A meaningful answer to the question whether science could be different requires that we specify what we mean by science. For a trivial way to identify a different type of science is to simply shift the meaning of the word.
Today, most popular definitions of science are highly inclusive. We use the name “science” for mathematics, physics, chemistry, biology, but we also talk about social sciences, behavioral sciences, and every now and then, new disciplines appear in academia that hasten to add the word “science” to their name. This inclusiveness is possible because many people prefer to define science on the basis of methodology, that is, a discipline is called scientific if it follows the “scientific method”.
Contrast this with the attitude expressed by Ernest Rutherford: “All science is either physics or stamp collecting” [1]. Rutherford invokes a deep fissure between physics and the other empirical sciences. (Rutherford did not refer to the formal sciences, such as mathematics and logic). Ever since Newton’s day, physics is based on fundamental theories of universal validity. That is, they form logically coherent systems, they admit no exceptions in their domain of validity, and they use mathematical reasoning in order to provide unambiguous predictions of astonishingly high accuracy. The other bodies of knowledge are, according to Rutherford, akin to stamp collecting, not because they are inferior in their subject matter, but because they lack fundamental theories of universal validity. They proceed by the collection of disparate facts, and they try to connect them through phenomenological laws that often admit many exceptions, and they cannot be brought into a logically coherent framework, unless that framework is based on or reduced to physics.
While Rutherford refrained from stripping the designation of science from “stamp collecting” disciplines, it is easy to imagine a culture that takes this extra step. The current inclusive charac terization of science is a consequence of historical contingency. It is an aspect of the professional identity of the academia, and this identity was formed because of the current central role of univer sities in the production and dissemination of knowledge. There is no historical necessity—perhaps not even an economic one—why universities should have taken up the responsibility of training an increasingly large fraction of the workforce, as they did during the twentieth century. We can imagine an alternate development, in which professional training was allocated to organizations of various types and names (schools, academies, institutes, study centers, and so on), with no connec tion to the traditions of the nineteenth-century European university. Some scenarios would involve a highly segregated academia, in which disciplines are ranked according to Rutherford’s criteria, each rank assigned to institutions of different name, and the prestigious designation of “science” only given to the top rank.
Shifting the boundary between science and non-science is a simple way of answering this es say’s question. But it is also uninformative. Differences in name and in prestige do not a genuinely alternate science make. For this reason, and for the purposes of this essay, we will adopt a very exclusive definition of science, for which such boundary shifts are impossible. We will focus only on disciplines that Rutherford would place in the same part of the divide as physics; as of 2023, this includes only physics, disciplines that are explicitly reducible to physics, such as chemistry, and the formal sciences.
Another way to trivialize the essay question is to refute that science leads to objective truths. This would mean that all products of scientific endeavor are culture-relative. Then, scientific facts can be no more than stamp-collecting, the mathematical structures of physics are simply organiza tional patterns, and physical theories are akin to stories philatelists say about their stamps. Hence, fundamental science is nothing but a genre of literature. It is doubtful that such a viewpoint can pass through logical scrutiny, but, certainly, if true, it would imply the existence of myriads of dif ferent sciences. But this attitude is self-defeating. These alternative sciences would lack the most important feature that we associate with science, the fact that at least some of its theories transcend culture, and describe the world as it truly is.
This is not to say that cultural variations in the practice of science are uninteresting or unim portant. One may compare fundamental science with the labor-intensive production process of an expensive spice like saffron, one gram of which requires the harvesting of more than 150 flowers. Science works with ideas rather than with flowers, but only a very small fraction of the harvested ideas makes it into the final product, namely, the core of our fundamental theories. There are sev eral ways that we can improve the saffron industry; in relation to efficiency, social responsibility, labor conditions, fairness of wages, and so on. However, the product will not be affected: saffron will remain saffron.
Certainly, we can make a better science by changing the cultural, political and economic context in which it operates. What we cannot do this way is to make a science that is different in its essence, namely, in its final product. Our fundamental theory for gravity will not change if the scientific community adopts one specific political ideology, if researchers become more moral persons, or if their salaries are doubled.
A third, more exciting way to subvert the question is to accept that the pillar upon which physics is built, namely, mathematics, could be radically different. The problem here is that nobody knows what “radically different” means when applied to mathematics. A person who can explain what a radically different mathematical science is, by the very fact of this explanation, will found a new domain of mathematics. Even the most radical of discoveries, such as the Pythagoreans’ discovery of the irrationals and Cantor’s formulation of actually infinite sets, were answers to outstanding issues in the mathematical problems of their day.
It is often suggested that an alternative mathematics that drops the notion of continuity and it is based only on discrete quantities might be possible. This narrative is partially motivated by the growth of computer science that is based on discrete, finitary mathematics, i.e., mathematics in which all quantities can be defined in a finite number of steps. Despite its popularity, this point of view is highly problematic. Our current mathematics is based on the deep interplay between continuum and discrete that is encapsulated in its foundations, namely, in the axioms of set theory.1 While there is a pervading feeling that something is still missing from the foundations, we do know that purely a finitary mathematics requires dropping out crucial axioms, and, as such, it cannot reproduce the continuum of standard analysis. This is a problem, because the continuum enters physics not only at the level of the geometry of space and time, but in the form of the complex numbers that are essential to quantum theory, and in the gauge symmetries of the Standard Model of particle physics.2If the standard notion of the continuum is ever abandoned in our mathematics, it will not be in favor of purely discrete or finitary mathematics, but in favor of other, novel structures, that provide a deeper understanding of mathematical infinity.
Hence, if we ever encounter an alien civilization that only employs discrete mathematics, chances are that its mathematics is not fundamentally different to ours, but truly inferior, and that its math ematicians will rush to adopt our mathematics, much like the empirical geometers of Babylon and Egypt rushed to adopt the axiomatic geometry of the Greeks from the very moment that they en countered it.
There are many researchers, especially in the field of quantum gravity, that look into a refor mulation of the foundations of mathematics, not in the simplistic sense of continuous vs. discrete, but in founding mathematics on structures other than set theory, for example, topos theory [3]. But any success in this direction, even if it leads to revolutionary breakthroughs, will be a natural continuation of existing science, born out of considerations that are already in place.
Even if a different mathematics were possible, the science that would incorporate it would have to describe the same phenomena as our science. But can an alternative description of the same phenomena be inequivalent to ours? Can we describe the propagation of electromagnetic waves in a way that is not mathematically equivalent to the description provided by Maxwell’s equations? Most physicists are highly skeptical about such an eventuality. To quote the Nobel laureate Sheldon Glashow [4]:
Any intelligent alien anywhere would have come upon the same logical system as we have to explain the structure of protons and the nature of supernovae.
By “the same logical system”, Glashow means that the theories must be mathematically equiv alent. There are several cases of mathematically equivalent theories in physics. For example, in classical mechanics, we can describe the change of a physical system either by considering the time evolution of initial data, or by identifying the correct scenarios for change through an optimization condition. The two descriptions are fully equivalent, and they are often viewed as facets of the same theory.
The only type of inequivalent description that physicists are willing to accept is an explanation by a better theory, that is, a theory that accounts for a larger domain of phenomena, and it approxi mates our current description in a particular regime. One example is the theory of general relativity that improves on Newton’s theory of gravity for the description of gravitational phenomena.
Certainly, history could have unfolded differently, and discoveries could have been made in a different sequence. The point is that the fundamental theories of physics are strongly interconnected on the grounds of logical coherence. In any society that supports a scientific community large enough to explore all accessible paths of inquiry, the logical coherence of a theory will eventually supersede the limitations of historical contingency.
The edifice of physics is like a labyrinthine library, to which it is very difficult to gain access. But once you find yourself in one room, it is only a matter of time, effort, and ingenuity to visit every single room in it, because no room is completely disconnected from the rest. Certainly, some connections are more difficult than the others, in some cases you have to go through unlit and unexplored corridors, and in some cases you have to wait until you obtain—through experiments— the proper light to see in the darkness. Even the current impasse in physics research in the attempt to construct a quantum theory of gravity is not caused by the absence of connections between our fundamental theories, namely, quantum theory and general relativity. If anything, there are too many connections; what is missing is experimental input.
We will illustrate the inter-connectedness of physics by means of an alternative-history scenario. Assume that human civilization developed in an Earth with an atmosphere so cloudy that it is impossible to discern stars and planets, but not so cloudy that we cannot see the Sun and the Moon. That Earth is otherwise identical to ours. We would still have solar and lunar calendars, but we would have no astronomy, no Ptolemaic and Copernican systems, no Kepler’s laws. Newton in that Earth would be a great mathematician, experimentalist, and alchemist, but he would have produced no Principia. Given the impact of Newton’s work, this might appear as an insurmountable obstacle to the development of physics. But there is another route to Newton’s laws of motion, or its logical equivalent, through the study of heat. A scientifically minded culture would develop thermodynamics, and any attempt to reconcile this with chemistry would lead to atomic theory, and then, to the explanation of heat in terms of molecular motions. Some form of classical mechanics would then ensue.
Does the inter-connectedness of physics make the existence of a different science impossible? To answer this, we consider the mathematical space Ω of all possible physical theories. This space is huge, as it contains even theories that cannot fully be conceived by the human mind, because they involve an infinite number of fundamental principles. The true theory of the world will be one among such theories in this space. Or perhaps, such a theory may not exist, and it is only possible to have an overlapping class of different theories, each describing a different aspect of reality.
In Fig. 1, we collapse the space Ω into two dimensions. The horizontal axis represents accuracy, that is, how close a theory is to the true theory and the vertical axis represents scope, namely, how large a chunk of reality it describes. The true theory/theories are represented by the orange region.
Figure 1: The reduction of the mathematical space Ω of all theories to two dimensions. The hor izontal axis represents accuracy, which increases from left to right. The vertical axis represents scope. The orange region is the correct theory: maximal accuracy and maximal scope. The blue region represents our science, and the green region a science that is fundamentally different from ours.
They have maximal accuracy, i.e., they are all the way to the right, and maximal scope, i.e., they extend from top to bottom.3 Our current theories of the world are represented by the blue region. The shape is uneven, because some domains of knowledge are more accurate than the others, i.e., they have advanced more to the right. For example, astrophysics is closer to the orange than biology, because it is possible to describe stellar formation and evolution from first principles of physics, something that remains impossible for even the simplest organisms. The scope of our present science is also limited, as there are domains of existence for which we lack a fundamental theory.
An alternative science that covers the same scope as the current one would just be more ad vanced or less advanced than ours. For a science to be truly different, (i) it should have a different scope than ours, and (ii) in that scope, it should be at least as advanced as our science. For example, it would correspond to the green region of Fig. 1. Note, the green science may very well have some overlap with ours, but this should be relatively small. If green science caught a sufficiently large blue chunk, the interconnections in the latter would enable the green science to cover the whole blue range. Then, we would not talk about a different science, but about a better science.
The two sciences are analogous to two armies that want to cross a dense and dangerous forest. They both move towards the east and they both want to get out of the forest, but they have different starting points. They must scavenge in order to eat, so they spread out as they proceed. If the forest is too large or if the armies are too small they will never meet, they do not even suspect the existence of each other. It will be a great shock if they ever meet, but then, they may very well decide that crossing will be easier if they merge.
In this scenario, a genuinely different science should be based on domains for which we currently lack a fundamental theory, that is, stamp-collecting sciences in Rutherford’s terminology. At the moment, we classify our empirical sciences 4into four broad domains: physical sciences, biological sciences, cognitive and behavioral sciences, and social sciences. We exclude physical sciences, because they are fully grounded on physics. We also exclude social sciences, because the very structures and phenomena that these sciences try to explain are culturally dependent. It is therefore difficult to conceive how they could develop an overarching framework that transcends culture. Thus, we are left with two primary domains of knowledge upon which to base the green science: the domain of life and the domain of the mind.
Biological sciences advanced beyond mere stamp collecting during the past century, and they have made great progress towards a solid foundation that is based on biochemistry and evolutionary theory. Chances are that they will go further than that, as they will become increasingly mathemat ical during the coming century. However, at the moment, they still lag far behind the fundamental theories of physics, in terms of universality and predictability. It is not difficult to envision a differ ent science that would build biology on mathematical foundations of equal universality as physics, and it would proceed from there to cover other aspects of experience, from inanimate matter to mind and society.5
The problem with this idea is that a mathematical foundation for biology that is separate from that of physics seems to contradict our present understanding. After all, biochemistry is supposed to be fully derived from quantum theory. The only obstacle to the first-principles derivation of the properties of all biomolecules is computational power, and this may plausibly be resolved by the development of quantum computers. Nonetheless, many people argue that some explanatory patterns of biology are independent of the explanatory patterns of physical science. In particular, the ubiquitousness of natural selection at all levels of biological organization (organisms, cells, and so on) insulates each level from reduction to the underlying biochemistry. This is an ongoing debate in philosophy of biology [5], but no matter how it is resolved, the grounding of present-day biology upon physics at the ontological level remains unquestioned.6
If this grounding is true, there can be no biology-based science that is essentially different from ours. Such a science is possible only if it involves concepts that are irreducibly biological, that is, concepts that cannot be grounded on physics. Current biology explicitly disavows such concepts. They are supposed to be remnants of the past. One example is Aristotle’s idea of biological tele ology, that is, the idea that the structure and function of organisms, and presumably of the whole biosphere, is fundamentally goal-directed. A biology-based alternative science is not impossible, but if it exists, our current understanding of biology has to be deeply flawed.
Hence, we are only left with the sciences of the mind as a foundation of a different science. The situation is more promising here than in the life sciences, because the former sciences have not progressed from the stage of stamp collecting. Certainly, the amount of information about mental and brain processes that has been collected during the last century is staggering, but this information is not unified, even partially, by a fundamental theory of mind.
More importantly, there is little evidence that grounding a theory of mind in physics is possi 6
ble. There exists a strong intuition that mental phenomena are of a different nature than physical ones, and the existence of mind-body interactions is a common-sense belief. There is no scien tific substantiation of this belief, but neither is there of its currently popular competitor that mental phenomena are reducible to physical ones. Widespread arguments that mind-body interaction is incompatible with physics are problematic, because they involve a 19th century understanding of physics, and they ignore the abstract mathematical nature of our fundamental theories [6].
At the present stage of knowledge, it is plausible that the fundamental theory for the world (the orange region in Fig. 1) has both mental and physical entities as its primary elements, one not reducing to the other. Any theory that incorporates modern physics must be mathematical, which implies that mind is to be characterized by a mathematical lawfulness, different from that of physics [6, 7]. We can therefore envision an alternative history, in which scientists would have approached the orange theory from the direction of the mind, that is, they would have constructed a mathematical psychology, called Psychics, which they would use as a basis for their description of biological phenomena and inanimate matter. Then, a major scientist in the twentieth century of their time-line, perhaps named Karl Gustav Jung, would assert that “All science is either psychics or coin collecting”.
This sequence of discoveries may appear implausible from our perspective. In fact, it is so alien to the evolution of our science that it warrants the name of a genuinely different science. However, its roots may not be completely disconnected: the idea of the mathematical lawfulness of the mind originates from the same philosophical tradition with that of the mathematical lawfulness of matter, and it is at least as old as Plato [8].
To summarize, the main assumption in our analysis is that science moves towards a true theory of the world. Then, a different science is one that moves towards the same goal but through paths that have little overlap with ours. At our present state of knowledge, our best bet for a different science is a science that would be based on a non-reductionist theory of mind. This identification is time sensitive: the other science should not have had sufficient time to enter deeply into the domains of physics that our science has explored. If we encounter an alien civilization with such a science, the two traditions will enter into dialogue, and they will quickly merge. Then, there will be only one science, and we will have to ask the same question anew.
NOTES NOTES Notes
1In the most popular axiomatic system for set theory, continuity enters via the axiom of infinity and the axiom of choice. The former establishes the existence of infinite sets, and the second establishes the existence of infinite sets with an uncountable number of elements. They are both required in order to establish the continuum that is employed in calculus and differential geometry, and hence, in physics [2].
2Certainly, we can approximate many, if not most, calculations that require the continuum with discrete calculations, but all discrete objects we employ to this end (e.g., lattices) must be embedded into a continuum structure. A purely discrete object that makes no reference to the continuum does not, in general, have the appropriate topological structure to approximate, say, a four dimensional geometry that solves Einstein’s equations.
3A point in Ω is mapped into a region in two dimensions, because we think of the procedure as akin to coarse-graining in statistical mechanics. We use two degrees of freedom to describe theories, while the space Ω is described by an infinite number of degrees of freedom.
4We only consider empirical sciences, because formal sciences, such as mathematics and logic, provide the background to all rational activity, so they must be shared by both our science and the alternative one. Furthermore, we already discussed the implausibility of alien mathematics as a basis of a different science.
5Many biologists would not accept that biology should be judged on criteria based on a science with a different subject matter. Biology is based on a different intellectual tradition, the notion of an organism has no analogue in physics-based sciences, and mathematization of biology may not lead to progress. Be that as it may, when discussing the possibility of an alternative science, it is difficult to imagine a biology-based science that would be comparable to ours in terms of universality and predictive accuracy, unless its foundations are mathematical.
6A crucial reason for the broad acceptance of natural-selection explanations is that they allow for the ontological reduction of biological processes to physics, at least in principle. From a physics perspective, natural selection is nothing an effective law of correlations at a coarse-grained level of description. It appears in specific regimes, for example, whenever we have a formation of imperfect replicators with copying fidelity within a specific range of values. It is not fundamentally different from other effective laws for coarse-grained macroscopic systems (e.g., fluids), and it is only a matter of historical contingency that it was found in a setting of biology.
REFERENCES REFERENCES References
[1] The first reference to this quote is in: J. D. Bernal, The Social Function of Science (London: G. Routledge & Sons Ltd., 1939), page 9.
[2] T. Jech, The Axiom of Choice (Amsterdam: North-Holland, 1973).
[3] C. J. Isham, Topos Methods in the Foundations of Physics, in Deep Beauty, ed. H. Halvorson (Cambridge: Cambridge University Press, 2010).
[4] S. Glashow, The Death of Science?, In The End of Science? Attack and Defense, ed. R. J. Elvee. (Lanham, Md.: University Press of America, 1992).
[5] See, for example, chapter 4 in A. Rosenberg and D. W. McShea, Philosophy of Biology, A Contemporary Introduction (New York: Routledge 2008).
[6] C. Anastopoulos, Mind-Body Interaction and Modern Physics, Found. Phys. 51, 1 (2021).
[7] D. Chalmers, Facing Up to the Problem of Consciousness, J. Consc. Stud. 2, 200 (1995); The Puzzle of Conscious Experience, Sci. Am. 273, 80 (1995).
[8] Plato, Timaeus (Athens: 360BC); See translation by R. Waterfield, Timaeus and Critias (Ox ford: Oxford University Press 2008).