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."
"Okay."
"It looks blue, to us with no alterations or filters, let's say."
"Okay."
"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."
"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."
"Sure."
"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.

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