On busy mornings

I am not an especially busy person – in fact I like to think of myself as semi-retired – but how busy my life seems on weekday mornings! There are so many things to do in such a short time before rushing out the door! Must life really be so complicated?

Here are the things I need to do between waking up and leaving for work:

Things to Do

  1. toilet
  2. shave
  3. boil kettle
  4. bring milk inside and put in fridge
  5. make tea
  6. on Mondays and Thursdays, do Stoutness Exercises (don’t ask!)
  7. make breakfast
  8. get dressed
  9. turn on the internet
  10. pack bread and fruit for lunch
  11. get leaves from garden for salad component of lunch
  12. eat breakfast
  13. wash up breakfast things
  14. make bed
  15. brush teeth
  16. If last to leave the house – check that lights and appliances are off and doors are locked
  17. unlock bike

Here are the things I need to get together for my journey to work:

Things to Take

  1. lunch components (see above)
  2. security access card for work
  3. USB stick with programs for work computer
  4. house keys
  5. mobile phone
  6. shoes (by front door – not to be worn in the house)
  7. bike pannier
  8. bike helmet and other safety gear
  9. sunglasses
  10. wet weather gear if there’s a chance of rain

This seems like a ridiculous lot of stuff to do and to take. Am I really such a shallow, materialistic, object-dependent person that I need all this?

I try to compare it with what I would do if I were a hunter-gatherer. I suppose I would take a spear and another sharp rock for cutting up a kill. But not much else. As regards things to do, it might be a bit more involved. I would have to agree with the other men in which direction we would head in search of prey, and what our tactics would be. Maybe I would take a pouch of edible roots or a slab of dried meat to sustain me on the hunt, but I doubt it. Yes, I think my morning routine is definitely more complex than that of a stone-age man. What is my excuse?

I do think I have an excuse for most of those things, and here is my attempt to say it – an attempt to defend (some of) the complexities of modern urban life.

Food

The food bits are justified by the fact that I seem to function rather poorly on only one meal a day. Perhaps ancient hunter gatherers were accustomed to eating a large meal only once a day, before sleeping (as a lion does), but I lose energy if I don’t have three. So if I have to travel to a place several kilometres away to earn my living, I need to make arrangements for two of my daily meals before I leave.

On the other hand, if I am honest, I must admit that this may be just a matter of comfort. I haven’t tried getting by on just one meal per day. Maybe once I got used to it I could function just as well. I might be hungry for much of the day, but so what?

So I think I should chalk up all the food-related items to my modern, urban, sybaritic lifestyle. It’s possible that I’m wrong, and my effectiveness during the day would be impaired without three meals. But I’m not going to do the experiment to find out.

So, at the expense of admitting my softness, I have dispensed with items 3-5, 7, 10-13 and 15 in the first list and item 1 in the second.

Turning to the other end of the alimentary canal, even Stone Age men and non-human animals have to excrete, so I’m not going to beat myself up over item 1 on list 1.

Clothes and Grooming

Next, grooming! I think I can gain some ground here, because I don’t do ridiculous things like mutilate my body with bones through my nose, rings to stretch my neck, rocks to stretch my earlobes or gashes across my chest to demonstrate my masculinity, nor do I wear ungainly head-dresses made of eagle feathers or moose antlers. In fact, my clothing and grooming style is a paragon of minimalist functionality compared to those of many Stone Age peoples.  Even shaving, although a little time-consuming, is practical in that it avoids the need to maintain cleanliness and hygiene of facial hair. Together with having almost no hair on top of my head, that makes staying clean a pretty easy job.

Sure, I wear more clothes than my Paleolithic cousins did, but that gives me the advantage of being able to control my temperature and risk of sun damage better than if my only choice was between wearing a bear skin and going naked.

Does all the bike gear sound like too much paraphernalia? One does feel a bit like one is about to make a moon shot before one goes out the door. But then, consider what is being achieved: I travel the seven kilometres from my house to my office in about twenty minutes, with minimal expenditure of effort and no pollution, while dodging my way through crowds of inexpertly-driven 1-2 tonne metal monsters travelling at unsafe speeds in erratic directions. I’d like to see Ugg do that and survive!

It’s hard to think of a Stone Age equivalent to my Stoutness Exercises. I imagine that hunter-gatherers had to do enough heavy lifting in everyday life – rolling boulders off cliffs onto mammoths and so on – that there was no need to do extra exercises. I’m going to count them as part of grooming. Maybe my being able to do <number deleted> push-ups is as much my vain attempt to assert masculinity as a cave-man’s chest scars.

Internet

I’m not even going to try to defend Number 9 ‘turn on the internet’. The internet is a useful tool but in the mornings I mostly just use it for wasting time reading other people’s opinions. Maybe I could classify that under the general heading of Games, but I don’t know if cave men had much time for games.

There’s one area where the internet is useful in the morning though, and that’s to tell me the weather forecast. I used to get that off the radio, but I had to wait around for it, so the internet is a superb time saver. Cave man had neither, so he occasionally got caught out without his wellies, or froze to death or got blown off a cliff by the wind.

Yes, knowing the weather forecast is one of the genuine major improvements of modern life.

In the ‘things to do’ list that just leaves the last two items – turn off lights etc and unlock bike.

Electricity and Fire

If the cave man was in a family group, he probably was rarely the last to leave, as there would always be people staying in the camp to tend babies or do other chores. But it is conceivable that, if they did leave for a few hours, they would extinguish any camp fires, partly to conserve fire wood and partly so as not to leave smoke signalling to hostile tribes the presence of the undefended camp. Turning off electrics is broadly similar to that, so I think I need feel no shame at the comparison.

Security

The last To Do item, and two of the remaining Things to Take, are about security – keys, access cards and locks. Do they have a Stone Age equivalent, I wonder? Did they have possessions that they needed to keep safe, and if so from whom? Once they developed agriculture – crops and herds – they would have wanted to secure them from marauding human and non-human animals, but what about hunter-gatherers? The only things I can imagine them owning are tools like flints, spears and pouches, furs and other rough clothing, and food. Such things would be kept within the family group while sleeping, and where appropriate, taken with them when out hunting and gathering. If there were no nearby tribes, security would not be a concern, but if there were, conflicts over resources would easily arise. Theft and violence could be frequent occurrences. In such circumstances, one imagines they would take precautions, such as maintaining a watch at night and erecting barricades or booby-traps around their camp.

Living in a major city, I am surrounded by other humans, a small number of whom would be quite happy to take my things, and sometimes do. My possession of a few keys and a security card seems a reasonable analog to a system of barricades, booby-traps and watchmen, and I reject your insinuation that I am paranoid. At least I haven’t clubbed any intruders yet.

USB stick

Is there any stone-age equivalent to the USB stick? My stick holds a bunch of files that I need to work on (encrypted, of course) and papers I need to read, plus a few amusements such as electronic versions of Charles Dickens novels, music and podcasts. In so far as the stick holds thing I need for my work, which I need to earn my daily bread, I suppose it corresponds to paleolithic work tools such as spears and flints.

A USB stick actually makes me less object-dependent than a typical office worker of fifteen years ago, who would have had to take files and papers home if she wanted to work on them. And it’s certainly a lot lighter and easier to fit in a pocket than a spear or a club.

Communication

There’s one thing left – my mobile phone. I concede, I have no excuse whatsoever for that.

I can make feeble protestations that it would allow me to call for help if I got into a Difficult Situation, but I’ve never done that so far (perhaps because I take so much other precautionary stuff with me) and I doubt I ever will.

I think a mobile phone might have actually been of more use to a cave man than to me. He could have rung up his wife on the way back from a hunt, and said ‘Hi honey, you won’t believe the enormous bison we’ve killed. Can you stoke up a big fire and sharpen the butchering stones ready for us to arrive in about half an hour?’

So who wins?

To summarise then, I am softer and more paraphernalia-obsessed than my paleolithic ancestor, to the tune of two extra meals per day, a broadband connection and a mobile phone. Beyond those, I have longer lists of things to do and to take than he did, but that’s appropriate given how much more I achieve in the course of a day. I concede that I live a fairly pampered and baroque existence, but perhaps not quite as extravagantly so as it might seem at first.

It appears to be customary for both essayists and journalists to end an article with a pat phrase that sums up their writing in a semi-humorous way, and I have always tried my best to honour that tradition. On this occasion however, I find myself bereft of pat phrases, so I will just have to stop here.


Do predictions have a truth value?

An old philosophical question is whether a prediction, by which I here mean a statement about the future such as

P: ‘it will rain on Sydney Town Hall at 1pm tomorrow’

is true or false at the time it is made, or whether it is neither, and only becomes true or false when the event to which it refers occurs, or fails to occur by the  predicted time.

I think whether you accept that a prediction currently has a truth value depends on whether you subscribe to an A or B theory of time.

The ‘A theory of time’ holds that the future does not exist but is in the process of being created. Under this interpretation most predictions have no truth value. There will be some exceptions, which are things that have to be true, such as: “at 1pm AEST on 1 Jan 2013 it will either be raining on Sydney Town Hall or it won’t”. But I don’t think they’ll be very interesting. This one about rain in a given spacetime location is just a particular instance of a logical rule of inference – the ‘law of excluded middle’. It is true even though the events to which it refers have not yet happened because, no matter how the future unfolds, the prediction will be true.

The A theory does not seem to me to be compatible with a belief in absolute determinism – that is, that there is only one possible future, which will inevitably unfold under entirely deterministic laws of nature – the ‘clockwork world’. Under the most widely-accepted interpretations of quantum mechanics there is an irreducible randomness at the quantum level that makes determinism impossible. There is a minority view held by some physicists that future discoveries will be made that dissolve the apparent quantum randomness by revealing underlying deterministic processes. A-theorists would have to eschew such a view though, as a future that is completely determined by the present state of the world seems as real as the past.

Under the B theory of time, all of spacetime exists as a four-dimensional block in which separate events may be earlier, later or contemporaneous with one another (under Einstein’s Theory of Relativity, the ordering of events is not uniquely determined. For two events u and v, u may be earlier than v in one reference frame and later than v in another), and the passing of time is just our subjective experience, as the trajectory of our life is embedded in that block. Under this theory, every proposition about events in the spacetime has a truth value, seen from a timeless framework that transcends the block, including propositions about spacetime events later than the time the proposition is stated. The passing of time only changes our ability to know the truth value, not its existence.

The rest of this essay considers the question in the context of the A theory.

A common argument from those that hold predictions do have a truth value is that a prediction is just a proposition about the future, and propositions are either true or false. If one accepts this then there is nothing more to say. But whether we accept it depends crucially on the definition of proposition. For a start, one would have to disallow as propositions all statements that are incoherent, such as “nibble, squawk, omnipotence“, “the colour of my aura is five” or “one of Jim’s legs is both the same“. But doesn’t coherent simply mean that the statement has a truth value (that is certainly the problem with these three examples)? If so, it becomes far from obvious that a prediction is a proposition, because it is incoherent unless it has a truth value. So one has to suppose the conclusion – that the prediction has a truth value at the time it is made – in order to prove it.

Alternatively, if we do not require that all propositions are coherent then the second part of the argument fails: a prediction being a proposition does not entail that it has a truth value.

One can argue that a prediction does not have a truth value by asserting that the statement ‘it will rain tomorrow’ has no meaning – it is as incoherent as “nibble squawk omnipotence” This seems a very strong and surprising claim, but it is not easy to see a rebuttal. It is hard to explain what the meaning of the statement is without simply restating it, at best substituting some synonyms for the words therein.

Why do people so often say things like ‘it will rain tomorrow’ then, if they have no meaning? I think the answer is that people generally don’t, or if they do they don’t mean what they say. What they do say, if they’re careful about their words, is:

P1: “I believe that it will rain on Sydney Town Hall at 1pm tomorrow

The crucial difference from P is that P1 is a statement about the present not the future. It is describing a current state of the speaker’s mind, saying that it holds a certain belief. This doesn’t help much with the dilemma though, because we can ask ‘but what is it that the speaker believes?’ We can rewrite P1 as:

P2: “I believe that P

and it looks like we’re back where we started.

Are we really though? A statement of belief can be interpreted as a statement of what appears most probable, given the information available to the speaker. That information includes observations about the past and current states of the world, together with some knowledge of the laws of nature that govern how the state of the world evolves over time. Viewed thus, P1 is equivalent to the following statement:

P3: ‘Most of the possible states to which I believe the planet Earth can evolve at 1pm tomorrow, starting from its current state, include rain falling on Sydney Town Hall

P3 is a statement about the present, as it is a statement about the now-existing set of solutions to a set of mathematical equations that represent:

  1. the current state of the world, and
  2. the laws of nature under which states can evolve, as the speaker understands them
Because P3 is about the present, it has a clear meaning and will be true or false at the time it is said. In fact, because it is a statement about the speaker’s beliefs, it will only be false if the speaker is lying. P3 is not rendered false by the speaker having mistaken beliefs about the laws of nature or the current state of the world. It is true even if her beliefs are wrong, just as it is true when a madman sincerely says ‘I believe I am the Emperor Napoleon’, but not if he says ‘I am the Emperor Napoleon’.
Note that it is necessary to couch the statement P3 in probabilistic terms because of the uncertainty arising from:
  1. quantum randomness, and
  2. the speaker’s necessarily incomplete understanding of the laws of nature

We can sidestep the second of these sources of uncertainty by considering the statement:

P4: ‘Most of the possible states to which the planet Earth can evolve at 1pm tomorrow, starting from its current state, include rain falling on Sydney Town Hall

In contrast to P3, P4 may well be false if the speaker has an erroneous understanding of the laws of nature, or the current state of the world. That is because P4 is a statement about the laws of nature and the current state of the world, rather than about the speaker’s beliefs about those things.
Finally, the residual (quantum) uncertainty can be removed from P4 only if the laws of nature are, contrary to current mainstream scientific opinion, deterministic. Only then can the following statement be coherent:

P5: ‘The state to which the planet Earth will evolve at 1pm tomorrow, starting from its current state, includes rain falling on Sydney Town Hall

As noted earlier though, determinism appears incompatible with the A theory, so this statement only makes sense within a B theory, under which statements about the future are generally regarded as having a truth value.

Conclusion

Let’s summarise. What do A and B theorists make of the following statements, made at spacetime location (x,t)?

  1. Event E happens at spacetime location (x’,t’).

For a B-theorist this statement has a truth value, which is determined solely by whether E happens at (x’,t’), regardless of the value of t. For an A-theorist the statement does not have a truth value if t<t’.

  1. I believe that event E happens at spacetime location (x’,t’).

This has a truth value for both A and B theorists, but in both cases the truth value depends solely on the speaker’s beliefs at time t, not on whether E happens at (x’,t’).

  1. Given the state of the spacetime in the spatial neighbourhood of (x,t), event E probably happens at spacetime location (x’,t’).

This has a truth value for both A and B theorists, which is determined by the states to which the state of the world can evolve starting at (x,t) under the non-deterministic laws of nature. This is a purely mathematical statement, not about reality. For a B-theorist, this statement can be true even if E does not happen at (x’t’).


Hilbert’s Hotel

Theologian William Lane Craig, in his resuscitation of the Kalam Cosmological Argument, relies on a proposition that ‘an actual infinite cannot exist’. His primary argument in favour of this proposition is a reference to Hilbert’s Hotel and the apparent paradoxes it creates.
Hilbert’s hotel is a thought experiment devised by the early 20th century German mathematician David Hilbert. It is a hotel with an infinite number of rooms, all of which are full. A new guest arrives wanting to stay and is told all the rooms are full. But the hotel manager makes room for the new guest by moving the guest in room N to room N+1, for N=1 to infinity, and putting the new guest in room 1. Craig adduces the apparent absurdity of this as a compelling reason why an actual infinite, by which we presume he means an infinite set of objects each comprised of a finite, nonzero amount of matter, cannot exist.
But why is the outcome absurd? It is unusual, but there are many things in the universe that are strange and unusual. Is the sticking point that an empty room appears to have been created where none previously existed? If so then that problem is resolvable, by considering the process of transition to the state in which all the guests, including the newcomer, are accommodated. To do so we need to consider the process by which the hotel manager effects the transition, bearing in mind that we are dealing with a hypothetical physical situation here, so the laws of physics must be obeyed.
One possible such process is as follows: the manager writes an order, addressed to all guests, stating that, on receipt of the written order, each guest should:

  1. pack up and move out of their room
  2. go to the room numbered one greater than theirs and deliver the letter to the guest in that room
  3. when the guest in that next room has moved out, move into that room.

In this scenario, there will always be one guest without a room, as they wait for the next guest to vacate. This situation persists forever because the manager’s message only proceeds at a finite – indeed a very slow – pace. So it would appear that no extra room has been created: we had one person without a room as soon as the new guest arrived, and we still do, in perpetuity. It’s just that the person without a room changes every few minutes.
OK then, but what if the manager asks all guests to move at the same time – does that remove the need for all this infinite waiting outside rooms? Maybe. Let’s see.
How can the manager ask all the guests to move at the same time, bearing in mind that this is a physical hotel in a physical world, and hence must obey the laws of physics? Well, he could transmit his order by email so that it flashes up on a large electronic screen prominently situated in each hotel room. Let us assume the message is transmitted at the speed of light – physics dictates that it cannot travel any faster – from the manager’s office adjacent to room 1. The message says ‘To all guests: on receipt of this message please immediately pack up and move to the room with number one greater than yours. The occupant of that room has been instructed to move to another room. Thank you for your cooperation. By order of the manager.’ Seeing the message, all the guests start packing up and moving. On arriving at the next room, they have to wait while it is vacated. The waiting time, including the time taken for the guest to travel form the door of her room to the door of the next room, will be a minimum of d/c where d is the distance between rooms and c is the speed of light. It will be longer if the guest in the next room is out, or if they weren’t paying attention to the screen and so did not see the message at the earliest possible moment. If the guest’s walking speed is v (which must be less than c) then the guest will spend time of at least d/v outside a room, longer if they have to wait to be admitted to the next room.
As in the previous scenario, the room shuffle will never be completed, as there will always be an infinite number of rooms at which the manager’s message – travelling at the fast but finite speed c – has not yet arrived. At any point in time there will be a very large number of people outside their rooms as they walk from one room to the next. As the typical time taken to move from one room to the next is d/v and the delay from one room receiving the message to the next room’s receiving it is d/c, there will typically be (d/v)/(d/c) = c/v people in the corridor at any time after the first few minutes. Based on a typical walking pace of 1m/s this means there will always be about 300,000,000 people in the corridor. Clearly this situation is much worse than with the hand-written message.
In fact, however you try to arrange the transition, it will always involve at least one person being without a room for an infinite amount of time.
Although it is possible for all the existing guests plus the newcomer to be accommodated in the hotel without having to create new rooms, the transition from the existing state to a new state where all are accommodated involves an infinite amount of homelessness. This seems unsurprising, given the hotel was full to start with. So, when we take account of the process of transition, there are no miraculous or absurd consequences that cause us to conclude that an actual infinity cannot exist.
Hilbert’s thought experiment can be extended to allow an infinite number of new guests to arrive, or even an infinite number of coaches each carrying an infinite number of new guests. As with the single new guest, these new guests can be accommodated in the existing set of rooms together with the existing guests. But, as in the above scenario, the transition will still involve an infinite amount of homelessness.
A further twist on the hotel ‘paradox’ is the situation where a guest leaves. In this case all the guests move down a room, thereby moving towards a state in which all the rooms are occupied again, despite the departure. This version is easily understood by inverting the logic above and thinking of a room without a guest in the same way as we previously thought about a guest without a room. Hence the transition will involve one or more rooms being empty for an infinite amount of time.
Craig’s assertion that an ‘actual infinity’ is impossible relies on being able to deduce an absurdity from the existence of such an actual infinity. That absurdity must be something other than our scepticism that a hotel with an infinite number of rooms could exist, otherwise the argument becomes circular: ‘an actual infinity cannot exist because I consider the existence of an actual infinity to be absurd.’ If, when the new guest arrived, the manager were able to wave a wand and make all the guests instantaneously and simultaneously teleport, with all their luggage, into the next room, then we would have an apparent absurdity via the immediate accommodation of the newcomer despite all the rooms being full (that is the absurdity adduced by Craig as proof that an actual infinity cannot exist). Such an action can be contemplated in mathematics, but Craig has no objection to mathematical infinities (‘potential infinities’). It is actual, physical infinities that he claims are impossible. But by considering the problem of transition, which only exists for physical infinities, we see that it is precisely the constraints imposed by physics that prevent the absurdity from arising.
One might object that this is a nitpicking point about transition and that, after the transition is complete – i.e. after an infinite period of time has passed – everyone including the newcomer will be accommodated and we will have a physical absurdity. This objection is easily dismissed on the grounds that:

  1. we will never get to the point when an infinite amount of time has passed
  2. after a finite period of time all the guests will have died (or disintegrated by slow radioactive decay even if the guests are androids and hence not vulnerable to death); and
  3. after an infinite period of time, nothing should surprise us – think monkeys typing Shakespeare

The conclusion is that, whatever arguments might be made against the possibility of an actual infinite, Hilbert’s Hotel cannot be one of them.