April 06, 2012

Speed Reading: Reflections

Follow-up to Speed Reading: Taking care, moving backwards, slowing down… from Midgley, Christopher - Pointless twaddle and meaningless diatribes

Tutor was Han-Na Cha.

Before we start: results on how much I comprehended or how well I remembered were likely contaminated by memory training I was doing at the same time. Good thing these results weren’t supposed to be formal or anything, and indeed had no way of properly being measured!

The best thing from the sessions was probably just a realization of the state of affairs (I read quickly) and a formalization of the effects of things I do (why they’re beneficial, why they aren’t) and that the (obvious in retrospect) answer to the question “how do I get better at X” is “do X a lot”.

On the not so well side, reading non-linearly seems to increase the risk of reading over material you’ve already read, especially if you’re able to do impressive things like forget section headers soon after you read them (which happened almost inevitably without some recitation).

TODO differently: Put the memory techniques into the program itself, as opposed to a “hey it would be cool if I did this” item that only comes up when I remember to do it. Comprehending stuff is easier if you can remember what came before :P

On the other not-so-well side — slowing down is hard, because by nature I don’t do it. It’s like improving my handwriting, or that “fingers on home row” typing, because my natural typing involves my hands moving all over the place, and my natural handwriting is a spider’s crawl — it’s just not natural for me, so I fall back into habits as soon as I stop thinking about it and sometimes even while thinking about it, because the behaviour is instinctual, in the same way that my fingers have a habit of hitting ‘n’ between ‘ght’ and ‘ing’ so the outcome is fightning.


March 16, 2012

Speed Reading: Taking care, moving backwards, slowing down…

Follow-up to Speed Reading: Even though I am a mathematician… from Midgley, Christopher - Pointless twaddle and meaningless diatribes

Tutor was Han-Na Cha.

Points were read symbols until you get as good at reading symbols as words and try reading out of order because I’ve found previously that focusing on more than two things at the same time is a good way to forget what I’m doing and not get much done :). If we need three, an additional (fair) one could be slow down your default reading speed to increase comprehension - it wasn’t until the session where I, not thinking I was doing anything differently, hit 650 wpm as my normal speed and realised that that was so much faster than other people read. A rough timing showed that my speed of reading fiction (at least on a screen) is about that quick as well (around 150,000 words in a four hour block). I think my reading speed is slower when it comes to books (although I haven’t tested this); I do the vast majority of my reading from a screen.

Let’s comment on the second one first, because that’s shorter. If a summary, or key point list, is offered at the end, it’s convenient to do that -> section headings -> start, linearly forward to get some indication of where it’s going and which parts to skip over. If not, the section headings themselves offer a decent summary (often, yet not always).

Onto the first: reading symbols. We begin, naturally, with an example.
(\forall x,y)(\forall \epsilon > 0)(\exists \delta)(|x-y|< \delta \Rightarrow |f(x)-f(y)|<\epsilon)
This one is the definition of continuity of a function f everywhere. Once again, the brackets here provide an obvious chunk. Draw attention, here, to the first triplet:
(\forall x,y)(\forall \epsilon > 0)(\exists \delta)
This is /also/ a chunk: that is, it’s a combination you see a lot, and it’s also the initiation step for this sentence: we have initiation, followed by statement. It’s also importantly different from
(\forall \epsilon > 0)(\exists \delta)(\forall x,y)
which is used for uniform continuity, despite sharing all three chunked phrases, with two paired.

Unsurprisingly, it turns out the way to get better at reading is to read more, and look out for the patterns that emerge.


March 08, 2012

Emotional Intelligence: Reflections; an Afterword

Follow-up to Emotional Intelligence: An Amnesiac Discovery from Midgley, Christopher - Pointless twaddle and meaningless diatribes

Tutor was Samantha Tarren.

Commentary: We begin with the second point, “I don’t feel sadness”, or at least its twin “I don’t remember feeling sadness”. It’s looking like this is a coping mechanism of sorts, with the final stage being “forget the problem ever existed”. We have the sequence: observe problem, contemplate reasons for problem, decide only own opinion matters, tease out explanation/learning, focus on something else, forget journey and only remember results. I’m not sure why it wound up like that. I can garner the feeling back if I try, but I’m not sure why I’d want to. I used to dwell on this sort of thing for days, which is probably why I expunged it: it’s not a nice thing, even if it helped me get my thoughts in order/focus/write. I couldn’t deal with it and had no idea where it came from, so I “dealt” with it by ignoring it until it went away. But here I am, dealing with depression through arrogance and apathy.

We then move on, linearly, to the first part, “why do I not want to do things?”. It turned out there were a lot of these: “there is too much to do”, “there is too little to focus on”, “I have other things to do”, etc. As stated in the overview, however, I noticed, went “huh.”, and then went for business as usual, so I can’t even be sure I was correct! I’m not even all that good at differentiating them, these reasons underlying the feeling. Also, remembering how I felt in the past is a trick for feelings as..specific as these.

Overview: Well, I solved one problem. Yay.

For the other, however, I was asking the wrong question. The aim was not “why do I not want to do things?”, it was “how can I make myself do things, considering my current state?”. Realising how I felt was the first step, but it is also important to try doing things in different states, in different ways, to find the most effective. As it was, I was reflecting, noting the results, and then ignoring them in favour of the “brute force” approach that worked reasonably well for a variety of feelings in the past, instead of considering a specialization.

So I suppose we have here a lesson: ask the right questions. Don’t split things into steps so fine you forget your own head - remember what the aim is.


February 24, 2012

Speed Reading: Even though I am a mathematician…

Tutor was Han-Na Cha.

First, on subvocalization: attempting to consciously destroy all subvocalization also destroyed my speed and any comprehension I had of the text. Comprehension-wise, I find the voice ‘reads’ the text a little behind my eyes (and far faster than I could speak it aloud), which I find helpful. Despite this, it’s difficult to tell exactly what I subvocalize: focusing on the process interferes with it.

However, I think reducing it in certain areas will increase speed (while slight!) and possibly (hopefully!) comprehension. This is a very maths-related area, so I’ll add some examples.

Example 1: [1\quad 2], (1,2) and \{1,2\} are all different: the first is a vector, the second a tuple, the third a set. However, I take no time to /read/ the symbols surrounding the numbers - they are merely interpreted.

Example 2: x < 2 is probably pronounced “x is less than 2”, but while reading it as part of a series of equations, I don’t subvocalize it as such - just sort of understanding it. This is an aid to comprehension, as focusing unnecessarily on the symbol detracts from the meaning.

Example 3: \exists and \forall are pronounced “there exists” and “for all” respectively; I do subvocalize these (in full! there ex-ists! bleh!) and (likely) focus too much on them. Taken from my metric spaces notes: a sequence is Cauchy if:
(\forall \epsilon > 0)(\exists k \in \mathbb{N})(\forall m,n \geq k)d(x_n,x_m) < \epsilon
In this case, this example is healthily chunked already - each bracketed section is a phrase and together it forms a sentence. The order is important and only the whole statement together makes sense. Reading it should be a bit slower than a sentence because you actually have to understand each part before moving on - they’re all important.

In short, I suppose the aim here is to become as good at reading symbol-heavy sentences as I am wordy sentences.

In second; my current mode of reading is linear, but jumpy. I begin at the beginning and go forth, occasionally hopping back and forth to section titles to see where I’ve come from and where I’m heading until I reach the end, whereupon I stop. A nonlinear arrangement would likely serve better: the headings, a summary (if present), the end, the beginning, for instance. So I suppose a relevant ‘goal’ is try that.


Emotional Intelligence: An Amnesiac Discovery

Follow-up to Emotional Intelligence: Illness Interferes. Irksome. from Midgley, Christopher - Pointless twaddle and meaningless diatribes

Tutor was Samantha Tarren.

On the not-working side: I did a lot of work this week. Unfortunately, it was all on the same thing, which I've been working on for about two weeks. I'd been putting off parts because I thought they'd be boring; they were (incipient boredom), but when my code didn't work I found I couldn't leave it alone - that the solution would come to me if only I stayed at it (unreasonable eagerness). After completing it, though, I feel somewhat burnt out.

On the "I can't remember the last time I felt sad" time: it appears that statement was literal. I felt sad yesterday, but all I can remember from that is "huh, guess I do feel sad, I'll have to blog about that". Unfortunately I cannot remember the circumstances or the reason that lead to the emotion, or how I felt at the time (I am great at forgetting things, clearly). Suppressed or ignored, I don't know. Such a curious happenstance.


February 15, 2012

Emotional Intelligence: Illness Interferes. Irksome.

Follow-up to Emotional Intelligence: Crying as you Solve Problems from Midgley, Christopher - Pointless twaddle and meaningless diatribes

Tutor was Samantha Tarren.

SMART goals were twofold:

The first; on the ‘motivation’ side: consider reasons for not wanting to work. Chosen to avoid time management crossover, though I’m not taking that workshop.
Current progress: illness: reasons are “lethargy” and “i feel crap”. Reasons are actually valid, so no progress here.

The second on the “I don’t feel sadness and that’s fine” side, consider why.
Current progress: I was too ill to bother feeling anything but lethargic.

In short, illness meant I accomplished nothing worthwhile, going through my days in a haze, and the primary emotion I felt was lethargy. Didn’t even get fired up.

I did learn that I consider both “lethargy” and “solipsism” as emotions, though. The latter is a philosophy! They’re probably made up of little emotional “elements”, except lethargy might be a “lack” of these elements (anti-elements?). Well, that’s irrevelant.

While I’m actually doing something, it’s fun unless I get stuck. The feeling of “OH!” is great, even if my ideas are completely incorrect, it’s still nice to think back on. Additionally obtaining an answer feels great even if I have the feeling that it’s probably wrong.

Essentially I’ve found a few things, none of which were what I was looking for.


February 04, 2012

Emotional Intelligence: Crying as you Solve Problems

Tutor was Samantha Tarren.

Consideration.

Notice the feeling of not wanting to work on something. Evaluate it. Query the reasons for existence. While working on something, query those feelings, too, for completeness’s sake.

Note feelings of annoyance/anger/frustration when they arise, and why. Note consequences. Query whether this human emotion known as “sadness” would be more appropriate (knowing me, the answer I’ll likely come to is “no”!).

One thing that (likely?) had an effect on my lack of feeling sadness would be my dad’s refrain of “don’t get sad, get mad! Getting upset never helps anything.” – and I think he was right. Depression just interferes with discussing the issue and fixing it; and generally interferes with contemplation. Then again, the latter also applies to anger, which can also lead to impulsiveness, although I’ve also been able to focus it into improving my work – but then I’ve been able to do that perfectly well without that consideration simply from the knowledge that it was wrong or imperfect as it stood, so who knows in the end?

Enough meandering, we’ll see how this plan goes.


January 12, 2012

Obviousness – norm implies metric

We have a norm, which satisfies positivity, linearity and the triangle inequality. We have a metric, which satisfies positivity, symmetricity and the triangle inequality. We wish to prove that every norm is a metric. "Obviously", the only property we need to prove is... the triangle inequality.

At the time, I couldn't see how linearity implied symmetry was obvious. Now, I think it's about as obvious as the triangle inequality was - there's a step to take, even though it's simple.

Linearity requires that ||cx||=|c|||x||\text{ for } c \in \mathbb{C}. Symmetricity requires that d(x,y)=d(y,x).

To prove it, we let d(x,y)= ||x-y|| = |-1|||x-y|| = ||-x-(-y)|| = ||y-x|| = d(y,x).


January 05, 2012

[citation needed]; the difficulty of finding things

Typing in “tower property” in Google, I find that the first result is the ever ubiquitous Wikipedia (whose mastery of SEO means it turns up, with an occasional irrelevant article, on whatever subject you could care to name) article on Expected Value, in this case. Actually typing in “tower property” returns the article on “law of total expectation” which is apparently the one of its myriad names that Wikipedia has decided is most common. Looking at the other results on Google, even adding a helpful “statistics”, I find that “tower property” doesn’t appear to return anything else relevant. In fact, the only other place I can find it called “tower property” is in my notes :)

For nameless results, I find my best bet is simply to type in the result itself. For example, that E[XY]=E[YE[X|Y]] is proven at the end of this pdf document, which is likely lecture notes. If something has a lot of roots or powers, this is somewhat less applicable.

As of yet, I’ve not been able to find anything on what my notes refer to as “Fisher’s theorem”. It’s a theorem named after a famous mathematician who had many theorems named after him (some with others), so we’re already off the a bad start trying to find it. The theorem reads:

Let X_i \sim N(\mu, \sigma^2) be indepedent random variables. Define \overline{X}=\sum_{i=1}^n X_i and s^2=\frac{1}{n-1}\sum_{i=1}^n (\overline{X}_n-X_i)^2. Then:
*\overline{X} \sim N(\mu,\frac{\sigma^2}{n})
*\overline{X} and s^2 are independent.
*\frac{(n-1)s^2}{\sigma^2} \sim \chi^2_{n-1}
*\frac{\overline{X}-\mu}{\sqrt{s^2/n}} \sim t_{n-1}

It looks like it has something to do with sample mean and variance, but I’m only taking the first module on this topic, so what its use is I can’t say.


P4: It's All in the Presentation

Tutor was Bev Walshe.

Retrospective:
I now know more about giving presentations – while the vast majority of this was learned /in the workshop/, I can at least say I’ve learnt to look out for things to use.

I am still not calm most of the time – the only way I deal with it for now is taking a brief pause, and when that fails to calm my racing heart I get more nervous – OH NO WHY ISN’T IT WORKING – so for now my strategy is to try to avoid it in the first place, or just ignore it.

I haven’t had a chance (or haven’t taken a chance) to present to a large group of people – my favourite, as is, is one or two people asking questions as we go along – this enables me to keep up the interaction and remain fairly casual.


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