We write in response to the call from the 2020 Decadal Survey to submit white papers illustrating the most pressing scientific questions in astrophysics for the coming decade. We propose exploration as the central question for the Decadal Committee’s discussions. The history of astronomy shows that paradigm-changing discoveries were not driven by well-formulated scientific questions, based on the knowledge of the time. They were instead the result of the increase in discovery space fostered by new telescopes and instruments. An additional tool for increasing the discovery space is provided by the analysis and mining of the increasingly larger amount of archival data available to astronomers. Revolutionary observing facilities, and the state-of-the-art astronomy archives needed to support these facilities, will open up the universe to new discovery. Here we focus on exploration for compact objects and multi-messenger science. 1. The exploration question There has been a long-standing tension in our discipline between the ‘exploration’ approach and the more physics-based ‘question-driven’ approach. 1.1 The question-driven approach This approach seeks to formulate the most important open questions in our discipline. It is based on our present knowledge of the field (both theoretical and observational) and is formulated usually as a way to constrain and/or advance a currently proposed cosmological or astrophysical scenario. ‘Question/hypothesis-driven’ has been the preferred approach in the last few decades and is used to justify both observing proposals and proposals for new instruments and telescopes. Most talks at conferences and papers are framed based on this question and answer approach. This is how we teach our students to approach research. This is the approach formulated in the Decadal Survey call for white papers. This approach addresses the ‘known unknowns’: for example, the way to best constrain the cosmological parameters of our universe, and lately the search for dark matter and dark energy, and the definitive discovery of gravitational waves. The question-driven approach continues to be fruitful, and it gives us a certain sense of control in our progress, but -by its own natureis also a limited and limiting epistemology. For example, it can bias our knowledge. As expounded in a recent article with reference to extra solar planets “the key is to make sure that science policy permits discovery for the sake of discovery and not for finding Earth-like planets, which we have prejudiced to be of greatest interest (D. J. Stevenson, CalTech, Physics Today, Nov. 2018)”. The same opinion can be easily shaped to apply to other fields of astrophysics. The question-driven approach does not address the ‘unknown unknowns’ that by their nature cannot be addressed as well-defined ‘important questions’. 1.2 The exploration approach This approach, i.e. gaining the capability to find new questions, rather than solving known ones, is the only way we can address the unknown unknowns. Harwit (1984) calls this ‘discovery space’. The notion that most of science is undiscovered and that ‘out of the book’ thinking may be needed for real progress is making fast inroads (e.g., see the book ‘Ignorance: How it Drives Science’ by S. Firestein, 2012). How to best foster the discovery of unknown unknowns is particularly poignant for astronomy, which throughout its history has been first and foremost exploratory. The real big paradigm shifts in astronomy and astrophysics have occurred when new approaches have significantly opened up the discovery space, revealing unforeseen views of the universe. These approaches may have been framed as a way to address important questions of the time, but the real advances were from serendipitous discoveries. The discovery space may have been increased by means of new telescopes and instruments (both hardware and software), and also by unanticipated data repurposing. Famous examples of discoveries stemming from exploration include: • The Galilean Moons of Jupiter, the metal composition of the Sun and stars, the HR diagram, the expansion of the Universe, large scale structure, hot Jupiters (driven by improvements in optical telescopes and spectrographs); • Quasars, radio galaxies, the microwave background, pulsars, superluminal motion, fast radio bursts (following the invention of radio telescopes, VLBI, and search in the archives in the case of bursts); • Black holes and their mass range, dark matter, dark energy, super-starburst galaxies (from the availability of new space-based observing windows, X-ray, IR, and high resolution optical imaging with HST, and availability of multi-wavelength archives). These foundational discoveries for the present understanding of the Universe and its evolution were not in any way anticipated. Most of them were fostered by the use of increasingly larger telescopes and more sensitive instruments, able to explore different parts of the electromagnetic spectrum. Others were surprising results of the data analysis. Given the increasing availability of large and survey data sets in our open archives, a new hybrid approach, question-driven exploration, has emerged, where astronomers have mined these data and researched the literature guided by relatively vague questions, finding answers, new questions, and surprises. A similar approach is making inroads in biology (Elliott et al 2016). In this white paper we discuss the ‘exploration question’, providing examples relevant for the field of compact objects. We include both serendipitous discoveries and question-driven explorations, resulting from unanticipated analyses of multi-wavelength survey data (Section 2). In Section 3, we address our recommendations for increasing the discovery space. 2. Exploration in Compact Objects Given the nature of exploration, it is not possible to give definite questions that need to be addressed in the near future. Rather, we provide a few examples of (1) serendipitous unexpected discoveries (unknown unknowns) and their potential for changing established paradigms; and (2) new research avenues posed by asking very general questions (known unknowns). We do not mean to provide an exhaustive survey of such discoveries, but only to illustrate our case with a few representative studies. Although there were a few theoretical predictions beforehand, compact objects are excellent exemplars of discoveries made through exploration. In the space of a few years, neutron stars were found both as pulsars, seen as “scruff” in radio survey data (Hewish, Bell et al. 1968), and as bright periodic X-ray sources; black holes were found as rapidly variable X-ray sources and, later, dynamically with spectroscopy of the secondaries of faded X-ray transients (McClintock and Remillard 1986). Gamma-ray bursts discovered at the same time (Klebesadel et al., 1973) were mysterious for decades but also implied compact objects. Fast radio bursts are a more recent discovery and may be connected with compact objects. In addition to being totally unexpected discoveries, compact objects (including stellar-mass black holes and neutron stars), required observations at wavelengths other than the wavelength of their discovery (typically X-ray, radio or gamma-ray) before their true nature could be determined. An explanation for radio pulsars was developed within months of their discovery (Gold 1968), for X-ray binaries within years of discovery (Pringle & Rees 1972), and for gammaray bursts we are only now, more than half a century later, beginning to understand their nature: • Radio pulsars provided us with the first (indirect) evidence for the existence of gravitational waves. Pulsar glitches led to the recognition of solid crusts on neutron stars, and neutron stars offer ways to test the nature of the strong nuclear force via their equation of state. • X-ray binaries use the most efficient means known of extracting energy from matter. Their messy phenomenology revealed its hidden order when color-color and color-intensity diagrams from archival data showed clear paths between different accretion states (Done & Gierlinski 2003), reflecting the balance of disk and jet emission as accretion rates change. • The known mass range of stellar black holes was greatly extended by LIGO gravitational wave detections (Abbott et al 2017a). Joint observations of gravitational wave signal GW170817 by the LIGO-Virgo detector network and transient electromagnetic counterparts from multiple telescopes resulted in a triumph for multi-messenger astronomy: discovery of an inspiraling binary neutron star (Abbott et al. 2017b). • Bright X-ray bursts (discovery paper, Grindlay, Gursky et al 1976) are energetic phenomena typical of accreting neutron stars in binaries, associated with thermonuclear flashes on the NS surface (see e.g., review Lewin et al 1995). • Gamma-ray bursts, which are the most energetic phenomena known to humanity, have been connected with neutron star mergers, resulting in the first multi-messenger observations of gravitational wave events (e.g., Haggard, et al., 2017). Multi-wavelength light curves can provide a physical view of the phenomenon (Kasliwal et al. 2017). • Fast Radio Bursts are transient phenomena lasting only milliseconds, are suspected of being compact objects, and many are being discovered by an instrument designed to look for redshifted 21cm hydrogen emission (Chime/FRB Collaboration 2019). There are dozens of ideas about what they might be, but no way to discern between them. FRBs may provide new cosmological tests (Jaroszynski, 2019). The archival data available at different wavelengths provide a resource for exploration, both for identifying new phenomena that may be related to compact objects, finding precursor objects, and investigating systematics in newly identified classes. For example: • A blind search for pulsations of 13 years of XMM observations containing 50 billion photons led to the discovery of th