Mathematical Intelligence

K.I.T.T. AI driven vehicle from Knight Rider TV Series. Photo Credit: Wikimedia Commons

One of the main problems in AI can be the lack of a mathematical definition of intelligence. The concept of intelligence is not related to optimization. Optimization is usually an automatic process based on mathematical algorithms. With the development of artificial intelligence we have found a link between them, however, this must be researched a little more.

The very first attempts to introduce intelligence in control systems were done through logic algorithms. Logic can be expressed in mathematical functions and then, logical reasoning can be considered a mathematical one.

It is true that AI algorithms can be used to solve some problems of optimization: however, they cannot provide an exact solution in mathematical terms for many problems.

As artificial intelligence has evolved from automation, we usually look at intelligence as a process of automation. But if we look in deeper, we can find that the process of intelligence usually tries to escape from automation algorithms. AI in control systems has been mostly used to provide supervisory control. I am going to put an example in order to illustrate this concept.

Imagine a mobile robot or a car driven by AI. The optimal route from a point A to a point B is a straight line. We do not need AI in order to make that the device reaches the point B. AI is required when we cannot define the optimal route. If there is an obstacle in route of the mobile robot, it must change the automatic calculation in order to describe a new path. The intelligence of the device lets to escape from the optimal path because it can incorporate new information from the environment.

Intelligence is not the capability to solve formal problems only but the capability to adapt itself to different scenarios too. In this point, we can link intelligence with complexity. A complicated system has a lot of interconnected parts and its state is deterministic. A complex system has a lot of interconnected parts and its state have a certain degree of uncertainty.

To consider that intelligence is logical reasoning is to focus it on the support of the analysis of complicated systems; however, complex systems require more things than logical reasoning.

These problems arose in the early days of artificial intelligence. The answer for the analysis of uncertainty was the definition of new logic, known as fuzzy logic, that lets to provide a single solution for a problem where state variables are under uncertainty. Tools like experts systems were adapted to use of fuzzy logic.

Complex systems are characterized because they can change sharply their behavior under unexpected events. Intelligence offers solutions to those changes trying to preserve the system under control. In the example of the mobile robot, AI would calculate a new path to the point B after the detection of an unexpected obstacle in the way. In this case, AI is not optimizing the path but abandoning it after the unexpected event. The system is, then, under control because it is following a new path although it cannot follow the previously defined one. On the other hand, a probabilistic system would have calculated the initial path considering the probability of finding an obstacle in the way but this probability is impossible of knowing in most situations.

This concept can be very important when we are using big data to determine the behavior of a system. We use big data in order to define probabilities that can be incorporated to the algorithms. We are assuming that we can avoid any unexpected event increasing the amount of information, what is very vain as I am going to explain now.

When we play the dice, we assume that the probability of getting a certain result is 1/6 because we assume that it was perfect and homogeneously constructed from a physical viewpoint. If we accept that it was not perfectly built, we can use the big data. Once it has been thrown out many times, we can get different probabilities from the historic data that would adjust to its defects. But it does not provide information about a new dice. We cannot define a probability for the new dice, only the possible results without a probability for any of them. The result must be seen as uncertainty instead of risk.

Intelligence is a way to cope with complex systems and environments. Great geniuses of science have been people that have been able look at certain problems in a way far from the mean. Intelligence never has been a matter of statistics calculation but a matter of changing models of analysis. It has been related to the enlargement of the system domain to provide more general solutions and to apply it to a particular one. It is a matter of better identification of problems instead of simple logical or probabilistic reasoning. Perhaps, complexity analysis can provide a good starting point to produce new AI algorithms from a mathematical viewpoint.


Artificial Intelligence and moral

Humanoid Robot. Photo Credit: Public Domain

There are many people worried about AI however there are few people worried about human stupidity. This is a sign of the decadence of our societies, although there is a simple explanation. Stupidity is something natural that surrounds us from our birth. We have learnt to cope with stupidity however; many people are not trained to cope with intelligence.

I always say that stupidity is worse than evilness because the evil know their limits but the stupid do not. In terms of risk analysis evilness is under control, however, stupidity is uncontrollable. Following this concept, from a political viewpoint the establishment of high moral standards without the establishment of high education standards for people with power is something useless.

When common people think about AI, they are confusing intelligence with evilness. Evilness is a moral affair but intelligence is not. For the great philosophers like Kant reason and moral are intellectual abilities. Kant explains that there are many things that cannot be known through pure reason however we can made a lot of things like moral judgements because our nature need of them, although we cannot define them like absolute truths.

From an industrial viewpoint, AI is interesting in order to provide reason for a machine, in order that it can improve the effectiveness and the efficiency of any decision-making process. This is related to the Kantian concept of pure reason, and it is very far from the Kantian concept of moral.

Kant was the first philosopher that tried to establish the limits of reasoning. As reasoning has limits, it is possible to keep it under control and, AI is not related to moral because moral is out of the domain of reason.

In this point, detractors of AI would say that it is its problem but it is not the real problem. In the same way as human nature requires moral judgements that are not provided by the pure reason, we could program and provide moral judgements for AI devices out of the reasoning engine. Any AI would have the moral that we program for it. Again the problem about the moral of any AI is related to the moral judgement of their programmers. An example of this could be the three laws of robotics by Asimov. Moral establishes principles of behavior that are applied in front any decision of action in order to get a moral judgement to define the action as good or bad. But this would be out of any pure reasoning process. The problem that arises here is who has to define the moral for robotics because what is good for a person can be bad for another one.

This conceptual scheme is easily understood for the traditional implementation of AI under logic algorithms, however, it is more difficult to implement in other kind of AI based on neural nets, for instance. Conceptually, we would need to train the neural net to learn the operational function and to learn the moral one.

In the film “I, robot” Will Smith’s character hates robots because one of them decided through probabilities to save him instead of another person. The question here is: Would he hate humans if a man decided to save him because he was a public servant and the other person not, for instance, deciding through a political prejudice? Of course, he as a policeman was prepared in order to give his life to save other people and in both cases it would not be considered.

A vision of the AI brain

Drawings by Santiago Ramón y Cajal, taken from the book “Comparative study of the sensory areas of the human cortex”. Photo Credit: Public Domain

The language is very important in terms of solving logical problems, because it is the support of our reasoning. When we are working with people from different countries sometimes the use of some words does not produce a totally precise translation. For instance, in Spanish language the official meaning of the word intelligence can be both “the capability for solving problems” and “the capability for understanding”. Oxford learner’s dictionary defines the word intelligence as “the ability to learn, understand and think in a logical way about things; the ability to do this well”. Both concepts are similar however the latter term is more related to logic and the former one is more related to action. Languages are developed during a lot of years by a society in a certain environment under certain circumstances. Looking at these definitions, for the Englishman, intelligence lets us to understand the world, and for the Spaniard, it lets us to change it.

This different precision about the meaning a word can have influence in all aspects of the culture in general, and in the scientific and technological one in particular. The English concept is adequate for supporting science and the Spanish one for supporting Engineering.

This fact is more important in the field of Artificial Intelligence. In this case the RAE’s Spanish Official Dictionary defines Artificial Intelligence as a “scientific discipline concerned with creating computer software running operations similar to those ones made by the human mind as learning or logical reasoning”, and Oxford learner’s dictionary defines it as “an area of study concerned with making computers copy intelligent human behavior”. Again we can find slightly differences, the Spanish definition is problem centered (the design of software running certain tasks) and the English one is description centered (human behavior).

These conceptual differences can drive to different focuses to the development of AI. An engineering vision would try to make advances in the development of pieces of software that can solve practical problems themselves through the use of some kind of learning ability and logical algorithms. A scientific vision would try to understand how the human brain is working and how its behavior can be emulated.

These two approaches have been followed for many years providing their own results. Initial successes of AI were provided by software tools far from human brain as expert systems; however, more recent advances as deep learning are more bio-inspired.

A conventional electronic system is not usually considered as AI, because, from a conceptual viewpoint there are differences between learning and memory. A typical computer has memory, but memory itself does not imply learning.

For an electronic engineer, the memory is a device that can store or reload the state of the registers of a microprocessor in a certain instant of time. A piece of software controls how the microprocessor uses the internal registers and the memory. This one can be used to store the state of a system in a certain instant of time. A memory that stores only the state of a system in an instant of time is useless as an intelligent device because we cannot make predictions about the future with a single piece of data. In order to anticipate the future to solve any problem, mathematical scientists use extrapolation techniques. The simpler technique, the linear one would require at least two points in the past in order to anticipate the future. We do not need only have memory. We need to have stored historical data in order to drive any intelligent action. Any electronic system that only analyzes a single instant state to make an assumption instead of a longer historical evolution cannot be considered intelligent from a mathematical (scientific) viewpoint. The current interest on big data is related to this. We are assuming that the larger the information stored the better the extrapolation about the future that we can do. This concept is not only time related but space related too. The higher the dimension of the space of characteristics is, the better the extrapolation about the future state is. An intelligent system can improve its performance with the size of the memory. This is a good reason why the size of the brain is related to the intelligence of species. A greater brain can store and process more data although intelligence is not only memory.

Another important property of any intelligent system is feedback. Any intelligent system trying to solve problems must have a metric to analyze its performance to accomplish the problem. In mathematics when a mathematician proposes a hypothesis as true and finally he reaches an absurd conclusion, it can assure that the initial hypothesis was false. Any decision-making system that proposes a solution through extrapolation needs to analyze if it is getting closer to the solution and in other case the system should learn from it and change.

An important characteristic of the human brain is its plasticity, and its ability to learn and change. That is the reason why the use of bio-inspired techniques provides good results as practical systems solving problems and the scientific approach to AI must never be forgotten.

AI Based Economy

Reproduction of Maria of the film Metropolis at the Science Museum. Photo Credit: Jeremy Tarling

One of the main challenges of our time is the development of new applications with smart machines. We are expecting a revolution in many industries due to the use of artificial intelligence in business processes. In fact, some experts are advancing that many businesses would change hugely due to the incorporation of this new technology.

This process of change has begun yet. Many large companies have introduced the use of bots for many tasks, from customer support to decision making related to financial investments.

Technology changes are common in any civilization; however, in this case, there is something different. Most technology changes have been related to the support of brute force, reducing the physical effort of humans in production activities, and most recent changes have been related to the simplifications of bureaucratic processes through IT technology, however, AI is substituting humans in tasks that require decision making. AI is driven to managing activities at higher or lower degree.

The aim of moving workers from physical activities to managing ones is well seen by most people, however, from managing activities workers will be moved to… what?

The answer to this question is easy. In an economy dominated by AI, human workers are required for creative tasks and leisure related tasks. Design, innovation, research and development would be incremented. Marketing and fashion would drive the consumption. People will move from manage the production of goods and services to manage the change itself. Changes in technologies and in the promoted goods would be commoner due to both technology changes and fashion changes.

We can expect that the world will change in order to provide a different kind of society where people would be dedicated to humanities, politics and science. This one should be a better society were people would be dedicated to study, training, research, commerce, interpersonal relationships, sports and leisure.

The complexity of technology would provide a competitive advantage for large organizations that it would be tried to be preserved. In this scenario, as the control of the production would be under AI software, the control of economy could be under people controlling that AI software. Many markets could be under the control of AI developers, however, many others that depends more on people preferences and fashion would be under people controlling the mass media as usual.

More people with higher education would drive to more democratic societies, demanding better governance in their states.

This scenario, that seems to be a paradise, has got its own risks. First of all, it would be necessary to manage that process, in order to provide a smooth transition between current economy and future one, avoiding social conflicts that are common in process of change. It will be very important for the rulers to know the limits of these technologies and the probable effects on the society. On the other hand, there will be other risks related to the triumph of technology. For instance, humans can feel comfortable in such kind of society stopping their impulse to improvement. In that case, the society would stop its evolution. The feeling of power that mankind has got over the societies it has created could disappear, because the demand of a single person would not fight against an automated machine in the same way that it cannot fight against bureaucracy. In full automated society but bad designed from an economic and social viewpoint there could not be room for many human impulses and people cannot exist opposite to their own nature.

Many people are advancing that AI will suppose a revolution but it is important to notice that history has shown us that not all the revolutions will produce a better society. It depends on how revolutionary leaders act later.

Cybersecurity: A Little Introduction

Logo of WarGames Film produced by Universal Artists

Internet was built in order to provide full access from anywhere. When DARPA funded the development of internet, it was trying to assure that the destruction of a centralized computing center would never avoid a fast response to a nuclear attack from the enemy. Those engineers were searching for a network configuration that could provide fast reconfiguration. TCP/IP protocols were born in this way. The TELNET standard was created in order to have a direct link to remote computer as if the operator was in front of the mainframe. However, nowadays, the port 23 is usually blocked by most firewalls.

TELNET protocol is not commonly used due to its lack of encryption. Different protocols were developed later as SSH. More complex and secure protocols can be used instead. On the other hand, text terminals are a reminiscence of the past, now people use graphic interfaces instead. Sometimes it is interesting to review the history in order to understand which one is the true aim of many things before criticizing them.

Modern people consider computer security as a defense tool; however, remote access was conceived as a defense tool. From a military viewpoint, connectivity, instead of firewalling, is a defense tool in a nuclear world. A firewall is similar to a company of soldiers defending a nuclear silo. It is not defending directly our lives but protecting a deterrence weapon.

This discussion is very interesting because in the civil world we are very worried due to data hacking; however, we do not care about the effects of a lack of connectivity. Modern societies have usually got a lot of people in the streets demanding more security; however, security is provided by connectivity and the access to information. For instance, a piece of fake news is not a problem by itself. The problem of fake news is that corrupted or manipulated information is equivalent to unavailable information. Democracy resides on proper information for voters. Majorities can never be owners of the truth if they have not a proper access to the full real information. In a competitive world deception is used many times to increase the competitiveness, and information analysis instead of direct assumptions is required to assure that managers are making the best decisions. In a business, management, data analysis and decision making techniques are required in order to drive a company. The complexity of problems and the competitive environment produce that better decisions are made by experts instead of a majority of employees.

The higher the number of people accessing to computer system the higher the probability that information can be hacked and got illegally or corrupted. Limiting the access to information we are increasing the security of the system, but we are limiting its functionality. Encrypted access to computer systems introduces an additional advantage: Encrypted communications are less hackable and they can provide a way of authentication of the identity of the user better than a simple password. The use of encryption systems lets to increase the number of users without a huge increase of the probability of hacking. Connectivity can be preserved through encryption systems because it makes more difficult the hackers’ activity, but the cost of the computer system and its maintenance is higher and it requires specialized personnel with higher qualifications.