Seven Dimensions

Comments · 1.1K

• HB

  @HBMmaster · 4 years ago

  it's very fun seeing "the seven C's" in a more serious context like this. great explanation of these concepts

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• EP

  @epsilonengineer373 · 4 years ago

  First Astronaut: Wait, It&apos;s all Linear Algebra???<br>Second Astronaut with gun: Always has been.

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• LE

  @lewismassie · 4 years ago (edited)

  When I was struggling to memorise all the equations for my exams I realised if I could reverse engineer the positions of the equations from the units I wouldn&apos;t have to memorise the actual equations themselves. It wasn&apos;t until I had a casual chat in my university lab some years later that I found out it was called Dimensional Analysis.<br><br>This obviously goes a lot deeper than my own brain could come up with (7-dimensional vectors was where you surpassed me) but this was still very interesting

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• TO

  @tonaxysam · 4 years ago

  Who would have thought that the 7 C&apos;s would have a sequel

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• SU

  @SuperSulc · 4 years ago

  The algorithm thinks i&apos;m much smarter than i really am.

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• BA

  @barigamb · 4 years ago

  This entry is criminally underrated.

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• PY

  @Pyotyrpyotyrpyotyr · 4 years ago

  I graduated university for engineering, and this video taught me linear algebra in a more intuitive way than university ever did.

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• PO

  @PopeGoliath · 4 years ago (edited)

  This feels like a Part 1, Where part 2 goes on to define a new, mathematically optimal measurement system.

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• UN

  @UnitaryV · 4 years ago (edited)

  The conversion matrix only handles matching dimensions across systems, but not the actual numerical value. However, what if we included the number 10 as an additional &quot;unit&quot;? It seems like that provides the last piece of the puzzle to perform full unit conversions, with the slight drawback that the resulting numbers would be expressed as non-integer powers of 10 (the speed of light becomes 10^8.477m^1s^-1 instead of the usual scientific notation form of 2.998*10^8m/s). Though a little odd at first, it&apos;s not wrong. In fact, it&apos;s a step up from the matrix at <a href="https://www.youtube.com/watch?v=bI-FS7aZJpY&amp;t=605">10:05</a>, which converts the speed of light c to m/s, with nothing indicating the value of 2.998*10^8. By adding an extra row at the bottom for the &quot;unit&quot; 10, containing 8.477 (the log of 2.998*10^8 in base 10) in the first column and appropriate values for the rest, the matrix becomes a bonafide unit converter that converts the numerical values too, instead of just matching the dimensions of the systems. Note that an extra column must also be added on the right for the unit 10, containing five 0&apos;s and a 1, so that we end up with a 6×6 invertible matrix.<br>https://imgur.com/a/qMakuIY<br><br>We can also choose to use any number greater than 1 other than 10, but that would change the values in the final row. For example, if we wanted to use e as our additional &quot;unit&quot; instead of 10, we would divide the entire final row (except the 1 in the corner) by log_10(e).

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• WA

  @WaluigiisthekingASmith · 4 years ago

  I actually realized this a while back when I had a physics problem that forgot to give the mass of some object and, since there was a unit of mass in the answer but nothing involving mass was allowed in the answer it was unsolvable. In general this is a really good introduction to the idea of dimensional analysis. Dimensional analysis says that given some set of base quantities trying to derive some other quantity the answer is always the base quantities combined to get the one you want times some function of all of the dimensionless quantities

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• JA

  @JacenLP · 3 years ago

  &quot;Doing LA to it&quot; sounds so violent yet graceful. I like it :D

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• MA

  @MaxG628 · 4 years ago

  I really like using physics to motivate change of basis. It works a lot better than “I’m going to plot points in the plane using a system other than (1,0) and (0,1) because I hate myself”. At the same time I think I learned something about physics, too.

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