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A valley in the Alps

How to measure consciousness

What is consciousness? Is it an all-or-nothing affair? Or are some beings more conscious than others?

Even though we may not know the answers to many of these questions, we have some clues. It seems intuitively obvious that a bacterium is more conscious than a rock but less than a person. This may be wrong, but on the surface it seems plausible. I think I have found a way to show that, indeed, this is the case. What follows is my take on the matter.

There is already a serious attempt at describing and measuring consciousness: I am talking, of course, of Tononi’s famous Integrated Information Theory. My gut feeling -though I have very little more than that- is that Tononi’s theory at least partially describes some of the conditions for consciousness. It also seems obvious to me that highly conscious organisms will have high values of “phi,” Tononi’s measure of consciousness. However, as Scott Aaronson points out in his blog, there may be many systems with a high “phi” but nothing that we could call consciousness.

I think Tononi is missing something, and that something is the rest of the world. That is: when Tononi talks about a conscious system, he only talks about that system, but not its surroundings. But consciousness is not just consciousness: consciousness has to be consciousness of something. Organisms evolved to perceive the world around them and make sense of it in order to survive. Consciousness cannot be understood without this.

I propose that the degree of consciousness of a being is proportional to the correlation between its internal states and the state of the universe. That is: the more sensitive the internal state of a being is to the state of the universe, the more conscious it is.

This will be clearer with an example. Think about a rock: its behaviour is completely determined by its weight, shape and current position. Let’s say this rock is in a valley in the middle of the Alps: the shape of the peak 50 km from it has no bearing whatsoever on the internal structure of the rock. Neither does the colour of the tree 20 m from it, nor the rattle of the wings of a crow in the distance. Only the most immediate vicinity (and hardly so) has an influence on the internal state of the rock. I don’t need to know what is happening around the rock to understand its crystalline structure.

How about a person? Well, this morning I happened to be in that valley, looking at the mountains around me. It turns out that the shape of the peak 50 km from me had a notable influence on my internal state, as it determined the firing of my neurons. So did the rattle of the wings of the crow. Of course, the cow pasturing besides me may have felt similar things. Is it as conscious as I am? Hardly. For example, I have studied physics and know about the Big Bang and inflation. My mental states are, therefore, determined by things that happened billions of years ago and which are completely outside of the realm of what a cow may wonder about. Yesterday I was reading about the history of Rome: this means that events that transpired thousands of kilometres from my current position have a measurable influence on my internal state. I am highly interconnected with the rest of the universe. In fact, I am a more faithful mirror of the cosmos than a cow or a rock. It is safe to say, then, that I am more conscious.

How could we measure this? How can we put a number on the degree of consciousness? I have a couple of ideas, but they are half-baked (I thought of this barely 4 hours ago.) The first is to use a measure from physics called “entanglement entropy,” which measures the degree of entanglement between two systems. A highly conscious system should exhibit a high entanglement entropy between itself and the rest of the universe. Since one could theoretically add entanglement just by adding things to the system, I think that probably entanglement entropy density would be a better candidate, but the idea is the same.

Unfortunately, this would be very hard to calculate for a system such as a human. There may be other measures, based on classical probability theory. For example, I could ask myself how different my mental states would be if I changed a certain chunk of the universe, then measure the degree of correlation. This would certainly be easier, though I would have to find a systematic way of going about it. There may already be some way of measuring this type of correlation that I am not aware of: if so, please leave it in the comments and I will be eternally grateful. It could also be that the measurement is related to Tononi’s “phi,” but adding the extra requirement that the processing links to some entity outside the conscious being.

This is as far as my thoughts go as of now. I am dumping them here in hope of some sort of feedback though, after how long this blog has been in hibernation, I would be surprised to get any. If you’re still there and feel like dropping a line, it would be most welcome.

Why Most Bloggers Are Actually Software (Including Me)

Disclaimer: don’t take this post too seriously. It’s a playful bike digression.

The other day I was on my bike and decided to forego all safety and embark upon a journey of philosophical investigation. The idea was to find out how far I could take the idea that I am a common observer in the universe. That is: out of the (relatively uncommon) observers in the universe, if there is such a thing, I am an average one.

Human brain

An average human brain (Photo credit: EUSKALANATO)

The first thing I came up with was: if I am a common observer, I should live in the most likely time period. That is, the time period with the largest amount of humans. Being a human in the present is much more likely than being a human at any time in the past (we are way, way more people), so that seemed to agree with observations. However, that brought about a disquieting thought: the fact that I am alive now and not in the future means, again assuming I am an average observer, that humans are more common now that in the future. That is, things aren’t looking up, guys. This could be because humans merge into something like eGod or because we get wiped out by:

  • Stupidity
  • Incompetence
  • Machines
  • Meteorites
  • Climate change
  • Killer cockroaches
  • Justin Bieber

But then I kept on thinking and I realized I am not a very common observer. I have a physics degree and a blog; I have also published a book. This puts me in a relatively uncommon portion of the population. There’s more: I was not counting animals, but why shouldn’t I? Animals are also observers. They are in all likelihood conscious, at least mammals. So in this sense I am extremely uncommon: I am a very special type of mammal with a moderately unlikely trait distribution.

There could be several explanations for

Survivor :: clouds not photoshopped [explored =) ]

The future’s looking bright (Photo credit: Nhoj Leunamme == Jhon Emmanuel)

this (again, assuming I am an average observer.) The first one is that animals are not observers and that, despite my relative uncommonness, I am still well within the statistically explainable margin for a human. The other is that, somehow, humans with my characteristics are much more common than it appears. But why would that be?

So I started thinking about possible reasons for that and came up with this: what if, in the future, the humans/machines/super-intelligent cockroaches there is decide to start simulating past humans? Would they just simulate any random human? Probably not.

Now, if I was a human/machine/demigod with a huge computer and I was asked to build a human, here’s what I would do: I would build a huge neural network and train it to give the same responses as a certain person from the past. For that, I would need a lot of information on that person: the more data, the more accurate the simulation. For example, if someone wanted to simulate me, they would need a software brain capable of coming up with this blog post. You see where I’m going with this, right?

What I’m trying to say is that the machines/overlords/whatever would only simulate humans they had substantial amounts of data for. What humans would those be? Well, people with a digital trail mostly. Bloggers, journalists, facebook addicts. Maybe famous people with well documented lives and published works they could draw on.

So is it possible for me to be an average observer? Yes, if I am a simulated one.

Summarizing: I’m either not average and quite lucky/unlucky or I am a simulation reconstructed from blog posts and other media.

Want immortality? Start a blog.

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Introducing Psychohacking

Not long ago, Johannes introduced me to a website called Medium, which aims to raise the level of the debate by promoting the kinds of thoughtful posts that don’t get easily shared elsewhere. I thought it was a great idea and checked it out immediately: I was impressed. It is beautifully designed and easy to read. Even though, for the moment, the wealth of content is relatively poor (not many people know about it yet) it looks like the kind of platform many of us have been dreaming of.

I therefore decided to publish my latest article, Introducing Psychohacking, there. I did it to experiment, partly, and because there is a feature that I find extremely interesting: it is possible to add comments to single paragraphs. This makes the debate much more fluid and contextualized and allows people to leave their thoughts as they read. I just wish WordPress had something like that.

Anyway, there it is: feel free to check out the article or, at least, the website. It is truly amazing in design and concept.

Oh, I also created another website (yes, I’m a little hyperactive!) at However, I have no intention of ever updating it: the idea is to create a community and let it take care of everything. Probably it will never bear fruit, but domain names are cheap and I already have decent hosting. So I gave it a try.

On an unrelated note, I hope I can post more regularly, though I promise nothing. Some days I am so exhausted I can barely read, let alone write something coherent. I hope this exhaustion wears off eventually.

All the best,


Bohemian Gravity: Physics Is Phun

So, I miscalculated again. It turns out I’m working so hard I don’t really have time to write every day. Add to that the fact that I have some friends visiting in 3 days and you have a recipe for disaster. Maybe I’ll have to revisit my blogging frequency.

I had a little time on my hands, though, and thought I’d share this thing I found online some days ago. Whether you’re a physicist or a fan of Bohemian rhapsody, you’ll probably enjoy it. It’s not much, but it did make my day. Enjoy!
By the way, if you understand anything at all thanks to the articles in this blog I’ll consider myself a happy guy.

Finding the Family Tree of Languages

Today I am going to go completely off topic and share a crazy idea that I had while talking to my wife. I am not a linguist and my understanding of the field is limited to say the least, so you should consider this as an adventurous suggestion that someone who actually knows linguistics could take up or dismiss as complete idiocy.

I’ve always been fascinated by linguistic family trees. I find it amazing that someone can analyze different languages and figure out how they are related and even the geographic place they came from. The way this is done is by looking at word structure and phonetics and then comparing different tongues using a statistical model. However, I’ve always been a bit disappointed about the fact that, after a certain threshold of ten thousand years or so, languages become so different that the method is no longer applicable.

Today I was taking a walk with my wife and I found a curious coincidence between Spanish, English and Chinese. I was telling her than being “orgulloso” of someone means to be proud of someone and asked her how to say that in Chinese, which is “jiao ao.” Then I told her that being “orgulloso” can have a different meaning, that of being a proud person, and asked her how to say that in Chinese. Surprisingly, she answer was the sam

e. And that got me thinking: in both Chinese, English and Chinese, the adjective for being proud of someone is exactly the same as that for being a proud person, but it didn’t have to be this way. Yes, it makes sense in a way, but there are many other words with subtle differences that have different words in English and the same in Chinese, such as “hear” and “listen” which are just “ting” in Chinese, or “let” and “make” which are both “rang” in Chinese.

So then I thought about this: how about using semantics instead of morphology? One could make a list of words with double meanings and synonyms and then compare it to that same list from a different language. The more shared structures, the closer the languages would be. This, hopefully, could be applied beyond the 10,000 limit of the other method.

Of course, without some solid evidence behind it this is just a house of cards. So what I would do first would be to apply this idea to languages whose relationship is already known in order to see if it makes the right predictions: if it does in a sufficient number of cases, we could then extrapolate the method to other families which cannot be analyzed in the previous way.

I know this is a considerable deviation from my subject matter, but heck, I am interested in almost everything and I thought some of my readers may enjoy this too. More physics and philosophy coming soon.

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Mammoths and Chickenosaurus

I just read this very interesting article by Leonard Finkelman in Massimo Pigliucci’s blog “Rationally Speaking.” It is about de-extinction: bringing species back to life. If you’ve followed the science news in the last two months you probably know what I’m talking about. Finkelman argues that:

1. De-extinction is not possible.

2. De-extinction should not be attempted.

I agree with both, but since the thought of dinosaurs and mammoths makes me giddy as a schoolboy I’ll cover my ears, sing “tralalalalala” and pray that nobody listens to his admonishments. I will now reproduce a very sketchy version of his arguments and, most importantly, a summary of how different attempts at de-extinction work.

Dodo, based on Roelant Savery's 1626 painting ...

Gone the way of the Dodo. (Photo credit: Wikipedia)

So, some background on de-extinction. First, mammoths: not long ago, some preserved mammoth blood was found in the Russian tundra. This, apart from being awesome, would give scientists enough DNA to attempt to clone one of these furry elephants. All they need to do is replace the nucleus of an elephant egg with a mammoth cell and work their magic. Of course, the “magic” is complex and involves several technical difficulties: for example, it is not enough to have a viable nucleus. We need a cell with the right chemical components to allow this nucleus to work. If you insert a mammoth cell nucleus into a chicken cell, you won’t get much. In this sense, real de-extinction is not possible, meaning that the cloned animal won’t be exactly a mammoth.

There is another, more technical sense in which Finkelman argues that de-extinction is not possible, but I don’t think it’s a sense any of us would care about, since it’s mainly semantics. At the end of the day, I am seeing a mammoth? (or something that is indistinguishable from a mammoth?). If the answer is yes, it’s good enough for me.

Now, chickenosaurus. I have to say this one really gets my mojo going. The idea is this: most evolutionary changes happen by activating or deactivating certain genes, which actually stay there. It is possible to reverse these changes by re-activating or de-activating those genes. So, for example, I can take a chicken and make it grow a tail and a pair of claws through a surprisingly simple process. I can keep doing that with other parts of the animal until I get something that looks just like a non-avian dinosaur. People are now attempting this and it is absolutely awesome. I don’t care if it’s a “real” non-avian dinosaur or not.

I want to see those chickens.

Artist's depiction of a Dilophosaurus wetherelli

Artist’s depiction of a Dilophosaurus wetherelli (Photo credit: Wikipedia)

So the question now is: should we do this? Should we spend millions of dollars in this kind of research? FInkelman argues we shouldn’t. For starters, bringing a species (that, he argues, is not really a species but just an individual that resembles a species that’s gone) back to life is costly, much more than actually not driving it to extinction in the first place. Second, the possibility of de-extinction may make people less careful about making species extinct. After all, we can just bring them back whenever we want! Third, the cost of bringing a minimum viable population size to life would be prohibitive so, in practice, we would just have a couple beasts for showing in zoos, not a brought-back-to-life species. Finally, shouldn’t all those millions of dollars be invested in something that’s actually useful?

I think he has a point. More than one, really. Very good ones, all of them. He is right. We shouldn’t do this. It’s pointless and expensive.

But, mammoths!


I mean… come on, man.

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4th of June

So apparently it’s the anniversary of the Tiananmen massacre and the Chinese government has gone into full overdrive. This means I can’t even get pictures to download, thanks to the Great Firewall disrupting all traffic from overseas. So I will write this short post to express how much this pisses me off and promise to deliver something tomorrow.

I have actually already written something, but apparently it’s not meant to be published.

I can’t wait to leave. Less than a month now and they can have their country all to themselves.

(Small side-note: a combination of clouds and pollution made it look like it was night at noon today. Spectacular. I’ve been riding my bike with a mask for the last month).

Anyway, sorry for the rant. Will post something tomorrow.

Oh, and I posted this in the wrong blog by mistake. Sorry if you got it twice.

Big Science Magazine

Lately I’ve been preoccupied with my move and quite stressed and moody (sorry if it shows in the comments). I’ve also been working on a video-game to teach physics, writing my novel and preparing a new webpage. Yes, I’m a bit hyperactive. Yes, you read right: a new webpage. In this case, I made the design myself, which explains why it looks like crap.

Onion 2

Just like the onion.

Anyway, it’s called “Big Science Magazine” and it’s like The Onion but about science (and mostly for scientists: I’d say at least half the jokes will be undecipherable by laypeople, sorry). It’s the place where I go when the seriousness of this blog becomes too much to bear.

There is very little content so far (I’ve written around 15 posts in 3 days) but some of you might enjoy it.

Just thought I’d let you know.


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This is a quick note to let you know I’m going to have a pretty hectic week and probably will do very little blogging or none until Sunday. So I apologize in advance if I don’t respond to some comments or don’t pop by to visit for a while.
Anyway, see you soon and thanks for your patience!

Why Quantum Mechanics is Quantum

One, if not the defining property of quantum mechanics is that it stuff is quantized. This means that it comes in discrete, countable chunks, like 1, 2 and 3. This chunkiness arises, weirdly enough, from the fact that particles behave like waves. In this post I will show you how this happens in a pretty rigorous way and I will even give you a taste of what the real mathematics look like.

You can imagine a quantum particle as a wave. In fact (and not going into the intricacies of field theory) the equation governing the behavior of quantum particles is a wave equation: the particle-like behavior comes later, when we make a measurement. So if you imagine a quantum particle as a wave you’re being as faithful to the mathematics as you can be.

Before we delve into the bizarreness of quantum waves, we can take a look at normal waves. In each wave there is something that propagates. For example, for the waves in a pond what propagates is a certain height of the water. In the case of sound waves, what propagates is a difference in pressure.wave_props

For each wave in the world, we have three essential properties: their amplitude, wavelength and their frequency. The wavelength is just the distance between two consecutive crests. The frequency is how many times per second these crests go through a certain region. See the picture for more details. The amplitude of a wave in water is just its height; in the case of sound, it is a pressure difference. What’s important about amplitude is that its square is equal to the wave’s intensity, which in sound waves means how loud they are.

Quantum waves are just like any other wave: they have a wavelength, a frequency and an amplitude. The difference is that what propagates is a little abstract. The amplitude of a quantum wave is just a (complex) number that we just call “amplitude.” However, when we square it we get the probability that a particle is at that point. That is, what propagates in a quantum wave is an amplitude, of which the probability is the square.

Let’s look at an example: imagine the picture above is a quantum wave. Since both the parts with negative and positive amplitudes will have a positive squares, the probability of finding the particle there is high. On the other hand, the probability of finding the particle in the middle points (halfway between a peak and a valley) is zero.

The frequency of a wave (quantum or not) is related to its energy: the more frequency, the more energy. This makes sense: it’s not the same to be hit by on sea wave each minute than by a thousand in a second. In quantum mechanics, this also holds. In fact, the Energy is directly proportional to the frequency:

E = h x f   (where h is the Planck constant)

Now let’s see how the “quantized” behavior arises from the wave-like properties of matter.

Imagine I have a certain particle in a box. Because 3D boxes are too complicated, I will imagine it’s a 1D box. Since it’s not a particle but a wave, it should look something like this:

Particle in a box wavefunctions

Particle in a box wavefunctions (Photo credit: Wikipedia)

Now notice the following: since the height of the line represents the probability of finding the particle there, the height has to be zero at the walls. That’s because there’s a wall, so the particle can’t be there. This severely restricts our choices of wave: we can only have waves such that their extremes on both sides of the box are zero. Hence the different shapes depicted above. Those are all our choices!

Now, as you can see, the higher we go, the higher the frequency and the lower the wavelength. This means that, the higher we go, the higher the energy! Also, those are the only energies allowed: we can’t have other energies because they would require different wave shapes and we can’t have that, because the wave has to be zero in the extremes.

Ta-dah! And that’s why we say energy is quantized. Almost the exact same happens to electrons in atoms, for example.

Now we can use the number of peaks and valleys as a label for our energies. For example, the lowest energy has only one peak, so we call it E1; The second one has both a peak and a valley, so we call it E2. And so on. We could go on forever! But the particle has to have an energy that is either E1, E2 or En, where n is any number.

Now here comes the math part, so feel free to tune out. If you don’t, though, you’ll get the enormous reward of being able to understand the mathematical notation of quantum mechanics. We simply use this:


All this means that the particle has energy E1. That is: “the particle’s state (the Greek letter phi) is such that its energy is number 1.”

Now, it turns out that a particle doesn’t have to have an energy of E1 or E2. Since this is quantum mechanics, a particle can have many energies at once. When we perform a measurement, though, we will only obtain one of the values. For example, this equation:


Means that the particle has energies 1, 2 and 5 simultaneously. The numbers A1 before are the amplitudes: they tell us how likely it is that we will get energy 1, 2 or 5. The probability of finding the particle in state n is equal to An squared. Therefore, the sum of all the As squared must equal one (in physics we express probabilities in fractions of one, not in percentages). Now, you will remember that we can have any energy En for any n up to infinity. We can, then, picture each state as a vector. For example, the one with energy 1 will be:

(1, 0, 0, 0, 0, …) (and so on to infinity.) (Notice how only the first slot is filled)

The one with energies 1, 2 and 5 will be:

(1, 1, 0, 0, 1, 0, …) (and so on to infinity.) (Notice how only the slots 1, 2 and 5 are filled, one for each energy)

Hence what I said in this post: in quantum mechanics, each state is an infinite-dimensional vector. One dimension for each possible value of the energy.

Again, I’ll leave it here, before things become too long or too frustrating. Feel free to ask any questions in the comments section. It feels lonely if you don’t.

PS Note for physicists: yes, I omitted a lot of stuff. Yes, I didn’t explain eigenvectors, eigenvalues and how you could express things using different bases. Yes, I didn’t normalize the vectors when I put them in parentheses form and I forgot the different amplitudes. Yes, I was not thorough. But I think this time the lack of thoroughness was thoroughly justified: if I had been more precise I’d just have lost most people halfway through. And the basic idea is still there.

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