As we go about our daily lives, we tend to assume that our perceptions — sights, sounds, textures, tastes — are an accurate portrayal of the real world. Sure, when we stop and think about it — or when we find ourselves fooled by a perceptual illusion — we realize with a jolt that what we perceive is never the world directly, but rather our brain’s best guess at what that world is like, a kind of internal simulation of an external reality. Still, we bank on the fact that our simulation is a reasonably decent one. If it wasn’t, wouldn’t evolution have weeded us out by now? The true reality might be forever beyond our reach, but surely our senses give us at least an inkling of what it’s really like.

Not so, says Donald D. Hoffman, a professor of cognitive science at the University of California, Irvine. Hoffman has spent the past three decades studying perception, artificial intelligence, evolutionary game theory and the brain, and his conclusion is a dramatic one: The world presented to us by our perceptions is nothing like reality. What’s more, he says, we have evolution itself to thank for this magnificent illusion, as it maximizes evolutionary fitness by driving truth to extinction.

Getting at questions about the nature of reality, and disentangling the observer from the observed, is an endeavor that straddles the boundaries of neuroscience and fundamental physics. On one side you’ll find researchers scratching their chins raw trying to understand how a three-pound lump of gray matter obeying nothing more than the ordinary laws of physics can give rise to first-person conscious experience. This is the aptly named “hard problem.”

On the other side are quantum physicists, marveling at the strange fact that quantum systems don’t seem to be definite objects localized in space until we come along to observe them — whether we are conscious humans or inanimate measuring devices. Experiment after experiment has shown — defying common sense — that if we assume that the particles that make up ordinary objects have an objective, observer-independent existence, we get the wrong answers. The central lesson of quantum physics is clear: There are no public objects sitting out there in some preexisting space. As the physicist John Wheeler put it, “Useful as it is under ordinary circumstances to say that the world exists ‘out there’ independent of us, that view can no longer be upheld.”

So while neuroscientists struggle to understand how there can be such a thing as a first-person reality, quantum physicists have to grapple with the mystery of how there can be anything but a first-person reality. In short, all roads lead back to the observer. And that’s where you can find Hoffman — straddling the boundaries, attempting a mathematical model of the observer, trying to get at the reality behind the illusion. Quanta Magazine caught up with him to find out more. An edited and condensed version of the conversation follows.

QUANTA MAGAZINE: People often use Darwinian evolution as an argument that our perceptions accurately reflect reality. They say, “Obviously we must be latching onto reality in some way because otherwise we would have been wiped out a long time ago. If I think I’m seeing a palm tree but it’s really a tiger, I’m in trouble.”

“Evolution has shaped us with perceptions that allow us to survive. But part of that involves hiding from us the stuff we don’t need to know. And that’s pretty much all of reality, whatever reality might be.”

DONALD HOFFMAN: Right. The classic argument is that those of our ancestors who saw more accurately had a competitive advantage over those who saw less accurately and thus were more likely to pass on their genes that coded for those more accurate perceptions, so after thousands of generations we can be quite confident that we’re the offspring of those who saw accurately, and so we see accurately. That sounds very plausible. But I think it is utterly false. It misunderstands the fundamental fact about evolution, which is that it’s about fitness functions — mathematical functions that describe how well a given strategy achieves the goals of survival and reproduction. The mathematical physicist Chetan Prakash proved a theorem that I devised that says: According to evolution by natural selection, an organism that sees reality as it is will never be more fit than an organism of equal complexity that sees none of reality but is just tuned to fitness. Never.

You’ve done computer simulations to show this. Can you give an example?

Suppose in reality there’s a resource, like water, and you can quantify how much of it there is in an objective order — very little water, medium amount of water, a lot of water. Now suppose your fitness function is linear, so a little water gives you a little fitness, medium water gives you medium fitness, and lots of water gives you lots of fitness — in that case, the organism that sees the truth about the water in the world can win, but only because the fitness function happens to align with the true structure in reality. Generically, in the real world, that will never be the case. Something much more natural is a bell curve  — say, too little water you die of thirst, but too much water you drown, and only somewhere in between is good for survival. Now the fitness function doesn’t match the structure in the real world. And that’s enough to send truth to extinction. For example, an organism tuned to fitness might see small and large quantities of some resource as, say, red, to indicate low fitness, whereas they might see intermediate quantities as green, to indicate high fitness. Its perceptions will be tuned to fitness, but not to truth. It won’t see any distinction between small and large — it only sees red — even though such a distinction exists in reality.

But how can seeing a false reality be beneficial to an organism’s survival?

There’s a metaphor that’s only been available to us in the past 30 or 40 years, and that’s the desktop interface. Suppose there’s a blue rectangular icon on the lower right corner of your computer’s desktop — does that mean that the file itself is blue and rectangular and lives in the lower right corner of your computer? Of course not. But those are the only things that can be asserted about anything on the desktop — it has color, position and shape. Those are the only categories available to you, and yet none of them are true about the file itself or anything in the computer. They couldn’t possibly be true. That’s an interesting thing. You could not form a true description of the innards of the computer if your entire view of reality was confined to the desktop. And yet the desktop is useful. That blue rectangular icon guides my behavior, and it hides a complex reality that I don’t need to know. That’s the key idea. Evolution has shaped us with perceptions that allow us to survive. They guide adaptive behaviors. But part of that involves hiding from us the stuff we don’t need to know. And that’s pretty much all of reality, whatever reality might be. If you had to spend all that time figuring it out, the tiger would eat you.

So everything we see is one big illusion?

We’ve been shaped to have perceptions that keep us alive, so we have to take them seriously. If I see something that I think of as a snake, I don’t pick it up. If I see a train, I don’t step in front of it. I’ve evolved these symbols to keep me alive, so I have to take them seriously. But it’s a logical flaw to think that if we have to take it seriously, we also have to take it literally.

If snakes aren’t snakes and trains aren’t trains, what are they?

Snakes and trains, like the particles of physics, have no objective, observer-independent features. The snake I see is a description created by my sensory system to inform me of the fitness consequences of my actions. Evolution shapes acceptable solutions, not optimal ones. A snake is an acceptable solution to the problem of telling me how to act in a situation. My snakes and trains are my mental representations; your snakes and trains are your mental representations.

How did you first become interested in these ideas?

As a teenager, I was very interested in the question “Are we machines?” My reading of the science suggested that we are. But my dad was a minister, and at church they were saying we’re not. So I decided I needed to figure it out for myself. It’s sort of an important personal question — if I’m a machine, I would like to find that out! And if I’m not, I’d like to know, what is that special magic beyond the machine? So eventually in the 1980s I went to the artificial intelligence lab at MIT and worked on machine perception. The field of vision research was enjoying a newfound success in developing mathematical models for specific visual abilities. I noticed that they seemed to share a common mathematical structure, so I thought it might be possible to write down a formal structure for observation that encompassed all of them, perhaps all possible modes of observation. I was inspired in part by Alan Turing. When he invented the Turing machine, he was trying to come up with a notion of computation, and instead of putting bells and whistles on it, he said, Let’s get the simplest, most pared down mathematical description that could possibly work. And that simple formalism is the foundation for the science of computation. So I wondered, could I provide a similarly simple formal foundation for the science of observation?

A mathematical model of consciousness.

That’s right. My intuition was, there are conscious experiences. I have pains, tastes, smells, all my sensory experiences, moods, emotions and so forth. So I’m just going to say: One part of this consciousness structure is a set of all possible experiences. When I’m having an experience, based on that experience I may want to change what I’m doing. So I need to have a collection of possible actions I can take and a decision strategy that, given my experiences, allows me to change how I’m acting. That’s the basic idea of the whole thing. I have a space X of experiences, a space Gof actions, and an algorithm D that lets me choose a new action given my experiences. Then I posited a W for a world, which is also a probability space. Somehow the world affects my perceptions, so there’s a perception map P from the world to my experiences, and when I act, I change the world, so there’s a map Afrom the space of actions to the world. That’s the entire structure. Six elements. The claim is: This is the structure of consciousness. I put that out there so people have something to shoot at.

But if there’s a W, are you saying there is an external world?

Here’s the striking thing about that. I can pull the W out of the model and stick a conscious agent in its place and get a circuit of conscious agents. In fact, you can have whole networks of arbitrary complexity. And that’s the world.

The world is just other conscious agents?

I call it conscious realism: Objective reality is just conscious agents, just points of view. Interestingly, I can take two conscious agents and have them interact, and the mathematical structure of that interaction also satisfies the definition of a conscious agent. This mathematics is telling me something. I can take two minds, and they can generate a new, unified single mind. Here’s a concrete example. We have two hemispheres in our brain. But when you do a split-brain operation, a complete transection of the corpus callosum, you get clear evidence of two separate consciousnesses. Before that slicing happened, it seemed there was a single unified consciousness. So it’s not implausible that there is a single conscious agent. And yet it’s also the case that there are two conscious agents there, and you can see that when they’re split. I didn’t expect that, the mathematics forced me to recognize this. It suggests that I can take separate observers, put them together and create new observers, and keep doing this ad infinitum. It’s conscious agents all the way down.

If it’s conscious agents all the way down, all first-person points of view, what happens to science? Science has always been a third-person description of the world.

The idea that what we’re doing is measuring publicly accessible objects, the idea that objectivity results from the fact that you and I can measure the same object in the exact same situation and get the same results — it’s very clear from quantum mechanics that that idea has to go. Physics tells us that there are no public physical objects. So what’s going on? Here’s how I think about it. I can talk to you about my headache and believe that I am communicating effectively with you, because you’ve had your own headaches. The same thing is true as apples and the moon and the sun and the universe. Just like you have your own headache, you have your own moon. But I assume it’s relevantly similar to mine. That’s an assumption that could be false, but that’s the source of my communication, and that’s the best we can do in terms of public physical objects and objective science.

It doesn’t seem like many people in neuroscience or philosophy of mind are thinking about fundamental physics. Do you think that’s been a stumbling block for those trying to understand consciousness?

I think it has been. Not only are they ignoring the progress in fundamental physics, they are often explicit about it. They’ll say openly that quantum physics is not relevant to the aspects of brain function that are causally involved in consciousness. They are certain that it’s got to be classical properties of neural activity, which exist independent of any observers — spiking rates, connection strengths at synapses, perhaps dynamical properties as well. These are all very classical notions under Newtonian physics, where time is absolute and objects exist absolutely. And then [neuroscientists] are mystified as to why they don’t make progress. They don’t avail themselves of the incredible insights and breakthroughs that physics has made. Those insights are out there for us to use, and yet my field says, “We’ll stick with Newton, thank you. We’ll stay 300 years behind in our physics.”

I suspect they’re reacting to things like Roger Penrose and Stuart Hameroff’s model, where you still have a physical brain, it’s still sitting in space, but supposedly it’s performing some quantum feat. In contrast, you’re saying, “Look, quantum mechanics is telling us that we have to question the very notions of ‘physical things’ sitting in ‘space.’”

I think that’s absolutely true. The neuroscientists are saying, “We don’t need to invoke those kind of quantum processes, we don’t need quantum wave functions collapsing inside neurons, we can just use classical physics to describe processes in the brain.” I’m emphasizing the larger lesson of quantum mechanics: Neurons, brains, space … these are just symbols we use, they’re not real. It’s not that there’s a classical brain that does some quantum magic. It’s that there’s no brain! Quantum mechanics says that classical objects — including brains — don’t exist. So this is a far more radical claim about the nature of reality and does not involve the brain pulling off some tricky quantum computation. So even Penrose hasn’t taken it far enough. But most of us, you know, we’re born realists. We’re born physicalists. This is a really, really hard one to let go of.

To return to the question you started with as a teenager, are we machines?

The formal theory of conscious agents I’ve been developing is computationally universal — in that sense, it’s a machine theory. And it’s because the theory is computationally universal that I can get all of cognitive science and neural networks back out of it. Nevertheless, for now I don’t think we are machines — in part because I distinguish between the mathematical representation and the thing being represented. As a conscious realist, I am postulating conscious experiences as ontological primitives, the most basic ingredients of the world. I’m claiming that experiences are the real coin of the realm. The experiences of everyday life — my real feeling of a headache, my real taste of chocolate — that really is the ultimate nature of

“Es divertido tratar de imaginar una cuarta dimensión. Podemos razonar de que si pudiéramos viajar en ella, podríamos escapar de dentro de una esfera sin ir a través de su superficie.”

“En la teoría especial de la relatividad, Einstein nos ha dado la razón para mirar al tiempo como una especie de cuarta dimensión imaginaria que difiere de cualquiera de las dimensiones normales de espacio tanto como el número uno difiere del número imaginario i.

“En la teoría general de la relatividad, hay sugerencias de que el efecto de la gravitación es deformar el espacio-tiempo de cuatro dimensiones en una quinta dimensión, lo que sería como deformar un mapa de Europa para que se ajuste a un globo que representa la tierra.

“Poincaré en su interesante libro,” Ciencia e Hipótesis, intentó en 1903 explicar como sería la evolución probable de la ciencia si hubiera ocurrido que la atmósfera de la tierra, como la de Venus, hubiera sido perpetuamente nublada. Sin la capacidad de observar las estrellas y el sol, la humanidad se hubiera mantenido durante mucho tiempo con la creencia de que la tierra es plana.

“Muchos de ustedes tal vez han visto el pequeño libro titulado ‘Flatland / escrito en 1885 por un autor quien se da el nombre de A. Cuadrado, y que se dice que es Edwin A. Abbott. Les propongo describirles un mundo real en dos dimensiones en el que se producen fenómenos que son análogos a los descritos en ‘Flatland’ “”.

Irving Langmuir (1936)

Areas of interfacial research that were often of greater scientific interest,
relating to observations of bubble and fluid droplet motion, fluid instabilities,
thermocapillary migration, interfacial turbulence, the behavior of thin liquid
films, coalescence phenomena, etc., variously engaged the attention of
leading scientists [Thompson (Lord Kelvin) 1855, Plateau 1869, Rayleigh
1878, Gibbs 1957], often at early stages of their careers. [Thus, for
example, the first publications of the youthful Einstein (1901) and Bohr
(1909) dealt with interfacial phenomena.]

Irving Langmuir

Albert Einstein

Revisión el día martes 18-11-14

prog_mat_ope3

La revisión del examen 3 es el miércoles 25 de junio de 2 pm a 3:30 pm. Las soluciones están publicadas y la simplicidad de los ejercicios en este examen solo da para corregir por resultados, por favor evite revisiones de preguntas que tengan la solución errónea.

Muchas gracias

Premio nobel en Química 2008

Looking at a cell through an optical microscope is like a satellite view of New York City. You can see Central Park, buildings, streets and even cars, but understanding the cultural and economic life of the city from the distance of Earth orbit is difficult, maybe impossible.

Likewise, biologists can easily see large structures inside a cell like the nucleus with its folded-up chromosomes and the energy factories of the mitochondria. But most of the details of how a cell functions — the locations of specific proteins, the mechanisms used by the cell to send messages back and forth, the transportation system that moves proteins from place to place — were too small to be seen.

Nowadays, using the same optical microscopes, biologists can see what was once invisible with the help of a fluorescent protein that is the focus of this year’s Nobel Prize in chemistry. The prize was awarded to Osamu Shimomura of the Marine Biological Laboratory in Massachusetts and Boston University, Martin Chalfie of Columbia University and Roger Y. Tsien of the University of California, San Diego.

The protein, known as the green fluorescent protein, or G.F.P., was for years just a biological curiosity from a glowing jellyfish.

It was found in the summer of 1961 when Dr. Shimomura, then a researcher at Princeton, and Frank Johnson, a Princeton biology professor, collected 10,000 Aequorea victoria jellyfish in the waters off Friday Harbor in Washington State. They were looking for what made the jellyfish glow at its edges, and from the 10,000 jellyfish they extracted aequorin, a bioluminescent protein that flashes blue when it interacts with calcium.

In the jellyfish, Dr. Johnson and Dr. Shimomura also discovered a smaller protein, the green fluorescent protein, which is fluorescent rather than luminescent. Bioluminescent proteins require other molecules to provide energy in order to light up. Fluorescent proteins do not. The G.F.P. proteins absorb the energy of ultraviolet or blue light and re-emit the energy as green light.

For biologists, that is an important advantage, because cells with G.F.P.-tagged proteins do not have to be swathed in additional chemicals to make them shine.

G.F.P. remained largely a curiosity until 1992, when Dr. Chalfie used it to make E. coli bacteria glow. He then made individual cells inside C. elegans roundworms glow.

The key to the use of G.F.P. is that biologists now know the gene that produces it. When they want to track the activity of a particular protein in a cell they first must identify the gene that produces it. Then, they can splice in the gene for G.F.P. next to the new gene. The result is that the protein is produced with a slight modification, an attached fluorescent snippet.

All that remains is to shine ultraviolet light on the cells. The tagged proteins glow, revealing their locations.

That is like sticking a GPS tag on every police officer or every delivery truck or every Wall Street trader in New York City. Suddenly, scientists could track the movements of groups of proteins in real time, and a hubbub of activity came into view.

For example, Jennifer Lippincott-Schwartz, a researcher at the National Institute of Child Health and Human Development, has used G.F.P. to follow not only where proteins are moving in a cell, but also where a given protein is present in the largest numbers. Brightness indicates how many protein molecules there are.

Her observations on the traffic patterns of proteins contradicted some long-standing ideas about how some newly made proteins make their way through a structure known as the Golgi complex en route to being secreted out of the cell. Many biologists thought of it as a conveyor belt system carrying the proteins in an orderly fashion. “With this type of imaging approach, we could show that was wrong,” Dr. Lippincott-Schwartz said.

Instead, a newly made protein moves through a series of compartments. When it enters one, it bounces around with other proteins already there; periodically, by chance, one of the proteins is bounced to the next compartment. Thus, the movement was more akin to the diffusion of a gas than a conveyor belt.

Before the advent of the G.F.P. technique, the primary method for pinpointing proteins was to synthesize an antibody that would hook onto a protein and attach fluorescent snippets to the antibodies. The antibodies, injected into a cell, would attach to the proteins, and the biologists could see where they were.

Designing the antibodies was not easy, and each protein required a different antibody. A larger limitation was that that the cells had to be immobilized and “fixed” — killed, in other words.

“Even though it was great,” Dr. Lippincott-Schwartz said, “it certainly was not optimal.”

Other scientists including Dr. Tsien worked out clever ways to study some proteins in living cells. Dr. Tsien and his collaborators were able to extract the proteins they wanted, attach fluorescent molecules to them in the laboratory and then inject the modified proteins back into the cells, taking care not to damage the proteins or kill the cells.

This technique was limited and arduous, leading Dr. Tsien to seek alternatives. By mutating the G.F.P. gene, Dr. Tsien’s lab was the first to make a gene that produced a blue fluorescent protein. Fluorescent proteins now span the spectrum from violet-blue to red and even infrared.

In one study, Dr. Tsien and his collaborators tagged two different proteins that attach to calcium, an important messenger within cells, with two different fluorescent colors. In the presence of calcium, the two proteins stick together, and the colors change noticeably.

A variation of the idea has been used for a sensor of glutamate, an amino acid that is the most common neurotransmitter for exciting neighboring neurons in the human brain. One of the students in Dr. Tsien’s laboratory took a bacterial protein and engineered it with a cyan tag at one end and a yellow tag at the other. When the engineered bacterial protein attaches to glutamate, it changes shape, and again the color changes.

http://www.nytimes.com/2008/10/14/science/14gree.html?_r=0

Scientists have put to rest the age-old question of how geckos stick to walls. The answer is van der Waals forces, molecular attractions that operate over very small distances. The researchers are already trying to use their discovery to make wall-climbing robots and design materials that stick to dry surfaces.

At least since Aristotle, scientists have wondered how geckos stick to walls. They long ago ruled out hypotheses involving sticky secretions, suction cups, and tiny hooks, leaving only two possibilities. One is that the tropical lizards stick to surfaces via a thin film of water. Because water molecules are polar–their electrical charges are unevenly distributed–they might stick to some polar molecule in geckos’ feet. The other possibility is that geckos stick because of the van der Waals force. This force comes from fluctuations in charge distributions between neighboring molecules, which need not be polar; their charge fluctuations naturally fall into synch, creating an attractive force.

Semiconductors helped decide between the two hypotheses. Biologist Kellar Autumn of Lewis and Clark College in Portland, Oregon, and colleagues tested whether geckos could stick to silicon dioxide, which is polar, and to gallium arsenide, which is not. The lizards’ feet were equally sticky on the two surfaces, proving that van der Waals forces are at work, the team reports in the 27 August online issue of the Proceedings of the National Academy of Sciences. The reason a gecko foot adheres–and yours doesn’t–is that it is coated with millions of tiny hairs (ScienceNOW, 8 June 2000).

Anthony Russell of the University of Calgary calls the study “elegant,” but says the complex hairs and feet of the 850 known species of gecko still hold plenty of secrets. In particular, nobody knows what adaptations work on which kinds of natural surfaces. To Matthew Tirrell, dean of engineering at the University of California, Santa Barbara, that means new inventions based on gecko hair will not be simple to design.

Autumn and his team are undaunted. They already hold two patents based on their discovery and are even working with the iRobot company in Somerville, Massachusetts, and the U.S. Department of Defense to build a wall-climbing robot. “I can’t watch the Spider-Man movie without thinking, ‘We can do better than that,’ ” he says. “After all, geckos eat spiders.”

http://news.sciencemag.org/2002/08/how-geckos-stick-der-waals

Items

1. Reúnete con tus compañeros de grupo.
2. Envía tu historia creativa antes del Sab 28 de junio a las 12:01 al correo marquezronald.ula.ve@gmail.com.
3. Publica tu historia creativa en el grupo de facebook después de las 12:01del Sab 28 de junio

Del curso “Creativity: Music to my Ears” de la Universidad de Stanford, por Tina Seelig.

Ejer 1

Resolución Ej 2 En el ejercicio del examen el compuesto C es el que se llama D en la resolución