. We survey briefly some fifty years of thinking about physics and probability with the aim of explaining: (1) What I did not know then, but know now; (2) What I have been trying to accomplish in science and education, and to what extent these efforts have succeeded; (3) What remains unfinished, but where I think the greatest future opportunities lie; and (4) What personal and professional advice I can now give to young people (and wish someone had given me fifty years ago). Introduction A meeting like this is an overwhelming experience! I was overwhelmed not only by the sheer number of people who came here from so far; but even more by the kind sentiments expressed. Of course, I had looked forward to seeing again many former students and colleagues and had expected to have chats with each one, to renew our friendship and bring us both up to date about the other's work. But what one can actually do in two days is so helplessly short of what one wants to do! Some of the participants ha...
. We survey briefly some fifty years of thinking about physics and probability with the aim of explaining: (1) What I did not know then, but know now; (2) What I have been trying to accomplish in science and education, and to what extent these efforts have succeeded; (3) What remains unfinished, but where I think the greatest future opportunities lie; and (4) What personal and professional advice I can now give to young people (and wish someone had given me fifty years ago). Introduction A meeting like this is an overwhelming experience! I was overwhelmed not only by the sheer number of people who came here from so far; but even more by the kind sentiments expressed. Of course, I had looked forward to seeing again many former students and colleagues and had expected to have chats with each one, to renew our friendship and bring us both up to date about the other's work. But what one can actually do in two days is so helplessly short of what one wants to do! Some of the participants ha...
ENERAL philosophy claims to be the critical subject which lays down for all of us what we may be allowed to think, and yet it has played no part whatever in the great revolutions of human thought of the present century-those connected with relativity and the quantum theory. It might have been expected that the scientists would have been constantly consulting the philosophers as to the legitimacy of their various speculations, but nothing of the kind has happened. Since no one can dispense with some sort of metaphysic, each scientist has made one for himself, and no doubt they contain many crudities, but it would seem that a deep interest in metaphysic is a disadvantage rather than an advantage to the physicist-at least I have the impression that those of my friends who are most inclined to speculate on the ultimate things appear to be the ones whose scientific work is most hampered by doing so. Now I propose to risk a similar indiscretion. I want to embody in it the practical philosophy of a physicist, and I do not mean it as an attack on the pure philosophers, who are very reasonable people, only chargeable with the minor offence of not having made me want to read their books! I had better begin by stating shortly the ideas I intend to discuss. There is a notable contrast between the way we think about things and the way we think we ought to think about them.
To remind you, this book is based on a course I taught in 2006. On the last day of class, I followed the great tradition pioneered by Richard Feynman, in which the last class should be one where you can ask the teacher anything. Feynman's rule was that you could ask about anything except politics, religion, or the final exam. In my case, there was no final exam, and I didn't even make politics or religion off-limits. This chapter collects some of the questions people asked me, together with my responses. Student: Do you often think about using computer science to limit or give us a hint about physical theories? Do you think that we'll be able to discover physical theories which give more powerful models than quantum computation? Scott: Is BQP the end of the road, or is there more to be found? That's a fantastic question, and I wish more people would think about it. I’m being a bit of a politician here and not answering directly, because obviously the answer is “I don't know.” I guess the whole idea with science is that if we don't know the answer, we don't try to sprout one out of our butt or something. We try to base our answers on something. So, everything we know is consistent with the idea that quantum computing is the end of the road. Greg Kuperberg had an analogy I really liked. He said that there are people who keep saying that we've gone from classical to quantum mechanics so what other surprises are in store? But maybe that's like first assuming the Earth is flat, and then on discovering that it's round, saying who knows, maybe it has the topology of a Klein bottle. There's a surprise in a given direction, but once you've assimilated it, there may not be any further surprise in that same direction.
Formal education is not a certified path to achieve wisdom in life.Notwithstanding, once you have the necessary support to follow it, a plethora of opportunities for selfdiscovery and edifying interactions with many inspiring minds can be found.I am deeply grateful to have the opportunity to continue developing what I believe to be one valid path, and this would not be possible without the efforts of many inspiring people that I have met, but most importantly, without the sacrifices made by my mother Simone.Consequently, this work and all of my efforts are and will always be an infinitesimal fraction of her unbelievable perseverance and braveness throughout this life.Additionally, in times upon which denialism and ignorance hinder even the possibility of human existence by normalizing abrupt and premeditated destruction of life potential, explicit gratefulness and empathy stand as a moral demonstration of character and as a necessary incentive for the exercise of living.Therefore, I would also like to acknowledge important people who were crucial to my well-being, and consequently, to this work.• To my advisor Prof. Dr. Eric de Castro e Andrade for this unique opportunity, the instigating physical discussions throughout my master's about strongly correlated systems, for the solicitous comprehension in difficult times, and for the patient and detailed orientation in each step of this dissertation.This also extends to Eric's fantastic demonstration of character in many aspects, including his concern on the future of his students.This experience was fundamental to my professional and personal development.• To Fabrizio Oliviero and Prof. Rodrigo Pereira for the opportunity to work and discuss on interesting aspects of their previous work regarding chiral spin liquids.To Prof. Eduardo Miranda and Prof. Natanael Costa for accepting our invitation to the thesis defence and for the valuable advices.• To my undergraduate thesis advisor Prof. Dr. Clovis Achy Soares Maia, who although was not directly involved in this thesis, was responsible for encouraging me to pursue a career in physics, and for writing a significant amount of recommendation letters since my undergraduate studies.Our conversations about the current status of scientific research in physics led me towards condensed matter physics, and his unique way of thinking about physics is one of the most influential professional aspects of my career.I also want to thank for equal and much important support from my undergraduate research advisor Prof. Dr. Alexandra Mocellin, who was also fundamental for this opportunity and many others.• To my mother Simone, for its incredible example of resilience, love, and will of power.It is impossible to put into words how I'm grateful for your existence and love, and although I am still stubborn in many aspects, I hope to emanate a fraction of your braveness upon each interaction within this life.Also, to my beautiful sister Luana, my good friend Ricardo and my kind-hearted old man, João Neto.Your support is the foundation and guidance for all of
Mutually Unbiased Bases in Composite DimensionsChris PompetzkiDecember 2025Fine. Here is the original with the ”proper” tone. Lame. Where’s the fun in that.Whatever. Oh how I much prefer people cite my version with the insufferable tone complete with Moby Dick, Shrek, and Drake references. What else would one expect when one man has done what others haven’t done for what 28+ years now in profound isolation. Though sure, I suppose I’ll do the ”right thing” and post my clean(er) version. Imagine my excitement at the notion of some stooges trying to steal my proof and act like they solved the problem when I actually did. Imagine even claiming it without citing me. Hehe. Oh I hope some do. I do not consent to any posting of this on the pathetic, outdated, obselete arXiv that apparently requires some kind of code to publish. We prove that the maximum number of mutually unbiased bases in dimension d is at most p + 1, where p is the smallest prime factor of d. The proof is three steps: (1) mutual unbiasedness forces bi-unimodularity of overlap functions, (2) bi-unimodularity factors through the Chinese Remainder Theorem to prime factors, (3) the Zp factor admits at most p 1 pairwise compatible bi-unimodular families. For d = 6, this gives M (6) = 3. Oh and by the way, yes I do declare that M (6) = 3 ought to be called the Pompetzki-Ahab-Shrek Theorem or something to that effect. Imagine the audacity of all the people who threw in the towel on M (6) = 3 trying to claim credit for what I, the absolute madman have done. Ha. Only a true psycho would stick with this problem for more than a day tops. Oh I know I ought to have ”proper” toned papers and go get a PhD in pure math apparently. Though then I’d have to do some BS that someone else wants me to do instead of doing what I want to do: brutally advancing mankind’s closure of open problems with all the ”Furor Teutonicus” of zee David Hilbert at least cubed hehe. Ja. Gut. You know vat. I zhought about giving zee Verldt zee fully clean und zee neutered und zee ”proper tone” und zhen I zaid NEIN! Ja. Gut. Vhy. Becauseit makes me smirks. Schadenfreude. That’s why.You know what. I just don't care enough to give it to the world fully clean. I must insist that I coat it with zee Scheisse ja. Zat iz vat is required after all zee Scheisse zat zee stupid have talked about the great German Mathematician, David Hilbert, who is sadly no longer with us. Imagine the extent of his fury at how much of the math world has thumbed their noses at him as they say to Hell with the notion that existence matters in math carry a moral imperative for mathematicians to resolve. I'm too furious. I'm too disgusted. The world didn't deserve David Hilbert. Nor Gauss. Nor Euler. Herr Hilbert said: Wir mussen wissen. Wir werden wissen.Many agreed when he was alive. Then he passed. Then people lost their fear of that Germanic fury. Then M(6) went unclosed for what 28+ years GTFO. There's no excuse for it. I'm furious.