dstyrb

Hahaha, I like how they include: "If it is multiplied by 2, 3, 4, 5, or 6, the answer will be ... 2/7, 3/7, 4/7, 5/7, or 6/7 respectively."

Was it surprising to multiply 1/7 by two and get 2/7? Has science gone too far?

In Germany, for every full time employed researcher at universities, there are 2 full time administrators... And the researchers still do all their own paperwork for grants, travel, etc.

I don't agree with how you frame the academics as the bad guys. I do agree the system is FUBAR.

There is a tremendous failure on the behalf of universities in the way they hire academics and how they treat them.

Universities preferentially hire world class _researchers_ so that they pull in maximal grant money which they can then leech upwards of 70% in dramatically overstated "lab fees". Then, they force these researchers to go through pointless habilitation exercises and then teach classes which, the vast majority of the time, have nothing to do with the academic's research. A new professor will likely be forced to teach the most advanced classes that are not specialty classes (in physics say Electrodynamics, or Quantum Mechanics) because no one wants to teach the hard subjects that aren't their own field. This means that the new professor, for the first several years, will spend 10+ hours a week studying the concepts themselves to they can adequately teach the class.

Then, in most situations, the academic, on tenure track is simultaneously forced into a support administrative position. They are required to arrange anywhere up to half a dozen business trips a year which entails days of planning, applying for permission, purchasing fare and lodging (of course out of the researcher's own pocket), applying for reimbursement, etc. And god forbid you host a meeting yourself, that has a whole slew of it's own responsibilities. Then of course there's the day to day applying for major grants which you need to do yearly, applying for purchase permission for lab equipment which, depending on your lab can be once every few years (computer labs) to once every few weeks (geophysics for example buying reagents). Also you need to organize and attend anywhere from 1-10 meetings / invited lectures per week.

This person, who has gone into academia because of their passion for a specific aspect of their field now spends the vast majority of each day micromanaging students, studying a topic they don't care about, teaching that topic to a class of students who likely also don't care, filling out redundant and often confusing legalese style paperwork and teaching the exact same skills over and over again to the steadily coming and going research assistants.

And _none of this matters a tic on the resume_. All that people care about is the paper output, which is what the researcher wanted to do in the first place. Is it really a mystery as to why your undergraduate professor seemed pissed off and stressed out?

The problem is universities hiring world class researchers to do administration and teaching when they should be hiring administrators and teachers. Researchers should work at research facilities like Fermilab, CERN, NASA etc. Does it really fucking matter if your Physics 1 professor got a Nobel Prize back in the 60s?

Also most academics I know don't share your perceived opinions of looking down on undergrad students, the general public, grad students, etc. Most of them are just really disappointed that they can't do what they got into the business to do and are used to dealing with people who don't care about them or their passions at all.

Why are half of the charts missing axis labels?

Figure 1 is completely non-essential and just repeats the prior sentence in huge text.

Figure 2 I guess is "percentage of people doing once per day" from the following sentence, which does not reference the chart and uses different numbers than the chart.

Figure 3 pyramid plot seems like a fairly suboptimal visualization choice usually reserved for abstract hierarchies like human needs, not for trends and percentages because it has no numeric information.

Figure 4 should read "Total Number of Worldwide Internet Users (In Billions)", the growth would be the derivative of this plot (which actually would have some cool features from 2013-2015 and 2005-2009 that I would be interested in knowing about).

Nothing is technically wrong with Figure 5, however I immediately question numbers like 71,727,551, rounding them is more professional. Also a nice touch would be to have the names drawn on the pie slices, instead of using a legend.

No clue what Figure 6 means. In the world? In the USA? In a specific age group? The next sentence talks about Millenials...

Most of the time the text has little or nothing to do with the associated graphic.

I was wrong. My initial approach appears to be the ninja approach like sampo said above. I got 50% -_-

    import numpy as np
    import random as rnd
    import math as m

    chords = []
    samp = 10000
    for c in range(samp):
        #random point on infinite plane is described by a  single coordinate
        dist = rnd.uniform(1., 1000.)
        #DO NOT KNOW HOW TO DO INTERNAL SLICES

        #ignore all possible lines that do not intesect circle
        xsec_half = m.atan(1./dist)
        angle = rnd.uniform(-xsec_half, xsec_half)

        #make 2 points on the randomly chosen line
        x1, y1 = -dist, 0
        x2, y2 = dist, 2*dist*m.tan(angle)

        #copy and paste some shit from wolfram alpha
        dx = x2-x1
        dy = y2-y1
        dr = (dx**2 + dy**2)**0.5
        D = x1*y2 - x2*y1
        
        sqr = (dr**2 - D**2)**0.5

        xa = (D*dy + np.sign(dy)*dx*sqr) / (dr**2)
        xb = (D*dy - np.sign(dy)*dx*sqr) / (dr**2)

        ya = (-D*dx + np.abs(dy)*sqr) / (dr**2)
        yb = (-D*dx - np.abs(dy)*sqr) / (dr**2)

        chords.append(((xa-xb)**2 + (ya-yb)**2)**0.5)

    print len([a for a in chords if a > 3**0.5])/float(samp)

Basically make the unit circle at 0,0. Pick any radius up to infinity (infinite plane). By symmetry, we don't need 2 coordinates, just a distance from the circle.

Choose any angle from that point which will draw a vector that intersects the circle (to not waste CPU). Calculate the length of the intersecting chord.

I was really surprised by the distribution of chord lengths, it peaks at chord lengths of 2.0, which is the maximum chord length, and falls exponentially with smaller chord lengths. I don't know what I expected, but not that.

It would assign a probability approaching zero as the plane approached infinity, yeah, I agree.

But I think I have a way around that.

I don't think so, like say you had a point outside the circle, and from that point you equally selected angles to slice the space in. You would get systematically longer slices than if all your slices are cut parallel to each other (and you ended up with the same number slicing the pizza).

edit: I worked it out and you're right, I get the same answer as the ninja one.

I don't agree with any of these solutions. In my opinion the circle should be positioned in an infinite plane, then random vectors should be drawn on the plane and ignored unless they intersect the circle. Then after making some large amount of intersecting vectors you calculate. I'm guessing that this essentially reduces to the random endpoints method.

The other two methods don't make sense at all to me. Random chords is just obviously not a random sampling of possible vectors-- it's essentially the same as sampling a gaussian(x) distribution using an equal sampling in x and ignoring the fact that a gaussian is a PDF and you can't sample that way, you need to invert it into a CDF and take an equal sampling in _y_. Very basic I think...

And random midpoint doesn't strike me as random either as it forces the orientations of the vectors to be non-random and systematically smaller than random because of the pi*r^2 area-dependence of concentric circles...

But, what do I know.