The best software

somethingsimple 3 months ago

> Software is the currency that we pay to solve problems, which is our actual goal. We should endeavor to build as little software as possible to solve our problems.


ScottBurson 3 months ago

My point today is that, if we wish to count lines of code, we should not regard them as “lines produced” but as “lines spent”: the current conventional wisdom is so foolish as to book that count on the wrong side of the ledger. — E. W. Dijkstra


That’s why the best choice of software is often no software …

— Coding Horror

— by Jeff Atwood


— Write dumb code

— Hacker News



2018.05.01 Tuesday ACHK

Problem 14.4b1.1

Closed string degeneracies | A First Course in String Theory


(b) State the values of \alpha' M^2 and give the separate degeneracies of bosons and fermions for the first five mass levels of the type IIA closed superstrings. Would the answer have the different for type IIB?


Type IIA closed superstrings


In closed superstring theories spacetime bosons arise from the (NS, NS) sector and also from the (R, R) sector, since this sector is “doubly” fermionic. The spacetime fermions arise from the (NS, R) and (R, NS) sectors.

p.322 \alpha' M_L^2 = \alpha' M_R^2

 \frac{1}{2} \alpha' M^2 = \alpha' M_L^2 + \alpha' M_R^2
 \alpha' M^2 = 2 \left( \alpha' M_L^2 + \alpha' M_R^2 \right)
  = 4 \alpha' M_L^2

Equation (14.77):

\text{type IIA}:~~~(NS+, NS+), ~(NS+, R+),~ (R-, NS+), ~ (R-, R+)


What is the difference of the meanings of R+ and R-?

R+ states are world-sheet bosonic states.


It thus follows that all eight | R_a \rangle states are fermionic and all | R_{\bar a} \rangle are bosonic.

Be careful:

Here, “fermionic”/”bosonic” refers to the world-sheet fermions/bosons, not the spacetime ones.


Identifying | R_a \rangle as spacetime fermions and | R_{\bar a} \rangle as spacetime bosons is not an alternative either, since spacetime bosons cannot carry a spinor index.


How come the R+ cannot be the left-moving part?


A strategy then emerges. Since all states in the R sector have a spinor index, we will only attempt to get spacetime fermions from this sector. We also recognize that all fermions must arise from states with the same value of (-1)^F.

Me@2015.09.11 10:36 AM: In other words, it is a convention:

Following Gliozzi, Scherk, and Olive (GSO) we proceed to truncate the Ramond sector down to the set of states with (-1)^F = -1.

— Me@2018-05-01 05:59:53 PM



2018.05.01 Tuesday (c) All rights reserved by ACHK