Stuff I have been up to

I have been busy everywhere except on this blog. Here are a few highlights, mostly my public outreach:

Long term survival

On BBC Future I have an essay concluding their amazing season on long term thinking where I go really long-term: The greatest long term threats facing humanity.

The approach I take there is to look at the question “if we have survived X years into the future, what problems must we have overcome before that?” It is not so much the threats (or frankly, problems – threat seems to imply a bit more active maliciousness than the universe normally brings about) that are interesting as just how radically we need to change or grow in power to meet them.

The central paradox of survival is that it requires change, and long-term that means that what survives may be very alien. Not so much a problem for me, but I think many disagree. A solid state civilization powered by black holes in a starless universe close to absolute zero, planning billions of years ahead may sound like a great continuation of us, or something too alien to matter.

Debunking doom

Climate doom is in the air, and I am frankly disturbed by how many think that we are facing an existential threat to our survival in the next decade or so – both because it is based on a misunderstanding of the science (which is not entirely easy to read), and how it breeds fatalism. As a response to a youngster question I wrote this piece on the Conversation: Will climate change cause humans to go extinct?

Robots in space

In Quartz, I have an essay about the next 50 years of space exploration and whether we should send robots instead: We should stop sending humans into space to do a robot’s job.

As often the title (not chosen by me, I prefer “A small step for machinekind”) makes it seem I am arguing for something different than I am actually arguing. As I see it, sending machines to space makes much more sense than sending humans… but given the very human desire to be the ones exploring, we will send humans in any case. Long-term we should also become multiplanetary if only to reduce extinction risks, but that might require sending robots ahead – except that in order to do that we need a lot of cheap, low-threshold experimentation and testing.

Good versus evil, Moloch versus Maria

Last year I participated in the Nexus Instituut “intellectual opera” in Amsterdam, enjoying myself immensely. I ended up writing an essay AI, Good and Evil… and Moloch (Official version Sandberg, A. (2019) Kunstmatige intelligentie en Moloch. Tijdschrift Nexus 81: De strijd tussen goed en kwaad. Nexus Instituut, Amsterdam (Tr. Laura Weeda)).

My main point is that evil is usually seen as active maliciousness or neglecting others, suffering itself, or meaningless/removal of meaning. Bad AI is unlikely to be actively malicious and making machines that can experience suffering is likely tricky, but automation that perform bad actions without caring is all too simple. The big risk is getting systems that are effective at implementing pointless goals too efficiently, destroying value (human or other) for no gain, not even to themselves. A further problem is also that these systems are systems, not individuals. We tend to think of AI as robots, “the AI” and other individual entities, when it just as well can be an ambient functionality of the wider techno-social world – impossible to pull the plug, with everybody complicit. We need better ways of debugging adaptive technological systems.

Life extension

On Humanity 2.0 I discussed/debated digital afterlives with Steve Fuller, Sr. Mary Christa Nutt, James Madden and Matthew Harvey Sanders. Got a bit intense at some points, but there is an interesting issue in untangling exactly what we want from an extended life. Not all forms of continuity count for all people: a continuity of consciousness is very different from a continuity of memory, a continuity of social interactions or functions, or leaving the right life projects in order.

Other stuff

Hacking the Brain: Dimensions of Cognitive Enhancement. A paper on cognitive enhancement, the final fruit of the “comparing apples to oranges” Volkswagen foundation project I participated in.

The GoCAS existential risk project final outputs arrived in the journal Foresight. I have two pieces, There is plenty of time at the bottom: The economics, risk and ethics of time compression and the group-written Long-term trajectories of human civilization.

I have also helped a bit with an Oxford project on sensitive intervention points for a post-carbon society. Not all tipping points are bad, and sometimes cartoon heroes may help.

Grand futures

Behind the scenes, my book is expanding… whether that is progress remains to be seen.

I have given various talks about some contents, but there is so much more. I think I have to do a proper lecture series this fall.

A bit of existential hope for Christmas (and beyond)

Existential hope is in the air. The term was coined by my collegues Toby and Owen to denote the opposite of an existential catastrophe: the chance that things could turn out much better than expected.

Recently I had the chance to attend a visioning weekend with the Foresight Institute where we discussed ways of turning dystopias into utopias. It had a clear existential hope message, largely because  it was organised by Allison Duettman who is writing a book on the topic. I must admit that I got a bit nervous when I found out since I am also writing my own grand futures book, but I am glad to say we are dealing with largely separate domains and reasons for hope.

Now I extra am glad to add a podcast to the list of hopeful messages: the Future of Life Institute had me on the podcast Existential Hope in 2019 and beyond. It includes not just me and Allison, but also Max Tegmark, Anthony Aguirre, Gaia Dempsey, and Josh Clark (who also interviewed me for his podcast series End of the World).

I also participated in the Nexus Instituut event “The Battle between Good and Evil”. I assume the good guys won. I certainly had fun. I ended up arguing that good is only weak compared to evil like how water is weak compared to solid object – in small amounts it will deform and splash. In larger amounts it is like the tide or a tsunami: you better get out of the way. In retrospect that analogy might have been particularly powerful in the Netherlands. They know their water and how many hands (and windmills) can reshape a country.

Do we really have grounds for existential hope?

A useful analysis of the concept of hope can be found in Jayne M. Waterworth’s A Philosophical Analysis of Hope. He defines that hoping for something requires (1) a conception of an uncertain possibility, (2) a desire for an objective, (3) a desire that one’s desire be satisfied, and (4) that one takes an anticipatory stance towards the objective.

One can hope for things that have a certain or uncertain probability, but also for things that are merely possible. Waterworth calls the first category “hope because of reality” or probability hope, while the second category is “hope in spite of reality” or possibility hope. I might have probability hope in fixing climate change, but possibility hope in humanity one day resurrecting the dead – in the first case we have some ideas of how it might happen and what might be involved, in the second case we have no idea even where to begin.

Outcomes can also be of different importance: hoping for a nice Christmas present is what Waterworth calls an ordinary hope, while hoping for a solution of climate change or death is an extraordinary hope.

We may speak of existential hope in the sense that “existential eucatastrophes” can occur, or that our actions can make them happen. This would represent the most extraordinary kind of hope possible.

But note that this kind of hope is potentially “hope because of reality” rather than “hope in spite of reality”. We can affect the future to some extent (there is an interesting issue of how much). There doesn’t seem to be any law of nature dooming us to early existential risk or a necessary collapse of civilization. We have in the past changed the rules for our species in very positive ways, and may do so again. We may discover facts about the world that greatly expand the size and value of our future – we have already done so in the past. These are good reasons to hope.

Hope is a mental state. The reason hope is a virtue in Christian theology is that it is the antidote to despair.

Hope is different from optimism, the view that good things are likely to happen. First, optimism is a general disposition rather than directed at particular hoped for occurrences. Second, hope can be a very small and unspecific thing: rather than being optimistic about everything going the right way, a hopeful person can see the overwhelming problems and risks and yet hope that something will happen to get us through. Even a small grain of hope might be enough to fend of despair.

Still, there may be a psychological disposition towards being hopeful. As defined by Snyder in regarding motivations towards goals this involves a sense of agency (chosen goals can be achieved) and pathways (successful plans and strategies for those goals can be generated). This trait predicts academic achievement in students beyond intelligence, personality, and past achievement. Indeed, in law students hope but not optimism was predictive for achievement (but both contributed to life satisfaction). This trait may be more about being motivated to seek out good future states than actually being hopeful about many things, but the more possibilities are seen, the more likely something worth hoping for will show up.

If there is something I wish for everybody in 2019 and beyond it is having this kind of disposition relative to existential hope. Yes, there are monumental problems ahead. But we can figure out ways around/through/over them. There are opportunities to be grabbed. There are new values to be forged.

The winter solstice has just passed and the days will become brighter and longer for the next months. Cheers!

Blueberry Earth

[Update: I have a paper version of this essay on arXiv:1807.10553, extending and correcting some of the results.]

Supposing that the entire Earth was instantaneously replaced with an equal volume of closely packed, but uncompressed blueberries, what would happen from the perspective of a person on the surface?

Unfortunately the site tends to frown on fun questions like this, so it was in my opinion prematurely closed while I was working out the answer. So here it is, with some extra extensions:

The density of blueberries has been estimated to 625.56 kg/m3, WillO on Stackexchange estimated it to 13% of Earth’s density (5510*0.13=716.3 kg/m3), so assuming it to be around $\rho_{berries}=700$ kg/m3 appears to be reasonable. Blueberry pulp has a density similar to water,  980 to 1050 kg per m3 although this is both temperature dependent and depends on how much solids there are. The difference to the whole berries is due to the air between the berries. Note that these are likely the big, thick-skinned “American” blueberries rather than the small wild thin-skinned blueberries (bilberries) I grew up with; the latter would have higher density due to their smaller size and break far more easily.

So instantaneously turning Earth into blueberries will reduce its mass to 0.1274 of what it was. Gravity will become correspondingly weaker, $g_{BE}=0.1274 g$.

However, blueberries are not particularly sturdy. While there is a literature on blueberry mechanics (of course!), I did not manage to find a great source on their compressive strength. A rough estimate is possible: stacking a sugar cube (1 g) on a berry will not break it, while a milk carton (1 kg) will; 100 g has a decent but not certain chance. So if we assume the blueberry area to be one square centimetre the breaking pressure is on the order of $P_{break}=0.1 g / 10^{-4} \approx 10,000$ N/m2. This allows us to estimate at what depth the berries will start to break: $z=P_{break}/g_{BE}\rho_{berries} = 11.4188$ m. So while the surface will be free blueberries they will start pulping within a few meters of the surface.

This pulping has an important effect: the pulp separates from the air, coalescing into a smaller sphere. If we assume pulp to be an incompressible fluid, then a sphere of pulp with the same mass as the initial berries will be $\rho_{pulp} r_{pulp}^3 = \rho_{berries}r_{earth}^3$, or $r_{pulp} = (\rho_{berries}/ \rho_{pulp} )^{1/3}r_{earth}$. In this case we end up with a planet with 0.8879 times smaller radius (5,657 km), surrounded by a vast atmosphere.

The freefall timescale for the planet is initially 41 minutes, but relatively shortly the pulping interactions, the air convection etc will slow things down in a complicated way. I expect that the the actual coalescence will take hours, with some late bubbles from the deep interior erupting fairly late.

The gravity on the pulp surface is just 1.5833 m/s2, 16% of normal gravity – almost exactly lunar gravity. This weakens convection currents and the speed with which bubbles move up. The scale height of the atmosphere, assuming the same composition and temperature as on Earth, will be 6.2 times higher. This means that pressure will decline much less with altitude, allowing far thicker clouds and weather systems. As we will see, the atmosphere will puff up more.

The separation has big consequences. Enormous amounts of air will be pushing out from the pulp as bubbles and jets, producing spectacular geysers (especially since the gravity is low). Even more dramatic is the heating: a lot of gravitational energy is released as the mass is compacted. The total gravitational energy of a constant density sphere of radius R is

$\int_0^R G [4\pi r^2 \rho] [4 \pi r^3 \rho/3] / r dr$ $= (16\pi^2 G\rho^2/3) \int_0^R r^4 dr$
$=(16\pi^2 G/15)\rho^2 R^5$

(the first factor in the integral is the mass of a spherical shell of radius r, the second the mass of the stuff inside, and the third the 1/r gravitational potential). If we ignore the mass of the air since it is small and we just want an order of magnitude estimate,  the compression of the berry mass gives energy

$E=(16\pi^2 G/15)(\rho_{berries}^2 r_{earth}^5 - \rho_{pulp}^2R_{pulp}^5)$ $\approx 4.3594\times 10^{29}$ J.

This is the energy output of the sun over half an hour, nothing to sneeze at: blueberry earth will become hot. There is about 573,000 J per kg, enough to heat the blueberries from freezing to boiling.

The result is that blueberry earth will turn into a roaring ocean of boiling jam, with the geysers of released air and steam likely ejecting at least a few berries into orbit (escape velocity is just 4.234 km/s, and berries at the initial surface will be even higher up in the potential). As the planet evolves a thick atmosphere of released steam will add to the already considerable air from the berries. It is not inconceivable that the planet may heat up further due to a water vapour greenhouse effect, turning into a very odd Venusian world.

Meanwhile the jam ocean is very deep, and the pressure at depth will be enough to cause the formation of high pressure ice even if it is warm. If the formation process is slow there will be some separation of water into ice and a concentration of other chemicals in the jam ocean, but I suspect the rapid collapse will instead make some kind of composite pulp ice. Ice VII forms above 9 GPa, so if we just use constant gravity this happens at a depth $z_{ice}=P_{VII}/g_{BE}\rho_{pulp}\approx 1,909$ km, about two-thirds of the radius. This would make up most of the interior. However, gravity is a bit weaker in the interior, so we need to take that into account. The pressure from all the matter above radius r is $P(r) =(3GM^2/8\pi R^4)(1-(r/R)^2)$, and the ice core will have radius $r_{ice}=\sqrt{1-P_{VII}/P(0)}$  $\approx$ 3,258 km. This is smaller, about 57% of the radius, and just 20% of the total volume.

The coalescence will also speed up rotation. The original blueberry earth would of course make one rotation every 24 hours, but the smaller result would have a smaller moment of inertia. The angular momentum conservation gives $(2/5)MR_1^2(2\pi/T_1) = (2/5)MR_2^2(2\pi/T_2)$, or $T_2 = (R_2/R_1)^2 T_1$, in this case 18.9210 hours. This in turn will increase the oblateness a bit, to approximately 0.038 – an 8.8 times increase over Earth.

Another effect is the orbit of the Moon. Now the two bodies have about equal mass. Is the Moon bound to blueberry earth? A kilogram of lunar material has potential energy $GM_{BE}/r_{moon} \approx$ 1.6925 $\times 10^{5}$ J, while the kinetic energy is $2.6442\times 10^5$ J – more than enough to escape. Had it remained the jam ocean would have made an excellent tidal dissipation mechanism that would have slowed down rotation and moved blueberry earth towards tidal lock with the moon much earlier than the 50 billion years it would otherwise have taken.

So, to sum up, to a person standing on the surface of the Earth when it turns into blueberries, the first effect would be a drastic reduction of gravity. Standing on the blueberries might be possible in theory, except that almost immediately they begin to compress rapidly and air starts erupting everywhere. The effect is basically the worst earthquake ever, and it keeps on going until everything has fallen 714 km. While this is going on everything heats up drastically until the entire environment is boiling jam and steam. The end result is a world that has a steam atmosphere covering an ocean of jam on top of warm blueberry granita.

Ten years closer to the future

It is the best place in the world to work.

Why Cherry 2000 should not be banned, Terminator should, and what this has to do with Oscar Wilde

[This is what happens when I blog after two glasses of wine. Trigger warning for possibly stupid cultural criticism and misuse of Oscar Wilde.]

From robots to artificiality

On practical ethics I discuss what kind of robots we ought to campaign against. I have signed up against autonomous military robots, but I think sex robots are fine. The dividing line is that the harm done (if any) is indirect and victimless, and best handled through sociocultural means rather than legislation.

I think the campaign against sex robots has a point in that there are some pretty creepy ideas floating around in the world of current sex bots. But I also think it assumes these ideas are the only possible motivations. As I pointed out in my comments on another practical ethics post, there are likely people turned on by pure artificiality – human sexuality can be far queerer than most think.

Going off on a tangent, I am reminded of Oscar Wilde’s epigram

“The first duty in life is to be as artificial as possible. What the second duty is no one has as yet discovered.”

Being artificial is not the same thing as being an object. As noted by Barris, Wilde’s artificiality actually fits in with pluralism and liberalism. Things could be different. Yes, in the artificial world nothing is absolutely given, everything is the result of some design choices. But assuming some eternal Essence/Law/God is necessary for meaning or moral exposes one to a fruitless search for that Thing (or worse, a premature assumption one has found It, typically when looking in the mirror). Indeed, as Dorian Gray muses, “Is insincerity such a terrible thing? I think not. It is merely a method by which we can multiply our personalities.” We are not single personas with unitary identities and well defined destinies, and this is most clearly visible in our social plays.

Sex, power and robots

Continuing on my Wildean binge, I encountered another epigram:

“Everything in the world is about sex except sex. Sex is about power.”

I think this cuts close to the Terminator vs. Cherry 2000 debate. Most modern theorists of gender and sex are of course power-obsessed (let’s blame Foucault). The campaign against sex robots clearly see the problem as the robots embodying and perpetuating a problematic unequal power structure. I detect a whiff of paternalism there, where women and children – rather than people – seem to be assumed to be the victims and in the need of being saved from this new technology (at least it is not going as far as some other campaigns that fully assume they are also suffering from false consciousness and must be saved from themselves, the poor things). But sometimes a cigar is just a cigar… I mean sex is sex: it is important to recognize that one of the reasons for sex robots (and indeed prostitution) is the desire for sex and the sometimes awkward social or biological constraints of experiencing it.

The problem with autonomous weapons is that power really comes out of a gun. (Must resist making a Zardoz reference…) It might be wielded arbitrarily by an autonomous system with unclear or bad orders, or it might wielded far too efficiently by an automated armed force perfectly obedient to its commanders – removing the constraint that soldiers might turn against their rulers if being aimed against their citizenry. Terminator is far more about unequal and dangerous power than sex (although I still have fond memories of seeing a naked Arnie back in 1984). The cultural critic may argue that the power games in the bedroom are more insidious and affect more of our lives than some remote gleaming gun-metal threat, but I think I’d rather have sexism than killing and automated totalitarianism. The uniforms of the killer robots are not even going to look sexy.

It is for your own good

Trying to ban sex robots is about trying to shape society into an appealing way – the goal of the campaign is to support “development of ethical technologies that reflect human principles of dignity, mutuality and freedom” and the right for everybody to have their subjectivity recognized without coercion. But while these are liberal principles when stated like this, I suspect the campaign or groups like it will have a hard time keeping out of our bedrooms. After all, they need to ensure that there is no lack of mutuality or creepy sex robots there. The liberal respect for mutuality can become a very non-liberal worship of Mutuality, embodied in requiring partners to sign consent forms, demanding trigger warnings, and treating everybody who is not responding right to its keywords as suspects of future crimes. The fact that this absolutism comes from a very well-meaning impulse to protect something fine makes it even more vicious, since any criticism is easily mistaken as an attack on the very core Dignity/Mutuality/Autonomy of humanity (and hence any means of defence are OK). And now we have all the ingredients for a nicely self-indulgent power trip.

This is why Wilde’s pluralism is healthy. Superficiality, accepting the contrived and artificial nature of our created relationships, means that we become humble in asserting their truth and value. Yes, absolute relativism is stupid and self defeating. Yes, we need to treat each other decently, but I think it is better to start from the Lockean liberalism that allows people to have independent projects rather than assume that society and its technology must be designed to embody the Good Values. Replacing “human dignity” with the word “respect” usually makes ethics clearer.

Instead of assuming we can a priori figure out how technology will change us and then select the right technology, we try and learn. We can make some predictions with reasonable accuracy, which is why trying to rein in autonomous weapons makes sense (the probability that they lead to a world of stability and peace seems remote). But predicting cultural responses to technology is not something we have any good track record of: most deliberate improvements of our culture have come from social means and institutions, not banning technology.

“The fact is, that civilisation requires slaves. The Greeks were quite right there. Unless there are slaves to do the ugly, horrible, uninteresting work, culture and contemplation become almost impossible. Human slavery is wrong, insecure, and demoralising. On mechanical slavery, on the slavery of the machine, the future of the world depends.”

AMA on Reddit

I have been doing an AMA on Reddit. Everything from transhumanist activism and the end of the Earth to why we haven’t fixed baldness yet.

I like the format, although it stresses me out.

Awesome blogs

I recently discovered Alex Wellerstein’s excellent blog Restricted data: the nuclear secrecy blog. I found it while looking for nuclear stockpiles data, but was drawn in by a post on the evolution of nuclear yield to mass. Then I started reading the rest of it. And finally, when reading this post about the logo of the IAEA I realized I needed to mention to the world how good it is. Be sure to test the critical assembly simulator to learn just why critical mass is not the right concept.

Another awesome blog is Almost looks like work by Jasmcole. I originally found it through a wonderfully over the top approach to positioning a wifi router (solving Maxwell’s equations turns out to be easier than the Helmholz equation!). But there are many other fascinating blog essays on physics, mathematics, data visualisation, and how to figure out propeller speeds from camera distortion.

Quantifying busyness

Tempus fugit

If I have one piece of advice to give to people, it is that they typically have way more time now than they will ever have in the future. Do not procrastinate, take chances when you see them – you might never have the time to do it later.

One reason is the gradual speeding up of subjective time as we age: one day is less time for a 40 year old than for a 20 year old, and way less than the eon it is to a 5 year old. Another is that there is a finite risk that opportunities will go away (including our own finite lifespans). The main reason is of course the planning fallacy: since we underestimate how long our tasks will take, our lives tend to crowd up. Accepting to give a paper in several months time is easy, since there seems to be a lot of time to do it in between… which mysteriously disappears until you sit there doing an all-nighter. There is also the likely effect that as you grow in skill, reputation and career there will be more demands on your time. All in all, expect your time to grow in preciousness!

Mining my calendar

I recently noted that my calendar had filled up several weeks in advance, something I think did not happen to this extent a few years back. A sign of a career taking off, worsening time management, or just bad memory? I decided to do some self-quantification using my Google calendar. I exported the calendar as an .ics file and made a simple parser in Matlab.

It is pretty clear from a scatter plot that most entries are for the near future – a few days or weeks ahead. Looking at a histogram shows that most are within a month (a few are in the past – I sometimes use my calendar to note when I have done something like an interview that I may want to remember later).

Plotting it as a log-log diagram suggests it is lighter-tailed than a power-law: there is a characteristic scale. And there are a few wobbles suggesting 1-week, 2-week and 3-week periodicities.

Am I getting busier? Plotting the mean and median distance to scheduled events, and the number of events per year, suggests yes. The median distance to the things I schedule seems to be creeping downwards, while the number of events per year has clearly doubled from about 400 in 2008 to 800 in 2014 (and extrapolating 2015 suggests about 1000 scheduled events).

Plotting the number of events I had per 14-day period also suggests that I have way more going on now than a few years ago. The peaks are getting higher and the mean period is more intense.

When am I free?

A good measure of busyness would be the time horizon: how far ahead should you ask me for a meeting if you want to have a high chance of getting it?

One approach would be to look for the probability $Q(t)$ that a day $t$ days ahead is entirely empty. If the probability that I will fill in something $i$ days ahead is $P(i)$, then the chance for an empty day is $Q(t) = \prod_{i=t}^\infty (1-P(i))$. We can estimate $P(i)$ by doing a curve-fit (a second degree curve works well), but we can of course just estimate from the histogram counts: $\hat{P}(i)=N(i)/N$.

However, this method is slightly wrong. Some days are free, others have many different events. If I schedule twice as many events the chance of a free day should be lower. A better way of estimating $Q(t)$ is to think in terms of the rate of scheduling. We can view this as a Poisson process, where the rate of scheduling $\lambda(i)$ tells us how often I schedule something $i$ days ahead. An approximation is $\hat{\lambda}(i)=N(i)/T$, where $T$ is the time interval we base our estimate on. This way $Q(t) = \prod_{i=t}^\infty e^{-\lambda(i)}$.

If we slice the data by year, then there seems to be a fairly clear trend towards the planning horizon growing – I have more and more events far into future, and I have more to do. Oh, those halcyon days in 2007 when I presumably just lazed around…

If we plot when I have 50%, 75% and 90% chance of being free, the trend is even clearer. At present you need to ask about three weeks in advance to have a 50% chance of grabbing me, and 187 days in advance to be 90% certain (if you want an entire working week with 50% chance, this is close to where you should go). Back in 2008 the 50% point was about a week and the 90% point 1.5 months ahead. I have become around 3 times busier.

Conclusions

So, I have become busier. This is of course no evidence of getting more done – a lot of events are pointless meetings, and who knows if I am doing anything helpful at the other events. Plus, I might actually be wasting my time doing statistics and blogging instead of working.

But the exercise shows that it is possible to automatically estimate necessary planning horizons. Maybe we should add this to calendar apps to help scheduling: my contact page or virtual secretary might give you an automatically updated estimate of how far ahead you need to schedule things to have a good chance of getting me. It doesn’t have to tell you my detailed schedule (in principle one could do a privacy attack on the schedule by asking for very specific dates and seeing if they were blocked).

We can also use this method to look at levels of busyness across organisations. Who have flexibility in their schedules, who are so overloaded that they cannot be effectively involved in projects? In the past, tasks tended to be simple and the issue was just the amount of time people had. But today we work individually yet as part of teams, and coordination (meetings, seminars, lectures) are the key links: figuring out how to schedule them right is important for effectivity.

If team member $j$ has scheduling rates $\lambda_j(i)$ and they are are uncorrelated (yeah, right), then $Q(t)=\prod_{i=t}^\infty e^{-\sum_j\lambda_j(i)}$. The most important lesson is that the chance of everybody being able to make it to any given meeting day declines exponentially with the number of people. If the $\lambda_j(i)$ decline exponentially with time (plausible in at least my case) then scheduling a meeting requires the time ahead to be proportional to the number of people involved: double the meeting size, at least double the planning horizon. So if you want nimble meetings, make them tiny.

In the end, I prefer to live by the advice my German teacher Ulla Landvik once gave me, glancing at the school clock: “I see we have 30 seconds left of the lesson. Let’s do this excercise – we have plenty of time!” Time not only flies, it can be stretched too.