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 the world expert 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 tell us a bit about your early journey you were a young prodigy you graduated high school at the age of 15 got your phd at 22. 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 several reasons i mean uh just you know socially uh academically and i i wanted to uh get out and uh 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 to hong kong i lived in hong kong for one year because my my my dad was working there and because of the uh miss 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 that was uh uh appropriate i guess i i you know i had always been sort of a head in math and uh the only way to deal with that was for
me to skip a a grade and skip and and go to the high school 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 you know where where i really wanted to be was college
right i wanted to be in a um in a in a place where where you know uh you know and and and and and of 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 be able to choose uh what to study and advance at your own pace and you know all of these these wonderful things um and and you know so then i i returned from hong kong to the u.s and was in uh uh public high school for 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 basically suggested to the school uh well why doesn't he just uh uh do do online learning right and do like 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 uh that that's you know uh uh um and uh so i sort of seized on that as my excuse i um uh um uh i i i think i just seen a brochure
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 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 want i want to give this a try and uh my my uh parents you know allowed me to 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 old
high school who was very very good and who was you know trying to advocate for me and he was like okay guess what you know i just got it so that so that scott can take the uh the epgy program and we said too late sorry 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 problems as it as at high school but you know at least you know i was uh uh you know i was able to take courses that were a lot more interesting 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 freshman but you know but with a year of college credit so i uh i did that um you know i was i was very you know just very disappointed in the tie
at the time at how things turned out because you know i got rejected from 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 but then there was one problem that they
required a high school diploma before you could enroll there with which i didn't have uh and so so we needed we realized that i needed a ged from you know well okay my my old high school you know oftentimes once all on one's old high school we'll just give you a diploma after you've gone to clarkson my high
school would not do that because they said i was missing phys ed i would have to you know spend the summer doing phys ed but uh um uh so uh you know and then new york state said uh we can't give him a ged because you have to be 17 to have a ged and he's 15. um and and my mom eventually convinced them
to make an exception and uh give me a ged so that so i said so then i went to cornell i mean i've met other people who were homeschooled who you know actually did things that were more radical than than what i did i mean i i was accelerated by three years you know that was all and then after i
was in college i didn't really accelerate anymore because you know i felt like i was you know in an environment you know where i i wanted to be and uh you know from now on these are the the main limitations were were internal they were they were no longer external was it intimidating being in classes
with people three or four years older than you uh the truth is you know i would say the majority of them didn't even know that i was younger if they knew it was uh uh like in uh you know maybe uh in an oddity a little bit but then they didn't care that much right i mean
because you know it's it's not like i was a 10 year old right i was uh you know i mean by the time i started at cornell i was 16 by then and um um you know i uh um uh so i i feel like um um um academically it was fine i mean you know the main issue was was social right you know and my my parents had you know
had warned me that okay you know if to skip grades is going to completely screw up my social life and uh you know it's going to make dating you know incredibly difficult and and so on and so on and i i sort of brushed all of that aside you know in my my you know i mean um um um you know
of course that all turned out to be true you know i got i got my uh phd uh before basically before uh i i learned how to drive really or or or learned how to have any kind of a social life you know to speak of i mean or you know any any kind of a dating life really uh but um so you know i did things in a
weird order you could say and and and and that did cause you know an enormous amount of stress for me but but my main argument was that you know i was already socially unhappy in high school right i was i i was already miserable you know without having skipped grades and so i felt like you know as
long as i'm going to be miserable socially anyway as it seemed at the time you know i would be that you know at least i could be learning stuff at least at least the academics could be better yeah and as far as the academics go uh what were the advantages and disadvantages of specializing so early
well i mean i i don't get to re-run my life multiple times and and compare uh um but i i think that um um you know mainly i'm i'm i'm grateful that i had the opportunity to uh you know to sort of learn about stuff that that interested me and and it was not it was not just you know that you know i i wanted to
take only math and cs and nothing else right it was not like that i mean i uh i took uh uh you know plenty of humanities in in college right and uh uh but you know i i wanted to uh sort of have some some freedom to uh you know i i pick what what to learn about right i mean like in
in in high school uh you know humanities means uh you know the five paragraph essay right it means uh uh you know you basically have to regurgitate what the teacher wants from you right and you know if you try to you know do your own thing write things in your own way then you will actually
fail right and uh you know this i i learned this from experience you know this is not theoretical right uh and um you know so even even even the humanities right i was a lot happier with in college than i was in high school uh so it so it wasn't just a matter of of specialization
but but partly it was i mean i think that by the age of uh 16 or so i i knew what what i was passionate about it was the fundamentals of computing right and understanding what computers could or couldn't do and i was ready to be to be learning about that and working on it and um you know i think that there there is
you know the the entire concept of you know of sort of teenager hood right that like people are are you know from the age of 12 to 18 or now maybe even 20 or so we're still basically children right i think that that's largely a modern construction right if you go back even a few hundred years
you know by the time someone is a teenager right they're they're an apprentice right they can work you know uh you know they can be learning while they're also you know working and they can be they can be learning you know the trade that they choose and um so so so i think that that that's actually
natural right i don't feel like i'm that unusual in that respect i think you know i mean you know you know unusual in some respects but but not in in in wanting to sort of get started with life when you know i was 15 or 16. yeah i had tyler count on the podcast and he started um he knew he wanted to be an economics
professor basically in his early teens and he was reading and preparing for that um from that time on economics professor is not what you know one often thinks of as like a child you know or an adolescent realizing that they want but that is the that that that uh for for uh in the case
of tyler cohen i could easily believe that is there some special advantage of learning the fundamentals of the field you know you're going to go into early on so instead of except for the fact that you just get more years to accumulate knowledge is there the special advantage of learning it in your
early years you know i'm not sure yeah it's a it's a very interesting question i mean you know what one one could imagine 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 this right like you know an obvious one would be learning languages right where you know there there's a window where you know children can just soak up languages you know like a sponge and you know after that window uh okay one you know you can learn a language but it will be a
difficult you know intellectual puzzle and you'll never speak it as well as a as a as a native five-year-old will speak it right so um so it it it could be like that but it could also be that uh you know like our our our our our brains are not uh really adapted for for learning any of this stuff
right i mean like you know uh when we get to you know theoretical physics theoretical computer science and so on right you know all of it is is uh is is like you know learning a language that we don't natively speak right and and on that on that model it would just be a question of getting a
head start of of you know of how much time you have to spend on it uh i would i would love for someone to research that question because i i don't know the answer i have heard uh well so you as you know like many of the important discoveries and quantum mechanics were made by people where who
at the time were very young right and that's an interesting fact not only did i learn that stuff early on but like they made those contributions early on yeah but but that's not just quantum mechanics i mean that's uh all over you know math and and physics right there's i mean i mean i mean newton was uh you
know about 22 right when he uh you know had his miracle year uh you know of uh uh inventing calculus you know discovering the laws of mechanics um yeah i mean no i mean i mean you know i'm already old by the standard 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 know so that that that's that's another empirical question that i wonder about right is it that people's brains actually slow down as they as they get older or is it simply that
they have less motivation or less free time right i mean like i got in in my case you know having two kids you know get clearly given me enormously less time for research right and you know when like in those cases where i'm you know traveling where i'm you know away from the kids for a week you know maybe like
i can work again and it sudden you know it feels a lot like it did when i was in my 20s right and so um you know yeah and and and then there's also the issue of motivation right that like uh when i was uh before i was established you know like my my entire conception of myself you know
my entire like uh uh goals for my life were wrapped up and you know succeeding in research you know at uh uh you know doing whatever it took and now you know it's more like you know i i have all kinds of other concerns i have my own students uh to worry about you know my my postdocs
my my kids of course uh my my my blog you know the popular things i write and you know research just feels like one more thing that i do right that my my identity is not as much wrapped up in so you know i i i may have also gotten dumber right that's that's certainly possible right but you know it's hard to
disentangle from those other factors yeah you're the third person and i 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 that you know people make like very
important discoveries at young ages but they make lots of seemingly uncorrelated important discoveries at young ages so as you know like einstein did um brownian motion um uh special relativity what was the third one there were three more well there was the photoelectric yeah that's right
uh and these don't seem superficially at least to be related and yet it's interesting to happen in the same year but what do you think explains that phenomenon uh in in in in in the case of einstein uh i mean you know you're asking me to explain einstein's miracle year i mean that's that
that's a that's a that's a that's a tall order i mean i mean one one can one can say certain things like you know one can say that you know physics in the early 20th century was ripe for these you know for for for these interrelated revolutions right of relativity and quantum mechanics right you know i mean you know if if it
wasn't einstein it would have been someone else you know uh uh not long after with all of those things i'm general relativity which you know which took einstein a decade longer you know that was the one thing where if it hadn't been for einstein then you know it it for all we know it might have been
decades before anyone else did that but uh you know the the um you know the stuff that he did uh in his uh in in in 1905 i mean you know they were all things that physics was kind of ripe for maybe it took you know one person just looking at things in a sufficiently different way
um you know i'm not i'm not i'm not sure really but uh um but you know but but also it might be you know the confluence of all of those things is part of why you know we think of einstein as einstein right you know there were there were there were many other great physicists you know around the same time
you know who may have done you know one or two things of that caliber right but but you know uh uh but but but but but only only einstein does that those three 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 rereading the lecture notes from your quantum information science class and there's the lecture on quantum teleportation and you were answering how is it how do people figure this kind of stuff out and you say it's worth pointing out
that quantum mechanics was discovered in 1926 and that quantum teleportation was only discovered in the 90s and of course quantum computing uh i'm a big fan of david deutsch and he discovered it or he thought of it in the 80s it seems like these ideas were ready to pluck you know
back when quantum mechanics was developed why did it take so long to have these ideas plucked yeah that's a that's a that's an extremely interesting question um i i mean you know the the the whole idea of of thinking about quantum entanglement you know and not as something like metaphysically
weird or or you know uh spooky or basically how do we explain this away how do we get rid of this but in terms of how do we use it right how do we use it for you know to improve uh information processing right i think that that's that's a point of view that uh as far as i know really only started with
uh with john bell in the 1960s right with uh you know bell having this remarkable insight uh that that you know you could you could you could do this uh experiment to test the prediction of entanglement and and distinguish it from any possible theory involving you know local hidden variables
right and uh um you know and then 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 until the 80s uh and you know there are there are a few things that i could say here
i mean um um one is that when when quantum mechanics was discovered in the in the 20s uh it was not at all clear to the people who who discovered it that this was sort of a a final form that the laws of physics would take right you know they thought you know i mean uh uh that there was a large
contingent that that thought that uh you know this this is some you know uh scheme that that sort of represents our current knowledge but you know but clearly one one you know what one has to improve on it right and then i mean that was very much einstein's point of view for example and i think also schroedinger's
uh and and then uh you know like bohr and heisenberg uh you know they were very much you know opposed to to looking for something beyond quantum mechanics but uh um but but but sort of not um you know they that like like they they sort of sort of not not in a way that was sort of you know
in inspiring more research about what you could do with quantum mechanics right they just wanted everyone to just sort of shut up and stop stop asking about these things right so you could say you know even though bohr was right and and einstein was wrong uh on the issue of local hidden variables
uh you know there's a there's a deeper sense in which which you know einstein was the more right one and sort of putting his finger on you know there is something here that we do not yet understand and that we need to understand right and you know indeed you know that i'm sorry uh and you know indeed indeed that that
that that thing would not be understood really until until the discovery of the bell inequality in the 60s the other um you know issue is that when quantum mechanics was was discovered into the you know the the 30s you know there was so much to do in terms of you know figuring out how
chemistry works right just just applying quantum mechanics to understanding the real world around us right that and uh and and you could say on on the other side in computer science you know the i mean for god's sakes the entire notion of a universal computer was just being born right
the whole note you know the whole field of classical computing was only just being born right so there was sort of so much you know on the plates of both sides that that uh you know it was you know it might have seemed wildly premature to anyone to to combine the two right and then uh of course world war ii you know
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 know and then after that i mean i think the theoretical physicists were very uh uh focused on just you know
this zoo of new particles that were being discovered and in formulating quantum field theory you know it was very very much out of fashion for for decades to think about the you know the the fundamentals of quantum mechanics itself and you know in the meantime uh um um
you know people were finally you know building uh commercializing figuring out the uses for classical computers that was a you know a very young area itself and i mean the the entire theory of computational complexity which you know is sort of an intellectual prerequisite to quantum computing
right that only developed in the 1960s right you know and then the theory of you know p and np and np completeness that was only the 1970s right so now you know if we think about you know the the people who could have combined these these fields i mean i i think of you know i think of john von neumann as
an obvious possibility because he was you know of course an uh uh one of the the great uh uh uh um pioneers of both of computer science and of quantum mechanics right in fact you know he invented the uh notion of entropy of quantum states and uh uh but you know he just he had a
lot of other things on his plate and then he died early he died in the 50s right i mean you know alan turing was also you know of course you know founder of computer science who is also uh passionately interested in the foundations of quantum mechanics you know as we know from his his letters uh to his friends
uh you know he uh he he died when he was 42. right so so you know what whatever the case you know i feel like quantum mechanics and the theory of computing were both in place by the 1930s but there was a lot of other stuff on 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 maybe a decade after that people start thinking about quantum computation interesting 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 to think seriously about um quantum computing was that he took the menu world's interpretation seriously and because people before him hadn't taken many words seriously they hadn't
been able to contributing sorry go ahead go on go on okay maybe maybe maybe should i respond to that one yeah okay so that is definitely true for deutsch right and i know you know uh deutsche well you know and then you know and he uh uh uh actually you know became a big believer in the many worlds
interpretation when he was here at ut austin right as a student as you know and he he heard uh hugh everett himself give a lecture about it uh bryce dewitt who was uh uh uh uh one you know one of the main early proponents of the many worlds interpretation was also here at ut austin and uh had a big role had a
big influence on on deutsche and you know and deutsche was was thinking about uh you know how would you sort of make you know sort of shake people how would you sort of make them realize that quantum mechanics is universally valid that it applies at all scales well 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 point conceptually it is almost like making a superposition over you know a brain that can think different thoughts
right and uh and then you know if you could have that then then you know the whole idea of the uh that observers collapse the wave function just by being observers is no longer terrible but so one one problem is that richard feynman had the idea of quantum computing around the same time as deutsche did
right and fine men i mean he was certainly aware of the many worlds interpretation he was aware of effort but but that was not his motivation for thinking about quantum computing uh he was you know as as usual he he was much more practically focused he was thinking about how do we simulate uh physics you know
how do we simulate nature with a computer and if we use classical computers we suffer this exponential slowdown right and uh so can we build a new kind of computer that will that will solve that problem and give us a 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 computation can you make computation inherently reversible you know and all kinds of other issues right that are there that are not about you know exponential speedups but that
was also one of the intellectual streams that sort of led directly to quantum computation right so so i think that what you said is very much true for deutsche but you know there were others you know besides deutsch who were thinking about these things feynman was only one there were there
were others as well i think you know benioff uh uh you know and several others and um you know uh um you know few few people 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 touring were trying to solve the separate philosophical problem when they came up with their model of computation um at least in part okay so the second theory i've heard is that uh since the 1970s that academia has been less open to new ideas 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 is possible that in some parts of academia you know it has become harder to explore new ideas you know i uh than it did
than it once was um you know i could believe that about the social sciences i could believe that you know about parts of medicine you know people used to do just completely crazy things just you know invent some new concoction inject themselves with it you know see what happens you know write an article about it
you know whereas today you know it might take like a billion dollars of investment before you could even get to the point where you know anyone would consider it remotely ethical to do such a thing right so uh on the other hand 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 cosmology and things like that i i think if anything things have gone in the 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 with no filter right uh you know and and i think that that is that is somewhat transform the the scientific landscape uh um you know because i mean we still have journals but you know journals are now just like
a final stamp of approval that you know in many fields is yeah i mean it's important when you're looking for jobs or things like that but journals are no longer gatekeepers to you know that can sort of prevent people from seeing your paper right and so uh so you know if you just look at the
quantum physics you know archive every day you will see so many far out ideas right it is so 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 right i mean
today the the problem is more than like there are so many you know bold new ideas that you know of course you know most of them won't go anywhere right most of them will fail right and you know and so there's there's so much to sift through if you're you know looking for what is
what is what is actually going to be revolutionary 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 people with phds working within the system uh well okay
i mean those are those are not uh uh uh exhaustive categories right because you know there there are um you know there there are there there have been uh breakthroughs that have come from people who were not in academia um very often what you find is that these are people who were sort of on the margin of
academia like they got a phd and then they left you know the the academic world or they uh they did part of a phd or or or things like that right there was a uh famous case of yi tang zhang who was this mathematician from from china right who uh uh um proved that that there are infinitely
many pairs of primes at most 70 million apart right which was you know a major advance in number theory right and this was a guy who would like he had gotten a phd in math in 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 jobs but you know but but continued working on math uh so um i don't you know i mean i mean uh you know i i hear all the time from you know people who are who are like complete uh auto detects you know who uh you know
taught themselves yes and and you know that they think that they've solved the p versus np problem or whatever right i i've uh uh um you know that that is uh uh um you know that that that is usually someone who just doesn't understand the question who has just made some you know uh uh uh um [Music]
you know and and and and then and then you know i mean there is a distinction because some sometimes people you know uh who sort of teach themselves the field they just you know they they really want to learn they just want an expert to talk to you know who will tell them like here's
here's where you're on the right track here's where you know you you made a mistake and they will thank you for that right other times you get people who really dig in their heels and you know you know the establishment is is censoring me and uh you know i had when when i taught at mit i had you know someone
uh uh like writing to the president of mit to try to get me fired uh uh you know i had another one sending me death threats you know uh because um um you know like very very specific you know i had to actually contact the police about them uh you know because i would not publish their you know
proof of p equals np or their refutation of quantum computing on my blog right so you get you get you get you get 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 subjects in college studied cs or math or physics and then went out into industry right but maintain this connection you know maintain their sort of curiosity about fundamental questions and some of those people uh uh you know actually want to continue to do research and uh
i'm actually uh co-authoring a paper with one of them right now uh you know i posted this survey article about the busy beaver function uh on my blog recently and uh uh you know there was a um um you know i guess a a hobbyist who who solved some of the open problems really it was a survey and uh yeah
and and had a lot of new ideas and and he and i are going to write a paper about it now oh cool interesting by the way is that strong the same one that uh co-authored the nielsen textbook on quantum information no no no no there's a a yi tang zhang and then there's a uh the mathematician and then isaac
chwang is the physicist who co-authored the nielsen text okay go ahead my mistake um so let me ask you about busy beaver um i was is the proposition three was that uh you can't i i have no memory for the numbering of propositions so okay uh can you actually just explain what the beaver function is before i ask
yes okay sure so so the busy beaver function is a really really remarkable uh uh sequence of hyper rapidly growing uh 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 we would like to say let me let me start with what we'd like to say we'd like to say you know the um uh you know if i want to name the biggest number that i could possibly think to define then why not just say you know the biggest number that can be named using a thousand words or fewer
okay or something like that right and but then uh i have to be careful because there's an inherent paradox there right which is i also could have said like one plus the biggest number that can be named with a thousand words or fewer but then that that you know i just named that with fewer than a thousand words
right and so uh uh um so so so so from this you know the the conclusion that uh you know logicians philosophers drew more than a hundred years ago is that the concept of naming a number you know in english is not as clear as we think it is right it it leads to paradox if you're if you're
not careful about it uh but but uh uh but what what what if we could uh name a number in a way that was completely unambiguous uh well you know since then since alan turing in the 1930s we have had such a way 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 okay and uh you know now you have to be careful what do you mean by by that right because of course a computer program could run forever right it could start just it you know i
could we could easily write a program that says do print not print nine loop right and it would just print an infinite sequence of nines so what we do is we restrict attention to those computer programs that eventually hold right we say among let's say for a given n we consider all of the possible
computer programs that are n bits one and say there were two to the n power of them or at most two to the n power right many strings will just uh lead to things that are not even programmed you know they won't even compile so we'll throw those away right now among all of the valid and bid programs some of them run
forever we just run them on a blank input so we throw those away as well right we consider only the ones that eventually stop and now among all of the ones that stop we take the one that runs for the longest number of steps the largest number of steps until it stops and that number of steps that is what we
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 the 1930s he said busy beaver of n is the largest finite number of steps
that any end state touring machine can run for okay and uh uh this so so so 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 know you can uh
you know basically uh uh uh if you are in a contest to name uh name the largest number and if you say busy beaver of a thousand then you will utterly destroy any opponent who doesn't know about the busy beaver function or about anything similar to it okay so um and you know so yeah one one can say further remarkable
things about this function like that you know only a finite number of values of the function can actually uh uh be proven uh from the axioms of set theory right for reasons of girdles in completeness theorem basically uh uh after a certain finite point you know the the values of this function
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 you know if you if you look if you take the busy beaver function as rado defined it in the 60s only four
values of the function are known okay that busy beaver of one is one busy beaver of two is six busy beaver three is 21 and busy beaver of four is uh a hundred and seven busy beaver of five it is only known that it's at least 47 million okay you know and we don't know how much bigger it might be busy beaver of six
uh it's at least about ten to the thirty six thousand okay might be much bigger busy beaver of seven uh it's at least ten to the ten to the 10 to the 10 to the 18 million you know and it might be enormously larger still okay just to just to give people an idea 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 how you learned to write so well it was there in such a way that non-expert like me could understand it and just to clarify
from my own understanding it's not that busy there isn't a function that for any n is greater than busy beaver of n it's just that it it won't busy b where it will eventually be with more states than 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 very concrete thing right you know like it's six or it's 21 right but you know if you look at the rate of growth of these integers right it will dominate and eventually dominate any computable function
right and and and in practice not just eventually but very very quickly yeah and you show very elegantly in the paper that that means you can independently prove the whole thing problem and go to the completeness theorem um yeah yeah um looking at i mean i mean i mean like the uh the the unsolvability
of the halting problem girdle's theorem like these things are so intertwined like there are many many different way you know ways to prove them all right but the the busy beaver function gives you one way that yeah you can prove uh that you know that you you can you can use it to prove independently that
there is an uncomputable function uh you can use it to prove girdles and completeness theorem right okay uh so my quest the proposition three was the one that said um okay for any axiomatic theory you can't approve all of busy viewer with it um right so my question was um
can you keep even though there's no systematic way to extend our set theory is there plausibly a way that you can keep extending it uh such that you can prove 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 down busy beaver of five okay uh you know now now my guess would be that the the the resources of of you know existing set theory are are perfectly enough to do that right but but you know we don't even know that right so i so four years ago
uh uh a um a student of mine uh named adam yadidia and i decided to uh you know look into a question that for some reason no one had looked at before which was uh uh uh you know at like what is the smallest end for which we can actually prove that the value of busy beaver of n
is independent of set theory right like it was clear that there is some n for which this is true but are we talking about 10 million or are we talking about 10 right so uh so so in practice what this problem boils down to it is almost like software engineering like you have to construct a touring machine that uh
checks all of the theorems of set theory and it halts only if it finds a contradiction right and you have to build such a touring machine with as few states as possible okay you can build such a machine with 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 girdle's theorem does not allow right so um so what we managed to do is we managed to find such a machine with 8 000 states okay about 8 000 states you know that was after a lot of optimization
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 the name of stefan o'rier uh has managed to improve our bound and got it to under 800 states
yeah okay and that that is the current record now if you could get that down to like you know you know i you know it is a wonderful question could you get it down to like 10 states or something like that right and you know that that would tell us that we have to already go beyond the current axioms of set theory
you know even to just get the next few values of the busy beaver function right but maybe not maybe maybe maybe you can even get a hundred of them with with existing set theory right we we don't know now what you can do is um you know you know 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 exactly where that point is but one can then extend it by what are called large cardinal axioms right which basically assert that there exists an infinity that is
bigger than any infinity that can be defined in zf set theory right or you know you can you can say you know you know and um you know where infinity is of various particular kinds right and uh you know and and and presumably one could then settle more values of the busy beaver function that way right but but the issue is
you know no matter what set theory you think of right as soon as you can build a turing machine that enumerates all of the theorems of that set theory then however many states there are in that touring machine 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 become more and more complicated right right right we we we we know that uh and uh and and as as you said right there will never be a systematic way to search for it for them
because if there were then that would make the busy beaver function computable right um and you know and and what it means for there to be no systematic way to search is that you know you could we could keep like proposing more and more set theories and then if you look at modern you know uh
mathematical logic set theorists do this right they do propose more and more large cardinal axioms but sometimes they actually discover that their axioms are inconsistent right or you know they they sort of uh provisionally you know adopt an axiom and use it but the community is not really convinced
that it won't lead to an inconsistency right so that you know there's no surefire way to think of these axioms and and be confident that that that you know uh uh the the the that that you actually still have a consistent system okay let me offer a very very simple thought experiment uh yeah
okay so uh this is inspired by that joke that if you shoot enough sunlight at the earth it'll shoot it'll shoot a tesla back right uh okay so the idea is uh if the touring principle is true you 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 simulating all that is a computable function and if you can check in like every hundred years and see what is the biggest busy beaver number that humans have proven this century what is the biggest busy or
number proof of 100 centuries is that not a computable function where that uh tells you busy beaver of n indefinitely higher as long as oh well well it it it would give you a way to compute arbitrary values of the busy beaver function if humans were indeed to to continue uh
uh you know you could say uh uh uh under the assumptions that number one you know the uh uh you know uh uh uh um you know ev everything in our physical world is computable i mean you know we we we let that you and i just let that assumption pass almost without comment right although you know of course that's an
enormous question in itself right with some brilliant people like like penrose on the on the other side of that but all right but but you know and then just so assuming that that you know uh everything we're doing is computable and also assuming that we could somehow you know continue finding more and more
values of the busy beaver function indefinitely right if that were true then we would 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
way out would be to say well you know our quest to compute more and more busy beaver numbers will come to an end right okay that's very interesting and yeah in fact there there has not been a another busy beaver number determined since the early 1980s yeah that's interesting which is when
busy beaver four was bend down okay okay so i'm looking forward to the paper you published with the um with the hobbyist bruce smith is his name brute smith okay very interesting um okay so let me ask you now uh i i remember in class last year you said you know that basically we have a very a few very important
quantum algorithms like grover's and shores that are discovered in the 90s and now a lot of stuff now is just an extension of those algorithms what do you think is the potential of finding is there a good reason to think that there are other quantum algorithms to be discovered that are as
fundamental and important as grover's insurers were i would i would love it if there were right i i'd be i'd be thrilled uh to you know discover such an algorithm have one of my students discover it right you know this is this is uh um you know what i you know i mean i mean that's that's the kind of discovery
that we that we enter this field for right i mean you know now now uh um you know if if if we're being intellectually honest you know we have to admit that you know it's it's been 25 years since grover's algorithm was discovered 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 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 variations
of of shores and grover's algorithms uh uh you know including what are called quantum walk algorithms uh including um you know phase estimation based algorithms um and uh you know and and and some some totally different quantum algorithms were also discovered although you know the problems they
solve or maybe more obstructs right or you know heart you know it's harder to explain what what problem they're they're they're solving uh and you know so so you know you could you could wonder you know is it is it is it lack of imagination on on on on uh on our part or is it you know i mean i the the you know
another uh possibility is you know if you look at the history of classical computer science you know what you find is that there are a few basic techniques that were discovered very early on in the history of classical cs one of them is dynamic programming like uh you know dividing you know
breaking down your problem like recursively into sub problems right you know we could say you know in general recursion right so you know divide and conquer uh greedy algorithms uh you know uh uh convex programming you know linear programming uh you know uh um um gaussian elimination right uh and
you know and and and most of the you know i mean the field of classical algorithms is enormous and yet you know most of the classical algorithms that we know are somehow built up out of these motifs that are this that were discovered very 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 you know that people noticed as soon as they started looking right and then you know and then you know you can go much further but but you go much further by by
building on the basic things that you have right and so so uh so so maybe we should think of shore's algorithm and grover's algorithm not as just specific algorithms but as sort of some of the basic design motifs of the world of quantum algorithms and you know it's not it's not surprising that they were discovered
very early on just like dynamic programming was discovered you know right at the beginning of the history of classical algorithms so um uh you know so you know i mean i mean that's that that's that's one point of view now another point of view is you know if like when when people ask
for for more quantum algorithms or you know they'll say they they they hold us to account for our failure to discover more quantum algorithms you know i i like to answer that question with another question which is what are the problems that you would like these algorithms for right and and amazingly that that
question almost always stops you know they ask it right because like they didn't even you know well well uh because because no matter what problem they name you know there's an excellent chance that people in quantum algorithms have thought about it you know and we know you know something
about how much speed up you can get from a grover type algorithm you know but uh we have good reasons to think that you're not going to be able to get better than that or you know i mean or you know we or or we say well maybe there's like if in the case of the graph isomorphism problem
yeah sure maybe there's a polynomial time quantum algorithm but probably just because there's a polynomial time classical algorithm right and that you know and it's just it's that that hasn't been discovered yet right although you know there's been major progress toward it uh so so uh you know no matter what
problem they name right i mean probably someone has studied it in the context of quantum algorithms and i could then tell them for that problem you know exactly what is the current situation and you know what what are people stuck on you know and and so it might be that if we want to
discover fundamentally new quantum algorithms that the way to do it will be to realize fundamentally new problems right problems that people hadn't even thought about just designing an algorithm for you know uh previously right you know the way um you know another thing you know another way that i like to put it is
you know like like in any you know in any given area of math or science right there is this phenomenon of low-hanging fruit that gets picked very very early on right and uh and then those of us who come into the field a little bit later have to just have to weep higher you know if we want to uh find any fruit
right but uh the you know i think the the ultimate solution to the problem of low-hanging fruit being picked is to find a new orchard you know and uh so so you know figure out what our you know potential problems that quantum computers could solve that that no one has been thinking about
uh before you know maybe people actually starting to get quantum computers as they finally are today that they can experiment with will help stimulate the discovery of those you 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 algorithms yeah so so it is um uh uh you know like anything where it's sort of as basic as grover's algorithm that you just look at uh you know the way that amplitudes are changing over time and think that an
algorithm is going to exist right that probably would have been snapped up by now this because quantum algorithms have become so much more sophisticated uh compared to what they were 25 years ago okay but there are some problems where uh there is some evidence that a quantum algorithm might exist
uh even though we don't we don't yet know it if if it does exist a good example is computing the edit distance between two strings right which means the minimum number of insertions and deletions and changes that i have to make to change one string to another string this is a fundamental problem for a dna
sequence alignment for example uh the best known algorithm for it takes quadratic time it's based on dynamic programming in fact uh and you know there is some evidence that there might be a quantum algorithm that would take n to the three halves time or something like that but but if so
uh uh it has not yet been discovered so um so so so so so there are cases like that um um no gotcha okay um the next question i wanted to ask you was why do many of the important discoveries not just in this field but in many other fields come from closely communicating groups of collaborators or people within such
groups um you said on sean carroll's podcast that uh uh uh shaw and grover were collaborators about labs and i'm i'm not sure that they actually were collaborators i mean they they uh they they worked in the same building i believe you know i think they they you know you know i think the the
discovery of shores algorithm created a lot of excitement you know uh well you know all over the place but certainly at bell ebbs which is where sure was right and i think that grover who worked also at bell labs but in a completely different department i think he was affected by that excitement
and uh um you know i'm not i'm not even uh uh i'm not even sure if if if they knew each other prior to grover's discovery of groceries but uh um i could i could i could i could ask them that but uh uh um but but you know i mean more more broadly uh you know it is certainly true that uh in the history of of
i of ideas like you know uh uh you know major innovations seem to come in clusters all the time bell labs was a huge example of that right i mean the uh um um you know the shores and grover's algorithms were really really at the tail end right of you know the the heyday of bellabs right which was
mostly the uh uh you know the the 40s 50s 60s 70s right but i mean uh you know you had the invention of the transistor you know the communication satellite uh and so many other things right uh from this one place um uh um you know another example uh uh would be um um you know i mean
we you know we could take uh athens and the ancient world right we could take a florence uh 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 physicists who
who revolutionized the world uh now uh uh you know this might be because you know something about the environment right that uh uh uh uh you know the that uh um um you know ideas bounce off of each other right people see something they see someone achieve something spectacular and they're
either you know inspired by that or they they uh they they view it as a challenge you know they they want to compete against that and come up with their own thing right you know a a a silicon valley whereas you know would be another big example although more for technology than for science right uh uh so that that would that
would be one one explanation and a different explanation would be that you know these certain places at certain points in time just you know attract all of the people who who you know maybe anyway would have had these great ideas but you know that kind of person wants to go to these
you know these these centers you know wherever they are and so so so so so these centers will just collect the kind of people who are likely to 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 interesting to the listeners in your paper on why philosophers should care about complexity um you talk about how the difficulty in finding nash equilibria might be relevant to discussions on economics can you explain uh can you explain this yeah okay so so
there was a uh big advance in theoretical computer science uh 14 years ago when uh it was uh uh the uh theoretical evidence was finally uh discovered for why computing a nash equilibrium is a hard problem basically and yeah and then this this confirmed a suspicion that people had had for a long time right because
uh you know if we look at uh uh a von neumann equilibrium right which is like an equilibrium of a uh um let's say of a two player zero sum game right then you know this can be found easily you know using linear programming okay um but uh a a nash equilibrium is somehow a more complicated beast
right and uh uh it's you know you know the way that nash proved that they exist in the 50s was uh using the uh what's called the kakutani fixed point theorem right it's some fixed point theorem from uh topology uh and and if you try to actually unwind the existence proof into an actual algorithm to calculate
the equilibrium then what you get is an algorithm that ends up taking exponential points right it you know it eventually hits the equilibrium but it it you know it uh it may have to follow an exponentially long trail before it reaches it uh if you're interested in this the best
by far the best things that have been written about it i think are by christos papademitrio okay uh who uh and um when papademitria was one of the discoverers in the uh uh in 2006 uh along with goldberg and dos kalakas of this this hardness theorem which you know it doesn't prove that it's hard to
find a nash equilibrium and that doesn't even prove that it's np hard uh this problem kind of doesn't have the right structure to be an np complete problem uh just because of nash's theorem that tells us that a nash equilibrium always exists right like in order to be np complete in
any way that we currently under understand there has to there has to be a decision problem you know is there a solution or is there not a solution right but for finding a nash equilibrium there always is a solution right there there's only the problem of how to find it um but what was shown is that basically
finding a nash equilibrium is at least as hard as any other problem for which you know a solution is guaranteed to exist because of the same kinds of principles okay so uh so it's sort of it is complete for that complexity class of problems for which you know a solution is guaranteed to exist for the
for this sort of reason so you know what does this mean for for economics well it it it's not clear right if it has a sort of direct implication but it it sort of it fits into this general narrative of uh you know just because an equilibrium exists you know that's that's not the end of the story
right i mean you know if the market can't actually find the equilibrium right in in any we could say you know if if calculating this equilibrium would take exponential time then we shouldn't expect the market to be able to find it either right and so uh you know now now economists are are well aware right that
that there are these issues right that that you know uh uh you know people are not perfectly rational you know even if even if they want to be perfectly rational which they don't always uh you know being perfectly rational might involve computations that they're just not able to do right
and and and you know and they've you know with varying degrees of success you know they've tried to account for such phenomena but you know i would say you know the the you know nash equilibria are so central to economic theory right that you know the hardness of finding nash equilibria i think you know is a uh uh um
you know maybe maybe a non-trivial 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 well so in terms of like uh central planning in order to
satisfy some constraints said by bureaucrats might be like an mp complete problem where it's like well i you know i i want i want i i want to separate two two different things right one is lack of knowledge right about what is going on in the economy so forth and the other one is lack of
ability to do computations on the knowledge that you have right so so you know the the hardness of nash equilibria is talking about the latter issue yeah i mean you know they're they're they're related in a way right they're both you know they're they're they're both different kinds of deviations
from perfect omniscience right but they're but there are different kinds of deviations from omniscience and you know in in in theoretical computer science you know very very often we have to distinguish them uh so uh um you know i mean often like people will ask me if some problem is you know is or isn't and be
complete when you know what they what they really mean is like how hard is it to collect the information right which is you know it's kind of like a apples and oranges it's a category mistake right once you know it's for like to even talk about whether a problem is in p or as an np or whatever we assume that
an input is given to you right so all of the information that you need you know you have it in front of you and then you know we are exclusively concerned with the difficulty of calculating something about that information right uh now there is there is also you know the the difficulty that uh uh
you know people who are in uh uh you know economic actors you know don't uh uh have the information that they need or certainly central planners you know don't have the information that they need right and there's act there actually is a whole subfield of economics you know that's the economics of
information right how much do you pay to to learn something about you know what is going on or how do you hold uh uh how do you design an auction in a way that you elicit the information that you want from the participants in the auction and things like that i think that economists maybe
have an easier time dealing with those things or you know that stuff has been better integrated into economics 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
anything chapter of quantum computing since democritus um you have a student to ask you uh what what complexity classes creativity and you say uh part of what you say is um we've got a billion years of natural selection giving us a very good toolbox of heuristics of solving certain kinds
of surge problems like problems in np um but that makes it kind of sound like we have more heuristics to solve these problems than chimpanzees do chimpanzees have more than anne's uh i don't know if this is how you meant it but do you see like the algorithm for creativity as a thing you have or you don't have
or is it like you you just have better heuristics for searching through different i don't i don't i don't know that there is such a thing as the algorithm for creativity right in fact you know you know the phrase is almost oxymoronic right that if there were such an algorithm
well then whatever it output would no longer be creative would it because it would just be the output of that algorithm right uh so you know i think that uh um you know the uh you know it it it seems like there is such a thing as you know general purpose reasoning ability or general purpose ability to invent
creative solutions to problems which uh you know let's say you know einstein had more of than some random person off the street but the random person off the street has more of than a chimpanzee and a chimpanzee has more of than an ant but it is somehow very very hard to
to articulate what we mean by that you know in a way that would actually support these you know comparisons across you know vastly different evolutionary histories and and goals in life and all these things 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't and that's like the only demarcation that matters um yeah i think deutsch is like he's incr like incredibly optimistic and also incredibly categorical in his thinking right you know i don't know anyone else
who was sort of as optimistic or you know and hardly anyone else who is as black and white right uh i mean i i um uh you know it it it it does seem likely that there is some kind of threshold that you cross in going from a chimpanzee to a human right where like yes you know a chimpanzee is smarter than a cow
right but like you know if you you stare at both of them you know it doesn't seem like you know the chimpanzee is noticeably closer than the cow is to you know being able to land on the moon right or or uh or or um um proof from auslan's theorem right or or any of these things right and uh uh you know with
with um um um humans you know you you had like a in in in succession you had you know a few you know extremely important milestones that you know that had not been crossed before in the animal kingdom right you have a universality of of language right you know i mean the ability to
have a recursive language that can sort of uh um you know uh express thoughts of you know uh uh unbounded complexity uh you had uh you know the the invention of writing you know the ability to transmit those thoughts across generations uh you know the the uh um you know a number system that could refer to
arbitrarily large numbers you know and then you know uh uh uh computers you know which are which are universal machines right the ability to uh build these kinds of machines and you know and all of this went along with you know being able to explain the world around us uh in you know in in uh uh
you know in in explicit theories you know to uh uh uh you know to an extent that no animal species no other animal species uh uh was ever able to do um having said that you know i don't i don't actually know uh if people are are universal explainers that is you know i i i have um
you know uh uh i i i have no idea if we can explain everything or even if we can explain everything that is explainable uh you know i of course i i hope that we will continue being able to explain a lot more than we can explain right now right but i mean you know deutsch you know uses words in unusual ways like he uh
um like like when he he he talks about why he is so optimistic you know part of his optimism is like you know when he uses the word people he also includes extraterrestrials right so he says like oh yeah you know it's possible that humans on earth will just all kill themselves out you know there will be a
nuclear war or an environmental catastrophe but that's not a big deal because people in the broader sense of you know life elsewhere in the universe will uh go and do all the amazing things anyway that we would have done i mean 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 know not only what does he mean by a universal explainer but even what does he mean by people right uh his claim on the universal
explainer part is that um just as many worlds is the most part harmonious way to describe quantum mechanics so you don't have to like postulate an arbitrary uh uh you know collapse uh since we have no reason to expect this thing since we have no proof that there are things we cannot explain the most part
harmonious explanation is that we can explain everything okay i i i don't know i mean you know there are there there are certain questions like like the hard problem of consciousness let's say or a question question of what why is there a universe at all where you know it's not just that we
don't have an explanation it's that the the mind sort of spins in circles when we try to contemplate what could possibly consist of an explanation right what what what what could an explanation possibly look like even in principle right uh now that that that that that could just be a lack of imagination
right but you know it could be that there are you know i mean i mean like like we all know you know the two-year-old who just you know you you know asks why and then you tell them and they ask why and you tell them and you know and then they ask why and you know after after you know a
a half dozen y's you know you're all the 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 could be that you know there are there are questions with with the
property that you know that every um um um so okay i mean i mean i mean i mean i mean i mean first of all you know uh i think even even deutsche thinks that that we will not you know that there is no one time where we'll have an explanation of everything right because because deutsche you know says that each
uh each each question that we answer will lead to further questions right you know each each time you explain something uh you know there's there's then the question of you know whatever the explanation is based on you know why is that right so just like that two-year-old right we can always dig deeper and
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 like with with with uh uh uh um you know you need more and more resources to to compute more
and more values of the busy beaver function and so you'll never know all of them it's that there are fixed values like busy beaver of 800 right where the the existing axioms of set theory you know provably will not suffice to let you determine that right and so likewise for all i know
there could be fixed questions where you know maybe the hard problem of consciousness maybe why is there a universe where what we currently consider to be an explanation just will not suffice to ever explain these things um but but i but i don't know i you know uh uh i feel like um um unlike deutsche you
know i don't want to assert that i know the answer from first principles i you know i i want to continue looking for explanations of these things 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 that into more than it is right let's not take a a useful heuristic and elevate it into a basic principle of reality right uh but on this point um deutsche wrote a book in uh called the fabric of reality where he talked about how gold's incompleteness theorem actually
um verifies the importance of creativity so that if we need to come up with new axioms to prove busy beaver of that's that's the point of creativity and um as far as like 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 imagine a possible mind and that might that might itself be an artifact of our mind we can't imagine a possible way that you could solve it regardless of what kind of mind you had the final question is what advice would
you give to a 20 year old who is interested in technical subjects not maybe he's not doing a phd program like you were at the time but yeah interested in technical subjects um just learn all that you can i mean you know they're they're uh you know has never been a time when sort of more
resources were available to anyone who wants to to learn things so so uh um you know take courses talk to your professors um um you know go go go on the internet and uh or you know we re read books uh you know delve deeply into a a subject and um uh you know and and uh you know you you might be surprised at uh
sort of how how low the barriers sometimes are right they're like if you you know you know let let's say that it was quantum computing that you were interested in right it doesn't have to be it could be anything else but you know if you you know the entire literature of quantum computing
pretty much is available for free on you know on archive.org and uh you know if you go and like look every every night at the new quantum computing papers that come out and just flag the ones that are interesting to you and read them you know each paper will raise new questions that that the authors don't
know the answer to or yet uh and you know sometimes they'll be explicitly listed in an open problem section you know other times you know it'll be ones that you could think of and uh you know you can um uh you know you can study those problems uh you know if you have ideas about them you can
uh you know talk to to the authors of the paper um and uh yeah you you know it it it might 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 the world expert 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 right and you know once you've done that then you can you know write an article about it or you know do a do a project about it
and then you know that will lead to more things right it will lead to uh you know maybe collaborations in the future uh you know and it will lead to you know you you can then try to become an expert on something a little bit wider and something a little bit wider and so on yeah that that's very excellent advice i
love that okay well uh professor thank you so much for your time hey if you enjoyed this podcast please consider sharing it with your friends and posting it on social media word of mouth is incredibly valuable for a new and a small podcast like this one so thanks for watching