I was familiar with it - with the magnitude of the "natural length scale of quantum gravity" - when I was 10 years old. Every person who claims to be interested in fundamental physics but who also reveals his or her "surprise" that the effects of quantum gravity cannot be directly seen in existing experiments is simply dumb beyond imagination.
Is quantum gravity directly relevant for people's everyday lives? Was it ever argued to be relevant? Is it a new situation that most people don't really care about fundamental physics or any other theory-loaded science?
Did the people on the street in the s say that they gave a damn? That's because they didn't. All of them have always known that these effects couldn't be directly seen because they're associated with extremely short distances and durations and extremely high temperatures. And indeed, it became possible to unequivocally say a lot of statements about the nature of phenomena that are crucial near the Planck length. The topology of space can change; the total number of dimensions visible at this scale must be 10 or 11 whenever all other "obscure" degrees of freedom are geometrized; black holes preserve the information, even during the evaporation; strings, branes, and various topological defects are parts of the spectrum whenever certain moduli approach the asymptotic regimes.
I could write thousands of pages of much more specific and quantitative predictions of string theory: Generating predictions is what string theorists are doing all the time. The fact that these predictions cannot be tested in your basement is not a flaw of string theory but an obvious consequence of the very choice of the questions: we want to study quantum gravity, the processes at the "natural scale". These processes simply can't be testable in your basement, because of a simple calculation that even kids should be able to understand.
This has nothing to do with string theory per se: it is a property of the very questions we are asking. The argument that quantum gravity is inherently untestable could have been made more than years ago.
But if someone had used it to suppress all research of the subject in or so, he would have killed hundreds of amazing insights that came out of this research. Many of them tell us seemingly "divine" answers to difficult questions about quantum gravity while others tell us answers to completely different questions - like those about the collisions of gold ions - that turned out to be connected with quantum gravity.
The people who are trying to suppress the research of string theory today are surely trying to eliminate many discoveries that will be made in the future. Paradoxically enough, it was string theory that has also found a possible flaw in Planck's estimate - i. And the extra dimensions themselves may still be a few microns in size. Predictions of low-energy physics that follow from the high-energy starting point are the "theoretical way" that connects the observations with the mysterious fundamental scale.
String theory reproduces all of physical quantities of low-energy gauge theories coupled to Dirac fermions including all loop effects, non-perturbative effects, renormalization rules, confinement, Higgs mechanism, etc. It parameterizes the low-energy parameters differently than QFT - in terms of discrete data instead of continuous data which might perhaps be viewed as "less convenient" ones but they are equally consistent. String theory is as correct a description of these non- gravitational observations as quantum field theories are.
You can't really say that it is "empirically worse off" than quantum field theories. And its theoretical status is surely better off than in quantum field theories: it incorporates gravity including loops and other quantum effects! And string theory is actually linked with pretty much all interesting directions in phenomenological "particle physics beyond the Standard Model", including supersymmetry, GUTs, deconstruction, and others. Reality: String theory is absolutely robust.
It can be demonstrated that there exists no consistent way to deform it or "slightly modify" its rules of the game. It is the first theory known to the mankind that has no adjustable dimensionless non-dynamical parameters whatsoever.
The adjective "malleable" associated with string theory is completely absurd. On the other hand, much like other theories in science, string theory predicts many solutions - many potential "vacua" - where physical phenomena might in principle take place.
Let me emphasize the difference again: we have entirely fixed rules but there exist many ways how to live according to these rules. But the number of predicted solutions, whether it is larger or smaller than you expected, can never be used as an argument for or against the validity of a theory.
It is simply a feature of the theory and one needs actual further tests to decide whether the feature - or the prediction, if you wish - is valid or not.
At this point, we don't have empirical data about these issues. Genetics is arguably disappointing because it doesn't show that the human DNA is unique.
It doesn't quite prove the existence of God who created humans to His own image. We cannot see God's DNA in the sequences that would distinguish us from monkeys and other life forms that were not created to His image.
What can they do about their disappointment? Well, they may pray and they may dream about a different, better Universe where God's traces can be identified in our DNA and where this preferred DNA sequence of God may be calculated. The calculation could perhaps use some hints from the Bible, they think. But that's about it: they can't do much more than that in the past, they could at least burn the heretics at stake to get some relief and so far they haven't presented the Biblical calculation.
The human DNA doesn't show any uniqueness of the human race. It cannot be calculated from the first principles. It is disappointing and ugly. It is true and paramount for biology, too.
Sorry: but maybe humans are not that special, after all. It might perhaps be the right time to start to consider this possibility, years after it was demonstrated to be true. There is only one theory and the wide variety of DNA sequences is an essential feature or a prediction of this theory!
Many people, including your humble correspondent, would sentimentally prefer a theory where all the other vacua were absent. It would simplify our life a lot. But science is not about a wishful thinking. The large number of vacua that are a priori usable instead of ours has been established to be very large. It is extremely unlikely that this insight will ever be undone. The only big related question that remains to be answered is whether physicists have any chance to identify the correct vacuum.
The anthropic people have essentially given up, believing that the "landscape" is just too vast and too chaotic: they use circular reasoning to assure themselves that our Universe has to "live" in a large, chaotic segment of the landscape where nothing can be determined with any certainty. And they think that vague statistical analyses of the landscape and qualitative predictions are the only possible advances that can be done beyond the present point, in the future.
And they might be right or "effectively right", for one reason or another. The other people, including myself, know that at least in principle, there can exist all kinds of methods to determine which vacuum is actually right - either by analyzing their detailed theoretical properties and comparing them with the experimentally measured properties of our world; or by finding a hypothetical selection principle that makes our vacuum and perhaps a few other vacua dramatically more likely than others.
Whether our vacuum is "random" and "anonymous" or whether it can be identified - and whether it makes sense to spend time with this big task which is a different question!
So far the right vacuum hasn't been identified, so the anthropic opinion is confirmed by the "status quo" in the same way as the opinion that "science has ended" was confirmed by the "status quo" at any other point in the history of science, too, until the following morning when science continued.
But the observation that at some level, there exists a large number of candidates for "the vacuum" has been pretty much established at least in the case of supersymmetric AdS vacua where the number of possible subtleties that could "kill" the vacua seems extremely low. In fact, our world doesn't look "quite so unique and symmetric" and it indicates that the number of "equally fundamental or symmetric" vacua must be much larger than one, to say the least. And yes, I consider the people who disagree with this statement to be complete deniers of the scientific evidence.
The large number of vacua in quantum gravity is an established fact of science. It will never be undone, much like we will never return to the idea of a Flat Earth.
This insight is not the last insight of science but it is an insight of science. Misunderstanding: Second of all, string theory is only formulated perturbatively. A full non-perturbative definition of the theory doesn't exist.
Reality: This statement is also wrong and even if one formulated a more careful but similar statement that would be technically correct, it would be morally wrong because the same thing could be said about quantum field theory, not just string theory, so one can't ever justify the application of this observation as an argument against the step or leap from quantum field theory to string theory.
More generally, it is also sociologically illogical to present quantum field theory and string theory as "foes" because they are not only equivalent in some contexts but a large portion of the best QFT experts in the world are actually string theorists.
That's completely equivalent to the situation in quantum field theory. There are some subtle remaining problems with supersymmetry on the lattice, despite the progress in deconstruction etc.
But whatever these problems are, they are equally serious or equally solvable for string theory and for quantum field theory because in this subset of backgrounds, they're really the same theories. An ordinary quantum mechanical model - with degrees of freedom X,P,theta extended into matrices - can be demonstrated to coincide with M-theory in dimensions if the size of the matrices is sent to infinity.
We can calculate physical quantities for finite N and send N to infinity, to obtain the M-theoretical result. It's as well-defined as undergraduate quantum mechanics.
If you are irritated by the absence of strings in the dimensional vacuum and by the absence of an adjustable coupling constant "g" in the BFSS matrix model, you may also write down the non- perturbative definition of screwing string theory due to your humble correspondent that was later renamed to matrix string theory by Dijkgraaf, Verlinde, and Verlinde DVV.
Nevertheless, the exact, non-perturbative definition exists for any "g". You don't have to expand anything. In fact, the key new contribution by DVV was to show that you could expand matrix string theory in "g" - and get the right stringy perturbative interactions, as I expected - which required some extra work.
But it's also the case that we don't possess non-perturbative definitions of all quantum field theories, either. Even if we had these definitions, it wouldn't mean that we can immediately calculate all non-perturbative phenomena out of them. When you try to calculate physics of a strongly coupled system, you always need some kind of cleverness - e. This general wisdom holds for string theory and for quantum field theory, too besides condensed-matter physics: ask the fractional quantum Hall effect people where their stunning pride comes from!
In string theory, we know many more non-perturbative phenomena - and many more of their relationships - than we know in quantum field theory. So once again, the situation in string theory is better than the situation in quantum field theory. The higher number of string-theoretical non-perturbative effects, dualities, and insights to learn may be attributed to the "larger size" of string theory.
But again, this "large size" shouldn't be surprising because string theory is understood to be a broader theory that should include all correct wisdom of quantum field theory, general relativity, and much more. So it must obviously tell us much more about the fundamental objects, phenomena, and their relationships.
And it is doing so beautifully, indeed. Theories should be as simple as possible but not simpler. As Edward Witten correctly observed, string theory has proven to be remarkably rich, more so than even the enthusiasts like your humble correspondent tend to realize.
There are still many things to be learned about non-perturbative and perturbative? Misunderstanding: Third, string theory describes perturbative expansions about fixed spacetime backgrounds.
Reality: First of all, this half-incorrect statement irrationally mixes two issues that have nothing to do with one another. In the previous section, we have explained that it is simply not true that string theory is only known or defined perturbatively.
After all, most of the insights found since are actually concerned with non-perturbative physics. Many non-perturbative effects, quantities, and their relationships are known. Explicit non-perturbative definitions of some vacua are known, too. So the adjective "perturbative" makes the sentence incorrect.
Now, remove this word and think about the statement that string theory expands physics around fixed spacetime backgrounds. It is true and it is inevitable, too.
Every consistent theory of quantum gravity must be doing so, at least when it gets to the "real work". If you consider infinite spacetimes - such as AdS spaces or flat spaces - they have a particular behavior in the asymptotic region at infinity.
All doable processes can only deal with a finite amount of energy and a finite amount of energy is never enough to "rebuild" the space at infinity.
That's roughly. As long as a theory is consistent with the very simple observation that a doable finite-energy experiment cannot rebuild the space at infinity, it associates a superselection sector with every classical configuration or every quantum state in its Hilbert space.
There is no way to avoid it. So any particular calculation of the Hilbert space has to be made for particular choices of the superselection sectors - for particular behavior of spacetime at infinity. Again, a theory that doesn't allow the space to extend to these asymptotic regions or that doesn't allow the geometry in these regions to be described by a well-defined geometry fails to agree with the very existence of space that is demonstrably much larger than the short-distance fundamental scale, to say the least and is instantly ruled out.
These asymptotic regions may have many shapes - and flat and AdS-like backgrounds are the simplest ones to be described by accurate equations - but such fixed asymptotic regions of spacetime must be allowed and respected, otherwise the theory would be instantly dead.
Misunderstanding: Any respectable fundamental theory of quantum gravity must be background-independent. Reality: The topic of background independence, which is pretty much equivalent to the previous section but I have also divided the discussion into two parts, in order to follow the cartoon , has been explained many times.
The people who like to say the same stupid thing as the boy from the cartoon usually severely misunderstand what the adjective "background-independent" means: the meaning they actually associate with this quasi-religious adjective is incompatible with basic physical consistency criteria.
They think that their "background independence" should prevent a theory from considering physics at specific backgrounds, in specific superselection sectors. Carlo Rovelli even thinks that one should find a background-independent propagator. He may even believe that he has found one. Propagators are defined to be the inverse continuous matrices of quadratic fluctuations around a particular background: they're determined by the kinetic quadratic terms in the action expanded around the background.
No background, no propagators. As argued above, every consistent theory living in an infinite space must agree with the existence of superselection sectors; must allow for the existence of realistic superselection sectors that resemble the nearly flat space we inhabit; and must be able to predict what happens in these sectors because virtually all quantitative questions we can ever ask about in physics have this form and it is highly questionable whether there exist any quantitative yet background-independent questions at all.
The people who use the word "background independence" incorrectly and quasi-religiously don't seem to get any of these points. And maybe, they're getting these points but they have already switched to a dishonest discourse in which it is better for them to repeat things they know to be untrue. That's widely believed to be the case of Mr Lee Smolin.
Second, there is a question whether the very character of a theory depends on the "background" or the "superselection sector". It can be demonstrated that string theory doesn't depend on the background: the local phenomena are always isomorphic.
While the separation of the states into superselection sectors is inevitable in any physical theory, the character of local physics should be independent of the choice of the sector. It can be demonstrated in perturbative string theory and other formulations of string theory that the identity of the theory is independent of the superselection sector. A modification of the background can be shown to be physically indistinguishable from a condensation of a particular configuration of strings or their non-perturbative counterparts, if we consider non-perturbative physics that existed in the original background: see, for example, Why there are gravitons in string theory.
So physics of string theory is surely independent of the background: every choice of the background leads us to the same theory. A completely different question is whether this independence is "obvious": physicists ask whether it is "manifest". The latter is pretty much an aesthetic, not physical, question, and our sense of beauty may often mislead us. As in most questions, the background independence is manifest in some approaches but not others. For example, there exists a way to define string theory that is very analogous to quantum field theory with infinitely many fields, if expanded into point-like component fields.
It's called string field theory not to be confused with all of string theory: "string field theory" is just a small sub-discipline within string theory. It works well for open strings only, especially if they're bosonic, but it gives us a new perspective on many questions related to perturbative physics and D-brane states. String field theory for the dimensional open bosonic string can be formulated in a manifestly background-independent way.
Yes, I've been designing T-shirts with this equation. The condensation of "infinitesimally perturbed strings" generates the whole background, smooth geometry, and its nilpotent BRST operator.
But you should have already understood that real, quantitative physics only begins when one picks a background, a superselection sector. Before one does so, many of the objects are too formal and cannot be associated with particular numbers. A physicist should always be careful about such formal manipulations: he should always ask whether his formula can generate very particular numbers that can be in principle both calculated and measured in the appropriate Universe. Martin Schnabl was extremely conservative about this important principle which is why his new remarkable "vacuum solution" to string field theory, once it was found, was and is so much more meaningful - and so much more correct and important - than dozens of "formal" results that generated "infinity minus infinity" expressions whenever you wanted to analyze them in detail.
His solution is linked with some rather deep mathematics on the boundary between complex calculus and number theory , too. So the genuine lesson is that any respectable framework in quantum field theory or any theory that generalizes it must eventually admit background-dependent calculations, in a sharp contrast with the stupid boy's proposition in the cartoon. Background-independent formulations - if they exist - must always be understood as a first, philosophical step to formulate the detailed, background-dependent theories.
Only the latter can produce meaningful, measurable numbers that can be compared with observations. It would be very pleasing to have a complete description of string theory that would cover all corners of its "landscape" and allowed us to calculate the properties of all vacua as solutions of some universal equations. Deep physicists have spent years with attempts to find such universal equations and they will surely continue to do so in the future, to one extent or another.
I didn't want to mention that the list includes your humble correspondent because I found the word "deep" more important and I wanted to avoid any self-glorification. On the other hand, such beautiful and universal equations that treat all possible corners of the landscape "democratically" are not guaranteed to exist. In some sense, we should expect that they don't exist - at least not to the extent to "directly tell us" which objects are weakly coupled at any point - because such equations would present all possible objects in all regions of the landscape as "equally fundamental" and "equally manifest" even though many of them are complicated bound states of each other.
Moreover, whether these equations exist or not has no impact on the question whether string theory is the correct fundamental description of the world around us as long as we determine our conclusions by the evidence rather than by the prejudices. Misunderstanding: Fourth, in string theory, the Dirac operator and the gauge fields are But in string theory, the Dirac operator and the gauge fields are derivable, omnipresent, and essential aspects of low-energy physics that can be deduced to exist in any realistic enough vacuum.
They play the same important role for the low-energy physics as they always did; the low-energy equations usually hold exactly in string theory, too. On the other hand, these old concepts are no longer the deepest or the "only deep" principles that underlie physics. In most approaches to string theory, they're secondary and can be shown to be consequences of more powerful unifying principles that generate other physical phenomena, too.
For example, the gauge fields with Yang-Mills symmetries and the fermionic matter fields that follow the Dirac equation are just two consequences of the conformal symmetry in perturbative string theory or superconformal symmetry: the superconformal zero mode on the worldsheet must annihilate the physical modes which directly gives us the Dirac equation in spacetime - nice. And the same conformal symmetry applied to closed strings with antiperiodic fermions also implies the existence of the metric tensor with the diffeomorphism symmetry also known as gravity in general relativity , the critical dimension, and many other things.
String theory also allows us to derive new, fundamental, and unexpected facts about gauge fields and the Dirac operator look e. At any rate, I know too much about the world to realize that evil must be confronted with fists. That's why I fully endorse the clever girl's reaction to the piles of rubbish that the talkative boy was emitting.
And to make it really clear how much I endorse her ;- , let me reproduce her classical answer to her obnoxious foe in its entirety. Summary: PAK! You keep talking like a bitch, I'm gonna slap you like a bitch.
You can see that Clifford Johnson is using gloves to communicate with the excessively zealous anti-scientific commenters who are spamming his blog with bullshit. That can't protect him from trash- talking at aggressive smear blogs such as Not Even Wrong. There's no peaceful way to deal with this situation, Clifford. So I kindly ask all the female readers to give a proper thrashing to every man who will emit the same crap as the unfriendly boy from the cartoon.
I hope it is sufficiently politically correct for clever girls to beat disgraceful, dishonest, and sub-par kibitzers like the well-known one from Columbia University. Thanks a lot. However, there is a certain sense in which I am superstitious and for which I have no rational explanation. I'm also willing to bet that you are superstitious too, and I'll prove it. I told you that you were superstitious. If you want to gauge to what degree you are superstitious, then ask yourself how much money needs to be under the ladder before you are willing to pick it up.
Electromagnetism is mediated by photons, the weak force is mediated by the W and Z bosons, and the strong force is mediated by gluons. It is postulated that particles called gravitons are responsible for gravity but the Standard Model does not include gravity but gravitons are great fun in Star Trek episodes.
For a simplified view of this, one can imagine the fermions interacting with each other by exchanging force carriers. This exchange of force carriers results in the appropriate force between them. There are six types of leptons: the electron, the electron neutrino, the muon, the muon neutrino, the tau, and the tau neutrino.
It should be apparent that the particles appear to be grouped into pairs: for each particle there is an associated neutrino. Triplets of quarks bind together to form protons up, up, down and neutrons up, down, down which make up the nuclei of atoms. Quarks have the strange property that they cannot be seen individually at low energies. The fermions are grouped into three categories called generations. The first generation consists of the electron, the electron neutrino, and the up and down quarks.
The second generation consists of the muon, the muon neutrino, and the strange and charm quarks. The third generation is the tau, the tau neutrino, and the top and bottom quarks. Each of the three generations are identical except for significant differences in the masses of the particles. So why are there three generations and not two or four or even more?
Who the hell knows? So let's finally get around to explaining the cartoon. For this we will need a bit of history. The first of the fundamental particles to be discovered was the electron in The existence of the neutrino was proposed in the early s in order to make certain energy calculations come out correctly.
However, direct evidence for the existence of neutrinos didn't come until the mid s. In , the muon was first discovered although it wasn't until when physicists figured out what the hell it was.
The muon is essentially a heavier copy of the electron as explained above concerning the three generations. It seemed very mysterious why nature should have a second heavier copy of the electron. It was by this process that the muon was first detected in The equations in the last panel of the comic describe the process by which pions decay to produce muons.
OR NOT. Thank you so much for posting comic For years I've had a crush on this gorgeous female co-worker but I've never had the guts to ask her out. Now, after being primed by your Magic Eye message, I've finally blah, blah, blah The scientific explanation for how Magic Eye images work is rather simple.
The image consists of a series of repeating patterns. For the type of autostereogram that I used in the comic, the image appears as a random set of dots when viewed normally. However, when a viewer looks at the image at close distance while crossing her eyes at just the right angle, each of her eyes are fixed on a different set of an adjacent pair in the repeating pattern and her brain mistakenly perceives the two patterns as a single image at a different distance.
We got well over 80, visitors the other day thanks in part to Digg, reddit, Wil Wheaton, Operation Agitprop, StumbleUpon, and all you bloggers that linked here.
This is my obligatory self-deprecating humor comic. Every new webcomic has to have one. It took him him 24 hours and 4 minutes to recite 67, digits on November 20, It should also be noted that Akira Haraguchi, a man from Japan, recited pi to 83, digits and , digits on two separate occasions but these performances have not yet been verified so they are still unofficial. Here are the current top ten official record holders:.
Without getting into too much detail, the U. The algorithm was subsequently promoted by the U. National Security Agency. Although nobody knows for sure whether anybody is in possession of the secret numbers, the discovery of the flaw and the endorsement by the NSA certainly raised some eyebrows.
The KH naming system was initiated in with KH Incrementing numbers following the KH indicated changes in instrumentation. To my knowledge, the most recent unclassified KH designation was KH from a satellite launched in Given the understandably secretive nature of intelligence agencies, it is reasonable to assume that classified reconnaissance satellites currently in orbit probably have an equivalent KH designation higher than I took a stab in the dark and picked KH for the comic. As of this writing, the official record for the fastest computer in the world belongs to a computer system called Roadrunner which is housed at Los Alamos National Laboratory.
Roadrunner posted a top performance of 1. The NSA has always played an important role in the development of the supercomputer industry and they have always been at the forefront of supercomputing research. They currently house some of the most powerful computers in the world at their headquarters in Maryland. Beyond yottaflop, numbers have not yet been named. The title of this comic, Secrets and Lies, is taken from a book by the same title written by information security expert Bruce Schneier.
Each letter of the keyword has a numerical equivalent which is determined by its position in the alphabet. Suppose that the keyword is of length n. To encrypt a plaintext message, it is first split into blocks of length n. Then each letter of each block is replaced by another letter that exists to its right in the alphabet.
The amount of this shift is determined by the numerical equivalent of the corresponding number in the keyword mod For example, if the the keyword is AMY, the numerical equivalents of the letters are Now suppose the plaintext message is BOB. The O gets replaced by the letter 13 places to its right. Since this shift is calculated mod 26, it gets replaced by a B.
Similarly, the last B gets replaced by the letter 25 places to its right, A. Hence, the encrypted message is CBA. If you know the keyword, then decrypting the message is simply a matter of reversing the process.
The key that I used for my puzzle was simply the first 30 digits of pi with each digit representing the amount of shift. The first 30 digits of pi are:. The quote in the original blog post is from the book Tristram Shandy by Laurence Sterne. Sterne took and modified the phrase from the Poliicraticus [Statesman's Book] by John of Salisbury, a twelfth-century churchman. The phrase can be translated as:. The three dimensions of space and the one dimension of time must be joined to form a four-dimensional spacetime.
Since it is difficult to visualize no less draw four dimensions, it is sometime convenient to think of spacetime using just two dimensions of space and one dimension of time as illustrated in FIG. Of course it should be understood that any representation in this three-dimensional spacetime could, in principle, be extended to four dimensions. Hence every point of a spacetime diagram represents an event — a point in space at a moment in time — and a particle in this diagram would be represented as a line, called a world line, as shown in FIG.
A closed timelike curve CTC refers to the world line of an object that returns to its starting point forming a closed loop. As things stand today, there is nothing within the laws of physics that would prevent the existence of CTCs. In the mids Scottish physicist James Clark Maxwell formulated the equations that unified electricity and magnetism.
I won't explain Maxwell's equations but I'll show them to you just because they look so cool. The following is one form of Maxwell's equations:. These equations show that a time-varying electric field produces a magnetic field and that a time-varying magnetic field produces an electric field.
An electric field and a magnetic field can sustain each other and form an electromagnetic EM wave that propagates through space. EM waves have many similarities with certain types of mechanical waves such as the waves that can be seen on the ocean. The distance from one crest to the next is called the wavelength. In fact, light itself is an example of electromagnetic waves. Visible light consists of electromagnetic waves with wavelengths in the approximate range to nm to x 10 -9 meters.
Other examples with which you are undoubtedly familiar include radio and TV signals, X-rays, and microwaves — each with a different range of wavelengths. The frequency can be thought of as how many times per second a crest of the wave passes a particular point as the wave moves. If a crest passes through a particular point once a second, we say that its frequency is 1 hertz Hz.
EM waves have been detected with frequencies ranging from at least 1 to 10 24 Hz. This broad spectrum of frequencies is known as the electromagnetic spectrum. Brown doesn't count. Just in case you were wondering, yes, this is a snippet of actual code that I wrote well, OK,… I improvised a little with the comments.
The code was part of my final project for a computational biology course. The project involved finding optimal parameters for artificial neural networks through evolutionary algorithms. Now I'll be the first to admit that I'm a terrible programmer, but I slogged through it and the final product was about lines of spaghetti code.
The program wasn't very efficient in terms of speed and memory usage due to heavy modularization and my injudicious use of serialization. However, it was quite effective at identifying certain promoter DNA sequences.
For me, writing it was a labor of love. The idea of artificial neural networks ANNs can have its origin traced to a paper written in by neurophysiologist Warren McCulloch and mathematician Walter Pitts [1].
In the paper, they described how nerve cells could possibly replicate certain logic functions that are essential for the operation of computers. It was believed that ANNs would be capable of performing some of the computing capabilities of a biological brain. It is now known that the neural processes that occur in the brain are fundamentally different and more complex than most artificial models, but ANNs are still known to be useful for many kinds of computational tasks and have remained an active area of research for purely theoretical reasons as well.
In biological systems, the neuron is the fundamental functional unit of all nervous system tissue. A biological neuron is composed of a soma or cell body that contains a cell nucleus and a branching dendritic tree dendrites that extends from the cell body. The dendrites can form connections synapses with other neurons.
The dendrites collect electrical signals from the other neurons. The signals are then integrated in the soma and a response is generated and propagated along a branching axon to other neurons see FIG. By some estimates, a single neuron can be connected to as many as 20, other neurons.
The computational ability of the brain is believed to arise from this massive networking between the neurons and learning is believed to occur through the formation of new connections and by the strengthening or weakening of synapses. If a sheet of neocortex from a typical human was stretched out flat, it would be about the size of a dinner napkin.
By comparison, the cortical sheet from a chimpanzee would be about the size of a business envelope and, for a rat, it would be about the size of a postage stamp. Some anatomists have estimated that a typical human neocortex contains about 30 billion neurons and that a typical neuron forms between to 10, synapses with other neurons.
Even using the lower estimate of , that evaluates to an astounding trillion synapses! An artificial neural network may be defined as:. It resembles the brain in two respects: 1 Knowledge is acquired by the network from its environment through a learning process. In an artificial neural network, each functional processing unit performs a simple computation: it receives signals from input links and computes an output which is sent to output links.
The computation consists of two components. First is a linear combiner that computes the weighted sum of the input values and the second is a nonlinear activation function that transforms the weighted sum to a final output value.
A single processing unit by itself is not very powerful. Just as in a biological brain, the computational power is derived from the combination of many units in a network.
The network topology and the connection weights are linked to the specific computational problems that the network is able to solve. Neural networks are often organized in the form of layers of neurons. In general, three classes of network architectures [2] may be specified as: 1 single-layer feedforward, 2 multilayer feedforward, and 3 recurrent networks.
A single-layer feedforward network consists of a layer of input neurons and a single layer of output neurons that performs the computation. The input layer sends its output to the output layer but not vice versa. Multi-layer feedforward networks are characterized by the presence of one or more hidden layers that perform some. The presence of hidden layers allows the network to perform certain computational tasks that single-layer networks cannot.
As with a single-layer feedforward network, each layer receives signals only from previous layers in the network. A recurrent neural network differs from feedforward networks in that neurons may feed its output to other neurons in previous layers.
The presence of these feedback loops may have a significant impact on the learning ability of the network. Training a neural network is a process by which the network learns relationships between inputs and specified output targets. Often this training process consists of a repetitive process using an optimization algorithm that adjusts the system's connection weights.
During training, each input pattern is propagated forward through the network and the output is compared with the target. The goal is to implement a method that adjusts the synaptic weights such that the errors are minimized. First of all, spin, by definition, is the internal angular momentum. And angular momentum is, by definition, the observable that is conserved as a consequence of the rotational symmetry of the laws of physics. That's the most general definition that follows from Noether's theorem.
It follows that in quantum mechanics, the angular momentum is always given by the generator of the rotations. That must be true in any consistent quantum theory. In quantum field theory, the electron's spin arises because every electron is an excitation of a Dirac field that transforms as a spinor. Quantum field theory has to be the right low-energy approximation of any viable theory that has a chance to go beyond quantum field theory, too.
So the spin's origin may be reduced to the case of quantum field theory. That's the case of string theory, too. In this way, one gets the full supermultiplet - both the fermionic as well as the bosonic states - at the same moment. The total angular momentum of a string comes from the spin of the zero modes as well as the nonzero modes - and from both bosonic and fermionic degrees of freedom on the world sheet.
Reconciling loop quantum gravity with a half-integral spin remains a matter of wishful thinking. There are many ways to see that one can't get e.
Half-integral spin is one of the ways to show that discrete models of the reality can't be consistent with basic features of the reality such as the existence of fermions, especially the chiral ones. What you write about modelling spin's electron as an extended object is refuted in the first part of your very question. A century ago, people would think about electron as a classical object. Obviously, those attempts were totally incompatible with quantum mechanics and other facts.
There has to exist a degree of freedom that has a half-integral spin to start with, and RNS superstring theory only explains its deeper origin, but can't replace it by something completely different.
Graduate student Y: You mean that undergraduate? The one who always talks? The kid who never says anything, he just talks? I really hate […]. Algebraic geometry pretty much sucks. Physics is the science, the knowledge; math is just the language — […].
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