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The Toybox

people for the conservation of limited amounts of indignation

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universal constants are not so much
The problem with my entire hypothesis is, I didn't document when I was drinking diet soda regularly. OTOH, I have my chat logs with svmadelyn when I was talking about this Mysterious Rough Rashy Thing that was freaking me out on my face. It looked fine but felt a great deal like when I accidentally mildly acid-burned myself with this face stuff, and seriously, mock if you want, I mock myself when I think about it. Cortisone took care of it in a few days and that was around the time I was All Diet Coke, Let Me Die Time.

But Diet Pepsi Maximum (it's with ginseng?), and a day or two later, it's back. Stopped drinking, is shrinking and vanishing.

My body is up to something here. I don't know what. But I swear to God if end up in a bubble with only my laptop, or eating vegan raw foods only, something is going to break, and it might be my sanity. I haven't heard good things about total breaks from reality very often.

Also, hi. I'm bored. While working. Anything interesting going on? *hopeful*

Also, is there a scientific law covering probability in physics? I'm not even sure how to phrase the question. I'd like to say this is about precognition, but it's not exactly; is there a field covering the scientific study of probability and odds? Or rather, what level of accuracy is required to be considered consistently accurate in predicting future events based purely on current data? Is there a threshold percentage that has to be reached?

...this is going to be something hideously mathematical and statistical, isn't it?

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Check their sugar substitute, I doubt it's the high fructose corn syrup because you'd be getting the rash all the time if it was (unless it's in direct amounts). The fake sugar though could be doing weird things to you.

Also you could totally attempt to prod me into writing more fic. (In about 20 minutes).

Also, hi. I'm bored. While working. Anything interesting going on? *hopeful*

How about the science of orgasms?

Hey, be glad you figured out what was making so you sick so quickly. Is it all soft drinks, or just the diet ones?

So far, if I'm right, it's Diet Pepsi, Diet Coke, and Diet Dr. Pepper, all I drank in the last two months, in the period fo time of two skin rashes nad one unfortunate reaction to a change my generic for my medication. So--I'm thinking I might need to be tested.

You mean like thermodynamics and statistical mechanics? Basically that's what you get when you apply probability theory to classical Newtonian mechanics. I mean, you haves Newtonian laws, apply those to problems involving many bodies via probability theory (like probability distributions and such), rather than just two, and you arrive at the classical thermodynamic laws. The problem with classical mechanics is of course if you have a number of bodies that is between two and "a lot" because then you can't solve the general equations except numerically, like the famous three body problem, made worse if you have four or more. I mean, thousands bodies like in a classical gas is much better for predicting accurately than four.

Or do you mean things like chaos theory? I mean, like in "deterministic chaos" a system is so sensitive to initial condition changes that you can't measure the initial state exactly enough to predict, i.e. nearby initial values won't result in nearby end results, even though you know the laws by which it is governed. So chaos theory deals with that, mostly make possible because computers can do many iterations now, so you can get a grip on overall system behavior numerically, like with turbulences and such. There are methods to tell whether a system you observe is just random noise or chaotic, but it's sometimes not trivial.

Do you midn if I email you and nymphaea1 (below) tonight or tomorrow? I need more detail, but I'm not sure I have the right question, so I may need to outline what i have in mind.

I don't know how helpful I'll be, but sure. I've never been that fond of the statistical math, and I have only a very general idea about chaos theory, but I can try.

Also to maybe clarify my previous reply wrt your prediction problem, what I meant with my points with a concrete example would be something like this:

Say you want to predict whether some satellite you lost control of will fall harmlessly into the ocean or turn your city into a crater. And you know all the basic natural laws that are relevant, like obviously gravitation, but maybe also atmospheric factors like wind, friction once it hits air, how the material withstands heat, whatever. Obviously what you want ideally would be to arrive at some sort of function, one where you could just input all your variables (speed, direction, atmospheric conditions...) with their margins of error and it will output where the satellite will hit and whether it will remain in one part, and how large the margin of error for that is. Like you would have f(a, b, c, d...)= point of impact +/- margin of error.

Now the problem is that even relatively simple natural laws like classic gravitation come as differential equations that don't necessarily have complete solutions you can arrive at (see the whole three body problem). Everybody knows of course the solutions of the gravitation differential equation for two bodies, that are the conic sections, like the basic kinds of simplified paths for celestial bodies, i.e. you have ellipses for a planet rotating around a sun, or hyperbolas and parabolas for two bodies that are not bound together, like say a comet passing through. That is called the "two body problem". Obviously in our solar system we don't really have a two body problem, so early on people tried to solve the differential equation for three bodies and more bodies. You can find some solutions, that is people found some orbits that would solve the differential equations for three bodies like the conic sections do for two, like Euler and Lagrange found some in the 18th century, but not all possible solutions, only special cases, also soon there was the realization that some solutions would be "chaotic".

That is people found solutions that are very sensitive to changes in the initial conditions, which is obviously bad for predicting, if your initial variable is a miniscule bit different but the outcome is radically different.

Also, some of the solutions come in approximations, i.e. you get a series that you can prove is convergent, rather than the simpler kind of solution.

Obviously if you introduce more natural laws than just simple gravitation it gets harder and harder to find complete solutions to your equations, even just finding some that are convergent series, and even if you found one solution, there's no guarantee that you found all, even if you simplified.

So, the neat simple function is not really an option if you want to decide whether to flee the city because it will be hit by your satellite or stay watching it fall prettily into the water on tv. What you can do however, especially if you have a computer (but this kind of numerical analysis existed before, and there were strategies to make equations manageable afaik, it's just magnitudes easier now), is to approach it iteratively, because after all you still assume your satellite is deterministic (i.e. you know all the relevant laws and have those equations and it is not interfered with by completely random events like say quantum phenomena on a microscopic level, like radioactive decay). The basic idea of that is you go the brute force route and instead of solving a differential equation, you approximate things by breaking it up into small time elements rather than infinitesimal ones. You have your satellite in it's initial state, apply all forces that are present in that moment, get the result for say a second later, and do that again and again, until your satellite fell down somewhere. Of course there are problems, like what if your system is chaotic and a minuscule difference in initial conditions would make it fall in a completely different place. So you do it again and again with tiny variations to all variables. Then you map those results and get a model of how your system behaves. The pretty graphics associated with chaos theory are things like that.

(sorry I'm so rambly! Anyway my previous comment went on too long,here's the rest.)

And if your system is not chaotic, you can then make a prediction with the margin of error depending mostly on how well you measured the initial variables and what kind of approximations you made along the line. Numerical analysis has a long tradition and theory framework of approximately solving differential equations for that.

If your system is chaotic, it kind of depends on the kind of chaos, like some systems that are chaotic overall still behave "normally" in some segments of initial conditions, but chaotic in others, like imagine it like water flowing: the current in many areas is predictable and smooth, and if you drop in something you will know where it will arrive, and if you drop it just a bit to the left, it will still be carried in the same area in general. You are out of luck though if drop your thing into a turbulence area.

As that whole ramble shows predicting a single system that is not extremely simple has some problems in physics, which is why it is so great that things become better again once you have say many bodies and can use statistics to predict the average of the whole system rather than trying to predict how every single body behaves. Then in addition to the error that comes in from imprecise measuring, you have standard deviations and such, and predicts probabilities.

Just stop drinking that crap. :-) (Honestly, I stopped drinking sodas in college and I don't miss them at all. You can load real tea up with enough sugar to get your rush and miss all the fun chemicals.)

How is the Heroes-watching going?

is there a scientific law covering probability in physics

God, I should know this, but sadly, that is no longer the case. My solution? Watch Numb3rs. (Everyone should watch Numb3rs.) *g*

I'd like to say this is about precognition, but it's not exactly; is there a field covering the scientific study of probability and odds? Or rather, what level of accuracy is required to be considered consistently accurate in predicting future events based purely on current data? Is there a threshold percentage that has to be reached?

I don't know if the field of physics in particular has a particular term for this or if I am understanding your question exactly, but modeling probability and odds is a branch of statistics in general. There's not really one particular set level of accuracy at least in biological fields (which is really the only one I can speak to). It really depends on a case by case basis. Some systems have more noise associated with them than others. Like, for example, if I were studing the level of expression of a particular gene in corn grown in a field as compared to a lab, I'd expect more noise in the field grown corn just because there's more environmental variation that I'm never going to be able to control for in the field. Generally, in predicting a future response based on present data you don't predict an exact response. Bases on the noise in your data (generally translated into standard error or variance) you'd create a prediction interval. To use an easier measure, if I doing some study on nitrogen and corn growth, based on my data I might be able to say that at 10 ppm nitrogen use at 5 weeks I could expect the height of an individual corn plant to fall between 35 and 55 cm 95% of the time. My model would be giving me an average of 45 cm but that's an average. Obviously, not all plants are going to fall right on the line, so you have to provide a range. To decrease your range, you have to take the noise out of your system by perhaps more tightly controling environmental factors. Now, physics by nature is less noisy than biological studies, so perhaps they are able to control accuracy a bit better.

Oh, I forgot to mention--when modeling anything, a key point that altogether too many scientists forget in any field is that you can't predict beyond the range of your data. So if I had only studied levels of nitrogen between 0 parts per million and 200, I couldn't predict what would happen at 250.

I have no idea how to ask the question. I'll probably email tonight or tomorrow? I think between you and ratcreature this is what I needed to know, but I'm still not sure how to phrase the question.

Yes, this is for fic, because I'm totally a masochist. *g*

You can e-mail me tonight. I'm a bit brain-dead from writing law school essays, but I'll bring my stat book home and attempt to help you as well as I may.

I am sorry if it seems like I was ignoring your e-mail. I didn't even see you'd sent one until just now. As it turns out, my hotmail account logged it as unsafe apparently and now I can't open it. Possibly if you have another e-mail account you could e-mail me from there or I could PM you my school e-mail address.

I just got back the bounce!

Um, thegateway address *hates* livejournal.com addy right now and I have no idea why. Email seperis at gmail.com and I'll resend to that email.

Oh email. You were supposed to make life *easier*.

Ack! Women should avoid all colas! The phosphates in colas leach calcium from your bones. They also block calcium supplements, so taking extra calcium supplements to counteract the phosphates won't help. Seriously, soda in general is the worst stuff for you ever.

In general for statistically predicting future events or just identifying patterns, you can use regression models of increasing complexity. I do it for econometrics, but given the right inputs, I can't imagine why you wouldn't be able to use it for physics. Of course, the method has its limitations, but they're the limits of statistics and prediction everywhere.

My mother kept me away from aspartame when I was a child, telling me that I was allergic to it. It's one of the artificial sweeteners they use in diet sodas -- I wasn't allowed to drink diet anything when I was little.

Now, I don't know if I'm still allergic to it, but I'm also afraid to try it and find out.

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