to which a system, product or service can be used by specified users to achieve specified goals with effectiveness, efficiency and satisfaction in a specified context of use.'

One shorthand way of expressing this is that utility is 'whether the functionality of a system in principle can do what is needed' [591, p. 25]. In practice, whether people can do anything concerns—among other things—usability.

The utility of an interactive system concerns its match with the tasks of users. If the match is good, the tool has high utility; if the tasks that users want to do are not supported by the tool, the tool has low utility.

Usability concerns how easily computer-based tools may be operated by users trying to accomplish a task. Usability differs from utility. Usability concerns whether users can use the product in a way that makes it possible to realize its utility; utility is about whether the goal is important to the user. Ideally, the user can use the tool without unnecessary effort so that the use is direct, transparent, and unnoticeable.

Usability is one of the best predictors of users' willingness to adopt software. For example, the User Burden Scale is a questionnaire for measuring the felt burden in software use [806]. It consists of six subscales: difficulty of use, physical burden, time and social burden, mental and emotional burden, privacy burden, and financial burden.

The move toward a local food economy is not just about freshness and food miles and carbon footprints and soil organic matter. It is all of those things, but it’s also about the deeply human desire for connection

However, self-attention alone is permutation-invariant, i.e., if we reorder the rows of X, then the mechanism has no built-in sense of which token came first. Since word order matters, we must inject positional information. We often add a position vector pt to the token embedding: h(0)_t = e(xt) + pt One classical choice for the positional encoding is called the sinusoidal positional encoding. pt[2k] = sin(t / 10000^{2k/d}), pt[2k+1] = cos(t / 10000^{2k/d}) The sinusoidal features give each position a distinct geometric signature across many frequencies. Nearby positions have related encodings while distant positions remain distinguishable. This lets the network reason about relative offsets.

For example, in control-theoretical analysis, we see the interaction as dynamically changing states.

For example, in interaction-as-rationality, courses of action emerge as a joint function of the user's goals and capabilities and the properties of the environment.

For example, interaction-as-tool-use focuses on this idea (Chapter 19). Tools change people and their activities; in turn, this changes the tools.

In the case of particle physics, the propositions that make up a theory may concern the nature and behavior of particles.

The basic assumption under-lying theories of rationality is that people choose how to act according to their benefit; in otherwords, they are rational.

For example, word predictionusage may not be beneficial if the word suggestions are poorly suited to the individual’s language orif the user can type words faster than the time required to scan and select among word suggestions.

The effect of such automation critically dependson how well its design appreciates the actor’s unique capabilities.

Text entry can also be seen as a task where different subtasks are shared between the human and the computer (Chapter 20).

One example is autocorrect, which automatically corrects typing errors while the user is typing. Another example is the use of word predictions, which allow the user to select a word from a set of word suggestions instead of typing out the word in full.

Tool use alsotriggers the concept of accessibility.

Text entry is also a good example of tool use (Chapter 19). A text entry method is a tool that allows the user to communicate with someone or something, typically other people or a service, using asynchronous text messages and longer documents.

When you enter a letter (a turn), a small pop-up appearsfor you to confirm your press (a turn). A word prediction list may show possible completions of theword. At every press, these are updated, over time forming a graphical dialogue between the userand the system.

The essence of dialogue is that communi-cation is organized in sequences of turns.

Viewing text entry as a control problem can providea more in-depth understanding of the human perceptual and motor control aspects of text entry,such as a user’s ability to touch individual letter keys on a touchscreen keyboard or a user’s abilityto perform a touchscreen gesture.

Interaction is understood as actions and reactions that minimize the discrepancybetween the present state and the goal state.

In text entry, the theory provides us with concepts andmetrics that aid our understanding of typing performance.

For example, the information rate ofa text entry method can be quantified using the concept of throughput from information theory.

First, text entry can be seen as the transmission of typed information to a computer.

Informationtheory provides a rigorous formalism to understand and quantify interaction via the concept ofpassing messages through a noisy channel.

Usability refers to the ease with which a tool is operated.

The explanatory power of a theory refers to the empirical accuracy and coverage of the explanations offered by the theory.

In structural determination, the end results of the interaction are jointly determined by multiple causes that make up the whole.

In statistical determination, there is a stochastic relationship between the two entities.

To conclude, Bunge’stypology is useful in understanding the landscape of HCI theories.

For example, in control-theoretical analysis, we see the interaction asdynamically changing states.

Each state dynamically leads to a new state depend-ing on the forces involved.

For example, ininteraction-as-rationality, courses of action emerge as a joint function of the user’s goals and capa-bilities and the properties of the environment.

In structural determination, the end results of theinteraction are jointly determined by multiple causes that make up the whole.

Here, the statistical model (regression) links the time it takes for a user toelicit a response to the design of the task environment (distance and width of buttons).

In statistical determination, there is a stochastic relationship between the two entities.

The pressing of a button would count as a mechanistic determination.

According to Bunge, causal determination is only one of the forms of causal relationships usedin scientific theories.

What happens in interaction is mutually determined by the human and the computer. In other words, what happens in interaction cannot be attributed solely to the human or the computer—the two must be considered together.

However, such a description does not count as a theory ofinteraction because it does not link the effect back to the cause. It is silent on how the design ofthe button affects its pressing.

The theory starts with a high-level statement: The motorsystem is a limited-capacity channel. From there, it derives propositions about the relationshipbetween performance and interface design through the construct of a target.

"Average movement time can be predicted as linear regression to the index of difficulty."

"The difficulty of selecting a target is proportional to its distance and inversely proportional to its width (index of difficulty)."

"If the user tries to increase speed, accuracy will be compromised, and vice versa: An increase in accuracy reduces speed."

“Attempts at reaching a target are limited by the speed and variance (accuracy) of themovement involved.”

In the case of particle physics, the propositions that make up a theory may con-cern the nature and behavior of particles.

A proposition is a claim about the world.

By now, it should be clear that the term interaction covers a lot of ground in human–computerinteraction (HCI).

Phenomena in interaction are emergent, that is, they are not attributable to the user or to the computer alone.

Interaction is a dynamic phenomenon that unfolds over time as users and computers influence each other.

What happens in interaction cannot be attributed solely to the human or the computer—the two must be considered together.

Populations and Samples In statistics, we generally aim to study a population. You can think of a population as a collection of people, things, or objects under study. To investigate the population, we select a sample. Sampling involves selecting a portion (or subset) of the larger population and studying that portion (the sample) to gain information about the whole population. Data are the results obtained from sampling a population. Because it often requires a great deal of time and money to examine an entire population, sampling is a highly practical technique. For example, if you wanted to compute the overall grade point average (GPA) at your school, it would be reasonable to select a sample of students. The data collected from the sample would be those students' GPAs. In presidential elections, opinion polls typically sample 1,000–2,000 people. These polls are meant to represent the views of the entire country. Manufacturers of canned carbonated drinks take samples to verify that a 16-ounce can actually contains 16 ounces of the b

We encounter and use data in our everyday lives. In this chapter, you will learn how to organize and summarize data. Organizing and summarizing data is known as descriptive statistics. Two common ways to summarize data are by graphing and by using numbers (for example, calculating an average). After studying probability and probability distributions, we can use formal methods to draw conclusions from reliable data. These formal methods are called inferential statistics. Statistical inference uses probability to determine how confident we can be in the conclusions we draw

And it will turn out that the scope and limits of what we can know where the micro-world is concerned parallel the scope and limits of what Thomism says we can know by reason alone about the existence and nature of God.

Example of a Research Process A successful research process should go through these steps: Decide on the topic. Narrow the topic in order to narrow search parameters. Consider a question that your research will address. Generate sub-questions from your main question. Determine what kind of sources are best for your argument. Create a bibliography as you gather and reference sources.

phototropins can dynamically relocalize, showing partial redistribution to the cytosol or to distinct membrane subdomains

new functions

vesicle-mediated intracellular trafficking

eyespot

Types are themselves typed objects, the type of atype will be a special constant called a sort. There is at least one sort called Type. Different PTSdepend on the set of sorts we start with (each sort corresponds to a certain universe of objects)and also which products can be done (in which universes).

Actions are judged on the sum total of their consequences (utility calculus)

Actions are judged on the sum total of their consequences (utility calculus)

Ethics Frameworks Don’t Guarantee Moral Goodness

Being and becoming an exemplary person (e.g., benevolent; sincere; honoring and sacrificing to ancestors; respectful to parents, elders and authorities, taking care of children and the young; generous to family and others). These traits are often performed and achieved through ceremonies and rituals (including sacrificing to ancestors, music, and tea drinking), resulting in a harmonious society.

Hast ever seen an eagle chain’d to earth? A restless panther in his cage immured? A swift trout by the wily fisher checked? A wild bird hopeless strain its broken wing

A poison’d sting in every social joy, A thorn that rankles in the writhing flesh, A drop of gall in each domestic sweet, An irritating petty misery, That I can never look on one I love, And speak the fullness of my burning thoughts?

4

Conclusions

Superficial thrombophlebitis may occur spontaneously, often in pregnant or postpartum women or in individuals with varicose veins, or it may be associated with trauma, as with a blow to the leg or following intravenous therapy with irritating solutions. It also may be a manifestation of systemic hypercoagulability from abdominal cancer such as carcinoma of the pancreas

A Visa credit card company charges a 1.5% simple interest finance charge each month on the unpaid balance. If Martha owed $2,350 and has not paid her bill for three months, how much does she owe now? Solution Before we attempt the problem, the reader should note that in this problem the rate of finance charge is given per month and not per year. The total amount Martha owes is the previous unpaid balance plus the finance charge. A=$⁢2,350+$⁢2,350⁢(0.015)⁢(3)=$⁢2,350+$⁢105.75=$⁢2,455.75 Alternatively, we can compute the amount directly by using formula A=P⁢(1+r⁢t)

Why did so many people see it?

the statements an observer can make about the universe are divided into at least three groups: those that we can judge to be true, those that we can judge to be false and those whose truth we cannot decide upon at the present time"

constructive proofs in analysis may ensure witness extraction, in such a way that working within the constraints of the constructive methods may make finding witnesses to theories easier than using classical methods.

Angel financing often occurs at such an early stage in the business that it is difficult to assess a value for the firm. Angel investors often circumvent this problem by holding a convertible note

To an intuitionist, the claim that an object with certain properties exists is a claim that an object with those properties can be constructed. Any mathematical object is considered to be a product of a construction of a mind, and therefore, the existence of an object is equivalent to the possibility of its construction.

Mundini

For these dangerous and divisive elements the legislation proposed in the Race Relations Bill is the very45 pabulum they need to flourish. Here is the means of showing that the immigrant communities can organise toconsolidate their members, to agitate and campaign against their fellow citizens, and to overawe and dominate therest with the legal weapons which the ignorant and the ill-informed have provided

The cloud no bigger than a man's hand, thatcan so rapidly overcast the sky, has been visible recently in Wolverhampton and has shown signs of spreadingquickly. The words I am about to use, verbatim as they appeared in the local press on 17 February, are not mine,but those of a Labour Member of Parliament who is a minister in the present government: 'The Sikh communities'campaign to maintain customs inappropriate in Britain2 is much to be regretted

They found their wives unable to obtain hospital beds in childbirth, their children unable to obtain schoolplaces, their homes and neighbourhoods changed beyond recognition, their plans and prospects for the futuredefeated; at work they found that employers hesitated to apply to the immigrant worker the standards of disciplineand competence required of the native-born worker; they began to hear, as time went by, more and more voices25 which told them that they were now the unwanted.

Nothing is more misleading than comparison between the Commonwealth immigrant in Britain and theAmerican Negro. The Negro population of the United States, which was already in existence before the UnitedStates became a nation, started literally as slaves and were later given the franchise and other rights of citizenship,to the exercise of which they have only gradually and still incompletely come. The Commonwealth immigrantcame to Britain as a full citizen, to a country which knew no discrimination between one citizen and another, and15 he entered instantly into the possession of the rights of every citizen, from the vote to free treatment under theNational Health Service.

In 15 or 20 years, on present trends, there will be in this country three and a half million Commonwealthimmigrants and their descendants. That is not my figure. That is the official figure given to parliament by thespokesman of the Registrar General's Office.

A week or two ago I fell into conversation with a constituent, a middle-aged, quite ordinary working manemployed in one of our nationalised industries. After a sentence or two about the weather, he suddenly said: "If Ihad the money to go, I wouldn't stay in this country." I made some deprecatory reply to the effect that even thisgovernment wouldn't last for ever; but he took no notice, and continued: "I have three children, all of them beenthrough grammar school and two of them married now, with family. I shan't be satisfied till I have seen them all5 settled overseas. In this country in 15 or 20 years' time the black man will have the whip hand over the white man."