Saturday, January 25, 2014

Solution interview part 2

"So let's say we have a flashlight that shines a beam of light that is 449 nanometres and we call that blue."
"It looks blue, to us with no alterations or filters, let's say."
"So now the flashlight is now moving away from us very fast, let's say 70 percent of the speed of light."
"Yeah. It's red."
"Very good, special relativity. But not red. Let's say it's 440 nanometres."
"Okay?" Sam asked.
"I'm not sure what you mean," said Mark.
"Well, it's not blue any more. It looks slightly green."
"Sure," said Mark, beginning to see the trap.
"It's not blue any more but nothing has changed, just the motion of the flashlight relative to the observer."
"Aha, yes. I see. But that's just due to the observer. Another observer would see it as blue when the flashlight approaches. If the original observer began to follow the flashlight, he would see it as blue again."
"Perhaps. Again, that's high-school special relativity. You studied bachelor's level physics."
"I'm not sure what you want," said Mark.
"So what I'm asking about is what are colours, and your definition of colour is that it was a frequency. We tend to use wavelengths, but you get the idea."
"So I'm showing you that the frequency (or I guess the wavelength) of the light hasn't changed. It's still a blue light from a flashlight. The only difference is the flashlight is in a fast moving car. But it looks a bit green to someone who sees it receding. No filters, no problems with glasses or lenses or anything like that."
Mark realised he was stumped and sat silently. He tried another angle he remembered. "Maybe it's the twin paradox. In order for the blue light to recede, it must have accelerated. This changed the frames of reference and broke the symmetry somehow."
"Of course it's possible," said Sam. "The flashlight could be thrown really quickly and that changes my simple example but not much. Let's just say the observer uses his own frame of reference and sees a blue flashlight approach and then pass him at 70 percent of the speed of light. It's the same question of what colour is because the flashlight doesn't change but the wavelength measured by the observer does change. Hence, the observer would record different colours of light from the same blue flashlight."
Mark thought for a minute and tried another angle. "The Doppler effect is just a distortion caused by the motion of the flashlight. The observer in the same reference as the flashlight would see blue. The light doesn't change but the measurements from a different frame of reference are obviously going to be different. It's not a paradox, just an effect of the geometry."
"I like the logic," Sam said, using the agree-first tactic. She continued, "Okay, well, you studied general relativity as well. The same effect occurs without any need for motion. Let's say a stationary blue flashlight is pointed at a stationary observer (or effectively, they have the same frame of reference). But this time they stand in a large gravitational field of a star or maybe a black hole. Gravity will bend space-time and this bending will produce a similar effect to the Doppler change and the blue light will travel along a slightly longer path than a straight space-time line without the gravity influence and the light will be measured with a slightly longer wavelength than blue."
Mark was finally out of options and shrugged his shoulders.
"Okay," said Sam. "Let's keep moving then. Don't feel badly if you don't know the answers. It's my job to probe to find out where your strengths and weaknesses are. This is all part of the interview process."
Mark nodded.
"Just speaking philosophically, without the need to go down the special and general relativity black holes, what do you think colour is?" Sam asked. She clarified, "As we have been discussing, let's consider the colour blue."
"It's just something that we humans agree upon by putting a label on our perception.  I guess."
"That's a much nicer answer, I think," said Sam. She had learned to always agree with someone first before destroying their arguments. It made people feel better. She continued, "So when I see a shade of colour on a white piece of paper, I call it 'blue' and when you see the same shade of colour on the same white piece of paper, you call it 'blue' too. So we would agree."
"Unless I'm colour blind," Mark joked.
Sam nodded, "Supposing we are both capable of seeing the same colours and we speak the same language. Of course. Now the hard part comes when I view the paper in white light so I see blue but you view the paper in green light and it appears black."
Mark muttered to himself. "It's not a fair comparison. The green light has very little light for the blue colour to reflect. The white paper appears green to me so it's not the same observation."
"I like that thinking. Okay, let's make it fair. I put a blue swatch of cloth in a tapestry among other colours that are arranged in a particular pattern. It doesn't matter exactly. There are red, green, yellow, orange, and so forth pieces of cloth in a tapestry. We both observe the colour of the swatch and say, 'blue', so we agree."
"The same cloth like in a quilt?" asked Mark.
"Yes, exactly. But now we move this blue swatch into a different area of the tapestry. You'll have to believe me on this one, but the swatch appears orange. The surrounding colours have created an optical illusion in which the brain will perceive the colours differently and make adjustments."
"Oh, you mean, like an optical illusion," said Mark "Well, that's just a trick of evolution. If our ancestors needed to see an orange tiger from behind a tree, we needed certain faculties to spot the predator and thus live longer to procreate or take care of our young. Those who didn't develop the same faculties were eaten by the tiger. Rawr!" he exclaimed holding up his hands in menacing claw shapes.
Sam was taken aback but recovered. "I appreciate the enthusiasm," she said. "Evolution is a good example, assuming that is correct. It's important to be well-rounded and to think of concepts from many areas of science, philosophy, math, and so forth. You're right that optical illusions are just side-effects of some engineering trade-off. Humans work and evolved on a planet that is lit by a sodium lamp and we operate at scales of centimetres to kilometres. So we perceive light well enough to live long enough to spot the tiger," here Sam tried to say "rawr" and clawed her hands like Mark had done, "but that doesn't really answer the question of what colour is."
Mark shrugged.
"I think the idea of a 'label for perception' is quite good," prompted Sam.
Mark nodded. "It's just a symbol. We call a fork a fork for no good reason. We call something we see blue and we agree it is blue."
Sam nodded as well. "Just a symbol. Let's say we can point to that symbol in the brain. We hook you up to a brain scanner and when you see blue or you think of the colour blue then we look at the screen and point at your brain and say, 'there is blue right there'."
Mark nodded.
"But when they hook me up to the same machine and I see the colour blue or I think of the colour blue, a different section of my brain lights up."
Mark thought for a moment. "Of course, because we have different brains. You're a woman... no offense." Sam shook her head and smiled. "Well, I mean, everyone is different. Men and women, me and you. The homeless guy on the street..."
"I agree," said Sam. "Every brain is different. So how is the symbol represented if there is not common test to see that this one particular idea of 'blue' is the same in my head as in your head, or in the head of someone else?"
"The idea is the same... The concept..." Mark struggled.
Sam laughed. "The idea, yes, but what is the idea and where is it stored? How does it exist and how do we measure it?"
Mark frowned.
Sam said, "It's okay, you're doing great. Now, let's take the same line of reasoning about colour and apply it to something else. Let's say that 'blue' is this nebulous concept of a colour that doesn't exist. It's an idea. It has no physical properties and exists in the nether region of thought. That's why I start with colour, because people always think that maths, physical laws, logic, and numbers are absolute. But they're easily swayed with colours or the existence of God, or anything else that's quote-unquote intangible. Now for the real question, based on what we just talked about. Are you ready?"
Mark nodded. He was showing signs of wear and tiring out.
"What is the number one?" Samantha asked.

Thursday, January 23, 2014

Solution interview

Samantha Griffen put on her yellow safety glasses and switched on the laser. A bright green line traced the space between a complex set of mirrors and lenses laid out in a pattern on her laboratory table. She pushed a button that dusted the table with a fog machine so that the path of the light could be traced in full. She jabbed her finger and mouthed the numbers "one, two, three..." as she counted and mentally checked off each piece of equipment for correct placement. She froze on number eight, bit her lip, and then nodded in agreement. When she had finished her mental checklist she turned to the computer display behind her and tapped a few commands. She touched a big green button labeled "START" on the screen. The screen asked her if she was sure and she touched "YES".
Her phone twerked to the rhythms of a gangster rap tune, which startled her. She fished the phone out from under her white laboratory coat and checked the screen. The colours looked strange through the yellow filter of her glasses but she could read the display well enough. She grimaced in annoyance at the reminder that she needed to attend an intern interview on the third floor. Sam touched the big red button labeled "STOP" and turned on one heel to go upstairs to the third floor conference room. She muttered and cursed under her breath as she turned out the lights and walked out of her laboratory on the second floor. The screen asked the empty room if anybody was sure.
Sam arrived on the third floor and cautiously checked the window to the interview room. Fortunately, the intern had his back to the glass and didn't see her. The intern was wearing a grey hoodie with the name of a college or football team on the back. Sam couldn't read the name or recognise the logo. The intern was hunched over and although Sam couldn't see what he was doing, recognised the posture as a person who was typing on their phone. She wrinkled her nose at the disrespect the kids showed by not dressing up for an important interview and texting their friends about the parties going on later in the evening. She scanned the intern's CV quickly before deciding to walk into the room.
"Hello," Sam said and introduced herself as she sat down. "I'm Sam Griffen in the theoretical physics lab. I read your CV briefly but why don't you bring me up to speed on yourself a little bit and tell me what you're looking for."
"Ok," said the intern, barely looking up from his phone. "My name is Mark Thorne and I wanted to get a summer job working in the lab to get some credits for my grad program. I'm..." he said but was cut off.
"Please put your phone down and take off your hood so I can see your face properly," Sam interjected. "No  offense, but I like to see who I'm talking to." Sam tried to put on as nice a smile as she could manage and hoped that it took away from her curt tone. "You're not Mark Zuckerberg," she tried to joke but realised it probably wasn't a better attempt than trying to smile.
"Ok," said Mark and pulled his hood back and placed his absurdly large phone down on the table. "Sorry, ma'am," he apologised. Mark was wearing huge headphones that covered his ears.
"It's ok," said Samantha. "At least you apologised. Would you mind taking your headphones off? I want to pretend you can hear what I'm saying." She tried to smile and then gave up.
"Sure," said Mark. He pulled his headphones off and put them on the table next to his phone.
Sam continued, "You said your name was Mark Thorne. I see that you were an undergrad at LYU. Your father is Julian Thorne?"
"No, ma'am, my father is Jason. Julian was my grandfather. How did you guess that?"
Sam shrugged. "I started out at the LYU lab as an intern. All the buildings are named after Thornes. I met your grandfather and made a grant proposal to him."
"Cool," said Mark. He smiled broadly.
"My father was Jules Griffen."
"Oh," said Mark. "I guess I know some stuff about Julian but that was a long time ago." Mark shrugged.
"Yeah," Sam answered, simultaneously surprised and saddened by how young and old people were in academia. "Sorry to derail you," she said. "You should continue to give me your background. Maybe go over this past year's studies and your major."
"Yes, ma'am, thank you," said Mark. "I, um, majored in applied physics and graduated from LYU with honours. I was thirteenth in my class and I had a GPA..." here Sam harrumphed unintentionally. "I'm sorry?" Mark asked.
Sam stifled a giggle. "I'm sorry," she said. "Thirteenth out of seventeen? I've been there."
Mark looked hurt. "Out of 28," he said. "I had a GPA of three point eight nine in my major."
Sam smiled. "What was your actual GPA?" she asked.
Mark paused for a while and said, "My actual GPA was a little bit lower. I graduated with honours, as I said." He paused again then hurried on, "I came here to Micron U to get my master's in mathematics, but I, uh, decided I wanted to do computer science instead. You know," he said as if Sam would know.
Sam nodded. It was best to let people explain themselves even if she knew what they were going to say. The maths program had a lot of dropouts. Students often thought that maths were simple numbers and letters. After being stripped of everything the knew about the fundamentals of arithmetic and calculus, the students were left wandering dazed in an infinite field of symbolic soup that never firmed.
"I, um, liked computer science more than math. I guess it's easier." He laughed nervously and charged ahead. "Anyway, I got my master's in computer science last year and decided to pursue my PhD in Big Data Modeling. I think I have a really good idea to study how large data is captured and processed. Like, on the Internet." Mark nodded, unsure how he should continue.
"Ok," said Sam. "What was your thesis presentation for your master's? I didn't go to the comp-sci presentations."
"Um, yes, it was, um, a game theory optimum strategy for heads-up limit poker."
"I think I remember hearing about that. You wrote a program that was easily beaten by one of the undergrads," Sam said. "I was just talking to Roy Jarvis about that last week." Sam tried to suppress another laugh. Roy had told a very funny story about an undergrad whose mathematics proof had been sound but his implementation in a computer program had left a lot of questions. The program had been able to play poker against other undergrad-written bots but was unable to beat a mildly competent online player.
"Well, yes, ma'am, my program had some issues. My roommate could beat it handily. The algorithm I got from the open source library didn't calculate hand odds correctly so I had to do a lot of hacking to fudge it. I wasn't able to get it finished in time. But it got the main idea of what I was trying to prove correct," Mark said.
Sam asked, "Did he know he was playing against a program?"
"Of course," said Mark. He helped me write some of it.
"What if someone had played against your program but didn't know it was a program?"
"We did that against some online players. My roommate was able to connect my program to an online site and play against humans for play money."
"Ah, I see," said Sam. "You wanted to write a bot to make a lot of money and happened to use it for your dissertation."
"Sort of," Mark agreed. "If it made money, we could have gone that way instead."
"Okay. Let me ask you a few questions then. These questions might sound a little strange but I'm trying to see what kind of thinker you are and how you solve problems. So I'm not looking for perfect answers. I'm not looking just for answers either. A lot of times there are no provably correct answers to questions. I encourage you to ask questions to figure out details and I do want to hear your reasoning even if you don't know the answer. It's not important that my lab interns know everything about every fact of science and what I'm doing. They need to follow clear directions like 'turn off the switch now' without asking too many questions. But they also need to be able to follow me when I say, 'help me setup this reflector'. Does that make sense?"
Mark nodded.
"Okay, I like to start with this question: Why is the sky blue?"
"Huh," said Mark and smiled broadly.  "That's an easy one. I don't think the sky is blue. If you look at a sunset, you wouldn't say the sky is blue. And at night, the sky is black."
"Black at night? Or no colour at all?"
"I guess no colour on a dark night."
"But clearly if you go out on a bright sunny day in June like today, you see blue."
"That's just the light scattering in the atmosphere."
"I agree. But if you took a photograph with a camera of just the sky, you don't generally see blue. You might see white or yellow in your pictures."
"Um, I think it's the frequency of light. Blue is a high frequency and it's harder to pick up with the camera's sensors," Mark said.
"Nice. The frequency of the colour is a good point. The fact that the camera sensors cannot pick it up as well as other frequencies is good. You mentioned at night there's a lack of colour. What about when the moon is out and full?"
"I don't really follow about the moon?" he asked.
"Well, the moon is bright," said Sam. "Not as bright as the sun, say. However, the light from the moon is the same light as from the sun, it's just a reflection wouldn't you agree?"
"Sure," said Mark.
"So the light from the sun is reflected back to earth by this huge mirror called the moon, yet we don't see a blue sky or even a faint blue tone at all."
Mark was silent.
Sam waited a few seconds, then gently prompted, "Remember, I want to hear you think things out."
Mark nodded and spoke haltingly. "Well, I guess maybe there is a little blue. Maybe a halo around the moon. Could that be it?"
Sam shook her head. "The halo is probably due to the way the cornea and lens are constructed in your eye. We could also see flare from a camera lens but those are just imperfections in the construction of the viewing apparatus, not an artifact of scattering in the sky. I don't want to give it away, though."
"An artifact of the sky," said Mark and was silent again. As Sam was about to prompt him, he said, "I see, you mean that the sky is blue is just back scatter from sunlight. The camera and the eyeball..."
"Retina and brain as well," said Sam.
"Yes, all of that. All of those are not capturing the actual physical properties of the sky, which has no intrinsic colour to it." He trailed off and then started speaking again. "The moon isn't a mirror anyway. It reflects light but it must absorb some light and reflect other frequencies."
"I like that," nodded Samantha. "The part about the sky's intrinsic quality and the fact that reflections interfere with the path of the light and also modify the light's properties as they interact in the media. I like that. What else about the sky and the colour do we know?"
"I don't really know where you want to go with that," said Mark.
"Let's say you observe the sky from somewhere else, like from high on Mount Everest or from outer space?"
"The air would be really thin. So you wouldn't see anything." Mark was warming up to the topic now. "In fact, from outer space there is so little atmosphere you don't see any blue sky, just the earth itself and clouds..."
"Yes, clouds. Are they part of the sky?" Samantha asked.
"Yes, just moisture. They are white, grey, yellow if it's smoggy..."
"Okay, enough about the sky for now," said Samantha. "Regarding blue as we're discussing: what is this thing, colour?"
"It's just a frequency of light," said Mark.
"Not just frequency," said Samantha. "Right now the world looks really yellow and green."
"You're wearing laser glasses," Mark said and laughed.
"That's right. But if I look at a blue laser, what do I see?"
"Green?" Mark guessed.
"No," said Samantha. Yellow filters absorb everything except yellow. I see a yellowish tint to everything. If a laser were pure blue I usually just see a black colour. The absence of colour for that beam path through the yellow glasses."
"Ok," said Mark.
"What I'm saying is that the light is blue, yes?"
"The frequency is 449 nanometres, say."
"But yet I don't see blue."

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