This is the Nadir

I am at something of a crossroads being about (hopefully) to embark on a graduate education in mathematics or physics. Many things are uncertain for me, most fundamental among these is my financial instability. Since essentially 100% of my financial support has been dependent on my participation in the realm of undergraduate academia I find this moment unsettling. I can see far enough to know that the sources of money that I have relied upon thus far cannot carry me for more than a few extra months but I do not yet have some other means of support. President Bush is now former president Bush and we finally have a leader who has the potential to be more than an embarrassment. I can feel my mathematical and physical knowledge approaching a sort of critical mass which will allow me for the first time to really fully function as a mathematician and physicist in the professional sense.

I feel that this is a time filled with potential both for me individually and from a wider perspective. Usually the declaration that one is at a low point of life is a negative statement. But implicit in the declaration of the lowest point is the idea that this is the point where things took the turn upwards.

This is probably not even a local minima for my life but that doesn't matter, the declaration of a nadir is intended as the declaration of an upward arc in the future.


P.S. As an interesting side note I will mention that as I wrote this I got an e-mail confirmation of a tutoring position. Looks like I was within about 3 minutes or so of hitting the low point of my financial situation. Now lets hope that my graduate admissions go well.

Normal Sea

When I think of the word normalcy I can't help but think of it as split into "normal sea". While it is often good to talk about things as though there were no real "normal", this is not the case. If you ask me to define "normal" and I tell you that normal, in the sense I am using it, means conforming to the standard or the common type (thank you dictionary.com). You might say that nobody really fits this description since everybody is quite different from everyone else and so there really is no "normal" but if you have a shuffled deck of cards there are 52! different configurations. You can't point to a particular configuration and say "that's the normal one!" it wouldn't make any sense. But intuitively what we mean is that a "normal" configuration is one that people would believe occurred by chance. If the deck is perfectly ordered 2 through ace and by suit we would probably conclude that the deck had been intentionally ordered that way.

While it is true that intrinsic to any such judgement of which card configurations are "random" (and therefore normal) and which ones are not is to put some sort of structure on the cards which is not fundamental to them as objects. Likewise I agree that there is no fundamental structure intrinsic to human beings which allows us to say what is "normal" however that does not rob the word of all meaning or use. To be normal means a great many things and to be abnormal has an even greater myriad of meanings. Rather ironically once we consider about 20 different independent criterion of "normal" the majority of people will end up being highly abnormal with respect to at least one of these criterion (assuming the standard bell curve).

I often times however observe the realm of "normal" wherein a vast sea of people live. It seems that as a group the majority of human beings strive for this concept of normalcy. To be normal is to have privilege and power, society bends to the will of the normal or at least to the will of what is percieved normal. In many ways what is normal is actually determined not by the general consistency of a populace but by the distribution of power within a culture.

as time goes by

Perception of time is a funny thing. We can perceive time to be going very quickly or slowly depending on our mental state. I have always found it fascinating that people are capable of assimilating vast amounts of information in the form of written stories that they would not be able to consume if it were in the form of a movie. That is not to say that for everyone or every book a book would take less time to purvey the information of a story than a movie. Rather I'm saying that the upper limit of how quickly a story of a particular length can be absorbed is limited in the case of a movie to the regular flow of time. Just as in a book we can give the viewer the impression of months or weeks passing when only a few seconds of viewer time have passed. In a book all it takes is "weeks passed" while in a movie a quickened sequence of images (say of the sun rising and setting) would also do the trick.

Interestingly any movie represents vastly more information than any book. That is if we wanted to write down a sequence of symbols that would allow someone to reproduce a book our job is already done the book is composed of a sequence of symbols. For the movie the task is a little harder but it is also fairly easy to do. In fact because it is more robust than the analog method of storage all movies are now recorded digitally which is to say they are recorded as a sequence of symbols. Most of the information which we capture with a movie is nothing that anyone will ever give the slightest attention. The fact that there are exactly 137,021 leaves distinctly visible in scene 2 at second 12.6 is not something that a viewer is capable of taking away from the film. The precise nature of the tapestries behind the dueling figures is not important. In a book the author could not give us such details even if they wanted to because the line "he tied his shoe" could then take hundreds of pages to fully describe.

Because of the incredibly streamlined way that the information of a story is contained in a stream of language it is possible to experience a book much much faster than you can experience a movie. Jenna reads twice as fast as I do but that does not in any way diminish her capacity to believe the action. Of course if you have ever (and I have) watched a movie at 1.5x or 2x the normal speed while you can still understand what is going on (most of the time) the degree of approximation to reality is quite lost.

The question I have then is this, how fast is a human being capable of experiencing a compelling story? If someone reads the lord of the rings trilogy in a little over a week reading every day for a number of hours we would not begrudge them the claim that they "experienced" the story in the books. At least I would not though I would be more than happy to raise the question more seriously. However if someone else were to read all three books in the span of an hour or two I might not be so willing to accept that what they had done constituted "experiencing" the story. Even if I could then quiz them and found that they had precisely the knowledge of the tale that the other slower reader had that would not demonstrate to me that the two people had an equivalent experience with the book.

But where do I draw the line? At what point is someone experiencing the book too fast? Very probably we should make our judgment based not on how quickly someone assimilates information but on the mechanism of assimilation. Did the person who read the books in an hour visualize all of the scenes? Did they let themselves feel fear or sadness? Did they hear the distinct voices of the characters in their minds? If they didn't but the slower reader did then it is easy to give the slower reader the label of "experiencing" the story whereas the quick reader perhaps simply absorbed it.

Different types of processing take different amounts of time within the brain. I don't know precisely what the figures are but it takes more time for someone to hear someone say "it was an apple" than it takes for someone to envision an apple. Thanks to our wonderful visual processing capacity when we read we recognize the different shapes and can process the information from written words much faster than we could process the information if someone said it out loud. But sensory processing is not really absolutely necessary to understand a story. You can understand the statement that "then the spaceship exploded in a brilliant silent flash" without visualizing it. In the end all the generated imaginary sensory information will fade away. You probably won't remember what you imagined the black hole to look like but you will remember that while they were trying to fix the engines to escape the black hole the crew accidentally blew themselves up.

That is to say that in the end your mind will probably only see fit to store the semantic information not the generated sensory information. More to the point your brain saves a summary of the information and then you can generate at will any sensory information you like. Of course this may not be true of all people and sometimes the only thing you might remember from a book is a powerful image that took your fancy. But the essence of the issue is that even if you remember the book in a sensory way the information is conveyed in a semantic manner. When I say the word "pink" while I am giving you a sensory input that input is in no way pink. The word "pink" is just a series of sounds and in your mind the word is assosciated with the visual input which is gotten from seeing the color pink. So even in the case of a stunning description of a visual display in a book it is perfectly possible (and even probable) that you store the image away not as an image per se but rather as enough semantic information to be capable of regenerating that image.

All of this rambling is intended to help in the analysis of a question about virtual realities. The examples of movies and books are both examples of virtual realities in the case of a movie and a book both are capable of giving impressions of stories that take years in only a few moments. Because of the purely semantic nature of books they are capable of transmitting stories much more rapidly than are movies. The question is this: In the future how quickly will it be possible to transmit experiences?

Lets say a person is capable of experiencing completely immersive VR how fast can we push the brain into experiencing a story? If we are stuck simply giving direct sensory input then we don't really have control over how fast someone experiences something. This mode of immersive VR is something akin to the holodeck where the experiences happen in real time. But what about an the immersive VR version of a movie? Where all of your emotions and reactions and sights etc are already predetermined for you and shaped to give you the experience the creator wished to give. I would be willing to bet that we could up the clock rate of the brain in a situtation like this. Since responses aren't required you could push the experience faster and faster. At this point I am only guessing but I would be willing to bet that you could make someone experience a complete 24 hours worth of experiences within the span of 4 hours. That is I'm betting that you could trick the brain into experiencing things about 8 times faster than normal. This is because for the most part our brains operate on a tick rate of something like an observation a second or maybe a little slower. But in cases where our brains have to react to something very quickly we can act and think in a time span of as little as a tenth of a second or so.

Finally though we come to the area of memory implantation. I see no reason that in the space of a few hours it wouldn't be possible to implant decades worth of memories into someones brain. Perhaps the capacity to do this will never in fact be possible but lets think of the implications for a moment. This would very likely be a much more effective way of giving sculpted experiences to people instead of making them experience them in fast forward. In the space of a few hours you could get the memories of having been part of a story that could have lasted weeks or months or years. If it were possible to make the memories more or less perfect instead of the usual patchy memories people actually have how would this differ from being able to sit back and watch it at will? This would be the sort of perfect rewind and fast forward we would already know what happened and what would happen and how we felt at each moment. This is fundamentally different from a story which it is possible to transmit now even though we all have experience with these kinds of stories. Is such a thing even desirable?

Why shouldn't the rules change?

I have become fond of games which allow you to modify the rules by which the game is played while you are playing the game. I just bought a game called Fluxx and as it so happens basically the whole idea is to alter the rules of the game to make yourself win. Obviously the rule changes are themselves operating within a larger framework which one might arguably say are the real rules of the game. For instance the new rule cards can't contradict one another if a new rule card would contradict an old one then the old one is discarded and the new one takes its place. There are a few other such sub-rules which constitute an underlying framework to the world of rules that can change but saying what they are won't further the discussion.

What I really want to talk about is the assumption that the rules don't change in the physical world. Believe it or not this is the principle of relativity on which Einstein built his special (and later general) theory of relativity. So Einstein was kind of saying we don't want anyone changing the rules, they have to be the same everywhere at all times. In this case "same" means more or less that you have to be able to apply the formalism in the same way regardless of if you are moving or not or what time it is or if you are on mars or earth. The first question I want to ask is whether or not this is more like saying that the underlying framework rules cannot change or is this saying that we can't ever lay any new rule cards?

The framework which underlies physics is mathematics and the fundamental rule of the framework of mathematics is consistency. There are arguably infinitely many different ways in which the game of physics could be played. Possibly there are only a finite (but vast number) of ways as some string theorists think. The particular number isn't important but the thought that there could be other ways of doing physics that are still logically consistent is basically the same as saying ok well you could play the game with different rule cards on the table and still not break the framework. Einstein is saying that the cards never get mixed up. If the big bang played the f=ma card then that's how it is end of story. I find it kind of ironic that later in life while fighting with quantum mechanics Einstein would propose the hidden variables idea which basically equates to saying that physics acts differently at different times and different places because we see random stuff happening but physics must be deterministic. Of course for Einstein the idea was that eventually a deeper theory would be uncovered which would replace these hidden variables and keep physics as being both deterministic and free of time and place.


This is an interesting idea, and an old one. The game that we think we are playing is almost certainly not the game we actually are playing. In fact at the moment since we are sure we are playing a game within a framework that requires consistency we know that the model of the rules that we have is wrong because general relativity and quantum mechanics disagree with each other. There could be many many possible "real" rule sets that we are working towards but what if the rules don't exist at all? What if the laws of physics are actually constantly changing and what we think we are trying to model is just some sort of crazy long term average? This actually has sort of happened to physicists already they found out that just about every law of physics was in the quantum world just a long term average. So we reformulated the laws of physics so that anything that was subject to fluctuation was no longer part of the rules but merely part of the specific situation. But there is a fundamental difference between considering f=ma to be a long term average accounting for the complicated random interactions of things and thinking that the interactions themselves occur according to random rules. Take the good old time independent schroedinger equation Hp = Ep where p is the wave function H is the Hamiltonian and E is the energy. Usually we think of the randomness as inherent in p not in H but in a way revisiting the hidden variables of Einstein we could try to hide the randomness in H instead. I'm sure you could come up with a completely equivalent description of quantum mechanics this way making the interactions of particles be totally deterministic but acting according to random rules. I imagine it would be a lot more difficulty than its worth but I would also be willing to bet some fun stuff would come out of it.

As a final side note I often wonder if logical consistency is actually a fundamental requirement of the laws of the universe. Human minds work in worlds where inconsistency is rampant. We find consistency incredibly useful but not absolutely necessary. This is in fact the way that the laws of physics have worked out as well we know that they are inconsistent but that they are consistent within small domains or at least relatively consistent and we find that consistency useful. Ultimately though utility outweighs consistency and we are free to use inconsistent and blatantly incorrect models and theories just so long as in the end we get an answer and can have some confidence in it. Of course even though quantum mechanics and relativity are inconsistent with each other they are operating in a larger realm where the people using them are able to evaluate whether the disagreement matters at the moment. So people impose consistency when necessary which puts us again back into the world where everything must mesh logically. All I can say I suppose is that it would be a stunning blow to the world of philosophy and physics were someone somehow to prove that physical laws which have consistency as a requirement cannot produce certain behavior that is in fact observed. In other words if a Godel came along and proved a very general theorem about how physical theories can act and then proved that if there is consistency then there is "incompleteness" in some sense. I wonder if that lies somewhere down the road for us.