Travis Garrett's Blog

Larger than our Hubble volume...

2010-06-03T21:14:00.000-07:00

Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760) from teamfresh on Vimeo.

However, the CMB is a fairly uniform temperature, and space is quite flat... If one adds a scalar field to GR in such a way that the potential energy is much larger than the kinetic energy, then spacetime responds by growing exponentially. This inflation provides a nice explanation for the uniform temperature of the CMB and the flatness (among other things). The scalar field can then decay at a point and bring inflation to an end, as it did in our region of the multiverse after expanding the scale of the metric by about a factor of e^60. However, generally speaking there will be regions where the scalar field has not yet decayed and inflation is continuing. After each e-fold expansion, the spacetime volume will have grown by a factor of e^3 ~ 20, thus if the probability that the scalar field does not decay is greater than 1/20, then inflation will continue forever - this is eternal inflation. If the e-folding time is the Planck time, which is ~ 5*10^-44 seconds, and there have elapsed ~ 1.37*10^10 * 365 * 24 * 3600 seconds so far in our Hubble volume, then there has been expansion in scale over the multiverse of about e^(8*10^(61)) since the big bang... In fairness however, the video didn't exhaust the Mandelbrot set...

Boo Bear sez: I made you a video

2010-03-26T21:30:00.000-07:00

click picture...

Church-Turing...

2010-03-26T21:07:00.000-07:00

Baby Bryce is Here.

2009-09-04T15:44:00.000-07:00

alphajet et mirage 2000

2008-03-11T21:56:00.000-07:00

Crazy Mountain Bike Downhill

2007-08-01T13:28:00.001-07:00

Testing video posting.

More Wedding Photos

2007-07-15T15:33:00.000-07:00

Well I've now successfully defended and turned my dissertation in, so I thought I'd post some more wedding photos. Luckily my uncle, Paul Hersey, is a professional and so he did the photography for us. The first is a collection of shots from the evening before when we all went out to eat -- Katie seems to be having a good time. The next is a wide angle view of the ceremony, followed by a shot of all the family members. The final shot is of Katie and I under a huge Magnolia tree (it's a very neat, and very large tree -- the central trunk has low-lying branches that dive back into the ground to form sattelite trunks, some of which had satellites themselves, and even a couple of those had their own satellites -- I didn't know that magnolias did this). The wedding was held at the Horace Williams House in down town Chapel Hill -- it's a historic building that also serves as an art museum. Oh, and I thought the wedding went quite well too :-).

Let's see here, where was I...

2007-06-30T12:50:00.000-07:00

Right then, picking up where I left off, I finished the papers later in the summer of 06, but my advisor decided that we should also investigate eccentric binary inspirals, which turned out to be quite interesting. That brings us through the winter of 07, and then it was time to write my dissertation. Well, I've just finished it and here we are, one year later. I'll defend in a few days, on July 10th. And oh yeah, I got married to Katie on May 19th, and I also got a postdoc starting this fall at LSU :-).

Gravity Wave Course

2006-06-30T19:52:00.000-07:00

Hmmm, the blogging around here has been, uh, rather light for a while now - but fear not, this blog hasn't been abandoned! I'm working on my first scientific papers which should go out before all too long - the code is fast, stable, and accurate. I'll blog about them after they go up on the arxiv. In the mean time here is a nice online gravity wave course from Caltech.

Neural Nets

2006-03-31T20:46:00.000-08:00

Here are a couple of neat videos that my friend David pointed me towards: Modeling the Neocortex, and Hacking the Brain. I also talked with Vincent recently about the tricky problem of figuring out the algorithm that directs how synaptic strengths are modified in the brain. I'm a bit tired from frisbee today, so I'll talk about it in a lot more depth tomorrow.

Right Now

2006-02-28T23:48:00.000-08:00

Right now, somewhere out in soft wet dirt in England, one particular Mimivirus is infecting an individual Ameoba, thus replaying a scene that has occurred countless times during the Earth's several billion orbits around the sun.

Right now the sun is setting on Petropavlovsk-Kamchatsky in the volcano strewn Kamchatka peninsula in eastern Russia. I'd imagine many of the residents are looking forward to spring. Are any of them in an existentialist mood as they settle in for the night? The colors of the sunset, perhaps, inspiring them for the moment to not take reality for granted, as it is so easy to do?

Right now, out in the cold waters of the northern Pacific, an individual blue whale is swimming alone in the darkening waters. I wonder what it's consciousness is like. Is it just a river of sensory input and emotions, forever living in the present moment, as some of the Buddhist monks attempt? How similar are it's sensory experiences and emotions to ours? Does it contemplate the past and plan for the future?

Right now a giant storm, the size of one of Earth's continents, is churning in the clouds of saturn. As exceedingly large as planet Earth is, with all of it's rich lifeforms, and the brains of six and a half billion people, each one an exceedingly complex structure, all of it is easily dwarfed in size by the majestic outer planets. While flying in a plane and looking out the window and using powers of ten one can almost get a feel for the size of the Earth, but the mind reels when faced with the colossal cold clouds of saturn.

Right now the entire universe exists.

Luminescent Owls

2006-01-29T06:19:00.000-08:00

So I was having my usual midday walk through McCorkle Place on campus when I saw something pretty neat - a hawk chasing an owl! The big grey owl flew into a large hole in the ancient Davie Poplar and the hawk, dropping the pursuit, flew up into the branches of another tree. Where upon it was then chased off by yet another hawk that swooped in after it. Usually it's quite cool to just see one hawk soaring around, so this was something else. I was also amused to see the complete absence of any squirrels in the park, as it is usually knee-deep with them. I imagine there wouldn't be any people out walking if there were a couple of hungry tigers and a grizzly bear prowling around. After another couple of hours of coding I went back out for another walk and found the owl was still perched in the same large hole in the poplar tree. Convinced it would stay there for a few more minutes, I went to go get Val and his camera, and we got the following picture (Ok Val hasn't sent the picture yet - I'll add it when he does).

So I then go googling around to learn about owls, and I found something that I thought was really amusing. Everyone probably heard about the Will o' the Wisp when they were kids - stories of mysterious glowing lights that would float over the countryside at night. Well, while browsing through the articles on the Owl Pages I found this: A Review of accounts of luminosity in Barn Owls Tyto alba. He is arguing that bioluminescent owls are to explain for the Will o' the Wisp myth! Why would the owls be glowing? The first explanation proposed is that from time to time the owls will get bioluminescent organic material in their feathers from roosting in old trees that have luminescent bacteria or fungi growing in them (like Foxfire - see picture below).

The article linked to above then goes on to suggest that this is not the correct explanation, but rather that some owls are naturally bioluminescent. This seems a great deal less plausible to me than foxfire-smeared owls, although it isn't completely inconceivable. Genome sequencing is going be much cheaper in the future (I look forward to having mine decoded), and by the 2020s most animals and plants (and a lot of the fungi and bacteria) should be sequenced, so perhaps at that point you could just go over to google and simply ask "Hey, are there any owl genes that could code for bioluminescent proteins, or are perhaps a mutation or two away from doing so?" and get a quick answer (I suspect it would be no in this case).

So, have any glowing owls actually existed over the centuries, out swooping after field mice in the cool night air, to the bewilderment of onlooking European peasants? It's a charming idea, but it might just be the result of an overactive ornithological imagination. Then again, I wouldn't be surprised if they do exist - the earth, at 510 million square kilometers in surface area, is a rather large place, and is filled with all sorts of fascinating creatures.

RNA interference

2006-01-09T00:31:00.000-08:00

2006 started out rather badly for me, as I was sick as a dog when the ball dropped (specifically, a dog with an adenovirus infection). Now a week later I feel mostly better, but I'm still coughing a good bit, especially when I try to go to sleep. Anyways this has gotten me interested in current research for curing diseases, and in particular a new technique that I had heard about for the first time earlier in 2005: RNA interference. It is a very neat technique that has apparently been around for hundreds of millions of years in eukaryotes - helping them to fight viruses and aiding in gene regulation - but we only discovered it existed quite recently.

Here's the idea. In general a virus will slither up to a healthy cell and insert it's genetic code (either DNA or RNA) into it, and this code will then instruct the cell's ribosomes to produce the proteins needed to construct many more copies of the virus. Some viruses belong to the double stranded RNA (dsRNA - see virus classification) group, which insert complementary strands of their RNA into the cell, and many other viruses use dsRNA during their life cycle. The presence of dsRNA in a cell is a sign of viral attack, since the normal messenger RNA (mRNA) produced in the nucleus is single stranded, and fittingly it is this dsRNA that the cell's RNA interference mechanism uses to fight back against the viral infection. When the Dicer enzyme finds a long dsRNA segment, it will cut out a short chunk from it, around 20 base pairs long, thus destroying the original dsRNA (the short excised segments are called small interfering RNA - siRNA). Furthermore, other proteins will then join with the siRNA segment, forming a RNA-induced silencing complex (RISC). The RISC molecule becomes activated when one half of the siRNA double strand is peeled off (which requires some energy to break the hydrogen bonds). Now the activated RISC will check with other messenger RNA strands, and if it finds a sequence that complements it's own siRNA strand then it will chop that mRNA segment in two, destroying it. Thus introducing a dsRNA segment that corresponds to a particular gene into a cell will result in the suppression of that gene, a surprising result if one doesn't know about the mechanism that lies behind it (as it was at first - gene therapies that were intended to increase the purple pigmentation in petunias ended up producing white flowers...).

RNA interference should allow for all sorts of great targeted attacks against the bacteria and viruses that stalk us. Any pathogen that attacks us will necessarily use genes that we don't - thus we should be able silence those genes, and the illness as well, by introducing the corresponding dsRNA segments. That said, while initial trials have shown promising results and more are in the pipeline, we probably won't see widespread RNAi therapies for another 10 or so years, as they will have to go through FDA approval and so forth. In the near term the most exciting aspect of RNAi will be it's use in decoding the genome: essentially by targeting one gene at a time and turning it off with RNAi and seeing the resulting effects in the cell, you can figure out what that gene does.

Math, Matter & Mind

2005-12-21T03:20:00.000-08:00

I found a neat paper on the arxiv recently:

On Math, Matter and Mind

by Piet Hut, Mark Alford, and Max Tegmark. They discuss the metaphysical foundations of reality, using an apparent paradox by Roger Penrose as a focal point (amusingly enough I also found the paradox while skimming through his new book). Here's the paradox: physics makes a compelling case that Matter is a particular type of Math, it is also abundantly clear that the Mind is equivalent to a particular arrangement of matter, and finally it is reasonable to conclude that Math is a one type of idea that the Mind can create. Thus we have that Mind ⊂ Matter, Matter ⊂ Math, and Math ⊂ Mind: each phenomenon in the triangle is a proper subset of the previous one!

Here's generally how the three authors resolve the circular paradox. Tegmark takes the 'Fundamentalist' view point, arguing that it is valid to assert both that matter ⊂ math and mind ⊂ matter but not that math is an invention of the human mind - arguing rather that humans are merely discovering mathematical structures that already exist. Alford takes the 'Secularist' view - to him it is clear that both matter and minds are real phenomenon, although he doesn't care to hypothesize which is more fundamental, and he thinks that math is an abstract creation of the mind. Hut takes the 'Mystic' viewpoint: he doesn't claim that any of the three Ms is a subset of another, but instead conjectures that all three are equally important facets of some deeper and yet undiscovered structure.

My views lie somewhere between Tegmark's and Hut's. Tegmark makes the same two assumptions about reality that I made in the 3 questions posts: first, that the universe is a mathematical structure, and second that all mathematical structures exist (name this vast collection the ensemble). Working in this framework it is thus clear that our material universe is just one type of mathematical structure among many, and our minds are just one type structure in our universe - thus matter ⊂ math and mind &sub matter. This explains, as Wigner put it, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (I found it amusing that they use this great phrase a lot in their paper, since I had also included it in a new paper of mine that I'm writing).

My thoughts start to diverge with Max after that however. He thinks it is plausible that we could find a final theory of everything - a final, exact mathematical structure in the ensemble that is our universe. I come to the opposite conclusion with regards to the ensemble - I suspect that we will be forever finding that our current laws are in fact only approximations to yet more complex structures, since the more complex structures vastly outnumber the simpler ones. Thus, for statistical reasons, there will never be a final theory. In Max's view, our's is a rather simple universe, and in order to help explain this fact he proposes that only Gödel-complete (fully decidable) mathematical structures have physical existence, a restriction that dramatically shrinks the ensemble. This seems like madness to me (although it deserves more carefull thought), and furthermore it seems against the spirit of the ensemble, at least as I understand it: there can be no distinction between mathematical structures and physically realized structures. I strongly suspect that there is no upper bound to the complexity of structures in the ensemble - in fact, going even further, I suspect that there isn't even an upper bound to the number of axioms that will eventually be used to build interesting structure - and this incredible structure will come into play as we dig ever deeper into the substrate of reality. Let me quote Hrbacek and Jech from their Introduction to Set Theory:

"As Gödel assures us in his Incompleteness Theorem, no axiomatic theory can decide all statements of arithmetic or set theory. We can thus feel confident that the enterprise of getting closer and closer to the ultimate truth about the mathematical universe will continue indefinitely."

I also think that observers play an absolutely key role in the mathematical ensemble. The Observer Class Hypothesis proposes that observers form by far the largest class of information in the ensemble, precisely because observers can study any other type of structure. This thus explains why we are observers. Since we do happen to be observers (or minds that extract information from exterior sources) we tend to take being observers for granted, but it must be explained. The Observer Class Hypothesis is testable - it requires that there is no upper bound to the complexity of information that we will eventually be able to process, which in turn requires that scientific and technological progress never halt, so that we can construct arbitrarily complex computers (aka minds). Thus in the end it would be valid to say that math ⊂ mind, and indeed this is why we are minds!

Puzzle:

2005-11-21T19:56:00.000-08:00

What is this?

Click on the picture to go to google maps, and head on over to the Sahara desert. Turn on the satellite images and search the desert for the black spot - it shouldn't be too hard to find, as the giant spot, looking like a tear in the fabric of reality, is over 10 miles across. I found it randomly while wandering through the Sahara - the whole desert is fascinating really. Also check out the giant light blue sand wastes in northern Algeria and central Chad.

December Update: Ok, here's the answer. I thought it was a giant open air oil reserve at first, but in fact it is an exotic volcano: Waw an Namus.

Animals

2005-10-21T15:22:00.000-07:00

I rescued a turtle last thursday night. I was driving home in the rain, and almost ran over him as I made the last turn into the apartment. I parked the car, scooped him up, and carried him down to a nearby creek. Unlike the previous turtle that I saved several months ago, this little fellow didn't hide in his shell the whole time as I carried him, but rather made a bold swimming motion through the air. It was a hell of a lot of fun. I could rescue turtles in the rain all day long.

Early Wednesday morning, Katie woke me up in the monotone grey light of a very cloudy dawn. And for a neat, and slightly disconcerting reason. Thousands of small black birds were swarming high up in the trees outside our apartment, sloshing back and forth from tree to tree in cantankerous waves. Some migratory flock no doubt, they were long gone by later that morning. It was their shrill, ominous cries that really perturbed one's ... sense of ease. It was the sort of thing you'd observe about an hour before the world came to a abrupt, dramatic end. But I suppose I was in that weird state of consciousness where you are awake for a few moments before falling asleep again and re-awaking a couple hours later at the usual time. Kind of like normal consciousness, and yet, not...

Energy

2005-09-29T19:46:00.000-07:00

Hurricane Katrina and Rita's destruction of oil refineries and the resulting rising gas prices have got me thinking about energy policy again, and in particular the specter of peak oil. Some are saying that we have already reached peak oil and that supply will decrease by 3% a year from now on, and that for all practical purposes it will dwindle to zero by 2035. Indeed, if this was our only good source of energy then many of the resulting doomsday scenarios would be valid, but there is still plenty of energy to be had. As Hubbert himself noted, the most promising candidate is nuclear energy, as we have an almost limitless supply of fuel, particularly if we use breeder reactors.

It wouldn't be a bad idea at all to start building new nuclear reactors right now - but something like 6 dollar a gallon gas in 2007 would no doubt provide the necessary impetus. 6 dollar a gallon gas would also further spur the development of hybrid cars. The ideal hybrid would have enough battery power so that the internal combustion engine wouldn't even be needed as long as the car was driven less than 30-50 miles a day. We already have battery technology that can achieve this, and this would allow for probably 90% of the energy used by the car to come from a plug in the garage as it charges overnight. You'd need to use gasoline if you were going to the mountains for the weekend, but even at 10 dollars a gallon this wouldn't be that big a deal - a 500 mile round trip in your 50 mpg hybrid would come out to 100$ - still less than hotel and food. And what do you know, after a bit of mid-blog googling, I find that they are already at work on such things: Plug-in Hybrid.

Observers are Information

2005-09-07T17:48:00.000-07:00

In the previous 2 posts I argued that the ensemble (the collection of all mathematical structures) exists, and that observers form the largest class of information in the ensemble - which explains why we are observers. However, it might not be obvious at first that an explanation is needed for why existence entails being an observer, so it is important to emphasize the nature of the problem. The key is that any moment of consciousness is just another type of information, no more and no less. For instance, at any moment in time some subset of the neurons in an awake persons' brain will be firing, and it is the abstract connected graph formed out of those active neurons that is equivalent to that person's conscious experience. That is, the vast connected graph formed from the interacting neurons actually is the conscious experience.

There is a significant caveat to this - in fact only a subset of the patterns formed by the firing neurons will be equivalent to the conscious experience, as many of the other areas of the brain are responsible for the preprocessing of the information that the conscious areas then utilize. For instance, Christof Koch argues that the V1 area in the visual cortex is not the seat of conscious perception, but rather collects, organizes, and refines the information coming in from the retina for use by subsequent areas like the Medial Temporal Lobe.

There is still an intuitive disconnect towards idea that specific abstract connected graphs could be equivalent to mental experiences such as the sensation of color. This is the hard problem from the philosophy of consciousness, and it is likely that we won't have a completely satisfying answer until we understand in depth how the experiences arise from the interactions of the neurons. However, I have come up with a simple counterargument to the reflexive disbelief that the topologies for firing neurons could be equivalent to the subjective experiences of various qualia. The key is to again consider the mind as a giant connected graph. This giant graph is comparing to small subsets of itself: one, the self-referential idea of connected graphs, and two, some particular sensory perception (say the vivid orange color of a carrot), and, not surprisingly, finding that they don't "feel" the same. Nor should they - the two areas of the brain will be connected in very different ways, and we don't have any direct access to all the unconscious subroutines in the brain that provide our consciousness with high level abstract data. If the human brain had the ability to directly observe the status and connectivity of its own neurons, then there would likely be a lot less mystery to the subject. And its not surprising that it doesn't - it would require a lot more neural hardware for such introspection, and there may be no simple path for such hardware to evolve, or a compelling biological pressure for it to do so. However, it will be available for advanced artificial intelligences in the decades to come, who will thus be able to understand themselves at a much deeper level, as well as having a means to develop all sorts of intriguing enhancements to their consciousness.

So our various conscious experiences as observers of a complex exterior reality are nothing more than particular types of information. There is nothing intrinsically special about them, no essence of vitality that breathes life into them. And all other things that exist (like universes and mathematical structures and so on) are just particular forms of information as well. Thus the quandary is now thrown into high relief: why does existence entail being a member of the class of information that describes observers? And the Observer Class Hypothesis answers: because there are categorically more observers than any other type of information, since observers can observe and subsume any other type of structure. And the OCH predicts that there is no upper bound to the complexity of information that we will eventually be able to absorb - a rather audacious bet. The longer that we can continue to upgrade the power of our brains, thus allowing us to think exponentially more diverse thoughts, then the greater confidence we can have that the OCH is correct, and the better we will understand why we exist. If the OCH is correct, then the journey will always be just beginning.

3 Questions - Part 2

2005-08-29T22:03:00.000-07:00

In the last post I asked three fundamental questions:

A: Why do I exist?
B: Why does anything exist?
C: Why does existence take the form of being an observer who evolves in time within a vast universe?

Since I do happen to exist, I was able to think about things for a while, and came up with two plausible assumptions about reality: first, that our universe actually is a mathematical structure, and second, that all mathematical structures exist. These assumptions lead to a statistical meta-prediction: if they are correct then we will forever be finding new phenomenon that require us to expand our previous theories, i.e. we will find physics to be bottomless. And they answer questions A and B: there is no distinction between possible and realized structures, and so they all exist within the ensemble. Note, however, that this does not mean anything goes! For instance {4 is Prime} and {f(x)=x^2 is the solution to df/dx=f} won't be elements of the ensemble. Indeed, most random sentences that one could form will correspond to no structure within the ensemble. There is natural structure within the ensemble. Clearly observers form one class of information within the ensemble. Thus question C becomes: why does existence entail being a member of the observer class?

The Observer Class Hypothesis (OCH) proposes a statistical answer to question C: observers form by far the largest class of information in the mathematical ensemble, and this explains why what it is to exist is to be an observer. Observers form the largest class precisely because they observe: they can selectively extract information from any other type of object in the ensemble. They can observe things in their physical environment like trees and moons and planets, and then with the scientific method figure out things like photosynthesis and the inverse square law. Or they can directly explore abstract objects in the ensemble like busy beaver programs, or the Banach-Tarski Paradox. Thus the observer class is something like the power set of the ensemble (quick note on the terminology - I suspect that the observer class is not a formal set, but rather a proper class, like the Universe in set theory: V = {x:x=x})

If a set X contains N elements: X = {X₁,X₂,...,X_N}, then the power set P(X) - the set of all subsets of X - will contain 2^N elements. Thus P(X) contains vastly more elements than X - in fact, if we let N be countably infinite, then there will be an uncountable number of elements in P(X). It is then tempting to argue that the ensemble is like a countable number of pieces of information, and that there are an uncountable number of observers extracting information from them. If this was the entire contents of the ensemble, then it would make the counting problem very easy, however this is quite likely not the case. In general it seems that there are two likely scenarios: either the ensemble is a countable collection of finitely complex structures, or, if it is meaningful to talk about infinitely complex individual structures (like uncomputable reals), then there is no upper bound to the cardinality of objects in the ensemble.

It is a good bit easier to consider the first case: a countable collection of basic structures, and a countable number of observers extracting information from them. But then how can the observers form the largest class? As I mused in a previous post, I think the key is to introduce a constraint. For instance, there are a countable number of both prime and composite integers, but if we introduce the constraint of only considering integers less than N, then the density of primes falls off as ~ 1/ln(N) as N goes to infinity (if the Riemann Hypothesis is correct!) Likewise, we only consider observers that can process ideas that contain less than N bits at time t. That is, if idea X_i takes I(X_i) bits to express (in some representation), then observer Y_j can only consider X_i if I(X_i) < M_j(t), where M_j(t) is Y_j's memory at time t. And why is observer Y_j so constrained? Because he/she/it is a concretely realized computer within some physical background (the physical background being some mathematical structure in the ensemble).

I posit that if observers can increase their memory capacities M_j(t) boundlessly as time progresses, by redesigning their brain architectures and utilizing ever deeper physical structures (which will be available if the ensemble exists), then they will form the largest class in the ensemble. This is because observers will be able to learn any idea in time, and thus all forms of information are subsets of the observer class. Time evolution is key, since, in contrast to static structures, it allows for each observer to absorb any combination of structures. One might try and construct the power set of observers, in an attempt to break the OCH by forming an even more vast set, but in fact this is just another collection of structures that observers extract information from (indeed, thinking about other people is one of our primary mental activities). Amusingly, any collection of structures that one could try and construct such that they would be more vast than the observer class is still going to be described by an observer, and is thus self defeating. Still, this is a bit vague, and it would be good to place the OCH on a more formal grounding. The technique of forcing from set theory looks intriguing, and might be modified to this end.

The testability of the OCH comes through the requirement that there is no finite upper bound to the power of computers that we will eventually be able to build. Thus scientific and technological progress must never halt, but rather continue to press onward, perhaps even exponentially. The primary next step is the development of human level artificial intelligence, which will then rapidly lead to the evolution of vastly more intelligent computers. These very smart creatures could conceivably run into an absolute design wall at some point, perhaps imposed by physical limitations, and not be able to grow any more intelligent, which would falsify the OCH for them. However, if the ensemble does exist, I posit that these scenarios will be vastly outnumbered by those where there is no upper bound to the power of computers we will build and no limit to the complexity of ideas we can think and sensory information we can absorb. The longer that this proves to be true, then the greater confidence we will have that the Observer Class Hypothesis is correct. We shall see!

3 Questions - Part 1

2005-07-28T23:06:00.000-07:00

Three deeply intertwined questions:

A: Why do I exist?
B: Why does anything exist?
C: Why does existence take the form of being an observer who evolves in time within a vast universe?

In order to give a possible explanation for A and B, let's first examine a simplified C: what is this reality thing anyways? Well, we are most immediately familiar with our own conscious experiences - indeed, they are the only things that each of us can be 100% positive exist! Our sensory input reveals to us a complex exterior world, which we can then form ideas about. One good meta-idea is to make our proposed ideas about this exterior reality testable: i.e. if an idea correctly models some phenomenon of the world, then it predictions for that phenomenon will be verified. Iterate this trial and error method many times over, building upon previous successes, and you can discover a set of theories that model the structure of the universe very well.

With the discoveries of Boltzmann, Einstein, Bohr, Schrodinger, Heisenberg, Pauli and Pauling and many others some 100 (± 20) years ago, it became clear that the laws of chemistry (and thus biology and neuroscience and the rest of reality) were many body approximations of fundamental physics, thus beginning the unification of all natural phenomenon into a coherent explanatory structure (say that three times fast!). And I think that it is very likely that physics, the substrate of reality, isn't just very well described by mathematical structures, but actually is a mathematical structure. Given the successes of General Relativity and Quantum Field Theory, it isn't too ambitious to attempt a complete description of the foundations of our universe - perhaps string theory will succeed in this endeavor.

One might object that just because a complete description was found, that doesn't mean the universe actually is that description - our universe is the rich unfolding of those laws acting on vast numbers of particles, resulting in the quirky history we find ourselves in (say you sitting in that chair, reading this right now, with those trees out the window swaying as those particular clouds blow by, etc...). I.e. there is a crucial distinction between implicit and explicit representations of information - between, say, the short program, and it's it long output. This view is tempered by the Many Worlds Interpretation of quantum mechanics. In short it states that there isn't just this reality we find ourselves experiencing - this particular permutation of atoms - but indeed all histories, all possible permutations of atoms, exist. When experiments are set up just right, and there are only a few interacting particles for which we can receive all information on their states, we can observe very nearby histories through interference (i.e. the double slit experiment, and the first quantum computing results). But usually vast numbers of particles are involved and we only receive partial information on their states, and the resulting decoherence leads to the apparent collapse of the wavefunction and our single history experiences (i.e. you don't receive any information from the photons that comprise the magnetic field in the Stern-Gerlach experiment, and thus you only see up or down for each electron). The view that the universe is actually the collection of all possible permutations of matter and energy (with specific weightings for different permutations...), 'feels' a great deal more mathematical. It is still on the explicit side of things - but explicit structures are no less mathematical than implicit ones: for instance, the generating algorithm for the Mandelbrot set and limiting behavior of all the points in the complex plane under that recursive algorithm are both mathematical structures. Thus, if one was to find a successful theory of everything, it would then be valid to declare that our universe is in fact a mathematical structure.

The thing is, I doubt we will ever find a absolute, final theory of everything! We still start from the natural assumption that our universe is a mathematical structure. But then it is just that - another type of mathematical structure, and it acquires no special status just because it happens to contain observers. This spurs the next natural assumption: that all mathematical structures exist - there can be no difference between possible and realized mathematical structures. Name this giant collection of mathematical structures the ensemble. But our universe is not just one member within the ensemble! Rather there will be a vast class of structures that have the same limiting behavior as we observe in our universe. A couple of the structures in this class will bottom out and not be much more complex than the laws we have confirmed to date, but these will be vastly outnumbered by those with far deeper structure. Thus, if this is correct and all mathematical structures exist, then one statistically predicts that we will never find a final TOE, but rather we will always be finding fundamentally new phenomenon (Dark matter? Dark Energy?...) that require expanding and generalizing the previous laws. Each structure in this class would be well defined and finitely complex, but the aggregate effect of all of them would cause the universe's laws to be bottomless.

Thus we have formed a possible explanation for question B (and A as well since A ⊂ B) - all possible structures exist, and this explanation makes the meta-prediction that we will always be discovering ever deeper mathematical laws for reality.

Next, question C...

Massively Parallel

2005-06-11T21:49:00.000-07:00

Well, the recent news that Apple is going to switch to Intel processors is certainly interesting. After doubting the wisdom of the move at first, I am now quite excited about it. In general it's good to keep relationships nice and fluid as it helps to drive competition and progress.

In particular however, there are all sorts of very exciting technologies being developed, which is renewing my hope that we will have cheap 100 Teraflop computers by 2020 - perhaps a good bit sooner! 100 Teraflops is an exciting number: Carngie Mellon computer vision researcher Hans Moravec estimates that the human brain processes information at an effective rate of about 100 Tflops. Hans arrives at the figure by estimating that the neurons in the retina make one billion calculations per second, and then scales this up by a factor of 100,000 for the volume of the whole brain. It took approximately one billion years for 100 trillion atom cells to evolve, and another billion for them to evolve into 100 trillion cell humans with our 100 teraflop brains. We are now going to reproduce this feat in about 100 years - some 10 million times faster. In general the first step is now complete - single processor speeds probably can't be pushed orders of magnitude faster in GHz. The next step is to arrange large numbers of these processors in order to make massively parallel machines.

We are already heading down this path. Dual core computers are available now, and AMD's quad core chips are on the way in 2007. By 2015 we will have computers with 100's of processor cores, if Intel's researchers have their way. There are other fascinating advances as well. In order to feed 100's of fast processors you need very high bandwidth, something that recent advances in getting silicon lasers to work will likely help with. Furthermore the processors will need a lot of data to chew through, which new forms of solid state memory should provide. For instance Ovonyx is working on a promising new type of optical memory that switches between crystalline and amorphous states when prodded electrically.

*Oops, violating causality a little bit here: I wrote most of this post in early June a little while after the Apple announcement, but then got absorbed by the Arnowitt Deser and Misner 3+1 splitting of spacetime, and am now finishing this post on July 1st.

100 Trillion

2005-05-31T20:05:00.001-07:00

Hmmm, May has been a quiet month, blog wise - very busy otherwise! I'm working on a very cool research project which is nearing completion - a teaser photo is pictured below. A lot more on this to come soon - as well as blog posts on the anthropic landscape, nanotechnology, and water: cool, refreshing water!

Infinite tower

2005-04-16T00:16:00.000-07:00

Here is a cool puzzle I invented recently: Let x = Exp[pi/2], and y=x^x^x^x^... - i.e. y is an infinite tower of exponents of x (and to make the evaluation order explicit we can write it as: y=x^{x^{x^{... ). Find a finite solution for y!

The Color Graph Hypothesis

2005-03-31T15:00:00.000-08:00

To celebrate my blog's first birthday, I'm going to speculate about a cool idea I've been mulling over. I've always greatly enjoyed my sensation of color. It's perfectly clear that this phenomenon - say for instance the hot pink that one sees from the Hydrogen Emission Spectrum - is a product of the patterns of firing neurons in the brain. But in particular, I've been thinking that it should be possible to discover precisely what types of patterns of neurons are responsible for the sensations of different colors. Say you are viewing a clear blue sky over a smooth field of fresh green grass (I'm ready for spring!). The 470 nm Rayleigh scattered photons entering the eye will preferentially activate the blue cone cells in the bottom half of the retina, while the 530 nm photons reflected off of the grass will trigger the green cone cells in the top half of the retina. After some basic preprocessing of the image by the retinal neurons (for instance find the location and orientation of the borders between objects), the encoded image is sent via electrical impulses along the optic nerve to the visual cortex. We effectively see about a million "pixels", with most of our resolution concentrated in the center of our visual field (this high resolution is produced by the fovea), and the optic nerve is composed of about 1 million individual fibers. The brain itself contains around 100 billion neurons, so if we estimate that the visual cortex gets 10 billion neurons in order to create our perception of the image, then we can have about 10,000 neurons dedicated to each effective pixel in our visual field.

So the visual field is mapped out by 1 million different 10,000 neuron pixel groups. The hypothesis is then essentially that these 1 million groups are wired together in a very similar way. Consider just the color blue that we are sensing at one specific point in our visual field, which was triggered by a region of blue cone cells in the retina, and processed by the corresponding pixel group in the cortex map. This sensation of blue must be equivalent to (that is, it actually is) some specific pattern of neurons firing within the group of 10,000, perhaps a particular subset of 1,000 neurons. Furthermore it isn't the organic basis of the neurons that is so important in producing the conscious phenomenon of seeing blue, rather it is the pattern formed out of the neurons, essentially a connected graph with the nodes being equivalent to the neuron bodies and the paths the dendritic connections between them (although the specific chemistry of the neurons is of course crucial in evolving the brain states forward in time...). It is the topology of this particular connected graph that is the conscious sensation of the color blue. Furthermore, this is why I posit that the structures of all the million different pixel groups must be very similar: the sensation of blue across the top half of the visual field is the same, so there must be the same connected graphs (composed of firing neurons) in each of the 10,000 neuron pixel groups. And within the 10,000 neuron groups there would be other structures that enable the sensation of other colors, and of light levels and depth and movement and so on (with intermediate colors achieved by activating several neural graph subsets simultaneously).

While currently it would probably be quite challenging (and somewhat dangerous) to actually do experiments on this, it seems that in principle you should be able to test the idea. That is you would cut a very small hole through the skull to the visual cortex of a volunteer, and then while the patient is awake you can show them a slideshow of pure colors, and one should be able to detect the same pattern of neurons being activated over and over again all across their visual field, then switching to another consistent pattern when another color is shown on the screen and so on. In fact, prehaps you could show, say, a small red circle moving slowly across a background of white, and then you should be able to track the connected graphs forming the sensation of red moving around in the visual cortex.

Unfortunately, I'm pretty sure we're still a ways away from having sensitive enough instrumentation to be able to do this. But once we do it would be immensely cool to be able examine the different connected graphs that are equivalent to the sensations of different colors. Of course, it may well be that the color graphs for different people are quite different, so that perhaps your sensation of the color orange is like my green, or (and I bet this is more likely) they are totally different, so that each of us can't even conceive of the other's (at least with our current, upgrade-incapable biological brains). Indeed this brings us to the question of how the topology these graphs is programmed in the first place. My bet is that the genetic code does not specify a particular connectivity for each different color, but rather gives a general algorithm that will converge on some solution. One imagines a young baby looking up at a colorful mobile while the crib, and as the distinct brightly colored objects rotate through the baby's visual field, the baby sees each object shimmer through a dizzying rainbow of different colors, but over the weeks each object will converge to one stable color, so that the red of a plastic toy boat looks the same anywhere in the visual field (the neural networks group at Texas has done some interesting work on self-organization algorithms in the visual cortex along these lines).

Bubbles and Neutralinos

2005-03-03T19:30:00.000-08:00

I listened to Andrew Sonnenschein from Chicago give an interesting colloquia on Thursday (pdf on his website) - it was a cool mixture of cosmology, high energy and nuclear physics, and engineering. That is, they're working on a project to detect WIMPs. In particular, neutralinos (which are superpositions of the supersymmetric partners to the Higgs and W bosons (and others)), are likely candidates for dark matter. They're working on a bubble chamber method - reviving the old particle detection techinque for modern day physics. Bubble chambers were abandoned for accelerator physics in the 70s since they can't reset very quickly, but they are suitable for dark matter detection: hopefully every now and then, one of the cold dark matter particles drifting around the galaxy will collide with a nucleus via a weak interaction, and imparted kinetic energy will be sufficient to overcome surface tension effects and cause a bubble to quickly form in the superheated liquid in the test chamber.

There are many groups working in this area. Intriguingly, data from the DAMA group at Gran Sasso in Italy appears to show positive detection for WIMPs in the form of an annual modulation of detections: the Earth orbits the Sun at about 30 km/sec, and the Sun orbits the Milky Way at around 230 km/sec, and so the velocity of the Earth with respect to the galactic dark matter background oscillates yearly by about 7% (the Earth's orbital plane is inclined by 60 degrees with respect to the Sun's). And indeed DAMA has apparently found a consistent yearly oscillation with the right phase in the hit rate (although the variation is small ~ 1%). However, Richard Schnee gave a colloquia today presenting the CDMS (Cryogenic Dark Matter Search) project, and their current null detection result appears to contradict the DAMA result. They bring disks of Germanium down close to absolute zero (with lots of shielding and in the SOUDAN mine in order to eliminate as much background as possible), and then listen for phonons resulting from occasional nuclear collisions with WIMPs. So far they haven't heard any, and upgrades with much more test mass in the future will test various supersymmetric theories stringently. It will certainly be very exciting when we discover what the dark matter is made of (or at least some of the components!).

Goodbye Eric Heape

2005-02-28T19:30:00.000-08:00

Eric was a great person, and my friend for many years. He cared a lot about animals, and was getting his Ph.D. in Charleston in neuropharmacology. I'll miss him. Since he died, I've been remembering all the things we did over the years. All those moments in time. I remember the summer that we and Tom Stec spent in Columbia, renting out the second floor of an old farm house. I remember the fireflys in the back yard in the evening, and walking around the neighborhood at dusk, and drinking a lot with good friends. I remember driving with him in the old Escort up to Clemson on the weekends to see Shelley and Dave and Bill. And our suite at Governor's school with Dave and Pete, so many years ago, and sneaking off campus with everyone at night to go swimming in the cold lake in the spring. Just slowly fading memories in my mind now. Maybe not. Perhaps the entirety of spacetime does exist, and those events are still taking place, always have, always will be. Just arrangements of atoms. Perhaps the evolution of quantum states is indeed unitary, and thus all permutations of atoms exist, and so Eric is still alive, just somewhere else - very, very far away in another branch of the universal wave function. Still, all of those possibilities are very distant from the here and now, from these atoms at this point in time, me sitting here and writing this. But then this moment will drift away too. So I smile at my future self who will read this at some point in the future, and I know he will smile back, and we will both miss Eric. Such is existence.

Flotsam and Jetsam

2005-02-12T17:15:00.000-08:00

A current sampling of the odds and ends bubbling through my mind:

I'm thinking a major refinement of the Observer Class Hypothesis (i.e. that observers form the largest set of information, precisely because they can and do extract information from any structure, in effect becoming the power set of all information) is the necessity of constraining observers, so that they, say, can only think thoughts of a finite complexity at a given point in time. In other words a particular observer Yi can only think thought Xj if the number of bits I(Xj) it takes to express Xj is less than or equal to Yi's memory Mi: I(Xj) < Mi. Then all of these variables are promoted to functions of time Mi(t) etc. and those Yi that can increase Mi(t) the most then go on to dominate the counting - so you are most likely to be a Yi(t) such that Mi(t) ~ Exp(t), as is generally the case now. But why would the observers be constrained to finite memories? - because they are physically realized computers! - embedded, say in some general spacetime with some physics and composed of the basic mathematical building blocks described by that physics. You then have to specifically manipulate that physics in order to increase M. All of these constraints help to build actual structure as opposed to noise, you only count over the real structure. This is why we are not, for instance, completely abstract turing machines out floating unmoored in idea space and extracting information randomly - all possible rules for extracting any amount of information would thus exist, and so really there is very little information in this set up, so it is thus a very unlikely mode of existence.

I've thought of a nice analogy for this, and it starts with a question: what fraction of the integers are prime? Well, given different arrangements, they converge to any percentage you want, say 50-50: 2,4,3,6,5,8,7,9,11,10,13,12... - indeed there are uncountably many different ways to get any real ratio. This is the long way of saying that we are trying to do something silly - comparing the sizes of 2 countably infinite sets (actually this reminds me of the fun real analysis result that if you have a sequence of positive numbers that converges to zero, but whose sum diverges to infinity, then you can make it so the alternating sign sum (i.e. multiplying the k'th term in the sum by (-1)^k) converges to any real number you want, by arranging the order of the terms). But if we introduce a constraint, namely considering the fraction of integers less than or equal to N that are prime, everything changes! This constraint on the problem immediately produces a huge amount of non-trivial structure - namely, if the Riemann Hypothesis is correct, then the fraction converges to 1/ln(N) in the limit of large N. On a moment's consideration, the similarity between the two cases is startling...

Let's see, in other news I've been emailing David Chandler which is great fun. He pointed me to the beta version of maps.google.com which is a lot of fun because it is so fast - you can find your childhood home quickly, then zoom out several levels, scroll over the state and see where you went to college, zoom out a ways and follow an interstate across the country... Also, the fact that David works at google made me then realize that I don't know how it actually works, but I think I figured it out while riding the bus to campus over the last few days. Say we have a million proper nouns that the engine has cataloged, each of which perhaps occurs on average on a million webpages. OK, no problem, arrange the nouns in alphabetical order over a series of computers, with each noun linked to a rank-ordered list of all the websites that contain it, so when that noun is searched for you go directly to it's location and fetch the links to the top ranked sites. But it's much more complicated than that - you can search for two words at once - say "giraffe" and "lagrangian", which, what do you know, apparently occur together in 137 websites! Obviously you can't keep an alphabetical listing of all words pairs - we'd then be up to a trillion entries, and you still can search for 3 words at a time and so on. Simple brute force comparison of the websites in "giraffe" and "lagrangian"'s lists would also be crazy - that's a trillion comparisons to make! It seems like you need to keep the website lists themselves alphabetically arranged, and then just run the lists together through the processor, essentially like you were going to make a larger alphabetical list out of the two, and whenever a common entry occurs, spit it out into the results. But there is complication after complication - for instance you can also search for "giraffe lagrangian", i.e. those words occuring in direct succession on a website (which doesn't occur, well at least not for a few more hours presumably) - so now you have to keep at which points the word occurs in the webpage so you can compare those as well - you're going to need a lot of data tags. Luckily the problem parallelizes quite well - I wonder how many processors are used on average per query. And then you want to have evolutionary neural nets crawl over all the data and extract general ideas so that they actually understand the information and so forth...

Let's see, I also went out to dinner with Katie to a new upscale mexican restuarant last night. I drank a beer and thoroughly enjoyed the meal, the orange-yellow-blue southwestern art, and the pink noise of the chattering intelligentsia around us. I realized towards the end that my consiousness was almost completely composed of sensory input during the meal - no thoughts or ideas, or at least only those running on autopilot. I then, amusingly, formed a theory that the beer helped to revert me to this ancient form of consciousness, and expounded upon my revelation on the way to the car to Katie, not getting the meta-Magrittean joke in doing so for a few more moments... Still, interestingly, in a way I feel most 'awake' (i.e. the least amount of running on autopilot, as it were), when talking internally to myself, and fully aware that I am doing so. Which only happens now and again, maybe a couple times a week. Note to self: do this at least once a day...

Also, the air today was very clear, with the bare tree branches in sharp contrast with the faint blue cloudless sky. It's almost like being in a hard vacuum, except it was also windy, and I could breathe, among other things.

Time

2005-01-25T18:08:00.000-08:00

Every now and again I take notice of the passage of time itself. Most recently I was drinking a sip of coffee and then suddenly the ephemeral, knife-blade like flow of time became the prominent center of my attention: I 'watched' myself take the sip, and then sat there and 'felt' that moment slide inexorably away - first the sip was just a few seconds ago - almost close enough to 'touch', and then it steadily drifted further and further away.

It then occured to me that it didn't necessarily have to be like that for a conscious being. Say you have physically downloaded all the neural patterns of your brain into a very advanced computer using some sort of fantastic futuristic nanotechnology. You could then change the programing of your own mind. In particular, imagine watching 2 movie screens right next to eachother, which are displaying the same events, only there is a small delay in the second screen. You could then have a huge series of such screens, perhaps each one delayed by one frame, so that you would be simultaneously experiencing an entire smooth chunk of time flowing into the future, instead of just the razor-thin 'present' that we have always been constrained to. Naturally we can't realistically follow more than a couple screens, but in this new malleable brain you could multiply the structures of your visual cortex a thousand times over, feeding each copy a slightly more delayed image.

And that would just be the beginning of the fun. Next, in order to further differentiate the different moments in time, perhaps you could derive whole new types of colors that would be used at different points in the segments of time that you simultaneously experience. Imagine watching a sunset, say with a cloud up high that reflects a deep red color that remains fairly constant during the time segment (say just a minute for now) that you are currently experiencing. You can then first imagine changing that red color continuously throughout the segment, so that the leading edge is the red we are familiar with, but it morphs into orange and then yellow, and so on so that it is purple by the end of the minute being simultaneously experienced - the color changes adding more depth to the range of time. But of course we can't steal from the other colors, so red would have to blend into some new color red2 which would become red3 further back in the segment and so on, with yellow and green and all the others also simultaneously evolving into yellow2 and green2 and so on.

Portals

2005-01-12T11:10:00.000-08:00

A link from plastic on next generation television technology got me thinking. The nanotube aspect is cool and they've done some work on it here at UNC - essentially the ends of the tubes are very sharp, and thus when a voltage is applied there is a very strong electric field at the tip so they eject electrons easily.

In particular, the idea of these enormous televisions with possibly very high resolutions got me thinking of a really cool (and very expensive) art project you could do. Imagine a flat circular television some 10 feet in diameter with a per-square-centimeter resolution like a computer monitor, so that the whole thing would need some 100 million pixels or so. You'd have to have a mini-supercomputer just to process the data. And the image would be coming in from some big cluster of video cameras somewhere else in the world - let's say for the first one a skyscraper in Tokyo looking out over the city - which would be seemlessly spliced together for the super-high res. TV. And that would be it - it would broadcast that view 24 hours a day, 365 days a year, the webcam to end all webcams. You'd have the TV set in a thin seemless metal disk, perhaps on a pedestal set 3 feet off the ground, otherwise completely freestanding out in some public space, and it would be just like a wormhole portal to another place like you read in science fiction. The key would be the huge resolution - it wouldn't be like staring at a computer image on a screen, it would be like you were really there yourself - you could watch the clouds slowly morph and the shadows creep as the sun moved through the sky, and all the people and cars moving on the streets below. You could have another image on the opposite side of the disk, maybe a live feed looking up into the Himalayan mountains, and there could be other disks in the public space, looking out on the beaches of Hawaii, the city of Cairo with the pyramids in the background, the Canadian rockies while it's snowing, maybe one in Athens with the sun setting. Also, if you could get a live continuous feed of a low earth orbit satellite looking down on the earth that would be awesome - in fact, since this would take a while to be realized, maybe the opposite side of that disk could be a continuous feed of whatever galaxy or quasar the James Webb space telescope was currently observing.

No more free lunch...

2005-01-08T13:07:00.000-08:00

Here's a nice article by Herb Sutter making the case that further advances in computing power will be gained by developing multiprocessor technology, as opposed to continuing to ramp up the GHz. Apparently Intel is planning on creating chips with hundreds of cores eventually. Which is fine by me! Programming for parallel machines is somewhat trickier, but is natural enough once you get used to it. Say your program is looping over discrete time steps, with different nodes handling different areas of the computation (perhaps subvolumes in a 3-D model). Each node in turn will likely need to both work on data that will be sent to to other nodes (perhaps boundary conditions), and also work on completely internal data. It then makes sense to do the boundary calculations first, send off the results through the network, then work on the internal data, and by the time that is finished, the boundary data from other nodes should have arrived, allowing the next time step to immediately proceed. There are all sorts of tricks to be invented, and most programs that need huge amounts of processing power can be largely parallelized. Vector processing should be kept in mind too - ClearSpeed's CSX600 chip gets 50 Gflops running at 250 MHz with 96 processing elements - and all that with under 5 watts of power. That would get you to 100 Tflops - the current peak for supercomputers, and the estimated power of the human brain - with only 10,000 watts (which would be about 100 times less efficient than the human body - not bad though!). A.I. research, in particular, should be able to thrive on multiprocessor systems, since the human brain itself is a paragon of parallel design, with some 100 billion neurons, each one connected to some 1000 others.

Junk DNA?

2005-01-05T09:12:00.000-08:00

Science magazine's # 5 story of 2004 is about the growing realization that much of the so called "junk DNA" which doesn't directly code for proteins (some 95% of the genome), does in fact provide important gene expression regulation functions, as well as code for transposable sequences that can jump around the genome, and for tiny RNA molecules (i.e. ncRNA - noncoding RNA, instead of messenger RNA for example), among other things. In fact, the complexity of an organism doesn't appear strongly linked to the number of genes it has (we're down to ~ 20,000-25,000), but in fact is linked to the percentage of the DNA that is noncoding (humans - highly complex mammals - also have a relatively high percentage of non-coding DNA). See for example: Taft and Mattick's paper, from the Quantitative Biology section on arxiv. There's a website dedicated to the subject too: Noncodingdna.com. The tiny RNA molecule coding sequences are particularily amusing - one of the theories for the origin of life is the RNA World hypothesis, which holds that RNA strands were the beginning point for life, since they can both self-replicate and also catalyze some chemical reactions like proteins. Perhaps these tiny RNA molecules are a 3 billion year old link to the origins of life on earth.

I've also had a pet theory for a while now that the non-coding DNA sections are important in accounting for all the subtle differences between people. When it is not being actively replicated or translated into RNA, DNA is coiled up tightly and wrapped around spool-like histone proteins. Thus the idea is that the differences in the A-T and C-G hydrogen bond strengths and the frequencies with which these base pairs occur in the junk DNA surrounding a given gene will subtly affect how easily the DNA is uncoiled and thus slightly affect the expression rate for that particular gene. This could then lead to, say, all the subtle variations in facial structures between different people (which our brains are so primed to detect), or perhaps partially account for differences in the inherent affinities of different brains. Presumably this could become testable after we gain more understanding in designing DNA and in protein folding and function.

Flux

2004-12-10T13:51:00.000-08:00

UNC is currently in the middle of a very large construction program. Every third building is being torn down and replaced or stripped down to a structural skeleton and refurbrished. Severe thunderstorms moved through late last night (presaged by a cinematic bout of fog that sublimated yesterday afternoon) - I was woken around 4 am by a giant roaring crack of lightning that couldn't have been more than fifty feet away, close enough trigger a cringe of existential fear as I was catapulted back into consciousness - and so today everything is wet. All the construction sites splotched over campus like a symbiotic blight are now mired in clay-orange mud. Squirrels toil among the gravel and exposed pipes. Walls of new brick ascending next to the bombed out old, sheets of dingy plastic blowing over old metal beams. And so I thought that this was a agreeably natural state for things to be in, phenotypes in flux, as opposed to a more naively picturesque and timeless environment. It reminds me of a forest with saplings emerging among mossy downed trunks, miniature landslides being swept away by streams of clear water cutting into their vertical banks, newly exposed julia roots tasting the air. As I am wont to do, I then imagine the cheerfull chaos as entire planets are dissassembled in order to make use of all their atoms, not just the thin shell on the surface. Doubtlessly there will be some humans, still enamoured of their cells, mucking about in the maelstrom of activity, like squirrels in the soft dirt, while their terrible children, alien as trilobites, pluck tiny strings and form sweeping enigmatic plans.

Flashlight

2004-11-04T20:58:00.000-08:00

Another idea - at times it occurs to me how vast the realm of possible conscious states is compared to what you experience at any one moment in time. Consider just vision - as I've argued in other places, we have an effective resolution of about a million pixels (there are several million color sensitive cone cells - mainly located in the center of our perception - and some hundred million light intensity sensitive rod cells intermixed there and dominating further out {which is why its easier to see faint stars when not looking directly at them}, but all this visual information is compressed by the retinal neurons before sending it down the optic nerve to the visual cortex) so if each pixel can see a million different colors, there are (10^6)^(10^6) different possible images we could see, an astounding number. Likewise, out of all the possible thoughts we can have and memories we can access, we only focus on some tiny subset at any one point in time (our RAM is much smaller than our hard drive, so to speak). I've thought of a pleasing metaphor to sum this up: consciousness is like exploring the Grand Canyon with a flashlight on a cloudy night. It's actually quite nice, all sorts of colorfull rocks and hardy vegetation of various sizes, but every so often the thick clouds will part and the bright moon shines down, vaguely illuminating the vast dramatic landscape out beyond. And even then one can't even begin to imagine the lush jungles soaking in the monsoon, the cracking ice of the glaciers sliding down the mountains, and the waves of blowing sand drifting towards the giant crashing waves of water under the glaring noon day sun, all of it far over the straight-line curve of the horizon.

Life goes on...

2004-11-03T21:39:00.000-08:00

Well, I have been quite negligent of my poor blog for the last month and a half - should try not to let that happen again. All sorts of thoughts should be recorded... Start with a small one - riding back from the movie theatre on Halloween night with Katie (saw the spooky "The Grudge" appropriately enough), and early on during the drive a big grasshoper hopped onto the windshield down by the wipers. We figured it'd be blown off as we accelerated to higher speeds, but it hung on, first sheltering behind the wipers, and then just holding onto the windshield even as we went past 50 mph. It made it all the way home, where upon - of course - we poked at the intrepid insectoid castaway, which in turn naturally prompted a startling POP-jump and away it flew.

New thoughts on statistical metaphysics, which I'm thinking of changing the name to the Observer Class Hypothesis. I think it is key that we are not abstract turing machines out floating unmoored in the ensemble (so to speak), but rather physically realized computers embedded in a reality. This is because, being so embedded, we are constrained in the information we can process - we only have so much memory M, and can thus only consider ideas Z that can be encoded in M or less bits: I(Z) ≤ M (all of this will be later upgraded to be functions of time: M(t)...). Now, when first considering the ensemble it may seem like a hopeless mess - any group of structures of a certain type would be offset by another group of the opposite type, or for any 'function' ƒ(...) you will also have it's inverse, so you can't prove ƒ. But this does not hold if we order the information by size. There, if we, say, only consider all programs Z such that I(Z) ≤ N for some bit length N, then you only get some program behaviors and not others. Constraining the system brings about structure: Constraints ⇒ Structure. I.E. that's why we are physically realized computers, embedded in an immediate exterior reality from which we draw most of our information, and which we must successfully explore and manipulate so that M(t) ∼ e^(αt) ...

More soon.

Chemical bonds and bounds.

2004-09-12T18:41:00.000-07:00

Had a couple martinis and fruit smoothies with Katie last night and thus some interesting conversations too. Staring into the pureed strawberries, blueberries, peaches, and soy milk and feeling satisfyingly healthy, I wondered what exactly was so beneficial about the emulsion of water, sugar, cellulose and delightfull esters. Perhaps the body makes use of all sorts of trace chemicals from the plants, or maybe it "enjoys" breaking them down with various enzymes, insofar that doing so necessitates the expression of said various enzymes, and thus using the system keeps it well oiled. Maybe not, but the immune system needs such pressures to keep it up and running, and a similar phenomenon is seen with the benefits of slight amounts of toxins (Hormesis).

This quickly leads one to wonder what the limits are for the capabilities of carbon based organisms. In one sense it seems likely that we are near the top, almost every molecule in our bodies is serving a purpose, either storing information in DNA or transporting energy as ATP, or forming the cellular membrane or one of the transport chains in it, or just one of the water molecules that allows all enzymatic chemistry to take place. But then genetic evolution must proceed continuously along minimas in abstract fitness space, perhaps there are much deeper minimas off the beaten path which are separated by insurmountable peaks. And it seems a bit overly redundant to repeat the same DNA sequence in each of our bodies 1000 trillion cells - so much more information could possibly be stored! Sure, you couldn't design an organism that could jump 100 meters up into the air or eat lava, but, perhaps, could you design one with an extremely adaptable enzymatic digestion system, so that when presented with almost any organic compound it could experiment with it at a purely chemical level, designing a way to break it down and extract energy from it, or at least not be poisoned by it? So that, say, you could step out from your spaceship onto an alien ecosystem on a planet orbiting Vega, break off one of the spiraling purple branches from the surreal shrubbery, and chew on it contemplatively, as your high tech innards deduce the molecular structure in real time, extracting energy from familiar carbon-hydrogen bonds, and thwarting the advances of opportunistic alien viruses? Could such a system be prevented from immediately digesting itself, or effectively neutralize the inevitable hyper-cancers (perhaps via a recursive series of preventative mechanisms, each with a very low probability of failure...)? Could such a system be realised in a 100 kilogram, 100 watt organism, so that it could also run a four minute mile and do calculus?

Here comes Frances

2004-09-02T21:19:00.000-07:00

Awesome movie of Frances from the GOES satellite.

note to self -

2004-09-01T19:53:00.000-07:00

More cool stuff in Jech's Set Theory - in chapter 12 we get to Models of set theory, where you form languages: L = {P,..,F,...,c,...} with relations P, functions F, and constant symbols c. They consider up to countable languages: |L| ≤ ℵ0 - I wonder if uncountable languages could form a usefull representation for statistical metaphysics - where you build up to them in a limit process by always selectively adding on higher order rules (more Ps,Fs, and c's) not derivable from the previous ones.

Already September first, and another big hurricane is on the way - Frances. Gaston blew through on Monday. Also getting close on my research - whittling the problem down to something I can model - the problem is that I have to use a lot of spherical harmonics to resolve small objects far away from the origin, and the problem grows as N^5. I can invent all sorts of tricks to simplify things, but are they valid?...

Found a cool mandelbrot set program - click on the picture below for the link. And here's another site which gives a good introduction to the theory. Oh, and I ran across Ed Witten's web site which has some nice papers on it.

Transvision & Set Theory

2004-08-25T19:47:00.000-07:00

So I went to the transvision conference... I thought my talk went quite well, lots of young people had insightfull questions and seemed quite excited about Statistical Metaphysics. I'm still talking to Anders Sandberg about it too, he's concerned about the noise ASORs dominating the counting, which they do unless you introduce representation independence (which also conviently converts complex explicit ASORs into nice finite implicit ASORs). He suggested reading Gregory Chaitin's work, which had I linked to before, and now I've gone ahead and read his online book Meta Math, which is quite good. In particular he suggests that perhaps infinite precision reals don't exist, i.e. there are only infinite sets of finitely complex objects. I need to hunt down his more formal books where he defines algorithmic complexity... This also generally reminds me of Murray Gell-Mann's thoughts on complexity - i.e. the interesting stuff is inbetween minimal and maximal entropy. I've also had some conversations with Rudy Rucker who leans the other way, so that all these infinitely complex sets (large cardinals and so on) exist. He acutely points out that the number of permutations of observers is always countable at any finite time (i.e. at any finite complexity). Indeed, I've been thinking about splitting the argument for both cases - infinite sets containing only finitely complex structures, and those also containing infinitely complex objects (like un-nameable reals). If evolving observers form the largest subsets (largest proper classes?) of these classes, then it is explained why we are observers, and we get a hell of a falsifiable prediction as well! Actually, that reminds me - I've started reading Thomas Jech's Set Theory so I can place all this in a more formal langauge, and amusingly enough, immediately on the 3rd page we introduce the INFORMAL concept of classes! It's stated that this is because classes are easier to work with than formulas, which is reasonable enough, but then on the next page we define the universal class: V = {x:x=x}, the class of all sets. We can't define the set of all sets due to things like Russel's Paradox (i.e. the barber that shaves all people who don't shave themselves... more here and history), which in set theory means we have to drop the axiom Schema of Comprehension: Y={x:P(x)} for the weaker axiom Schema of Separation: Y={x ε X:P(x)}. All sets are classes, but classes that are not sets, like the universe V, are proper classes. Very interesting stuff.

The talks at Transvision I was most interested in were scientifically oriented, like Aubrey de Grey's idea of designing enzymes to break down chemical waste that our lysosomes are incapable of splitting, like oxydized cholesterols. Rafal Smigrodzki argued that we will be able to replace our mitochondrial DNA, which doesn't have nearly as much error correction as nuclear DNA. Furthermore he suggests that we don't have to use virii as the transport mechanisms to replace the DNA, but instead use special protein structures that can pass through both the cell and mitochrondrial membranes. Ramez Naam also talked about some intriguing neural implant upgrades - 16,000 pin grids are being developed I believe.

The CN tower is pictured below, and the conference was in the building to the left. After the talks on Saturday night I walked down to it, and it takes an amusingly long time to get to it (maybe 10 blocks?) - it really is quite big!

3x+1

2004-08-14T12:13:00.000-07:00

...,37,112,56,28,14,7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,...

2004-08-04T10:03:00.000-07:00

Some more good blogs via boinboing: Neuroscience book writers Matt Webb (I love the background graphics) and Tom Stafford. And pictured is a drawing I did of a rather unlikely scenario suggested by Doug Hofstadter (GEB pg. 383: "an upside down dog flying through the air with a cigar in its mouth"), and it is hopefully somewhat reminiscent of Rene Magritte.

2004-07-30T21:41:00.000-07:00

(In his spirit...) The particular class of permutations of some 10,000 trillion trillion atoms - many ancient supernova ash - that conspired to form Francis Crick's brain and body have given up the ghost in our local branch of the universal wavefunction. He will not be forgotten.

The sky was beautifull today, July 30, 2004. After yesterday's dramatic storms, the sky was a deep clear blue this morning with friendly puffy white cumolous clouds that you could almost reach out and touch. Then, as dusk approached the clouds that remained were brilliant faint cirrus, and as the sun set and the tree tops were that wonderfull golden-green, the clouds glowed white, infinitely far away. And in the dark, through the tree branches, a bright white full moon rises.

2004-07-28T14:40:00.000-07:00

The picture below is from Jared Tarbell's complexification.net, got there from a link on BoingBoing. He does lots of wonderfull, interactive computer art, and he's also featured at levitated.net. I also found this cool compilation of tall buildings from moma.

Oh, and today's fun integral is ∫ 1/(1+e*Cos(x))^2 dx, with 0 < e < 1, evaluated from 0 to 2π ...

2004-07-25T13:52:00.000-07:00

Lots of links, part 2. First, one of the classics: Gödel's incompleteness theorem. Perhaps after going through the proof in detail I could come up with more rigorous mathematical arguments for Statistical Metaphysics, although stat meta certainly isn't any one particular formal system (which is also why Gödel-like proofs do not invalidate it - if anything they corroborate it, i.e. we will always need to add interesting new axioms...). And some more neural network webpages I found from Jenny Orr, and Ben Best. Apparently back-propogation is a big deal for training the networks, although you also don't want to overtrain them so that they can generalize better (which can be done by adding random variations). I wonder if just iterative evolutionary processes can be enough to train them - doing lots of local mutations on the connection strengths for different members of a 'species' and then selecting the best one (round-robin tournament?) and making more variations around it... And this talk of competition reminds me that I watched Lance finish off the Tour de France this morning, which was quite inspiring. And oh yeah, I met a cool new physics graduate student Michael Good last week, who is also interested in the mathematical foundations of reality. Apparently his former advisor David Finkelstein also proposes that all mathematical structures exist, which then leads to the natural statistical conclusion that we will always find more complex mathematical generalizations in physics.

2004-07-24T21:01:00.000-07:00

More links... I found this fractal website from pages on cellular automata. It's an old-school late 90's site (with updates up through 2003), which makes me a little nostalgic - I've been online for almost 10 years now! Looking forward to the web in another 10. And this philosophy site from Stanford is (unintentionly) humorous - he goes on and on saying that it is not necessarily the case that Turing machines are capable of emulating the mind, finishing with: It is an open question whether a completed neuroscience will employ functions that are not effectively calculable. i.e. he suggests that the operation of the brain could depend on functions like the halting probability, which is absurd. The brain is a neural network working in the classical limit, and even if essential quantum effects played a role (not likely - Tegmark argues decoherence occurs at around .1 picosecond) the atoms in the brain can be simulated to arbitrary precision as programs like Gaussian make clear.

2004-07-20T15:22:00.000-07:00

After googling for Conway yesterday, I found some cool Game of Life links: such as this quick one, and this fairly cool collection hosted at UNC's very own www.ibiblio.org: lifepatterns, which among other things has a link to Rendell's turing machine.

2004-07-19T12:52:00.000-07:00

Awesome: hyperreal numbers and surreal numbers. I particularily like that Conway developed surreal numbers while studying the game of go.

2004-07-16T23:20:00.000-07:00

Here's the picture I talked about in the previous entry. And what do you know, it looks like they're maybe 5 centimeters long... Also, if you look closely you can make out the tiny flashes of color on the ends of the droplets. The beach was a lot of fun. For some reason I really enjoy being out on the beach during the brightest high noon (mad dogs and Englishmen?) - and when you think about it, it is a fairly rare type of place within the galaxy... It was also really nice to relax, see the family, and work on some side projects. Started writing up some string theory in latex, and I'm thinking that doing a numerical project with membranes would be a good idea, maybe get a paper out on it before I graduate. Seeing the equations really drives home that we are composed of mathematical structures. Speaking of potentially large-dimensional matrices, I also worked on my neural-net go-playing program, which I think will have at least 7 different indices. And I'm working on a follow-up to the primordial soup story which should be awesome.

It's been a busy week, but I've got some good analytical calculations for my paper done. One amusing thing I did was go to the math/physics library to get a resource for the calculation, and seeing Newton's principia made me stand back and look at all those books and appreciate how much has been done in the last couple hundred years. I spent a good couple hours going though books with interesting titles and reading bits in them. Exponential growth... Oh, and I went out with Katie at sunset and had sushi tonight, to celebrate her getting a job, and that was a lot of fun.

2004-07-12T12:14:00.000-07:00

Allison is coming home from Australia soon, so I thought I'd post another picture from the trip - this one's from Hong Kong. And I just got back from Hilton Head. Random impression - coming back from the beach at high noon, I'd wash off the salt water in the outdoor shower. With the sun shining down from overhead, the falling water droplets were dazzingly bright - they seemed to form centimeter-long sparks of pure light. Thinking about it now, the water droplets had fallen about a quarter of a meter, giving them a speed of v=(2*9.8*.25)^.5, about 2 meters per second. So if the eye was seeing in .1 second 'snapshots', then the streaks of light should be 20 centimeters long. Hmmm... They did flash in and out of the field of vision almost as fast as possible - say I was seeing .02 second glimmers, that would give 4 centimeter long streaks, which still seems a little long. I took a photograph of the shower in the sunlight, maybe that could help resolve the issue if the shutter speed is known. Still, the most hypnotic thing about watching it was that there were tiny refracted rainbows just barely visible at the ends of the falling water droplets - shards of red and yellow glinting at the edge of perception.

2004-06-26T13:22:00.000-07:00

Some Space Elevator links I found on slashdot - isr link, and one from wikipedia. It's very impressive that such a thing is even possible, allthough I'm still not confident that it will actually be built. Not only do 60,000 kilometers worth of the carbon nanotubes have to be manufactured, it all must be imperfection free - it really is as strong as the weakest link. They need to figure out a better way of holding tubes together as well - pressure bonding them together has been suggested.

2004-06-24T12:27:00.000-07:00

Two websites on Gerontology - i.e. the science of aging: Chris Smelick's (I taught his physics lab, he encouraged me to start my website): Biological Gerontology and João Pedro de Magalhães' Senescence.

2004-06-21T18:33:00.000-07:00

I thought this description of the air-braking of the space shuttle was also cool, got the link from slashdot where they are talking about the space ship one flight.

2004-06-21T14:51:00.000-07:00

I thought this website was interesting: Retrofuture. Still, exponential technological and scientific growth continues unabated, if perhaps not in the directions people had predicted several decades ago. Along more tradiationally awe-inspiring lines, today Scaled Composites launched a man into space (barely, but an excellent start) with only 20 million in start-up capital, and they're looking pretty good for winning the X-prize. They have much more ambitious plans in the works as well, including eventually leaving the earth's gravity well entirely. Also, IBM's Blue Gene prototypes are crawling up the top 500 supercomputer list.

2004-06-16T21:18:00.000-07:00

Another great picture from Allison, who I will write an email to very soon! Also some cool links: Gregory Chaitin's home page, which has interesting discussions of meta-mathematics which I tend to agree with - he states that it will probably be necessary to keep on adding different interesting axioms, just as one would expect with the ensemble. Then there is Robert Munafo's home page which includes an excellent long discussion on very large numbers*. And also Sean Carroll's blog, which he is quite good at updating.

* - Ok, here's my really big number system, which I think I came up with in my first year of college. Recursive exponentiation is key. Define the function n-star-x: n*x = x^(n-1*x), with 1*x = x. Thus 3*3 = 3^3^3 = 3^27 ~ eight trillion. Let alpha = (10^100)*(10^100), i.e. google star google, a rather large number. The next obvious step is beta = alpha*(alpha*(...*(alpha*alpha)))) where ... indicated alpha repititions of the n-star-x function. You can call this beta=alpha**alpha if you like. Thus we have described very large numbers with only a little bit of information - so the next logical step is to state the existence of numbers which are the largest that can be explicitly described in N bits, say gamma = largest finite number describable by beta bits. Amusingly enough, this is the current limit of research according to Robert's webpage - they call them busy-beaver turing programs.

** Also the APOD picture for Wed. was my favorite galaxy M87, although M83 is pretty good too, both the galaxy and the band (also listening to black dog these days). I'd rather like to visit M87 at some point in the future. The weather has also been amusing recently, with thunderstorms pouring rain furiously while the sun can still easily be seen shining, and then stopping on a dime, a soaking deluge becoming a fine mist in 30 seconds.

2004-06-10T09:03:00.000-07:00

Back from the cape. Here's a test print that my Granddad gave me, which is really cool I think, somewhat surreal with the dark trees and bright yellow flowers.

2004-06-02T20:55:00.000-07:00

Been a while since I've updated! - but I've been very busy. And now my favorite month has already passed, and won't return for 11 more months. That's all right, its more valuable that way - but it always passes so quickly. Usually it's just small moments in time which are ephemeral, but it seems like the whole month of May is. Hmmm, last time I had a pause where I think to myself - here I am at this moment in time - I was checking the tire pressure for Katie's car out in the hot sun - you almost sort of breath in the asphault, and its not a bad thing - shortly before she had driven off to see her parents. I love those moments, perhaps I should try and train myself... Been very busy with the research and Statistical Metaphysics though. I've finished my statmeta paper and presented it to the transhumanist conference people, we'll see what they think of it. They'll be astounded if they have any sense. And the research is so close to completion but it's not quite acting like I had expected - is it real behavior or a numerical chimera???

More random impressions - was reading Perdido Street Station before going to bed recently, and the characters go to consult an giant interdimensional spider for some cryptic, oracle-esque advice. I wouldn't mention it, but that night I had dreams of spides all over the place, including a hazy shape I saw in the dark, then turning on the light to see a giant spider on a glass of water I was drinking - but then rationalized that it was OK - big and yellow so it must be a friendly garden spider. And I wouldn't normally mention that sort of thing either, but the next morning the pinky finger on my right hand sort of itched/burned, but it didn't climb out of low level conscious thought until that afternoon when I thought clearly to myself that hey, my finger feels like its been dipped in weak acid, and inspecting it closely I find two tiny red dots rights next to the fingernail.

I had another memorable thought as I was driving home from the mall with Katie at dusk, and driving along the back roads we were enjoying the long 3-foot grass that was growing along side the road, and I thought to myself that I would probably be nostalgic for this sort of thing when I am a thousand years old.

Oh yeah, and I saw a brilliant bright blue meteor zip across the sky earlier tonight as the sun was setting.

2004-05-09T18:08:00.000-07:00

Cool computer art site.

2004-04-30T11:14:00.000-07:00

Another great site here with tons of pictures of the earth taken from the I.S.S.

2004-04-30T10:02:00.000-07:00

Magnificent.

2004-04-27T15:42:00.000-07:00

Amazing huge surf movies - got the link from futurehi which I'm thinking about writing for.

I also found a great mathematical physics blog by John Baez.

2004-04-25T22:31:00.000-07:00

I really like this picture of a forest dragon that Allison took in Australia.

So, getting back to the Lee Smolin visit. OK, he builds on the idea that collapsing black holes could have Bojowald bounces through the singularity, thus seeding baby universe big bangs, furthermore if the fundamental constants change slightly at each bounce, then those universes that have conditions best suited to produce more black holes will dominate the counting, and you would expect to find yourself in a universe with physical constants at least close to a local maximum for producing as many black holes as possible. Indeed it appears we do - one indicater is the masses of neutron stars - the lower the upper bound the better, and all observed so far do have the low value of 1.4 solar masses. Also the nuclear chemistry in stars leads to heavy element production in large stars, which is good for both life and black hole production...

That said, Lee didn't really push his theory very hard - because the fine details aren't there yet at all. For instance, in string theory the physics is determined by the geometry of the compactification of the higher dimensions. This geometry would melt at each bounce, so it's not clear in what manner it recrystallizes afterwards, and whether it would likely be similar to the previous compactification (good for evolutionary cosmology), or completely random (bad - and seems more likely...).

2004-04-22T13:19:00.000-07:00

Mothers Against Boomerangs! - my parents should bring me one back from Australia. Also want to try posting pictures see how this goes:

Seems to work well!

More good news - I got the Space Grant! And I also got into the Gmail beta! Woot!

More thoughts on physics to come - i.e. Lee Smolin's talk on Monday...

2004-04-17T22:19:00.000-07:00

I think it's about new right now too, or getting close. The APOD picture for Saturday got to me - we really have been up there and walked around on it. We need to return.

2004-04-17T22:18:00.000-07:00

Hmmm, this Fermi energy thing has me thinking about black hole singularities... With Quantum Loop gravity it is concievable that you could avoid the mathematical singularities from classical General Relativity by having discrete nodes in space, perhaps then all the particles that fall into a black hole would be compressed together in a volume a couple Planck lengths long - but then what about the fermi energy due to the exclusion principle? - it would be vastly larger than the original mass.... More later...

2004-04-17T16:13:00.000-07:00

Not surprisingly my 1 kg holographic-principle-breaking neutron black hole doesn't work - for a cold dense Fermi gas, the Fermi energy is hbar^2/mass*(6pi^2/v)^2/3, where v is the reciprocal of the number density v=V/N where V is the volume and N the number of particles. For a kilograms worth of neutrons squeezed down almost to its schwarzchild radius (10^-27 meter), the Fermi energy for the quarks becomes an absurd 700 trillion kilograms. Thus the combined weight of the now ultra-relativistic quarks would be about that of the Milky Way.

2004-04-17T16:12:00.000-07:00

Here's a cool math site - integers are laid out on a line with even spacing, and the line is spun to form a spiral, and there are emergent lines with high prime densities...

2004-04-13T11:50:00.000-07:00

Smash Hit Tom from Plastic pointed me to this cool link which gives simple numerical results for collisions of asteroids with the earth. Needs to be a 3-D hydrodynamic code though, so you could make a movie of the results...

2004-04-13T11:39:00.000-07:00

Trying out the new feature on BoingBoing that links to blogs that link to stories on BoingBoing, which I often do. Since linking to the actual news item on BB that states this is just too damn meta, I'll link to the next link which is some amusing pictures Cory took of a graveyard in England.

2004-04-12T21:45:00.000-07:00

This Link shows the most recently updated pictures to livejournal blogs - can be really funny and occasionally NSFW.

2004-04-12T21:40:00.000-07:00

More on the holographic principle and black holes from a conversation with Tobin Fricke on Live Journal.

There is a theory going around - the holographic principle - that the amount of information that can be stored in a region goes as the surface area of the region (let's just say a sphere) and NOT the volume. For instance this meshes with black hole thermodynamics - the temperature is related to the mass (inversely - a black hole's Hawking radiation has an average wavelength the size of the black hole, so a solar mass black hole would emit 1.5 kilometer radio waves - i.e. it would be much colder than the current microwave background) and thus to the surface area of the event horizon. Another derivation is given by UNC's own Jack Ng and Hank Van Dam - gr-qc/0403057 - check it out, it's an easy read. Thus my instinct when presented with something like this is to try and break it - and since the volume grows much faster than the surface area it seems like you should take a giant volume and then cram as much matter (and thus info) inside it as possible. The problem is that a black hole's radius grows that much quicker - the event horizon is linear in mass: R=2M (G=c=1). Thus very large black holes have very low average densities - indeed as I found (trivial really), current intergalactic densities give a black hole radius of about the radius of the visible universe. So to break the volume/area thing you actually want to go to small volumes or else you'll form black holes immediately. Let's see, the earth has a mass of about 10^25 kg, which is 10^52 protons, and a Schwarzchild radius of about 1cm, and Lplanck = 10^-33 cm, so there are 10^66 Planck lengths squared on an Earth sized black holes - no good. Hold on, matter at nuclear densities also won't work no matter how small, but taken at schwarzchild radius density... OK 1 kg of neutrons is ~10^27 particles, with a RBH~10^-27 meter = 10^7*Lplanck, so there are ~ 10^15 possible bits on the horizon according to the holographic principle, but 1 bit/neutron would bit 10^27 bits! You can beat it at tiny volumes! I'm going to have to look at this more, but the densities here are much higher than nuclear density - not that this would stop a theorist! Thanks for getting me back onto this Tobin! I'll see if the details pan out... For one thing it would be a quark-gluon plasma, not neutrons - but I don't think the binding energy mass would increase much - only gets big when you try to separate them. Ah, but they are fermions - degeneracy pressure would push the temperature and energy way up - have to check it out.

Oh yeah, and we're not in a black hole because there must be matter beyond our visible horizon at 13.7 billion light years - can tell that because from measuring the CMB radiation we know space is very flat. If it was a vacuum outside, our visible universe would collapse to a singularity in time T=pi/2*(3/(8*pi*G*rho))^1/2, rho~10*10^30*10^11*10^11/(10^10*10^16)^3=10^-25kg/m^3, so T=2*10^17 seconds, which, I'll be damned, is about the age of the universe. But then the metric for a collapsing ball of dust is the same as the Freidmann-Robertson-Walker metric, so maybe I shouldn't be surprised. Huh. So the evolution of the universe forward from the big bang really is very similar to a black hole collapse. Lee Smolin has the idea that collapsing black holes seed new baby universes - then if the physical constants can change at each singularity the system will evolve towards universes that have physical constants most favorable to the formation of lots of new black holes - these will dominate the counting. That's looking even clearer to me now. I can't wait to talk to Lee on Monday, he's coming to give a colloquia. I need to really go back and look at Martin Bojowald's singularity evolution code...

2004-04-12T14:44:00.000-07:00

Posted this over at LiveJournal on the connection between General Relativity and gravitons.

Yeah, gravitons and Classical GR are somewhat disjoint. In GR you can assume weak feilds (chap 18 in Gravitation, or MTW as we call it), i.e. guv=nuv+huv where g is the metric (u,v indices) n is the metric for flat space - Minkowskian - and h is a pertubation on n, with |h|<<|n|. You can then get various things out of h, like Newtonian gravity (laplacian psi = rho...) and then post-newtonian effects (precession of Mercury's orbit, gravitational redshifting and time dilation - and hopefully frame dragging will be detected shortly with Gravity probe B). Using a 'Lorentz' gauge, you can also get box(h)=T, i.e. the wave equation. So in the weak field limit you can think of h as a separate field on top of a flat background, and you quantize just h (creation and annhilation operators for quanta of h with certain momentum), and this spin 2 field is the graviton, all of this following the standard prescription of quantum field theory for QED and so on. Note in string theory also you have this spin-2 h field on top of a fixed background metric. So String theory will not be the final theory, we'll probably also need to unite it with quantum loop gravity for the strong field limit, although this is probably premature since we can't even extract the minkowski spacetime limit from quantum loop gravity yet! Not to mention classical GR needs it's strong field limit tested also, which hopefully will be done with LIGO and LISA, and it may well not hold up. Lots of people are also trying to modify GR due to dark matter and dark energy - mostly dark energy I think because gravitational lensing makes it fairly clear there are smooth galactic scale lumps of matter out there.

2004-04-12T14:41:00.000-07:00

Amusing collection of perpetual motion devices, and some very good stereogram illusions too.

2004-04-01T11:13:00.000-08:00

Top 100 April Fools Hoaxes ever.

2004-03-27T08:54:00.000-08:00

Really wonderfull space colony website. Lots of great paintings of the rounded rotating interiors of different designs.

2004-03-26T12:11:00.000-08:00

Hmm, didn't really mean to post that, but needed to print out a progress report for my advisor and given the strange printer setup here that was the fastest way. Seems appropriate for a blog tho.

2004-03-26T11:38:00.000-08:00

Travis Garrett: Spring 2004 Research Summary.

I am still working on my first large project, a 3-D computer simulation of a binary star inspiral using a co-rotating reference frame and a scalar gravity approximation (Watt&Misner gr-qc/9910032). I think the code is almost finished: the evolution for the individual spherical components works well (the hardest part probably being transparent boundary conditions - always some numerical reflection), and the synthesis code works well also. The primary problem is getting the proper evolution of the system since it depends on very delicate spatial derivatives (evolving using geodesics...). I am trying to get around this through several different approximation methods and I suspect I will be successful soon. When I am I will write my first paper on it, and go on to have my prelim. The PhD project will be on the same problem, only using tensor fields. I want to write at least 4 papers in my remaining 2 years here, at least a couple on the main research I describe here, but a couple of shorter ones also - talking to Martin Bojowald I have some ideas on evolving through singularities using a discrete mesh at the Planck scale (and as a relativitist I should have some grounding in quantum loop gravity, which I'm studying now), on a similar line I'm looking at Jack's work on quantum foam, might be good for a quick paper, and I also still have an interest in evolving large systems of particles - like globular clusters or colliding galaxies, and have some code written for those, might get a quick paper out on those also. I'm also 60% the way through a formal write-up of Statistical Metaphsyics, where I derive being an observer from all mathematical structures, although I'm not sure where I'd publish it (but Max Tegmark thinks I should publish it somewhere, perhaps a philosophy journal). In any case, I've got a lot to do.

2004-03-24T12:54:00.000-08:00

I just noticed something interesting. For a certain amount of mass, if you compress it enough it will form a black hole with radius R=2MG/c^2, where M is the mass, G is the gravitational constant, and c is the speed of light. For the sun this radius is about 1.5 kilometers. For all the mass in the visible universe, the black hole radius is (drumroll), the current radius of the universe. More on this latter...

2004-03-23T10:41:00.000-08:00

hee-hee

2004-03-23T10:23:00.000-08:00

and a good nanotech page.

2004-03-23T06:31:00.000-08:00

Cool Chinese Architecture

2004-03-15T12:12:00.000-08:00

Interesting talk by Sean Carroll on eternal inflation and creating a low entropy situation at the big bang. Some inflationary models use a scalar field throughout space, then rolling down the potential hill of the field will deposit some of the potential energy into spacetime, causing it to expand. Then quantum fluctuations can take you back up the hill a bit, for even faster expansion, and even in a universe that has been spread out very flat by one inflationary period, one region of it can make another quantum jump and create another inflationary bubble. Any one finite region of space will thus get expanded into an infinite volume - going either direction in time no less! - and thus for every finite region entropy will increase indefinitely in both time directions. Thus our big bang with it's low entropy was not special - it was a perfectly typical and infinitely repeating situation.

2004-03-11T19:30:00.000-08:00

Just wanted to add a little more to flying dreams: I had another dream when I was about 14 where I actually got to float in the air (even better!). Still it was only a foot or two in the air, and there was a trick to it - you had to focus on it very hard, and cross your eyes. I'm pretty sure the inspiration for that one was the magic eye stereogram books, where the computer arranged random dots would make 3-d images if you focused your vision either in front of or behind the page. Also interesting was that in the dream I was floating over my bed, and bright orange light was spilling in through the window. I then wake up and its morning and the bright sunshine is shining on me, so it was very disappointing - hey I was floating a second ago, and it was right here!

Now that I think about it, I have very fond memories of having my bed right up next to the window - the sun shining in in the morning is always nice (I always want the windows in my bedrooms to face southeast), but best were the cool cloudless summer nights with the full moon shining over the field of grass, almost bright enough to maKe out color. Maybe a few whispy cirrus clouds, and the night sky wasn't even particularly dark - more of a light grey. Just the cool air and the moon and a few stars over the grass.

2004-03-11T10:40:00.000-08:00

Had an amusing dream last night - one could make small objects (glasses, pencils...) float in the air, if they were very finely balanced and placed in the correct position. In my dream I rationalized this by saying the centripetal acceleration from the rotation of the earth was holding them up - they were in geosynchronous orbit! This would be possible at the equator if the earth sped up so that we had about 1 hour days, which is much faster but not as if it would be flashing night/day like a strobelight. Likely dream motivation: I've been rereading the Hitchhiker's Guide before I go to bed, and am at the point where Arthur learns to fly by ignoring gravity...

2004-03-10T11:50:00.000-08:00

More neural networks stuff. In Hebbian learning neurons will form random dendrite connections to each other, then the connections that are used frequently - they correctly model information - are reinforced, and the others for which the firing is asynchronous (the two neurons are not communicating) fade away. Iterate the process and you evolve a complex network.

2004-03-09T11:56:00.000-08:00

Some cool pdfs on neuron cell structure from mni - the Montreal Neurological Institute.

2004-03-08T14:04:00.000-08:00

Update - was being silly, scored a 15 on this test which is a little above average. Sure, its obvious for most of the questions which way they will sway the result, but I still answered truthfully.

New chess program Hydra is doing well against others, and uses FPGA - Field Programmable Gate Array. FPGAs are cool because AIs will need to be able to evolve their neural networks, as the brain does by varying dendrite connections, and FPGAs thus allow for hardware evolution in addition to software modification. Sure, all Turing equivalent, but FPGAs can be much faster in some circumstances.

2004-03-07T19:57:00.000-08:00

Hmm. its 11 at night, and it turns out I am going to update my blog on its 3rd day of existence. Got a new CD player since the old one died after 7 and a half years (I fixed it for a week then it died again) - can get a 300 disk player for only 200 dollars, I guess because it is rapidily becoming archaic tech. Thus could put almost all my CDs in, and hearing some of the old ones made me remember softmore year of college and got me a little depressed, which is kind of rare. Actually read today on plastic about mind-reading - rather just picking up emotional cues from other people in their subtle facial expressions, and they not surprisingly said that autistic people do the worst at it, but more interestingly there is a sort of continuous distribution from them to the most sensitive. Made me wonder where I lie on the scale, and while of course I find my own emotional range and frequency to be perfectly fine and normal, I suspect I may be a little more to the autistic side. Maybe I'm being silly, but then I do prefer to spend most of my time inside my own head, thinking my thoughts - just 80% introverted I guess, although the 20% outgoing is quite...

Anyways, decided me and Katie should go out and have some fun, we saw Starsky and Hutch, which was ideal, and then messed around in barnes and noble for a while - read some of Smolin's new book and got inspired - I really need to work on both my physics and metaphysics very hard tomorrow. A dramatic storm blew through, the kind where little orange scroll bars appear at the bottom of the TV warning you about it, lightning and howling gusts of wind and everything, early on in March too.

Only a small selection of my experiences for the day, I guess the rest will fade into the depths of time, but then perhaps so will everything else when the stars all die trillions of years from now - in those small number of realities (but still very real) where complexity doesn't grow forever. Goodnight.

2004-03-06T11:53:00.000-08:00

Programming DNA? Sounds pretty good for nanotech...

2004-03-06T11:08:00.000-08:00

Been an interesting couple dozen hours - saw Lorenza'a day old baby yesterday, she had a full head of hair, was very quiet and observant, and had oddly capable seeming hands for a newborn, not that I've met many. There is the idea, perhaps with some validity, that the years seem to go by quicker when you get older beacuse each one is a smaller percentage of time compared to your whole life. Thus me, Mark, and Heather spent a couple months of subjective time with the baby by visiting with her for 15 minutes. And it seems reasonable, looking into its eyes, that their brains are forming connections at a million a second. Have too, have many trillions yet to go...

Had a couple beers that night with Mark, Heather, Constantine, and Gongpu at 'He's Not Here', out under the trees and night sky, and chatted about the big bang. For some reason, I'm getting nostalgic about it, which is ridulculous. Time keeps passing... As far as the universe is concerned, my life so far has been about a hundreth of a second.

Katie went to take her big test this morning, so I went for an adventure - I'd always heard that there was a bike trail through the woods to the east of campus, but I'd never been on it the 2 years I've lived here. Even though its been raining a good bit today, I figured that would just make it more fun, and it was. Its nice to get away from the constant stream of words and thoughts in ones mind, and they do leave dependably when you're riding a bike down a thin, twisting, steep, muddy, rocky, jutting-root-infested trail. A couple times thoughts would start to re-emerge more successfully when the going got easier, thankfully one that crystalized several times was: "continue to keep an eye on the trail you damn fool!"

Got a tiny little scratch on my leg and then some mud on that, and amusingly that was enough to get it a little infected, it stung and got red. Thankfully some of the thousand trillion cells that work together to form Travis thought to wash the leg with soap.

2004-03-05T10:35:00.000-08:00

First post on my new blog - check out this cool email from my dad:

Hey Guys,

Mom and I saw some interesting wildlife behavior today at HH I thought
you would want to read about.

It was sunny and warm today (Sunday) if you weren't in the wind. We
walked and ran on the beach, and on the way back we walked along the bike
path that crosses to the other side of the road from the little bridge
by Morning Beach. You know the rectangular pond that is connected to
the canal that runs beside the path. Today, there were 12 pelicans in
that pond flying up a few feet and then splashing back down, over and
over. It turns out there was a huge school of mullet trapped in the pond
because the water in the canal was only a few inches deep. The pelicans
would rise up in groups of 3 to 6 and hit the school at the same time.
The simultaneous attacks must have confused the fish because the
pelicans kept on catching them. It was deliberately synchronized and
coordinated hunting, which I have not seen before with pelicans. At any given
time, about 3 of them were taking breaks on the bank to rest and digest.
Then they would switch off with others. The attacks were almost
continuous and each dive bombing took only a few seconds. We watched them for
half an hour and during that time they must have caught about 2 fish
per minute. They were doing the same thing an hour earlier when we passed
by on our way to the beach. There were hundreds, maybe 1000 fish in the
school. I think a lot of animals are smarter than we give them credit
for, birds anyway.

Dad