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Visualising random variables

terrytao.wordpress.com

40 pointsbaoyu12 comments

Displaying a a function with changing values, instead of a static one, does change how you process the information. This gives an advantage to computer screens over chalkboards.

I am not sure about the implementation. The author seems new to webdesign. He spends 2 paragraphs explaining how he made the image changes, hint, he used a looped gif. Then he has an idea of an "after image" but then admits he cannot do it. The numbers dancing around at the end is hard to digest. It's clear that one is not moving, but that is about it.

In the comments Rahul posts a graph where circles are plotted and fade over time with random inputs. He then plots various functions where the grouping is obvious and easily digestible.

Overall it looks like a great collaboration. Someone having an design idea but incapable of executing, and something else doing a better technical implementation. While the idea is completely unoriginal, its still a fun story.

I'd just like to draw attention to this comment:

> The author seems new to webdesign.

The author of the post is Terry Tao, one of the greatest living mathematicians and recipient of the Fields medal.

I imagine that he may indeed be somewhat new to web design, however I doubt that learning it is high on his list of priorities.

EDIT: No snark intended here, by the way. I thought the context of who Tao is was important.

Considering he now has two jobs, 1) to be an actual mathematician, and 2) to fulfill his "popular" role, I'd say that this post was rather trivial except for the last line. Even two entirely random distributions, can be correlated 100%, such that some function of both of them is entirely static/constant. I'm not sure why you are defending what is indefensible. His accolades aren't some unpierceable armor for everything he does. But I'm not trying to be snark either. I do agree, the truths that he can uncover are a lot more important than any popularity pandering.

The mathematician in me is somewhat relieved to see there are some things I'm better at than Terry Tao :)

I see. You mean mathematics and web design.

> When teaching mathematics, the traditional method of lecturing in front of a blackboard is still hard to improve upon, despite all the advances in modern technology.

i completely disagree on a multitude of fronts

what is meant by 'traditional'? my understanding of plato's academia was it was a forum for discussion stead some silent note taking mass attempting to keep pace with an informer whose information is variant based on how they slept and whether they ate recently

current academic lectures need to go away

i'd rather see professors make succinct learning material, a la well edited video lectures andor notes, and offer them to students as suggested material and have a weekly meeting where the material is discussed

also, technology has always informed mathematics and trying to deny that in lieu of, what i assume is, some personal distaste for contemporary technology and its uses seems disingenuous

when i research mathematics i sometimes take time away with a pencil and paper, but usually only to find new directions to lead an idea; in the vast majority of my work i collaborate with a computer

i like using many mediums for expression, but if i were forced to choose one over the other i would definitely choose the computer

i can always do what i do on paper with a computer, the opposite would leave me severely wanting

Most post secondary math, especially proof-oriented abstract math- analysis, topology, abstract algebra, probability and measure- all the kind of stuff that Tao probably teaches- really cannot be visualized with modern technology and relies more on pen-on-paper/chalk-on-board walkthroughs. In that context, Tao is spot on that modern tech is of little use in exposition.

how does that logic follow

i feel fairly confident that anything you do on a chalk board i can do on a computer, unless you can offer an example of what you mean by 'cannot be visualized with modern technology '

also, my comment spoke directly of what i think you are referring to in using the word 'exposition'.. perhaps you meant 'extempore'?

why does the academic system think, assume, require andor expect their professors to be good public communicators?

The interactivity and dynamicism of the chalkboard can't really be reproduced in ppt or pdf. Go look at some MSRI videos for example: http://www.msri.org/workshops

i shutter to think that someone assumes if i say i use a computer to collaborate on mathematics research they think i mean with either powerpoint or pdfs?!?

'interactivity and dynamicism of the chalkboard' reads like laughably obstinate bias

http://acko.net/blog/mathbox2/ is a great example of what interactivity and dynamicism really can be

https://hn.algolia.com/?query=acko.net&sort=byPopularity&pre...

your msri videos are perfect examples of what i think is wrong with academia

one person standing in front of a group of silent onlookers making incomprehensible scribbles on a medium that the onlookers are unable to interact with or permute

then to take that presentation and put it online raw and unedited

i picked a random video: https://www.msri.org/workshops/705/schedules/20915 ; feel free to watch its 51 minutes or skip around.. i challenge anyone to go jump straight to minute 9 and read what is written there, i have worse handwriting than this professor and i know you would be unable to read this comment if i were required to write it by hand

how much of the video is actionable information?

how much time is the viewer just sitting, silently, waiting for the professor to finish writing words just spoken? what benefit is there for me to watch someone as they write?

http://www.3blue1brown.com/ is a great example of well edited content

i'd rather professors make edited versions of their intended presentations, give them to students, and then this lecture hall could be filled with conversation and imagination stead the sound of chalk being dragged across slate

It's possible to make something similar with Excel. Something like

  A1 = "X"      B1 = Integer( 6 * Random() + 1 )
  
  A2 = "Y"      B2 = Integer( 6 * Random() + 1 )
  A3 = "X+Y"    B3 = B1 + B2
  
  A4 = "Z"      B4 = 7 - B1
  A5 = "X+Z"    B5 = B1 + B4

And then press "F9" to refresh the random values and get new ones.

visualising random variables:

https://www.youtube.com/watch?v=5P6Dihkrvus&list=PLm5k2NUmpI...

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