Jump to content


Senior Members
  • Content Count

  • Joined

  • Last visited

  • Days Won


taeto last won the day on March 2

taeto had the most liked content!

Community Reputation

73 Excellent


About taeto

  • Rank

Profile Information

  • Location
    Hong Kong
  • Favorite Area of Science

Recent Profile Visitors

1421 profile views
  1. Hi kemfys, actually that is exactly what a ring means. It is possible to add elements, and the addition is commutative. It is possible to multiply elements, but the product is not necessarily commutative. Matrices over fields like \(\mathbb{Q},\) \(\mathbb{R},\) and \(\mathbb{C},\) are examples of rings. To say that a matrix is "over a field" means that all the entries of the matrix belong to this field. In the case of a \(2\times 2\) matrix this would be all four entries. Matrices over a commutative ring like \(\mathbb{Z}\) still form a ring themselves. I think that I get that you want to consider matrices over rings that are not necessarily fields, or even commutative rings like \(\mathbb{Z}.\) Maybe you should simply work through some examples to experience how it works. It seems that if you have \(2\times 2\) matrices \(x\) and \(y\) as variables and you require your matrix \(P\) to equal the matrix \(Q,\) then it leaves you with four equations (expressions that should be equal to \(a,b,c,d\)) in eight unknowns (the entries of the matrices \(x\) and \(y\)). In the general case the answer should be yes, you can find a solution. Though usually the complete solution consists in a 4-dimensional solution space.
  2. Not sure if we are doing this and just being kept in suspense. I like optimization problems. Rather, from having to teach calculus to engineering students, I am no longer all too bothered by them. So I came up with a puzzle. Say we have M moles of electrons and want to pack all of them into a ball-shaped container of radius R, and there should not be anything in it than just electrons pure. Disregarding the amount of energy needed to assemble the electrons, which is a standard exercise to calculate, what would be the optimal choice of material to use for the container itself, also from an energy standpoint? That is, to construct a container able to contain one mole of electrons within a proton radius ought to be fairly energy consuming. Whereas to contain the electrons within the radius of the observable universe should be a piece of cake.Well, not inside our own observable universe, since we do not want to have to first clear out all the stuff that is here; so we just do it somewhere else.
  3. It is given that \(b\) and \(c\) are not equal? From which ring(?) do you take your \(x\) and \(y,\) and how is \(x \otimes y\) defined? Do \(x\) and \(y\) have to be \(2 \times 2\) matrices?
  4. It seems we agree on this, or at least something very close to it. To simplify more, it could be useful to introduce (in your notation) b = Pi/2 - a. Either way this is a function of t which is not constant. As t grows, the point (0,y) moves upwards on the y-axis.
  5. It is just another mountain, a little closer to the surface than normal. And very close to the intersection of Greenwich and the Equator. The numerologists ought to be attracted to it like (insert favorite disgusting insects) to (insert excretion by favorite domestic animal). Does it look volcanic, so that it might have been an actual island previously? St. Matthew Island?
  6. I see lots of underwater mountains in the same extended region of the Atlantic. Seen from satellite they all look different from this one. Not similar.
  7. True, it is close to (0,0). I looked at that already. Clicking on the map gives -0.004955, -0.023410. The blob should probably not be there, but it represents cases that belong randomly elsewhere on the globe. The satellite however, why should satellite data be collected in a fashion so that pixels from other places get thrown into this location? On the other hand, if it is a genuine geological feature, it seems rather unique.
  8. I noticed on the Johns Hopkins map of the Covid-19 outbreak a big blob off of the west coast of Africa. Not sure what to make of it, I took a look at Google Maps to see if there is any populated island located south of Accra and west of Gabon just outside the bay of Guinea. But the map shows no land area. However there is a kind of unusual structure apparently not far below water surface in this location. In the first of the below satellite shots it is only a little cross shape. Magnification shows an uncharacteristic looking feature about 2x2 kilometers in size.
  9. This is shaping up to become one of the biggest conspiracy plots of this decade.
  10. I cannot find it either. Anyway, it means what it means 😂
  11. I think that I begin to accept that this is physics-math speech and not mathematics speech. It does not mean that I understand much. I know of Hausdorff dimension, which may be non-integral. I do not know what you mean by a 'tube' exactly, but I can imagine a topological definition of an infinite tube, though not one that satisfies the dimensional requirement, so that part alone is exciting. But skipping over that, I know the term 'Planck length' and the concept of 'radius', but I have never heard of the 'Planck radius'. Did you invent this notion?
  12. Sorry to be a stickler for wanting to know what words mean 😉.
  13. Thanks a lot Kart! Ah, so I see the term is 'viable', not 'alive'. A typing exercise for a new intern perhaps 🤔.
  14. Very curious about the title of that link. So the virus lives for a while, then it dies? When is it pronounced dead? After losing an envelope? Or its own capsid? What kind of 'air particle' does it inhabit? Does it need protective cover, or is it possibly just its own 'air particle' like a tiny dust grain? Similar questions for 'living on a (hard) surface'.
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.