brettcap

00:00:00.000 The first part of this ended really abruptly and quickly, or because my audio failed, so I

00:00:16.800 I'm going to continue with the Infinity Hotel explanation of the different kinds of

00:00:24.520 We've just learned there are kinds of infinity called countable infinities.

00:00:29.160 That's how to explain what the uncountable infinities are, but first I'll go to the book

00:00:36.560 It is mathematically possible to overwhelm the capacity of infinity hotel.

00:00:41.880 In a remarkable series of discoveries in the 1870s, cantile proved among other things

00:00:48.600 In particular, the infinity of the continuum, the number of points in a finite line, which

00:00:53.680 is the same as the number of points in the whole of space or space time, is much larger

00:01:00.320 Cantile proved this by proving that there can be no one-to-one correspondence between

00:01:07.680 That set of points has a higher order of infinity than the set of natural numbers.

00:01:13.360 Now David then goes on to give a version of that proof.

00:01:18.440 There are many versions of the diagonal argument in showing that certain kinds of infinity

00:01:25.400 Just go through an explanation of a diagonal argument and then go through another kind

00:01:30.800 of explanation or a description really of how certain kinds of infinity are countable

00:01:38.240 Let's have a look at a certain kind of diagonal argument.

00:01:41.880 So if you go online or you go to a textbook and you look up what a diagonal argument is,

00:01:47.960 what you'll often find is the argument expressed in terms of binary numbers.

00:01:56.240 So the simplest sequence of binary numbers might be the binary number of zero and of

00:02:01.360 course zero would be represented as any infinite set of zeros or we can have an infinite

00:02:11.200 set of ones or we could have alternating zeros and ones.

00:02:25.360 I'm not really going to be concerned about what these numbers actually represent in base

00:02:31.440 Let's change the order of that sequence, maybe we could have two ones, two zeros.

00:02:43.400 For people listening on audio, basically I've got a sequence of nothing but zeros, then

00:02:51.040 Then I've got a sequence of alternating 0, 1, 0, 1.

00:02:55.000 Then I've got a sequence of alternating 1, 0, 1, 0.

00:02:58.960 Then I've got a sequence of double 1, double 0, double 1, et cetera, off to infinity.

00:03:06.320 So if you write down every single permutation of zeros and ones in an infinitely long

00:03:12.640 list, will you nonetheless not be able to capture a certain pattern of zeros and ones?

00:03:20.840 In fact, there is going to be, even if this list was infinitely long and so that you went

00:03:26.000 on, such that your next sequence was double 0, double 1, double 0, double 1, and then triple

00:03:31.520 1, triple 0, triple 1, triple 0, and et cetera, you just kept on doing that and you try

00:03:35.440 to shuffle around every single possible way of writing zeros and ones.

00:03:40.600 Is there a number that you could write of zeros and ones that would not appear in an infinitely

00:03:53.760 Take the very first one, which is nothing but a series of zeros, and take the first

00:04:04.560 What I'm going to do to that 0 there is to change it from being a 0 into a 1, all

00:04:12.960 Now let's go to the second number in my sequence, and that's just a series of ones.

00:04:17.000 I'm going to take the second of those digits there, that's a 1, and I'm going to circle

00:04:22.520 that, and I'm going to change it from what it is, which is a 1, into a 0.

00:04:28.720 I'm going down to the third number now, and I'm going to take the third number on that

00:04:32.160 list, circle it once more, it happens to be a 0, I'm going to write down a 1.

00:04:37.920 And then on the fourth number, I think you get the picture now, we're going to find

00:04:41.640 the fourth number in that sequence, circle it, and write down a 1.

00:04:47.120 I'm going to repeat that, for every single number in the list, off to infinity.

00:04:53.160 And what I will have constructed, up here at the top, is a number, which by definition

00:04:58.360 is different to every single other number in the list.

00:05:01.320 So even though that number is infinitely long, even though that list is infinitely long,

00:05:05.960 and would appear if it's an infinitely long list, such that every single number in that

00:05:09.960 list is different to every other number, and I've gone through every possible permutation

00:05:13.760 that I can, one would think that I have constructed every single number that could possibly

00:05:18.160 be constructed from 0's and 1's, but no, because here, by definition, at the top, I've

00:05:24.160 constructed a number that does not, is not identical to any number in this list, it's

00:05:29.520 different by one digit from every single number in this list, it's different to this

00:05:33.640 one, because it's got a 1 there instead, it's different to this one, because it's got

00:05:38.200 No number down here will be the same as that number.

00:05:40.800 I've found a number that does not appear in an infinitely long list of 0's and 1's, where

00:05:47.520 every single number in that list is constructed of nothing but 0's and 1's.

00:05:51.720 So this is very profound, this says that this number here is not in the list of the infinite

00:06:00.320 So there must be a set of numbers bigger than this countable list, and it's countable

00:06:05.040 because it's ordered, okay, there is a specific pattern that we're following here.

00:06:09.360 This one doesn't appear anywhere in an infinite pattern, it's a different kind of number.

00:06:15.600 Well it's part of a sequence of uncountable numbers, it doesn't appear in the countable set.

00:06:27.120 Sometimes people can struggle with the diagonal argument, in trying to understand the

00:06:32.480 I find this version a little bit more intuitive, it's not a proof that there exists uncountable

00:06:37.000 infinities, but I think it's a clear explanation.

00:06:50.640 There's the classic countable set, the set sometimes called n for the natural numbers,

00:06:56.040 sometimes 0's excluded, so we've got 0, 1, 2, 3, 4, etc.

00:07:04.920 Well, any of your so-called times tables, 0, 2, 4, 6, 8, etcetera, 0, 3, 6, 9.

00:07:19.360 Now these sets are of the same size, even though it would appear that not every element

00:07:24.720 of the first set, 0, 1, 2, 3, 4, appears in the second set, 0, 2, 4, 6, 8.

00:07:31.240 So the second set is missing all the odd numbers, doesn't that mean it's missing half

00:07:37.640 Both of them are countable, you can count, 2, 4, 6, 8, 10, 3, 6, 9, 12.

00:07:45.800 They're both infinitely big, now although both of them are infinitely long and infinitely

00:07:50.080 large, both of them are smaller than other kinds of infinity.

00:07:56.520 In particular, the infinite number of integers here, counting numbers, 0, 1, 2, 3, 4, is

00:08:03.200 not as big as the number of numbers we say in mathematics, the number of real numbers, between

00:08:11.400 I'll say that again, there are more numbers between 0 and 1 than there are integers from

00:08:24.560 Well, as I've said over and again, 0, 1, 2, 3, 4 is countable, but what is not countable?

00:08:31.120 What is an uncountably large number of numbers are all the numbers between 0 and 1.

00:08:54.280 What's a bit smaller than, what's a bit smaller than 1.5?

00:09:14.840 Let's try and count the numbers between 0 and 1.

00:09:23.240 I certainly know what comes next down here with the integers.

00:09:29.280 But if I want to count the real numbers, all of the decimals, let's say, between 0 and

00:09:38.200 I don't know where to begin counting after 0.0, 0.001, we'll know it's not that because

00:09:45.680 there's something even smaller than that, 0.00001 and even smaller than that.

00:09:51.440 It doesn't matter what number you pick, however small it is, I can give you another

00:09:58.360 And that means I cannot count the numbers between 0 and 1.

00:10:05.520 Therefore, because the number of members is so large that not only is it infinite, you

00:10:12.480 can't even begin counting them, it's larger than the ones where at least you've got a

00:10:21.400 So that's an intuitive way of trying to understand the difference between countable and

00:10:27.560 Okay, after that long digression, let's go back to the book.

00:10:31.440 David writes, so there is an uncountable infinity of real numbers between any two distinct

00:10:40.240 Furthermore, there are uncountably many orders of infinity, each too large to be put into

00:10:45.720 one-to-one correspondence with the lower ones. Another important uncountable set is the

00:10:51.880 set of all logically possible reassignments of guessed to rooms in infinity hotel, or as

00:10:56.960 the mathematicians put it, all possible permutations of the natural numbers.

00:11:01.680 And so reordering the natural numbers in different orders, there's an uncountably large

00:11:07.760 So I'm skipping a bit here and going on to the story of the puppy.

00:11:15.280 That's not a real puppy, we don't have to worry.

00:11:18.000 David writes, infinity hotel has a unique, self-sufficient, waste disposal system.

00:11:23.520 Every day, the management first rearrange the guests in a way that ensures that all rooms

00:11:27.920 are occupied, then they make the following announcement.

00:11:30.840 Within the next minute, law guests, please bag their trash and give it to the guests in the

00:11:37.720 Should you receive a bag during that minute, then pass it on within the following half

00:11:45.320 To comply, the guests have to work fast, but none of them has to work infinitely fast, or

00:11:51.320 Each of them performs a finite number of actions as per the hotel rules.

00:11:55.320 After two minutes, all these trash moving actions have ceased.

00:11:58.320 So two minutes after they begin, none of the guests has any trash left.

00:12:06.320 Well, basically that's because there's this sum.

00:12:12.320 Begin with one minute, and then the next thing we'll tell to do is half a minute, and

00:12:16.320 then the next thing we'll do is go to the hotel to add a quarter of a minute.

00:12:20.320 And we just keep halving the previous number and then adding together the entire sequence.

00:12:25.320 Now, if you know how to add together infinite sequences, in any third series of numbers rather,

00:12:33.320 But if you don't, then all you need to do is to take out a calculator and you will see

00:12:41.320 In fact, you can prove that it identically equals two, but you can at least demonstrate to yourself

00:12:46.320 with nothing but a calculator that sure enough, 1 plus 0.5 plus 0.25 plus 0.125,

00:12:57.320 So after that process, David writes, all the trash in the hotel has disappeared from the universe.

00:13:04.320 No one has put it nowhere, every guest has merely moved some of it to another room.

00:13:09.320 The nowhere, where all that trash has gone is called in physics as singularity.

00:13:13.320 Singularities may well happen in reality inside black holes and elsewhere, but I'd address.

00:13:17.320 At the moment, we are still discussing mathematics, not physics.

00:13:22.320 Of course, infinity hotel has infinitely many staff.

00:13:25.320 Several of them are assigned to look after each guest.

00:13:28.320 But the staff themselves are treated as guests in the hotel,

00:13:31.320 staying in numbered rooms and receiving exactly the same benefits as every other guest.

00:13:36.320 Each of them has several other staff assigned to their welfare.

00:13:39.320 However, they are not allowed to ask those staff to do their work for them.

00:13:42.320 That is because if they did this, the hotel would grind to a halt.

00:13:49.320 That is the whole point of the Infinity Hotel thought experiment.

00:13:52.320 The flacious idea of delegating all ones' work to other staff in higher-damned rooms is called an infinite regress.

00:13:58.320 It is one of the things that one cannot validly do within infinity, skipping a little bit.

00:14:04.320 One day in Infinity Hotel, a guest's puppy happens to climb into a trash bag.

00:14:09.320 The owner does not notice, and passes the bag with the puppy to the next room.

00:14:17.320 The receptionist announces over the public address system.

00:14:20.320 We apologise for the inconvenience, but an item of value has been inadvertently thrown away.

00:14:24.320 Law guests, please undo the trash moving actions they have just performed in reverse order,

00:14:29.320 starting as soon as you receive a trash bag from the next higher-numbered room.

00:14:37.320 Because they are fellow guests in the higher-numbered rooms and not returning any either.

00:14:41.320 It was no exaggeration to say that the bags are nowhere.

00:14:45.320 They have not been stuffed into a mythical room-number infinity.

00:14:51.320 No one has done anything to the puppy except move it to another numbered room within the hotel.

00:14:59.320 It is not anywhere in the hotel or anywhere else in a finite hotel.

00:15:07.320 In however complicated a pattern, it will end up in one of those rooms.

00:15:14.320 Every individual action that the guest performed was both harmless to the puppy and perfectly reversible.

00:15:20.320 Yet, taken together, those actions annihilated the puppy and cannot be reversed.

00:15:26.320 Reversing them cannot work because if it did, there would be no explanation for why a puppy arrives at its owner's room and not a kitten.

00:15:32.320 If a puppy did arrive, the explanation would have to be that a puppy was passed down from the next higher-number room.

00:15:39.320 But that whole infinite sequence of explanations never gets around to explaining why a puppy.

00:15:48.320 What if one day a puppy did just arrive at room one having been passed down through all the rooms?

00:15:56.320 In physics, the nowhere from which a puppy would have come is called a naked singularity.

00:16:02.320 Naked singularities appear in some speculative theories and physics, but such theories are rightly criticized on the grounds they cannot make predictions.

00:16:09.320 As Hawking months put it, television sets could come out of a naked singularity.

00:16:13.320 It would be different if there were a law of nature determining what comes out.

00:16:16.320 For in that case, there would be no infinite regress and the singularity would not be naked.

00:16:20.320 The big bang may have been a singularity of that relatively benign type.

00:16:25.320 I said that the rooms are identical, but they do differ in one respect.

00:16:29.320 So given the types of tasks that the management requests from time to time, the low-numbered rooms are the most desirable.

00:16:34.320 For instance, the guest in room one has the unique privilege ever having to deal with anyone else's trash.

00:16:40.320 Moving to room one feels like winning first prize in a lottery.

00:16:46.320 But every guest has a room number that is uniquely close to the beginning.

00:16:51.320 So every guest in the hotel is more privileged and almost all other guests.

00:16:55.320 The cliched politicians promise to favour everyone can be honoured in infinity hotel.

00:17:03.320 That is one of the attributes of the unbounded growth of knowledge too.

00:17:06.320 We are not only just scratching the surface, we shall never be doing anything else.

00:17:13.320 So there is no such thing as a typical room number at infinity hotel.

00:17:16.320 Every room number is untypically close to the beginning.

00:17:19.320 The intuitive idea that there must be typical or average members of any set of values is false for infinite sets.

00:17:27.320 The saying is true of the intuitive ideas of rare and common.

00:17:31.320 We might think that half of all natural numbers are odd and half even.

00:17:37.320 So that odd and even numbers are equally common amongst the natural numbers.

00:17:41.320 But consider the following rearrangement and I will write this down up here.

00:17:55.320 So this is the sequence more or less that David is written down in the book.

00:18:01.320 And as we can see here, all we have done is move the odd numbers after the even numbers,

00:18:07.320 such that we have got two even numbers together, and then we have got an odd number.

00:18:11.320 So 1, 2, 4, 3, 6, 8, 5, 10, 12, 7, and you can do that forever.

00:18:17.320 And this would make it appear that the odd numbers are half as common as the even numbers.

00:18:23.320 And it gets worse. I mean what if we were to write down something like that we write down just the sequence of even numbers all the way up to 20.

00:18:42.320 And then I did 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 3.

00:18:51.320 What would that mean? That the odd numbers are now 1 tenth as common as the even numbers?

00:18:58.320 We could do it every millionth, every millionth number we could write down an odd number and the rest could be even numbers.

00:19:06.320 And we'd never run out of either. What does this mean?

00:19:10.320 That's quite profound. I'll read the section where David remarks on precisely that.

00:19:15.320 That makes it look as though the odd numbers are only half as common as the even ones.

00:19:19.320 Similarly we could make it look as though the odd numbers were 1 and a million or any other proportion.

00:19:24.320 So the intuitive notion of a proportion of the members of a set does not necessarily apply to infinite sets either.

00:19:33.320 Now David moves on to discussion about probability. And so let's read that section here.

00:19:39.320 He writes, after the shocking loss of the puppy the management of infinity hotel want to restore the morale of guests.

00:19:45.320 So they arrange a surprise. They announced that every guest will receive a complimentary copy of either the beginning of infinity or his previous book, the fabric of reality.

00:19:54.320 They distribute them as follows. They dispatch a copy of the older book to every millionth room and a copy of the newer book to every, to each remaining room.

00:20:03.320 Okay, so we've got the fabric of reality in one out of every million rooms, apparently.

00:20:09.320 Suppose that you're a guest at the hotel. A book gift wrapped in opaque paper appears in your room's delivery shoot.

00:20:16.320 You are hoping that it will be the new book because you have already read the old book.

00:20:20.320 You're fairly confident that it will be because after all what are the chances that your room is one of those that receive the old book?

00:20:28.320 Exactly one and a million it would seem. But before you have a chance to open the package there is an announcement.

00:20:34.320 Everyone is to change rooms to a number designated on a card that will come through the shoot.

00:20:38.320 The announcement also mentions that the new allocation will move all the recipients of one of the books to odd number rooms and the recipients of the other book to even number rooms.

00:20:48.320 But it does not say which. So you cannot tell from your new room number which book you have received.

00:20:54.320 Of course there is no problem with filling the rooms in this manner. Both books had infinitely many recipients.

00:21:00.320 Your card arrives and you moved your new room. Are you now any less sure about which of the two books you have received?

00:21:08.320 Presumably not. By your previous reasoning there is now only a one and two chance your book is the beginning of infinity because it is now in half the rooms.

00:21:19.320 Since that is a contradiction your method of assessing those probabilities must have been wrong.

00:21:24.320 Indeed all methods of assessing them are wrong because as this example shows in infinity hotel there is no such thing as the probability that you have received one book or the other.

00:21:35.320 So this is me talking now. This is a profound insight into the nature of probability and how it cannot apply to infinite sets.

00:21:44.320 What we had here was a thought experiment that set things up such that it appeared as if one out of every million rooms in infinity hotel had a copy of the fabric of reality.

00:21:57.320 And the rest had the beginning of infinity. And so you would presume on the basis in which it is stated that the probability of you going into a random room into infinity hotel that you would find the beginning of infinity.

00:22:09.320 Because it seems like far more of those rooms have the beginning of infinity.

00:22:15.320 However once the instruction comes through that everyone who received let's say the beginning of infinity is to move to an even number room and everyone who received the fabric of reality was to move to an odd number room then in performing that exact action you now move to one of the rooms.

00:22:36.320 But you don't know which one it is. All you know is that you have moved into either an odd number room or an even number room and the odd number rooms contain beginning of infinity and the even number rooms contain the fabric of reality.

00:22:48.320 But that seems to conflict with what you already assumed which is one out of every million rooms contains the fabric of reality and now it appears as though one in two rooms contains the fabric of reality.

00:23:00.320 How do we square these two things we square these two things because that way that intuition of thinking about probabilities as applied to infinite sets doesn't work.

00:23:13.320 I'll continue reading David writes mathematically this is nothing momentous.

00:23:18.320 The example merely demonstrates again that the attributes probable or improbable rare or common typical or untypical have literally no meaning in regard to comparing infinite sets of natural numbers.

00:23:30.320 But when we turn to physics it is bad news for anthropic arguments. Imagine an infinite set of universes all with the same laws of physics except that one particular physical constant let's call it D has a different value in each.

00:23:43.320 Strictly speaking we should imagine an uncountable infinity of universes like those infinitely thin cards but that only makes the problem I am about to describe worse so let us keep things simple.

00:23:55.320 Assume that of these universes infinitely many have values of D that produce astrophysic and infinitely many have values that do not.

00:24:04.320 Then let us number the universes in such a way that all those with astrophysic have even numbers and all the ones without astrophysic have odd numbers.

00:24:13.320 I'll just pause there before I go on now why would David talk about having a constant that leads to astrophysic.

00:24:21.320 Well people involved in or interested in SETI or who write about the possibility of intelligent life out there. They often confine their discussions to how do we detect astrophysic.

00:24:34.320 Why on earth would that be the measure of finding intelligence out there.

00:24:38.320 Well if you're looking for intelligence the best way that we know currently according to the SETI project anyways to listen.

00:24:46.320 To listen to in particular radio signals coming from deep space.

00:24:51.320 And if you're listening for radio signals you're probably listening for people who are deliberately sending them in our direction and they'd probably be some kind of astrophysic.

00:25:07.320 This does not mean that half the universes have astrophysic.

00:25:10.320 Just as with the book distribution in infinity hotel we can equally well label the universes so that only every third universe or every trillionth one had astrophysic.

00:25:21.320 So there is something wrong with the anthropic explanation of the fine-tuning problem.

00:25:24.320 We can always make fine-tuning go away just by relabeling the universes.

00:25:29.320 At our whim we can number them in such a way that astrophysic seem to be the rule or the exception or anything in between.

00:25:36.320 Now suppose that we calculate using the relevant laws of physics with different values of D.

00:25:44.320 We find values of D outside the range from say 137 to 138.

00:25:49.320 Those that contain astrophysic as a very sparse.

00:25:52.320 Only one in a trillion such universes has astrophysic.

00:25:56.320 Okay this is a complete diversion by me but it's an area I'm interested in so indulge me for a moment.

00:26:13.320 The 137 to 138 is actually the reciprocal of what is known as the fine structure constant.

00:26:19.320 And so I'll just mention that very very quickly as to what the fine structure constant is for anyone else who happens to be interested in astrophysics.

00:26:28.320 So the fine structure constant is known as alpha and alpha is unique, not unique.

00:26:37.320 But it's special because it is something called a dimensionless constant.

00:26:41.320 And it's actually a constant that's made up of other really cool constants.

00:26:46.320 So the charge on an electron squared divided by Planck's constant multiplied by the speed of light.

00:26:55.320 Now the dimensions of that, well it has, it's dimensionless because it has no units.

00:27:02.320 So this isn't in terms of meters per Coulomb or kilograms or anything like that.

00:27:08.320 The constants all cancel out and so you end up with just a number.

00:27:14.320 And what's often used is one over alpha and one over alpha happens to have the value very close to 137.

00:27:24.320 So I think it is checking the internet right now.

00:27:40.320 And the fine structure constant among other things determines the strength of the electromagnetic force.

00:27:49.320 And the uncertainty in this number here is extremely small.

00:27:53.320 So we can measure the fine structure constant really well.

00:27:56.320 It's called the fine structure constant because when you look at things like emission spectra made up of these bright lines when you pass light,

00:28:03.320 let's say coming from a star through something through a telescope and then through a thing called a spectroscope.

00:28:08.320 And you split it up into all the colors of the rainbow or whatever the colors coming from the star happen to be.

00:28:14.320 You notice that there is a fine structure to those lines and the fine structure constant gives us a way of the distance between these lines can give us a measure of what the fine structure constant actually is.

00:28:31.320 And so we can measure the fine structure constant here in the laboratory on earth in stars that are near to us in the galaxy.

00:28:38.320 And in stars and quasars on the other side of the universe. And this is what certain astrophysic is doing.

00:28:45.320 They're trying to measure whether or not the fine structure constant has changed over time because if it did, that would suggest something more rather remarkable.

00:28:52.320 It would suggest that the laws of physics are not precisely the same here on earth as they are on the other side of the universe.

00:28:58.320 For a while there we thought we had found a difference in the fine structure constant.

00:29:02.320 But the fact is that that was shown to be systematic error in the experiment. But if the fine structure constant was changing, then the explanation for a changing fine structure constant over time could mean that Planck's constant had changed.

00:29:17.320 The speed of light had changed or that the charge, the elementary charge on an electron had changed.

00:29:23.320 And any one of those three things would be remarkable. Perhaps all three could be changing, but the simple fact is it's rather boring conclusion to the moment. There is no such evidence for a changing fine structure constant.

00:29:35.320 So that's where the number 137, I'm guessing, has come from. It doesn't seem like an accident to me.

00:29:42.320 All right. Okay, so I'll just repeat what I've read there, David wrote, we find that for values of D outside the range of 137 to 138, those that contain astrophysicists are very sparse.

00:29:55.320 Only one in a trillion such universities has astrophysicists. Within the range, only one in a trillion does not have astrophysicists.

00:30:03.320 And for values of D between 137.4 and 137.6, they all do. Okay, so this seems to suggest that the value of D, Alpha, is key to whether or not a particular universe is going to have astrophysicists.

00:30:22.320 Going to have the conditions right, astrophysicists. Let's keep on moving, David writes, let me stress that in real life we do not understand the process of astrophysicists formation remotely well enough to calculate such numbers.

00:30:32.320 And perhaps we never shall as I shall explain in the next chapter.

00:30:35.320 But whether we could calculate them or not, and Tropic theorists would wish to interpret such numbers as mean that if we measure D, we are unlikely to see values outside the range from 137 to 138.

00:30:47.320 But they mean no such thing for we could just relabel the universes, shuffle the infinite pack of cards to make the spacings exactly the other way around or anything else we liked.

00:30:59.320 So this is really important for people interested in questions about fine structure as a layperson I am interested in that question.

00:31:06.320 There's been a lot of books written on this topic. And this is an important factor keep in mind that many people have written books on this topic do not grapple with.

00:31:18.320 But there is this mathematical argument about the way in which we can order this infinite set.

00:31:27.320 And that just because we find outside of the range for some particular constant that it is highly unlikely, apparently, for something like astrophysicist to emerge to evolve to be possible in those universes.

00:31:43.320 A reordering of that infinite set because when we're talking about possible universes with different physical laws, what we're actually talking about is a class of universes, an uncountably large class of universes.

00:31:57.320 And so we could reorder those universes in whatever order we like, such that the astrophysicist appear probable or improbable.

00:32:05.320 And David goes on and he talks about Lee Smolens idea about how black holes could themselves give rise to new universes, which is an interesting idea.

00:32:23.320 And just move right to the end of this section, not this chapter, but this section where David writes, none of the anthropic reasoning theories that have been proposed to solve the fine-shinning problem provides any such measure.

00:32:37.320 Most are hardly more than speculations of the form.

00:32:42.320 What if there were universes with different physical constants?

00:32:45.320 There is, however, one theory in physics that already describes a multiverse for independent reasons. All its universes have the same constants of physics.

00:32:54.320 And the interactions of those universes do not involve travel to or measurement of each other.

00:33:03.320 That theory is quantum theory, which I shall discuss in chapter 11, skipping a very short part and David writes.

00:33:11.320 Infinite means something like bigger than any finite combination of finite things, but that informal motion is rather circular.

00:33:17.320 Unless we have some independent idea of what makes something finite and what makes a single act of combination finite.

00:33:24.320 The intuitive answer would be anthropocentric. Something is definitely finite if it could be in principle being encompassed by a human experience.

00:33:36.320 Was Kantor experiencing infinity when he proved theorems about it? Or was he experiencing only symbols?

00:33:42.320 But we only ever experience symbols. One can avoid this anthropocentrism by referring instead to measuring instruments.

00:33:49.320 A quantity is definitely neither infinite nor infinitesimal if it could in principle register on some measuring instrument.

00:33:56.320 However, by that definition a quantity can be finite even if the underlying explanation refers to an infinite set in a mathematical sense.

00:34:03.320 To display the result of a measurement, the needle on a meter might move by one centimeter, which is a finite distance.

00:34:08.320 But it consists of an uncountable infinity of points.

00:34:12.320 This can happen because although points appear in lowest level explanations of what is happening, the number of points never appears in predictions.

00:34:22.320 Just pausing that just to highlight that. That will become important in a moment when we get to the paradoxes of zino.

00:34:27.320 So I'll say that again that although points appear in lowest level explanations of what is happening, the number of points never appears in predictions.

00:34:38.320 Continuing. Physics deals in distances, not numbers of points.

00:34:44.320 Similarly, Newton and Liebnerts were able to use infinitesimal distances to explain physical quantities like instantaneous velocity.

00:34:51.320 Yet there is nothing physically infinitesimal or infinite in say the continuous motion of a projectile.

00:35:02.320 Only the laws of physics determine what is finite in nature.

00:35:07.320 Failure to realize this is often caused confusion.

00:35:10.320 The paradoxes of zino of elia, such as that of the Achilles and the tortoise were early examples.

00:35:15.320 Zino managed to conclude that in a race against the tortoise, Achilles will never overtake the tortoise if it has a head start.

00:35:22.320 Because by the time Achilles reaches the point where the tortoise began, the tortoise will have moved on a little.

00:35:29.320 By the time he reaches that new point, it will move on a little further. And so on. Add infinite.

00:35:34.320 Thus the catching up procedure requires Achilles to perform an infinite number of catching up steps in a finite time, which as a finite being he presumably cannot do.

00:35:44.320 So I'll pause there. Let's refer back to what was just said.

00:35:49.320 Physics deals in distances, not number of points.

00:35:54.320 This is the solution to zino of elia's conundrum that he was in.

00:36:00.320 Now I used to argue that there were two ways of going about this.

00:36:04.320 On the one hand you can talk about adding up that I had that sequence up before.

00:36:08.320 Let's say you want to traverse a total distance of two meters.

00:36:15.320 Well first you have to walk one meter and then you have to walk 0.5 meters and then 0.25 meters and then 0.125 meters, etc.

00:36:22.320 And so it would appear that given that each individual step taken takes a finite amount of time and there's an infinite number of steps.

00:36:31.320 Then no matter how short the amount of time given there's an infinite number of steps required, each requiring a finite amount of time, it's going to take an infinite amount of time to move two meters.

00:36:45.320 The mathematical argument is well you can add up 1 plus 0.5 plus 0.25 plus 0.125, etc. etc. and get to 2.

00:36:55.320 Similarly all you're really arguing is that you're taking your two meters or whatever happens to be, the distance of two and you're splitting it up into an infinite number of points.

00:37:07.320 The resolution to any of this, to any time we have a supposed paradox of being able to move through an infinite number of points, but each step along the way taking a finite amount of time, adding up to an infinite amount of time, therefore making motion impossible.

00:37:24.320 Is that your not physics is not does not deal in infinite numbers of points, physics deals and distances.

00:37:33.320 And if you want to get from point A to point B, that's a distance and that will take you a certain amount of time.

00:37:38.320 What's not going on is you actually taking time to go an infinite number of points.

00:37:46.320 That's the incorrect way of putting the problem. Let's return to the book, which explains it far more clearly than I did.

00:37:55.320 Did you see what Zino did there? He just presumed that the mathematical notion that happens to be called infinity faithfully captures the distinction between finite and infinite, that is relevant to that physical situation, that is simply false.

00:38:09.320 If he is complaining that the mathematical notion of infinity does not make sense, then we can refer into Kantor, who showed that it does.

00:38:17.320 If he is complaining that the physical event of Achilles overtaking the tortoise does not make sense, then he is claiming that the laws of physics are inconsistent, but they are not.

00:38:26.320 But if he is complaining that there is something inconsistent about motion, because one could not experience each point along a continuous path, then he is simply confusing two different things that both happen to be called infinity.

00:38:38.320 There is nothing more to all these paradoxes than that mistake.

00:38:42.320 What Achilles cannot do is not deducible from mathematics.

00:38:46.320 It depends only on what the relevant laws of physics say. If they say he will overtake the tortoise in a given time, then overtake it he will.

00:38:53.320 If that happens to involve an infinite number of steps of the form, move to a particular location, then an infinite number of such steps will happen.

00:39:00.320 It involves his passing through an uncountable infinity of points, then that is what he does, but nothing physically infinite has happened.

00:39:09.320 Thus the laws of physics determine the distinction not only between rare and common probable and improbable fine-tuned or not, but even between finite and infinite.

00:39:19.320 Just as the same set of universes can be packed with astrophysicists when measured under one set of laws of physics, but have almost none when measured under another, so exactly the same sequence of events.

00:39:29.320 In general terms, the mistake is to confuse an abstract attribute with the physical one of the same name.

00:39:33.320 Since it is possible to prove theorems about the mathematical attribute, which have the status of absolutely necessary truths, then one is misled into assuming that one possesses up pre-order knowledge about what the laws of physics must say about the physical attribute.

00:39:56.320 Pause in there, David mentions absolutely necessary physical truths.

00:40:02.320 As he says in the fabric of reality, as he says in this chapter very shortly, and as he said in his Dirac medal award ceremony speech, the mathematics, mathematicians misconception.

00:40:15.320 A common theme amongst David's work absolutely necessary truths exist, and that is what mathematics is the study of.

00:40:26.320 But our knowledge of those absolutely necessary truths are not absolutely necessary truths.

00:40:33.320 That sounds too clever by half, but all it means is that our knowledge of anything is infallible.

00:40:40.320 And even though mathematics is a study of things that are not fallible, just as in physics, our study of the laws of physics are the study of things that are perfect.

00:40:54.320 They're out there, they have a certain final form, they are the laws that govern the universe.

00:41:04.320 Our knowledge of those laws are not those laws, the knowledge and the thing in reality are two quite different things.

00:41:16.320 The knowledge that we produce is always error, we contain errors, but it can be about things that are absolutely necessarily true.

00:41:27.320 I'm skipping a fair bit more of this chapter now. I'm skipping a significant part again now, and we're moving on to a section about the relationship between computation and mathematics and physics.

00:41:43.320 David writes, Turing initially set up the theory of computation, not for the purpose of building computers, but to investigate the nature of mathematical proof.

00:41:53.320 Hilbert in 1900 had challenged mathematicians to formulate a rigorous theory of what constitutes a proof.

00:41:59.320 And one of these conditions was that proofs must be finite.

00:42:03.320 They must use only a fixed and finite set of rules of inference.

00:42:07.320 They must start with the finite number of finitely expressed axioms, and they must contain only a finite number of elementary steps.

00:42:17.320 Computations, as understood in Turing's theory, are essentially the same thing as proofs.

00:42:21.320 Every valid proof can be converted into a computation that computes the conclusion from the premises.

00:42:27.320 And every correctly executed computation is a proof that the output is the outcome of the given operations of the input.

00:42:34.320 Now a computation can be thought of as computing a function that takes an arbitrary natural number as its input and delivers an output that depends in a particular way on that input.

00:42:44.320 So, for instance, doubling a number is a function. Infinity Hotel typically tells guests to change rooms by specifying a function and telling them,

00:42:53.320 and telling them all to compute it with different inputs, their room numbers.

00:42:57.320 One of Turing's conclusions was that almost all mathematical functions that exist logically cannot be computed by any program.

00:43:05.320 For the same reason that most logically possible reallocations of rooms in infinity hotel cannot be affected by any instruction by the management.

00:43:13.320 The set of all functions is uncountably infinite, while the set of all programs is merely countably infinite.

00:43:19.320 That is why it is meaningful to say that almost all members of the infinite set of functions have a particular property.

00:43:24.320 And also, as the mathematician code Girdle had discovered using a different approach to Hilbert's challenge,

00:43:31.320 almost all mathematical truths have no proofs. They are unprovable truths.

00:43:37.320 It also follows that almost all mathematical statements are undecidable.

00:43:41.320 There is no proof that they are true, and no proof that they are false.

00:43:45.320 Each of them either is true or false, but there is no way of using physical objects such as brains or computers to discover which is which.

00:43:52.320 The laws of physics provide us only with a narrow window through which we can look out on the world of abstractions.

00:43:59.320 All undecidable statements are directly or indirectly of our infinite sets.

00:44:03.320 To the opponents of infinity in mathematics, this is due to the meaninglessness of such statements,

00:44:08.320 but to me, it is a powerful argument, like Hofstra at a 641 argument that abstractions exist objectively.

00:44:16.320 For it means that the truth value of an undecidable statement is certainly not just a convenient way of describing the behaviour of some physical object like computer, or a collection of dominoes.

00:44:26.320 Interestingly, very few questions are known to be undecidable, even though most are, and I'll show a return to that point.

00:44:32.320 But there are many unsolved mathematical conjectures, and some of those may well be undecidable.

00:44:40.320 A prime pair is a pair of numbers that differ by two, such as five and seven.

00:44:45.320 The conjecture is that there is no largest prime pair, that there are infinitely many of them.

00:44:51.320 Suppose for the sake of argument, that is undecidable, using our physics.

00:44:56.320 Under many other laws of physics, it is decidable.

00:45:02.320 Again, the details of how the management would settle the prime pairs issue, and not essentially to my argument.

00:45:06.320 But I present them here for the benefit of mathematically minded readers.

00:45:10.320 Okay, so I'll go through this briefly, and then I'll explain a little about at least my interpretation of what I think.

00:45:18.320 The point is here about how if the laws of physics were different, or given the laws of physics we do have in this universe, how we can prove different things based upon the laws of physics.

00:45:37.320 They are the things that permit what can possibly be predicted within our universe.

00:45:41.320 And given that other universe, with different amino, a universe of different laws entirely, we could prove different things.

00:45:50.320 Okay, so David writes, this is how you would prove the prime pairs conjecture in a different universe.

00:45:57.320 Namely, the universe in which we find infinity hotel.

00:46:03.320 First, please check within the next minute whether your room number and the number to above it are both primes.

00:46:12.320 Next, if they are, send a message back through lower numbered rooms saying that you have found a prime pair.

00:46:20.320 Use the usual method for sending rapid messages.

00:46:23.320 Now one minute for the first step, and thereafter each step must be completed in half the time of the previous one.

00:46:30.320 Store a record of this message in the lowest numbered room that is not already storing a record of a previous such message.

00:46:38.320 Next, check with the room number one more than yours.

00:46:42.320 If that guest is not storing such a record as you are, then send the message to room one saying there is a largest prime pair.

00:46:51.320 Okay, at the end of five minutes, the management would know that true for the prime pairs conjecture.

00:46:56.320 So there is nothing mathematically special about the undercitable questions, the non-computable functions.

00:47:06.320 Different physical laws would make different things infinite.

00:47:12.320 Different truths, both mathematical and scientific knowable.

00:47:15.320 It is only the laws of physics that determine which abstract entities and relationships are modeled by physical objects,

00:47:20.320 such as mathematicians, brains, computers, and sheets of paper.

00:47:26.320 So what we saw there, if we have got an infinity hotel, which does not obey the laws of physics, we could prove the prime pairs conjecture, which we have no proof of here,

00:47:41.320 In infinity hotel, why does it have different laws of physical?

00:47:45.320 Well, one thing is an infinite number of steps can be completed, which requires energy in a finite amount of time.

00:47:54.320 Within five minutes, we can do an infinite number of steps, and presumably we are moving also, as we get towards the end of the computation,

00:48:02.320 well beyond the speed of light, asymptotically close to infinite speed.

00:48:08.320 That violates many laws of physics. Number one, probably, number one, it exceeds the speed of light.

00:48:18.320 The faster that we start to move, the more our momentum increases and our mass increase in the energy required to complete these, this is relativity, right?

00:48:28.320 The more energy required in order to move faster and faster and faster.

00:48:34.320 We can't do any of this, this is why infinity hotel has different physical laws, skipping a little again, and David writes.

00:48:41.320 But if the laws of physics were in fact different from what we currently think they are, then so might be the set of mathematical truths,

00:48:47.320 we would then be able to prove, and so might the operations that would be available to prove them with.

00:48:52.320 The laws of physics, as we know them, happen to afford a privileged status to such operations as not, and, and all,

00:48:59.320 acting on individual bits of information, binary digits, or logical true, true false values.

00:49:04.320 That is why those operations seem natural, elementary, and finite to us.

00:49:08.320 And why bit to, if the laws of physics were like, say those of infinity hotel,

00:49:13.320 there would be no additional privileged operations acting on infinite sets of bits.

00:49:17.320 With some other laws of physics, the operations not, and, and, or would be non-computable.

00:49:22.320 By some of our non-computable functions would seem natural, elementary, and finite.

00:49:27.320 That brings me to another distinction that depends on the laws of physics.

00:49:33.320 Brains are physical objects, thoughts are computations, of the types permitted under the laws of physics.

00:49:40.320 Some explanations can be grasped quickly and easily.

00:49:44.320 Like, if Socrates was a man, and Plato was a man, then both were men.

00:49:49.320 This is easy because it can be stated in a short sentence in a reliance on the properties of an elementary operation,

00:49:54.320 namely, and other explanations are inherently hard to grasp.

00:49:58.320 Because their shortest form is still long and depends on many such operations,

00:50:02.320 but whether the form of an explanation is long or short,

00:50:05.320 whether it requires few or many elementary operations,

00:50:08.320 depends entirely on the laws of physics under which it is being stated and understood.

00:50:12.320 Quantum computation, which is currently believed to be the fully universal form of computation,

00:50:17.320 happens to have exactly the same set of computable functions as Turing's classical computation.

00:50:23.320 But quantum computation drives a coach and horses through the classical notion of simple or elementary operation.

00:50:29.320 It makes some intuitively very complex things simple,

00:50:33.320 moreover the elementary information storing entity in quantum computation, the qubit,

00:50:38.320 quantum bit, is quite hard to explain in non-quantum terminology.

00:50:43.320 Meanwhile, the bit is a fairly complicated object from a perspective of quantum physics.

00:50:48.320 I'll just pause there, just a very brief comment on that section there,

00:50:52.320 where David wrote, Quantum computation, which is currently believed to be the fully universal form of computation,

00:50:58.320 happens to have exactly the same set of computable functions as Turing's classical computation.

00:51:04.320 That's an important note to make about quantum computation.

00:51:09.320 There is this misconception out that the quantum computers can actually compute a wider range,

00:51:15.320 have a greater repertoire of different computations than Turing's computation does.

00:51:23.320 A universal Turing computer can compute anything that a quantum computer can.

00:51:31.320 It's just that in many, many cases, the Turing computer would take,

00:51:35.320 even if it was operating at switching speeds at the speed of light,

00:51:39.320 and it had infinite memory, and the entire universe was a classical computer,

00:51:44.320 it wouldn't be able to reach the end of that computation within trillions of years.

00:51:49.320 Although it could do it, given an infinite amount of time,

00:51:53.320 it would eventually get to the end of the computation.

00:52:00.320 It's not efficient for certain types of problems.

00:52:03.320 The quantum computer is more efficient for certain kinds of problems

00:52:10.320 They can both compute the same overall number of kinds of computation.

00:52:16.320 They both operate on laws of physics in this universe.

00:52:21.320 The set of all possible computations is the same for both classical and quantum computers,

00:52:27.320 but the quantum computers are faster, much faster, for a certain set of computations.

00:52:34.320 So skipping a bit and David returns to a discussion about the mathematicians' misconception.

00:52:41.320 I really like this stuff, because it is such a misconception.

00:52:46.320 I don't think it's just a mathematicians' misconception.

00:52:51.320 therefore it's mathematics students' misconception,

00:52:56.320 because everyone's been indoctrinated with the stuff at school.

00:53:02.320 Whether a mathematical proposition is true or not,

00:53:09.320 but the proof of such a proposition is a matter of physics only.

00:53:13.320 There is no such thing as abstractly proving something,

00:53:16.320 just as there is no such thing as abstractly knowing something.

00:53:19.320 Mathematical truth is absolutely necessary and transcendent,

00:53:22.320 but all knowledge is generated by physical processes,

00:53:26.320 and its scope and limitations are conditioned by the laws of nature.

00:53:29.320 One can define a class of abstract entities and call them proofs or computations,

00:53:33.320 just as one can define abstract entities and call them triangles

00:53:39.320 But you cannot infer anything from that theory of triangles

00:53:43.320 if you walk around a closed path consisting of three straight lines.

00:53:47.320 Nor can those proofs do the job of verifying mathematical statements.

00:53:51.320 A mathematical theory of proofs has no bearing on which truths can or cannot be proved in reality,

00:54:01.320 has no bearing on what can or cannot be computed in reality.

00:54:05.320 So a computation or a proof is a physical process,

00:54:08.320 in which objects such as computers or brains physically model

00:54:11.320 or instantiate abstract entities like numbers or equations

00:54:18.320 It works because we use such entities only in situations

00:54:23.320 that the relevant physical variables in those objects

00:54:25.320 do indeed instantiate those abstract properties.

00:54:28.320 Consequentially, the reliability of our knowledge of mathematics

00:54:32.320 remains forever subsidiary to that of our knowledge of physical reality.

00:54:38.320 Every mathematical proof depends absolutely for its validity

00:54:42.320 on our being right about the rules that govern the behaviour

00:54:45.320 of some physical objects like computers or ink and paper or brains.

00:54:49.320 So contrary to what Hilbert thought and contrary to what most mathematicians

00:54:53.320 since antiquity have believed and believed to this day,

00:54:56.320 proof theory can never be made into a branch of mathematics.

00:55:05.320 The whole motivation for seeking a perfectly secure foundation

00:55:12.320 Mathematics is characterized by its use of proofs

00:55:20.320 In neither case is that the object of the exercise.

00:55:23.320 The object of mathematics is to understand or explain abstract entities.

00:55:28.320 Proof is primarily a means of ruling out false explanations.

00:55:31.320 And sometimes it also provides mathematical truths

00:55:36.320 But like all fields in which progress is possible,

00:55:38.320 mathematics seeks not random truths but good explanations.

00:55:43.320 Three closely related ways in which the laws of physics

00:55:49.320 in terms of a single finite set of elementary operations.

00:55:52.320 They all share uniform distinction between finite and infinite operations.

00:55:56.320 And their predictions can all be computed by a single physical object

00:56:05.320 one would need a one would in general need a quantum computer.

00:56:09.320 It is because the laws of physics support computational

00:56:13.320 and explain the behavior of very unhuman objects like quasars.

00:56:20.320 that mathematicians like Hilbert can build up an intuition of proof.

00:56:23.320 And must technically think that it is independent of physics.

00:56:28.320 It is merely universal in the physics that governs our world.

00:56:31.320 If the physics of quasars will like the physics of infinity hotel

00:56:34.320 and dependent upon the functions that we call non-computable,

00:56:44.320 With the laws of physics slightly more exotic than that,

00:56:47.320 we would not be able to explain anything and hence could not exist.

00:57:05.320 The physicist Eugene Wigner called this the unreasonable effectiveness

00:57:21.320 for what explains the unreasonable effectiveness

00:57:29.320 This is the argument that we are living inside of a simulation

00:57:33.320 and because a simulation would be based on software,

00:57:39.320 we should therefore expect that mathematics works inside of nature,

00:57:50.320 It's an infinite regress because what we really want to know is

00:58:03.320 who created God and apparently will not let us ask that question.

00:58:06.320 Well, if we're a simulation, on what computer are we running?

00:58:20.320 They are moving the problem from where it actually is

00:58:31.320 David writes about the limitations about what we can know.

00:58:36.320 And he says, how do all those drastic limitations

00:58:44.320 including the existence of the undecidable questions

00:58:46.320 in mathematics, square with the maxim that problems are soluble?

00:58:57.320 abstractly never appear as the subject of such a conflict.

00:59:06.320 about some attribute of the world of abstractions.

00:59:25.320 One does not understand a mathematical proposition

00:59:29.320 This is why there are such things as mathematics lectures

00:59:35.320 does not necessarily prevent a proposition from being understood.

00:59:42.320 to understand something about the abstraction in question,

00:59:45.320 and then to use that understanding to conjecture

00:59:47.320 how true propositions about the abstraction might be proved

1:00:04.320 One such example is the conjecture known in the jargon

1:00:16.320 but cannot be computed efficiently in the first place

1:00:22.320 that roughly approximates to what we mean by the phrase

1:00:34.320 that mathematical knowledge consists only of proofs.

1:00:40.320 there are fairly good explanations of why we should expect it

1:00:45.320 And so the same is thought to hold for quantum computers.

1:00:49.320 Moreover, a vast amount of mathematical knowledge

1:00:54.320 It includes theorems of the form if the conjecture is true

1:01:01.320 Theorems about what would follow if it were true.

1:01:04.320 Skipping a little bit, so David is emphasizing here how

1:01:16.320 there are statements that one can write down in mathematics

1:01:37.320 Then does the fact that there are truths about the physical world

1:01:41.320 I expect that one day we shall have the technology

1:01:43.320 to measure the number of grains of sand on earth exactly.

1:01:51.320 Indeed, I've already mentioned more drastic limitations

1:02:14.320 may never cause an unresolved conflict of explanations.

1:02:31.320 So three corollaries follow from this conjecture.

1:02:43.320 and what is boring is not a matter of subjective taste

1:02:47.320 And the third corollary is that the interesting problem

1:02:55.320 At present, we do not know why the laws of physics

1:02:58.320 and we do not know why the various forms of universality exist

1:03:01.320 that we do know many of the connections between them.

1:03:08.320 And when we do, there will be infinitely more left to explain.

1:03:15.320 on knowledge creation is that we cannot prophesy.

1:03:23.320 The limitation is not only consistent with the unlimited growth of knowledge

1:03:26.320 it is entailed by it as I shall explain in the next chapter.

1:03:32.320 I saw an advertisement for David Attenborough's latest documentary.

1:03:44.320 David Attenborough went to something that was terribly pessimistic.

1:03:52.320 And many nature documentaries now are terribly pessimistic.

1:03:56.320 And the thrust of one of the latest documentaries

1:04:02.320 In fact, this is a common theme now running through David Attenborough documentaries.

1:04:07.320 Is the natural world is swiftly coming to an end.

1:04:16.320 That something needs to be done in order to prevent

1:04:19.320 the virus that is human beings and technology and progress

1:04:26.320 In particular, when it comes to the very real problem of climate change

1:04:36.320 and the melting of Antarctica and rising sea levels,

1:04:46.320 if I went to a urologist and asked if I had cancer

1:04:55.320 I believe that the urologist has gone through sufficient training

1:05:06.320 of trying to figure out the truth of the situation.

1:05:14.320 that has led to the diagnosis of me having cancer.

1:05:23.320 of all these scientists, these climate scientists

1:05:27.320 and people who are checking the data have gotten the data right.

1:05:32.320 I could spend the time to go and check the data if I wanted to.

1:05:35.320 It doesn't seem of all the problems that are out there.

1:05:40.320 I am not animated that this is one of the most pressing problems of all.

1:05:45.320 There are many, many pressing problems from terrorism

1:05:51.320 to the sun suddenly doing something that we didn't expect.

1:06:06.320 So yes, absolutely anthropocentric climate change is a real thing

1:06:22.320 to anthropocentric climate change is encapsulated there in that paragraph.

1:06:30.320 It says, the most important of all limitations on knowledge creation

1:06:35.320 We cannot predict the content of ideas yet to be created later effects.

1:06:51.320 and this goes all the way back to when David Gabbier's first TED talk.

1:06:55.320 I mean, this is a decade now and no progress seems to have happened.

1:07:00.320 The solution appears to be to slow progress, literally to slow progress.

1:07:20.320 But this is not claimed to actually solve climate change,

1:07:26.320 Anyone can look up the modeling that if we were to reduce our use of fossil fuels

1:07:34.320 then the temperature of the Earth will still increase

1:07:36.320 because the amount of carbon dioxide will still increase.

1:07:43.320 which would cost more money than possibly the globe has,

1:07:48.320 but let's say we did, the temperature would still increase.

1:07:52.320 The polarized caps would still melt, the sea levels would rise.

1:08:02.320 So these are not solutions. So what should we do?

1:08:05.320 Well, one thing we should do is to actively cool the globe.

1:08:16.320 We could manufacture mirrors and put them in space.

1:08:24.320 But possibly more importantly, if the solution is,

1:08:29.320 if the problem is, the temperature is rising too much,

1:08:35.320 So therefore the solution is reduce the temperature.

1:08:39.320 Then what we need is knowledge about how to do that.

1:08:46.320 The more knowledge we can produce, the faster we can produce,

1:08:48.320 and the cheaper and more efficiently we can produce it, the better.

1:08:52.320 We don't know how we're going to figure out fusion.

1:08:57.320 I would hedge my bets and say fusion is physically possible here on Earth.

1:09:04.320 We know it's possible on the Sun, so if we could figure out a way to do it on Earth, fantastic.

1:09:10.320 Once we have small fusion reactors here on Earth,

1:09:14.320 the game over, problem solved. We don't have to worry about any other kind of form of energy.

1:09:19.320 Fossil fuel or wind power, solar power will have fusion power.

1:09:28.320 When the argument is given to us that we must move from fossil fuels

1:09:34.320 to other kinds of energy, not to solve climate change,

1:09:38.320 but merely to slow it down, people are engaged in prophecy.

1:09:42.320 What they're saying is that there is no other alternative,

1:09:47.320 that the knowledge to solve climate change will not be created.

1:09:54.320 where the only possible response to climate change

1:10:17.320 does not mean that we already know their solutions,

1:10:31.320 All kinds of creative thought involve judgments about what approaches might or might not work.

1:10:35.320 Gaining or losing interest in particular problems or sub-problems

1:10:38.320 is part of the creative process and itself constitutes problem solving.

1:10:44.320 does not depend on whether any given question can be answered,

1:10:47.320 or answered by any particular thinker on a particular day.

1:10:51.320 But if progress ever depended on violating a law or a physics,

1:11:10.320 took much longer to produce than any of the others.

1:11:19.320 I'm kind of buoyed by the fact that some of my favourite podcasts

1:11:23.320 that are out there actually are more infrequent even than minor.

1:11:34.320 that people are encouraging me to make these more frequently.

1:11:43.320 so another year in where we basically threw the entire book

1:12:00.320 It's going to be a diversion away from the beginning of an affinity,

Chapter 8, Part 2 "A Window on Infinity" from "The Beginning of Infinity" - some remarks.