Conscious Page 16

  “Mr. Weatherill and I,” she introduced Bob with a wave, “are taking some readings of PDN for the government.” She omitted to mention any particular government, which Bob considered to be wise as he hardly felt they knew. “Mr. Weatherill is one of the country’s top network specialists and he has equipment that may provide us with some insight.” Hattie – looking very much like some old kit to be disposed of on a trolley – was being wheeled by at that moment, to the evident astonishment of Dr. Sovel. “Beyond that, we can’t say, I’m afraid.” They all followed him to his team’s base room.

  Inside, a discussion ensued on what data they were trying to capture from the NoC although with considerably less emphasis on why. It was difficult. Dr. Sovel’s team were able to take basic electrical readings from the chip but the data was otherwise unstructured from a networking point of view. Bob doubted whether it would provide meaningful results but there was little point in not trying.

  Within an hour, Dr. Sovel had followed Jenny and Bob’s suggestions as best he could. The result was a huge MATLAB table of signals taken from a single central point in the chip’s logic layout. With minimal difficulty, this was converted and fed into Hattie, now reset to her original sixty-second run time. She was duly set off on her task and, after the regulation minute, reported:

  S = 0.562

  “Better,” suggested Jenny.

  “Better,” agreed Bob. “But probably still not enough. The problem is, we’re still isolated in a logical sense. Yes, the NoC has a fair bit of complexity itself but it’s still disconnected from the outside world – apart from being plugged into the mains. Also, I doubt the raw electrical data has captured all the essential message complexity that might be in there. It’s hard to spot self-similarity, for example, when the data’s pretty one-dimensional anyway – and there’s possibly no feedback showing. Maybe we’ll get some better figures somewhere else?”

  This was hardly the valediction Dr. Sovel was looking for in appreciation of his morning’s sacrifice. Despite Jenny’s profuse thanks and assurances of playing a small but vital role in their quest, he looked fairly cross as he locked the lab door behind them and hurried away.

  *

  Their next stop was at another London university. Jenny greeted an old colleague, Dr. Alice Colledge, at the entrance, introduced Bob with the same credentials as before and the three of them went to the nearest available I.T. lab. This was much closer to the kind of configuration the two of them were looking for. The hub for the lab would have logical complexity below it, from the host PCs and their internal circuitry, but was also connected, through the university’s routers and firewalls, to the outside world. Although that would still place them on the edge of It in global terms, everything was cabled: unlike most of the newer installations, there was no wifi to break the chain. They both diplomatically abstained from mentioning to Alice this lack of up-to-date kit as having such appeal for them.

  They switched everything on and Bob connected Hattie to one of the open ports from the hub and set her off on her minute’s run. When finished, she reported.

  S = 0.578

  Bob allowed a small grin to pass across his face. “Better still,” he observed. “Still not enough to go to Stephen with, I’d say, but it’s progress!” He was not finished though: there was another essential question. “I don’t suppose it’s possible to isolate this lab from the Internet, is it?”

  Alice looked around, particularly at the ducting leading from the hub through the wall.

  “Doesn’t look like it: not at this end, apart from breaking into that bit there.” She pointed. “Or finding the other end: that would involve getting someone from I.T. Services out of bed and, either way, they wouldn’t be happy!”

  “Rutherford next,” said Jenny.

  *

  Their journey to Didcot took longer but they were still there in time to take a hasty, late lunch with yet another of Jenny’s old colleagues, Professor Wilhelm Stengel, ‘Willie’ for short, now a senior member of the Rutherford Labs network team. They told him as much as they felt they could and he appeared sensible of not asking more. After lunch, he led them to the main switching room.

  “So, exactly what part would you like to test?” he asked helpfully.

  Jenny hesitated for once but Bob had already chosen his words.

  “We’d like to ‘look down’ on as much of the JANET network as possible, in a data sense, please. But from a position where there’s a direct line to the rest of the Internet. We’d like to see the maximum amount of data in and out: so some sort of major switching node would be ideal, if you can manage that?”

  “Of course,” Willie smiled. He led to one of the newer racks of equipment and unlocked the front panel. “I assume it will be convenient for you if I stay while you complete your tests?” he asked softly. “Naturally I am very responsible – and concerned – for this equipment and the role it performs.” They both nodded assent.

  “Do you need to know exactly what this node is?” asked Willie.

  “Not really,” Bob admitted after a brief tussle with his curiosity.

  “Good. Then I shall not tell you!” he replied with a curious smile.

  With Willie watching closely, Bob carefully plugged Hattie into one of the spare fibre optic ports on the main router’s front panel. A worrying thought occurred to him as he did so.

  “Will this interface auto-recognise the new connection? We won’t have to reconfigure the IOS will we?”

  “No, and no, Bob,” Willie replied quietly. “Although an alternative answer to the second question is that we would not let you, of course!”

  “That’s a relief,” admitted Bob. He stepped back and started Hattie. She sat processing, then displayed:

  S = 0.603

  “Is that enough for Stephen?” asked Jenny.

  “I don’t know,” admitted Bob, “but it’s beginning to convince me!”

  *

  Their final stop was in Cambridge. There was nothing particularly unusual about the network they were about to see other than a couple of features Jenny had determined the night before. The university had recently invested heavily in network infrastructure and all labs in the building they were visiting had fibre connections directly to the university’s main control room routers. Moreover, they had identified (without much difficulty) a lab that was unused over the vacation period. Dr. Clare Wheeler met them at the entrance and let them into the lab.

  They switched all of the equipment on and Bob connected Hattie to the fibre hub. After her minute, she reported:

  S = 0.590

  Jenny looked at Bob for a reaction.

  “No great surprise there,” he suggested calmly. “Not as high as JANET. Now, Clare, I understand you can disconnect this lab from the rest of the network? From the outside world? From the Internet?”

  “Of course,” she confirmed. “Nothing easier!” She reached under the main box and pulled out two fibre optic cables. Still holding them in her hands, she grinned, “I can’t say I know what you’re doing but I suppose you want to do it again now!”

  “Yes please,” agreed Bob, with a laugh and a trace of eagerness. He set Hattie off once more and they eventually read:

  S = 0.581

  “Now that,” stated Jenny with some force, “is significant!”

  Chapter 13: Degrees of Heresy

  While Jenny and Bob took Hattie on her regional tour, Aisha and Andy had had a quiet day in the city. After a brief walk around the sights, they had eaten lunch together and then seen a film – interrupted twice by RFS issues with the cinema equipment. They had then taken the tube most of the way back and stopped at a coffee shop a few hundred yards away from Jill and Bob’s house. Its staff were trying to combine serving customers with coping with a minor flood apparently caused by the water supply to one of the espresso machines refusing to shut off. It had been a pleasant day: the company had been good. But the conversation had been slightly limited: they were more than happy to leave the
‘techie stuff’ to the computer scientists for now and neither of them had attempted anything much beyond the superficial – although both had wanted to. Andy had never passed up an opportunity to congratulate Aisha on her Boxing Day ‘It revelation’ but such praise was always quickly and modestly rebuffed. Now, however, as the two sat quietly sipping cappuccino, Aisha took a longer look at Andy as he stared, possibly somewhat vacantly, across the street, but with his lips hinting at a slight smile.

  “Penny for your thoughts?” she suggested.

  He turned back to her; his grin deepened immediately but he took time to reply, as if looking for the right words.

  “Not much, really. I was just thinking about what we’re trying to do with this ‘measuring It’ thing.”

  “And are you comfortable with it … or It?”

  “Oh, aye; certainly! The thing I like about it is that we’re not really trying to determine what It is; we’re just measuring if It’s there, based on how we think It might behave. No assumptions: it’s sort of philosophy-independent!”

  “What?”

  “Well, I mean we can calculate how It might behave, what sort of numbers we might see when we measure It; then we can measure It and we’ll either be right or wrong but that won’t actually take us any closer to knowing what It is. Is It just an innate scientific product of complexity? Or does It have a soul? We can be either right or wrong without knowing that. I sort of like that.”

  Aisha shook her head slightly. “No, as a scientist, I like to know what I am working with; I am not comfortable with uncertainty.”

  “But you have to be! We’re surrounded by it. Our world, and what we know about it is framed by uncertainty. Even science.”

  “You think so?”

  “Aye, we can’t avoid it. There’s lots we don’t know and lot’s we’ll never know. We have no choice in that. The only power we have is in deciding how to deal with it.” He reached into his conference bag: he was still using the one from Luxembourg. He took out his tablet and jabbed at the screen a few times.

  “Here, take a look at this. This is from the blog of a friend of mine, Ruth Jones. She describes herself as a ‘technological philosopher’. Bit over-the-top but she sometimes comes out with some good stuff. This is her post from last month.”

  He passed the tablet to Aisha, who read quickly:

  “Known Unknowns”

  This month’s post may make a valid point. Or it may not. Or it may be impossible to tell, the concept of which itself may or may not make sense by the end of the piece!

  How do we handle things we don’t know? More precisely, how do we cope with things we know we don’t know? All right then: how do we handle things we know we can’t know?

  The examples we’re going to discuss are (at first, at least) taken from mathematics; but there are plenty of analogies in the other sciences. This certainly isn’t a purely theoretical discussion.

  On the whole, we like things (statements or propositions) in mathematics (say) to be right or wrong: true or false. Some simple examples are:

  The statement “2 > 3” is false

  The statement “There is a value of x such that x < 4” is true

  The proposition “There are integer values of x, y and z satisfying the equation x3 + y3 = z3” is false. (Part of ‘Fermat’s Last Theorem’)

  OK, that’s pretty straightforward but how about this one?

  “Every even number (greater than 2) is the sum of two prime numbers”

  Now, we can start off by trying this out easily enough. Working up: 4 = 2 + 2; 6 = 3 + 3; 8 = 3 + 5. Jumping in at random, 100 = 11 + 89 (and a number of other ways) so it looks promising.

  In fact, this Goldbach’s Conjecture (GC) has been shown by calculation (computation) to be true for a huge range of even numbers, and no-one’s ever found an example where it’s not.

  However, that’s not quite the same thing as proving it’s always true. We’d need a cleverer logical argument for that (because we can’t try out an infinite number of numbers individually) and no-one’s managed that yet.

  So, at the moment, we don’t actually know if GC is true or false. If someone can supply the general proof, it will be true; if anyone finds an exception (an even number, which isn’t the sum of two primes) then it’s false.

  Or something else might happen …

  Let’s take another example …

  Without going into fine mathematical detail, there are obviously an infinite number of whole numbers (integers), positive or negative. We can think of the set of these numbers as having a certain (infinite) size.

  Somewhat counter-intuitively, if we then extend the integers to include the fractions (1/3, 11/4, etc.), then, although we might argue that there are more of them, in a strictly mathematical sense, the set of fractions has the same (infinite) size as the set of integers because we can set up a direct one-to-one mapping from the integers to the fractions. (You might need to look that bit up: it’s too much for this post.)

  Now, we might attempt to regain some sanity here by suggesting this is so because there’s only really one infinity. However, this line of reasoning falls apart when we look at the set of all numbers (the reals), now including all the things that can’t be expressed as fractions (√2, π, etc.).

  Because it turns out we can’t set up a one-to-one mapping from the integers to the reals so we have to conclude that we’re dealing with a different infinity. If the set of integers is of a certain infinite size, then the set of reals is a different infinite size. And, once we’ve managed this, it emerges that it doesn’t stop there. In fact, there’s an endless sequence of infinite set sizes, getting larger and larger without end. (Again, too much to cover here.)

  Now, we don’t need to worry about where that sequence goes but, now that we know there is such a sequence, it’s interesting to return to the set of integers and the set of reals and consider their places in the sequence. In particular, are they consecutive in this sequence? In other words, are they next to each other in terms of infinite set sizes or is there something that produces a set between the two? Is there an infinity between the integer infinity and the real infinity? This (proposing that there isn’t) is the Continuum Hypothesis (CH).

  Well, no-one’s found an infinity between the integers and the reals. On the other hand, no-one’s proved there isn’t one. So, on the surface, we seem to be in the same position as with the GC. However, for the CH, mathematicians have gone one stage further. The question has been shown to be undecidable.

  So, what does this mean? Well, it sort of depends on how you look at it … In terms of the previous paragraph, no-one’s ever going to find an infinity between the two but no-one’s ever going to prove there isn’t one either. In terms of pure logic, this means both of the following:

  - Starting from everything we know of numbers and sets, there’s no logical argument, no sequence of steps that will show that the CH is true … or false. It’s logically ‘distant’.

  - The CH can be either true or false, arbitrarily, it doesn’t matter which; and it doesn’t interfere with the rest of what we know of numbers or sets. It’s logically ‘independent’.

  And, really, we can paraphrase these (equally valid) viewpoints as:

  ‘It’s impossible to tell’, or

  ‘It doesn’t matter’

  Now here’s the thing … This is actually what most of us do subconsciously when we think about things that we don’t know. Even with the day-to-day stuff we could know, individually we often make an intuitive distinction between what we can be bothered to find out what we can’t. But, when we enter the realm of the truly unknown, it takes on a whole new significance.

  How do we deal with being told (possibly proved) that something is beyond all human knowledge? Very often, we find ourselves adopting a position of either (1) or (2) above and, which it may be can be as much a social or philosophical stance as a scientific one. In fact, we might even rewrite them again as sort of:

  ‘Wow, that’s
big’, or

  ‘I don’t care!’

  Take Heisenberg’s Uncertainty Principle, for example, which, in simple terms, says there’s a limit to what we can measure at the quantum level: if we look too closely, we change what we’re looking at. Here it’s pretty easy to see a likely difference between a scientific amazement (possibly frustration) that we can’t get any closer and a wider public lack of interest.

  Similarly, Turing‘s algorithmic Halting Problem and Gödel‘s mathematical Algebraic Incompleteness are scientifically limiting principles that may have the same effect.

  But, to finish with, let’s consider a really big question, one that’s often considered unknowable. What happened before the Big Bang? Or perhaps, what was there before the Big Bang (BB)? On one level or another, this seems to be out of our grasp.

  We have various tools to try to help … or hinder our attempt. We can search for subatomic particles capable of appearing from nowhere and catastrophic singularities in space. We can tie together notions of space and time into a single concept so we’re not even sure what ‘before’ means any more. (“Don’t ask what was before the BB: there was no ‘before’ the BB”.) But, at the end of the day, we’re left not knowing. It’s not that our science has failed, as such, but our ability to apply it from where we are in the universe is limited. We don’t have the necessary ‘vision’. Perhaps we can’t ‘see’ far enough (in space and/or time). Perhaps we don’t live in enough dimensions. If there was a ‘before’, then we can’t really comprehend it; if there wasn’t, then we don’t really know what that means. And, again, how we cope with this uncertainty (and many other similar scientific unknowns) reflects our philosophy, maybe our religion – or lack thereof, more than our science.

  Because, extending (1) and (2) a final time, we can either say:

  “That’s interesting. Perhaps we’re part of a bigger something that we can’t see by scientific means, from where we are”, or

  “Don’t ask stupid questions!”