text:
RationalWiki's Q4 2016 Fundraiser
We are 100% user-supported!
Without you, there is no RationalWiki!
Goal: $5000 Donations so far:$5000
 100%

Fighting pseudoscience isn't free.
Help and donate today!

Bayesian

 The poetry of reality Extraordinary claims withextraordinary evidence Hot from thegiants' shoulders v - t - e

Bayesian refers to any method of analysis that relies on Bayes' equation. Developed by Thomas Bayes, the equation assigns a probability to a hypothesis directly - as opposed to a normal frequentist statistical approach, which can only return the probability of a set of data (evidence) given a hypothesis.

In order to translate the probability of data given a hypothesis$P(d|h)$ to the probability of a hypothesis given the data $P(h|d)$, it is necessary to use prior probability and background information. Bayesian approaches essentially attempt to link known background information with incoming evidence to assign probabilities.

Since the goal of science is to determine the probability of hypotheses, Bayesian approaches to analysis are a much more direct link to what we really want to know. They also help to elucidate the assumptions that go into scientific reasoning and skepticism. There is also increasing evidence that the human brain uses something very similar to Bayesian inference.

Bayes and probability

Probability of the hypothesis versus the data

The main focus of probability theory is assigning a probability to a statement. However, probabilities cannot be assigned in isolation. Probabilities are always assigned relative to some other statement. The sentence "the probability of winning the lottery is 1 in 100 million" is actually a fairly meaningless sentence. For example, if I never buy a lottery ticket my probability is significantly different than someone who buys 10 every week. A meaningful "sentence" in probability theory must be constructed with both the statement we seek to assign a probability to and the background information used to assign that probability. The essential form is "the probability of x given y is z." The probability calculus short hand for this sentence is $P(x|y)=z$.

When we seek answers to a question or understanding of a phenomenon we usually start by forming a hypothesis; data is then collected that seeks to provide information about the reality of that hypothesis. Ultimately we seek to know, what is the probability that our hypothesis is correct? In this case our background information is the relevant data we have collected. So in probability speak we seek to know what $P(h|d)$ is equal to. In this case h is our hypothesis and d is our data.

Things start to get a little complicated from here. Let's imagine we are asking a simple question, like "is this coin I have fairly weighted?" We hypothesize that if it is fairly weighted, flipping it should result in an equal numbers of heads and tails. We flip it 10 times and come up with 6 heads and 4 tails. With this information, can we answer the question of what $P(h|d)$ equals? The answer is that we cannot. The only question we can answer is what $P(d|h)$ is equal to.

This is a subtle but very important point. Given only a hypothesis and some relevant data, we can only ever answer how probable our data is given our hypothesis, not the other way around. These two pieces of information are not equal. To see why, let's form some probability sentences with everyday concepts and see what happens when we reverse them:

• The probability that it is cloudy outside given that it is raining does not equal the probability that it is raining given it is cloudy outside.
• The probability that someone is drunk given they consumed 10 beers is not equal to the probability that someone consumed 10 beers given that they are drunk.
• The probability that the Antichrist is coming given that it's in the Bible does not equal the probability that the Antichrist is in the Bible given that he is coming.

So given that $P(h|d)$ does not equal $P(d|h)$, what sorts of answers can we get about $P(d|h)$? This is the classic approach to statistics that has come to be called the frequentist approach.

Frequentist approaches

The frequentist approach is the standard statistical model taught in most high schools, colleges and graduate school programs. It seeks to find the answer to what P( d | h) equals. Based on our example of a coin being flipped, the frequentist essentially asks: if one did a whole lot of sets of 10 flips, how often would I get a distribution of 6 heads and 4 tails? The answer of course depends on whether the coin is fairly weighted or not. The frequentist will usually ask how likely that distribution is to appear if the coin is weighted fairly and if it is not weighted fairly. Since being weighted fairly means that the result of heads or tails is essentially random, that question can be generalized to asking what is the distribution if we assume our results are random. This is known as the null hypothesis and is the "omnibus" test for frequentist statisticians. You can take any data distribution and ask: what are chances of this data distribution appearing given it is caused at random? If there is a high chance that it can appear, then we say that it appeared as random. If there is a low chance it appeared, we say that something had to cause it. Usually some sort of percentage cut off is used, the standard being 5 percent, meaning that there must be less than a 1/20 chance of forming a given distribution assuming random cause before we are willing to say there must be a non-random cause. This is called "significance".

There are many complicated statistical procedures that can be used to further differentiate causes beyond just "random" or "non-random", but all of them rest on the same basic idea of providing some sort of arbitrary statistical cut off where we assume something is unlikely enough that it has to be something else. This, however, is not really the case. As previously stated, we cannot actually assign a probability to our hypothesis. If our data only has a 1% chance of appearing if the cause is random, this does not mean that there is only a 1 percent chance that the hypothesis that our cause is random is true or that there is a 99 percent chance that our data is caused by something non-random. The frequentist approach, while providing valuable information and hinting at the relationships between hypotheses, can not tell us the probability of a hypothesis being true.

To understand why this is the case, and to understand how we can do this, we must turn to Bayesian inference.

Bayes' Equation

We have generated our data, run all the stats on it, and come up with the encouraging results that our data should only appear 1 percent of the time if it's randomly caused. Why then are we not safe in assuming, at the very least, that it is not randomly caused and that our hypothesis is more likely than random chance? The answer to this question has to do with the prior probabilities of each hypothesis, or in Bayesian parlance just "priors." Let's illustrate this with a little story:

You're walking down the road when you hear a whisper in the alleyway calling you over. Curious, you enter. A stranger is standing against the wall. He tells you that he can predict any series of numbers that will be chosen by man or machine. This includes tonight's lottery numbers, and he is more than willing to tell you what they will be in exchange for $1000 in cash. That would certainly be a good deal... if his story is true. You, however, are skeptical of his claim for many obvious reasons and ask for him to prove it. The man agrees and asks you to pick a number between 1 and 5, you do so, and seconds later he tells you the exact number you picked. Would you hand over the thousand dollars now? Most people would not, for such a feat is not that impressive. Lets instead say he told you to choose a number between 1 and 100 and guessed it exactly. While this is more intriguing, it is probably not worth the$1000. What about 1 in 1000, 1 in 100,000, 1 in 1,000,000, 1 in 100,000,000? Eventually we will reach a point where we are convinced enough to turn over our money.

Now let's look at a different story. You enter a novelty shop at the local mall and spot a package of dice that tells you they are weighted to roll a 6 every time. Intrigued, you open a package and roll a die. Sure enough, it comes up 6. Are you willing to say that these dice are probably weighted? Maybe you will roll a second time, but how many people will remain unconvinced after the 2nd or 3rd roll? Not many.

So in the first scenario most people are willing to ascribe to random chance when it was only 1 in 100 or 1 in 1000 likelihood, while in the second a 1 in 6 or 1 in 36 chance was all it took to convince people that it was not random. What is the difference? It is the prior likelihood for each hypothesis that separates these out. In this first scenario nothing makes sense. Everyone knows psychic abilities have never been demonstrated, why is this guy in an alley and why is he selling a $100 million lottery ticket for$1000? Sure it might be true, but the chances are tiny. In the second scenario you are in a respected shop looking at a commercial good with clearly labeled and professional packaging, so it's probably telling you the truth about being weighted.

Let's break this down into something a little more quantifiable. For the sake of argument, let's assume that the chance the guy in the alley is telling the truth is 1 in 10,000,000. What is more likely; the 1 in 10,000,000 chance that he is telling the truth, or the 1 in 100 chance that he guessed your number randomly? In the second scenario, let's say that the chances the package is lying about the dice is 1 in 100, so the chances that it's lying and you randomly rolled a 6 is 1 in 600 while the chances that the package is telling the truth is 99/100 (100 percent chance you will roll a 6). In this case, the probability a single roll of a 6 with a die in a wrongly labeled package is far lower than the package being labeled correctly.

As these examples hopefully show, the only way to move from $P(d|h)$ to $P(h|d)$ is to take into account our prior beliefs about the probability of each hypothesis. The Bayes equation is the equation that relates $P(d|h)$ and our priors, and calculates what $P(h|d)$ equals. The equation is simple and is made up of three parts, the first is the priors which we just talked about or $P(h)$, the second is called the likelihood probability, which is simply $P(d|h)$, and the last is called the posterior probability, which is $P(h|d)$. Bayes equation then looks like:

$P(h|d) = \frac{P(d|h)\;P(h)}{\sum\limits_i P(d|h_i)P(h_i)}$

Since the posterior probability is the holy grail of most questions humanity has asked, understanding the Bayes equation and its parts and how they relate to each other can tell us much about the optimal way of gaining and testing knowledge about the world.

Bayes and Science

Science is predominantly interested in comparing various hypotheses to determine which are the more probable among a set. This means that, with very rare exceptions, the probability researchers want is $P(h|d)$. However, the vast majority of statistics used in modern publications are based on frequentist approaches that can only return $P(d|h)$. Since frequentist approaches cannot tell you directly about the probability of a hypothesis, various ad hoc approaches have been attempted to force the results to fit this mold. The most frequently used device is the concept of statistical significance. This approach assigns an often arbitrary cut off to $P(d|h)$ such that when the probability is below the threshold, it's “significant” and supports the hypothesis, and when it's above the threshold, a given hypothesis is rejected and random chance is favored.

While this approach is immensely popular and dominates current reporting techniques in most peer reviewed journals, it is fraught with problems (see: statistical significance for a discussion of these issues). Bayesian approaches offer a solution to many of the problems exhibited by frequentist methods. Since Bayes equation returned $P(h|d)$ directly, there is no need for arbitrary devices such as statistical significance. For these reasons, there is a growing group of researchers that advocate the use of Bayesian statistics in reporting on scientific findings.

However, Bayesian statistics is not without its own issues. The most prominent issue surrounds the construction of priors. Since priors are fundamental to any Bayesian approach, they must be considered carefully. If two different researchers used two different priors, then the results of the statistics would be very different. Since posterior probabilities from previous work can be used as priors for future tests, the real issue centers around the initial priors before very much information is available. Some feel that setting priors is so arbitrary that it negates any benefit of using Bayesian approaches. If no information is available when setting initial priors, most people will use what is referred to as uniform prior. A uniform prior merely sets all possible hypotheses to an equal initial prior probability. Another approach is to use a reference prior, which is often a complex distribution created to specifically eliminate as much role of the prior in calculating a posterior as possible. However, this method is criticized as essentially eliminating any gain from using a Bayesian approach at all.

Bayesian reasoning and the rational mind

For many years, social sciences used the formulated concept that humans were inherently rational to guide predictive models of social, political and economic interactions. This concept is often labeled Homo economicus and has come under fire for a myriad of reasons, not the least of which is that people do not appear to behave rationally at all. A great amount of evidence in both economics and psychology have shown what appears to be consistent sub-optimal and irrational reasoning in laboratory experiments. Several of the more widely cited examples are:

Co-variation analysis

When attempting to gather information about whether two variables correlate with each other, there are four frequencies that can be gathered :

1. A is present and B is absent
2. B is present and A is absent
3. A is present and B is present
4. A is absent and B is absent

Each of these should a priori carry the same weight when assessing correlation, but people will give far more weight to the case when both are present, and the least amount of weight to the case when both are absent.

Another related and classic task is the Wason selection task, where subjects are asked to test a conditional hypothesis ' if p then q '. Subjects are usually requested to turn over cards that obey the given rule. For example, the hypothesis might be "If there is a vowel on one side, then there is an even number on the other side" then four cards are displayed such that two cards show the p and q and two cards show not p and not q for example A,K,2,7. In classic reasoning the cards to turn over are p and not q (A, 7)as these are the only ones that could falsify the rule. Fewer than ten percent of people will follow this pattern and most will instead turn over p and q cards (A, 2). This is viewed as classic irrationality. Surprisingly, people fare a lot better on this task when the problem is formulated in terms of cheating in a social exchange, e.g. "A child can eat the dessert only if s/he ate the dinner".

Framing effects

Descriptions of events can often be phrased in more than one logically equivalent way, but are often viewed differently. One common example is reporting survival statistics after diagnosis of disease. People will feel more optimistic when told that they have a "75 percent chance of survival" than when told they have a "25 percent chance of dying." These statements are logically equivalent and should not invoke different responses, but they clearly do. This has also been assessed many times in risk tasks, where people are told they have a "75 percent chance of winning points" versus a "25 percent chance of losing points." People will select the task phrased in positive language and not select the task when phrased in negative language.

Bayes to the rescue

These examples plus others have been used to argue that people are actually irrational actors. However, these tasks are fairly contrived in the laboratory setting. The major missing ingredient in all of this is that people do not make choices in a vacuum. Prior information and experience can alter what choice is the most optimal. Reasoning that takes into account prior information along with basic logical and likelihood information is inherently Bayesian. A significant amount of evidence has emerged in the fields of cognitive psychology and neuroscience that humans use Bayesian approaches to asses their environment and make predictions. This occurs both at a low level in sensory processing, where neuron firing patterns seem to encode the probability distributions and handle the computations, and at a higher level of thought with people making executive decisions. When Bayesian approaches are used to analyze the above tasks, it turns out people are performing fairly optimally.

Subject performance in the co-variation tasks and task selection above makes a lot more sense when you consider that most conditional hypotheses are formulated for the rare events rather than the common events. For example, if we are testing the correlation that smoking causes cancer, we know that smoking is relatively rare, and we know that cancer is relatively rare, then the four types of frequencies should no longer be equally weighted. Since there are a lot of people who do not smoke and a lot who do not have cancer, finding someone who does not smoke and does not have cancer is going to happen far more frequently by random chance than finding people who smoke and have cancer. This is exactly the distribution of weighting we see in the laboratory tests.

For framing effects, it's important to realize that information in the real world is rarely communicated completely accurately. Social psychologists have found that people choose to phrase things in an optimistic or pessimistic fashion not randomly, but in a predictable way. People will describe a glass as "half-full" if it was empty and they watched it filled up half-way, but describe it as "half-empty" if it was full and was emptied by half. Therefore, taking into account social information and communication as background information, Bayesian reasoning may treat seemingly equivalent logical statements as actually conveying different information. Once again, this is how people behave in the laboratory.

Evidence then seems to point to the fact that people are Bayesian reasoners, and can perform far more optimally and rationally than they are usually given credit for.

Bayes and illusions

In addition to the evidence that higher order cognitive functioning follows a Bayesian approach, there is a lot of evidence that lower order systems in the subconscious also use an analogous method. It appears that neurons encode and analyze sensory information using firing patterns to form probability distributions. This means that both a likelihood and priors are calculated for any stimuli. This may help explain many interesting aspects of cognitive processing. One recent example is this block of text which has been circling around the internet:

 “”Aoccdrnig to rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

The ability to read this paragraph so easily can be attributed to the Bayesian nature of cognitive processing. The letters present, as well as the anchoring of the first and last letter, provide fodder for a calculation of word likelihood. Having learned the priors after exposure to many sentences over a lifetime, it is very easy to reconstruct the actual meaning, even though the input is jumbled. Bayesian analysis of sensory input may also be the cause of many optical illusions. One example is illusions that are based on concave and convex. Below are two copies of the same image, rotated 180 degrees with respect to each other:

The shift in concavity relies on a prior assumption that the light source comes from above. This is a perfectly sane and rational prior to build into the sensory system and would work under most conditions. But when there is actually no light source, and the difference in shades of color is real, the Bayesian mind winds up with the "wrong" hypothesis and hence the illusion. The "light from above" prior is one of the more specific Bayesian priors for optical illusions.

Another very powerful illusion created by the assumption of a light source is the Adelson's shadowed checkerboard illusion. This image is shown below. Take a close look at the squares marked A and B; they are actually the same shade of grey.

The illusion is caused because the various squares around A and B are shaded to create the image of a shadow. The prior assumption is that the difference in perceived shading is really due to a shadow cast by an unseen light source. The perceived brightness of the squares are then adjusted under the assumption of light and shadow.

One of the first optical illusions to be tackled in psychology is the famous Gestalt triangle shown below.

People tend to see a triangle occluding the other objects, rather than the other objects just lacking those pieces. Gestalt psychologists explained this as people processing objects as a whole rather than by pieces. The assumption is that there are three spheres and a dark lined triangle. The only way to make sense of this image then is to view an occluding second triangle. Knowing that the sensory system is Bayesian, this illusion can be explained more fully. A circle with a sector missing is a very rare occurrence. The prior for any such shape is that it is a whole sphere or circle. Additionally, the likelihood that all such objects with missing parts were to accidentally line up to create the shape of a triangle is very small. When these elements are combined in a Bayesian fashion, the hypothesis with the greatest probability is that there is an occluding triangle.

Sometimes the information a Bayesian analysis returns is ambiguous, with two or more competing hypotheses with about equal posterior probabilities. In this case, slight perturbations in the sensory stream (random noise, slight changes in perceptional environment, etc.) will cause the brain to switch back and forth between perceptions. This is probably the cause of the shifting in the perceived depth of the Necker cube shown below.

Optical illusions like the Necker cube that rely on ambiguous posterior probabilities can be highly sensitive to prior expectations. If two hypotheses for the perceived image are equal under uniform priors, then setting one prior higher than another should force the illusion to at least initially appear in that direction. Here is a test: this is an image of a rabbit.


text:
# The number of ways of partitioning the set {a,b,c,d} into one or more non empty subsets is

12 views

closed
The number of ways of partitioning the set {a,b,c,d} into one or more non empty subsets is
A. 14
B. 15
C. 16
D. 17

by (90.7k points)
selected

(b) {:("Partitioning",,"Number of ways"),(4"members",,1),(1+3"members",,(4!)/(1!3!)=4),(2+2"members",,(4!)/((2!)^(2)2!)=3),(1+1+2"members",,(4!)/((1!)^(2)2!2!)=6),(1+1+1+1"members",,(4!)/((1!)^(4)4!)=1),("Total",,15"ways"):}

format: plain


text:
# What's the difference between PLA and PAL logic devices? Is there one?

I've seen both PAL (which I understand is Programmable Array Logic) and PLA (I don't know what this one stands for. Programmable Logic Array?) used to refer to certain types of programmable logic devices that came before modern PLDs, CPLDs, and FPGAs. Is there a semantic difference between the terms, or are they two words for the same class of device?

• search for pal pla – jsotola Feb 17 at 19:10


text:
Ok so here is what im looking for.

thirdly provide evidence/proof of your God.

Example.
Abrahamic God:
Omnipotent(all powerful)
Omniscient(all knowing)
Omnibenevolent(all loving)
Define:
He created everything in 7 days. The universe is 6000-10,000 years old. etc...
Proof:
LooL you got me. Which is a pretty good reason why I dont believe in the Abrahamic God. But I dont claim to be omniscient. perhaps someone will beleive in the abrahamic God and have evidence for his/her existence.

edit/ if your God is already self-evident, provide proof for the attributes.

Last edited:

Related General Discussion News on Phys.org
My universe, my reality, my existence is my God, I am my God.
My God is all that is, my God is me.
My God is all around you and I.

I am an extension of my God. I am a part of my God, my God is a part of me. I am in control. My God is omnipresent, my God is omnipotent, my God is omnibenevolent. My God is the universe, my God is all that is within and without. My God builds the stars by himself, my God created me. My God is the creator, just as I am the creator. When I understand and know my God, all powers that my God possesses, I may possess as well. My God gave birth to me, my God is my Father, I am my God's offspring. My God knows no limitations, my God recognizes no restrictions. My God is everything that is, has been and ever will be. This is WHAT my God is.

We argue and fight about "who"... we never stop to figure out "what"...

Last edited:
err.

My universe, my reality, my existence is my God, I am my God.
You are your God. but then you say.
My God gave birth to me, my God is my Father

so everything is omnipotent according to
my God is omnipotent
But i dont follow that. Im definately not omnipotent. but ok you continue.
When I understand and know my God, all powers that my God possesses, I may possess as well.
and there is the scam/hitch. you have to follow and believe. before you get powers. but you dont get a reason to do so. which comes to the scam. they get you believing and string you along saying your almost there all the time.

Im allowed to call it a scam. as you missed the Mandatory most important part.
thirdly provide evidence/proof of your God.

No, you misunderstood, my Father is the universe and the universes creations; the sun, the earth, evolution, humans, then my actual father. It's all related. Without one, we cannot have the other, they all gave birth up to the point of the present, which is now me. When you understand and know yourself, others, and your universe and every law that exists in this universe, every philosophy, every color, every vibration, you learn, WE learn. You can then apply what you learn to your life. My proof of my God are these words that you and I are reading and typing. My God is not a who, it is a what. I am not here to prove who is wrong and right, I am here to share in truth. If you don't understand, then say you don't understand. Please, don't quote me and make false assumptions on the context of my speach. I'm not here to sell a book. So this cannot possibly be a scam. I am sharing my enlightenment, we can learn and discuss it together. There's no need to attack and assume fallacy. I'm not here to mislead, I'm here to expand and help any and all. Your mind is omnipotent.

Last edited:
Serpo said:
If you don't understand.. then say you don't understand.. please, don't quote me and make false assumptions on the context of my speach.
Lol. if i dont understand. i will say it. but from what you had put there. i understood what you said. now if what the words say isnt what you mean. thats not my fault. its your fault. as in your not being articulate.

My proof of my God are these words that you and I are reading and typing... my God is not a who.. it is a what.
Ok thats fine. Your God is the fundamental particles and forces. Thats cool. But when you have attributes like omnipotence. you need to provide proof of this.which u still havent.

I see, this will be a tear down session. I am the building and you are the steel ball dangling from the crane, have at it. I'm done.

I can only help you as much as you want to help yourself. Don't limit your ability to understand. A father is not limited to your biological human father. If what I mean isn't what you understand, then I am the one who understands what I mean and you are the one who doesn't, you see? I don't want it to get like this. I'm not here for an argument. Let's do this peacefully, please. It's not hard, try.

Omnipotent; your mind is all powerful. Without your mind, you cease to exist. Recognize this and you can become and do anything you so desire. Everything away from your mind is just an extension, including the body. All that is needed for enlightenment is the mind. Your mind is the Godhead of your existence and your reality. "Godhead", literally.

One must mold one's ego away from wanting to win, and into seeking and gaining truth and knowledge. If the ego is controlled, anything is possible. Get away from competitive nature and seek self pinnacle. When we compete with others, we are limited to the competition that we face. When we compete with ourself, we can create the competition to whatever level we'd like, we set the goals and the achievements. In doing so, we can reach heights never even imagined. You are your own worst critic, you are also your own best motivator. Everything must work both ways.

Last edited:
Serpo said:
I see, this will be a tear down session... I am the building and you are the steel ball dangling from the crane... have at it... I'm done.

I can only help you as much as you want to help yourself. Don't limit your ability to understand. A father is not limited to your biological human father. If what I mean isn't what you understand... then I am the one who understands what I mean... and you are the one who doesn't... you see? I don't want it to get like this... I'm not here for an argument... let's do this peacefully, please. It's not hard... try.
im not here to be converted or anything.........................
so enough preaching.

so either explain yourself and give logical evidence to why you believe it. or dont post here. follow the guidelines pretty much.

you defined. your almost trying to explain. but you dont have to. next is logical evidence or proof. which you havent given anything to.

oh and also. this isnt a tear down session(yet). I havent stated your wrong or anything like that. But until you give evidence for what you believe. It is meaningless beliefs. and if you believe in a scam. Like a pyramid scam. We have the right to call it so. Because that is what it is.

Serpo said:
Omnipotent; your mind is all powerful. Without your mind, you cease to exist. Recognize this and you can become and do anything you so desire. Everything away from your mind is just an extension, including the body. All that is needed for enlightenment is the mind.
Code:
om·nip·o·tent
Having unlimited or universal power, authority, or force; all-powerful
n.
1. One having unlimited power or authority: the bureaucratic omnipotents.
2. Omnipotent God. Used with the.
@dictionary.com
Well thats the definition of the word. So perhaps explain a little further? But perhaps your speaking of imagination. and its simple to defeat that. I give you a paradox and regardless of how "omnipotent" your mind is. you cant defeat it. Which is why its a paradox.

or are you explaining that people can unlock things like telekinesis and telepathy?

You are making me feel very inferior with your words. I'm not sure if that's what you're aiming for. But that is the feeling I am getting... if anyone else is reading this and they do understand my logic, chime in please. I can't explain it too much more... it has many meanings, as I have already pointed out. Yes. My explanation of the mind being omnipotent fits that definition perfectly. You have control over your every move, your every thought, your every second of existence and your every perception of reality.

I'm not here to convert you. I'm not here to preach. Only sharing. Make of it what you will, take it or leave it... but don't pre-dismiss it. I understand and respect your skepticism, but you can ask questions nicely.. and say things that are a bit less threatening... I mean no harm.

something like this... "next is logical evidence or proof. which you havent given anything to." You didn't need to add the last sentence.. just simply ask me what is you wish me to explain.

I will treat you respectfully, kindly and patient... I expect the same back. :) Thank you.

I may say some things you don't understand initially. It's my nature to take meaning and shrink it to its smallest size, while still keeping its meaning.

My words are all wound up tightly together, you have to be gentle when unwrapping.

Last edited:
Serpo,
The wisest thing on the subject anyone has ever told me on the subject of religion was Les Sleeth in another thread. (and my father is a minister, so that's saying something)

Les Sleeth said:
I don't understand the insistence that God be infallable and omnipotent. Considering it from a logic perspective, if there is a consciousness powerful enough to create this universe, this solar system, this planet, life (biology), and a central nervous system capable of housing consciousness, then that is one heck of a creator, perfect or not. That creator doesn't need to be "perfect" to create all that we find here. Maybe he/she/it is doing the best he/she/it is capable of.

Likewise, logically speaking a creator doesn't need to be omnipotent to create this universe; he/she/it only needs to be powerful enough to create a universe (that applies to omniscience too . . . i.e., just knowledgable enough know how to create the universe).

These old concepts are neither indicated logically, nor are they supported by any known evidence. IMO, they are merely assumptions made dogma by past popes and fed to the masses. I don't see why we need to attach those concept to God. All they do is raise doubt and drive some of the faithful crazy because they really don't make much sense.
I've read some of your other posts over the last few days, and frankly, I'm a little concerned for you. I've seen others like you, that have gone through an experience like yours. (and once it ended in a terrible conclusion, hence my concern). Heck, I can't say that I haven't been there before. I do think your heart is in the right place.

God to me is the universe in which we live, including the physical laws in which everything obeys.
My purpose here is to be thankful and try to effect change for the betterment of humanity/world/universe.
I don't think we are necessarily all tapped to become "fishers of men", and create mass converts, but to let it happen naturally.
I don't think our actions on earth have any ramifications on whether we reach a heaven or hell. (in fact, that is an attribute to religious dogma as well.) Basically, whatever happens after we die will be the same for everyone.

I can see myself as a God, (not the universal God) as well as everyone else on earth. (a God that just happens to be bound by the laws of physics).

As for proof, I don't have anything other than my thoughts and experiences. The only proof will be revealed when we die. I will admit that in my theory, God doesn't even have to exist at all. But you will have just as much luck proving my God doesn't exist, as I would proving he does.

RVBUCKEYE
you have very rational beliefs. and Imma assist you a little. Proof that you exist.

Rene Descartes.
I think therefore I am.

Essentially it goes.

I am thinking of a rose. This rose exists inside my mind. But The rose can only exist in my mind aslong as my mind exists.

So logically. My mind exists. which is dependant on my brain and body. So they must exist.

So this evidence would be perfect for you. The main reason why im not poking holes. Is because there is no spots that can be poked. There is no paranormal things. such as omnipotence or fancy imaginary people. My guess would be your an agnostic. or Apatheism

You see that a perfect god with omnipotence etc, cant logically exist. But perhaps there is a lesser being who did these claimed things.

The thing i find with that is. If not believing in the non-perfect-god. Essentially its an alien with lots of power and knowledge. and thusly even a human could attain this power. Not making the alien special at all. Well as special as say Michio Kaku compared with Joe Schmo

serpo
My explanation of the mind being omnipotent fits that definition perfectly. You have control over your every move, your every thought, your every second of existence and your every perception of reality.
that definately doesnt logically mean omnipotence. which means the power to do ALL.
well i definately dont have the power to lift 900 kgs of weight. so i conclude you dont mean omnipotence. which removes all the pseudo out.

Well, I think it is possible that God is omnipotent and infallible, I just don't think it's provable. Mr. Sleeth described it as a bit like Christian Mysticism. I am quite comfortable that I exist. My purpose is clear, and I don't even live up to my ideals, but I try. That's all I can ask of anyone.

RVBUCKEYE said:
Well, I think it is possible that God is omnipotent and infallible, I just don't think it's provable.
Thats just it. if its not provable or anything. plus that the definition alone is illogical. Then how could you believe it exist over top anything else, even the Invisible Pink Unicorn.

I agree it's weird. I'm not saying that it is true, or even needs to be true, and I don't believe it's true. Why others insist that this is so, I don't know. One thing about believing in a god that can do anything.....well, he can do anything. How do you convince someone that this way of thinking is wrong? You don't, it's none of our business.

Last edited:
That's Really Perfect in an imPerfect Way

"That creator doesn't need to be "perfect" to create all that we find here. Maybe he/she/it is doing the best he/she/it is capable of."
Posted by Les Sleeth

This may not be in keeping to the tradition I was trained in, however I feel this morning that it is quite simply the most loving and forgiving thing I think I have ever heard.
If we can forgive the creator for creation based on a love and understanding that what ever the creator is, is doing the best it can, then so much can be accepted and understood on the imperfect levels we attempt to comprehend .... EVERYTHING down the line ... In which case it must then be (Trying.."all the way down").

Yes Shoshana... Les sounds like a very bright man :) I'm glad he is explaining things as well. I opened up so that more of my kind who naturally understand will come forward in the future and guide us back to love and peace. It is true... to understand creation... you must also understand its faults. You understand its naturalness... you understand man's ego and expectation. You understand yourself. :) You're making me smile. I'm glad someone is understanding. Perfection can be found in imperfection. The only thing that kinda hit a sour note with me is the "trying part"... the creator is not trying... the creator just is. We must accept that the creator is the creation and in being so that we are capable of being the creator. Now let's do the best that he/she/it/US are capable of. We are the change, we are the responsibility... all that we seek is within us, and we are all within one another. We ARE the creation, we ARE the creators... We ARE the future. No matter how silly this sounds... this is all true, and we know it. To be completely honest, one must recognize one's own faults and admit them to self and others when need be. In honesty we find truth.

Last edited:
Serpo said:
Yes Shoshana... Les sounds like a very bright man :) I'm glad he is explaining things as well. I opened up so that more of my kind who naturally understand will come forward in the future and guide us back to love and peace. It is true... to understand creation... you must also understand its faults. You understand its naturalness... you understand man's ego and expectation. You understand yourself. :) You're making me smile. I'm glad someone is understanding. Perfection can be found in imperfection. The only thing that kinda hit a sour note with me is the "trying part"... the creator is not trying... the creator just is. We must accept that the creator is the creation and in being so that we are capable of being the creator. Now let's do the best that he/she/it/US are capable of. We are the change, we are the responsibility... all that we seek is within us. We ARE the creation, we ARE the creators... We ARE the future. No matter how silly this sounds... this is all true, and we know it.
Serpo,

With all respect due to this being an OPEN forum and my not wanting to discuss things with you privately, I must say that your stating that I "understand" has no attachment to your comments.

In fact I do NOT understand what drives you to place yourself in a position of leadership and insist that folks are unknowing if they do not subscribe to YOUR vision.

Frankly your comments are coming up with red flags all over them.

Do you think you might consider rejoining the rest of the humble human family of which you are a part and enjoy the comfort and joys of normal communications and friendships?

Expalin to me the meaning of normal communications and friendship? Is that a statement made out of the ignorance of solo perception? It's narrow minded to call an act of thought or being, normal. I'm not seeking a leadership position. I'm seeking peace on Earth and enlightenment in humankind. I'm not a monster, I'm not a communist. Sorry for assuming that you understood, it appeared as if you did. My apologies. What drives me is myself, and my enlightenment in knowing that we all have the potential if we ever so desire it, and the time is now. There are no limitations on this planet. The mind should recognize no restrictions. If I am bringing up red flags everywhere, I'd like to have them pointed out :) I apologize ahead of time. I am a part of the human family... but it is not so humble. Do they care to join US? I don't view a very primitive (in cosmic terms) species of ape which cannot even decide on who's God is correct as a humble family. Maybe we don't live on the same planet. :P Joking. I am no better than anyone else.. as I have stated and will continue to state. If you can find faults in what it is I say... then find the faults. Don't make assumptions about my ambitions... I don't treat you in such a way, nor should anyone else. If you'd like to know what my ambitions are, simply ask. This is not MY vision.. it is the vision of many. This isn't about religion, this is about emotion and awakening to who's in control, our potential to be the best that we can be and using that potential in a positive manner. If we fail to come to a global realization of these things, we will not move forward.. and we will continue to burn in this hell. Children will be killed, brothers, sisters, mothers, fathers, friends, aunts, uncles. Is this what we want? Why do we deny what the future will bring when there is no change in the people who are living it?

Last edited:
Serpo, friend, you just seem to be a little too manic. You posted before that you used mairjuana (in another thread), just cut that out for a while and come back to earth. What you are feeling, if it's anything like what I felt, is exciting. It's ok to be excited. Hopefully you can tell the difference between what is drug induced, and what is real. I apologise if that was too personal for you.

Last edited:
It wasn't meant as a personal attack, just humble concern for your well-being because I do care.

Anyway, the burden of proof is always on the side of the person making the claims, and Monkey99999, was asking you to prove your omnipotence. (although I will agree the concept of the post is a little underhanded. Who wants to post their beliefs only to be rediculed?)

Sorry, I took offence to "manic". Thank you for caring. I mean that. My omnipotence is the all powerful control I have over myself. The more I accept this the more control I gain. The more control I gain, the more potent I become. There is unlimited potential in the mind, it just takes effort. Time is precious... why waste it? Just do... do because it will pass you by if you don't... accept and believe. Often times we spend our whole lives pondering and not acting. When you ponder and you find the truths... you must act on them... or they are empty. I can play the piano, I can play both the bass and the guitar right handed and left handed, upside down and backwards right handed and left handed. All because I just decided to do it... I plan on doing many more "crazy"(whatever that means ? :P) things.. because I believe that I can do them... and I don't want to sit around and procastinate as time passes me by. We can do whatever we want. Once you assert yourself... you realize it's not so hard after all. Smile and think positive. It's the future that matters. The future is created in the present.

Anything and everything you've ever wanted to change... just do it... starting today your book is empty. Write a new story.

Also, some in my generation, and most of the generations coming after us will stop getting married. They will recognize that true love is not defined by law. They will recognize many things that we so blindly ignore, and are so blindly led into believing as truth and tradition. It is going to be a beautiful time. I and many others already recognize this.

Last edited:
RVBUCKEYE said:
(although I will agree the concept of the post is a little underhanded. Who wants to post their beliefs only to be rediculed?)
well i missed a bunch of long posts and i dont have the time yet to read them. but this post had caught my attention because of my name.

I must say though. This post is not underhanded at all. It is nothing at all like this. It simply follows that if your beliefs are rational and have a reason(evidence/proof) to believe the way you do. Then your beliefs cant be rediculed. But if your beliefs are such that they are completely without rational thought and without any reason. Then you should be rediculed.

Take Santa Claus for example. We know he doesnt exist. The people who created the myth admitted that they made him up. But what if you found a man. who is 40 years old, who honestly and truely believes that santa claus exists. Like not as a joke or anything. That he worships the elves and santa year round. People would want to send him to a psychiatrist. But what if the people who created the myth didnt break and admit that he didnt exist. That you simply have to use rational thought to determine if he existed or not. You would first figure this. http://jewel.morgan.edu/~salimian/humor/humor_008.html" [Broken] you would also find no evidence for his existence. where no presents just show up in your house.

So its logical not to believe in santa. and it would be right to redicule any person like the man above.

So if you want people to stop rediculing your beliefs. Perhaps a change of beliefs are in order? or perhaps state evidence that would make all redicule stop.

and according to
Mathew 10:1
10:1 And when he had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease.
which basically means that your average man can have the power to heal all disease. and im not saying to use the trepanning. This is the healing that you hear people claim they have pretty often. Guy touches blind person's eyes and they arent blind again type stories.

You show me one person who can do this. This would be huge evidence for the supernatural i would say. When you have evidence you then are the one who redicules the people without evidence.

"HAHA skeptic??? you skeptics are all alike. how can you not believe in Jesus when we have this evidence to prove it all." or whatever.

Last edited by a moderator:
What exactly is it that you are ridiculing me for? Are my philosophies not making sense? Perhaps they are above your intellectual capacity... or you really have just not taken the time to ask questions and understand yet because you want me to be wrong so badly? You ARE capable of understanding what it is that I am presenting here... just try it. I don't understand... please, just make me understand your reasoning. If that is at all possible. No one should ever be ridiculed. Only shown the path of truth. Ridiculing is for the insecure. Does it make you feel better or what? I don't get it at all. Your Santa story somewhat lends credence to my claims of the mind being omnipotent... thank you for clearing that up. :) See there is meaning in everything...

My evidence has been stated, the evidence that you have been providing has only been ridicule :( What does that do? Do you want us to get angry and fight? I still don't understand that philosophy... I don't intend on ridiculing you, even in points where I have seen you to be wrong. Let's not do that, it's pointless. Rather point out false evidence... my evidence is my proof... prove my philosophies to be false instead of just saying "you're not like everyone else... you MUST be ridiculed". First and foremost... let's get to the bottom of what it is you don't understand... then you can try and ridicule me. Don't ridicule before you understand. It doesn't make sense... patience... Unknowns, by default, are denied? That's not very philosophical, nor scientific. Investigate, please. I'm opening myself up for you... tear me apart... nicely. I'm giving you all of my time right now... the most precious gift to give in this life. Give me a nice gift back. Things are deeper than you imagine.

Last edited:


text:
### On the assessment of ground water parameter uncertainty over an arid aquiferOn the assessment of ground water parameter uncertainty over an arid aquifer

Access Restriction
Subscribed


text:
# Finding multiple topics in short texts

I am building a natural language understanding component for a dialog system. The input is a natural language sentence (usually a short one), and the output should be a set of zero or more classes from a pre-specified set. For example:

input: "I offer a salary of 20000 per month for work as a programmer with a company car"
output: ["OFFER(Salary=20000)", "OFFER(Job=programmer)", "OFFER(Car=yes)"]

I collected some examples from real dialogs, in order to train a classifier. My current approach is:

• Features: I take the words of each sentence as features (I also tried word bi-grams and letter n-grams but the performance was worse).
• Training: I train a separate binary classifier for each class. As positive examples, I take all sentences that have this class, and as negative examples, I take all sentences that don't have this class.
• Running: I run each of the binary classifiers on the new sample, and return the set of classes that correspond to the classifiers that answered 'yes'.

This approach lead to too many false positives. Since my dataset contains many sentences with many classes (about 6 classes per sentence), the classifier gets confused between words that belong to different classes. For example, it takes the words "work as a programmer" as positive signal to the class "OFFER(Salary=20000)", because they appeared together in many training samples.

So, I edited my training data and separated each sample sentence to several sub-sentences, such that each sub-sentence matches just one class:

input: "I offer a salary of 20000 per month"
output: ["OFFER(Salary=20000)"]
input: "for work as a programmer"
output: ["OFFER(Job=programmer)"]
input: "with a company car"
output: ["OFFER(Car=yes)"]

The new approach lead to too many false negatives: since every sentence is a negative example of all classes except its own class, the classifier takes the words "a salary of 20000" as negative signal to the class "OFFER(Job=programmer)". Therefore, for compound sentences such as "I offer a salary of 20000 per month for work as a programmer with a company car", the classifier finds a single class and misses all other classes.

I also created a mixed dataset - half of the one-class samples and half of the multi-class samples (the other half I used for testing), and got much better result. However, this approach seems like a hack, and I would like to know if there is a more professional approach.

Any suggestions for solution will be welcome...

NOTE: I use the winnow classification algorithm, which currently has the best score (I also tried Naive Bayes, SVM, neural network and perceptron).

--

Some numbers:

• Performance of classifier trained on multi-class sentences and tested on single-class sentences: Precision=69% Recall=97% F1=81%
• Performance of classifier trained on single-class sentences and tested on multi-class sentences: Precision=99% Recall=32% F1=48%
• Performance of classifier trained on a mixed dataset (1/2 single-class and 1/2 multi-class), and tested on the other half: Precision=88% Recall=89% F1=89%
• It might help just to change your point of view. It strikes me that this is not a classification problem, but rather it is an attribution problem. The distinction is that each phrase or sentence no longer needs to be put into one category, but rather can be assigned multiple attributes. From this point of view the problem turns into a collection of (practically) independent problems: you need a job description classifier, a salary identifier, and so on, each of which could be developed and run independently of each other (and even use different methods). – whuber Jul 10 '13 at 19:02

The approach of training the classifier on single-class "sentences" (actually, not necessarily sentences, but phrases) is promising, but where it breaks down is you are training the classifier on a different type of data than what you're using it on.

You need a pre-processing step that breaks the sentences down into phrases, and use that same phrase-level data for both training and actual classification. Then, in your reporting step, you could aggregate all of the positive phrase-level results to the level of the input sentence (each sentence is a list of phrases with some positive identification of classes, and so you would simply combine all of the phrase-level positive results).

This approach isn't perfect either - it will often fail properly account for contextual information like negation and pronouns. But, it's the next logical step if you're building it from the ground up.

• The problem is, I don't have an automatic way to split a sentence into phrases... I could do it manually in my annotated dataset, but I need the system to work automatically on new sentences. – Erel Segal-Halevi Jul 7 '13 at 4:04
• Agreed - you need an automated system for new sentences, but you also need to use the same system on your annotated data. Many people have worked on this problem already and published packages such as the Stanford Parser (nlp.stanford.edu/software/lex-parser.shtml) and the Parser package in the Natural Language Toolkit (nltk.org/api/nltk.parse.html#module-nltk.parse) – Jonathan Jul 7 '13 at 18:52
• I already tried those tools... the problem is that they are very noisy, especially when the sentences have spelling and grammar errors (as is common, for example, with ASR output). Therefore I now try a purely machine-learning approach. – Erel Segal-Halevi Jul 9 '13 at 19:18
• Ah - I didn't realize that. It still seems that the core problem is that a method which works very well on short phrases individually fails when confronted with longer sentences. You mentioned you tried using n-grams as a feature... perhaps you could try using them as a unit of analysis with words as a feature. And, aggregate findings across n-grams within a sentence. – Jonathan Jul 10 '13 at 17:20

2 disconnected thoughts:

• You don't say if the inputs are all from the narrow domain of hiring, interviews, job offers, benefits, descriptions, etc. If so a gazetteer approach may be fruitful, after building a list of a few hundred significant words/phrases, if it's not one of those infinite acronyms/synonyms domains. A good place to start is to search ACL anthology on "gazette", and lucene/SOLR text indexing has many capabilities in this area

http://aclweb.org/anthology-new/

• (A long shot but my jog memories) there's also a large body of research on parsing twitter 140 character messages for named entity recognition and topicality. This might not have anything to do with the type of data you're seeing, but just a thought.

I now discovered that this topic is called multi-label classification. Recently, many new methods have been developed for this task.


text:
# chainer.functions.contrastive¶

chainer.functions.contrastive(x0, x1, y, margin=1, reduce='mean')[source]

Computes contrastive loss.

It takes a pair of samples and a label as inputs. The label is $$1$$ when those samples are similar, or $$0$$ when they are dissimilar.

Let $$N$$ and $$K$$ denote mini-batch size and the dimension of input variables, respectively. The shape of both input variables x0 and x1 should be (N, K). The loss value of the $$n$$-th sample pair $$L_n$$ is

$L_n = \frac{1}{2} \left( y_n d_n^2 + (1 - y_n) \max ({\rm margin} - d_n, 0)^2 \right)$

where $$d_n = \| {\bf x_0}_n - {\bf x_1}_n \|_2$$, $${\bf x_0}_n$$ and $${\bf x_1}_n$$ are $$n$$-th K-dimensional vectors of x0 and x1.

The output is a variable whose value depends on the value of the option reduce. If it is 'no', it holds the elementwise loss values. If it is 'mean', this function takes a mean of loss values.

Parameters: x0 (Variable or numpy.ndarray or cupy.ndarray) – The first input variable. The shape should be (N, K), where N denotes the mini-batch size, and K denotes the dimension of x0. x1 (Variable or numpy.ndarray or cupy.ndarray) – The second input variable. The shape should be the same as x0. y (Variable or numpy.ndarray or cupy.ndarray) – Labels. All values should be 0 or 1. The shape should be (N,), where N denotes the mini-batch size. margin (float) – A parameter for contrastive loss. It should be positive value. reduce (str) – Reduction option. Its value must be either 'mean' or 'no'. Otherwise, ValueError is raised. A variable holding the loss value(s) calculated by the above equation. If reduce is 'no', the output variable holds array whose shape is same as one of (hence both of) input variables. If it is 'mean', the output variable holds a scalar value. Variable

Note

This cost can be used to train siamese networks. See Learning a Similarity Metric Discriminatively, with Application to Face Verification for details.

Example

>>> x0 = np.array([[-2.0, 3.0, 0.5], [5.0, 2.0, -0.5]]).astype(np.float32)
>>> x1 = np.array([[-1.0, 3.0, 1.0], [3.5, 0.5, -2.0]]).astype(np.float32)
>>> y = np.array([1, 0]).astype(np.int32)
>>> F.contrastive(x0, x1, y)
variable(0.3125)
>>> F.contrastive(x0, x1, y, margin=3.0)  # harder penalty
variable(0.3528857)
>>> z = F.contrastive(x0, x1, y, reduce='no')
>>> z.shape
(2,)
>>> z.data
array([0.625, 0.   ], dtype=float32)


text:
# Coprime automorphism-invariant normal subgroup of Hall subgroup is normalizer-relatively normal

## Definition

Suppose $G$ is a finite group, $K$ is a Hall subgroup of $G$, and $H$ is a Coprime automorphism-invariant normal subgroup (?) of $G$. Then, $H$ is normal in the normalizer $N_G(K)$. In other words, $H$ is normalizer-relatively normal in $K$ relative to $G$.

## Proof

Given: A finite group $G$, a Hall subgroup $K$ of $G$, a coprime automorphism-invariant normal subgroup $H$ of $K$.

To prove: $H$ is normal in $N_G(K)$.

Proof: Let $g \in N_G(K)$. Suppose $g$ has order $m$.

1. We can write $g = ab$ where $a \in K$ and the order of $b$ is relatively prime to the order of $K$.
2. Conjugation by $g$ can be expressed as a composite of conjugation by $a$ and conjugation by $b$, and $H$ is invariant under both: $H$ is invariant under conjugation by $b$ because this is an automorphism of coprime order. $H$ is invariant under conjugation by $a$ because $H$ is normal in $K$ and $a$ is in $K$.


text:
#### Vol. 6, No. 4, 2012

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Moduli of Galois $p$-covers in mixed characteristics

### Dan Abramovich and Matthieu Romagny

Vol. 6 (2012), No. 4, 757–780
##### Abstract

We define a proper moduli stack classifying covers of curves of prime degree $p$. The objects of this stack are torsors $Y\to \mathsc{X}$ under a finite flat $\mathsc{X}$-group scheme, with $\mathsc{X}$ a twisted curve and $Y$ a stable curve. We also discuss embeddings of finite flat group schemes of order $p$ into affine smooth $1$-dimensional group schemes.

##### Keywords
curves, group schemes of order $p$, moduli
Primary: 14H10
Secondary: 14L15


text:
# Kinetic energy change in virtual photon exchange

1. Dec 13, 2005

### El Hombre Invisible

I understand (vaguely) how momentum is exchanged via virtual photons in electromagnetic interactions. But how do the changes in kinetic energy occur?

For instance, a proton and electron are at rest separated by a distance x. The proton emits a virtual photon and recoils in the direction of the electron with momentum p. The electron absorbs the virtual photon and recoils in the direction of the proton with momentum -p. But the kinetic energy of the both the proton and the electron have increased. From whence this naughty energy appear?

If my example doesn't work, please replace with any other where a force acting on a charge changes its energy.

2. Dec 13, 2005

### lalbatros

From the potential energy.

3. Dec 13, 2005

### El Hombre Invisible

BUT... this is precisely my problem. Let me illustrate.

Proton and electron at rest, separated by distance x. The virtual photon of momentum p is emitted from the photon causing a recoil of -p. Potential energy is determined by distance, so to change potential energy the proton has to move. To move the proton needs kinetic energy, and a change in momentum necessitates this. But if the kinetic energy comes from the change in potential energy we have a first-mover type problem. Potential energy doesn't change until the proton moves, so how can it supply the kinetic energy to cause the motion to change the potential energy?

It gets worse for me. If the proton recoils at the instant the virtual photon is emitted, it will take T = x/c for that virtual photon to be absorbed, during which time the proton is moving and so the distance from the electron is moving, meaning the potential of the electron is changing. But the electron doesn't move until the photon is absorbed. So for x/c the change in the potential energy function of the electron does not cause a change in kinetic energy - this doesn't happen until momentum is transfered.

It's doing my head in. I could wait several years and learn it, but... I'm not going to.

Lastly, so far as I can tell, electric potential energy arises from the exchange of virtual photons. That is, as the electron nears the proton, the virtual photons it absorbs carry a higher momentum since the time between emission and absorption is less. In a sense, the potential of the electron increases with the energies of the virtual photons it absorbs (or could absorb). So I'm not even sure 'from the potential energy' is much different from saying 'from the virtual photons', which just brings me back to my original question.

I should have said, I know next to nothing about QED or QFT, and not much more about QM. We've studied old quantum theory, simple solutions to 1D time-independant SEs, quantum theories of matter (gases, conduction, etc). Almost no particle physics though.

4. Dec 13, 2005

### Staff: Mentor

How about this: the (classical) electrical potential energy is the total energy of the cloud of virtual photons that surrounds (say) a pair of charges? This is a half-assed guess on my part, because I have only a very slight acquaintance with QED, so I hope someone who actually knows QED can correct or expand on this if necessary.

5. Dec 13, 2005

### lalbatros

Hello El Hombre,

It looks like the quantum and the photons are only there for the decor.
Your question about time taken by the photon can be translated to classical terms.
Have a look at the classical field theory and retarded potentials, for example.

When one of the particles sets in motion, the available potential energy is converted in kinetic energy and -additionally- into instationary field energy. In a sense this make your question even worse. But this how things works: not only is the particle accelerated but it also radiates and dissipates energy. This why classical atoms would collapse. This why Rydbergs states collapse too. Nevertheless, energy is conserved: (kinetic energy + potential energy + field energy) remains constant. Therefore, the potential energy produces kinetics energy and field energy in another spectral domain (unstationary).

6. Dec 13, 2005

### El Hombre Invisible

Similar to my picture, so it's good to see someone more experienced than I am thinking along similar lines. I'm thinking there might be some problems considering it all of the virtual photons surrounding the pair of charges. Your classical potential energy is determined by your distance from the charge in question, so would seem to exclude those at other distances (which makes sense - if the electron is at distance r from the proton, virtual photons appearing at distance r + $$\Delta$$r aren't going to effect its mechanical energy). It seems more likely to me that your electrical potential energy is the supply of virtual photons coincidental with the charge's position (i.e. those with precise energy $$E = \frac{h}{4\pi c\Delta t}$$), from which the position dependancy of potential energy arises.

But I still don't see how this energy is transferred if all of the photon's energy arises from the HUP. The answer will, I'm sure, be blindingly simple, but those are the things I usually can't see.

7. Dec 13, 2005

### El Hombre Invisible

Hi

You are right insofar as I can ask the same question in classical physics. However, I think the answer in classical physics is: we don't know. The laws of electrostatic forces were known well enough, but the actual mechanism behind them is, AFAIK, the realm of QED and none other. The mechanism in QED by which momentum is transfered I (kind of) understand and am not aware of an equivilent in EM. But what is converted to kinetic energy and how, I don't know.

8. Dec 13, 2005

### Physics Monkey

El Hombre,

The key point when dealing with virtual particles is that they are not "on the mass shell". What this bit of jargon means is that the energy of a virtual particle isn't related to its momentum in the same way that you are familiar with for real particles. In particular, the energy of that virtual photon your proton emits is not given by $$E = p c$$ like for real photons. Instead, the energy and momentum of the virtual photon are determined by conservation of energy and momentum applied to the emission. I would encourage you to give it a try and see what you come up with for the photon energy.

With this in mind, you can take each of these virtual processes and associate an amplitude with it. To calculate physical quantities you have to sum the effects of each virtual process. In doing so, you find that the less "real" the virtual particle is, the less it contributes to the final result. The end result is that by summing contributions from these virtual processes one can obtain the Coulomb energy between two classical charges. I can show you the details of the calculation if you're interested.

Last edited: Dec 13, 2005
9. Dec 14, 2005

### Wishbone

I LOL'ed
________________

10. Dec 14, 2005

### lalbatros

El Hombre,

It is a good start point if you agree that in classical theory your question is answered simply by recognizing that fields can carry energy and exchange energy with particles. Then we are simply faced to a translation problem.

Now, from your discussion, it strikes me that nowhere the electrostatic field receives any quantum description. Would it not be the way to solve your question? In QFT, how would you described something like an electrostatic potential, or similar. Since, classically, the electrostatic potential is the source of energy you are looking for, I would expect that its QFT description would translate that somehow. I would guess that mathematically this reduces to something like a Fourier description of an electrostatic potential.

But I see another small difficulty with your question, regarding the uncertainty principle. Indeed you assumed your particles are at rest in the initial conditions. Probably this description has to be refined a little bit. And this rises another question: in QFT, are stationary fields possible?

Finally, my naïve picture: the static field might be grossly represented by a sea of photons with a broad spectrum and a space density increasing near the particles you considered. Might that not help to picture your question? Would that not indicate that real photons are involved instead of virtual photons?

If you can go forward with these naive comments, I would appreciate if you could point me to an introductory text on QFT where such ideas are developped in a more exact/mathematical fashion. I feel very unconfortable with mathematical physics text: I most often feel completely disconnected from reality (maybe an epr effect too).

thanks,

michel

11. Dec 14, 2005

### lalbatros

I was expelled from a lecture about banana orbitals ...
I could not stop laughing ...

I guess "retarded potentials" made you jump a state ?

12. Dec 14, 2005

### El Hombre Invisible

I'm not sure I can because I'm not sure I follow you. I understand that the momentum of the photon is determined by the conservation of momentum in the proton-photon system, so if a proton feels a recoil of $$\Delta p$$, the photon will have a momentum of $$-\Delta p$$ and all is well.

This recoil will correspond to a change in kinetic energy of the proton of:

$$E_{kin} = \frac{p^2}{2m_p}$$

How can this determine the energy of the photon? Let's say this recoil increases the kinetic energy of the proton. I don't see how I can then derive the energy of the photon on the basis of conservation of energy alone.

Can I have one more hint?

This sounds promising. Your statement about how "real" the virtual photon is suggests that the photon does have a real contribution as well as a virtual one, which at least gives some mechanism for transferring energy (though doesn't help me understand how it is conserved). On your point about how one can obtain the Coulomb energy from the virtual contributions, do you mean that the electric potential is essentially the sum of the virtual-only contributions to the process? That would mean that, classically, the potential energy converted to kinetic energy is the sum of the virtual contributions to the photon energies exchanged? That would also mean that these virtual photons permanently become real kinetic energy, at which point I conclude I have, again, misunderstood.

Thanks for all your help, not least for pointing out that I was using the wrong equations.

Last edited: Dec 14, 2005
13. Dec 14, 2005

### El Hombre Invisible

Hi Michel. This is what jtbell and I were discussing earlier and part of my last reply to Physics Monkey. In trying to translate the classical idea of electrostatic potential to QED, the virtual photons themselves would seem the prime candidate. The problem I have with this is that I was of the impression that all of the 'borrowed' energy of a virtual photon must be paid back - it cannot be converted to real kinetic energy. This may be my problem.

Yes, I am quite certain that my example is not sensible. It certainly doesn't seem very sensible from a classical point of view. Classically speaking, the electron has a negative potential energy and no kinetic energy - a zero mechanical energy. How, then, did it get there? Presumably by radiating its kinetic energy away. The electron cannot move away from it since it can only gain kinetic energy by lowering its potential further. In which case, in QM terms, it is confined and so MUST have kinetic energy. So, yes, my attempt at simplification may have over-complicated the question.

Absolutely - that is AFAIK how it is. However the mechanics involved don't follow easily from that for me (i.e. how the energy is supplied to the particles).

I don't see how. A real photon, as Physics Monkey pointed out, has energy-momentum relationship E = pc. Where would this energy come from? It cannot come from the change in kinetic energy of the proton, since this is far less than pc.

Who, me? If I could I assume I would not be asking the question. Someone else?

14. Dec 14, 2005

### erickalle

On a simpler note.
Something else which is doing my head in.
When an electron is moved away from a proton the convention says that the electron is raised to a certain potential. But has anybody around here had a thought for the poor proton? Is its potential not raised?
If we take a metal surface to the proton the result will be that the proton generates a mirror image and will be flying off to this image.

15. Dec 14, 2005

### El Hombre Invisible

Yes, it is.

????

This isn't very related to my question, is it...

16. Dec 14, 2005

### Physics Monkey

El Hombre,

Thanks!

Now, on to your question. The energy of the system before the virtual photon was emitted is $$m_p c^2$$, and the energy of the system after the virtual photon is emitted is $$m_p c^2 + \frac{p^2}{2 m_p} + E_\gamma$$, where I assumed the proton was initially at rest and the recoil was small so that non-relativistic formulas apply. Energy is conserved by the emission process so all you have to do to find $$E_\gamma$$ is equate the two and solve. It's completely analagous to the way you found the momentum of the photon. Don't be shocked if the answer looks weird, remember that the photon is virtual.

Last edited: Dec 14, 2005
17. Dec 14, 2005

### lalbatros

I cannot understand this statement:

In QFT just like in classical field theory, there should be a term for the potential energy. Isn't it?

Again, my naïve guess is that the -hypothetical- static field would be made up of a wide spectrum of photons. The accelation of the electron would produce a change is the field energy as well as the particle energy. The fields energy is not zero in the initial conditions, but it is stationary, as far as this makes sence in QFT (like for the question). After a short time, the total field energy should have decreased, and additonally the spectrum should have changed and become partly unstationary.

Now concerning my request for some reading:

I assumed that if you had such questions you might also have some interresting reading. Maybe also a small chance to find a readable one: one that puts the maths behind the scene instead of on the stage.

18. Dec 14, 2005

### El Hombre Invisible

Really? Well this is just the negative of the kinetic energy I mentioned earlier. So your answer is that I don't have to do anything to derive the photon energy from that - it just is it ('xcept times -1).

So if the energy-momentum relationship is simply:

$$E = -\frac{p^2}{2m_p}$$

then two virtual photons of the same momentum but emitted from charges of different masses will have different energies. Is there any idea why virtual photon energy depends on the mass of the emitter, other than conservation of energy?

And, of course, there are the two more obvious and no doubt related questions: how can the energy be negative, and where does $$\Delta E\Delta t = h/4\pi$$ come into it?

Thanks for all your help. I'm getting there.

19. Dec 15, 2005

### El Hombre Invisible

Hi

I read this in Wiki and it seemed to answer my question:

To consolidate this with my current (mis)understanding, since the virtual photon is a particle with fully defined momentum, it has the potential to be found anywhere. In the case of a proton and electron at rest:

p_____________________e

the proton may emit a virtual photon and recoil towards the electron. To conserve momentum, the photon has a momentum in the direction from the electron to the proton. Spatially it can be found anywhere, even behind the electron:

__p->_________________e-<-~~~~

Since the change in energy of the proton is positive and virtual photons conserve energy, the photon enery is negative. This means it is going the other way as if emitted by the electron:

__p->_________________e~~~~->+

This causes a recoil on the electron, so we have:

__p->____________<--e__

and energy and momentum are conserved.

Is this a vaguely decent layman's overview?

It would seem to me then that the only HUP inequality that matters is

$$\Delta p\Delta x >= \frac{h}{4\pi}$$

A change of momentum p will arrive at distance x from the emitter.

Last edited: Dec 15, 2005
20. Dec 15, 2005

### erickalle

Just a thought which popped up. It will be popped elsewhere.