The paper by Don N. Page discusses the puzzle of information loss in black hole radiation, a key issue in quantum mechanics and gravity. Hawking's original proposal suggested that black holes would eventually evaporate completely, leaving behind a mixed state of radiation, implying the permanent loss of information. However, this conclusion has been challenged, particularly in the context of semiclassical and classical approximations, which are not expected to be valid at the Planck scale. Page examines the possibility that information might escape gradually during black hole evaporation, rather than suddenly at the Planck scale. He argues that if information does indeed escape gradually, it may initially be so slow or spread out that it would not be detectable through perturbative analyses in the semiclassical regime. This is illustrated using a two-dimensional dilatonic black hole model, where the semiclassical approximation is valid until the black hole reaches a strong-coupling regime. Page further explores a more realistic model where the black hole and its radiation are subsystems of a larger, randomly mixed system. He derives expressions for the expected information content in the radiation at different stages of black hole evaporation. For a black hole in a box, he shows that the rate of information outflow is initially very low and becomes more significant only as the black hole emits most of its energy. This suggests that the information in the radiation would be spread out over a large number of measurements, making it difficult to detect or exclude through perturbative analysis. Page concludes that if information is gradually emitted, it would likely be too slow or spread out to be detected by perturbative methods. He also notes that no plausible nonperturbative mechanisms for information extraction from black holes are currently known, leaving the problem of information loss in black hole radiation unresolved.The paper by Don N. Page discusses the puzzle of information loss in black hole radiation, a key issue in quantum mechanics and gravity. Hawking's original proposal suggested that black holes would eventually evaporate completely, leaving behind a mixed state of radiation, implying the permanent loss of information. However, this conclusion has been challenged, particularly in the context of semiclassical and classical approximations, which are not expected to be valid at the Planck scale. Page examines the possibility that information might escape gradually during black hole evaporation, rather than suddenly at the Planck scale. He argues that if information does indeed escape gradually, it may initially be so slow or spread out that it would not be detectable through perturbative analyses in the semiclassical regime. This is illustrated using a two-dimensional dilatonic black hole model, where the semiclassical approximation is valid until the black hole reaches a strong-coupling regime. Page further explores a more realistic model where the black hole and its radiation are subsystems of a larger, randomly mixed system. He derives expressions for the expected information content in the radiation at different stages of black hole evaporation. For a black hole in a box, he shows that the rate of information outflow is initially very low and becomes more significant only as the black hole emits most of its energy. This suggests that the information in the radiation would be spread out over a large number of measurements, making it difficult to detect or exclude through perturbative analysis. Page concludes that if information is gradually emitted, it would likely be too slow or spread out to be detected by perturbative methods. He also notes that no plausible nonperturbative mechanisms for information extraction from black holes are currently known, leaving the problem of information loss in black hole radiation unresolved.