Shemesh b’Givon dom (Yehoshua ch 10) – While the sun stood still for the Jewish people to complete their battle against the Emori kings, presumably, had we been alive at the moment of that battle living in NY or wherever, we would have noticed the sun passing overhead as usual and our watch (or sun dial) would not have deviated from usual. How can the sun have been still in one location and moving overhead in another? The Maharal (Gevoros Hashem, Into II) writes that this is not a question for one who understands the concept of nes. A miracle creates a different perception of reality unconstrained by the laws of nature, and that perception is no less real than the laws of nature are. The person in NY living outside the plane of the miraculous would see the sun's usual passge through the sky; the person living within the plane of the miraculous experiences a completely different reality which is no less true.
In short, the Maharal allows for miracles to violate the law of noncontradiction: things can both be and not-be at the same time (for the record: others disagree). Maharal gives a list of many other examples, among them the miracle of the water of the Nile turning to blood. As explained in Midrash, when an Egyptian drank a cup from the Nile it was blood; if a Jew drank from the same cup it was water. How can the same physical reality be blood and not-blood at the same time? The answer is that physical reality is no more than perception, and perception is relative to the observer.
Rav Dessler (Michtav m’ELiyahu I:309) uses this premise to explain the famous gemara which teaches that Ya’akov Avinu did not die (Ta’anis 5). The gemara itself asks how that can be when he was embalmed, to which the gemara answers that the teaching is based on a derasha. How does that answer the question? Embalming is certainly what happened based on our physical perception of reality, but if within a different level of perception, Ya’akov is still with us, not just in the sense of his spirit being here, but actually alive. (This does bring to mind Schrodinger’s Cat.)
Two notes: Rationalists will dismiss the gemara claiming Ya’akov lives as simply meaning his spirit lives on. Problems: 1) Rashi in Ta’anis explains the maskana: “sevurim hayeu she’meis”, meaning he is still alive and they just thought he had died; 2) Why would the gemara make such a statement about Ya’akov and not the other Avos or any other Tzadikim? Doesn’t their spirit live on? 3) It means the makshan of the gemara made no sense; 4) See Gilyos haShas of R’ Akiva Eiger Kesubos 103 that Rebbi after death appeared in a body to his family to be motzi them in kiddush because tzadikim are “chaim”. Of course, you could overcome these hurdles – I’m just pointing them out for thought. Second note: on logic as an eternal inviolable construct, see the Chazon Ish ch 1 of Emunah u’Bitachon as printed in C.I. Taharos at the end. It is censored out of the edition printed separately, which should be enough incentive to look it up.