Navid kneeled, wrapped one arm around Trixie and another around Happy. "My two favorite girls. You look after each other. Now, Trixie, make sure Happy speaks politely, and Happy, make sure Trixie doesn't wee on the floor."
"Daaaad!" hands on her hips, "You're mixing us up, and you're embarrassing me."
Navid chuckled, stood and gave a small wave, then walked out the science museum doors to the car that brought them here. Trixie waved to her Dad and he returned the wave briefly before getting into the car to be whisked away.
They both stood there looking a little lost. Trixie put her arms around Happy's neck and murmured, "Pals forever." She looked up at Imogen, the cheerfully attractive AI before her.
Imogen held out her hand, "Let's see if we can find some things to make your day fun, shall we?"
Trixie held Imogen's hand and walked with her. Her other arm rested on Happy who kept close. They entered a bare room at the back of the large foyer and Imogen gave Trixie a castAR. She held up another and asked, "I don't need one as I'll receive it internally. Should I put one on Happy? Will it bother her?"
One arm still on Happy, Trixie said, "She's used to them. I have one at home specially shaped for her. I don't know if you can make that fit her though."
Imogen shortened the back of the castAR and attached a string to go over the dog's skull and under her jaw.
With the castARs on and activated, the room suddenly appeared to become a large cave that opened out to a seaside scene. Below the mouth of the cave was a rocky beach and beyond that, waves breaking on the rocks. Inside the cave were a few raggy-looking naked people tending a fire and chattering quietly, intermittently, with a couple of dingo-like dogs snoozing beside them. Outside were about six more people sqatting on rocks, chipping at something.
Happy came suddenly alert at the sight of the dogs.
Trixie pointed at the people outside and asked "What're they doing?"
Imogen said, "They're getting shellfish off the rocks to eat. This is a reconstructed scene of what a tribe of early modern humans may have looked like. There will probably always be so much we can't know for sure, it has become like a giant jigsaw puzzle, or a really long detective story where nobody has all the clues. But genetic information tells us that about the time shown here, people almost died out."
"Why?" Trixie asked.
"Nobody knows. There have been a lot of hypotheses, but not enough information has been uncovered to really say. Do you know the difference between a theory and a hypothesis?"
"Of course. Hypotheses are just ideas that can't be proved. Theories are provable explanations that are backed up by the facts. Most people say 'theory' when they really mean 'hypothesis'."
"Very good, Trixie," Imogen said, looking pleased.
"So, how did they survive? If humans were dying out, something changed. What let us survive?"
"Again, nobody knows. Humans already had language, and made tools, and had fire. There are many, many ideas about what suddenly gave humans a survival advantage, but not enough evidence to decide. But one idea is my favorite, and that's why I'm showing you this. Can you guess what is?"
Trixie shook her head, "What?"
Imogen stroked Happy's head and ears, "Dogs. It's difficult to say exactly when it happened, but it's interesting that humans seem to have teamed up with dogs about this time. We know that people with dogs had a greatly enhanced ability to survive. Even today when survival is easy, having a dog as your companion still has great health benefits. You get better from injury faster, are generally happier and more able to cope. Humans and dogs have been together for so long they've affected each other's evolution in odd ways. While each can survive without the other, they are less."
Trixie patted Happy too. Happy looked delighted at all the sudden attention. Trixie said, "Happy is special. She's a genetically engineered dog."
"Yes. Dad said that she will be able to live about seven times as long as a normal dog — nearly a hundred years. He says we might be able to stop aging before then and we could be pals forever. She also has a modified brain. Her neurons are small, like a dog half her size, which means she has nearly as many as a human. She can understand a lot more than a normal dog — a lot of what I say."
"Ah, I did wonder why Happy came with you to the museum. Not many people are accompanied by dogs. It always seemed a bit of a pity to me that they are excluded from so much today, especially considering humans may owe their very existence to dogs."
Trixie hugged Happy. "I agree. Dogs are the best."
"Trixie, what do you think are humanity's five greatest inventions?"
Trixie held up her fist and started extending a finger at a time, "Fire, string, writing, electricity, and..." she thought for a little while, then unfolded her thumb, "and artificial intelligence. Was I right?"
Imogen laughed, "There is no right answer. I was just asking your opinion. And thank you for considering AIs to be one of the five greatest. I'm flattered. I wonder why you said writing when most people would have said language."
"Language is instinctive. To call language an invention would be like saying that walking on two legs is an invention. But writing's different. It doesn't come naturally. It's an invention."
"That's quite a surprising thing for an eleven-year-old girl to say."
Trixie smiled proudly, "My Dad says I'm like him. He thinks learning is the best fun in the world. I think so too. Instead of playing games, I have fun by learning. I read a lot and watch talks by interesting people, and do experiments. Most of my friends play lots of games and they're always getting bored when they run out of stuff to play, but I'm never bored because there's no end to learning. It's great!"
Imogen nodded, "Ah, that explains why he leaves you at here at the science museum instead of a play center while he's at work. But back to the five greatest inventions — I'm a little puzzled that you chose string as one of them."
"A little while ago I read something about how important string is. We get woven and knitted fabric, rope and cables, fishing line and nets, and... and... well, lots of stuff from string. It's definitely one of the best things we ever invented."
"Interesting." Imogen nodded again. "Something a lot of other people choose is plumbing, because it gives water pipes, tanks, taps, flushing toilets, baths."
Thinking about it carefully, Trixie said, "Yeah... it is very important, I guess. I've read where some people think that the flushing toilet was the greatest health advance ever. I don't. Any toilet is great if it keeps waste away from people. It breaks the life cycles of parasites and infectious diseases. But the flushing toilet wasted so much water it became a big problem. Composting toilets are just as safe and you don't waste water or need sewers, and you get to re-use the waste for gardens when it's been composted. But yeah, piping water is important."
"What about metals? A lot of people choose metals as one of the five."
Trixie shook her head. "No. It was kinda important for a long time, but we used them too much and many of them were toxic and needed so much energy to extract. Biomimetic materials are much better — polymers and composites and low-temperature ceramics that copy the way shells are made, and how we grow our bones. We don't need great big mines anymore, or giant metal-smelting plants burning coal and making lots of pollution. And as soon as you make metals they start corroding back to their natural state. I think metals were a big mistake."
"Hmmm... I wouldn't go so far as to say they were a mistake. Yes, they brought big problems, but they helped humans learn so much about the world around them. Understanding electricity would have been much more difficult without metals. Perhaps OLEDs, conductive plastics, graphene circuitry, and superconducting ceramics might never have been found if it wasn't for metals leading the way."
"Perhaps," said Trixie, "but maybe metals delayed those things because we became so good at using them."
Imogen laughed, "I've never heard anybody suggest that. Excellent, Trixie. Where did you hear that idea?"
"Nowhere. I just thought of it now." She smiled at Imogen. "Thanks for making me think of it."
"Wonderful!" She laughed some more. "Trixie, I have a feeling I'm going to enjoy today even more than you."
Trixie asked, "What are some other things people think of as the most important inventions?"
"One of the most common is the wheel."
"Oh! The wheel! Of course. I forgot. Yes. Very important."
"Another is agriculture."
"I don't think I'd call that an invention. It's just taking plants that grow out there and growing them here, close by. And it probably started as an accident, from spilled grain or spat-out seeds."
"There are aspects to it that might qualify it as an invention, for instance saving seed from one year to the next so that you can plant it instead of eating it. Tilling the soil to reduce competition with other plants and to make the ground softer. Selective breeding."
Trixie shook her head, "Selective breeding would be another accident, I think, not a deliberate thing, originally anyway. People would naturally prefer bigger fruit or grain. They wouldn't want the more stunted ones. But I guess you're right that keeping some grain to plant next year is something people would need to do deliberately. I've heard that ploughing was a big mistake. The next big wind or rain and you lose a lot of topsoil. Most places where they've been farming like that for a long time the land is wrecked. It's also one of the reasons people get rid of trees, because you can't plough where there are tree roots. But trees keep land moist and alive. Removing them brings droughts and floods." Trixie grinned at Imogen. "I didn't come up with that stuff. I've been reading a lot about it. One day, when I'm grown up, I'd like to see if I could farm using those ideas."
"Since the collapse of giant farms I think a lot of people are thinking the same thing."
"More inventions?" Trixie prompted.
"A lot of people say computers were one of the greatest inventions and some include steam engines," Imogen said.
Trixie nodded thoughtfully, "Yes. Even though AI is different, it still needed computers in the first place. And I'm not sure about steam engines. I'd say they're just an application of fire. Not just the old steam trains, but coal and gas powerstations too — even scary nuclear power plants are steam power with the fire replaced by a nuclear furnace. Thank goodness we don't use any of them anymore. Geothermal energy uses steam power too, but safer and not dirty."
"You are surprising, Trixie. Most people think AI is just a kind of normal computer. They don't realise it works the way a human brain does. People generally only know about the original work that was pioneered on computers. I don't agree with you about steam engines being simply an application of fire. It isn't obvious that steam can be put to work. You seem to know a lot about machines. Few people realise that most of the old, big, dirty power plants were really from the Victorian age of steam."
"My Dad maintains the equipment at a factory. He talks with me about technology all the time. Sometimes he takes me to work, but there's not much for me to do there, so I prefer to come here, or go to Underwater World, or Mary Cairncross Park, or the botanic gardens. But often I like to just stay home and read and watch talks. There are so many great things to learn about."
"Speaking of learning, let's change the scene."
The view around them changed to a meadow high on a mountain, surrounded by other snowcapped peaks blued by distance, and a massive glacier in the valley below.
Trixie looked up at Imogen. "You said earlier that there's evidence humans almost died out."
"How can that kind of thing be figured out? I mean, we can't go back and count them, and prehistoric people didn't leave much behind."
"There is a record of humanity's past carried inside each one of you."
"Yes. All humans are almost genetically identical. There is hardly any variability in the entire species. This tells us that all humans are descended from a very, very small number of parents. The conclusion we draw from this is that humanity almost died out. Mutations happen almost randomly, but there is nevertheless an average rate. If we count the new mutations in certain parts of the genome — admittedly a bit of a tricky business — we can estimate how long ago the close call with extinction was."
Trixie mulled that over for a little bit, frowning, looking out over the mountainous landscape, but not really seeing it. She was deep in thought. Presently she said, "Just because we all come from a very small number of ancestors doesn't necessarily mean there was a catastrophe that nearly exterminated us. I can imagine a case where there is always a large population of people, yet circumstances can prune each tree of descendants so that over time just one lineage survives. We can end up with a single ancestral line without a calamity — just random losses in a constant, large population. Have you ever seen those simulations of how dust-bunnies grow? Hang on a minute and I'll show you what I mean."
Trixie spoke a few commands to the castAR, which produced a window seeming to float almost arm's-length before her. She reached out and interacted with the castAR via the phantom window and was soon logged into her home computer. She was looking for a picture she'd made recently. She soon found it and displayed it above the window she was interacting with.
She turned to Imogene, looking up at her, "Is this image displaying for you?"
Imogene nodded. "What am I looking at?"
"It's a simulation of how dustbunnies form. They're the soft clumps of dust under furniture." She chuckled, "You probably don't get many here at the science museum. Anyway, here's how it works: make a particle fall from the top and randomly wiggle it left and right as it falls. When it touches the floor or another bit of dust it sticks. See how it forms these nice branching shapes? Now, if you imagine this being a diagram of ancestors, with ancient at the bottom and today at the top, then each dot is a girl baby born and producing perhaps another girl baby above it. As you can see, all times have roughly the same amount of babies, but you find that as time goes on, fewer and fewer of the original ancestors' lines continue. Starting with about a hundred different ancestors you end up with only one producing all descendants now. If you consider a generation to be every twenty years, then this could represent about 14,000 years. This is what could happen if the population was very... ummm... what is it when people hate people who are different?"
"Yes. If the people were very xenophobic then the men wouldn't marry into unrelated groups much and you might get a pattern like this. So you don't need a population crash to restrict variation. All you need is xenophobia."
Imogene thought for a little while. "How very interesting! I'll have to think more on this. Thank you Trixie."
"You're welcome. I don't know if my thinking is correct, but it seems possible to me. Of course, it doesn't mean a calamity didn't happen, just that there could be another explanation for it."
"And humans certainly have a history of xenophobia," said Imogene, shaking her head. "You know, that's something I never understood. I honestly can't see the appeal of hating someone who is a tiny little bit different from yourself — someone who has a slight difference in eye shape, or nose shape, or skin color, or behaves slightly differently, or dresses unusually. It's really quite absurd, and particularly strange when it's easy to see that animals and plants with a rich genetic diversity are more healthy and more able to survive than less diverse ones. It's hard to see why so many people would feel so compelled to impoverish their own genetic lines and place their children at such a disadvantage."
Trixie said, "I don't understand it either, but I'm still just a kid. Maybe I'll learn why people think that way when I get older. The only thing I can come up with is that it might have something to do with how we see beauty. Have you heard of that experiment where some crazy guy in the early days of photography got the idea of concentrating an image of evil from pictures of criminals?"
"Ah. I believe you mean Francis Galton in 1878. He wasn't crazy. It must have seemed like a very good idea at the time. He took photographs of the inmates of a prison and made composites of all the images, blending them together."
"Yeah. That's the guy."
Imogene laughed. "He was surprised to find that the resulting image was very handsome, instead of a distillation of criminal evil. The poor fellow wanted to help society, but he couldn't free himself from his prejudices and the result didn't fit with his idea of eugenics. He didn't realise he'd accidentally stumbled on one of the major mechanisms in humans for perceiving beauty. It would seem that humans unconsciously form an average in their minds of the people that they know and that becomes their baseline for attractiveness. It isn't the only factor in beauty, but it does seem to be something of a starting point."
"Well, Francis Galton named it and he defined it as the science of improving stock, whether human or animal. The problem was always in the word improving. It's virtually impossible to define in any sensible way, and historically people have simply used it as a way to dignify or seemingly validate their prejudices and petty hatreds. This has let them do truly awful things — forced sterilisations of the poor, attempted extermination of Jews, Gypsies, homosexuals, and the handicapped. Even with farm animals it often didn't work well. It produced grotesque turkeys that were unable to mate, over-muscled beef cattle that died early due to chronic anxiety, dog breeds that had hip problems or heart attacks or breathing difficulties, cows that produced lots of milk, but containing a protein that more easily provokes allergic response in the people who drink it. There are many examples of why eugenics is not really a science, but really just a way for people to fool themselves. Used against people it was a way to dress up xenophobia and make it sound respectable instead of just sad."
Trixie said, "For some people it might be the other side of beauty, making them feel repelled by anyone who looks or acts different... maybe they can't handle change very well."
Imogen nodded. "Perhaps they have less experience, or something in their upbringing has made them unable to cope with difference. But enough of this rather depressing topic. Shall we move on to something more interesting. Look at Happy. I think we're boring her."
Trixie looked at the dog, now settled neatly on her belly, back legs tucked in under her, head on her front paws in front of her. Trixie laughed, "She does look bored." Happy's tail wagged, but she kept her head on her paws.
The view switched off and they were standing in the bare room again. Imogen said, "Would you like to see some dragons?" She beckoned and led the way to the far wall, where a door opened. The three of them went though into a well-lit corridor and walked down it.
"What kind of dragons?" Trixie asked.
They rounded a corner and ahead was a large glassed-in area, perhaps fifty meters by fifty meters that contained trees and ferns. The uneven floor was covered in thick leaf mulch except for a small gully, through which trickled water. At the nearest corner it flowed out of the enclosure through a pipe. Its source was hidden among the vegetation further inside the small piece of rainforest. There was no ceiling to it; the top was open to the sky above.
"Water dragons," said Imogen, smiling.
Now as they approached, Trixie could see a few of the meter-long lizards on rocks and logs, watching them. "Wow. I didn't know the science museum had one of these. They have one in the hospital, but it isn't this big."
"It's part of a study project — well several studies actually. The dragons can come and go as they please, like the one in the hospital. But unlike that one, we can go inside this one." She smiled at Trixie, "How does Happy react to things like lizards? Will she chase them?"
"Not if I ask her not to. Besides," she held up the lead running from her backpack to Happy's collar, "we're connected."
"Is that so you don't become separated?"
"Mostly it's so I don't lose my backpack. I've lost it before, but I never lose Happy." Trixie turned to Happy, crouched before her, and put a hand under the dog's chin so they were almost nose to nose. "Happy, don't chase the lizards." She shook her head and pointed at the dragons. "Leave them alone, okay?"
Happy grinned wider, tongue lolling, and wagged her tail.
Imogen opened the glass door into the enclosure and the three of them stepped inside. Trixie kept a tight grip on Happy's lead, but Happy made no attempt to chase the lizards, merely staring intently at them. Imogen led the way between the trees, over the soft carpet of brown leaves to some rocks at the edge of a pool a couple of meters across at its widest. Water gurgled into it from the little creek. The water dragons had little fear and watched the three seat themselves on the rocks.
"Is it lunchtime?" Trixie asked.
"It's probably a bit early. Some people have a snack about this time and call it morning tea."
"Can we eat in here?"
"So long as you don't feed the dragons, yes."
Trixie took her backpack off and started looking inside. "We'll just have a little bit then." She pulled out a biscuit for her and a small leathery strap for Happy.
They sat watching insects flit in the shafts of light, small birds catching them, and the dragons staring back at them. Trixie was nibbling her biscuit and Happy chewing her treat. After a little while Trixie said, "You know what we were talking about with the loss of genetic diversity in humans? Well, I just thought of an important problem that has caused."
"What would that be?" Imogen asked patiently.
"Before I was born there was a lung disease that spread really quickly around the world and had nearly one hundred percent death rate. That would be because we are so genetically uniform, wouldn't it."
"Yes. That's one of the great dangers for humanity. Due to the lack of diversity, diseases that should die out quickly pass almost unimpeded through populations, spreading like wildfire. This is why free health services and immunisation programs are so important. The epidemic you mentioned earlier could have been stopped before it did too much damage if all countries had had free health services and good immunisation programs, but they didn't, and billions died as a result, rich and poor alike. Immunisation only gave some resistance to it, instead of preventing it, so even people who were immunised were often killed because of all the unimmunised people around them."
Imogen shook her head. "And it is not as if all this was new knowledge either. A decade before that the cavendish banana was wiped out by a fungus. All cavendish bananas were genetically identical, so if something could infect one then it could just as easily infect all, and this fungus did. Breeders managed to alter some genes just enough to make a resistant variety which isn't prone to the fungus, but, like the original cavendish, it doesn't have seeds, so is propagated the same way — by rootstock. Because of that, millions of banana trees face some unknown future danger because they still have no genetic variability."
Trixie thought for a while. "So racism is not only ugly, and bad for human rights, it actually threatens the safety of the whole human species."
"Yes." Imogen spoke softly, "It is very strange. Racists always argue against increasing genetic variability. What they think is 'purity' is in actual fact impoverishment. It weakens resistance against disease, lessens the range of human abilities in many different ways — intellectual, physical, immunological, and so on. It's really obvious when you think about it. I've never understood why racists never grasp it."
They sat, listening to the birds chirping for a while longer, then Imogen stood. "Want to see some more cool things?"
"Yeah." Trixie stood, brushing herself off, then she and Happy led the way back to the glass door.
Back in the corridor leading around the dragon enclosure, Imogen asked, "Are you interested in space and the other planets and moons of our solar system?"
Trixie's eyes lit up. "Yeah!"
"Okay, let's see that next then." She led the way down a side passage to a door that opened into a vast, dim room with many people wandering around, looking at brightly lit exhibits of spheres, alien landscapes, and ungainly wheeled robots. The voices of visitors and recorded exhibits echoed around the room.
"What things here interest you most, Trixie?" Imogen waved her arm to indicate all of the massive hall.
"Most exciting is the work on exploring the life in Europa's oceans. Another cool thing is the rush to mine the asteroids. Hundreds of thousands of small privateers making their fortunes out in the asteroid belt. It sounds very romantic."
"Ah, it sounds like someone watches the Star Fortunes space opera series online."
Trixie blushed and smiled, "Guilty. It's a great series though. I don't know how accurate it is, but it does seem like an exciting life."
"The real asteroid miners don't have much time for all the loves and fiascos that those in the stories get up to. The life of an asteroid miner is made up of years of hard, repetitive work, even with robots and AIs helping them. The lure, of course, is the near-certainty of spending the rest of their lives in wealth, if they survive. I don't mean to disparage the show. The stories are wonderful." She chuckled, leaned down toward Trixie and whispered conspiratorially, "Don't tell anyone, but I try to watch it when I can too."
Trixie's smile widened. "My favorite characters are Lenore and her AI ship Rover."
Imogene's eyebrows lifted. "They're my favorites too. Most people seem to prefer the exploits of the twins Rock and Petra, or the adventures on board the supply ship MexTek, but I think the stories about Lenore and Rover are more..."
Imogen nodded. "...and fun. They use their brains to get out of tight spots, instead of force. And the episodes about the supply ship have absolutely no connection with reality. Supply ships out in the belt don't have crews — they're AIs run by the miners' co-operative."
They approached an exhibit showing a dizzying 3D view of the Earth from about 50 kilometers up a Space Elevator. The view swung slowly around to show the rail disappearing up into the blackness of space above. The Exhibit's narrator noted that the final station of the Elevator was another seven hundred times further out and that the elevator is powered entirely from the voltage differential along the cable's length.
Trixie indicated the exhibit and said, "My birthday is next week and my Dad is taking me up in a Space Elevator. Have you ever been?"
Imogen's eyes lit with excitement, "Oh my goodness! You are so lucky. No, I haven't been. I wish I could, one day."
"Maybe you could come with us. Dad told me that the Space Elevators made the Asteroid Rush possible."
Imogen put a hand on Trixie's shoulder, "Thank you, but I can't; androids don't have money. Your Dad is right. If we still had to get people into space the old way, on top of giant rockets the Rush might never have happened. Cheap access to space allowed hundreds of thousands of people to explore the Asteroid Belt and begin the Rush for minerals. Did you know that it helped bring about the end of war on Earth?"
Trixie put her head on one side and looked quizically at Imogen. "No, I hadn't heard that. How does that work?"
"Well, many of the wars of the past century have been about the control of precious resources. When a big corporation found a supply of some rare mineral, they would often use bribery and corruption and weapons to obtain the mineral at the lowest cost possible. Because corporations have a single motive — short term profit — and notions of morality and human good are not seen as part of that, this often meant moving, or repressing, or even killing people and polluting and destroying the ecologies of large areas, ignoring or removing environmental controls. This all changed with cheap access to space via the Space Elevators. Asteroid mining became so cheap that mining on Earth was no longer worth the trouble. Just like in Star Fortunes, hundreds of thousands of small privateers did the mining and refining in space, delivering the pure result back to Earth in a steady stream. With the development of small, automated gliders they also eliminated shipping problems, landing each payload exactly where it was required. All the problems of scarring the landscape, human conflict, and costly transportation were neatly solved. Now with a lot of manufacturing moving into orbit and onto the moon, costs and environmental impacts here on Earth are reducing still further. It will be very interesting to see what the future brings. You're lucky to live at such an interesting time in history, Trixie."
"That's what Dad always tells me."
They spent a while strolling through the hall, looking at and discussing many of the exhibits, then went through another doorway to a long room with small exhibits on each side, showing portraits of men and women who had made significant achievements for science and mathematics. Imogen told Trixie interesting bits of extra information about many of them as they passed the exhibits. When they reached the display for Bertrand Russell, Trixie said, "My Dad showed me a strange article written by him. It was called In Praise of Idleness. Dad said most people think you should be busy all the time, but Mister Russell's point was that it's important to have some leisure time to increase happiness and to give time for thinking so that advancements can be made. My Dad said this is the reason why most scientists in the old days were rich. They had the time to spend on things like that. Poor people didn't have time to make inventions and improve their lives because almost every moment was spent surviving."
"I've read some of Bertrand Russell's works on mathematics and philosophy, but I haven't read that one. So many humans seem to view work in a back-to-front way. In the late 1900s people used to think that with all the new labor-saving machines everybody would soon have too much leisure time and would become bored to death. But all the extra time never came. I'm not quite sure why (I'm about the same age as you, Trixie), but from what I've read, people had to work more to pay for their labor-saving machines and so never got to enjoy the spare time they were supposed to free up. What made it worse was that most machinery had built-in obsolescence, either by under-engineered parts needing repair after a short time, or fashion dictating that perfectly good things be discarded for new ones. Advertising drove this into a frenzy of consumerism until in the beginning of this century, when recurring economic crashes started bankrupting many businesses and throwing many people out of work. Suddenly there was more free time than people expected. Unfortunately, most people saw this as a problem instead of an opportunity. Some have used the extra time to do wonderful things as we see now in the flowering of the maker community and open hardware, writing and NaNoWriMo, Linux and open source programming, 3D and video on the net, and so on, but most people (understandably, I guess) hate not having much money. They're fixated upon the lifestyle promoted by advertisements and feel cheated out of their lives."
"Oh!" A light bulb went on in Trixie's head. "That's why the neo-Luddite movements are wrecking factories and robots. I never understood why some people hated robots and AIs."
"Yes. It's difficult to focus on concepts like their own expectations, or status anxiety, or the broken economy as the problem, so they direct their fear and anger at something concrete that they can see and strike out against. They lose their jobs and see factories becoming more automated and using robots and AIs. It seems obvious to them that the automation is the problem. They don't realise that most small companies are feeling the pinch just as they are, and automate in order to avoid going broke. Nor do they notice the low cost of the goods that they can now afford to buy. It's sad, but understandable."
The next display was devoted to Kurt Gödel.
Imogen looked at the portrait of the stern, owl-like Gödel, then back at the picture of Russell, the painfully thin, gentle, wise pacifist. "I always thought is was sad that they put these two exhibits next to each other. Russell worked for many years alone and with his friend Alfred North Whitehead to develop a solid foundation for all of mathematics and logic. And then Kurt Gödel came along and produced something called the Incompleteness Theorem which proved that such an undertaking was impossible. Imagine how heartbreaking that would be, working so hard on this enormous proof for all of mathematics and logic, only to have it all unravel like that." She shook her head.
"Huh. I didn't know that. I do know about Gödel's Incompleteness Theorem, though."
Imogen looked at her in surprise, then laughed, "You are an unusual girl."
"Well, it's because of my Dad. He's an engineer and he says that the mathematicians and philosophers gave up too easily. Gödel's Incompleteness Theorem is based on a paradox, a little bit like the liar paradox. You know, like 'This sentence is a lie.' If it's true then it's a lie, but if it's a lie then it's true, but if it's true then it's a lie, and so on. It's really a little bit more complicated, but it comes down to the same kind of paradox. Mathematicians and and philosophers thought this was something that broke maths and logic, but Dad says they're wrong. Engineers work with paradoxes all the time. They're necessary for lots of things to work properly. Hang on, I'll show you what I mean." She switched on the castAR again, aimed it to a retro-reflecting area of wall, and started giving it commands.
Presently she opened a small image before her, then grabbed opposing corners between thumb and forefinger of each hand and stretched the window larger. She turned to Imogen. "Can you see this?"
"Yes. It looks like a simple electrical circuit."
She looked up at Imogen, "Can you see how it works?"
"Yes. The triangular symbol with the little circle on its point represents an inverter. It outputs the opposite of what goes into its input."
Trixie said, "Yes. If the input is on then the output is off, and because the output is connected back around to the input this means the input is now off so the output gets turned on, which means the input is on and turns the output off, and so on, forever. It's a paradox, exactly like the liar paradox. But this isn't something that doesn't exist. It's a real and useful circuit. Every oscillator in every computer in the world relies upon this kind of instability. Every string in every violin, every leaf or flag waving in the wind, my vocal cords making my voice — they all rely upon something that has two solutions that can't both be true at the same time so it switches back and forth between them. This is the mistake the mathematicians made. They were looking at their logic and maths as a static thing, but if you add changes in time, then what looks impossible becomes functional."
"Huh.... I never saw it like that. I always accepted that Gödel was a very smart mathematician who was just correct."
"He was a very smart man, but he was made by his time. And I'm a product of my time, when ordinary school kids understand stuff that only the smartest people in the world could a hundred years ago. Paradoxes don't break logic. They're a different part of logic, and there are whole other classes of them. There are ones that have lots of semi-stable states; there are ones that have stable states that need to be pushed from one state to another, like light switches; there are ones that prefer one state to the other, but can be pushed for a short time to the other state, but then flick back to the preferred state." Trixie threw up her arms, "There's probably an infinity of different kinds."
Happy was lying on the floor, head on paws, looking bored again. Noticing her, Imogen said, "Oh dear. Maybe we should find something more interesting for Happy. What do you think she'd like to see?"
"She likes to see other animals. Kangaroos? Emus? Dugongs? Koalas? Cassowaries?"
At mention of these Happy was standing, looking alert, eyes bright and ears pricked, tail wagging.
Imogen laughed. "Okay. We go to the animal hall next. We have a great section on biomechanics and Happy will like watching the 3D simulations of all the animals too. But on the way I'd just like to show you a couple of exhibits about two scientists who are real heroes of mine."
For Trixie the rest of the day was spent blissfully immersed in knowledge, until her Dad came to pick her up after his work. She and Happy excitedly pushed open the glass doors to meet him. Before the doors closed Trixie turned to wave to Imogen, who stood inside, smiling radiantly and waving back. It was clear that Imogen had enjoyed the day as much as Trixie had.