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Scott Aaronson - Quantum Computing, Complexity, and Creativity
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Scott Aaronson is a Professor of Computer Science at The University of Texas at Austin, and director of its Quantum Information Center. He's the author of one of the most interesting blogs on the internet: https://www.scottaaronson.com/blog/ He was also my professor for a class on quantum computing. Episode Website: https://www.dwarkeshpatel.com/p/scott-aaronson Apple Podcasts: https://apple.co/3AXXrr2 Spotify: https://spoti.fi/3dYUCgc Follow me on Twitter to get updates on future episodes and guests: https://twitter.com/dwarkesh_sp Buy Scott's book on Quantum Computing since Democritus: https://amzn.to/3eanguN Timestamps 0:00 Intro 0:33 Journey through high school and college 12:37 Early work 19:15 Why quantum computing took so long 33:30 Contributions from outside academia 38:18 Busy beaver function 53:50 New quantum algorithms 1:02:24 Clusters 1:06:23 Complexity and economics 1:13:26 Creativity 1:24:07 Advice to young people
Segments Timeline
Becoming an Expert
Scott Aaronson discusses the journey to expertise, emphasizing that while it may take years to master a field, one can quickly become an expert in a narrow problem. He encourages listeners to focus on becoming the best in a specific niche, highlighting the importance of specialization in one's academic and professional journey.
"you know it might take you know years or decades to become you know an expert like in a whole field uh uh you know and you might be very far from that but it really doesn't take that long to become th..."
Becoming an Expert
Scott Aaronson emphasizes the importance of focusing on a narrow problem to become a world expert. He suggests that while it may take years to master an entire field, one can quickly become an authority on a specific topic, encouraging listeners to find their niche.
"you know it might take you know years or decades to become you know an expert like in a whole field uh uh you know and you might be very far from that but it really doesn't take that long to become th..."
Early Academic Journey
Scott shares his unconventional educational path, including obtaining a GED instead of graduating high school. He discusses his dissatisfaction with traditional schooling and his desire to pursue a college education earlier, reflecting on his experiences in both U.S. and Hong Kong schools.
"on one particular tiny little problem right and um you know so so try to you know become the world expert on on something you know you know even something very very narrow so professor erinson can you..."
Early Academic Journey
Scott shares his early academic experiences, including graduating high school with a GED at 15 and pursuing a PhD by 22. He reflects on his dissatisfaction with traditional schooling and his desire to engage in a more intellectually stimulating environment, which led him to seek alternative educational paths.
"on one particular tiny little problem right and um you know so so try to you know become the world expert on on something you know you know even something very very narrow so professor erinson can you..."
The Shift to College
Scott recounts his transition from high school to college, highlighting his eagerness to escape an unsatisfactory academic environment. He describes how he sought out more challenging courses and the freedom to learn at his own pace, which he found lacking in high school.
"i i didn't really graduate high school when i was 15. i got a ged uh from from from new york state uh but uh i um i was not happy uh in in high school for for several reasons i mean uh just you know s..."
Challenges of High School
Scott recounts his struggles in high school, including social and academic challenges. He describes how moving to Hong Kong disrupted his education and how he felt out of place in the traditional school system, ultimately leading him to seek a more suitable educational environment.
"can you tell us about um that yeah well i i didn't really graduate high school when i was 15. i got a ged uh from from from new york state uh but uh i um i was not happy uh in in high school for for s..."
Clarkson School Experience
Scott discusses his time at the Clarkson School, where he took college courses as a high school student. He reflects on the positive aspects of this experience, including engaging with professors and starting research, despite facing social challenges similar to those in high school.
"i mean i i had a i was in a weird situation because my um i i went to um uh public school uh uh in in the u.s for for for junior high and then and in pennsylvania actually and then my parents uh moved..."
Finding a Better Fit
After returning to the U.S., Scott discusses his experience in public high school and the limitations he faced. He highlights his parents' suggestion to pursue online learning, which was rejected by the school, prompting him to explore alternative options for his education.
"i mean i i had a i was in a weird situation because my um i i went to um uh public school uh uh in in the u.s for for for junior high and then and in pennsylvania actually and then my parents uh moved..."
Clarkson School Experience
Scott describes his time at the Clarkson School, where he took college courses as a high school student. He reflects on the positive aspects of this experience, including engaging with professors and starting research, which contrasted with his previous schooling experiences.
"i went to an american international school there but because of a mismatch between the way uh they think they did things in the u.s and in hong kong uh you know i was not able to do math uh that was t..."
College Admissions Struggles
Scott shares his disappointment with the college admissions process, detailing how he was rejected from most schools he applied to. He highlights the unique challenges he faced due to his unconventional educational background and the eventual acceptance from Cornell and Carnegie Mellon.
"between the way uh they think they did things in the u.s and in hong kong uh you know i was not able to do math uh that was that was uh uh appropriate i guess i i you know i had always been sort of a ..."
College Application Journey
Scott shares the challenges he faced while applying to colleges after his time at Clarkson. Despite being rejected by many institutions, he was accepted by Cornell and Carnegie Mellon, leading to a significant turning point in his academic career.
"and once um once once i had done that that was that was sort of a uh you know something something flipped for me right that you know i could actually do this i could uh uh get out of this environment ..."
Navigating GED Requirements
Scott explains the complications he encountered regarding his GED, which was necessary for his enrollment at Cornell. He recounts the bureaucratic hurdles he faced and how his mother successfully advocated for an exception to allow him to obtain the GED.
"that was sort of a uh you know something something flipped for me right that you know i could actually do this i could uh uh get out of this environment you know where where i really wanted to be was ..."
Navigating GED Requirements
Scott discusses the complications surrounding his GED requirement for college enrollment. He explains how his age and unique educational background created hurdles, but ultimately, his mother advocated for him to receive an exception, allowing him to attend Cornell.
"course you know i i somewhat uh uh you know had had an idealistic view of what college was but you know but of a place where ideas would matter more than popularity and uh where um you know you would ..."
Accelerated Learning
Reflecting on his accelerated academic journey, Scott discusses the advantages and disadvantages of specializing early. He expresses gratitude for the opportunity to learn about topics that genuinely interested him, while also acknowledging the social challenges that came with skipping grades.
"a place where ideas would matter more than popularity and uh where um you know you would be able to choose uh what to study and advance at your own pace and you know all of these these wonderful thing..."
Social Challenges of Acceleration
Scott candidly shares the social difficulties he faced as a younger student in college. He discusses how skipping grades impacted his social life and dating experiences, revealing the internal struggles he dealt with despite his academic success.
"it and uh you know and and then i i ran out of math to take right i took the uh um ap uh calculus and and then um the um uh you know my my my parents basically suggested to the school uh well why does..."
Accelerated Learning
Reflecting on his accelerated academic path, Scott discusses the social implications of skipping grades. He shares his experiences of being younger than his peers in college and how it affected his social life, while academically, he felt comfortable in the environment.
"for a year and um you know as i said i didn't like it and uh you know and and then i i ran out of math to take right i took the uh um ap uh calculus and and then um the um uh you know my my my parents..."
The Value of Early Exposure
Scott reflects on the benefits of being exposed to academic subjects at a young age. He draws parallels to historical figures in science and mathematics who made significant contributions early in their careers, suggesting that early learning can provide a head start in complex fields.
"stanford has this epgy program right where uh you can do these things and uh and you know my parents said they would pay for it uh the school said no uh that that's you know uh uh um and uh so i sort ..."
Social Challenges of Early Advancement
Scott elaborates on the social challenges he faced due to his early academic advancement. He acknowledges the difficulties in dating and social interactions, which were exacerbated by his age and the pressures of being in a higher academic environment.
"uh differential equations or whatever with the the stanford has this epgy program right where uh you can do these things and uh and you know my parents said they would pay for it uh the school said no..."
Academic Freedom in College
Scott expresses gratitude for the academic freedom he experienced in college compared to high school. He emphasizes the importance of being able to choose subjects that genuinely interested him, which contributed to a more fulfilling educational experience.
"for a place called the clarkson school in upstate new york uh which is a part of clarkson university but you can uh live there for a year and take college courses um you know and but it's it's uh it's..."
The Nature of Learning
Scott discusses the nature of learning complex subjects like theoretical physics and computer science. He raises questions about whether early exposure to these fields is beneficial, comparing it to language acquisition and the challenges of mastering difficult concepts later in life.
"and take college courses um you know and but it's it's uh it's for high school students right uh so uh um i said you know i you know you know even knowing very little about this i think you know i wan..."
The Window of Learning
Scott Aaronson discusses the critical developmental windows in childhood for learning complex subjects like languages and theoretical physics. He reflects on how early exposure can lead to mastery, drawing parallels with historical figures in science who made significant contributions at a young age, such as Newton and Einstein. This segment explores the implications of age on creativity and intellectual contributions.
"that you know while someone's brain is still developing right that it's good to be exposed to uh uh certain things at that age and you know i mean i mean like we we we we know examples that are like t..."
The Value of Specialization
Scott reflects on the advantages and disadvantages of specializing early in his academic career. He discusses how knowing his passion for computing fundamentals at a young age allowed him to focus on what truly mattered to him, shaping his future endeavors.
"do that you know we had the car all you know packed up to drive there and while you know when we were uh about to leave then finally you know there there was one you know actually math teacher at my o..."
Age and Intellectual Contributions
In this segment, Aaronson examines the relationship between age and the ability to make significant scientific contributions. He questions whether cognitive decline is a factor or if life circumstances, such as family responsibilities, impact motivation and time for research. The discussion highlights the balance between personal life and professional ambitions in academia.
"uh which is weird to think about but um uh but you know there there are also many examples of of you know great contributions that were made by people in their 40s their 50s their 60s right so so you ..."
Teenage Learning and Development
Scott challenges the modern perception of adolescence, arguing that historically, teenagers were often apprentices learning trades. He suggests that early exposure to complex subjects can be beneficial, drawing parallels to historical figures who made significant contributions at a young age.
"uh and um so i i went to to clarkson and i you know and i i generally had a very good experience there uh i mean um uh you know i mean i mean i mean i mean socially there were a lot of the same proble..."
Einstein's Miracle Year
Scott Aaronson delves into the phenomenon of 'miracle years' in science, focusing on Einstein's remarkable achievements in 1905. He discusses how young scientists often make groundbreaking discoveries and speculates on the factors that contribute to this trend. The segment raises questions about the interconnectedness of ideas in science and the readiness of the scientific community to embrace new concepts.
"promise we'll get to the technical questions eventually but you're the third person on the podcast i'm about to ask this question because it fascinates me miracle years as you mentioned it's not just ..."
The Importance of Early Exposure
Scott discusses the potential benefits of learning complex subjects during formative years. He compares this to language acquisition, suggesting that early exposure may enhance understanding and retention, although he acknowledges the need for further research on the topic.
"i was able to sort of meet professors get started doing research and uh and you you apply from um you know the idea is that after a year at this clarkson program then you apply to colleges as a freshm..."
The Ripe Conditions for Discovery
Aaronson reflects on the historical context of scientific discovery, particularly in quantum mechanics and computing. He discusses how the early 20th century was a fertile ground for revolutionary ideas, yet many concepts remained unexplored for decades. This segment emphasizes the importance of timing and the collective readiness of the scientific community to advance knowledge.
"there's three or four of them i'm glad i'm glad you brought up the topic of like yeah ideas being in the air and ready to pluck uh because this is this leads me directly to the next question i was uh ..."
Youth Contributions to Science
Scott highlights the trend of young individuals making significant contributions to fields like quantum mechanics and mathematics. He reflects on how early engagement in these disciplines can lead to groundbreaking discoveries, reinforcing the value of nurturing young talent.
"almost every college that i applied to you know i had a very weird background but i was lucky that uh cornell and carnegie mellon were kind enough to accept me and um so i i decided to go to cornell b..."
The Window of Learning
Scott Aaronson discusses the critical periods in brain development where exposure to certain subjects, like languages, can significantly enhance learning. He reflects on how early exposure can lead to mastery, drawing parallels with the contributions of young scientists in fields like quantum mechanics and physics. This segment explores the implications of age on creativity and intellectual contributions.
"that you know while someone's brain is still developing right that it's good to be exposed to uh uh certain things at that age and you know i mean i mean like we we we we know examples that are like t..."
Barriers to Quantum Computing
In this segment, Scott Aaronson outlines the various barriers that delayed the development of quantum computing despite the foundational work laid in quantum mechanics. He discusses the distractions of World War II, the focus on particle physics, and the slow evolution of computational theory. This analysis provides insight into the complex interplay of historical events and scientific progress.
"a little bit later uh stephen wiesner you know had the idea of uh um uh quantum money right or using the uncertainty principle for cryptography although he was again he was not able to publish that un..."
The Interplay of Quantum Mechanics and Computing
Aaronson discusses the convergence of quantum mechanics and computer science, highlighting key figures like John von Neumann and Alan Turing. He reflects on how their early deaths impacted the potential for interdisciplinary breakthroughs. This segment underscores the importance of visionary thinkers in shaping the future of quantum computing.
"intervened uh with you know um um you know and and uh uh the people who were doing fundamental science a lot of them went to work you know either at the manhattan project or bletchley park and uh you ..."
The Age of Discovery
In this segment, Aaronson examines the phenomenon of young prodigies in science, citing historical figures like Newton and Einstein who made groundbreaking discoveries at a young age. He contrasts this with later contributions from older scientists, pondering whether age affects cognitive abilities or if it’s a matter of motivation and life circumstances. This discussion raises questions about the relationship between age, creativity, and scientific achievement.
"uh which is weird to think about but um uh but you know there there are also many examples of of you know great contributions that were made by people in their 40s their 50s their 60s right so so you ..."
David Deutsch and the Many Worlds Interpretation
In this segment, Aaronson explores David Deutsch's perspective on quantum computing, particularly his embrace of the Many Worlds Interpretation. He explains how this viewpoint allowed Deutsch to conceptualize quantum computing in ways that others had not, emphasizing the significance of entanglement and superposition in understanding quantum mechanics.
"um i've heard two other theories and i want to see how what you think of them so the first one is i think i might be misquoting him but i think at some point david deutsch said the reason he was able ..."
Einstein's Miracle Year
Scott Aaronson delves into the concept of 'miracle years' in science, particularly focusing on Einstein's prolific output in 1905. He discusses how various groundbreaking discoveries, such as special relativity and the photoelectric effect, emerged in a short span, suggesting that the scientific environment was ripe for such innovations. This segment explores the interconnectedness of scientific ideas and the timing of their emergence.
"promise we'll get to the technical questions eventually but you're the third person on the podcast i'm about to ask this question because it fascinates me miracle years as you mentioned it's not just ..."
Feynman's Practical Approach to Quantum Computing
Scott Aaronson contrasts David Deutsch's theoretical approach with Richard Feynman's practical motivations for quantum computing. He explains Feynman's focus on simulating physical processes and how this practical need spurred the development of quantum computing, highlighting the different intellectual paths taken by these pioneers.
"you know if you could build a computer right that uh you know could do a superposition over of different computations and then you could see the results of interference between them right that at that..."
The Ripe Conditions for Innovation
In this segment, Aaronson reflects on the historical context of quantum mechanics and its delayed applications in quantum computing. He discusses how the scientific community was initially focused on understanding quantum mechanics rather than its practical applications. This exploration highlights the importance of timing and readiness in the scientific process, suggesting that the ideas were present but not yet fully realized.
"there's three or four of them i'm glad i'm glad you brought up the topic of like yeah ideas being in the air and ready to pluck uh because this is this leads me directly to the next question i was uh ..."
The Evolution of Quantum Computing Ideas
Aaronson discusses the evolution of ideas surrounding quantum computing from the 1970s onward, noting the influence of various intellectual movements. He emphasizes the importance of exploring the physics of computation and how these explorations contributed to the eventual realization of quantum computing.
"a a universal quantum simulator um you know i mean people were that there was also a whole movement in the 70s and 80s to think about the physics of computation including like the thermodynamics of co..."
The Interruption of War
Scott Aaronson discusses how World War II impacted the trajectory of scientific research, diverting many physicists to wartime projects like the Manhattan Project. He explains how this shift delayed the exploration of quantum mechanics and its applications in computing, emphasizing the broader implications of historical events on scientific progress. This segment underscores the interplay between external circumstances and the advancement of knowledge.
"a little bit later uh stephen wiesner you know had the idea of uh um uh quantum money right or using the uncertainty principle for cryptography although he was again he was not able to publish that un..."
The Foundations of Quantum Computing
In this segment, Aaronson outlines the development of computational complexity theory and its significance for quantum computing. He notes that foundational concepts in computer science emerged in the 1960s and 70s, setting the stage for the eventual realization of quantum computing. This discussion highlights the gradual evolution of ideas and the necessity of foundational knowledge for groundbreaking advancements.
"intervened uh with you know um um you know and and uh uh the people who were doing fundamental science a lot of them went to work you know either at the manhattan project or bletchley park and uh you ..."
Academia's Openness to New Ideas
In this segment, Aaronson reflects on the changing landscape of academia since the 1970s, discussing whether it has become less open to new ideas. He contrasts the current environment with past eras, noting the rise of pre-print servers that allow for greater dissemination of unconventional ideas in physics and computation.
"in this field are as uh are as uh uh um um uh uh um as uh as as messianic as deutsches about the many worlds interpretation it's interesting that that uh come to think of it that both deutsche and tou..."
The Role of Pre-Print Servers in Research
Scott Aaronson elaborates on how pre-print servers have transformed the scientific landscape, allowing researchers to share new ideas without the traditional gatekeeping of academic journals. He discusses the implications of this shift for the visibility of bold new concepts in quantum physics and computation.
"in um in in physics and and uh uh let's say uh uh uh you know um uh you know speculation about uh uh you know the uh you know foundations of uh of of computing and and and and uh and and and uh and co..."
David Deutsch and Many Worlds
Scott Aaronson shares insights on David Deutsch's contributions to quantum computing, particularly his embrace of the many-worlds interpretation of quantum mechanics. He reflects on how this perspective allowed Deutsch to conceptualize quantum computing in ways that others had not. This segment emphasizes the importance of theoretical frameworks in shaping scientific innovation.
"people's plates and you know the the idea of you know thinking of entanglement as a resource that only starts in the 60s computational complexity that only starts in the 60s and 70s and then you know ..."
Feynman's Practical Approach to Quantum Computing
Scott Aaronson contrasts David Deutsch's philosophical motivations with Richard Feynman's practical approach to quantum computing. He explains how Feynman focused on simulating physics with computers, leading to the foundational ideas of quantum computing, while also acknowledging the broader intellectual movements that contributed to its development.
"you know if you could build a computer right that uh you know could do a superposition over of different computations and then you could see the results of interference between them right that at that..."
Breakthroughs from Outside Academia
Aaronson examines the contributions of individuals outside traditional academic paths to the field of quantum computing. He shares anecdotes of notable breakthroughs by those who have left academia or worked on the fringes, emphasizing the value of diverse perspectives in advancing scientific knowledge.
"much crazy stuff that it's it's you know it's very hard to believe that that a modern day uh wiesner or or everett you know would feel any uh barrier to you know to getting their their idea out there ..."
The Evolution of Academic Openness
Aaronson discusses the changing landscape of academia since the 1970s, addressing the perception that it has become less open to new ideas. He reflects on how the introduction of pre-print servers has transformed the scientific landscape, allowing for a wider dissemination of unconventional ideas in fields like quantum physics.
"a a universal quantum simulator um you know i mean people were that there was also a whole movement in the 70s and 80s to think about the physics of computation including like the thermodynamics of co..."
The Spectrum of Ideas in Quantum Computing
In this segment, Aaronson discusses the wide range of ideas circulating in the quantum computing community, including those from self-taught individuals. He reflects on the challenges of discerning valuable contributions from the noise of numerous bold claims, highlighting the importance of expert guidance in the field.
"china i think but then moved to the us and then uh worked um making and making sandwiches uh you know just you know in order to like support his family and and you know work uh of various other odd jo..."
Collaborative Research Beyond Academia
Scott Aaronson shares his experience of collaborating with individuals outside academia on research projects. He highlights the potential for innovative ideas to emerge from unconventional sources and the importance of maintaining connections with curious minds in the field of quantum computing.
"the whole spectrum uh but um you know the the the other thing you you find is uh uh you know there are you know and and a lot of the readership of my blog comes from people who who studied technical s..."
Breakthroughs from Outside Academia
In this segment, Scott Aaronson examines the contributions of individuals outside traditional academic settings to the field of quantum computing. He shares anecdotes about notable breakthroughs from those on the margins of academia and discusses the spectrum of ideas that emerge from both established researchers and self-taught enthusiasts.
"and you mentioned uh weisner everett and both of them i understand we're kind of um i don't know look down at ostracize or something um is there is has that is that theory confirmed i think i mean it ..."
The Spectrum of Ideas in Quantum Computing
Aaronson elaborates on the diversity of ideas in quantum computing, highlighting the challenges of sifting through numerous bold proposals. He shares his experiences with unconventional thinkers and the importance of maintaining a connection to fundamental questions, even for those who have left academia.
"opposite direction uh and you know and then this is partly because we now have this pre-print server this archive where you know everyone can post you know all of their new research ideas you know wit..."
The Busy Beaver Function Explained
Scott Aaronson delves into the concept of the Busy Beaver function, a mathematical function that grows faster than any computable function. He explains its origins, defined by T. Rado in 1962, and how it relates to Turing machines. The segment highlights the paradox of naming large numbers and the implications of the Busy Beaver function in the realm of computability and logic.
"integers and the way that uh we we define it you know it was so it was it was invented in 1962 by a mathematician named t borrado and uh and and and basically what we do is um what we what what what w..."
Understanding Computability and Limits
In this segment, Aaronson discusses the limitations of computability through the lens of the Busy Beaver function. He explains how only a finite number of values can be proven from the axioms of set theory, referencing Gödel's incompleteness theorem. The conversation emphasizes the challenges in determining higher values of the Busy Beaver function and the implications for mathematical logic.
"that way is computer programs or touring machines and so we could say um think of the largest integer that can be generated by a computer program that is at most let's say a thousand bits in length ok..."
The Busy Beaver Function Explained
Scott Aaronson introduces the Busy Beaver function, a concept in theoretical computer science that represents a sequence of rapidly growing integers. He explains its significance in understanding computation and the paradoxes involved in naming large numbers, drawing connections to Alan Turing's work and the nature of computer programs.
"i'm sure your comment section an email fills up with these but have you um how many of the important ideas or do many important ideas in the field come from people outside academia or is it mostly peo..."
The Growth of the Busy Beaver Function
Scott Aaronson elaborates on the astonishing growth rate of the Busy Beaver function, illustrating how it surpasses any computable function. He provides specific known values and discusses the mystery surrounding higher values, which remain unproven. This segment underscores the significance of the Busy Beaver function in understanding the boundaries of computation and mathematical theory.
"call the nth busy beaver number yeah so uh uh so so so the way that rado defined this was using touring machines which is just one particular programming language the one invented by alan turing in th..."
The Busy Beaver Function Explained
Scott Aaronson delves into the Busy Beaver function, a concept introduced by mathematician T. Rado in 1962. He explains how this function defines the largest number of steps a Turing machine can execute before halting, emphasizing its rapid growth compared to any computable function. This segment highlights the paradox of naming large numbers and the implications of computability in mathematics.
"integers and the way that uh we we define it you know it was so it was it was invented in 1962 by a mathematician named t borrado and uh and and and basically what we do is um what we what what what w..."
Understanding Computability and Growth
In this segment, Aaronson discusses the implications of the Busy Beaver function's growth, which outpaces all computable functions. He explains how only a finite number of values can be proven from set theory, referencing Gödel's incompleteness theorem. This exploration reveals the complexities of mathematical logic and the limits of what can be computed.
"that way is computer programs or touring machines and so we could say um think of the largest integer that can be generated by a computer program that is at most let's say a thousand bits in length ok..."
Proving the Unprovable
In this segment, Aaronson explores the relationship between the Busy Beaver function and Gödel's incompleteness theorem. He discusses the implications of proving certain values of the Busy Beaver function and the challenges faced in extending set theory. The conversation highlights the intricate connections between computability, logic, and the limits of mathematical proof.
"you know we can we will you know presumably it has definite values right because it's this clearly defined function and yet we could we could no longer prove what they are okay so so right now only yo..."
The Quest for Higher Values
Scott Aaronson shares insights into ongoing research regarding the Busy Beaver function, including efforts to determine higher values and the implications for set theory. He discusses the challenges of constructing Turing machines that can prove these values and the significance of large cardinal axioms in extending mathematical frameworks. This segment emphasizes the ongoing quest to understand the limits of computation.
"if you have triggers and it will grow that's exactly what i meant when i said grows faster that right right i mean each particular value of busy beaver is just some positive integer right yeah it's ve..."
The Challenge of Proving Busy Beaver Values
Scott Aaronson elaborates on the challenges faced in proving values of the Busy Beaver function, noting that only a few values are known. He discusses the significance of the function in relation to set theory and the implications of finding a Turing machine that can determine these values. This segment underscores the intersection of computability and mathematical proof.
"you know the the the the amazing thing is one can prove that this function grows faster than any computable function okay so uh uh so you know no matter what uh uh uh you know sequence of integers you..."
The Role of Set Theory in Computability
In this segment, Aaronson discusses the foundational role of set theory in determining the values of the Busy Beaver function. He explains how the complexity of set theories relates to the computability of these values and the implications for mathematical consistency. The conversation highlights the ongoing exploration of set theory's boundaries and its impact on understanding computability.
"higher and higher values of a busy viewer uh that's a that's a that's a wonderful question uh um you know we we i i would say we we we don't really know yet right because right now we can't even pin d..."
Exploring Set Theory and Busy Beaver
In this segment, Aaronson and his interlocutor discuss the relationship between set theory and the Busy Beaver function. They explore the potential for extending set theory to prove higher values of the function and the implications of Gödel's theorem on consistency. This conversation highlights the ongoing quest in mathematics to understand the limits of computation.
"of how this function grows yeah yeah and by the way i recommend everybody who's listening to check out the busy beaver frontier paper because it was written in such a way that i also want to ask you h..."
The Search for Higher Busy Beaver Values
Scott Aaronson shares insights from his research on determining the smallest n for which the value of Busy Beaver is independent of set theory. He discusses the engineering challenges involved in constructing a Turing machine to explore this question, emphasizing the complexity of proving higher values. This segment illustrates the intricate relationship between computation and mathematical theory.
"higher and higher values of a busy viewer uh that's a that's a that's a wonderful question uh um you know we we i i would say we we we don't really know yet right because right now we can't even pin d..."
Thought Experiments on Computability
Scott Aaronson engages in a thought experiment regarding the computability of the Busy Beaver function. He discusses the implications of simulating the universe and the potential for discovering higher values of the Busy Beaver function. This segment raises philosophical questions about the nature of computation and the limits of human knowledge in mathematics.
"only uh n states then you've proven that that set theory cannot determine the value of busy beaver event because if it did then it would thereby determine its own consistency which is exactly what gir..."
The Limits of Computability
In this thought-provoking segment, Aaronson discusses the implications of the Turing principle and the computability of the physical world. He poses a hypothetical scenario about simulating the universe and the potential to compute Busy Beaver values indefinitely. This exploration raises questions about the nature of computation and the limits of mathematical discovery.
"right and you know a lot of coding and and and engineering and new and ideas right uh since then uh uh a uh again a a a hobbyist to come back to your earlier question someone outside of academia by th..."
The Future of Busy Beaver Research
In this concluding segment, Aaronson reflects on the future of research related to the Busy Beaver function. He discusses the challenges faced by mathematicians in determining new values and the implications for the field of computability. The conversation emphasizes the ongoing nature of mathematical inquiry and the quest for understanding the limits of computation.
"at whatever point you know zf set zermalo frankel set theory you know which is the the accepted basis for for you know most of mass at whatever point it runs out of steam you know we don't know exactl..."
Contradictions in Computability
Scott Aaronson concludes the discussion by addressing the contradictions that arise from the assumptions of computability and the quest for higher Busy Beaver numbers. He reflects on the historical context of the last proven Busy Beaver number and the challenges that lie ahead in mathematical logic. This segment encapsulates the ongoing dialogue about the boundaries of computation and mathematical truth.
"that then sets a bound on how many busy beaver numbers that set theory can ever determine right so so in some sense these set theories that can determine more and more busy beaver numbers will have to..."
The Busy Beaver Paradox
Scott Aaronson discusses the Busy Beaver function and its implications for computability. He explores the idea of simulating the universe and the limits of computation, questioning whether we can indefinitely extend our understanding of the Busy Beaver numbers. This segment delves into the philosophical and mathematical challenges posed by the Busy Beaver function, highlighting the tension between computability and the potential for infinite discovery.
"can simulate the earth and uh the solar system and everything on a very incomprehensively big computer right um with all the humans on it give given the appropriate initial data yeah yeah and so simul..."
The Busy Beaver Conundrum
Scott Aaronson discusses the Busy Beaver function and its implications for computability. He explores the idea of simulating complex systems and the challenges of proving higher Busy Beaver numbers, questioning whether the Turing principle holds true in the context of indefinite computation.
"can simulate the earth and uh the solar system and everything on a very incomprehensively big computer right um with all the humans on it give given the appropriate initial data yeah yeah and so simul..."
Quantum Algorithms: The Search for New Discoveries
In this segment, Aaronson reflects on the state of quantum algorithms since the discovery of Grover's and Shor's algorithms. He discusses the lack of fundamentally new quantum algorithms in the past 25 years and the importance of generalizations and variations of existing algorithms. Aaronson emphasizes the need for new problems to stimulate the discovery of groundbreaking quantum algorithms, suggesting that innovation may come from exploring uncharted territories in quantum computing.
"have a contradiction yeah yeah yeah so so then either everything is not either the touring principle is false or we can't indefinitely keep extending yeah yeah yeah you could say a a very conservative..."
Quantum Algorithm Discovery
Aaronson reflects on the potential for discovering new quantum algorithms beyond Grover's and Shor's. He emphasizes the importance of finding fundamentally new problems that quantum computers could solve, suggesting that the lack of new algorithms may stem from a lack of imagination or unexplored problem spaces.
"have a contradiction yeah yeah yeah so so then either everything is not either the touring principle is false or we can't indefinitely keep extending yeah yeah yeah you could say a a very conservative..."
The Nature of Algorithmic Discovery
Scott Aaronson examines the historical context of algorithmic discoveries, comparing quantum algorithms to classical algorithms. He discusses how foundational techniques in classical computer science were established early on and how they continue to influence the field. This segment highlights the significance of Grover's and Shor's algorithms as fundamental motifs in quantum computing, suggesting that the future of quantum algorithms may depend on recognizing and building upon these foundational ideas.
"right and uh you know you know maybe maybe no other quantum algorithm as fundamental as shores or grovers has been discovered you know in the last 25 years uh what we have um discovered uh you know as..."
Finding New Problems for Quantum Algorithms
In this segment, Aaronson addresses the challenge of discovering new quantum algorithms by identifying new problems. He discusses the phenomenon of 'low-hanging fruit' in scientific discovery and the importance of finding novel problems that quantum computers could solve. Aaronson suggests that as quantum computing technology advances, it may lead to the identification of new applications and problems, thereby stimulating further discoveries in quantum algorithms.
"think of that as a failure of classical algorithms right we just think of it as you know there are these fundamental features of the algorithmic universe that you know that people noticed as soon as t..."
The Evolution of Quantum Algorithms
In this segment, Scott Aaronson discusses the historical context of quantum algorithms, comparing them to classical algorithms. He highlights how foundational algorithms like Grover's and Shor's serve as motifs for future discoveries, and he questions whether the field has reached a plateau in innovation.
"years uh what we have um discovered uh you know as you as you learned because you took my class was uh you know a lot of you know an enormous number of generalizations and new applications and variati..."
Low-Hanging Fruit in Quantum Computing
Aaronson addresses the phenomenon of 'low-hanging fruit' in scientific discovery, suggesting that early breakthroughs in quantum algorithms may have set a high bar. He proposes that new discoveries may require identifying entirely new problems that quantum computers can tackle, rather than just refining existing algorithms.
"early on right and and we don't normally think of that as a failure of classical algorithms right we just think of it as you know there are these fundamental features of the algorithmic universe that ..."
The Potential of Quantum Algorithms
Scott Aaronson explores the potential for new quantum algorithms, citing specific examples such as computing the edit distance between strings. He discusses the current limitations of known algorithms and the evidence suggesting that quantum algorithms could outperform classical ones in certain scenarios. This segment emphasizes the ongoing quest for innovation in quantum computing and the importance of continued research to uncover new algorithmic possibilities.
"know new problems or new applications just like with grover's algorithm is there some reason to expect that from from first principles there are other algorithms that can be solved by a quantum algori..."
The Power of Intellectual Hubs
Scott Aaronson discusses the significance of intellectual hubs like Cambridge University and Silicon Valley in fostering innovation. He explains how these environments attract brilliant minds, leading to a synergy of ideas that can revolutionize fields such as mathematics, economics, and physics. The segment emphasizes the correlation between a conducive environment and the emergence of groundbreaking ideas.
"we could we could look at uh a cambridge university right right let's say you know at the the turn of the 20th century right that had just so many mathematicians economists uh philosophers uh physicis..."
The Search for New Quantum Problems
Scott Aaronson discusses the potential for new quantum algorithms by exploring previously unconsidered problems. He uses the example of computing edit distances in DNA sequence alignment to illustrate how quantum computing could revolutionize certain fields, despite the current lack of discovered algorithms.
"know new problems or new applications just like with grover's algorithm is there some reason to expect that from from first principles there are other algorithms that can be solved by a quantum algori..."
The Power of Intellectual Hubs
Scott Aaronson discusses the significance of intellectual environments, using examples like early 20th-century Cambridge and Silicon Valley. He explains how these hubs attract brilliant minds, fostering innovation through collaboration and competition. The conversation highlights the correlation between environment and groundbreaking ideas, emphasizing that while correlation doesn't imply causation, the presence of great thinkers in certain locations can lead to revolutionary advancements.
"we could we could look at uh a cambridge university right right let's say you know at the the turn of the 20th century right that had just so many mathematicians economists uh philosophers uh physicis..."
Complexity and Nash Equilibria
In this segment, Aaronson delves into the complexities of finding Nash equilibria in economics, highlighting a significant theoretical advancement in computer science. He explains why computing Nash equilibria is a hard problem and discusses its implications for economic theory, emphasizing that the existence of an equilibrium does not guarantee that it can be easily found in practice.
"discover these things right correlation doesn't equal causation in this case okay all right uh let me ask you now i've interviewed a lot of economists on this podcast i think this question will be int..."
Hayek's Knowledge Problem and Complexity
Scott Aaronson connects Hayek's knowledge problem to computational complexity, discussing how central planning can be likened to NP-complete problems. He explores the challenges of lacking information and computational ability in economic decision-making, emphasizing the importance of understanding these complexities in economic theory.
"result you know underscoring that that general point that that's incredibly interesting um do you think uh hayek's knowledge problem or the way he phrased it might be related to uh uh complexity as we..."
Complexity in Economics: Nash Equilibria
In this segment, Aaronson delves into the complexity of finding Nash equilibria in economics, referencing a significant theoretical advance in computer science. He explains why computing Nash equilibria is a challenging problem, contrasting it with simpler von Neumann equilibria. This discussion underscores the implications for economic theory, suggesting that the difficulty in finding equilibria may reflect broader issues in market behavior and rationality.
"discover these things right correlation doesn't equal causation in this case okay all right uh let me ask you now i've interviewed a lot of economists on this podcast i think this question will be int..."
Hayek's Knowledge Problem and Complexity
Scott Aaronson connects Hayek's knowledge problem to computational complexity, discussing how central planning faces challenges due to limited knowledge and computational abilities. He explores the relationship between lack of information and the difficulty of solving economic problems, emphasizing the importance of understanding both aspects in economic theory. This segment highlights the nuances of decision-making in economics and the role of information in achieving effective outcomes.
"result you know underscoring that that general point that that's incredibly interesting um do you think uh hayek's knowledge problem or the way he phrased it might be related to uh uh complexity as we..."
Creativity and Complexity Classes
Aaronson reflects on the relationship between creativity and complexity classes, suggesting that humans possess a unique toolbox of heuristics developed through evolution. He discusses the challenges of defining creativity algorithmically and compares human creative abilities to those of other species, emphasizing the nuances of measuring creativity across different evolutionary backgrounds.
"than the computational considerations okay that's incredibly interesting um just a few more questions okay sure yeah i'm going to bring this back to um david deutsch and creativity okay in the ask me ..."
Creativity and Universal Explainers
Aaronson reflects on the nature of creativity, questioning whether it can be algorithmically defined. He discusses the evolutionary advantages humans have in problem-solving compared to other species, while also addressing David Deutsch's concept of 'universal explainers.' This segment explores the thresholds of intelligence and creativity across species, emphasizing the unique capabilities of humans in understanding and explaining complex concepts, and the philosophical implications of such distinctions.
"than the computational considerations okay that's incredibly interesting um just a few more questions okay sure yeah i'm going to bring this back to um david deutsch and creativity okay in the ask me ..."
Universal Explainers and the Nature of Knowledge
In this thought-provoking segment, Scott Aaronson engages with David Deutsch's concept of 'universal explainers.' He discusses the thresholds of intelligence that distinguish humans from other animals and the implications of this distinction for our understanding of knowledge and explanation. Aaronson critiques Deutsch's optimism and explores the complexities of what it means to be a universal explainer.
"do you uh from the beginning of infinity do you buy david deutsche's uh term a universal explainer that people are universal explainers ai's will be universal explainers but uh non-human animals aren'..."
The Infinite 'Why' and the Limits of Explanation
In this segment, Aaronson elaborates on the nature of inquiry, likening it to a child's incessant questioning of 'why.' He emphasizes that each answer leads to deeper questions, illustrating the complexity of understanding fundamental concepts. He also introduces the busy beaver function as a metaphor for the limits of computation and understanding, suggesting that some questions may remain forever unanswered.
"that that may be called comfort to uh to to to to most of us here on earth right and so when he when he says something like people are universal explainers you know you always have to press him on you..."
The Limits of Explanation
In this segment, Aaronson explores the idea that some questions may be inherently unanswerable, such as the hard problem of consciousness. He draws parallels to the busy beaver function in computational theory, suggesting that there may be fixed questions that our current frameworks cannot address. He emphasizes the need for continued exploration and creativity in the pursuit of knowledge.
"that that may be called comfort to uh to to to to most of us here on earth right and so when he when he says something like people are universal explainers you know you always have to press him on you..."
Creativity and New Axioms
Scott Aaronson elaborates on David Deutsch's views regarding creativity and the necessity of new axioms in science. He discusses how creativity plays a crucial role in solving complex problems, such as the hard problem of consciousness, and the importance of not limiting our understanding to existing frameworks. This segment highlights the dynamic nature of scientific inquiry and the potential for new discoveries.
"way back at the big bang right you know you're you're back at uh uh uh you know the uh um um the the the beginning of the universe and you know they continue asking why right and and uh it it it it it..."
Creativity and the Hard Problems
Scott Aaronson connects creativity to the challenges of explaining complex phenomena, referencing David Deutsch's ideas on incompleteness. He discusses the hard problem of consciousness and the potential for new axioms to emerge in understanding it. Aaronson expresses a desire to continue seeking explanations rather than asserting definitive answers, highlighting the importance of creativity in scientific inquiry.
"deeper okay but now you know just to just to loop back to earlier in this conversation like if we think about the busy beaver function right we know that you know it's not just that uh um uh you know ..."
Advice for Aspiring Experts
In this concluding segment, Aaronson offers practical advice for young individuals interested in technical fields. He encourages them to leverage the wealth of resources available today, engage deeply with subjects, and strive to become experts in niche areas. He emphasizes that while mastery takes time, becoming knowledgeable in a specific problem can lead to broader opportunities and collaborations in the future.
"i think he thinks a hard problem consciousness can be solved but even if it can't be solved like the reason it's so hard is not because it's not an artifact of our mind it just seems like we can't ima..."
Advice for Aspiring Experts
In this concluding segment, Aaronson offers practical advice for young individuals interested in technical fields. He encourages them to leverage the wealth of resources available online, engage deeply with subjects of interest, and strive to become experts in niche areas. He emphasizes that while becoming an expert may take time, focusing on specific problems can lead to significant contributions and collaborations in the future.
"uh you know it can be when you're searching for explanations you know it can be psychologically helpful to you know assume that the explanation exists uh but you know but but uh let's let's not make t..."