Wikipedia:Reference desk/Archives/Mathematics/2016 April 1

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April 1

Imaginary

Is there such a thing as an imaginary frequency? Explane in the s plane. What is sigma?--178.101.224.162 (talk) 00:40, 1 April 2016 (UTC)

See imaginary frequency. StuRat (talk) 02:18, 1 April 2016 (UTC)

I am really confused about your question. I get the feeling that you are more interested in the s-plane and sigma than you are interested in "imaginary frequency". Maybe s = sigma + j omega . Note there is no imaginary frequency just because j omega is imaginary. 175.45.116.66 (talk) 06:05, 1 April 2016 (UTC)

See Harmonic oscillator. Bo Jacoby (talk) 20:21, 1 April 2016 (UTC).

The S-plane is the complex plane on which mathematical time domain functions are graphed as equations in the frequency domain. A real function (f) in time 't' is translated into the s-plane by taking the integral of the function multiplied by $e^{-st}$ from $0$ to $\infty$ where s is a complex number with the form $s=\sigma +j\omega$. ($\sigma$ is the lower-case character Sigma of the Greek alphabet). Coordinates in the s-plane use 'j' to designate the imaginary component, in order to distinguish it from the 'i' used in the normal complex plane. I think it unlikely that the OP needs the article Matsubara frequency that StuRat linked to as "imaginary frequency" but they may clarify whether it is relevant. AllBestFaith (talk) 02:36, 8 April 2016 (UTC)

Another universe

In anoother universe, would all our maths still work ok?--178.101.224.162 (talk) 00:43, 1 April 2016 (UTC)

Please define okay. 175.45.116.66 (talk) 02:10, 1 April 2016 (UTC)

At the top of the page, it says "We don't answer requests for opinions, predictions or debate." If there are any reliable sources that discuss the matter, they could be shared or summarized, but science doesn't know if there are other universes -- let alone how they might possibly work. Ian.thomson (talk) 02:13, 1 April 2016 (UTC)

We can list scientific theories about it. For example, one version of the many worlds theory is that the fundamental laws and constants of physics vary such that every possible combination exists in some universe. So, obviously science would then be different in each universe. I'm not sure if math would, too, but someone more familiar with the theory might know. StuRat (talk) 02:16, 1 April 2016 (UTC)

I'd consider that sharing a summary, since those articles are based on sources. And science is still going "that could be a thing" with the many-worlds interpretation. There's still the plenty of other interpretations. Ian.thomson (talk) 02:24, 1 April 2016 (UTC)

Re "would all our maths still work ok?": All of our math would still be correct, since math is not an empirical science but rather is an application of logic (precise wording of this last may vary by person). But would our math be useful in another universe? If not, then maybe we could develop more math that would be useful. But maybe not — see The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Loraof (talk) 17:38, 1 April 2016 (UTC)

there is no philosophical agreement as to what math is...see "foundational crisis in mathematics" "David Hilbert" "the philosophy of mathematics" "Bertrand Russell" "Kurt Gödel" "intuitionism" "formalism" "Frege" "Wittgenstein" and on and on...it has not been successfully shown that math and logic are the same thing...logic cannot compass even classical arithmetic via the "incompleteness theorems"...68.48.241.158 (talk) 01:49, 2 April 2016 (UTC)

Your math will work, but your diploma will not be accepted. Bo Jacoby (talk) 10:16, 3 April 2016 (UTC).

Mathematics is a behavior performed by mathematicians. If the other universe is unable to support mathematicians, then it cannot have mathematics either. Sławomir
Biały 13:02, 3 April 2016 (UTC)

That assumes a stance in the debate about whether mathematics is invented or discovered -- something that's rather controversial. (As the extensive "Contemporary schools of thought" section will show.) -- 160.129.138.186 (talk) 23:42, 4 April 2016 (UTC)

I think the question already assumes that stance. If mathematics is "real", then "the universe" is not part of the input when one considers mathematical questions. Sławomir
Biały 09:58, 5 April 2016 (UTC)

Sections for the 24-cell edge first and 24-cell face first?

Can anyone please describe the sections for the 24-cell edge first and face first? Coxeter has vertex and cell first, but I'm having problems picturing the edge first and cell first sections.Naraht (talk) 02:54, 1 April 2016 (UTC)

If I understand correctly, a vertex first section is the intersection with a plane perpendicular to a vertex, the vertex being taken as a vector from the center. An edge, face or cell first section would be the same only taking the vector from the center of the 24-cell to the center of the corresponding facet. The 24-cell is the intersection of the 24 half-spaces ±x_i±x_j≤2, so it would be a matter of finding the intersections of this set with the corresponding planes. Typical vertices, edge centers, face centers and cell centers of the 24-cell are given (up to scaling) by (0, 0, 0, 1), (0, 1, 1, 1), (0, 1, 1, 2) and (0, 0, 1, 1). So an edge first slice would be the intersection of the plane x₂+x₃+x₄=k with the above inequalities, and a face first slice would be the intersection of the plane x₂+x₃+2x₄=k with the above inequalities. Not really solving the problem here but stating it more explicitly which might help. --RDBury (talk) 05:55, 1 April 2016 (UTC)

The face-first middle section is a truncated hexagonal bipyramid. As you move away from the centre, alternate equatorial edges are truncated to form new hexagons. At the ends of the 24-cell the figure degenerates to a triangle.

The edge-first middle section is a hexagonal trapezohedron with a ring of hexagons stuffed into the centre. As you move away from the centre the faces at the top and bottom stop meeting precisely (alternate ones pull away). In the end it degenerates into a line segment. Double sharp (talk) 03:09, 2 April 2016 (UTC)

(Assuming verticies designated by the permutations of (+-1,+-1,0,0). For the face-first middle section, assuming that it starts with the face (1,1,0,0), (1,0,1,0), (1,0,0,1) the vertices of the 24 cell in the middle section are (0,-1,0,1),(0,-1,1,0), (0,0,1,-1), (0,1,0,-1), (0,1,-1,0), (0,0,-1,1) , what are values for the vertices at the hexagonal bifrustum top and bottom corners?

So pull the hexagonal trapezohedron apart at the equator, insert the hexagons on one size and twist the other side so it fits together? Are any of the vertices of the original 24-cell in the middle section?Naraht (talk) 18:27, 4 April 2016 (UTC)

Chains forming a matroid

When do the chains in a finite poset form the independent sets of a matroid? GeoffreyT2000 (talk) 23:17, 1 April 2016 (UTC)

The poset must be strongly graded (ranked, tiered), so that all maximal chains have the same length. Then perhaps you can use the exchange property to show that every vertex of rank r must be covered by every vertex of rank r + 1. --JBL (talk) 15:22, 2 April 2016 (UTC)