It seems, somebody removed the question so even I cannot see it and subtracted 100 from my reputation. What happens???

Please tell me how an abstract measure of the form

$$V=\int_{t_0}^{t_1} (t_0+t_1-t) \log \frac{p_1(t)}{p_0(t)}dt$$

can be "not mathematics"? Again, is probability theory mathematics? If yes, then this is also mathematics and it is research-level because discusses a little-known part of probability theory.

And please tell me why I was stripped of 100 reputation for this question?

"think it's important to distinguish 'language' and 'subject'. " - yes. Please tell me if probability theory is mathematical subject or not. The question was about probability theory.

Here's the text of the question, so that people know what we're talking about:

You all know that in today's world when it comes to measure value, most people would use dollar as a unit measure. There are other units though all of which can be more or less exactly converted to each other. But it seems that there is apparently no internationally-agreed theoretically-defined unit of value.

So my question is whether such abstract unit of value was indeed defined in any theoretical paper, about which I do not know?

Below are some my considerations about the topic.

First, it should be noted that economists developed concepts of personal value, marginal value, exchange value etc. These all mostly depend on which subject is considered and in what circumstances, sometimes can be derived following certain procedures from each other and can be measured in the same units, so such plurality should not mislead us.

1. It is indeed possible to postulate a unit of value as a value of say, 1 kg of gold. This definition is rather old and useful, but becomes problematic when there is no gold available.

2. Marxists seem to postulate the value as a measure of labour needed to obtain the commodity in question. The problem here is how to measure the amount of labour. In human-hours? Very inexact and completely non-abstract. Besides has little correlation with market prices.

3. Initially I thought that it may be possible to postulate a unit of value as a value o commodities which increase pleasure or reduce suffering twofold. This definition seems rather universal, but has the same problem: how to measure suffering and pleasure?

4. So I came to the following possible definition: unit value is the value of commodities which increase probability of a positive outcome e-fold for the following unit of time. Since a common negative outcome for all people and animals is death, it is possible to define a unit value as the value of commodities, which increases the chance of survival e-fold for the following unit of time, without creating any additional pleasure or suffering. We can then take a limit with the unit of time going to zero and integrate. Let $p_0(t)$ is the distribution of probability of survival without the commodity and $p_1(t)$ is the distribution of probability of survival with the commodity. Let $(t_0,t_1)$ is the interval of time through which the commodity affects the probability of survival (with t=0 being the present moment). Then value of the commodity V would be

$$V=\int_{t_0}^{t_1} ({t_1-t+t_0})\log \frac{p_1(t)}{p_0(t)} dt$$

If we take another logarithm base we can simply get another unit of value, proportional to the previous one. Following this definition it is possible to derive other concepts such as marginal value, exchange value (as a market equilibrium of personal values) etc.

This definition, though does not take into account possible sufferings and pleasure some commodities can provide, for example, the value of a box of cigarettes would be negative. But if we assign certain value to pleasure we can overcome this difficulty. Such value may be assigned based on empiric data regarding exchange rate of say, cigarettes and a commodity that increases survival without providing any pleasure.

So, I would like to hear any suggestions to improve this definition and possibly pointing to an existing abstract definition of this kind.

> Anixx- It was marked as spam.

This is even more fascinating! Am I effectively banned from MO now? What diseased consciousness one should have to count this question as "spam"?

> but you did not have a mathematical question about it, but rather a bunch of rambling pseudo-economics.

No. I asked a question about a proposed measure in probability theory. This is related to mathematical economics and game theory of course.

I agree with those that marked this as spam. The question had no mathematical content.

However, I would suggest not getting into protracted arguments with Anixx about this. Given past discussions on meta with him, I suspect that he is looking for a good fight. Let's not give him one. If we don't participate, the thread will die.

I think that as a community, we have a responsibility to respond to policy queries on meta, but only if those queries are made in good faith.

> I think that as a community, we have a responsibility to respond to policy queries on meta, but only if those queries are made in good faith.

This is a clear incitement for a conspiracy against me which is not of course a good-faith intent.

Regarding my intents, what can be a better faith than rigorously formulate and prepare a question which interests me and post it here only to find it deleted as "spam"?

P.S. Of course I do not want "good fight", I just asked the question to get it answered, and now I want explanation of what rules did I broke so not to break them in future. It seems the definition of "spam" is rather arbitrary, so I cannot be sure that my next question will not also be deleted as "spam".

Andy, I don't mean to flout your suggestion not to engage, but just a quick mention that (as I understand it) the listed reasons for closing, including the term "spam", are not chosen by us but by the stack exchange sites. There is a limited list of reasons to close and one can only choose what term seems to best fit the situation.

A generalized meaning of "spam" is an unwanted internet message; here the reason "spam" for closing would apply to questions where the question is buried under a disquisition that is not precise mathematics, making it unwanted or undesirable as far as MO is concerned. As far as I can tell there is a heavy empirical component to the question and therefore the question is not suitable for MO; ideally, we want crisp definitive mathematical questions which call for crisp definitive mathematical answers.

In cases I can think of, the background was more or less pure mathematics. Other sorts of questions not fitting into the ideal mold of crisp mathematical questions and answers work better as community wiki, but even there one should be disciplined and keep the question on-topic. The people who frequent this site are busy professional mathematicians and come here for mathematical interchanges; speculations drifting outside mathematics are by and large frowned upon.

Sure, okay. I don't want to get into a long discussion about this. The last thought I'll offer on this thread is that generally speaking, people who have not yet accumulated a lot of reputation, esp. anonymous users, have to go through a period of "proving" themselves; the best way is to do that is to stick to crisp and precise questions and answers at a level of interest that will engage pure mathematicians. One can relax a little more after one has gained some reputation within the community. Of course, there may be more of a hurdle for newish users who have gotten themselves embroiled in controversies, such as yourself.

I'm bowing out now...

Let me clarify some technical points. The process of closing a question orthogonal to the process of deleting it as spam/offensive. A question can be closed by five votes from 3k+ rep users or by a moderator. Independent of votes to close, a post can be automatically deleted as spam/offensive/grossly inappropriate if enough people flag it as such. If that happens, the post is deleted and the owner is penalized 100 reputation. Only 10k+ rep users and moderators can see the number of spam flags, and only 10k+ rep users and moderators can see deleted questions. Users can always see their own deleted answers. Your question was deleted, but not closed. (You're also confusing the roles of "administrator" and "moderator", but that's really not relevant here.)

A generalized meaning of "spam" is an unwanted internet message

If your post is deleted as spam/offensive, it means that members of the community think the post is a detriment to the site and that posting it on the site was sufficiently misguided that it should be penalized. This is the accepted definition of "spam" on MO. Your question was not about probability or about mathematics. I don't even think it was an economic question. It's a philosophical question, but it's unlikely to be a fruitful one. It's like somebody making up a precise quantification of "health" or some other intentionally vague concept. I can't help myself from illustratating the sorts of pointless discussion these things lead to: your definition of value has absolutely no bearing on my probability of survival, so the value it would assign to itself is zero.

If you don't agree with the MO community about what counts as mathematics, it will only frustrate everybody when you try to do mathematics with it. With that, I'll take Andy's advice and bow out.

> sufficiently misguided that it should be penalized.

Please tell me why this purely mathematical question asked in good faith should be 'penalized'?

I have to admit I have not read this thread carefully.

But it seems like we have a larger issue here that we have to think about.

There are a lot of people out there doing mathematical modelling who call themselves "applied mathematicians". They don't prove any theorems. They take complicated situations coming from, for example, ecology, figure out a sensible system of differential equations for them, point out some classical theorems which say that solutions to this set of equations exist and behave reasonably well numerically, run a simulation on their computer, vary a few parameters to see what happens (and maybe cite a theorem that says that behaviour of the system varies nicely as parameters vary), and publish a paper with the results.

The only difference between these people and those who would call themselves mathematical ecologists is that they tend do their work over several scientific areas rather than concentrating on a single one.

There are a fair number of math departments which are in fact dominated by such folks. (At least one pure mathematician has complained to me about the politics of working in such a department, including the unrealistic publication requirements being imposed on tenure-track pure mathematicians in the department. (For obvious reasons, this mathematician and the department will remain anonymous.))

Should these folks and their questions be welcome on this site? Or should we restrict this site to pure mathematics and the part of applied mathematics that proves theorems?

EDIT: I was confused when I wrote the earlier version of this post. I thought this was the thread discussing fractional iteration, not the thread discussing the "theory of value". I don't have anything useful to say in this thread, but the forum software will allow me to edit my post but not to delete it.