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For me this question is a symbol of problems that people’s intuitions are good at, but their mathematical models fail at.

  • We can certainly define the domain (set of possible words)
  • and we can define reasonable scalar-ish codomains (number of hit records, rankings by critics, faces on the people outside your show, …)
  • but how would you set up an optimisation problem to answer this question?

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It doesn’t just fail because it needs to be parameterised by

  • the history of other bands (“Lady Gaga”)
  • puns or linguistic meaning (“The Beatles”)
  • emotional tenor of the band’s songs (imagine if The BeeGees were instead called Thräsherdëth)

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but also because calculus' Really Cool Idea

finds no purchase since any 1-D lineup of all possible band names won’t be 𝒞¹ onto the success of the band.

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Like “What should I write about today?”, “What line of business should I get into?”, “What should I do with my life?”, and a lot of other “broad, open-ended” questions, choosing a band-name is something I don’t think can be mathematised today. It’s also a mental shorthand for me for any question that is going to be answered better by “art” than by “science”.




I asked a humanities professor who had left a university after 23 years if it was difficult to do. He said, “It was like checking out of a motel.”
Stanley Fish

(Source: The New York Times)










Without using a calculator or even pen and paper—or even doing the arithmetic in your head—¿which is the larger product? of:

  • 3.01 × 6.99
  • 2.99 × 7.01

You know 3 × 7  =  21. But what happens if you gently place your finger on the teeter-totter?

 

Although this is “just arithmetic” and so doesn’t require a learnèd vocabulary of higher mathematics, it touches on a few “higher maths” topics:

  • bilinearity being the way I would answer it “conceptually rather than computationally”
    Bilinear maps and dual spaces  Think of a function that takes two inputs and gives one output. The + operator is like that. 9+10=19 or, if you prefer to be computer-y about it, plus(9, 10) returns 19.  So is the relation “the degree to which X loves Y”. Takes as inputs two people and returns the degree to which the first loves the second. Not necessarily symmetrical! I.e. love(A→B) ≠ love(B→A). * It can get quite dramatic.    An operator could also take three or four inputs.  The vanilla Black-Scholes price of a call option asks for {the current price, desired exercise price, [European | American | Asian], date of expiry, volatility}.  That’s five inputs: three ℝ⁺ numbers, one option from a set isomorphic to {1,2,3} = ℕ₃, and one date.    A bilinear map takes two inputs, and it’s linear in both terms.  Meaning if you adjust one of the inputs, the final change to the output is only a linear difference.  Multiplication is a bilinear operation (think 3×17 versus 3×18). Vectorial dot multiplication is a bilinear operation. Vectorial cross multiplication is a bilinear operation but it returns a vector instead of a scalar. Matrix multiplication is a bilinear operation which returns another matrix. And tensor multiplication ⊗, too, is bilinear.  Above, Juan Marquez shows the different bilinear operators and their duals. The point is that it’s just symbol chasing.    * The distinct usage “I love sandwiches” would be considered a separate mathematical operator since it takes a different kind of input.
  • wiggly numbers
    image
  • ± ε
  • statistical robustness
  • tensor product of modules
    Tensor product of modules.png
  • isoperimetric inequality

I’ll leave the question/reasoning unanswered with a space for you to answer which is larger and why.

3±ε  ×   7∓ε    =    21±¿?

(Source: Wikipedia)




Both direct sum and tensor product are standard ways of putting together little Hilbert spaces to form big ones. They are used for different purposes. Suppose we have two physical systems…. Roughly speaking, if … a physical system’s … states are either of A OR of B, its Hilbert space will be [a] direct sum…. If we have a system whose states are states of A AND states of B, its Hilbert space will be [a] tensor product….
MEASURE SPACE   disjoint union  Cartesian product
HILBERT SPACE   direct sum      tensor product

John Baez

(Source: math.ucr.edu)





The Crown of Thorns is a woodworking technique using interlocking wooden sticks that are notched to intersect at right angles forming joints and self-supporting objects….
Large-scale crowns may use the principles of tensegrity structures, where the wooden sticks provide rigidity and separate cables in tension carry the forces that hold them together.

The Crown of Thorns is a woodworking technique using interlocking wooden sticks that are notched to intersect at right angles forming joints and self-supporting objects….

Large-scale crowns may use the principles of tensegrity structures, where the wooden sticks provide rigidity and separate cables in tension carry the forces that hold them together.


hi-res













Unaudited, these methods have allowed me to beat the market since the strategy started in September of 2000.

  1. Industries are under-analyzed, relative to the market on the whole, and relative to individual companies. Spend time trying to find good companies with strong balance sheets in industries with lousy pricing power, and cheap companies in good industries, where the trends are not fully discounted.
  2. Purchase equities that are cheap relative to other names in the industry. Depending on the industry, this can mean low P/E, low P/B, low P/S, low P/CFO, low P/FCF, or low EV/EBITDA.
  3. Stick with higher quality companies for a given industry.
  4. Purchase companies appropriately sized to serve their market niches.
  5. Analyze financial statements to avoid companies that misuse generally accepted accounting principles and overstate earnings.
  6. Analyze the use of cash flow by management, to avoid companies that invest or buy back their stock when it dilutes value, and purchase those that enhance value through intelligent buybacks and investment.
  7. Rebalance the portfolio whenever a stock gets more than 20% away from its target weight. Run a largely equal-weighted portfolio because it is genuinely difficult to tell what idea is the best. Keep about 30-40 names for diversification purposes.
  8. Make changes to the portfolio 3-4 times per year. Evaluate the replacement candidates as a group against the current portfolio.
  9. New additions must be better than the median idea currently in the portfolio. Companies leaving the portfolio must be below the median idea currently in the portfolio.
David Merkel