Time for a Change: Introducing irreversible time in economics - Dr Ole Peters

Time for a Change: Introducing irreversible time in economics - Dr Ole Peters

SUBTITLE'S INFO:

Language: English

Type: Robot

Number of phrases: 1229

Number of words: 8389

Number of symbols: 38680

DOWNLOAD SUBTITLES:

DOWNLOAD AUDIO AND VIDEO:

SUBTITLES:

Subtitles generated by robot
00:08
right let's jump straight into it so the title for my talk to it is time for a change except not really there was something missing from the title and that's a comma what I really wanted to talk about is not time for a change but time for a change because I think that we have left out time from our considerations of risk
00:40
especially risk management the way we think about risks investment ups and downs in in general so I think that time and it's irreversibility are really key to developing a better understanding now on this slide here you will notice a grasshopper and the grasshopper I met Gresham College I'm very very aware of the fact that I crash from college and a great honor to be here the
01:10
grasshoppers of course aggressions symbol in this coat of arms and I thought I put the grasshopper on all the slides of something some relevance to the gresham context so when you see a grasshopper in one of the slides tonight and I don't mention what that is about then please please do ask me now continuing with the playful theme because mathematics and everything else
01:41
in life really should be playful I thought I'd start tonight's lecture with my favorite game and the game has the following rules you're given a hundred dollars and you invest them in in this game but you're tossing a coin once the minute and if the coin shows heads you win 50 percent of your wager if it shows tails you lose 40 percent it's just to explain to you how this how this works over time people be repeating this game here's one one sequence we're playing
02:13
for five minutes it's very simple I'm tossing a coin now on the first two tosses here I lost 50% each of the wager at that time so on the first sorry 40% I lost 40% on the first toss I lost 40% I went down to 60th and I lost 40% of the 60 I went down further and so on then I gained I lost I gained so you get these trajectories of wealth developing over time in in this game I want to understand what happens in this game so
02:43
I thought I play I played a little a little longer now I'm playing this for an hour so I I have 60 coin tosses in this sequence here I'm playing it for a little bit longer because I'm thinking that perhaps I'll get some idea of the sort of general dynamics of this thing if I just watch it for a little while so this is the 60 minutes but I don't really see much in this trajectory I just see noise it just seems sort of random what we usually do in that situation is we'll try again and see what sort of spread we have right so I
03:16
played this 10 times for for 60 minutes and I developed these 60 these 10 trajectories and yeah we develop some idea for for how far they're spreading how much I could gain or could lose and so on how likely things may be maybe I want to play 20 sequences I could continue doing this if the screen will just fill up with colorful lines and eventually I'm action are learning very much so the next step in the analysis is to say let's let's average somehow let's
03:48
get rid of this this noise I'm really just interested in the fundamentals here so I'm now averaging at every minute at every moment in time I'm averaging over the 20 trajectories that that have generated and I'll get a line that looks like this you can see that it's less noisy but it's still it's still quite noisy so maybe 20 sequences is not enough I should order a thousand sequences it's still somewhat wobbly up there so how about a million sequences well that looks pretty good if I
04:19
averaged over a million sequences I can clearly see that this is a favor of the game and this is probably what our intuition would tell us right from the beginning we were tossing a coin there was a 50/50 chance of either losing 40 percent or gaining 50 percent now 40 percent is less than 50 percent so on average we should be gaining in this in this game and this is exactly what happens we regain on on average but what does it actually mean we looked at an
04:50
average and in this case the type of average is called an ensemble average and that's because we looked at this ensemble of a million players if you like who are playing this game or million trajectories that we that we generated that the immediate question is is this relevant to me because this is just an average and I'm I don't have access to that average I will just generate one trajectory and that will be me now the reason why that can be problematic is that I can't I can't go back in time if I don't like the result if I end up with a particularly unlucky
05:20
sequence I'll end up destitute but I can't go back and try again because I've already lost everything alternatively I could say I can't access parallel worlds where my luck was better or I can't force other people who played the game to share their phenomenal winnings with me so this may not be relevant for me I'm really interested in one trajectory so I want to see if I can get rid of the noise in this system in a different way and that's really the theme for for this lecture get rid of the noise through time rather than
05:53
considering many many parallel systems I want to consider what happens if I play this for a very very long time so let's do that this is the original sequence that I showed you right at the beginning when I'm playing this game tossing a coin once a minute for 60 minutes and now I'm saying I want to get rid of the randomness by considering longer and longer time sequences so I'll play it instead of for an hour for day here's what happens over day you can see that the fluctuations become smaller if you if you look at this it really just bounces up and down you don't know what
06:25
is happening here the fluctuations are a little smaller and this inset up here is just the original trajectory and these these lines you indicate that I'm blowing up the initial 60 minutes - to get to that inset so this is really just continuing the same game that I played in the beginning still to me this is pretty noisy so maybe I want to play for a week instead of just a day so now I'm playing for a week noise diminishes I'll play for a
06:59
year okay now I've played for a year for 12 months and the perhaps surprising thing is that I've lost the noise has completely disappeared so there's really no reason to believe that there's any uncertainty in this in this result but I'm losing so what on earth is going on I have two perspectives the first is the sort of intuitively right perspective we're averaging we have a favorable game we should be winning on average the
07:30
second perspective is a time perspective where and sort of averaging over a large ensemble I've averaged over time so essentially I've picked maybe I've picked one individual I just followed that for a very very long time and I could pick any single individual if I just follow it for long enough then the noise will average out over time but the effect of time is a different effect than the effect of averaging out over the ensemble now this ensemble perspective here over emphasizes the
08:03
exceptional successes so it contains phenomenally unlikely individuals that just made a killing in this game and I'll illustrate it in a second and they they pull up this average but that average is not reflective of what typically happens so if I took any one of them and I just play for a long time I will see that every single one of them will lose in the long run nonetheless this perspective may be relevant to a collective so if we really are a million people and we really aren't sharing our
08:34
resources this may be this may have some relevance on the other hand the time perspective clearly immediately has relevance to the individual to myself because I will only be one of those trajectories in this situation where averaging in the ensemble yields a different result from averaging over time is called non agar DISA tea so this is an on a gothic game now what does every DISA t/o I have to apologize for the resolution of the
09:06
screen here this would be red boxes Agnew DISA tee very unfortunately is used in different ways in the physics community from how it is used in the economics community in physics we've just seen that there are these two perspectives the ensemble perspective where you remove randomness from the system by letting an ensemble size go to infinity get very large to remove randomness the other perspective is to let time go to infinity become very large to remove randomness in physics when we say a system is ergodic we mean that both
09:40
perspectives are equivalent and therefore this last game was non negative in economics a Gurda City means that the laws of a process don't change at least this is what I've been able to extract from the economics literature so far now the logical relationship between these two uses of the word is that physics like audacity implies economics ethnicity but not the other way around so you can have many systems whose laws don't change over time meaning they are
10:11
a Ghatak in the way that economists use the word but they are not agaric in the sense that physicists use the word meaning that time and ensemble perspectives are different now it's said that this has something to do in this case in this game with with the distribution I said that there are very unlikely enormous enormous lis which individuals in the population that basically make up for all those poor souls who are who are losing overtime no
10:43
one has asked me yet about the the grasshopper now what I want to show you is a histogram so how many people in the population I'm now calling as a population is ensemble how many people in the population have a certain amount of of money so here's here's the wealth and on this axis here I'm drawing how many people there are with with a given wealth I'm starting every one according to the initial condition of the game and starting everyone at $100 and then I'll let time run and in minute of time I'm playing this for 60
11:16
minutes I will draw you this the cystogram okay I'll tell you why I put the graph suppose anyone what that yes ray you look like you might want to yes so that's good yeah no it has to do with the histogram the history of the word histogram was first used at Gresham College by one of your predecessors buying a Pearson yeah right so let's construct these 60 histograms over time there we go there they are constructed
11:54
so after 60 minutes this is what the distribution looks like in this system oh sorry I haven't told you what this green line means the green line tracks the wealthiest individual in the population so what happened after 60 minutes after we played this game for 60 60 times in a row a million people have played this one third roughly one third of the population is essentially bankrupt so they have less than $1 I just said that as an arbitrary limit for bankruptcy one of them has close to a hundred million dollars and that's what gives
12:27
you this average that has nothing to do with the typical experience the average is actually sitting somewhere somewhere around here at $2,000 but that's really just because of these very few exceptional outliers out there so this is what is happening in this game right that's my initial remarks and now we'll come to the actual talk this is the basic concept and I'll start I'll start applying that to a few classic problems
12:57
in economics the first will be the leverage problem so the question is how much should I invest in a favorable investment in a favorable game so let's look at these two perspectives again the time perspective and the ensemble perspective they both have problems the ensemble perspective looks very nice but the problem is that it's inaccessible we would have to be able to access all these parallel universes so if that's not really available to us the time perspective it doesn't look so
13:30
nice it's too risky but maybe maybe we can find a compromise maybe we can trade them off and somehow get the best of both worlds and the idea there is to keep some of your money but what happened here was that I was investing the hundred dollars that someone gave me in the beginning and then I kept investing whatever I had at every moment in time but I don't have to do that I could say well I'm not going to invest $100 I'll invest less so I'm investing less in a favorable game and maybe that's a good idea
14:02
because not investing something and sitting on it in this case is like freezing your money in time so you do have excess it's almost like you could go back in time because you can access that stuff that you haven't spent in the beginning so this is this is the the central ideas to keep some money safe in this game meaning reduce your leverage what we had here in the beginning was a leverage of 100% meaning we bet everything we had so I'll now sequentially reduce this
14:32
leverage and show you what what happens in the time perspective and in the ensemble perspective in the ensemble perspective you can already guess what happens it's a favorable game and now I'm investing less in it so my money will grow more slowly what's interesting watch what happens to the time perspective there as I'm investing less in every round in this favorable game I'm also losing less and I'm not just losing this I can actually go to the
15:01
level where I'm gaining so this idea of freezing money in time love not investing it keeping some of it safe actually works so I can turn this this game that and the time perspective was really horrendous and ruinous for us it can turn that into a favorable work a little thing by keeping some of my money safe and every time step so this is what what I did here if I continue reducing the leverage of course at some point you see the time perspective the time performance going down again because well you're investing less interesting
15:36
nothing of course I'm not gaining anything I can also short this game so can take the position of the house I can offer this game to people this is like short-selling a pretty good asset actually and that would be really stupid because it is a favorable game after all so if I'm shorting it that's that's not a good idea so you can see that selling short not not so good here what happens if we do the thing that is usually associated with the word leverage namely investing more than we own in every round I can do that by borrowing money
16:07
well let's do that we started with 100% let's go 250 well at 150 well you just saw what happened to until the time trajectory that it really collapses let's go to 200 oh my god but compare that to the ensemble perspective now the travel is that much of the mathematics that is used in the analyses investment analyses risk management analyses focuses on expectation values expectation values is another word for most horrible averages so we're really
16:38
often focused on this perspective and it's also that is the intuitive perspective for some reason that's how our intuition works I'll give you a favorable game you think on average it's fine that's true it just depends on what you mean by average so the ensemble average perspective just becomes better that and now the time has completely disappeared because at this leverage again t-to go bankrupt so you're just wiped out immediately I can keep going it just looks phenomenal and the in the ensemble perspective is the message here well what would be the message is from from these two perspectives if you're
17:11
really thinking about Possible's then the the recommendation of this game would be just leverage as much as you can the trouble is that you will immediately go bankrupt as we've seen in the time perspective the time perspective says there's an optimal leverage it says this is something that doesn't exist in the Azam ensemble perspective so it's not a disagreement a quantitative disagreement it's a qualitative disagreement the time perspective says an optimal leverage exists if we exceeded it's bad for you so in the in the case of our game the
17:43
optimal leverage was 1/4 invest no more than a quarter two gamblers these results unknown as the Kelly criterion and in gambling this is usually derived or losses I've only seen it derived from information theory we have used a different argument here so it's not so much that we've invented a new mathematics but we've invented a different interpretation maybe a ritual interpretation or a deeper interpretation than what is known in in
18:16
gambling we've used really the argument of time irreversibility that you can't go back in time the same techniques that we've developed you can apply to other to other processes for example geometric Brownian motion which is the most important mathematical model in in finance and I've written that up in a paper and I think it's dishonest to give a lecture and not show all the technical details of what I'm doing so I thought
18:50
I'd just give you all the technical details and you can read them for yourselves there they are it should be enough this is another way of illustrating this perspective so here you have you have many many worlds right so the ideas you start in one state of the world up there and time progresses down on this slide so this world has potential this world splits into potential futures as you go down the number of possible worlds increases
19:21
exponentially what reality does or time what time does is it picks out one trajectory through all these possibilities so that's reality one of those trajectories when we're thinking about the time perspective we are averaging along one of those trajectories when we're thinking about the ensemble perspective we are averaging across all the parallel worlds all the possibilities that could have that could have materialized so I come
19:52
to the second part of my talk there's an Petersburg paradox and again I won't go into too much technical detail but I'll give you a bit of the history of this problem which is really quite fascinating I believe the st. Petersburg paradox in essence I'm just giving you the essence of the problem it was noticed in the early 18th century that if you offer a ticket for a lottery that is associated with an infinite expectation value of
20:24
the payout depending on how you structure that lottery you can end up with a case where players are not willing to pay much for it so they have an infinite expected gain from this lottery but they're not willing to pay much for it and people who are baffled by that in the early 18th century of the reason for that of course instead I got a theory had not been developed and these ideas of Agra disa T are 115 years younger than that and the resolution
20:56
that I proposed that Michael was referring to earlier on is that the expectation value is really irrelevant to the player so he has no reason to behave according to it instead what really matters is the time average growth rate the way the player will fare over time in this case under multiplicative dynamics which is roughly which is not a bad approximation for for many wealth processes oh Michael is
21:28
pointing to a a grasshopper well what is that doing there now right so the solution is expectation really not really relevant to the player time average is on the other hand when you compute them and you compare them to human behavior they actually match so this perspective describes what people do very very well this paper that I wrote about that was published in the philosophical transactions by the Royal Society and I put the grasshopper on top
22:02
of the Royal Society and now someone can guess well so I just wanted to point out that Gresham College was really the the meeting point or the the origin of the Royal Society this is this is where that all started to another very nice connection will see more Royal Society later so I told you that I will talk a little bit about the history of this problem
22:32
and here it is but I would go a lot further back then then Michael had prepared you for so we'll jump right into the Middle Ages although I know very little about this I heard that John Duns Scotus a medieval philosopher was one of the first people to formally talk about the idea of parallel worlds of somehow consistent states of affairs
23:03
that could in principle occur so he had I'm sure that people had that know so much earlier on that there are these other possibilities out there we tend to think like that but but he made that somewhat somewhat formal in his philosophy then in the the 60 in the 1500s in the sixteenth century k'tano appears and I could probably give three lectures just about Gaddafi is really a fascinating man but in in the context of this lecture I'm mentioning
23:35
him because he wrote a book about games of dice roughly in the 1550s no one really knows when it was written because it could be published in his lifetime because of course it was sinful to gamble and this book was all about gambling it's actually a wonderful book and it's full of full of good advice because life's a gamble I guess in that book apart from lots of good advice and
24:06
deep insights he he begins to count favorable instances in in games of chance so he he gets very close to developing the idea of an ensemble average and of probabilities and so on so this is this is perhaps where the for most development starts the next two people I have on here Driggs that grasshopper should be pretty obvious to you Briggs of course was the first professor
24:40
of geometry at Gresham College and Napier invented the logarithm and Briggs then co-developed with Napier the logarithm and the date 1615 up here is the date of their meeting in in Edinburgh where Briggs suggested some changes to logarithms and tricks that computed a lot of them published big tables for shipping and so on navigation and now the reason I put this up here is that in this whole story when you get to
25:11
the actual technical details the logarithm is the key to almost everything this is absolutely wonderful function and I I recommend that you spend some time thinking about it but the real formal story starts in 1654 with an exchange of letters between Pascal and farmer and in that exchange of letters Pascal of imago essentially discussing the question how a bet the
25:43
pot in a bet should be split if the bet never never comes in so you're playing a game and you have to abandon the game before it's finished and everyone has bet something on the outcome of the game well but then you have to run away so you're maybe you're playing some game of dice and suddenly the police bursts in and you all have to jump out the windows because the gambling is illegal and you all run away and then later on you you assemble somewhere someone took the pot
26:14
of money with him and now you sit down and you say well but I had four points in this game starting at three and how do we split this pot and in a fair manner and first caliph Omar came up or mostly family came up with it with the idea of giving to everyone who was involved in this gamble the expectation value of his winnings at the moment the game was interrupted so this is where expectation values come from note that the idea of the expert
26:44
value is a moral idea the question was how do we split this plot in a fair way there's not really something about correct or right or wrong rose it was about fairness and the early debaters has a lot to do with moral concepts because color of course was famous for for using probability theory to justify his his religious beliefs now in this exposition I'm jumping straight to Nicolas Bernoulli I could talk about Huygens and Hallie and I have enough
27:15
time so I will mention something about those two Huygens has a interesting paper only three years after the exchange of letters between between Pascal and firma hogan's writes in one of his papers that it is really the same thing if if someone gives you either three or seven shillings with equal chance it is the same thing as if he should give you five feelings and this really summarizes the belief about randomness in the in the seventeenth
27:47
century the idea was that you can completely disregard fluctuations of course this idea that you're only focusing on the on the expectation value means you don't care about miss you don't care about fluctuations and it gets you somewhere but not very far in the in the 1690s Halle wrote a paper this is maybe the first paper about pricing financial products in these papers about pricing life annuity so
28:18
it's a particular kind of financial product the idea behind life annuities is that some king wants to go to war or build a castle to do fancy things that Kings do and he doesn't even have money but he has lots of subjects so he promises those subjects a pension for the rest of their lives and says well if you give me amount X now I will pay you amount y every month until until you die for the rest of your life the good thing
28:51
there for the King is that he gets a lot of money right now and sometimes that's that's needed like you want to go to war or you want to build a new palace and the trouble for the king is that he may charge the wrong price and then end up paying dearly for for this quick money that he needed so some of you have to balance these two and Hallie suggested that the price the king should charge as the expected payout and that he has to give the
29:22
people who buy this this insurance and that makes a lot of sense so think about what that means so expected payoff that means we are talking about ensemble averages that means we're talking about the ensemble perspective but what's the system here well the system really is an ensemble the king is interacting with many many individuals that are essentially independent systems so there this perspective works but that doesn't mean it works for everything it really is an ensemble internet works now in nineteen eighteen nineteen in 1713 Nicolas Bernoulli invented the listen
29:53
Petersburg paradox this idea of the very favorable lottery that no one wants to pay anything for and what he really wanted to do there Nicolas Bernoulli was smash this religious belief in expectation values he wanted to say no no no there's more to randomness than expectation values this must be clear to you Nicolas padule-- is also one of the first people to think about extreme values and in extremes you know that the expectation value is not very interesting if you're building a dike
30:25
you're not interested in the expected height of the next flood you're interested in the height of an extreme flood and the expectation value is really is really irrelevant there so he was arguing this point for ever and ever Nicolas was very very creative in his writing he was very playful with different ideas different games and randomness that he invented and this particular game the sim Petersburg paradox comes from an exchange of correspondence with with more more in 1713 so Nicolas Bernoulli invents this
30:56
game Daniel Bernoulli then proposes a solution and in that solution this is only for those of you who know what I'm talking about in that solution he proposes utility essentially proposes that people are not interested in the money they receive but they are interested in what that money means to them the usefulness of that money and now you can pick any function you like that translates an amount of money into a usefulness and you can pick that function in such a way that your
31:28
infinity in the expectation value disappears but that's a very arbitrary thing to do so it's a very dangerous thing to do because this function this utility function was not further specified yes you can get rid of the the the infinity but you introduce a lot of arbitrariness that's the problem in in the newly's solution in 1812 Laplace wrote a book he talks about probability theory and he mentions Daniel Bernoulli's solution to st. Petersburg
31:58
paradox and in doing so he corrects a little error that Daniel Bernoulli made now Laplace was a gentleman of course and he he did not mention that he was correcting the newly he just said oh this is how Bernoulli solved the problem but he didn't say that there was anything wrong with it he just said that he solved it in this way which wasn't quite true he just implicitly corrected something and then after Laplace everyone who talked about this in Petersburg paradox just quoted Laplace
32:29
you can see it in the notation so there's a famous textbook from 1865 by Todd hunter who talks about again the history of probability theory and he uses the same notation as as Laplace does when he talks about Bernoulli's problem and Bernoulli's solution so Laplace really solved the problem corrected everything and and so on still following the same idea of this utility of Bernoulli now something very major happened to the way we think about
32:59
randomness in the 1870s 1860s with the development of statistical mechanics so this is where everything changes this is where the idea of a greedy City begins everything that was before was only about expectation values was only about counting favorable instances in a set of possibilities essentially but in the 1860s 1870s Maxwell and Boltzmann were working on statistical mechanics so now they had a physical system and in this physical system you
33:33
could you can do experiments very controlled precise experiments so this is no longer this vague field of human behavior and how we feel what our characters are and so on we're now talking about molecules this is where this is where Maxwell and Boltzmann were coming from so they didn't have the excuse to introduce functions to get rid of strange behaviors of expectation values and that meant that they had to really dig deeper and find out what what the issues were and so maximum Boltzmann
34:06
said well it's it's we always use these expectation values but really the reason we're doing that is that in many systems or in some systems and the ones that we are dealing with right now the expectation values are identical to the time averages so there's there's the big insight and they said well of course that doesn't have to be that way sometimes they are very different so let's just call the systems method that works at gothic and that's where where the electricity notion comes from and web starts so from the 1870s we really
34:37
have different concepts in dealing with randomness than than before 100 years later so I will lie to you now in the 1950s Kandee published a paper where he used these ideas when he used the idea that what was really important to you is how you fare over time not in an ensemble of parallel worlds and hypothetical possibilities so he wrote this paper in
35:06
1954 it was immediately accepted and celebrated by the economics community and he received his Nobel Prize for economics only a few years later as did Ed Thorpe who then used Kelly's methods extended them a little and solved the problem of blackjack famously went to use could see him here in Las Vegas went to Las Vegas and actually demonstrated in a real-life experiment that you can
35:39
use these ideas to beat blackjack then in 1991 thomas cover wrote optimal portfolios and of course also received his Nobel Prize soon after for economics except that was all a lie these people never refused received Nobel prizes they were shunned by by the economics establishment instead something else happened in 1934 karl menger wrote a paper that proves that everything I've
36:11
just said in this whole lecture is wrong this was mathematically proven in 1934 and what happened after that was that in 1950 one can arrow looked at megohms paper and noticed that Vegas paper was quite hard to read so he tried to fish out the essential argument and the essential results and he wrote that down in a very clear in a very clear way in 1968 then Samuelson
36:43
I think introduced this new notion of ergodicity in economics and he said that well for something to be for us to be able to treat something scientifically that something has to be a gothic and you can see if he's using the notion of ergodicity that's prevalent in economics and that makes sense because he says the laws that govern the system mustn't change over time if they change over time what can we do with it we can't predict anything then what so that's right but that's not actually what people meant by agar DISA tea and
37:15
he didn't quite notice that so he said something is ergodic you can do science with it if it's not a ghatak all you can do is history you can just tell what happened in the past but it has no bearing on the future so that's that 1976 Markowitz mentioned that he accepts mengas argument from 1934 in 1977 Samuelson wrote another paper about Menger and he said that manga is a modern classic that stands above all
37:44
criticism in 2009 can arrow said that a deeper understanding referring to the newly a deeper understanding of this Sam Petersburg paradox was only achieved with manga in 2011 Peters that's me so that manga was wrong there's actually an error in in manga and the error goes as follows Megha needed to show and this is now where all the equations come in right I think this is the only slide
38:18
with equations so Megha needed to show that a quantity a plus B is infinite so he came up with the following argument he said well I can show that a is infinite positively infinite so I don't really have to worry about what B is because infinity plus anything is still infinity it's not bad but the problem is that B actually diverges negatively so it becomes minus infinity and it becomes minus infinity faster than a becomes plus infinity and the consequence of
38:49
that is that a plus B is not plus infinity but minus infinity so you can see that this is a somewhat subtle error and if that's in a paper that's not the clearest paper you've ever read then it's easy to read over it and not not see it still it's surprising that this stayed in the literature for 77 years without anyone pointing it out now what do you do when you see something like this you see a classic that stands above all criticism it's wrong now I should
39:21
mention that okay I lied about these people in their Nobel Prizes but these people all have Nobel Prizes so arrows Samuelson Markowitz are all economics Nobel laureates and I'm saying that the endorsements are endorsements of something that is false so I contacted can arrow and it took some time and help of good friends at the Santa Fe Institute Murray gell-mann was very helpful Jeff West was very helpful
39:52
and eventually the summer in August Ken was kind enough to meet up with me and sit down in a room we locked ourselves up for for three hours actually with Murray gell-mann and we went through every little detail in this problem in this manga problem and after our meeting Ken agreed that manga was indeed wrong so for me that's a big step forward and I'm moving Ken now Albert on this penultimate slide I will explain to
40:25
you why some people here on the right and some are on the left up there I have put ensemble perspective and up here I have put time perspective so the people who are closer to the ensemble perspective with me thinking I've put on the right and those who are closer to the time perspective when they're thinking I put on the left and following arrows statement that Megan was wrong I have moved him to the middle which is a good place to be so that's the end of the two specific problems I wanted to
40:55
talk about and I'll come to a few conclusions that I can draw out to any length but let's see a quick summary so what happened here we've really in this work we've reframed we reframed risk management how you think about risk instead of thinking about risk preferences and such things I want to think about the effects of time so the key concept really for me is time what you need to do to be able to do that and
41:26
this is this is really crucial I've seen this in comments on blogs that people have written so on that this is something that's difficult to get is you have to extend the probability spaces that you're used to thinking about to dynamical systems so the ideas it's not enough to think about just probabilities probabilities don't get you far enough in addition to the probabilities you need a dynamic you need to know how things move over time and that's actually not in classic measure theoretic probability theory so there's
41:58
a little addition but we know how to do that that's called dynamical Systems Theory we don't need any utility functions that's very nice and then I've just mentioned we found this 77 year old error in a paper that had been endorsed by several Nobel laureates we found a slight error and Bernoulli's work now the fact that we're finding these old arrows is just the reason for that is that we have a clearer conceptual framework and that makes it possible to spot these arrows it's not no one no one on any of these
42:30
slides is stupid they're all phenomenally intelligent people they're probably much smarter than I am but they had a different angle and therefore they couldn't they couldn't find these these arrows yes and the Kelly criterion is is out there it has a slightly different perspective the mathematics looked completely identical as long as you have multiplicative dynamics that's what the Kelly criterion is developed for our arguments of time averages extend beyond multiplicative
42:59
dynamics so what next what can we do with this that's all very nice we solved some classic problems that other people have solved before using different methods and we suggest a new one to us this is a proof of principle so we're saying this perspective that we've developed is very powerful because we can solve these old problems with new concepts and new concepts open up new possible questions other questions that you can address one well Michael actually protogynous in his introduction
43:31
this really makes you think about time versus parallel worlds in your in your daily life I think that there's something in our culture where we we undervalue time and we behave as if we had access to it two parallel worlds an example that I always think about is is mass production we have all these products that look exactly identical and if one breaks we can we could just replace it it's as if we could go back in time but as if we could switch it and I wonder if that does something to our
44:00
to our psychology to the way we approach life and and time well I don't think I have to tell anyone here that it's easy to underwear you time that that's really the only thing that is ever lost that has ever really truly destroyed us is time so I think there's there's a lot of deep thought in these concepts on a more practical level we can we can start thinking about market stability in in it in a completely different way and I have started doing that with my with my
44:32
colleague at the London mathematical laboratory Alex animal in a paper that we've what we've been unable to publish so far because we call a new concept stochastic market efficiency where we're saying that markets are efficient in a way different from how we usually think about them they are efficient in the sense that you can't beat the market by leveraging an investment in it and this is a really curious concept it makes a lot of sense because you can imagine if
45:03
if you could just do that everyone would do it but what if everyone did that well it's inconsistent it's unstable so there must be something more than just price adjustments there must be something like adjustments of fluctuations of correlations they're constrained by this new concept of market efficiency that you cannot beat the market by leveraging it another big area that opens up from this new perspective is inequality and
45:34
welfare economics and I just want to take you back to this to this very central slide to this talk where we have the two perspectives you know Samba perspective and the time perspective and the population average increases but the typical individual is is losing that says something you already know that it says something about the distribution here and well inequality in economic terms has something to do with the distribution so
46:07
we can learn something about the evolution of of these distributions and well really what does what this illustrates is a fundamental conflict between between a collective and an individual so you can have this sort of disenfranchisement where people feel they're not participating it's very nice that we see GDP for instance increase but we may not be participating and so it's it's even worse than that the typical individual main
46:41
be participating in economic growth that is that is evident in GDP because GDP is one of these ensemble averages so they're they're deep messages that goal that go far that they have big practical consequences finally now conclusions something I've learned in this project is that we really need to rethink the way we communicate in in economics and I mean this I mean the field the
47:13
scientific the academic field of economics no economics journal has published anything of what I've just mentioned here some rejection letters from economics journals know economics conference has let us speak we applied to conferences we said we'd like to come and tell you about something we found we have not been invited of course this has been published but it's been published
47:43
by other by other entities the Royal Society has published it the Santa Fe Institute has published it there's a TEDx talk on the Internet quantitative finance has published it there are various blogs that you can find and there's a lot of interest now from from financial firms another message that I'm taking home from from from this from this whole project is that I think we've given up too easily when it comes to economics scientifically we've given up too easily
48:15
and here's an argument that I've often heard made by people who deal with economic systems they say well economic economic systems cannot be predicted because of reflexivity it goes like this you make a prediction about a system then the system responds to your prediction and that invalidates your prediction so your prediction is useless but if you can't make predictions about something you also can't use scientific method because scientific method relies on predictions predictions are what you
48:46
use to test your hypotheses and if that doesn't work then just the whole framework disappears and this is actually a claim made by many who deal with economic systems they say this is a different animal you cannot you cannot treat that with scientific method I don't believe that I truly disagree and I think I've seen it in my work that it's it's right to disagree with this I believe that this is wrong first of all because not all predictions elicit a response what do I mean by that I mean
49:17
that I can make predictions about a system that are completely useless and I'm really into making useless predictions because I think that making useful predictions of focusing on them is is an anthropocentric so nature is much richer than that nature has much more structure then what is useful to humans and if we only focus on what is useful to humans and we miss a lot of that structure so research science also economic science should be driven by
49:48
curiosity not by fixing practical problems because furiosa tea gets you to those structures in nature that you can understand it's irrelevant whether that is useful or not in the end this may become useful but don't worry about it just let yourself be guided by by your curiosity and I think that we need to do that so let's make predictions that don't elicit responses meaning make Lieut useless predictions of course other predictions that are useful may still be valid actually if if they if
50:21
they recursively take the effects into account and the last line on the slide is this hints at a utilitarian understanding of Science in economics I mean I mean that in economics we seem to focus on the useful things and I say let's not do anything useful we're scientists we're not businessmen finally mathematics I really learned a lot about mathematics in this I was trained as a
50:52
physicist so for me the world started around 1900 there wasn't really anything before then and now I've looked at mathematics a little bit and it's just wonderful this goes back there were centuries before the 20th century and it actually goes back millennia and and you really begin to feel this that you're part of a part of a society of a community of people who've thought hard about difficult problems for thousands of years that's a wonderful wonderful
51:23
thing so mathematics is much richer than a tool that we use to I don't know what you use it for mathematics is much more subtle than then appreciated in in economics and I think we've seen that in these two notions of a Gerda City for example the the notion that the mathematicians have come up with the physicist mathematical physicists have come up with is is more refined it's more precise mathematics is also more vague strangely and that's because it's
51:54
really concept dependent so when you go through these through these old papers you're reading you're reading Bernoulli and you're asking yourself did he did he make a mistake here well you suddenly realize that depends it depends on what he was trying to say maybe he's talking about something completely different he had a different idea and this thing that seems wrong to me is not wrong it's wrong from my perspective or not from his perspective and mathematics is full of that things can be once you've established the concepts things can be
52:26
right or wrong correct or not in equation the two sides of the equation are the same or not but to get to the concepts to what's relevant that's really where where mathematics is a lot of fun mathematics is also more advanced I think that economics mostly uses mathematical techniques from from the 19th century at best of the early 19th century and finally mathematics is also more correct as we've seen in the case with manga and with that I thank you
52:58
very much for your attention

DOWNLOAD SUBTITLES: