Speaker 1: Hey, welcome to Stuff to Blow Your Mind. My name
Speaker 1: is Robert Lamb and I'm Joe McCormick, and it's Saturday.
Speaker 1: What does that mean, Robert, What means it's time to
Speaker 1: open the vault. It looks like it's already open, so
Speaker 1: let's get in there. There's a lot of P in here.
Speaker 1: There's also a lot of MP in here. Perhaps you
Speaker 1: can explain this to everybody. Smooth transition, Robert, very smooth.
Speaker 1: I like it. Uh. This is the episode on the
Speaker 1: P versus MP problem, a classic fascinating vexing problem in
Speaker 1: logic and math and computer science and uh. And in
Speaker 1: this episode we tackle the question of what it actually
Speaker 1: means to solve a problem. This originally aired on April twelve,
Speaker 1: and we're bringing it back for you now, so we
Speaker 1: hope you enjoy our exploration of the P versus MP problem.
Speaker 1: Welcome to Stuff to Blow your Mind from how Stuff
Speaker 1: Works dot com. Hey, welcome to Sceptable in your Mind.
Speaker 1: My name is Robert Lamb and I'm Joe McCormick. And
Speaker 1: today we're gonna be taking a look at the issue
Speaker 1: in computer science. Uh. Funny enough, I'd say that's not
Speaker 1: one of the science, as we dip into very frequently
Speaker 1: on this podcast. Yes, and I mean, really, we should
Speaker 1: probably just remind everyone to stick with us, trust us
Speaker 1: on this one. Uh, don't be scared off by the
Speaker 1: computer science thing. Don't be scared off by the P
Speaker 1: versus MP thing. It's it's it's all gonna make a
Speaker 1: type of sense at the end, hopefully. But I'm wondering
Speaker 1: if maybe we should dip into computer science more often
Speaker 1: because or at least wherever we can find a way
Speaker 1: to make the contents of it reasonably concrete, because, let's
Speaker 1: be honest, as we've discovered in researching this episode, it's
Speaker 1: very abstract, very difficult, and a lot of times hard
Speaker 1: to come up with ways of explaining that makes sense
Speaker 1: just just talking about it without visual aids or watching
Speaker 1: programs Exit Cute as an example. Yeah, it's definitely one
Speaker 1: of those topics that it's a swimming pool of a
Speaker 1: topic in which there is no gradual deepening from the
Speaker 1: kitty area to the deep end. It's just shallow, and
Speaker 1: at times it feels too shallow and then you're immediately
Speaker 1: out of your depth. Yeah, but if you're thinking of
Speaker 1: computer science, really does that fit with the show hold
Speaker 1: on for a second, because I think it does. Um.
Speaker 1: Computer science to me is a fascinating subject. Uh, and
Speaker 1: it's not just limited to how computers work. So my
Speaker 1: advice is, when you think about the idea of computer science,
Speaker 1: forget the computer sitting in front of you. That's not
Speaker 1: all it is. Computer science is really something more akin
Speaker 1: to the philosophy of logic, understanding the the underlying sorcery
Speaker 1: of how logic and math work in the universe we inhabit,
Speaker 1: and especially the science of how problems are solved. And
Speaker 1: certainly when you start bringing math into the equation here
Speaker 1: as well, I mean you're talking we're talking about the
Speaker 1: essentially the very fabric of the universe. We're talking about
Speaker 1: either the fabric of the universe, either the way the
Speaker 1: universe works, or this perfect creation that humans have come
Speaker 1: up with that so accurately describes how the universe works,
Speaker 1: and that is pretty mind blowing territory. Well, either way
Speaker 1: you look at it, there is something mystical about about
Speaker 1: the math that we walk on every day that you know,
Speaker 1: that makes up the fabric and the logic math, the
Speaker 1: math beneath our feet. You know, if you go with
Speaker 1: the max Tech mark idea of the mathematical universe. Some
Speaker 1: people don't like this idea because, like I don't understand
Speaker 1: what that means, but at least it's a very intriguing idea.
Speaker 1: I think his ideas that the underlying basis of all
Speaker 1: reality not just as described by math, but is math,
Speaker 1: and the universe is a mathematical object. But we're gonna
Speaker 1: get back to this idea of problem solving because today
Speaker 1: we want to focus on algorithms and on the inherent
Speaker 1: logic of problem solving in our universe, with some attention
Speaker 1: to a special example of one really interesting outstanding problem
Speaker 1: in computer science, and that's the P versus n P issue.
Speaker 1: If you've never heard of this before, don't worry. We'll
Speaker 1: explain what the terms mean in in a simplified manner.
Speaker 1: And uh I at this point also do want to
Speaker 1: give a shout out to our listener Jim in New Jersey,
Speaker 1: who has been encouraging me over email to tackle this
Speaker 1: issue for a while despite all the challenges, and has
Speaker 1: also sent some really helpful, uh really helpful guides and
Speaker 1: explainers on some stuff. He he learned about this when
Speaker 1: he was in graduate school. Yeah, indeed, and UH and
Speaker 1: I think this is great too, because this episode is
Speaker 1: coming on the heels of first of all, the Wicked
Speaker 1: Problems episode that came out a few weeks ago, as
Speaker 1: well as the more recent Cargo Cults episode which in
Speaker 1: which we discuss some outside context problems a little bit
Speaker 1: as well. So it's it's perfectly fitting that we would
Speaker 1: discuss another problem. Well, what does it mean inherently to
Speaker 1: solve a problem? If you get into the theory of
Speaker 1: problem solving? What what what does this process look like? Well,
Speaker 1: when it comes down just to the basics open and
Speaker 1: this also kind of gets into the whole Wicked Problems
Speaker 1: area of like, what's what's missing when you don't have, um,
Speaker 1: you know, everything you need to solve a problem for
Speaker 1: for a real problem, you have to be able to,
Speaker 1: of course, do to find what the problem is. A
Speaker 1: lot of a lot of attempts fail right there. Yeah,
Speaker 1: you've got to You've got to be able to say
Speaker 1: this is the thing you know and then you and
Speaker 1: then you have to be able to measure your success
Speaker 1: and check the solution. So you essentially have to be
Speaker 1: able to say, hey, this is wrong because of X.
Speaker 1: And then if you then figure out what x is
Speaker 1: and see if the equation balances out. Um, it sounds
Speaker 1: pretty simple. But like I said, as we discussed in
Speaker 1: Wicked problems, that's uh, it can be very difficult to do,
Speaker 1: especially in you know, the very complex social situations when
Speaker 1: you're dealing with with certainly some of the larger problems
Speaker 1: that we're going to talk about here, or even if
Speaker 1: you want to go into the simplest level, well, I mean,
Speaker 1: depending on what you would call simple. In fact, what
Speaker 1: we're going to be getting into today is directly referred
Speaker 1: to as complexity theory. Uh. So maybe it's not so simple,
Speaker 1: but at least simple in terms of not involving uh
Speaker 1: phenomena in the real world, but just math, just math
Speaker 1: and logic and and true versus untrue and UH and algorithms.
Speaker 1: So I think it's time to pull back the curtain
Speaker 1: a little bit and reveal some of the deep weirdness
Speaker 1: of the nature of algorithms and problem solving in our universe.
Speaker 1: So let's look at this P versus MP problem. This
Speaker 1: is something that comes from two of the great minds
Speaker 1: of the twentieth century, Kurt Girdle and John von Neuman,
Speaker 1: and in nineteen fifty six, Kurt Girdle, who's a mathematician
Speaker 1: and logician, wrote a letter to John von Neuman which
Speaker 1: kicked off this quest to solve one of the biggest
Speaker 1: questions in computer science, the P versus n P issue. Now,
Speaker 1: who were these guys, but both were titans of the
Speaker 1: twentieth century in terms of math, logic, and computers. Well.
Speaker 1: Godal is probably most famous for his first incompleteness theorem,
Speaker 1: and this states that any adequate um axiomatizeable theory that means,
Speaker 1: a theory that's based on self evident but unprovable proofs,
Speaker 1: is incomplete or inconsistent. Yeah. Girdle's whole incompleteness theorem set. Yeah,
Speaker 1: A couple of his incompleteness theorems essentially amount to the
Speaker 1: idea that any mathematical system that makes sense will have
Speaker 1: some statements that are true yet impossible to prove. It's
Speaker 1: sort of the idea that you can't ever know everything
Speaker 1: about a self consistent system. Yeah, and the the The
Speaker 1: implication here, according to theoretical physicist and mathematician Freeman Dyson,
Speaker 1: who has is also quite a giant in the field,
Speaker 1: is that mathematics is inexhaustible, that no matter how many
Speaker 1: problems we solve, will inevitably encounter more unsolvable problems within
Speaker 1: the existing rules. I take comfort in that measure of futility. Yeah,
Speaker 1: but there's also John von Neuman, the recipient of the letter.
Speaker 1: And von Neuman. I don't know what you've heard about him,
Speaker 1: but I'd say he's often considered one of the most
Speaker 1: intelligent people who ever lived that we know about at least,
Speaker 1: and 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
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 Neumann
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 this 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 in
Speaker 1: P issue in complexity theory is probably the most difficult
Speaker 1: and 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, the House of Works
Speaker 1: UH 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. Uh. Anyway, here we go. So we we
Speaker 1: got to start with the concept of algorithms. What what
Speaker 1: is an algorithm? Well, I'd say an algorithm is a
Speaker 1: self contained list of instructions to solve a problem. You've
Speaker 1: got a goal, and then you make us step by
Speaker 1: step list of things to do that gets you to
Speaker 1: the goal. A common example within a computer program would
Speaker 1: be a subroutine designed to sort a list of things.
Speaker 1: That's an algorithm. Yeah, and you know, algorithms are something
Speaker 1: we encounter on a just on a daily basis, especially online.
Speaker 1: I mean Facebook, Google. Both of these depend on ever
Speaker 1: changing algorithms to decide what you see and don't see
Speaker 1: on your feeds and on your search results. Yeah, and
Speaker 1: I think that's a great example of how complex algorithms
Speaker 1: can get. You've got the simple sorting algorithm on one hand,
Speaker 1: and then you've got the stuff that decides whether you
Speaker 1: only see political articles you agree with or whether you
Speaker 1: sometimes see stuff that's going to make you mad. So,
Speaker 1: when you're designing algorithms in in a computer science arena,
Speaker 1: or really to solve any problem, but we're mostly gonna
Speaker 1: be talking about computer programs, you compare how much time
Speaker 1: it takes to solve a problem with an algorithm, given
Speaker 1: the scope of a problem. So this is usually expressed
Speaker 1: in terms of inputs versus time. So I want to
Speaker 1: give a quick example with sorting. Like I said, you say,
Speaker 1: you're given a spreadsheet that includes a list of all
Speaker 1: the James Bond movies that exist currently in a random order,
Speaker 1: and you've got to write a computer program that sorts
Speaker 1: all of those lists of James Bond movie titles into
Speaker 1: a list in the order they came out. How would
Speaker 1: you do that? Now, there are a lot of ways
Speaker 1: you actually could approach the problem, and that they don't
Speaker 1: all take the same amount of time. Some are much
Speaker 1: more efficient than others. Here's one example. You could create
Speaker 1: an algorithm that goes like this. Step one, rearrange the
Speaker 1: entire list at random. Step two, check each movie in
Speaker 1: the list to see if it came out before the
Speaker 1: next movie in the list. If the answer is yes,
Speaker 1: all the way down the line, then the list is
Speaker 1: sorted correctly and you're done. If not, start over and
Speaker 1: rearrange it entirely randomly. Now, given enough time and a
Speaker 1: small enough data set, this algorithm will if eventually finished
Speaker 1: by blind luck. It is just brute force burning through
Speaker 1: computer resources wastefully in order to eventually solve the problem
Speaker 1: by blind block. But there are also much more efficient
Speaker 1: ways you could go about it. For example, you could
Speaker 1: go down the list comparing each movie to the next,
Speaker 1: and if the second movie came out before the first,
Speaker 1: you switch their order on the list and then go
Speaker 1: on like that. Uh, and then you do that until
Speaker 1: the list is sorted. But some problems are inherently a
Speaker 1: lot harder than others, and there aren't any algorithmic shortcuts
Speaker 1: like that that we know about. We don't know of
Speaker 1: any easy way to solve them. The only thing we
Speaker 1: know how to do is do that stupid brute force
Speaker 1: method where you just wastefully burned through computer resources until
Speaker 1: it's solved by time and force. And in fact, I'd
Speaker 1: like to make a comparison here in the you know,
Speaker 1: the efficient algorithm versus brute force methods, to what you
Speaker 1: might see in animals in the wild using intelligence to
Speaker 1: solve a problem. So like, if you're hunting another animal,
Speaker 1: you could use a brute force method of just running
Speaker 1: after the animal until it is tired or until your
Speaker 1: muscles have allowed you to catch it, and then killing
Speaker 1: it with the strength of your muscles. That's sort of
Speaker 1: the brute force method. Or you could set a trap,
Speaker 1: or you could build a weapon that these are shortcuts
Speaker 1: that make the process of hunting a lot more efficient.
Speaker 1: Now here's where we get to our main terms in
Speaker 1: this discussion, P and n P. P is going to
Speaker 1: stand for polynomial time and n P stands for nondeterministic
Speaker 1: polynomial time. You don't really need to remember that for
Speaker 1: the purpose of this discussion, because we're gonna make it
Speaker 1: a lot simpler. Yeah, I mean, this is one of
Speaker 1: the problems with the topic, is that like just the
Speaker 1: word just this the the the basic idea here of
Speaker 1: P and MP there, it's so dry and unrelatable. But
Speaker 1: allow us to explain. Yeah, okay, So the real difference
Speaker 1: has to do with um processes of solving problems on
Speaker 1: a determinus dick Turing machine, which is equivalent to the
Speaker 1: kind of computer you'd be using right now, you know,
Speaker 1: any device you have, versus a hypothetical nondeterministic machine, which
Speaker 1: in theory you could say works by magically guessing the
Speaker 1: answers to questions and then just checking to see if
Speaker 1: the magic guess is correct. But, like we said, we
Speaker 1: don't want to get too bogged down in all those details.
Speaker 1: So here's the simplified version. P is a set of
Speaker 1: all problems that can be solved by an algorithm quickly
Speaker 1: or easily or efficiently. This is the easy. The list
Speaker 1: of easy problems in computer science. N P, on the
Speaker 1: other hand, stands for answers that can be easily checked
Speaker 1: by a computer once you have them, but they can't
Speaker 1: necessarily be solved easily. Yeah. So it's difficult to place
Speaker 1: this in a non mathematical context. But one way I
Speaker 1: like to think about this is in terms of written reviews,
Speaker 1: for for albums, for for for musical albums. Um, because
Speaker 1: a good a good review, a good music review is
Speaker 1: is difficult to write, uh, and hard to find and
Speaker 1: hard to find. Yeah, Like in my own experience, you
Speaker 1: often find I mean, I I write many reviews of
Speaker 1: stuff of stuff from time to time, and that alone
Speaker 1: is challenging enough for me. But but yeah, when you
Speaker 1: even when you're looking out of the major publications, uh, yeah,
Speaker 1: it's hard to find one that feels just right. It's Uh.
Speaker 1: The average reader, though, can can swiftly judge to what
Speaker 1: extent they agree with the author, obviously, to what extent
Speaker 1: the author is just blowing smoke. We've all read those
Speaker 1: music reviews where you get the sense that the the
Speaker 1: author is really using the music as an excuse to
Speaker 1: sort of write his or her own poetry. Uh, they're
Speaker 1: on the page as opposed actually describing what the music
Speaker 1: is like. But but the reader knows. So the reader
Speaker 1: can can can look at the material and either believe
Speaker 1: them or you don't. Either you buy into their opinion
Speaker 1: or you don't. Yeah, so you could. You don't have
Speaker 1: the algorithm internally to efficiently right this piece of writing yourself,
Speaker 1: but you know it when you see it exactly. Yeah,
Speaker 1: it's kind of like pornography in that sens right. You
Speaker 1: might not be able to define clearly the difference between
Speaker 1: art and pornography, but you know it when you see it.
Speaker 1: Once you have that answer certificate there, you can check
Speaker 1: and by golly, it checks out. And I like that
Speaker 1: because it also gives a whole new meaning to the
Speaker 1: P and to the MP and H. Now, so there
Speaker 1: are a couple of other terms that matter there. There's
Speaker 1: MP hard, and this means that are problems that are
Speaker 1: as hard as any other MP problem essentially. And then
Speaker 1: there's also MP complete, which is a big issue in
Speaker 1: this arena, and this is problems that are m P
Speaker 1: and n P hard so you you can check the
Speaker 1: answer once you have it in in a reasonable amount
Speaker 1: of time, and their MP hard. Now, the interesting thing
Speaker 1: about MP complete problems is that it has been proved
Speaker 1: in the literature that if you have an algorithm that
Speaker 1: and efficiently solve one MP complete problem, it can be
Speaker 1: transposed to solve all of them. These problems reduced to
Speaker 1: each other. So if you if you can solve one
Speaker 1: MP complete problem in a reasonable amount of time, you
Speaker 1: have found the master key. And this in the universe
Speaker 1: kind of shrinks in response to this. So a classic
Speaker 1: example of an MP problem is the prime factorization problem
Speaker 1: that we use in encryption on the Internet. Again, we
Speaker 1: don't want you to get lost too much here, so
Speaker 1: here's the simple version with smaller numbers than usual. Let's
Speaker 1: say I just throw out a random number, and let's
Speaker 1: say it's a number of I don't know what's a
Speaker 1: good one skulls in a pile. So let's say I
Speaker 1: give you a number. Let's say there are seven hundred
Speaker 1: and twenty one thousand, four hundred twenty one skulls in
Speaker 1: a pile. It is now I tell you this number
Speaker 1: is the product of two prime numbers of skulls in
Speaker 1: a pile, but I don't tell you what they are. Now,
Speaker 1: how could you figure out what those two prime numbers
Speaker 1: of skulls in a pile are? For a computer with
Speaker 1: numbers this small, this wouldn't be all that big a deal.
Speaker 1: But we're we're gonna have to extrapolate too much bigger numbers.
Speaker 1: But for you, this would be really annoying to figure out, right,
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, I'm
Speaker 1: not gonna have time for all this prime number nuns. Now,
Speaker 1: since we've solved p 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 or 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 that takes
Speaker 1: almost no time at all. And in fact, I'd 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 you ages. It's going to
Speaker 1: be impossible. But if you already know a selected answer
Speaker 1: to test, you can I can see if that answer
Speaker 1: is right. Yeah, I mean this brings to mind. Uh,
Speaker 1: it's a bit like trying to crack a four number
Speaker 1: code on a simple combination lock, right, And I'm talking
Speaker 1: about a human doing this, not a computer. So it
Speaker 1: would take me as a human quite a while to
Speaker 1: test out all ten thousand possible solutions, but no time
Speaker 1: at all to check a solution that someone else had
Speaker 1: provided me. So you know, I'd be there all day
Speaker 1: just putting in each one of those ten thousand solutions.
Speaker 1: But but I can easily put in you know, uh,
Speaker 1: thirty three sixty six and see if that is correct.
Speaker 1: You found a really interesting request for help on this subject,
Speaker 1: and you, oh, yeah, yeah, there was because I wanted
Speaker 1: to check to make sure that my math was right
Speaker 1: on how many possible combinations. I was pretty sure it
Speaker 1: was the ten by ten by ten by ten thing.
Speaker 1: But I I did one of those searchers to just
Speaker 1: see people 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 contract actor's box, you know, like
Speaker 1: at a house we have a real estate agent. Yeah,
Speaker 1: and she says it's like a thirty dollar box. So
Speaker 1: she didn't want to just have it, you know, cut
Speaker 1: into and ruin it in order to get the keys out.
Speaker 1: She 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 once,
Speaker 1: and that cut it down significantly, just just more than
Speaker 1: five thousand. Yeah, just was like five thousand forty or something. Yeah.
Speaker 1: And and the person who supply the answer on this forum,
Speaker 1: they included a list of all of them for her convenience.
Speaker 1: So um, I and I don't know how that came out.
Speaker 1: I wonder 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 intact. That sounds like a fun saturday,
Speaker 1: you know, on the porch in front of the box
Speaker 1: with the case a 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. It
Speaker 1: seems to imply a scenario. It's like the Infinity Hotel. Well,
Speaker 1: I want to change it up and I want to
Speaker 1: call I want to call this the nationwide infection problem.
Speaker 1: So imagine that you are the vanguard of an alien
Speaker 1: species that has come to Earth and you want to
Speaker 1: land in a country, you say the United States, and
Speaker 1: infect at least one person in every township and municipality
Speaker 1: in this country with one of your larvae. But you've
Speaker 1: got limited time to do it. A k. You know,
Speaker 1: no Dilly dalian around. So what you're looking for is
Speaker 1: a route that you can plan out on your alien
Speaker 1: equivalent of Google Maps directions or or you know, your
Speaker 1: Apple Directions device that will tell you how to go
Speaker 1: to every single city and township in the country, only
Speaker 1: one time each in the shortest route possible. Okay, that's
Speaker 1: 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
Speaker 1: solution it visits every city only once, uh, then it
Speaker 1: is easy to check. You can check that very quickly.
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 check.
Speaker 1: You just see that it visited every city once and
Speaker 1: see how long it took. But if you're looking to
Speaker 1: verify whether a solution is in fact the shortest of
Speaker 1: all possible routes, that's not easy to check because you'd
Speaker 1: still have you'd essentially have to do the entire brute
Speaker 1: force method that way and compare or it to every
Speaker 1: other possibility. All possible routes have to be to have
Speaker 1: to be considered. So if if that's what you're going for,
Speaker 1: it's not hard to solve, easy to check, It's hard
Speaker 1: to solve and hard to check. But here's the big
Speaker 1: problem with the with the P versus n P issue.
Speaker 1: We know that P problems are a subset of MP problems,
Speaker 1: But what if the subset is actually the same as
Speaker 1: the set, Meaning what if all NP problems are actually
Speaker 1: P problems? Meaning what if all problems where we can
Speaker 1: check the answer are actually problems where we can solve
Speaker 1: them efficiently. We just haven't figured out how to solve
Speaker 1: them efficiently yet, Okay, or we haven't developed the here
Speaker 1: the machines they can do it. Yeah, yeah, So is
Speaker 1: that possible? And that's actually probably the single biggest open
Speaker 1: question in computer science today? Is P equal or not
Speaker 1: equal to n P? Are they or are they not
Speaker 1: equivalent sets. Now, the obvious answer is no, right, that
Speaker 1: seems intuitive, That seems that that seems to be the
Speaker 1: answer that that feels most in keeping with our our
Speaker 1: understanding of like the limits of human ability, the limits
Speaker 1: of human knowledge, and just sort of the fabric of
Speaker 1: our universe. Yeah, and so most computer scientists and mathematicians,
Speaker 1: I think agree that the more likely answer to this
Speaker 1: unsolved question is that P does not equal MP. I
Speaker 1: found one pole that was taken. It was more than
Speaker 1: ten years ago. I don't know if things have changed
Speaker 1: much since then. But in two thousand two, the University
Speaker 1: of Maryland computer scientist William I. Gas Arc did a
Speaker 1: poll of colleagues in complexity theory and UH. And he
Speaker 1: found the results. And so he found out of this
Speaker 1: poll of colleagues, sixty one of his colleagues thought that
Speaker 1: P did not equal MP. Nine thought that P did
Speaker 1: equal MP. And some of those that said that said
Speaker 1: they they said that basically just to be contrarian or
Speaker 1: to continue encourage people to research the possibility. UH. And
Speaker 1: then several other colleagues either offered no opinion or offered
Speaker 1: UH sort of complex answers that weren't yes. Or no.
Speaker 1: But so you can obviously see that the opinion that
Speaker 1: P does equal MP, or the prediction that that will
Speaker 1: be what's eventually proved, is the minority. It's not what
Speaker 1: we would tend to think is the more likely possibility. Okay,
Speaker 1: it's the more outsider consideration here. So let's assume for
Speaker 1: a second that that is the case that one day
Speaker 1: some amazing mathematician or computer scientists somebody comes along and
Speaker 1: they figure out a way to prove that P does
Speaker 1: not equal in P. Proof Proofs like this happen in uh,
Speaker 1: in math and computer science all the time. You might
Speaker 1: be wondering, how could that be proved, But people figure
Speaker 1: out ways to demonstrate logically that something is true like this.
Speaker 1: So let's say it's demonstrated that P does not equal MP.
Speaker 1: What are the implications. Well, mostly, I'd say not much changes.
Speaker 1: This is sort of the obvious conclusion. It's the one
Speaker 1: that wouldn't surprise us. In other words, all of our
Speaker 1: brute force problems remain brute force problems. UH. But if
Speaker 1: this is the case, it would still be useful to know.
Speaker 1: It would be useful that people wouldn't start floating into
Speaker 1: the sky. The great old ones wouldn't come back. It
Speaker 1: would just business is usual for most people. Yeah, so
Speaker 1: we we'd have a proof, so people could stop trying
Speaker 1: to solve it, and we'd be able to use the
Speaker 1: fact that P is not equal to MP as an
Speaker 1: assumption for other work in mathematics and computer science. So
Speaker 1: we just move on with our lives basically essentially. But
Speaker 1: here's where things get interesting. What would the implications be
Speaker 1: if P does equal m P. 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 MP. 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 if P equals n 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 tend to a discussion on on the topic
Speaker 1: a few years back. Yeah, so this research, it involves
Speaker 1: going through permutations of of different ways of folding proteins
Speaker 1: in a computer simulation. And this research could help cure
Speaker 1: diseases and treat medical conditions if we learned the right
Speaker 1: things about the behavior of how protein molecules fold up
Speaker 1: on one another and behave 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, maybe we cure cancer. Or if people
Speaker 1: 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 moves 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 to. This seems to
Speaker 1: be very much an argument in favor of their, of
Speaker 1: their being no equality are right. But you could also
Speaker 1: look at that look at it as an interesting comment
Speaker 1: on how different the world would be from how we
Speaker 1: assume it is if this were in fact the case.
Speaker 1: And it's interesting to note that we shouldn't assume that
Speaker 1: just because it doesn't feel like we live in the
Speaker 1: P equals in P world, that P equals MP is
Speaker 1: necessarily false. Our our intuitions about what's possible in the
Speaker 1: math and problem solving space have turned out to be
Speaker 1: very wrong in the past, and sometimes long standing problems
Speaker 1: in math and computer science are solved by uh, solved.
Speaker 1: They're solved or proved in ways that just seem extremely peculiar,
Speaker 1: Yet you can't deny the result. I can't help but
Speaker 1: circle back around to the earlier opinion that we mentioned
Speaker 1: was attributed to Freeman Dyson that mathematics is inexhaustible. If
Speaker 1: P equals MP, then the universe. Is the universe really inexhaustible? Yeah?
Speaker 1: And uh? And if P equals MP, does that mean
Speaker 1: that there is in a sense a universal algorithm out there? Uh?
Speaker 1: I mean there there is a theory of everything within
Speaker 1: our mathematical universes, as mass Max tech Mark argues in
Speaker 1: mathematical universe theory that we mentioned earlier. Because the tech
Speaker 1: Mark even go so far is to predict that a
Speaker 1: mathematical proof for a theory of everything could eventually fit
Speaker 1: on a T shirt. Well, I would kind of like
Speaker 1: to the universe. Yeah, I mean that's an interesting thought
Speaker 1: on its own. And tech Marks theories I I, as
Speaker 1: I think I said earlier in this episode, I find
Speaker 1: them very interesting, even if I'm not qualified enough to
Speaker 1: know whether they're really rigorous physics. I read that book,
Speaker 1: are our mathematical universe, and I found it amazingly stimulating.
Speaker 1: You know, he talks about different levels of of multiverse
Speaker 1: realities and what they each imply. Uh, and he gives
Speaker 1: a very, at least to the lay person, a very
Speaker 1: reasonable sounding explanation of how these are natural conclusions from
Speaker 1: what we know about physics. But I do want to
Speaker 1: use what you said as a sort of jumping off
Speaker 1: point to take a broader view about the algorithmic nature
Speaker 1: of reality. But first we're going to take a quick
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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, as you know,
Speaker 1: as this particular entity is trying to navigate a world
Speaker 1: of fixed and moving objects, generally to acquire some gold,
Speaker 1: to acquire food or or a mate. Uh, you could
Speaker 1: even you could probably even extrapolated as far to say
Speaker 1: to say that that an object obeying gravity is kind
Speaker 1: of engaging in a sort of non mental problem solving
Speaker 1: in a way, in in a limited way. Um, I
Speaker 1: guess what 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, and retain only the teleology exactly that
Speaker 1: there there are there are steps towards a purpose, but
Speaker 1: you don't have to know what the purpose is, and
Speaker 1: you 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 consists 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. That's essential here. Uh. It sends out
Speaker 1: limbs to find food and when it finds us food source,
Speaker 1: it spreads over, it secretes the digestive enzymes and has
Speaker 1: its meal. When it doesn't, yeah, it's pretty it's pretty great.
Speaker 1: Essentially the 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
Speaker 1: chemicals for inter cellular communication. And that the method allows
Speaker 1: them to perform such feats and this is generally and
Speaker 1: this 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 um of the world, of some
Speaker 1: of the great highway systems. They can model cancer growth. Um,
Speaker 1: let me go to a little detail about the silk
Speaker 1: road thing, and this is this gets into exactly what
Speaker 1: we're talking earlier about an algorithm attempting to to plot
Speaker 1: a course, right and having to hit all those stuffs
Speaker 1: the salesman problem that we're discussing earlier. Okay, So back
Speaker 1: into computer scientist Andre Adamantski from the University of the
Speaker 1: West of England. He took a globe. Okay, and you
Speaker 1: can do this at home probably, I guess, if you
Speaker 1: have access to the materials. He took a globe and
Speaker 1: he coated it with auger all right, this, of course
Speaker 1: is the stuff in a petri dish that you know
Speaker 1: bacteria grows up. Yeah. Uh and then he um. And
Speaker 1: then what he did is he removed uh, the augur
Speaker 1: from the areas over the ocean, so it's just covering
Speaker 1: the continents and the land at this point. And then
Speaker 1: he placed oat flakes at the locations of twenty four
Speaker 1: different major cities on the globe, so that's a food source. Okay.
Speaker 1: Then he introduced the slime mold. Alright. He did this
Speaker 1: thirty different times. In each time the slime mold conquered
Speaker 1: the world in a slightly different way, establishing trade routes
Speaker 1: between the various oats cities. Yeah, and it's uh there
Speaker 1: their pictures out there. This is pretty remarkable, uh because
Speaker 1: it it maybe a little bit scary because you see
Speaker 1: these ten drils just spreading out all over the world.
Speaker 1: It managed to plan out engineering projects that, of course
Speaker 1: humans can only dream of right now, like Transatlantic bridges.
Speaker 1: Obviously we're not going to do that. It wasn't, I didn't.
Speaker 1: I don't think it was ever able to really conquer
Speaker 1: the Pacific. Pacific was just too too uh too great
Speaker 1: of a distance without Augur there for it to grow on. Uh.
Speaker 1: But but it also managed to recreate the Silk Road
Speaker 1: as well as the modern Asian Highway network, which consists
Speaker 1: of about the eighty seven thousand miles of roads running
Speaker 1: between thirty two countries. So it exactly it provides a
Speaker 1: great example of uh, not a problem solving intelligence, but
Speaker 1: an algorithmic problem solving organic system. Of course, this I
Speaker 1: do think raises the specter of the question how do
Speaker 1: you tell the difference between an algorithm and intelligence? Unless
Speaker 1: you want to be anthropomorphic and say, well, intelligence is
Speaker 1: consciousness and the ability to love and yeah, and then
Speaker 1: we start gazing down that of this right, Yeah, yeah,
Speaker 1: we get back to some of the problems we've discussed
Speaker 1: in relation to AI in the past. How do you
Speaker 1: know when you created it? If you can't really say
Speaker 1: what it is, it becomes this this problem. We can't
Speaker 1: even define the problem, So how can we come up
Speaker 1: with the solution or check the solution? Yeah, And it's
Speaker 1: funny that we were talking earlier about about sets that
Speaker 1: sort of recursively consume one another. Is one set within
Speaker 1: another set, but then the first set is the second
Speaker 1: set is also in the first set. Now, we just
Speaker 1: gave an example of how nature can be like an algorithm.
Speaker 1: But you can also say that plenty of algorithms and
Speaker 1: computer science have been essentially derived from nature. Yeah. Um,
Speaker 1: And there's a great example of this with ants. So
Speaker 1: ant colonies. We've discussed ance here in the podcast before
Speaker 1: and I'm sure we'll cover them again in the future.
Speaker 1: You know that they're complex societies, and we see plenty
Speaker 1: of examples in which colonies accomplished complex tasks that exceed
Speaker 1: the individual capacities of a single ant. Of course, so
Speaker 1: they worked together and they're able to solve problems, and
Speaker 1: this is mound mind. Yeah, exactly, it's the the the
Speaker 1: the the emergent intelligence of the group, the swarm intelligence. Um.
Speaker 1: This is a particular note to computer programming as though,
Speaker 1: as we see how they're self organizing capacities and distributed
Speaker 1: organization enable them to solve difficult optimization and distributed control problems. Okay,
Speaker 1: So back in a Stanford study looked at how harvester
Speaker 1: ants determine how many foragers to send out. Of course,
Speaker 1: so they're sending out a rating party, right, Uh, which
Speaker 1: is you know, more complex than than than you might think,
Speaker 1: because you get down to the basic you know, how
Speaker 1: many do you send out? You know, what's the way time? Uh?
Speaker 1: And then they compared this to the manner in which
Speaker 1: a 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 in anyway, it's a it's
Speaker 1: 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. This is so
Speaker 1: that's that's Internet, except instead of you have an ant UM.
Speaker 1: So it's a TCP influenced algorithm that accurately matched ant
Speaker 1: behavior in the experiment. So it's an example of ants
Speaker 1: reaching the same place as our computer programming UM. So basically,
Speaker 1: they created a TCP program that accurately predicted how the
Speaker 1: ants were going to act. Yeah, we've definitely talked on
Speaker 1: the other podcasts that I do with Jonathan Strickland and
Speaker 1: Lauren Vogelbaum Forward Thinking. We talk about biomimetic robotics a
Speaker 1: lot about ways that robots can be inspired by the
Speaker 1: 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 Zurix Institute of Pharmaceutical Science has explored the
Speaker 1: possibility of using ant algorithms to search for new composite
Speaker 1: agents in the development of new pharmaceuticals. And this gets
Speaker 1: down to the whole situation discussing earlier about do you
Speaker 1: do you take a brute uh ranked approach to finding
Speaker 1: out which connections amid all these possible connections are the
Speaker 1: ideal ones to then test and explore. Um. So they've
Speaker 1: looked into the possibility of using an ant based algorithm
Speaker 1: to find though to do essentially, you know, magically guess
Speaker 1: those uh those those the 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 allile into the genome. You
Speaker 1: very one gene from the existing model, so you've random that.
Speaker 1: That's step one. And then step two test against the
Speaker 1: baseline performance rate of the standard allile in the environment
Speaker 1: or you know, the individual steps here would be attempt
Speaker 1: to copy. If copying succeeds, go to one or return
Speaker 1: to the first step. If copying fails, return void. It's
Speaker 1: almost like a computer program. Yeah, I think I think
Speaker 1: there's a very strong case to be made there. I mean,
Speaker 1: earlier I made that I said that gravity an object
Speaker 1: of baying gravity and is it is in a way
Speaker 1: kind of obeying a certain algorithm. It's kind of problem solving.
Speaker 1: So this I think this FITSI 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 six book.
Speaker 1: Darwin's dangerous idea was which was a lot about the
Speaker 1: implications of evolution beyond just explaining the diversity of species
Speaker 1: on Earth. Evolution is a sort of principle that extends
Speaker 1: even beyond biology. But this universal driving force that that
Speaker 1: drives design through the design space, and the way he
Speaker 1: would explain it. But uh so, of course, not everybody
Speaker 1: agrees with that interpretation, thinks that an algorithm is a
Speaker 1: good way of thinking about evolution. But I've got another
Speaker 1: follow up question that's kind of interesting to me, if
Speaker 1: evolution is an algorithm, is it an efficient algorithm or
Speaker 1: a brute force algorithm? Oh, now that's a good question.
Speaker 1: I mean it seems to me kind of like it
Speaker 1: would be a brute force algorithm, right, because you're you're
Speaker 1: trying any number, it's you know, just brute force combinatrix.
Speaker 1: You're trying something. Here's a pair of genes, here's an alleal.
Speaker 1: Does that work? Now? Okay, throw in the trash. It
Speaker 1: seems very wasteful. Yeah, here's a lizard with spots, here's
Speaker 1: one without spots. Which one gets eaten? Which one continues?
Speaker 1: That sounds like kind of a brute brute force You're
Speaker 1: just like throwing out all the produce possible prototypes and
Speaker 1: uh and seeing what then you see what happens. And
Speaker 1: I think this would actually be one way of framing
Speaker 1: the difference between the standard scientific materialist view of evolution,
Speaker 1: which I think would probably be is best I can tell.
Speaker 1: I bet that'd be the brute force method. And then
Speaker 1: some types of believers in intelligent design. Right, So if
Speaker 1: you are somebody who believes um, you you accept the
Speaker 1: evidence for evolution and common descent, but you simply believe
Speaker 1: the process was guided in one way or another. You
Speaker 1: think aliens or a god or some other you know,
Speaker 1: powerful supernatural or or other worldly technological force interfered with evolution,
Speaker 1: maybe reached in to cause specific mutations to the terrestrial
Speaker 1: genes space at key points. That sounds like that would
Speaker 1: be optimizing the algorithm, right, like somebody's introducing artificial efficiency.
Speaker 1: But then again, i'd i'd be interested in hearing from
Speaker 1: the evolutionary biologists and geneticists sat there in the audience
Speaker 1: on this one. Like, if you accept the idea that
Speaker 1: natural selection is like an algorithm, is it a brute
Speaker 1: force algorithm unless you go to the intelligent design hypothesis?
Speaker 1: Or are there other ways of thinking of the algorithm
Speaker 1: as in some way optimized by material cir substances. And
Speaker 1: since you did mention god or the gods here would
Speaker 1: the god in this scenario that Okay, so this is
Speaker 1: a force coming from outside our universe, then perhaps in
Speaker 1: this scenario our world is is a P does not
Speaker 1: equal in P universe, but the realm of the gods
Speaker 1: is a P equals in P universe. Uh Well, I
Speaker 1: mean that's an interesting way of putting it, because they
Speaker 1: can they can knock it out right there, Gods, they're
Speaker 1: basically limitless. Well, it's infinite possibility, I mean, the whole
Speaker 1: the realm of mathematics and logic is. In many ways,
Speaker 1: it often signals to me the sort of underlying hint
Speaker 1: of infinite possibilities but also infinite constraints. At the same time.
Speaker 1: Mathematics is both infinite power and ultimate helplessness. You know,
Speaker 1: it's the power to accomplish anything and the inevitability of
Speaker 1: being thwarted and destroyed by processes beyond your control. Uh,
Speaker 1: it just sort of makes everything good and bad possible. Well,
Speaker 1: it sounds like you're talking about the gods again. It
Speaker 1: could be yeah, all right, So there you have it.
Speaker 1: P m P P versus m P P equals mp
Speaker 1: P does not equal mp. Hopefully at this point you
Speaker 1: have if you if you didn't know what any of
Speaker 1: this stuff was about beforehand, you have a much better
Speaker 1: grasp on the idea. You can at least realize why.
Speaker 1: It is a topic that people continue to discuss and
Speaker 1: even argue about. But if you want to get into
Speaker 1: the actual details of of it, there are plenty of
Speaker 1: good resources out there on the internet. If you are
Speaker 1: a math and computer science and logic inclined to person
Speaker 1: who has a good abstract mind for that kind of thing.
Speaker 1: But either way, I do want to remind you to
Speaker 1: always think about the algorithmic nature of the ground beneath
Speaker 1: your feet and the laws that govern the way the
Speaker 1: way everything around you works, the logic of reality. Is
Speaker 1: there a problem solving process inherent to everything that's going
Speaker 1: on around you all the time? I don't know. It's
Speaker 1: it's a strange specter of an idea to keep behind
Speaker 1: your head at all times. Yeah. Again, like when a
Speaker 1: when like a walnut falls out of a tree, there
Speaker 1: are certainly there's an there's an algorithm at play right
Speaker 1: as to how exactly it's going to make it to
Speaker 1: the ground, which branches is going to hit? I guess
Speaker 1: that depends on your perspective. Is there is there a goal,
Speaker 1: there is something happening or did something just happen? I
Speaker 1: don't know, man, it's pretty far out. Well, let's not
Speaker 1: get too much into weird stone or territory. Here at
Speaker 1: the end, I do want to say, right here at
Speaker 1: the end, if you are somebody who's involved in mathematics
Speaker 1: or computer science and uh, and you would like to
Speaker 1: write in to tell us about one of the one
Speaker 1: of the more detailed or complex aspects of this that
Speaker 1: we didn't get to. Like we said, we we gave
Speaker 1: you the very simple version. Please right in and we'd
Speaker 1: love to 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, uh some science fiction that definitely weighs in
Speaker 1: on this. Um. You know, I was trying to think
Speaker 1: of specific examples from N. N. Banks culture books because
Speaker 1: the cour they have these minds, these ais that are
Speaker 1: incredibly powerful, But for the life of me, I can't remember, uh,
Speaker 1: exactly where they they weigh in in terms of the
Speaker 1: or we're indeed, um Banks is universe there weighs in
Speaker 1: on the on the the P and P spectrum. Hey.
Speaker 1: But in the meantime, you want to check out this
Speaker 1: and other pieces of content, head on over to stuff
Speaker 1: to Blow your Mind dot com. That's the mothership. That's
Speaker 1: where we have all the articles. That's where we have
Speaker 1: blog posts, we have links out to social media, we
Speaker 1: have some videos, uh, be sure to go there. Hey,
Speaker 1: and if you listen to us on what iTunes, Spotify,
Speaker 1: Google Play, however, you get your podcasts um it's possible
Speaker 1: to do, so leave us a nice review there, give
Speaker 1: us a little boost in the algorithm that ultimately uh
Speaker 1: determines our eight. You can tweak that at that hour,
Speaker 1: and you can reach out as a as an outside
Speaker 1: force like a god, and shift things in our favor.
Speaker 1: So invite you to do stuff. And as always, if
Speaker 1: you'd like to get in touch with us, and we
Speaker 1: really hope you do, you can email us and blow
Speaker 1: the mind at how stuff works dot com for more
Speaker 1: on this and thousands of other topics. Is it how
Speaker 1: stuff works dot com.