Speaker 1: Welcome to Stuff to Blow your Mind from how Stop
Speaker 1: works dot com. Hey, welcome to Spectable in your Mind.
Speaker 1: My name is Robert Lamb and I'm Joe McCormick. And
Speaker 1: today we're going to be taking a look at issue
Speaker 1: in computer science. Uh funny enough, I'd say that's not
Speaker 1: one of the sciences we dip into very frequently on
Speaker 1: this podcast. Yes, and I mean really, we should probably
Speaker 1: just remind everyone to stick with us, trust us on
Speaker 1: this one. Uh, don't be scared off by the computer
Speaker 1: science thing, don't be scared off by the P versus
Speaker 1: NP thing. It's it's it's all gonna make a type
Speaker 1: of sense at the end, hopefully. But I'm wondering if
Speaker 1: maybe we should dip into computer science more often because
Speaker 1: or at least wherever we can find a way to
Speaker 1: make the contents of it reasonably concrete, because, let's be honest,
Speaker 1: as we've discovered in researching this episode, it's very abstract,
Speaker 1: very difficult, and a lot of times hard to come
Speaker 1: up with ways of explaining that makes sense just just
Speaker 1: talking about it without visual aids or watching programs execute
Speaker 1: as an example. Yeah, it's definitely one of those topics
Speaker 1: that it's a swimming pool of a topic in which
Speaker 1: there is no gradual deepening from the kitty area to
Speaker 1: the deep end. It's just shallow, and at times it
Speaker 1: feels too shallow, and then you're immediately out of your depth. Yeah.
Speaker 1: But if you're thinking, kind of computer science, really does
Speaker 1: that fit with the show? Hold on for a second,
Speaker 1: because I think it does. Um. Computer science to me
Speaker 1: is a fascinating subject. Uh, and it's not just limited
Speaker 1: to how computers work. So my advice is, when you
Speaker 1: think about the idea of computer science, forget the computer
Speaker 1: sitting in front of you. That's not all it is.
Speaker 1: Computer science is really something more akin to the philosophy
Speaker 1: of logic, understanding the the underlying sorcery of how logic
Speaker 1: and math work in the universe we inhabit, and especially
Speaker 1: the science of how problems are solved, and certainly when
Speaker 1: you start bringing math into the equation here as well,
Speaker 1: I mean you're talking we're talking about the essentially the
Speaker 1: very fabric of the universe. We're talking about either the
Speaker 1: fabric of the universe, either the way the universe works
Speaker 1: or this perfect creation that humans have come up with
Speaker 1: that so accurately describes how the universe works, and that
Speaker 1: is pretty mind blowing territory. Well, either way you look
Speaker 1: at it, there is something mystical about about the math
Speaker 1: that we walk on every day, that you know, that
Speaker 1: makes up the fabric and the logic math beneath the
Speaker 1: math beneath our feet. You know, if you go with
Speaker 1: the Max teg Mark idea of the mathematical universe that
Speaker 1: some people don't like this idea because, like I don't
Speaker 1: understand what that means. But at least it's a very
Speaker 1: intriguing idea. I think it. His idea is that the
Speaker 1: underlying basis of all reality not just as described by math,
Speaker 1: but is math, and the universe is a mathematical object.
Speaker 1: But we're gonna get back to this idea of problem
Speaker 1: solving because today we want to focus on algori rhythms
Speaker 1: and on the inherent logic of problem solving in our universe,
Speaker 1: with some attention to a special example of one really
Speaker 1: interesting outstanding problem in computer science, and that's the P
Speaker 1: versus n P issue. If you've never heard of this before,
Speaker 1: don't worry. We'll explain what the terms mean in a
Speaker 1: simplified manner. And uh I at this point also do
Speaker 1: want to give a shout out to our listener Jim
Speaker 1: in New Jersey, who has been encouraging me over email
Speaker 1: to tackle this issue for a while despite all the challenges,
Speaker 1: and has also sent some really helpful, uh really helpful
Speaker 1: guides and explainers on some stuff he he learned about
Speaker 1: this when he was in graduate school. Yeah, indeed, and
Speaker 1: uh and I think this is great too because this
Speaker 1: episode is coming on the heels of, first of all,
Speaker 1: the Wicked Problems episode that came out of a few
Speaker 1: weeks ago, as well as the more recent Cargo Cults
Speaker 1: episode which in which we discuss outside context problems a
Speaker 1: little bit as well. So it's it's perfectly fitting that
Speaker 1: we would discuss another problem. Well, well, what does it
Speaker 1: mean inherently to solve a problem? If you get into
Speaker 1: the theory of problem solving? What what what does this
Speaker 1: process look like? Well, when it comes down just to
Speaker 1: the basics open and this also kind of gets into
Speaker 1: the whole Wicked Problems area of like what's what's missing
Speaker 1: when you don't have, um, you know, everything you need
Speaker 1: to solve a problem for for a real problem, you
Speaker 1: have to be able to course do to find what
Speaker 1: the problem is a lot of a lot of attempts
Speaker 1: fail right there. Yeah, you've got to you've got to
Speaker 1: be able to say this is the thing you know,
Speaker 1: and then you and then you have to be able
Speaker 1: to measure your success and check the solution. So you
Speaker 1: essentially have to be able to say, hey, this is
Speaker 1: wrong because of X, and then if you then figure
Speaker 1: out what X is and see if the equation balances out. Um,
Speaker 1: it sounds pretty simple. But like I said, as we
Speaker 1: discussed in Wicked Problems, that's uh, it can be very
Speaker 1: difficult to do, especially in you know, the very complex
Speaker 1: social situations when you're dealing with with certainly some of
Speaker 1: the larger problems that we're going to talk about here,
Speaker 1: or even if you want to go into the simplest level, well,
Speaker 1: I mean depending on what you would call simple. In fact,
Speaker 1: what we're going to be getting into today is directly
Speaker 1: referred to as complexity theory. Uh. So maybe it's not
Speaker 1: so simple, but at least simple in terms of not
Speaker 1: involving uh phenomena in the real world, but just math,
Speaker 1: just math and logic and and true versus untrue and
Speaker 1: UH and algorithms. So I think it's time to pull
Speaker 1: back the curtain a little bit and reveal some of
Speaker 1: the deep weirdness of the nature of algorithms and problem
Speaker 1: solving in our universe. So let's look at this P
Speaker 1: versus MP problem. This is something that comes from two
Speaker 1: of the great minds of the twentieth century, Kurt Girdle
Speaker 1: and John von Neuman. And in nineteen fifty six, Kurt Girdle,
Speaker 1: who's a mathematician and logician, wrote a letter to John
Speaker 1: von Neuman which kicked off this quest to solve one
Speaker 1: of the biggest questions in computer science, the P versus
Speaker 1: n P issue. Now, who were these guys, but both
Speaker 1: were heightens of the twentieth century in terms of math, logic,
Speaker 1: and computers. Well. Godal is probably most famous for his
Speaker 1: first incompleteness theorem, and this states that any adequate um
Speaker 1: axiomatizeable theory that means, a theory that's based on self
Speaker 1: evident but unprovable proofs, is incomplete or inconsistent. Yeah, Girdle's
Speaker 1: whole incompleteness theorem set. He had a couple of his
Speaker 1: incompleteness theorems essentially amount to the idea that any mathematical
Speaker 1: system that makes sense will have some statements that are
Speaker 1: true yet impossible to prove. It's sort of the idea
Speaker 1: that you can't ever know everything about a self consistent system. Yeah,
Speaker 1: And the the the implication here, according to theoretical physicist
Speaker 1: and mathematician Freeman Dyson, who has is also quite a
Speaker 1: giant in the field, is that mathematics is inexhaustible, that
Speaker 1: no matter how many problems we solve, will inevitably encounter
Speaker 1: more unsolvable problems within the existing rules. I take comfort
Speaker 1: in that measure a few tility. Yeah, but there's also
Speaker 1: John von Neuman, the recipient of the letter. And von Neuman,
Speaker 1: I don't know what you've heard about him, but I'd
Speaker 1: say he's often considered one of the most intelligent people
Speaker 1: who ever lived that we know about at least, And
Speaker 1: so maybe we call him a mathematician and a physicist,
Speaker 1: but he made contributions to numerous fields. He was a
Speaker 1: modern Da Vinci kind of you know, a polymath and so,
Speaker 1: and that includes computer science, for example, the von Neuman
Speaker 1: architecture in the history of computer design, which is basically
Speaker 1: it's a way of controlling the interaction between processing operations
Speaker 1: the CPU and the memory of a computer and this
Speaker 1: letter in nineteen fifty six from Girdle to von Neuman
Speaker 1: started this process of looking into the question of whether
Speaker 1: P does or does not equal in P. Now, like
Speaker 1: I said, we're about to explain what all the terms
Speaker 1: here mean. But I do want to note at the
Speaker 1: outset of this explanation that you know, on the show
Speaker 1: we always try to do our best to present our
Speaker 1: subjects accurately but then at the same time be understandable
Speaker 1: to the average person. And this, this P versus INP
Speaker 1: issue in complexity theory is probably the most difficult and
Speaker 1: abstract subject I've ever tried to cover on a podcast.
Speaker 1: So we'll have to do our best to explain the
Speaker 1: issue and its implications without losing you in asphyxiating clouds
Speaker 1: of abstraction. Yeah, I mean basically that the house stuff
Speaker 1: works mission overall is to demystify your science and UH
Speaker 1: topics like this can be a bit difficult because you
Speaker 1: don't want to through the explanation just mystify it even
Speaker 1: more for the average listener exactly right. So this is
Speaker 1: necessarily going to involve a lot of simplified versions of principles.
Speaker 1: We won't be able to go down uh, and explore
Speaker 1: all of the complex details behind these principles. But we
Speaker 1: hope that you computer scientists and mathematicians out there will
Speaker 1: not be too scandalized or think we're doing violence to
Speaker 1: your subject. Anyway, here we go. So we we've got
Speaker 1: to start with the concept of algorithms. What what is
Speaker 1: an algorithm? Well, I'd say an algorithm is a self
Speaker 1: contained list of instructions to solve a problem. You've got
Speaker 1: a goal, and then you make a step by step
Speaker 1: list of things to do that gets you to the goal.
Speaker 1: A common example within a computer program would be a
Speaker 1: subroutine designed to sort a list of things. That's an algorithm. Yeah,
Speaker 1: and you know, algorithms are something we encounter on a
Speaker 1: just on a daily basis, especially online. I mean Facebook, Google.
Speaker 1: Both of these depend on ever changing algorithms to decide
Speaker 1: what you see and don't see on your feeds and
Speaker 1: on your search results. Yeah, and I think that's a
Speaker 1: great example of how complex algorithms can get. You've got
Speaker 1: the simple sorting algorithm on one hand, and then you've
Speaker 1: got the stuff that decides whether you only see political
Speaker 1: articles you agree with, or whether you sometimes see stuff
Speaker 1: that's going to make you mad. So when you're designing
Speaker 1: algorithms in in a computer science arena, or really to
Speaker 1: solve any problem, but we're mostly gonna be talking about
Speaker 1: computer programs. You compare how much time it takes to
Speaker 1: solve a problem with an algorithm given the scope of
Speaker 1: a problem. So this is usually expressed in terms of
Speaker 1: inputs versus time. So I want to give a quick
Speaker 1: example with sorting. Like I said, you say, you're given
Speaker 1: a spreadsheet that includes a list of all the James
Speaker 1: Bond movies that exist currently in a random order, and
Speaker 1: you've got to write a computer program that sorts all
Speaker 1: of those lists of James Bond movie titles into a
Speaker 1: list in the order they came out. How would you
Speaker 1: do that? Now, there are a lot of ways you
Speaker 1: actually could approach the problem, and that they don't all
Speaker 1: take the same amount of time. Some are much more
Speaker 1: efficient than others. Here's one example. You could create an
Speaker 1: algorithm that goes like this. Step one, rearrange the entire
Speaker 1: list at random. Step two, check each movie in the
Speaker 1: list to see if it came out before the next
Speaker 1: movie in the list. If the answer is yes, all
Speaker 1: the way down the line, then the list is sorted correctly,
Speaker 1: and you're done. If not, start over and rearrange it
Speaker 1: entirely randomly. Now, given enough time and a small enough
Speaker 1: data set, this algorithm will eventually finish by blind luck.
Speaker 1: Is just brute force burning through computer resources wastefully in
Speaker 1: order to eventually solve the problem by blind block. But
Speaker 1: there are also much more efficient ways you could go
Speaker 1: about it. For example, you could go down the list
Speaker 1: comparing each movie to the next, and if the second
Speaker 1: movie came out before the first, you switch their order
Speaker 1: on the list, and then go on like that. Uh,
Speaker 1: and then you do that until the list is sorted.
Speaker 1: But some problems are inherently a lot harder than others,
Speaker 1: and there aren't any algorithmic shortcuts like that that we
Speaker 1: know about. We don't know of any easy way to
Speaker 1: solve them. The only thing we know how to do
Speaker 1: is do that stupid brute force method where you just
Speaker 1: wastefully burned through computer resources until it's solved by time
Speaker 1: and force. And in fact, I'd like to make a
Speaker 1: comparison here in the you know, the efficient algorithm versus
Speaker 1: brute force methods to what you might see in animals
Speaker 1: in the wild using intelligence to solve a problem. So,
Speaker 1: like if you're hunting another animal, you could use a
Speaker 1: brute force method of just running after the animal until
Speaker 1: it is tired or until your muscles have allowed you
Speaker 1: to catch it, and then killing it with the strength
Speaker 1: of your muscles. That's sort of the brute force method.
Speaker 1: Or you could set a trap, or you could build
Speaker 1: a weapon that these are shortcuts that make the process
Speaker 1: of hunting a lot more efficient. Now here's where we
Speaker 1: get to our main terms in this discussion. P and
Speaker 1: n P. P is going to stand for polynomial time,
Speaker 1: and in P stands for nondeterministic polynomial time. You don't
Speaker 1: really need to remember that for the purpose of this discussion,
Speaker 1: because we're gonna make it a lot simpler. Yeah, I mean,
Speaker 1: this is one of the problems with the topic is
Speaker 1: that like just the word this, this the the the
Speaker 1: basic idea here of P and n P. There, it's
Speaker 1: so dry and unrelated, doble, But allow us to explain. Yeah, okay,
Speaker 1: so the real difference has to do with um processes
Speaker 1: of solving problems on a deterministic Turing machine, which is
Speaker 1: equivalent to the kind of computer you'd be using right now.
Speaker 1: You know, any device you have versus a hypothetical nondeterministic machine,
Speaker 1: which in theory you could say works by magically guessing
Speaker 1: the answers to questions and then just checking to see
Speaker 1: if the magic guess is correct. But, like we said,
Speaker 1: we don't want to get too bogged down in all
Speaker 1: those details. So here's the simplified version. P is a
Speaker 1: set of all problems that can be solved by an
Speaker 1: algorithm quickly or easily or efficiently. This is the easy
Speaker 1: the list of easy problems in computer science. N P,
Speaker 1: on the other hand, stands for answers that can be
Speaker 1: easily checked by a computer once you have them, but
Speaker 1: they can't necessarily be solved easily. Yeah, so it's difficult
Speaker 1: to place this in a non mathematical context. But one
Speaker 1: way I like to think about this is in terms
Speaker 1: of written reviews for for albums, for you know, for
Speaker 1: for musical albums, um. Because a good a good review,
Speaker 1: a good music review is difficult to write, uh, and
Speaker 1: hard to find and hard to find. Yeah, like in
Speaker 1: my own experience you often find I mean, I I
Speaker 1: write many reviews of stuff of stuff from time to time,
Speaker 1: and that alone is challenging enough for me but but yeah,
Speaker 1: when you even when you're looking out of the major publications,
Speaker 1: uh yeah, it's hard to find one that feels just right.
Speaker 1: It's uh. The average reader, though, can can swiftly judge
Speaker 1: to what extent they agree with the author, obviously, to
Speaker 1: what extent the author is just blowing smoke. We've all
Speaker 1: read those music reviews where you get the sense that
Speaker 1: the the author is really using the music as an
Speaker 1: excuse to sort of write his or her own poetry.
Speaker 1: Uh there on the page episodes actually just describing what
Speaker 1: the music is like. But but the reader knows. So
Speaker 1: the reader can can can look at the material and
Speaker 1: you either believe in or you don't. Either you buy
Speaker 1: into their opinion or you don't. Yeah, so you could.
Speaker 1: You don't have the algorithm internally to efficiently right this
Speaker 1: piece of writing yourself, but you know it when you
Speaker 1: see it exactly. Yeah. It's kind of like pornography, and
Speaker 1: that's it. It's right. You might not be able to
Speaker 1: define clearly the difference between art and pornography, but you
Speaker 1: know it when you see it. Once you have that
Speaker 1: answer certificate there, you can check and by golly, it
Speaker 1: checks out. And I like that because it also gives
Speaker 1: a whole new meaning to the P and to the NP.
Speaker 1: And now, so there are a couple of other terms
Speaker 1: that matter. There's MP hard, and this means that are
Speaker 1: problems that are as hard as any other MP problem essentially.
Speaker 1: And then there's also MP complete, which is a big
Speaker 1: issue in this arena, and this is problems that are
Speaker 1: m P and m P hard. So you you can
Speaker 1: check the answer once you have it in in a
Speaker 1: reasonable amount of time, and they're in P hard. Now,
Speaker 1: the interesting thing about MP complete problems is that it
Speaker 1: has been proved in the literature that if you have
Speaker 1: an algorithm that can efficiently solve one MP complete problem,
Speaker 1: it can be transposed to solve all of them. These
Speaker 1: problems reduced to each other. So if you if you
Speaker 1: can solve one MP complete problem and a reasonable amount
Speaker 1: of time, you have found the master key. And this
Speaker 1: in the universe kind of shrinks. Yeah, in response to this,
Speaker 1: So a classic example of an MP problem is the
Speaker 1: prime factorization problem that we use in encryption on the Internet. Again,
Speaker 1: we don't want you to get lost too much here,
Speaker 1: So here's the simple version with smaller numbers than usual.
Speaker 1: Let's say I just throw out a random number, and
Speaker 1: let's say it's a number of I don't know what's
Speaker 1: a good one skulls in a pile. So let's say
Speaker 1: I give you a number. Let's say there are seven
Speaker 1: hundred and twenty one thousand, four hundred twenty one skulls
Speaker 1: in a pile. It's a lot skulls, it is. Now,
Speaker 1: I tell you this number is the product of two
Speaker 1: prime numbers of skulls in a pile, but I don't
Speaker 1: tell you what they are. Now, how could you figure
Speaker 1: out what those two prime numbers of skulls in a
Speaker 1: pile are? For a computer with numbers this small, this
Speaker 1: wouldn't be all that big a deal. But we're we're
Speaker 1: gonna have to extrapolate too much bigger numbers. But for you,
Speaker 1: this would be really annoying to figure out, right, Oh yes,
Speaker 1: because there's no simple, efficient way to do it. You'd
Speaker 1: pretty much have to get out a huge list of
Speaker 1: all the prime numbers between zero and seven thousand, four
Speaker 1: hundred one and start trying multiplying them together to see
Speaker 1: if they give you the right answer. Yeah, And in
Speaker 1: this situation, I imagine it's like the opening scenes of Terminator,
Speaker 1: And I'm probably already pretty distracted by the Pyramids of
Speaker 1: Bone and the Hunter Killer. The Hunter Killers exactly how
Speaker 1: I'm not gonna have time for all this prime number nuns. Now,
Speaker 1: since we've solved the equals in p at this point,
Speaker 1: they don't have rubber skin anymore. They figured out how
Speaker 1: to how to get through the problem to make the
Speaker 1: bio org suits. So, yeah, you're you're in a real
Speaker 1: rush here. But anyway, back to the problem. Yeah, there's
Speaker 1: just no fast, simple, easy way to solve this. And
Speaker 1: if you use numbers large enough, this type of problem
Speaker 1: is excruciatingly slow, even for computers to conquer by brute force.
Speaker 1: But let's say I told you the two prime numbers
Speaker 1: are seven hundred and fifty seven and nine hundred and
Speaker 1: fifty three piles skulls in a pile. It would be
Speaker 1: trivially easy for you to check and see if that's
Speaker 1: the correct solution. You just have to multiply them and
Speaker 1: see if you get the right answer, and it takes
Speaker 1: almost no time at all. And in fact, I really
Speaker 1: only need to tell you one of the numbers because
Speaker 1: you already know what they're supposed to multiply too, so
Speaker 1: you could just divide that by the one number. So
Speaker 1: here's an example. This is a problem that if you're
Speaker 1: going to try to solve it starting with no information,
Speaker 1: it's just going to take ages. It's going to be impossible.
Speaker 1: But if you already know a selected answer to test,
Speaker 1: you can check and see if that answer is right. Yeah,
Speaker 1: I mean this brings to mind. Uh it's a bit
Speaker 1: like trying to crack a four number code on a
Speaker 1: simple combination lock right, And I'm talking about a human
Speaker 1: doing this, not a computer. So it would take me,
Speaker 1: as a human quite a while to test out all
Speaker 1: ten thousand possible solutions, but no time at all to
Speaker 1: check a solution that someone else had provided me. So
Speaker 1: you know, I'd be there all day just putting in
Speaker 1: each one of those ten thousand solutions. But but I
Speaker 1: can easily put in, you know, uh, thirty three sixty
Speaker 1: six and see if that is correct. You found a
Speaker 1: really interesting request for help on this subject in you
Speaker 1: Oh yeah, yeah, there was because I wanted to check
Speaker 1: to make sure that my math was right on how
Speaker 1: many possible combinations. I was pretty sure it was the
Speaker 1: ten by ten by ten by ten thing. But I
Speaker 1: I did one of those searchers to just see people
Speaker 1: asking math questions online. And I found one where, um,
Speaker 1: this user apparently had a combination lock or it maybe
Speaker 1: it was like a contractor's box, you know, like at
Speaker 1: a house we had real estate agent. Yeah, and she
Speaker 1: says it's like a thirty dollar box. So she didn't
Speaker 1: want to just have it, you know, cut into and
Speaker 1: ruin it in order to get the keys out. She
Speaker 1: wanted to, but she didn't know what the combo was,
Speaker 1: so she wanted to just enter all the possible combinations
Speaker 1: to get it. And here's the here's the caveat though
Speaker 1: she knows that no number was used uh more than
Speaker 1: once and that cut it down significantly, just just more
Speaker 1: than five thousand, yeah, just like or something. Yeah. And
Speaker 1: and the person who supplied the answer on this forum,
Speaker 1: they included a list of all of them for her convenience, so, um,
Speaker 1: and I don't know how that came out. I wonder
Speaker 1: if she then took that list and just painstakingly, uh
Speaker 1: spent the time to try each one out, or if
Speaker 1: she decided, you know, actually that inputting all those numbers
Speaker 1: is not worth the thirty dollars that I would save
Speaker 1: by keeping the box attacked. That sounds like a fun Saturday,
Speaker 1: you know, on the porch in front of the box
Speaker 1: with a case of beer. Hopefully it's nice weather. But anyway,
Speaker 1: So yeah, this is problems that can potentially be brutally
Speaker 1: hard to solve, but they're easy to check once you
Speaker 1: have a certificate of the answer. Another classic and often
Speaker 1: cited example of an MP complete problem is the traveling
Speaker 1: salesman problem. Now I think something is exciting because now
Speaker 1: we have something with more of an anthropomorphic name smply scenario.
Speaker 1: It's like the Infinity Hotel. Well, I want to change
Speaker 1: it up, and I want to call I want to
Speaker 1: call this the nationwide infection problem. So imagine that you
Speaker 1: are the vanguard of an alien species that has come
Speaker 1: to Earth, and you want to land in a country,
Speaker 1: say the United States, and infect at least one person
Speaker 1: in every township and municipality in this country with one
Speaker 1: of your larvae. But you've got limited time to do it. Okay,
Speaker 1: you know, no dilly dalian around. So what you're looking
Speaker 1: for is a route that you can plan out on
Speaker 1: your alien equivalent of Google Maps directions or or you know,
Speaker 1: your Apple Directions device that will tell you how to
Speaker 1: go to every single city and township in the country
Speaker 1: only one time each in the shortest route possible. Okay,
Speaker 1: that's not easy. If you just had four or five cities,
Speaker 1: this wouldn't be such a big deal for a computer
Speaker 1: to figure out. Once you start adding hundreds or thousands
Speaker 1: of cities, how is it going to figure this out?
Speaker 1: The only way we know of is back to brute force.
Speaker 1: It could try one method, so well, you go to
Speaker 1: city A, and then city B, and then city C
Speaker 1: and then D and go all the way around the
Speaker 1: country and see how long that takes. And then it
Speaker 1: could try again with first city B and then A,
Speaker 1: and then the same from there and then so you
Speaker 1: end up getting these exponentially multiplying combinations there. It is
Speaker 1: just going to take massive amounts of time and computing
Speaker 1: power to figure out what is actually the shortest trip. Now,
Speaker 1: you might already see an issue with including this problem
Speaker 1: within in P and actually reade an interesting blog post
Speaker 1: by somebody writing for for IBM about how, under certain
Speaker 1: conditions this problem actually isn't in P depending on how
Speaker 1: you define what you're checking for, Like if you're just
Speaker 1: looking to check that a given route is a correct solution,
Speaker 1: it visits every city only once. Uh, then it is
Speaker 1: easy to check. You can check that very quickly. All right,
Speaker 1: this comes down to accurately defining the problem right exactly now.
Speaker 1: If you're looking to check that it visits every city
Speaker 1: only once under a certain mileage, that's also easy to checking.
Speaker 1: Just see that it visited every city once and see
Speaker 1: how long it took. But if you're looking to verify
Speaker 1: whether a solution is in fact the shortest of all
Speaker 1: possible routes, that's not easy to check because you'd still
Speaker 1: have you'd essentially have to do the entire brute force
Speaker 1: meth that that way and compare it to every other possibility.
Speaker 1: All possible routes have to be have to be considered.
Speaker 1: So if if that's what you're going for, it's not
Speaker 1: hard to solve, easy to check. It's hard to solve
Speaker 1: and hard to check. But here's the big problem with
Speaker 1: the with the P versus n P issue. We know
Speaker 1: that P problems are a subset of MP problems, But
Speaker 1: what if the subset is actually the same as the set,
Speaker 1: Meaning what if all NP problems are actually P problems?
Speaker 1: Meaning what if all problems where we can check the
Speaker 1: answer are actually problems where we can solve them efficiently.
Speaker 1: We just haven't figured out how to solve them efficiently yet, Okay,
Speaker 1: Or we haven't developed the here the machines that can
Speaker 1: do it. Yeah. Yeah, so is that possible? And that's
Speaker 1: actually probably the single biggest open question in computer science today.
Speaker 1: Is P equal or not equal to n P? Are
Speaker 1: they or are they not? Equival valence sets? Now, the
Speaker 1: obvious answer is no, Right, that seems intuitive, That seems
Speaker 1: that that seems to be the answer. That that feels
Speaker 1: most in keeping with our our understanding of the limits
Speaker 1: of human ability, the limits of human knowledge, and just
Speaker 1: sort of the fabric of our universe. Yeah, and so
Speaker 1: most computer scientists and mathematicians, I think agree that the
Speaker 1: more likely answer to this unsolved question is that P
Speaker 1: does not equal MP. I found one pole that was taken.
Speaker 1: It was more than ten years ago. I don't know
Speaker 1: if things have changed much since then. But in two
Speaker 1: thousand two, the University of Maryland computer scientist William I.
Speaker 1: Guess Arc did a poll of colleagues in complexity theory
Speaker 1: and UH and he found the results. And so he
Speaker 1: found out of this poll of colleagues, sixty one of
Speaker 1: his colleagues thought that P did not equal MP. Nine
Speaker 1: thought that P did equal MP, And some of those
Speaker 1: that said that said they they said that basically just
Speaker 1: to be contrarian or to continue encouraging people to research
Speaker 1: the possibility. UH. And then several other colleagues either offered
Speaker 1: no opinion or offered UH sort of complex answers that
Speaker 1: weren't yes or no. But so you can obviously see
Speaker 1: that the opinion that P does equal MP, or the
Speaker 1: prediction that that will be what's eventually proved, is the minority.
Speaker 1: It's not what we would tend to think is the
Speaker 1: more likely possibility. Okay, it's the more outsider consideration here.
Speaker 1: So it let's assume for a second that that is
Speaker 1: the case that one day some amazing mathematician or computer
Speaker 1: scientists somebody comes along and they figure out a way
Speaker 1: to prove that P does not equal in P. Proof
Speaker 1: Proofs like this happen in UH, in math and computer
Speaker 1: science all the time. You might be wondering how could
Speaker 1: that be proved, But people figure out ways to demonstrate
Speaker 1: logically that something is true like this. So let's say
Speaker 1: it's demonstrated that P does not equal MP. What are
Speaker 1: the implications. Well, mostly I'd say not much changes. This
Speaker 1: is sort of the obvious conclusion. It's the one that
Speaker 1: wouldn't surprise us. In other words, all of our brute
Speaker 1: force problems remain brute force problems. Uh. But if this
Speaker 1: is the case, it would still be useful to know.
Speaker 1: It would be useful to people. Wouldn't start floating into
Speaker 1: the sky, the great old ones, wouldn't come back, It
Speaker 1: would just the business is usual for most people. Yeah,
Speaker 1: So we we'd have a proof so people can stop
Speaker 1: trying to solve it, and we'd be able to use
Speaker 1: the fact that P is not equal to MP as
Speaker 1: an assumption for other work in mathematics and computer science.
Speaker 1: So we just move on with our lives basically essentially.
Speaker 1: But here's where things get interesting. What would the implications
Speaker 1: be if P does equal MP. Well, right off the
Speaker 1: top of my head, of of course, what comes to
Speaker 1: mind is the the the use of encryption that we've
Speaker 1: already talked about. Like that's really like our most everyday
Speaker 1: interaction with with the idea of of of P and NP. Yeah,
Speaker 1: I mean, why is it not easy for me to
Speaker 1: get into those photos you have on your phone? Whatever
Speaker 1: they are? Well, it's because it's because we use these
Speaker 1: encryption methods, and almost all current encryption methods would be
Speaker 1: subject to UH. They just depend on the fact that
Speaker 1: you don't have, you know, tons of supercomputers and time
Speaker 1: to sit around trying to brute force crack into people's junk.
Speaker 1: But if you were able to reduce those problems to
Speaker 1: UH to essentially easily solvable problems, problems that could be
Speaker 1: solved in regular polynomial time, the P class then suddenly, yeah,
Speaker 1: by by encryption essentially, I mean, we can't know for
Speaker 1: sure exactly how big a deal this uh this would
Speaker 1: be in terms of applied sciences and technology, but the
Speaker 1: likely implication UH seems to be that any job currently
Speaker 1: hindered by the limits of brute force computation would be revolutionized.
Speaker 1: So yeah, there's the there's the prime factorization issue that
Speaker 1: that feeds into encryption. And the informal way of summing
Speaker 1: this up is that, you know, if if if our
Speaker 1: present methods of encryption and data security are like a
Speaker 1: like a plastic diary lock on our information, every hacker
Speaker 1: on Earth might have access to a pair of fourteen
Speaker 1: inch bolt cutters of the equals in p on the
Speaker 1: other hand, and this would be a positive. It could
Speaker 1: also mean that research projects that rely on brute force
Speaker 1: computation could also potentially see huge leaps forward. For example,
Speaker 1: one one that I saw, I've seen mentioned, and I've
Speaker 1: read about before is protein folding simulation. Have you ever
Speaker 1: read about this? Uh? Yeah, a little bit. Um. I
Speaker 1: think I tended a discussion on on the topic a
Speaker 1: few years back. Yeah. So this research, it involves going
Speaker 1: through permutations of of different ways of folding proteins in
Speaker 1: a computer simulation. And this research could help cure diseases
Speaker 1: and treat medical conditions if we learned the right things
Speaker 1: about the behavior of how protein molecules fold up on
Speaker 1: one another and be have in the body. But simulating
Speaker 1: all of these folding permutations is a brute force computing project.
Speaker 1: So if this actually reduced to a p problem, we
Speaker 1: might be able to hasten research that saves lives, maybe
Speaker 1: cure cancer. Who knows. Okay, so we're already we're looking
Speaker 1: at a world where maybe we have to go back
Speaker 1: to using just normal mail instead of email. But on
Speaker 1: the other hand, and maybe we cure cantor or if
Speaker 1: people I mean digital security, maybe could still be a thing.
Speaker 1: If people just come up with another method, we just
Speaker 1: our current methods would would possibly become obsolete. Yeah, and
Speaker 1: then the new method will be sealed envelope under your
Speaker 1: back or a chest buried in your backyard. Yeah, that's
Speaker 1: where you have to keep all You'd have to physically
Speaker 1: meet up with everybody to trade information with an agree
Speaker 1: on a password in person. You know. That would be interesting.
Speaker 1: Like trying to imagine a a digital civilization that suddenly
Speaker 1: has to become a non digital civilization, but wants to
Speaker 1: keep everything uh operating more or less as it did
Speaker 1: when it lives digital, you know, like they still want
Speaker 1: to use tender uh, but they can no longer use
Speaker 1: a true digital version of it. What does that even
Speaker 1: consist of? Oh wow, Yeah, that's fascinating. But of course
Speaker 1: the changes wouldn't just be in applied sciences and technology.
Speaker 1: One of the interesting things about this is multiple experts
Speaker 1: have commented that if we live in a P equals
Speaker 1: in P universe, we have been sorely mistaken about what
Speaker 1: reality is like. If this is the universe we inhabit,
Speaker 1: in fact, it is quite different than we thought. And
Speaker 1: one one thing I want to quote is by Scott Aaronson,
Speaker 1: who offers this as quote a physical philosophical argument against
Speaker 1: P equals in P, and he says, quote, if P
Speaker 1: equals in P, then the world would be a profoundly
Speaker 1: different place than we usually assume it to be. There
Speaker 1: would be no special value for creative leaps, no fundamental
Speaker 1: gap between solving a problem and recognizing the solution once
Speaker 1: it's found. Everyone who could appreciate a symphony would be Mozart,
Speaker 1: Everyone who could follow a step by step argument would
Speaker 1: be Gauss. Everyone who could recognize a good investment strategy
Speaker 1: would be Warren Buffett. It's possible to put the point
Speaker 1: in Darwinian terms. If this is the sort of universe
Speaker 1: we inhabited, why wouldn't we already have evolved to take
Speaker 1: advantage of it. That's a really interesting point. But at
Speaker 1: the same time, so he's framing it in terms of it.
Speaker 1: This is one among a list of arguments he gives
Speaker 1: that P probably does not equal and seems to be
Speaker 1: This seems to be very much an argument in favor
Speaker 1: of their, of their being no equality here, right, But
Speaker 1: you could also look at that look at it as
Speaker 1: an interesting comment on how different the world would be
Speaker 1: from how we assume it is if this were in
Speaker 1: fact case. And it's interesting to note that we shouldn't
Speaker 1: assume that just because it doesn't feel like we live
Speaker 1: in a P equals in P world, that P equals
Speaker 1: np is necessarily false. Our our intuitions about what's possible
Speaker 1: in the math and problem solving space have turned out
Speaker 1: to be very wrong in the past, and sometimes long
Speaker 1: standing problems in math and computer science are solved by
Speaker 1: UH solved. They're solved or proved in ways that just
Speaker 1: seem extremely peculiar. Yet you can't deny the result. I
Speaker 1: can't help but circle back around to the earlier opinion
Speaker 1: that we mentioned is attributed to Freeman Dyson that mathematics
Speaker 1: is inexhaustible. If P equals MP in the universe, is
Speaker 1: the universe really inexhaustible? And uh? And if P equals mp,
Speaker 1: does that mean that there is, in a sense, that
Speaker 1: a universal algorithm out there? Uh? I mean there there
Speaker 1: is a theory of everything within our mathematical universes, as
Speaker 1: math max tech Mark argues in mathematical universe theory that
Speaker 1: we mentioned earlier. Because the tech Mark even go so
Speaker 1: far as to predict that a mathematical proof for a
Speaker 1: theory of everything could eventually fit on a T shirt. Well,
Speaker 1: I would kind of like to do that the kind
Speaker 1: of universe. Yeah, I mean, that's an interesting thought on
Speaker 1: its own, and tech marks theories I I, as I
Speaker 1: think I said earlier in this episode, I find them
Speaker 1: very interesting, even if I'm not qualified enough to know
Speaker 1: whether they're really rigorous physics. I read that book Our
Speaker 1: Our Mathematical Universe, and I found it amazingly stimulating. You know.
Speaker 1: He talks about different levels of of multiverse realities and
Speaker 1: what they each imply. Uh, And he gives a very,
Speaker 1: at least to the lay person, a very reasonable sounding
Speaker 1: explanation of how these are natural conclusions from what we
Speaker 1: know about physics. But I do want to use what
Speaker 1: you said as a sort of jumping off point to
Speaker 1: take a broader view about the algorithmic nature of reality.
Speaker 1: But first we're going to take a quick break to
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Speaker 1: making that awesome website. So whatever the solution to P
Speaker 1: equals and P turns out to be. I think one
Speaker 1: thing that's very interesting about it is just the idea
Speaker 1: that this problem in computer science runs under the skin
Speaker 1: of everything that exists. You know, It's it's not something
Speaker 1: that people just made up. This is talking about a
Speaker 1: fact about the universe. That would be a fact about
Speaker 1: the universe whether we were here to discuss it or not. Yeah,
Speaker 1: I mean there's a certain amount of it's difficult, kind
Speaker 1: of to get to get outside of the mirror language
Speaker 1: of the situation when we're talking about problem solving, because
Speaker 1: we can't help but think about a human mind trying
Speaker 1: to solve a problem. But in a sense, problem solving
Speaker 1: takes place not only the human level, it takes place
Speaker 1: that at at at at the animal level, at as
Speaker 1: you know, as this particular entity is trying to navigate
Speaker 1: a world of fixed and moving objects, generally to acquire
Speaker 1: some goal, to acquire food or or a mate. Uh.
Speaker 1: You could even you could probably even extrapolate it as
Speaker 1: far to say to say that that an object obeying
Speaker 1: gravity is kind of engaging in a sort of non
Speaker 1: mental problem solving in a way, in in a limited way. Uh,
Speaker 1: I guess I'm just trying to drive home here, is
Speaker 1: that when we continue to talk about problem solving here,
Speaker 1: it's like trying not to think about it as much
Speaker 1: within in the human realm, because it is we're about
Speaker 1: to see it gets well outside of it, remove the
Speaker 1: consciousness from it, retain only the teleology exactly that there
Speaker 1: there are, there are steps towards a purpose, but you
Speaker 1: don't have to know what the purpose is, and you
Speaker 1: don't even have to realize you're taking steps right now.
Speaker 1: A great example of this is the slime mold. So
Speaker 1: slime molds don't have brains. They consist of a single
Speaker 1: cell containing millions of nuclei and they form a network
Speaker 1: of protoplasmic tubes to creep toward a food source along
Speaker 1: the shortest path. And that's essential here. Uh. It sends
Speaker 1: out limbs to find food, and when it finds food source,
Speaker 1: it spreads over, It secretes too digestive enzymes, and has
Speaker 1: its meal. When it doesn't, yeah, it's pretty it's pretty great. Essentially,
Speaker 1: have a blob, right and when it doesn't find food,
Speaker 1: then the limb you know, dies in retreats back. So
Speaker 1: in this it creates a network for transporting nutrients and chemicals,
Speaker 1: for inter cellular communication and the method allows them to
Speaker 1: perform such feats and this is generally and this is
Speaker 1: in lab environments. Uh, such feats as solving a maze,
Speaker 1: like a straight up maze that you would put a
Speaker 1: mouse in, as well as when presented with a miniaturized
Speaker 1: earth environment. Uh, they can they can recreate some of
Speaker 1: the great trade routes of the world, some of the
Speaker 1: great highway systems. They can model cancer growth. Um. Let
Speaker 1: me go to a little detail about the silk road thing,
Speaker 1: and this is this gets into exactly what we're talking
Speaker 1: earlier about an algorithm attempting to to plot a course
Speaker 1: right and and having to hit all those stuffs the
Speaker 1: salesman problem that we're discussing earlier. Okay, so back into
Speaker 1: computer scientist Andre Adamanski from the University of the West
Speaker 1: of England. He took a globe. Okay, and you can
Speaker 1: do this at home probably, I guess if you have
Speaker 1: access to the materials. He took a globe and he
Speaker 1: coated it with auger. All right, this, of course is
Speaker 1: the stuff in a peat free dish that you know
Speaker 1: bacteria grows up eat. Yeah. Uh and then he um.
Speaker 1: And then what he did is he removed uh, the
Speaker 1: auger from the areas over the ocean, so it's just
Speaker 1: covering the continents and the land at this point. And
Speaker 1: then he placed oat flakes at the locations of twenty
Speaker 1: four different major cities on the globe, so that's a
Speaker 1: food source. Okay. Then he introduced the slime mold. Alright.
Speaker 1: He did this third any different times, and each time
Speaker 1: the slime mold conquered the world in a slightly different way,
Speaker 1: establishing trade routes between the various oats cities. Yeah, and
Speaker 1: it's the picture their pictures out there. This is pretty remarkable,
Speaker 1: uh because it and maybe a little bit scary because
Speaker 1: you see these ten drils just spreading out all over
Speaker 1: the world. It managed to plan out engineering projects that,
Speaker 1: of course humans can only dream of right now, like
Speaker 1: Transatlantic bridges. Obviously we're not going to do that. It
Speaker 1: wasn't I don't. I don't think it was ever able
Speaker 1: to really conquer the Pacific, be Pacific was just too
Speaker 1: too uh too great of a distance without agur there
Speaker 1: for it to grow on. Uh. But but it also
Speaker 1: managed to recreate the Silk Road as well as the
Speaker 1: modern Asian highway network, which consists of about the eighty
Speaker 1: seven thousand miles of roads running between thirty two countries.
Speaker 1: So it exactly it provides a great example of uh,
Speaker 1: not a problem solving intelligence, but an algorithmic problem solving
Speaker 1: organic system. Of course, this, I do think raises the
Speaker 1: specter of the question how do you tell the difference
Speaker 1: between an algorithm and intelligence unless you want to be
Speaker 1: anthropomorphic and say, well, intelligence is consciousness and the ability
Speaker 1: to love and yeah, and then we start gazing down
Speaker 1: that of this right, Yeah, you know, we get back
Speaker 1: that to some of the problems we've discussed in relation
Speaker 1: to AI in the past. How do you know when
Speaker 1: you created it? If you can't really say what it is,
Speaker 1: it becomes this this problem. We can't even define the problem,
Speaker 1: so how can we come up with the solution or
Speaker 1: check the solution? Yeah, and it's funny that we were
Speaker 1: talking earlier about about sets that sort of recursively consume
Speaker 1: one another. Is one set within another set, but then
Speaker 1: the first set is the second set is also in
Speaker 1: the first set. Now we just gave an example of
Speaker 1: how nature can be like an algorithm. But you can
Speaker 1: also say that plenty of algorithms and computer science have
Speaker 1: been essentially derived from nature. Um and yah, there's a
Speaker 1: great example of this with ants. So ant colonies we've
Speaker 1: discussed adnce here in the podcast before and I'm sure
Speaker 1: we'll cover them again in the future. You know that
Speaker 1: they're complex societies, and we see plenty of examples in
Speaker 1: which colonies accomplished complex tasks that exceed the individual capacities
Speaker 1: of a single ant. Of course, so they worked together
Speaker 1: and they're able to solve problems. And this is mound mind. Yeah, exactly,
Speaker 1: it's the the the the the emergent intelligence of the group,
Speaker 1: the swarm intelligence. Um. This is a particular note to
Speaker 1: computer programming as though, as we see how they're self
Speaker 1: organizing capacities and distributed organization enable them to solve difficult
Speaker 1: optimization and distributed control problems. Okay, So back in a
Speaker 1: Stanford study looked at how harvester ants determine how many
Speaker 1: foragers to send out. Of course, so they're sending out
Speaker 1: a rating party, right, uh, which is you know, more
Speaker 1: complex than than than you might think, because you get
Speaker 1: down to the basic you know, how many do you
Speaker 1: send out? You know, what's the way time? Uh? And
Speaker 1: then they compared this to the manner in which a
Speaker 1: search engine brings back search results. So specifically, yeah, specifically,
Speaker 1: we're talking about transmission control Protocol or TCP, which, if
Speaker 1: you're like me, that's mostly something that you run into
Speaker 1: when you have to adjust something on your your Internet
Speaker 1: situation at home. Yeah, but but in anyway, it's a
Speaker 1: it's essentially an algorithm that manages data congestion on the Internet.
Speaker 1: So they they compared the two, right, and they combined
Speaker 1: the two, and they created the anternet. So that's that's Internet,
Speaker 1: except instead of you, you have an ant um. So
Speaker 1: it's a TCP influenced algorithm that accurately matched ant behavior
Speaker 1: in the experiment. So it's an example of ants reaching
Speaker 1: the same place as our computer programming UM. So basically
Speaker 1: they created a tc PEE program that accurately predicted how
Speaker 1: the ants were going to act. Yeah, we've definitely talked
Speaker 1: on the other podcasts that I do with Jonathan Strickland
Speaker 1: and Lauren Vogelbaum Forward Thinking. We talk about biommetic robotics
Speaker 1: a lot about ways that robots can be inspired by
Speaker 1: the ways that animals move, especially in mobile robotics. You know,
Speaker 1: how do you get a swarm of things to behave
Speaker 1: as a group correctly, and I'd imagine that this would
Speaker 1: be a very good example of how to control them. Yeah,
Speaker 1: you see swarm organisms used in various AI programs. I
Speaker 1: believe here Georgia Tech in Atlanta, they've used bees a lot.
Speaker 1: Oh yeah, yeah. And more recently, a two thousand fourteen
Speaker 1: study from Zero's Institute of Pharmaceutical Sciences explore the possibility
Speaker 1: of using ant algorithms to search for new composite agents
Speaker 1: in the development of new pharmaceuticals. And this gets down
Speaker 1: to the whole in a situation discussing earlier about do
Speaker 1: you do you take a brute uh strength approach to
Speaker 1: finding out which connections amid all these possible connections are
Speaker 1: the ideal ones to then test and explore. Um So
Speaker 1: they've looked into the possibility of using an ant based
Speaker 1: algorithm to find though to do essentially, you know, magically
Speaker 1: guess those uh, those those composite agents that that deserve
Speaker 1: further examination. Well, you know, one thing these examples in
Speaker 1: nature make me think about is an idea that really
Speaker 1: intrigues me, and that's the question of whether evolution by
Speaker 1: natural selection can itself be best interpreted as an algorithm,
Speaker 1: Because think about it. It's it's kind of an iterate
Speaker 1: and test style algorithmic procedure. Let me give you a
Speaker 1: list of steps. Step one, randomly introduce a change that
Speaker 1: would be like a mutant allele into the genome. You
Speaker 1: very one gene from the existing model, so you've random that.
Speaker 1: That's step one. Then step two test against the baseline
Speaker 1: performance rate of the standard allile in the environment or
Speaker 1: you know. The individual steps here would be attempt to copy.
Speaker 1: If being succeeds, go to one or return to the
Speaker 1: first step. If copying fails, return void. It's almost like
Speaker 1: a computer program. Yeah, I think I think there's a
Speaker 1: very strong case to be made there. I mean earlier
Speaker 1: I made that I said that gravity an object of
Speaker 1: band gravity and is it is in a way kind
Speaker 1: of obeying a certain algorithm. It's kind of problem solving.
Speaker 1: So this I think this fits Bill as well. Yeah,
Speaker 1: and I certainly didn't come up with this idea. I know,
Speaker 1: I've read about it in the philosopher Daniel Dennett, who
Speaker 1: advocated this point of view in this nine book. Darwin's
Speaker 1: dangerous idea was which was a lot about the implications
Speaker 1: of evolution beyond just explaining the diversity of species on Earth.
Speaker 1: Evolution is a sort of principle that extends even beyond biology.
Speaker 1: But this universal driving force that that drives design through
Speaker 1: the design space and the way he would explain it.
Speaker 1: But uh so, of course, not everybody agrees with that
Speaker 1: interpretation ation thinks that an algorithm is a good way
Speaker 1: of thinking about evolution. But I've got another follow up
Speaker 1: question that's kind of interesting to me. If evolution is
Speaker 1: an algorithm, is it an efficient algorithm or a brute
Speaker 1: force algorithm? Now that's a good question. I mean, it
Speaker 1: seems to me kind of like it would be a
Speaker 1: brute force algorithm, right, because you're you're trying any number,
Speaker 1: it's you know, just brute force combinatrix. You're trying something.
Speaker 1: Here's a pair of genes, here's an alleal. Does that work? Now? Okay,
Speaker 1: throw in the trash. It seems very wasteful. Yeah, here's
Speaker 1: a lizard with spots, here's one without spots, which one
Speaker 1: gets eaten, which one continues. That sounds like kind of
Speaker 1: a brute brute force You're just like throwing out all
Speaker 1: the produce possible prototypes and uh and seeing what the
Speaker 1: thing you see what happens, and I think this would
Speaker 1: actually be one way of framing the difference between the
Speaker 1: standard scientific materialist view of evolution, which I think would
Speaker 1: probably be is best I can tell. I bet that'd
Speaker 1: be the brute force method, and then some types of
Speaker 1: believers in intelligent design. Right, So if you are are
Speaker 1: somebody who believes um, you you accept the evidence for
Speaker 1: evolution and common descent, but you simply believe the process
Speaker 1: was guided in one way or another. You think aliens
Speaker 1: or a god or some other you know, powerful supernatural
Speaker 1: or otherworldly technological force interfered with evolution, maybe reached in
Speaker 1: to cause specific mutations to the terrestrial gene space at
Speaker 1: key points. That sounds like that would be optimizing the algorithm, right,
Speaker 1: like somebody's introducing artificial efficiency. Yeah, but then again, i'd
Speaker 1: i'd be interested in hearing from the evolutionary biologists and
Speaker 1: geneticists sat there in the audience on this one. Like,
Speaker 1: if you accept the idea that natural selection is like
Speaker 1: an algorithm, is it a brute force algorithm unless you
Speaker 1: go to the intelligent design hypothesis or are there other
Speaker 1: ways of thinking of the algorithm as in some way
Speaker 1: optimized by material circumstances. And since you did mention God
Speaker 1: or the gods, here would the God in this scenario
Speaker 1: that Okay, so this is a force coming from outside
Speaker 1: our universe. Then perhaps in this scenario our world is
Speaker 1: is a ped is not equal in the universe, but
Speaker 1: the realm of the gods is a P equals in
Speaker 1: p universe. Huh. Well, I mean that's an interesting way
Speaker 1: of putting it. Like they can they can knock it
Speaker 1: out right there, Gods, they're basically limitless. Well, it's infinite possibility,
Speaker 1: I mean, the whole the realm of mathematics and logic is.
Speaker 1: In many ways, it often signals to me the sort
Speaker 1: of underlying hint of infinite possibilities but also infinite constraints.
Speaker 1: At the same time. Mathematics is both infinite power and
Speaker 1: ultimate helplessness. You know. It's the power to accomplish anything
Speaker 1: and the inevitability of being thwarted and destroyed by processes
Speaker 1: beyond your control. Uh. It just sort of makes everything
Speaker 1: good and bad possible. But it sounds like you're talking
Speaker 1: about the gods again. It could be Yeah, all right,
Speaker 1: So there you have at p m p P versus
Speaker 1: m P P equals m p P does not equal MP.
Speaker 1: Hopefully at this point you have if you if you
Speaker 1: didn't know what any of this stuff was about beforehand,
Speaker 1: you have a much better graph on the idea. You
Speaker 1: can at least realize why it is a topic that
Speaker 1: people continue to discuss and even argue about. But if
Speaker 1: you want to get into the actual details of of it,
Speaker 1: there are plenty of good resources out there on the
Speaker 1: internet if you are a math and computer science and
Speaker 1: logic inclined person who has a good abstract mind for
Speaker 1: that kind of thing. But either way, I do want
Speaker 1: to remind you to always think about the algorithmic nature
Speaker 1: of the ground beneath your feet, and the laws that
Speaker 1: govern the way the way everything around you works, the
Speaker 1: logic of reality. Uh, Is there a problem solving process
Speaker 1: inherent to everything that's going on around you all the time?
Speaker 1: I don't know. It's it's a strange specter of an
Speaker 1: idea to keep behind your head at all times. Yeah. Again,
Speaker 1: like when a when like a walnut falls out of
Speaker 1: a tree, there are certain there's an there's an algorithm
Speaker 1: at play right as to how exactly it's going to
Speaker 1: make it to the ground, which branches is going to hit.
Speaker 1: I guess that depends on your perspective. Is there is
Speaker 1: there a goal, there is something happening, or did something
Speaker 1: just happen. I don't know, man, it's pretty far out. Well,
Speaker 1: let's not get too much into weird stone or territory here.
Speaker 1: And I do want to say right here at the end,
Speaker 1: if you are somebody who's involved in mathematics or computer
Speaker 1: science and uh and you would like to write in
Speaker 1: to tell us about one of the one of the
Speaker 1: more detailed or complex aspects of this that we didn't
Speaker 1: get to. Like we said, we we gave you the
Speaker 1: very simple version. Please right in and we'd love to
Speaker 1: share your thoughts with the rest of you guys. Yeah,
Speaker 1: and I'd also love to hear from anyone you know
Speaker 1: who's read some some science fiction that definitely weighs in
Speaker 1: on this. Um. You know, I was trying to think
Speaker 1: of sific examples from N. N. Banks culture books, because
Speaker 1: the courent they have these minds, these aies that are
Speaker 1: incredibly powerful. But for the life of me, I can't remember,
Speaker 1: uh exactly where they they weigh in in terms of
Speaker 1: the air We're indeed, um Banks is universe, their wigs
Speaker 1: in on the on the P and P spectrum. Hey,
Speaker 1: but in the meantime, you want to check out this
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Speaker 1: out of of and you can reach out as an
Speaker 1: as an outside force like God and shift things in
Speaker 1: our favor. So I invite you to do so. And
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