A Reason to Reason Everything List Puzzle

[PGC]

The summer let your hair down reason to reason super serious just for fun puzzle is here. No cheating, copying, pasting, pets, food, and/or beverages permitted. Violations will be punished by the Everything List’s all-important “nothing”. Enjoy: 

In the vast expanse of the multiverse, an Everything List Member named Dr. Quark travels between different branches of said multiverse using a sophisticated vessel. His vessel is equipped with a tuned Alcubierre drive, meticulously built by Brent and programmed by Quentin. The branch targeting system, a marvel of modern technology, utilizes a linguistic model (LLM) developed by John and Jason, with the linguistic interface engineered by Terren. The drive is powered by exotic matter, whose configuration and properties are extracted from the Universal Dovetailer using formulae devised by Russell and Bruno and implemented through Quentin's innovative software.

Dr. Quark's wife, Dr. Photon, possesses the extraordinary ability to teleport instantly to any branch of the multiverse, leaving behind a shimmer of quantum energy at her arrival point. She does this spontaneously and forgets dinner time in the home branch, particularly if she’s observing something aesthetically pleasing to her. Same it was for this evening. So Dr. Quark embarked with his vessel activating the sophisticated branch targeting system — though based on Jason's estimation formulae and by definition not always accurate—which guides him to a particularly vibrant and mysterious branch of the multiverse with violet stuff, where he hopes to find his wife.

The targeting system is probabilistic and spits out time, space, star system coordinates one attempt at a time. Therefore, Dr. Quark will always either land in the accessible environs of where Dr. Photon teleported to or not. Of course, every branch has, local to those coordinates, some non-zombie inhabitants. And the inhabitants of the relevant branches in this puzzle are Truth seekers (tell the truth) and Illusionists (who lie, of course). While all inhabitants can perceive the shimmer emanating from her teleportation arrival, locating Dr. Photon afterward proves difficult due to the vast number of nooks and crannies, we’ll say, of each branch.

Upon arrival this evening, Dr. Quark encounters five inhabitants who guess his purpose and greet him with knowing smiles. These inhabitants have the following names and make the following statements:

1. Alpha: "Dr. Photon is in this branch."

2. Beta: "Dr. Photon is not in this branch."

3. Gamma: "Dr. Photon was here yesterday."

4. Delta: "Dr. Photon is not here today, and she wasn’t here yesterday."

5. Epsilon: "Either Delta is an Illusionist or Gamma is a Truth Seeker."

Realizing the very serious weirdness of the situation, Dr. Quark pauses and asks, “Won’t one of you please make another statement?” At this point, Alpha speaks again: "Either Epsilon is an Illusionist or Gamma is a Truth Seeker."

The Grand Puzzle Multiverse Mega Question:

Is Dr. Photon on this branch of the multiverse? Reason accordingly THEN answer. Or just enjoy or ignore as it is kinda common ;-)

[PGC]

This straightforward puzzle got ignored with everybody arguing, splitting hairs, and reasoning on huge, sophisticated topics. Even by all of our self-reference experts! This insight is enough to justify its existence! 😂

The puzzle I posted is just one of many illustrations of how subjects making statements with assertions involving only if, and, or statements, that also make self-referential statements about themselves in a simple truth or lie setting can already get a bit fun. And we can reason and speak about such scenarios correctly, as long as we are clear with assumptions and rules (in contrast to inventing/changing them as we go along). And the contradictions and paradoxical scenarios that arise through reasoning, are not just "weirdness to be ignored";  they themselves can be exploited and bring clarity.

To illustrate, here is a SOLUTION that works:

Let's demonstrate that if Alpha is an illusionist, we get a contradiction. 

If we suppose that Alpha is an illusionist, then their second statement must be false, which means that Epsilon should be a Truth Seeker and Gamma should be an illusionist. Since Epsilon is a Truth Seeker, their statement is true, meaning either Delta is an illusionist or Gamma is a Truth Teller. But Gamma isn't a Truth Seeker (they should be an illusionist), which is why Delta must be an illusionist. Therefore, Delta's statement was false, so either Dr. Photon is in this branch today or she was here yesterday. Yet, Dr. Photon was not here yesterday, as Gamma said she was, and Gamma is an Illusionist, therefore she is in this branch today. BUT this makes Alpha's statement true, contrary to our initial assumption that Alpha is an illusionist!  Therefore Alpha cannot be an Illusionist and must be a Truth Seeker. This is why Alpha's first statement was true and Dr. Photon is in fact in this branch. Dr. Quark will find her with conventional travel first and get her home in time for dinner with the branch targeting system. 

Hope you tried, found, and enjoyed it!