How do facts in science differ from opinions

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Like evolution. Or gravity. But at no point have we proved anything. The scientific method is totally awesome. It is unparalleled in its ability to get answers that can help us extend life, optimize output, and understand our own brains. Scientists slowly break down the illusions created by our biased human perception, revealing what the universe actually looks like.

In an incremental progress, each study adds a tiny bit of insight to our understanding. But while the magic of science should make our eyes twinkle with excitement, we can still argue that the findings from every scientific experiment ever conducted are wrong, almost by necessity.

They are just a bit more right hopefully than preceding studies. The status quo is never good enough. Scientists want to know more, always. And, lucky for them, there is always more to know.

You need just to look back through history to see the different iterations of facts to make this insight seem obvious. Aristotle thought that the heart was the home of intelligence, and believed that the brain was a cooling mechanism for it. These changes occur after opinion transactions have taken place, defining a slow time scale for the network evolution. Hence we can write, 3 where means the set of nodes that are steps away from node , and is the number of steps needed to reach its most distant neighbours.

Note that this quantity is different for each agent, since it depends on the local topology of the network. The second term on the right-hand side of Eq. These are considered as reasonable assumptions based on simple social interactions. The last term on the right-hand side of Eq.

Note that in Eq. Thus the variables of totally convinced agents are set to the corresponding extreme value attained and their dynamics stopped. These agents cannot modify their state in subsequent times, but they are still linked to the network and taken into account in the dynamical evolution of the undecided agents. In this sense such limit values can be interpreted as final states of irrevocable decision. The rewiring scheme involves cutting certain links and creating new ones, as explained in detail in [18].

At the time of cutting an agent preferentially breaks its link with agent if there is large disagreement, as quantified by. Explicitly, its neighbours are chosen in decreasing order of the opinion difference for. Then the agent creates the same number of new links based on either of two link-formation mechanisms known as triadic and focal closure [19]. Like in the cutting procedure, new links are created in decreasing order of the opinion similarities and for ,.

In the rewiring scheme used here, agents can create links using these two mechanisms at will. In order to control the proportion between focal and triadic closure events we introduce a quantity , which can be used as a stochastic decision parameter for each event. In other words, before creating new links an agent chooses a random number from a uniform distribution, and then uses the focal closure mechanism if or otherwise the triadic closure mechanism.

Note that focal closure was not considered in [18] , [20] for the sake of clarity, since in the absence of an external field opinion formation is practically dominated by close interactions with neighbouring agents.

This might not be the case when the important feature is the external information given to all agents in the network, thus we will investigate the role of here. In order to apply this model to our present situation we need to reinterpret the meaning of and give a reasonable form for the external field representing the information given to the social group. We interpret as expert knowledge, only attained by learned individuals in the field of science of the question or issue.

On the other hand ignorance is represented by a very small magnitude , whereas describes people inclined to disagree with the sound scientific information or agree with unsound concepts, e. Total opposition to scientific truth corresponds to and we shall refer to such agents as fundamentalists from now on, since their attitude against new scientific evidence only reinforces their beliefs and instead of learning, they are stubbornly defending their position against. As the external scientific information is represented by the field in Eq.

The way this information is perceived by a particular agent should then be asymmetric, in the sense that it should help agents to learn and agree with the scientific truth. The simplest way to appropriately break the symmetry is by the linear expression, 5 where is a constant strength representing the raw external information given to everybody in the network, and the term in brackets reflects an instantaneous personal reaction to the field.

Observe that agents with positive are less affected by this term, while the ignorant and fundamentalist agents are very much in conflict with the field, either positive or negative. This mimics the fact that superstitious people are in general more prepared to believe anything without proof, and change their position with ease.

We have also tested quadratic and cubic expressions for the field and the qualitative behaviour of the model remains unchanged, although its analytic treatment becomes unnecessarily complicated.

Thus, we have opted for the simpler term in Eq. It should be noted that the effect of the attitude parameter is not directly affecting the response to the field, but it becomes extremely important when the third term in Eq.

In what follows we exhibit numerical results for this model. We have performed extensive numerical calculations using the model described above.

We first adjusted its parameters to produce the results already presented in [18] , [20] , where opinions and network evolve in the absence of an external field. We initialized the system to a random network configuration of nodes and average degree , and kept it so for all calculations.

We have tried networks of various sizes, and found that the effects of size scale exactly in the same way as the original model without field [18]. Accordingly, we fixed a set of random values for the individual attitudes from a uniform distribution with center and unit half-width, and chose the initial values of the state variables from a Gaussian distribution with zero mean, unit standard deviation and cut-off at.

With this set of parameter values the network splits in communities sharing the same opinion for , where is approximated by a time step of size.

In order to eliminate the effect of randomness in the calculations we start by setting , i. In this way we avoid the need for making averages and thus probe the sole effect of the field on the system by keeping the initial conditions fixed. In Fig. The right and left columns correspond to positive and negative field respectively and for the parameter values described above, as the magnitude of the field is increased.

Asymptotically stationary state of the dynamics for chosen initial conditions and parameters, as described in the text. Decided agents are represented by red or blue circles, and undecided agents by yellow or black squares. The right left column corresponds to positive negative field of increasing magnitude. All calculations were done with , i. The visualisation shows the basic asymmetry of the model: for stronger negative field the community structure is quickly lost and there is an asymptotic growth towards negative consensus, while for growing positive field fundamentalists linger in well-connected communities and ignorants slow down the drive towards positive consensus.

These results show interesting effects of the external field on the configuration of the network. First of all, the ratio between the number of experts and fundamentalists grows for positive field and diminishes for negative field, as expected, but their distribution in the system is not symmetric. This means that for growing positive field quite a few fundamentalists linger in several groups, and all eventually join in a single community that is much more interconnected than the communities of experts.

On the other hand, when a negative field grows in magnitude, i. In terms of the public perception of a concept promoted by raw external information , this implies that scientifically sound concepts associated with require a larger field magnitude to create opinion consensus in the network than concepts not validated by science i.

This surprising effect is in agreement with the behaviour of some real social networks for example, creationists are well organized in very interconnected communities [31]. Furthermore, Fig. These undecided agents some of them fundamentalists for a weaker positive field are forced by the large magnitude of to have the expert opinion but continually resist to do so.

Such undecided agents have small values i. In this sense the ignorants act as bridges between the tight fundamentalist community and the well-informed people.

In order to analyse the relationship between opinion and attitude in our model systems, we look at the ensemble averages and classify the agents into groups denoted by. Here the labels take the symbolical values for experts, ignorants with positive opinion, ignorants with negative opinion, and fundamentalists, respectively, and for attitude parameter and. Here the thin lines are drawn to distinguish all eight possible groups by value of and , while thick lines are drawn to separate the contributions of experts, ignorants and fundamentalists.

It is clear that a negative external field produces roughly symmetrical attitude distributions in groups of decided agents, a steady asymptotic growth to negative consensus, and a total lack of undecided agents.

On the other hand, for growing positive field it turns out that experts have mainly positive attitude, all fundamentalists have negative attitude, and there is a large amount of ignorants. Thin lines separate groups and thick lines divide the contributions of experts, ignorants and fundamentalists. Numerical results are shown as dots, while the corresponding analytical approximations are depicted as lines. The continuous line depicts the analytical approximation of its mean value over all agents.

All numerical calculations are averaged over realisations of the dynamics with. The asymmetry due to the external field is even more evident in the actual topology of the system. In this case we have a similar normalisation condition,.

The symmetry in attitude sign for negative field is also seen in the left part of Fig. Moreover, the fundamentalist community found for low has many connections when compared to its size. In addition to the simulations, considerable insight into the behaviour of the coupled dynamics of opinion and network structure can be gained with a relatively simple yet analytical mean-field approach, described in detail in section Materials and Methods.

It turns out that Eq. As shown in Fig. For increasing positive field the eigenvalue changes sign at a critical value , signalling a transition to a state where an attractive fixed point hinders most agents from attaining extreme values of opinion. As grows moves once again towards , implying positive consensus in the limit of infinite field. As seen in Fig. This is signalling a very slow transition to positive consensus as the positive field is increased.

We now turn to explore the changes introduced by varying the parameter from zero to one, measuring the relative amount of focal closure instead of triadic closure mechanisms used by agents in the network rewiring process. The effect of in the final state of the opinion dynamics is illustrated in Fig. We used the same set of initial conditions and parameters as in Fig. The main difference with the case is due to the fact that when grows it is easier for agents to find someone to create a new link with, resulting in a systematic loss of heterogeneous structure.

Indeed, for and as is increased communities of the same opinion quickly merge, the average degree in the network and the number of connections between the two remaining clusters grow, and the number of ignorants decreases. Asymptotically stationary state of the dynamics for the same initial conditions and parameters as in Fig. The left and right columns correspond to , respectively, as the parameter is varied from zero to one. An increasing amount of focal closure events results in a systematic loss of heterogeneous structure in the network, higher degree, and decreasing amount of ignorants.

There are several qualitative properties of the system that hold for all values of. First, the number of experts for positive field is always smaller than the number of fundamentalists for negative field of the same magnitude. One could infer from this that a true scientifically sound concept is more difficult to acquire than a wrong concept without scientific content.

Third, the communities of fundamentalists for positive field are more tightly connected than the corresponding groups of experts for negative field of the same magnitude, or in other words, disagreeing individuals are more sparsely distributed in the network for than for.

Finally, the undecided agents for positive field surround the largest cluster of experts and serve as bridges to the fundamentalist community. To further validate these results and take into account the relationship between opinion and attitude, we again perform averages over the relevant random initial conditions and parameters. Here we see that the number of undecided individuals gets minimized around.

This particular ratio between focal and triadic closure mechanisms optimizes the presence of experts for , although there is a persistent group of ignorants with both negative opinion and attitude constituting roughly of the network. Relative group size for experts, ignorants and fundamentalists a , relative group contribution to the average degree of the network b , eigenvalue associated with Eq. All calculations are averaged over realisations of the dynamics.

Non-zero values of the rewiring parameter retain the qualitative picture of the case shown in Fig. The minimum in the number of ignorant agents also shows in the relative group contributions to the average degree of the network, as shown in Fig. The fundamentalist group found in the region grows with , has mainly agents with negative attitude and a relatively high amount of connections and triangles.

Quite surprisingly, the average clustering coefficient of the network not shown here does not diminish when , but increases. This happens in spite of the fact that focal closure is not an explicit mechanism for the formation of triangles. Finally, in Fig. Incidentally, this also happens for and thus coincides with the minimum in the number of ignorants after the phase change has taken place. In the next section we will discuss and interpret these results in the light of social behaviour, by adjusting the field strength with the help of actual data extracted from extensive polls made in Mexico and Europe.

Surveys and polls do not exactly reflect public opinion, but at least they provide some measure of the public perception about the subjects under investigation. The reasons for the inaccuracies are many, not the least how the survey was conducted including what was asked and how the questionnaire was designed.

Most surveys could be regarded as snapshots of society without dynamical information. The survey carried out by the National Science Foundation [34] is an exception, where the data has been integrated from to Furthermore, it is difficult to follow the time development of opinion, as there has been a shift from measuring mostly literacy to matters concerning science and society [35] , i.

It is quite common that the results of the survey are presented by giving percentages of the responses of the population to a few answering-options in the questionnaire, without further details on the topology of the underlying social network and of possible relations between its individuals.

This lack of detail about social structure is unfortunate, since as evident from above our model could give very rich information about how society is organized and functioning. Here we will use two different surveys: the well-known Eurobarometer EU [36] and a Mexican survey Mx [37]. The Mexican Consejo Nacional de Ciencia y Tecnologa has carried out surveys on science and technology perception every two years, starting from Although the Mx survey follows the methodology of the EU survey, the multiple-choice answers are different.