Tsundoku and Kaizen

Tsundoku (noun)
Buying books and not reading them; letting books pile up unread on shelves, floors or nightstands.

I came across this word while browsing the internet the other day, and it stuck out to me. I think partly because I bought several books while studying for qualifying exams to reward myself once I passed, but they’re mostly still sitting on my bookshelves and nightstand [to be fair to myself, I’m halfway through one and I read very slowly]. I also think it stuck out because I’ve been interested in the idea of “wanting to want” for a while and I believe it’s related–at least for me.

Many of us have an idea of who we want to be. For some it may be in the form of a very clear vision and set of ambitions. For others, it might be a vaguer notion of “the ideal me.” We may find our inspiration directly from role models or we may amalgamate the hundreds of articles we passively read about how billionaire entrepreneurs wake up at 3:45am., exercise, and make another million dollars well before the rest of us normal people wake up.

I could tell you about the pomodoro technique to reduce procrastination, I could recommend site-blocking apps to help eliminate distractions, and I could tell you to lay out your workout clothes for tomorrow, but I’m sure you’ve heard all. This is not to dismiss these wonderfully helpful techniques; they work well for some people. For others though, we snooze, disable and laze our way back into our old habits.

Why though? Do we lack discipline? Are we not motivated enough? Is the status quo too comfortable?  Can we not overcome some internal/external obstacles? Are we bad at budgeting our time accurately? Or could it be something else entirely…something we don’t want to admit easily: Maybe we don’t want to be who we think we want to be. Perhaps we don’t want to do what we think we want to do. [Waking up at 3:45am doesn’t really sound that nice.]

I believe this is where I often confuse wanting something and wanting to want something. We may want ourselves to want to cook/exercise/read/meditate/etc, but we rarely find ourselves actually wanting to cook/exercise/read/meditate/etc. Is it that we want the benefits (tasty meals, an attractive body, knowledge, mindfulness, etc.) without putting in the work? From buying that once-used juicer to that treadmill that’s now gathering dust in the garage, we tell ourselves we are going to become a new better person, but too often we stay exactly the same.

So how do people change?

Kaizen (noun)
Change for the better; [now commonly used to mean] continuous improvement or the philosophy of making grand betterment through incremental steps

We’re presented with dozens of small decisions for how to spend our time each day. From my experience, these often subconscious choices are the most honest indication of what we actually want to do and who we want to be. Can it be changed? Yes, but probably not through drastic perturbations to our lifestyles that are difficult to sustain or not calibrated to our actual desire for change. [Sure, some folks have life changing moments–usually as the result of some sign from God type wake up call, but most do not and I would rather not wait for one to happen to me.]

The reasons to try achieving change in bite-sized pieces are many.  One is that by taking smaller steady steps we reduce the risk of failure. Of course some failure is unavoidable, but setting the bar too high makes it more likely that we will experience discouraging failures which can put us in worse positions. Coupled with that fact that habits are difficult to make and break, taking up to 9 months for some individuals, it’s clear that we shouldn’t be too distraught at failing to achieve even the smaller goals we set.

Another reason is that we aren’t as good at seeing the big picture as we think we are. Take climate change for example. Daniel Gilbert, Harvard psychology professor, argues that one of the reasons we have not been responding as well as we need to be is due to our rather poor ability to deal with distant threats. A continuous improvement process allows us to take on immediate tasks, evaluate the direction we are heading, and adjust. This is not antithetical to having big goals, but rather essential to it.

Me (pronoun)
A new method for understanding myself that I’ve recently taken up is to document my feelings and thoughts more. Despite having to work in the land of lemmas, logic, and layered networks for most of my day, I discovered that I use a lot of emotional reasoning when it comes to thinking about myself. Whether it’s perfectionism or impostor syndrome, my mood is quite powerful in deciding how I view myself. By externalizing everything onto paper, I find myself being significantly more sympathetic to myself–something I’ve struggled with for a while.

I hope that as this process of writing about myself (and reading about “myself” through psychology journals, philosophical meditations and other blogs) continues  I learn to appreciate what I have achieved and use it as fuel to achieve even more. I also hope that I learn to accept my failures and shortcomings as reflections of my inability to do something at one point in time rather than my inability to do something ever.

My life has been quite turbulent these past few months. Some old habits are on the way out while others are thriving. I’m realizing that the abstract ubermensch who I thought I wanted myself to be is not the person I am nor can be. And I’m okay with that. I’m not abandoning improving myself in any way. In fact I’m better suited to do it now more than ever.

Can you paint with all the colors of the integers?

I first encountered a variation of this problem while watching the film x+y, a drama about a boy participating in the International Mathematics Olympiad.

Suppose I paint the natural number 1,2,3,… red or blue, each number being painted exactly one color. Do you think you can always find two numbers a and b such that a, b, and a+b are all the same color, i.e. the triple (a,b,a+b) is monochromatic?

The answer is yes. In fact, if you are allowed to have a=b, then even in the worst case scenario you can find a solution without venturing past the number 5. This can be solved backwards: Assume 1 is red, then  in a worst case scenario 2 will be blue (otherwise you would have a=b=1 are red and so is a+b=2). By similar reasoning in the worst case scenario 4 is red, and thus 3 is blue (if 3 were red then we have 1, 3, and 4 are red). Now 5 is either blue or red but either way we have that (1, 4, 5) or (2, 3, 5) are monochromatic. So without even looking at the coloring of the numbers, we are sure to be able to find our monochromatic triple (a,b,a+b). If you aren’t allowed to have a=b, it’s a little more difficult but you can still do it. The worst case would look something like 1 Red, 2 Red, 3 Blue, 4 Red, 5 Blue, 6 Blue, 7 Blue, 8 Red, and regardless of what color 9 is, you’ll have your triple.

Now, what would happen if I were allowed to use more colors to paint? Suppose I can use 3, or 10, or even a million colors. Could I ever come up with a coloring of the natural numbers so that you won’t be able to find a monochromatic triple (a,b,a+b)? Obviously the technique above becomes much more laborious as at every step my repertoire of colors is rather large. Is there some number of colors that I can use though to make an impossible coloring, one in which you will not be able to find your monochromatic triple?

What if I further challenge you to look not for a triple (a,b,a+b) but instead for a 7-tuple (a,b,c,a+b,a+c,b+c,a+b+c) that is monochromatic? Or a 15-tuple (a,b,c,d, a+b,a+c,a+d,b+c,b+d,c+d,a+b+c,a+b+d,a+c+d,b+c+d,a+b+c+d)? Or worse, asking you to find an infinite set of natural numbers such that the sum of every finite subset is the same color. Are you feeling deterred by this Herculean task?

Fear not! For Hindman’s Theorem guarantees that regardless of how many colors I use, subject to it being finite of course, you can always do it. That’s right, even if I used a googolplex of colors, you can find an infinitely large set A of natural numbers such that ever finite subset S\subset A will have a sum \sum_{s\in S} s of the same color.

Note, we are not requiring that this set you find be closed under finite addition of repeated elements, i.e. if x is one color, we do not require x+x is to be the same color. This would actually be impossible even with just two colors as demonstrated by the coloring:

Red: 1
Blue: 2 3
Red: 4 5 6 7
Blue: 8 9 10 11 12 13 14 15
Red: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 …

Here, by creating lists that double in length and alternating between coloring the lists red and blue, every x and x+x are colored differently.

For more details I recommend taking a look at Baumgartner’s short proof of Hindman’s theorem, and also checking out the film x+y when you get a chance!

References:
0) https://arxiv.org/abs/0906.3885
1) http://math.stackexchange.com/questions/789443/hindmans-theorem-on-coloring-a-set-with-n-colours
2) https://terrytao.wordpress.com/2008/01/21/254a-lecture-5-other-topological-recurrence-results/

One day at a time

 

Expectations vs. Reality

If you asked me a year ago what I expected my second year of graduate school to be like, I might have answered: I would be done with my qualifying exams. I would have taken a bunch of interesting seminars. I would have picked my advisor. I would have organized awesome events. I would have had an awesome summer internship.

Yesterday, I found out that I did pass my final qualifying exam, a bit later than expected, but perfectly in line with what my department expects of its doctoral students. I only took one seminar but it led me to working on a fascinating project with the Yelp Dataset (blog post to follow). Unfortunately, I am not much closer to having an advisor. However, I helped organize some well attended events. I didn’t have an internship, but I still had an awesome summer and learned a lot of mathematics.

 

Lessons Learned

So what happened? I do not want to go into too much detail, but if you’re interested you can can get slight peek of the events by reading UCLA’s Discrimination Prevention Office Report here. In short, I spent much of the last year defending my rights and the rights of thousands of UCLA students to speak their beliefs. For this, I and a few other students faced large-scale, well-funded, highly-organized harassment and bullying. I was repeatedly ignored by Chancellor Gene Block, I was told to reconsider being involved with Palestinian activism by a high-ranking UCLA administrator, and–surprisingly–I was called a frog face. Ribbit!

In retrospect, I would not do everything the same way if given a second chance, but I do not regret the sacrifices I made. I learned a lot about myself, about my friends, about other graduate students at UCLA, about UCLA’s bureaucracy, and about the law. I made tons of new friends and grew as an advocate for Palestine and Free Speech. As the struggle for liberation and a just peace continues, I hope I continue to become more effective.

 

Moving Forward and Backward

Today, I and several others found ourselves the victims of another poster campaign on campus (see here and here). As you can see, it’s not new. In fact, you can read more about it here on UCLA Vice Chancellor Kang’s blog. As he mentions, these inflammatory posters violate Regulations Governing Conduct of Non-Affiliates in the Buildings and on the Grounds of the University of California. I’m not sure though if that means UCLA is planning on doing anything about it though. Is this selective enforcement? I can’t say for sure, but it feels like it. As for this round of posters, there was another game-changer that might test this theory:

screen-shot-2016-10-05-at-5-54-36-pm
Cropped shot of one of the posters. 
There were many posters, but as one of the posters depicts the Vice Chancellor himself, I expect the response from UCLA to escalate from the usual campus-wide email. The whole McCarthyist “Red Menace” depiction is just the racist cherry on top of their Hate Group sundae.

 

Damages and Remedies

Before concerning yourself though with how Jerry Kang is feeling. Let’s take a bird’s eye-view assessing the damage and harm done here. Jerry Kang is a double graduate of Harvard University who has had a long and successful career as a Professor of Law. He has tenure, a Vice Chancellorship, and a consistent salary of around $300,000. When you google his name, it is his research, his blogs, and his websites that show up first. Compare that to the other folks the posters targeted. They are students–mostly students of color–students seeking their first employment, students with less than a hundred dollars to their name. They have no safety net and when you google them, it’s not their own profiles that show up. I can’t even get started on discussing the mental health effects without wanting to write another blog post just about that. Look, I feel bad for him, but this isn’t even apples and oranges.

As for remedies, the administration needs to work on-and this is the operative word here-concrete steps to help its students. I cannot stress this enough. When faced with a multi-million dollar hate machine that funnels money into campaigns to smear students via websites, posters, PR firms, and search engine optimization teams, an administration that is sincerely dedicated to education would not merely send an email. As much as we all want to be civil about this and challenge bad speech with good speech, that strategy has proved to be ineffective here. The point of the posters is to deter future student activists  via guilt-by-association and reputation damage. UCLA has some obvious ways to deal with this. Positively promote these students, give them the stellar attention they deserve. Give them the resources that a multi-billion dollar institution has in order to amplify their voices.  Offer strong letters of recommendation to these students for their fortitude. And frankly, if the administration is not prepared to genuinely defend its students in these kinds of way, they should not waste students’ precious time with meetings.

 

Looking Ahead

Now, if you ask me now what I expect my third year of graduate school to be like, I would not even try to answer. Being at UCLA is exciting, and so are Palestine solidarity and mathematical research. Ultimately I’ll never be able to expect the unexpected, but I will be able to adapt. And that’s much more useful. 

I woke up today with a long to-do list that I’ve been saving up until I heard back about my results yesterday. These posters may have made the list longer, but like I said, I learned a lot from last year and I am pushing through. My education won’t be stopped. My activism won’t be stopped. I won’t be stopped.

Pandämonium: Fernweh, Wandertrieb Und Zugunruhe

Our experiences do not define us, yet we are nothing more than our past and our future. Compelled to make new mistakes and relive old ones.

To be content is to be unhappy. To idle is to die young. We desire change. Our instinct is to wander. I grow restless.

Time slips away as moments become shorter. Darkness deafens the fragile senses. The Silence is blinding.

Who knocks? Is it death? …Is it reality?

 

Speak English, please.

amn’t a linguist by training, but every so often I come across a peculiarity of the English language that makes me wish I were. Whether it’s the differences in zero-marking between British and American English or the fact that we can ask “Aren’t I?” but not say “I aren’t,” the language is riddled with curiosities that developed for one reason or another and, when I’m lucky, they carry funny names like the “expletive it.” I want to seize this opportunity to write down some of my thoughts on two phenomena I recently encountered for which there does not seem to be suitable references online. These notes are rough, so take it with a vaguely predicated amount of salt.

Now, I’m certainly not the first to say this, but not all of “the rules” of English make sense, nor do they always seem to help clear up meaning. Irregardless, as a former student of The Greek, The Latin, and The Arabic, I enjoy learning about these international laws governing our languages. And you should too, if for no other reason than to enforce arbitrary syntactic structures upon your peers’ utterances at the most opportune (inopportune for them, of course) times. Perhaps follow it up with a “Speak English, please” to add insult to insult. [Whenever I’m caught in this situation with my proverbial pants down, I plead ignonce.] In all seriousness though, I still find it to be a constant struggle to adhere to MLA, APA, CMS, and other TLAs and my writing is often riddled with confusing punctuation and even more perplexing quasi-verbiage.

Caveat lector: The following has some math(s), but I’ll try to keep it self-contained.

1) Perhaps no distinction annoys the Descriptivists more than the fewer vs. less divide of 1770. Purists treat this as a matter of life and death, as if it were an eleventh commandment decreed by God herself that for all instances in which objects may be counted one must use “fewer” and for all other instances one must use “less.” I very much doubt any person truly follows this to a T, and even the Merriam-Webster Dictionary of English Usage prefers the common usage of less in many instances. Notwithstanding, I believe I have found proof that this rule is not from God, but in fact man-made and impossible to satisfy. Consider the rational numbers and the real numbers, which consists of the rational numbers and the irrational numbers. There are infinitely many rational numbers and thus there are infinitely many real numbers, and certainly more real numbers than rational numbers. However, there are only countably many rational numbers while there are uncountably many real numbers. That is to say, we can count off the rational numbers in a systematic way (1/1, 1/2, 2/1, 3/1, 1/3, 1/4, 2/3, 3/2, …) whereas we cannot do so with the real numbers. Therein lies the problem. Are there fewer rational numbers than real numbers, or are there less rational numbers than real numbers? [A more symmetric phrasing is: which are there fewer/less of: rational numbers or real numbers?] In just one sentence we are talking about a single fundamental type of thing: numbers. Yet, numbers, when gathered in big enough groups, go from being countable to not. Thus it becomes ambiguous whether we ought to employ fewer or less. I do not know of other things that can be both countable and uncountable, but it seems almost ironic that “number” is the very word that leads to a contradiction of the fewer/less rule.

2) This second example has to do with adjectives, or modifiers, in a broad sense. There are lots of adjectives out there. Rumor has it, they’re in the top five most used parts of speech. As a refresher, here are some adjectives: blue, round, tall, fast, fake, honest, upcoming, fuzzy, melted, et cetera. How do adjectives work? You can learn more than you probably ever thought was possible here. There’s a surfeit of neat stuff, but let me break down the relevant bits. Functionally, what does an adjective do? It modifies a noun. How it does that depends on the adjective-noun combination.

Say you start with a noun, which naturally has some definition. The definition defines a set of properties that the noun satisfies. Then you modify the noun with an adjective. This modification usually has the impact of introducing further properties that the noun phrase (adjective + noun) satisfies. For example, suppose you have the noun “paper” which clearly has some definition. We know that papers can come in many colors though, so we modify it with an adjective to “blue paper.” We’ve now added the property of blueness to the set of properties, which causes a restriction. Simply put, the more properties there are that need to be satisfied, the fewer things there are that can satisfy all of them. Notice though that “blue paper” is both “blue” and “paper;” it satisfies two sets of properties, the first being the singleton set of blueness and the other being the set of properties of being paper. Phrased differently, “blue paper” is in the intersection of things that are blue and things that paper. Linguists call this kind of adjective “intersective.” For the mathematically inclined: \{\mbox{blue paper}\} = \{\mbox{blue}\} \cap \{\mbox{paper}\}.

Another kind of adjective is the subsective adjective, and as the name suggests it has to do with subsets. Take the noun “programmer.” Again it has a set of properties that define it. Now suppose we modify it with “clever” to get a “clever programmer.” We certainly still have that a “clever programmer” is a “programmer, i.e. \{\mbox{clever programmer}\} \subset\{\mbox{programmer}\}. However, just because someone is a “clever programmer” does not mean they are “clever”. It seems that rather than being another separate property that the “programmer” satisfies, the modification from “clever” affects a property. So instead of the property set expanding to include an additional property, “clever” alters a property within the set of “programmer” properties. The property adaptation in this case roughly is: “knows how to write computer code” becomes “knows how to write efficient computer code.”

Other types of adjectives may or may not exist depending on the school of thought you’re working with. A common example of this is the privative adjective with words like “fake.” A fake gun is not a gun and a gun is not a fake gun. Thus we have that the intersection of the modified and unmodified noun phrases is empty: \{\mbox{fake gun}\} \cap \{\mbox{gun}\} =\O. What we see is that property set for “gun” is not expanded by the adjective”fake,” but rather a crucial property (a gun discharges projectiles such as bullets) is negated (a fake gun cannot discharge projectiles). We can see something somewhat similar with temporally shifting modifiers like in the phrase “past president.”

In math(s) though, there seems to be some examples of adjectives which are distinctly different in behavior from the ones above. Rather than adding to, narrowing, or negating the properties, some adjectives widen. A clear example of this is in the noun phrase “general eigenvector.” One definition of an “eigenvector” of a matrix A is a vector x that satisfies the three properties that 0) x\neq 0, 1) \exists \lambda \in \mathbf{C}, m\in\mathbf{N},  (A-\lambda I)^m x= 0, and 2) m=1. A “generalized eigenvector” is only required to satisfy the first two properties, i.e. it is not required that m=1. So we have that \{\mbox{generalized eigenvector}\} \supset\{\mbox{eigenvector}\}. Other examples include skew fields, gaussian/eulerian/algebraic/etc. integers, and non-associative rings. By symmetry to the term subsective adjectives, I think (and a handful of other people on the internet agree) these adjectives should be called supersective. They have the ability to remove a property, and therefore loosen the noun phrase. Whether or not real examples exists outside of math(s), I am not yet sure. The closest I’ve been able to get to one is “dog food” vs “food” but please be careful.

So go ahead, Speak English, please.

Defiance, Riots, and Tear Gas

France Tennis Racket Tear Gas(3 June 2016 Nantes France) A protestor uses a tennis racket to return a tear gas canister during a demonstration to protest the government’s proposed labor law reforms in Nantes. Photographer: Stephane Mahe.

Palestine Lawyer Tear Gas Kick(12 October 2015 Ramallah Palestine) Hassan Ajaj: “I am part of my people, part of the Palestinian wish for liberation.” Photographer: Majdi Mohammed.

The Arab Refugee

Ants gnaw his flesh
Crows peck his flesh
The Arab refugee nailed to the cross.

The Arab refugee
Begs and spends his nights in railway stations
Crying his eyes out.
And Jaffa is just a small label
On a box of oranges.

Stop knocking on my door
There’s no life left in me.
And Jaffa is just an orange label
It leaves the dead undisturbed.

They’ve sold the memory of Saladin
They’ve sold his horse and shield
They’ve sold the grave of refugees.

Who would buy an Arab refugee for a loaf of bread?
My blood is running dry
But you go on laughing.
I am Sinbad
I store my treasures in your children’s hearts.

Ants gnaw his flesh
Crows peck his flesh
The Arab refugee begging at your door.

-Abdul Wahab Al-Bayati