## Calling all scientists: Do you understand math?

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## Would you understand what to do with this equation? $\prod_1^n{Volume_i}$

Yes
57
74%
No
9
12%
What's the question?
11
14%

Total votes: 77

kadamczy
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### Calling all scientists: Do you understand math?

I am having an argument with a fellow scientist whether or not the typical scientist would understand a specific math operator.

Scientists of XKCD: Without using google/wikipedia or any other online resource, would you understand what to do if presented with:
$\prod_1^n{Volume_i}$

Note: you need to be running the prosilver board style to see TeX. If you can't see it, it kinda looks like:
1n Volumei
(if the 1 and n were below and above the capital Pi)

I argue this is common enough for the typical scientist to understand.
Last edited by kadamczy on Fri Jul 22, 2011 4:33 pm UTC, edited 2 times in total.

Yakk
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### Re: Calling all scientists: Do you understand math?

I am not a scientist:
Spoiler:
As a non-scientist, I'd take that to be nonsense. Product over volumes? Dimensional analysis wut? (Result determined by scale of dimensional units, etc). And the product from 1 to i of volume_i is merely (volume_i)^i -- which makes it a pretty obtuse way of describing a simpler concept. So if I throw out the "product from 1 to n of (expression)", and assume that the i on top is supposed to indicate what variable we are iterating over, I once again get something strange -- a product over a single point (1) and not over a range. At this point, given that my 3 or so attempts to interpret it have outputting something closer to nonsense than sense, I'd assume that there is a typo, the writer is using some (unknown to me) convention, or that the writer doesn't know what they are talking about: which one I'd pick would depend on context. Maybe there is some obvious "container" that the iteration is over that the 1 would somehow refer to? Dunno
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

LaserGuy
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### Re: Calling all scientists: Do you understand math?

Yakk wrote:I am not a scientist:
Spoiler:
As a non-scientist, I'd take that to be nonsense. Product over volumes? Dimensional analysis wut? (Result determined by scale of dimensional units, etc). And the product from 1 to i of volume_i is merely (volume_i)^i -- which makes it a pretty obtuse way of describing a simpler concept. So if I throw out the "product from 1 to n of (expression)", and assume that the i on top is supposed to indicate what variable we are iterating over, I once again get something strange -- a product over a single point (1) and not over a range. At this point, given that my 3 or so attempts to interpret it have outputting something closer to nonsense than sense, I'd assume that there is a typo, the writer is using some (unknown to me) convention, or that the writer doesn't know what they are talking about: which one I'd pick would depend on context. Maybe there is some obvious "container" that the iteration is over that the 1 would somehow refer to? Dunno

Spoiler:
I don't think this is quite as uncommon as you think it is. In statistical mechanics, for example, you're occasionally required take the product over N volume integrals in phase space, and do end up with solutions that goes as [imath]V^N[/imath] I would interpret the indexing here to mean that you are talking the product over N different volumes, indexed from 1 to N.

Err... Wait. The i is on the top of the product as well. A product from i = 1 to i? I guess that would just mean that the answer is just [imath]Volume_1[/imath].
Last edited by LaserGuy on Fri Jul 22, 2011 2:56 pm UTC, edited 1 time in total.

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### Re: Calling all scientists: Do you understand math?

Voted no, as I'm not familiar with what that operation is asking of me. Obviously, I don't understand all of math.
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### Re: Calling all scientists: Do you understand math?

I understand what it is asking, but I don't understand how it's meaningful. i=[1,i] doesn't make sense.
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agelessdrifter
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### Re: Calling all scientists: Do you understand math?

I am not a scientist, but I am studying science and yes, I understand what you're going for, but the index doesn't make sense. That i on top needs to either be a number or some letter other than i for that expression to make sense.

D.B.
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### Re: Calling all scientists: Do you understand math?

I believe would know what to do with it as I'm familiar with the symbols, but given you haven't told us what it's actually intend to mean it's a little difficult to answer your question . Also not sure I count as a scientist, so have not voted.

Spoiler:
To check, I'm interpreting what you wrote as
$\prod_{j=1}^i\text{Volume}_i = \left(\text{Volume}_i\right)\left(\text{Volume}_i \right)\ldots \left(\text{Volume}_i \right)= \left(\text{Volume}_i\right)^i$

However, I would suspect that you meant was something more like
$\prod_{j=1}^i\text{Volume}_j =\left(\text{Volume}_1\right)\left(\text{Volume}_2\right) \ldots \left(\text{Volume}_i\right)$
?

EDIT: Ahh screw it. Voted yes.
Last edited by D.B. on Fri Jul 22, 2011 5:26 pm UTC, edited 1 time in total.

Gigano
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### Re: Calling all scientists: Do you understand math?

I am a scientist (biologist), and I think I understand what the mathematical expression means although I am not sure what its interpretation is:

Spoiler:
The expression equates taking the product of a certain amount of values for volume, with i being any discrete number. If there exist for example an n amount of volumes with different values, you multiply those volumes with each other. Volumei x Volumej x Volumek etc. could in a particular case be 30 m³ x 35 m³ x 89 m³.

Also, I think that the i on top needs to be an n, and the 1 ought to be some sort of index noting the particular volumes.
Last edited by Gigano on Fri Jul 22, 2011 4:35 pm UTC, edited 1 time in total.
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### Re: Calling all scientists: Do you understand math?

Yeah, the letter i is being abused in that notation. I am a physicist.
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kadamczy
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### Re: Calling all scientists: Do you understand math?

agelessdrifter wrote:I am not a scientist, but I am studying science and yes, I understand what you're going for, but the index doesn't make sense. That i on top needs to either be a number or some letter other than i for that expression to make sense.

doogly wrote:Yeah, the letter i is being abused in that notation. I am a physicist.

whoops good call, that's supposed to be an n on the volume. I was in a hurry when I wrote it. It is fixed now to represent how it is in the equation I'm proposing.

For the others so far: Thank you for your responses! This is only a subset of a much larger equation (for those who wonder what its purpose is).

doogly
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### Re: Calling all scientists: Do you understand math?

Yeah. It looks mostly like we're on our way to phase space and stat mech, but I suppose you could just want lots of volumes (more likely if you are a math person.)
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LaserGuy
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### Re: Calling all scientists: Do you understand math?

I'm a little surprised that you'd think scientists would not know this notation, TBH. I think multiple product notation was covered in high school for me. I can imagine there are some people who have probably never seen it since, because multiple products of this form are pretty rare in most applications, but it's something that I'd imagine most people who have done a bit of science/math are likely to have come across at some point in their academic careers.

Now, if you were asking someone to evaluate a more obscure (and unintuitive) operation like [imath](2k-1)!![/imath], you might get some more interesting responses.

doogly
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### Re: Calling all scientists: Do you understand math?

Or a personal favorite, $\frac{\bar{\Xi}}{\Xi}$
(it looks better on a blackboard)
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Yakk
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### Re: Calling all scientists: Do you understand math?

So a more polite way to do that is product(n=1 under, i on the top) of Volume_n.
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

doogly
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### Re: Calling all scientists: Do you understand math?

I'm usually accustomed to
i = 1...n
i = 1...N
n = 1...N
Your proposal, Yakk,
n = 1...i
seems off, but that is just unconventional and not abusive. I don't think it would be more polite though!
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Yakk
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### Re: Calling all scientists: Do you understand math?

Ya, I thought (from an earlier description) that the top index was supposed to be i.

So this is the more polite way to describe it:
$\prod_{i=1}^n{Volume_i}$
because it doesn't rely on implicit indexing. In a large equation, what index is being used can be confusing. In a small equation, when you have 1 loose index, you can work out "oh, so that attaches to that unnamed index".
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

kadamczy
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### Re: Calling all scientists: Do you understand math?

LaserGuy wrote:I'm a little surprised that you'd think scientists would not know this notation, TBH. I think multiple product notation was covered in high school for me...

I agree, I was appalled when I was told by my manager that he thought nobody would understand it. I work in the development of pharmeceuticals and most of us have at least one Ph.D. That being said, I've asked around 6 people so far and nobody has understood what the product operator is. I think I might have to define what the operator means below the equation (which is depressing)

Yakk: $\prod_{i=1}^n{Volume_i}$ is definitely a better presentation, I figured the index was implied, but it's better to be safe than sorry

KestrelLowing
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### Re: Calling all scientists: Do you understand math?

I'm not a scientist, I'm an engineering student.

That being said, I have no idea what that operator does. I don't think I've ever seen it. Now, if I knew what the Pi did, I might be able to figure out how to solve something like that.

But, engineers use math to actually do things, not to just prove something that didn't really need to be proved

doogly
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### Re: Calling all scientists: Do you understand math?

KestrelLowing wrote:But, engineers use math

Barely ; )
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nehpest
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### Re: Calling all scientists: Do you understand math?

As an engineering student and math fetishist, I understood the notation (it was corrected before I got here). That said, I've never been called on to use it (entering the thirdish year of an electrical eng program).
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### Re: Calling all scientists: Do you understand math?

doogly wrote:
KestrelLowing wrote:But, engineers use math

Barely ; )

That deserves at least an internet, in my book.
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qetzal
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### Re: Calling all scientists: Do you understand math?

Voted yes. For context, I'm a PhD molecular biologist, but I certainly knew what this meant in college, and probably in high school. (Hard to remember details from back then....) That said, I'd guess I'm more comfortable with math, and took more math classes in college, than the typical molecular biologist.

kadamczy,

I've worked in drug development as well (though not currently). What's the context in which you're using this? Not an SOP, I hope.

Sagekilla
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### Re: Calling all scientists: Do you understand math?

In the context of some condensed matter physics I've seen the following (severe abuse of notation, as is the thing mentioned up top):

$\int (\prod {dx_i}^3 ...)$

Which was taken to mean as

$\int {dx_1}^3 (\int {dx_2}^3 (...))$

And was further simplified to something along the lines of

$\int \mathcal{D}x ...$

Or alternatively I've seen [imath]{dV}_i[/imath] being used instead of [imath]{{dx}_i}^3[/imath].
I've also seen the "Volume" sort of thing up top before too.

So if I saw that type of operator, I probably would be able to infer from context what they're talking about.

But completely out of context, that's the most nonsensical thing I've seen.

Note: I've dropped most of the subscripts and bounds, as this is what I've commonly seen in the work I've been doing. wimpers
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### Re: Calling all scientists: Do you understand math?

doogly wrote:Or a personal favorite, $\frac{\bar{\Xi}}{\Xi}$
(it looks better on a blackboard)

Oy vey. I tried to turn my head sideways and read that as <1|l|1> at first

On the the things you could use a product of lots of volumes for:
Geometric mean.
Some unusual statistical tool on data with units of volume.
The denominator in a big ol' concentration calculation (e.g. A/Volume1 + B/Volume2...)

Please tell us kadamczy! We need to know!
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### Re: Calling all scientists: Do you understand math?

I am a professional horse trader.

I was trying to google 'calling all horse science entusiasts need recommendation to hire tutor for teaching my kid to understand 7th grade math'.

This was the first hit on my search so if anyone knows a good math tutor in Wallabe North Carolina I would be much obliged.
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### Re: Calling all scientists: Do you understand math?

doogly wrote:Or a personal favorite, $\frac{\bar{\Xi}}{\Xi}$
(it looks better on a blackboard)

Alright, I'll cave, what is that? And is it really math, or just a representation of some physics thing? Or is it just an evil symbol choice of symbols to represent something non-specific?

If it's just excessive use of greek letters, profs who do that are evil. I can barely write english legibly, much less weird greek characters...

doogly
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### Re: Calling all scientists: Do you understand math?

It is just a ratio of something you call xi and its conjugate. It is meant for pure notational sadism. Nothing with real, actual significance would ever get denoted this way conventionally.

...I still like it. I double majored in Classics and Physics back in undergrad, and I need to create opportunities to show off.
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### Re: Calling all scientists: Do you understand math?

Going to answer your actual question, rather than the form you put up, because that only gets at part of it.

The answer is yes, and no. I'm an epidemiologist, in case you want field specific data.

I understand some math. Based on my interactions (fairly heavy) with applied mathematicians, as much as mathematicians understand the systems I study. Which is to say, enough to know how to approach my problems, and possibly that there is undoubtedly *an* approach to a problem, even if I don't know what it is. The classic "there must be a tool for this..."

So modest general knowledge, some very, very specific knowledge (certain kinds of statistics, differential equations, random variables), but I'm not going to claim that I have the chops to go mano-a-mano with a field specialist. Just like they probably should't throw down when we start talking about infectious diseases.

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### Re: Calling all scientists: Do you understand math?

My doctorate is in anthropology. I have publications in medicine, geochemistry, zoology, as well as archaeology and social anthropology.

I had undergrad calculus, statistics and probability, and individual undergrad courses in regression analysis, finite analysis, and scaling. My graduate math courses were in algebra (mostly group&category theory), and topology (graph theory). I taught statistics for several years. Some of my publications/abstracts included 'mathy' topics;

1982 "Clinical Implications of Some Graph Centrality Measures," Hurd, G. S, Bonney Jennings. Sun Belt Social Network Conference, Tampa, Fl. February.

1982 "Adjacency Matrix Density and Consensus," Hurd, G. S., Kathy Hammond. Sun Belt Social Network Conference, Tampa, Fl. February.

1990 "The Application of Deridrich Tessellation to Social Network Analysis," G. S. Hurd, David Koisumi. Tenth Annual Sunbelt Social Network Conference, San Diego.

So, I would guess I understand a little math.

Your example made no sense to me at all.

My best guess would be either a repeated, or iterated function called "volume" on some range of ?real? numbers. I suppose you could say that "volume sub 3" (for example) was something like ("volume(volume(volume(object)))) U ("volume(volume(object))) U (volume(object)) if it was repeated (and group theoretic). (Is "group theoretic" like a groupie)?

I think I saw something like this once in an industrial chemistry paper. The problem was to model the production rate of a product as the amount of the reactants declined. They were using huge vats, so the probability that the reactants could "find" one another was greatly lowered as they were used up. If I recall, practical answer to the problem was to either agitate the fuck out of the vat, or use some continuous flow system with tiny reaction volumes and eliminate vats all together.

So, what in the hell does your experssion mean to you?

Third edited to add, the notion of "chemical product" sparked a lonely neuron to remember by loose association that your Pi notation could just have meant a repeated "product." But what might "volume (1)" times "volume (2)" mean exactly?

qetzal
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### Re: Calling all scientists: Do you understand math?

@Gary_Hurd

Capital pi means to multiply terms together, just like capital sigma means to add terms together. So, yes, the expression in the OP means to multiply n different volumes together. However, I don't know why the OP wants to do that. Charlie!'s suggestion of a concentration calculation is the best guess I've seen, but kadamczy hasn't seen fit to explain.

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### Re: Calling all scientists: Do you understand math?

Not a scientist, so I didn't vote but as a third year engineering student I understand and have used this notation mainly for dimensional analysis in fluid mechanics. It was taught in first year maths at university.

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### Re: Calling all scientists: Do you understand math?

Yes. That said, I understand the conceptual framework of most of the statistical equations I know, but given that a computer will work through them far faster than I would, I've never had to actually write most of them out and solve them by hand.

Edit: I'm pretty sure that that operator is often used for the likelihood function.

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### Re: Calling all scientists: Do you understand math?

I've seen it a handful of times so I know what it means, but repeated multiplication doesn't come up nearly as often as summing for example, and in my experiences it seems most teachers/profs seem to opt to just go x_1*x_2*...*x_n or something along those lines, rather than use Pi notation.

It's perhaps for the better since in some peoples handwriting the distinction between a lower case pi and an upper case one might be blurred.

gorcee
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### Re: Calling all scientists: Do you understand math?

It is unclear whether we're using Buckingham Pi notation or product notation. If there was a context, it would probably be clear, but lacking context, I find it difficult to determine whether someone really does or does not know what it means. Anyway, those are the only two somewhat standard nomenclatures for that symbol that I'm aware of. I've seen it used elsewhere in ad hoc circumstances, but those don't really count.

Seli
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### Re: Calling all scientists: Do you understand math?

While I am familiar with the Sigma notation for summations I cannot recall ever encountering the Pi notation for multiplications. I would have had to look it up or get it from context if encountered in the wild.
Speaking as a Chemistry PhD.

gorcee
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### Re: Calling all scientists: Do you understand math?

Another possible contextual argument:

The product notation is actually quite common in numerical analysis, which obviously has applications all over the place.

For instance, here is the WP article for the Lagrange polynomials: http://en.wikipedia.org/wiki/Lagrange_polynomial.

Or, you might encounter it in the definition of the factorial: http://en.wikipedia.org/wiki/Factorial

These are things that are mathematically-based, but used in science and engineering all over the place. However, they're probably encountered more frequently by folks doing modeling versus laboratory work.

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### Re: Calling all scientists: Do you understand math?

I'm finishing off my physics degree, and although I've never used that operator before I did know what I was. Like someone mentioned earlier I've just come across it in my experiences learning new things.

In any case the fact that it is a large greek letter is a big hint.
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### Re: Calling all scientists: Do you understand math?

I am a first grader at a science high school in Korea. I think the American equivalent would be 10th grade.
I know what that notation means but I have no idea how it should be interpreted. I am certain that at least 80% of the people in my year know what that means, and I am certain that everyone in higher grades know what that is. Perhaps we just use that more often?
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