<div className="mx-auto my-8 h-[700px] w-[350px] md:h-[1000px] md:w-[500px]">
 <ParentSize>
 {({ width, height }) => <TopTourismHeatMap width={width} height={height} />}
 </ParentSize>
</div>

According to the [United Nations World Tourism Organization (UNWTO)](https://www.unwto.org/), the [twelve most visited countries (by arrivals) in 2019](https://www.unwto.org/tourism-data/unwto-tourism-dashboard) (before COVID-19) are the countries in the above heatmap.

 
The ligher the color, the more travelers arrived during a given month and vice-versa.
The sorting of the heatmap could be less intuitive initially, but the idea was to
get a rough idea of where and when people visit these most popular destinations by
timezone / region (East --> West).
 
Right off the bat it is worth pointing out that France's figures might be a bit off.
According to UNWTO where the data was sourced, France is number one for most arrivals
in 2019 with almost ~91M arrivals. Unfortunately, the breakdown from each month reflects
only about half of that total. One or the other or both figures could be wrong, but
worth acknowledging.
 
Let us assume France did sit at around ~91M arrivals in 2019, one of the first thing
I noticed graphically is how stark the constrast is between the bottom half of the
twelve countries and the top half. Mexico, at rank 7 or ~45M annual arrivals is less
than half of France and the difference only gets larger for the other countries ranked
lower.
 
Cool, but why?
 
The inspiration behind the exercise was a desire to see if there are months you could
consider visiting (although it is historic) where you might be competing with less
visitors. A little off tangent, but much of the data is biased towards countries
in the Northern Hemisphere. I suppose intuitively it makes sense because the vast
majority of countries are in the Northern Hemisphere. Anyway, I started looking for
pockets of seasonality hotspots. Most of the European countries on the list are summer
hot spots. Japan, China, Thailand, United Kingdom, United States and Meixco on the
other hand, all seem fairly consistent month over month though there are some slight
peaks here and there.
 
If one really wanted to utilize some of this data of this for travel plans, it may
be interesting to cross-referencce climate / weather data with the monthly data to
see if there are months where there may not be as many visitors, but still have accomodating
weather.
 
An example is say you want to visit Italy, but summer peak months are just way too
crowded. You might prefer warmer weather or at least weather that's not cold so what
are some considerations? Italy's arrivals peak in August, but year-round, they're
getting at least ~3M arrivals per month. Only 4 months of the year have Italy's monthly
visitors below ~4M per month and those are January, February, November and December.
Looking at [weather data on Italy](https://weatherspark.com/countries/IT), these
four months definitely coincide with cooler weather; it is winter. That being said,
Italy is very popular almost year-round. Unfortunately the tradeoff is either more
arrivals for warmer average temperatures or cooler average temperatures for potentially
less tourist competition.
 
Godspeed!

Remember travel before COVID-19? What was it like then? Top twelve arrivals in 2019 via heatmap

Visualizing the twelve most visited countries in 2019

<Image
 src="/images/writings/word-search-01.png"
 width="1400"
 height="160"
 alt="Word Search"
 className="my-10"
/>

If an alien threatened to harm my goldfish unless I told it how to programatically generate a word search game/board, how would I do it? Alright, it's not that serious and no goldfishes were harmed in entertaining this prompt.

 
For posterity, this is [word search](https://en.wikipedia.org/wiki/Word_search).
 
I deployed a word search generator to [JAM Arcade](https://jamarcade.net/wordsearch)
recently and wanted to share how it manifested. You know, it would have been great
to say this was a breeze and a walk in a park to figure out, especially efficiently,
but it was a struggle, or euphemistically, a journey.
 
Let's start with context. The idea of creating a word search generator probably came
about 2016 - 2017. I started scribbling brief notes and exploring different methods
to generate an **N x N** or **N x M** board programmatically, but arugably spent
way more time thinking about performance. I'll add color to this in a follow-up,
but how do I know what word or words could fit where at a given time on the board?
 
The onion analogy is overused, but might be a decent one to use in this case. Envision
a finished board and step or work backwards to identify the layers. We'd probably
conclude by evaluating potential approaches that could generate these boards programmatically.
To digress a bit, it's worth noting board generation from a predetermined list of
words is a much different beast than generating a board from non-predermined list
of words. We'll focus the discussion on the latter.
 
So working backwards, what do we have? If the finished board is made up of searchable
words, the other letters filling up the rest of the board or non-words, are probably
randomly selected letters. Given that, outside of **p** number of words selected
for a given completed game board, which words get chosen, how do they get chosen
and where do the words come from?
 
We should have a mental model of how this might work conceptually. Let's walk through
it and perhaps discuss some pitfalls along the way as well.
 
First off, we need a dictionary of words available to us. On a Mac, your machine
should come with a `Dictionary.app` application. That's a good place to start, otherwise,
there are other [sources](https://www.wordnote.app/blog/why-i-built-dictionary-app)
could potentially be leveraged.
 
With a dictionary in hand, let us consider how to put words onto a board until each
cell in the grid is filled with a letter. Like many things in life, we can make progress
by building on top of previous steps; or in this case, one word at a time. As each
potential word fill up the grid, there should be a terminal condition to prevent
further words from being inserted onto the grid right? Afterall, the grid fills up
and it's not a great experience if you even manage to fill up every empty cell on
a board with a word. If that sounds like a plan, let's get into the nitty gritty.
 
Assume English and an **N x N** or **N x M** board and we'll discover rules and conditions
as we walk through what should be considered.
 

- The maximum length of a word is the upper bound of a given board's size. In n
 x n, it would be n and in an n x m board, it would depend on whether n or m is larger.
 This makes sense because you can't have a valid word that is longer than the length
 of the chosen board.

 

```python
MAX_WORD_LEN = max(board_length)
```

 

- The minimum length of a word is subjective. You could have one character letters
 as words such as "a", or perhaps two character words such as "to" or "in", but I'd
 argue the cons outweigh the pros of setting a minimum word length of 2 or less. Instead,
 I'd opt for a minimum word length of at least 3.

 

```python
# Three is pretty good. Average word length is ~4.7 characters (round upto 5)
MIN_WORD_LEN = 3
```

 

- Next is the sense of "direction". There isn't a "correct" direction a word must
 be placed in a word search grid so long as a word is placed in a straight line starting
 at either a [cardinal direction](https://en.wikipedia.org/wiki/Cardinal_direction)
 or [ordinal direction](https://www.geographyrealm.com/cardinal-directions-ordinal-directions/)
 and it's corresponding opposite direction. That may have been too verbose. In other
 words, a word should either be placed NS or SN, WE or EW, NESW or SWNE, NWSE or SENW
 within the word search grid.

 

```python
# Direction doesn't have to be an enum, but we'll use it in this example
from enum import Enum
from random import choice

class Direction(Enum):
 NS = 0
 WE = 1
 NWSE = 2
 SWNE = 3
 SN = 4
 EW = 5
 SENW = 6
 NESW = 7

selected_direction = choice(list(Direction))

```

 
Is that it? Do we have enough information now to put a word search game together
with these three rules? We could. It would probably be uninteresting though. As we
start picking random spots to inject words into the grid, we'll find out pretty quickly
that the first word and direction chosen to place within the grid will influence
the rest of the board; namely it'll just be a bunch of words that fit into the grid
in the same direction. Why? Because we haven't accounted for finding words that might
share one or more characters with existing words on the board. We haven't told our
program how to handle a scenario like this. We need to give words selected the ability
to intersect with any of the 8 directions should they share a letter in any given
cell.
 
Then there must be another constraint!

 

- For a given direction to insert a word with a known word length of being between the maxium length and minimum length, which cells will have shared characters and what position are those characters in?

 

Here's an example: Let's say `COY` and `CHEESE` are words that have been populated on the board previously. A few cycles later, pseudorandomization decides it wants a 4 letter word that either begins with `YC` or ends with `CY`. In a dictionary, we know that `pacy`, `lacy` or `racy` would be valid words to insert based on those consraints.

<Image
 src="/images/writings/jamarcade-ws-ex-01.png"
 width="280"
 height="180"
 alt="Example word search character share"
 className="mx-auto my-4"
/>

 
Let's look back really quick. Is that enough for us to go by to generate a board?
For the most part, yes. You could have a recursive or iterative method call to populate
the board by looking for a set of words to select from given the constraints of any
given open cell in the grid. If there are no words that fit that criteria, that's
okay - we just don't insert a word at the interation and find another open cell with
another set of constraints. Then at what point do you terminate the call? It's usually
reasonable to terminate when you have say 30% +/- a few percentage points of a board
filled with words to find. The rest of the cells should be populated by random letters.
 
Here's a very rough and bloated example of what that code might look like:

 

```python
# Return a set or a collection of words to randomly select
class WordSearchBoard:
	# ...

	def find_valid_words(self):
		open_grid_idx = random.choice(self.open_board)
		# Note: You may want to bias word len for various reasons
		# If so, see: https://stackoverflow.com/questions/20311223/how-to-implement-biased-random-function
		word_len = random.randrange(MIN_WORD_LEN, MAX_WORD_LEN)
		dir_dic = find_directions()
		shared_letter_constraints = self.get_letter_constraints(selected_open_grid_idx, word_len, dir_dic)

		# aggregate set / list of words together based on above criteria
		# ...
		word_lists = [[], [], []]
		words_from_constraints = set(word_lists[0]).intersection(*word_lists[1:])

		if len(words_from_constraints) = 0:
			return self.find_valid_words()
		else:
			return { cell_idx: open_grid_idx, words_avail: words_from_constraints }
```

 

With that, let's call it for this part. Look out for part II which is equally important if not more important. In the `find_valid_words` method there's some hand-waving going on with how to get a list of words to select from to place on a board.

 
Stay tuned!

What does it take to create word search boards programmatically? In pursuit of nostalgia.

Creating word search boards

To preface, this isn't anything concrete, but just a collection of thoughts after one of those Wikipedia rabbit hole binges.

 
I had read Peter Thiel's [Zero to One](https://www.goodreads.com/book/show/18050143-zero-to-one)
a few weeks back and was inspired to consume even more related content. When you
go down an internet rabbit hole you might pick up a nugget or two or you could end
up doomscrolling. Anyway, I was immediately drawn to a quote he made in 2013 at Yale
University, "We wanted flying cars, instead we got 140 characters." The qoute hit
me and with some fairly elementary mental gymnastic later, let's just say the dynamics
behind the assertion is complex, but let's entertain it.
 
How could we get to this futuristic future? Are the incentives and institutions around
"moonshots" for a lack of a better word, easily and readily available? Unfortunately,
I may have jumped the gun with the question.
 
We have bigger problems if the most admired profession in the United States according to a [Lego survey is becoming a Youtube star](https://www.prnewswire.com/news-releases/lego-group-kicks-off-global-program-to-inspire-the-next-generation-of-space-explorers-as-nasa-celebrates-50-years-of-moon-landing-300885423.html).
 
But, who am I to judge? In all seriousness, kids are kids. When I was a kid I wanted to be a doctor, lawyer and firefighter; I think in that order. Here I am, neither of those, but a "professional" in the software space.
 
I digress.
 
Back to the topic at hand - where's our flying cars and fusion power and light sabers?
 
A [paper](https://ideas.repec.org/p/spo/wpmain/infohdl2441-510i09nqpa8gfpt7na72sknq4q.html) in 2017 titled "Finance and Misallocation of Scientific, Engineering and Mathematical Talent" finds the share of STEM talents grew signficantly faster in finance than in other STEM sectors. The authors find a persistant wage premium for STEM graduates working in finance compared to other STEM sectors.
 
What's going on? Is there a brain drain going on from STEM talent flowing into finance? According to the paper? Absolutely.
 
What is sort of some consequences of this?
 
Here's a critique. In an article by the Washington Post in 2014 aptly titled, "[A black hole for our best and brightest](https://www.washingtonpost.com/sf/business/2014/12/16/a-black-hole-for-our-best-and-brightest/)", the article also cites a different [paper](https://www.kellogg.northwestern.edu/faculty/nathanson/files/Allocation.pdf) by Harvard University and the University of Chicago stating that every dollar a worker earns in a research field spills over to make the economy $5 better off. Similarly, every dollar a worker earns in finance, makes the economy 60 cents worse off.
 
As the article continues, the [finance industry makes up under 8% of the economy (GDP)](https://apps.bea.gov/iTable/?reqid=150&step=2&isuri=1&categories=gdpxind#eyJhcHBpZCI6MTUwLCJzdGVwcyI6WzEsMiwzXSwiZGF0YSI6W1siY2F0ZWdvcmllcyIsIkdkcHhJbmQiXSxbIlRhYmxlX0xpc3QiLCIxNSJdXX0=). [BLS' employment by major industry](https://www.bls.gov/emp/tables/employment-by-major-industry-sector.htm) lists financial activities at approximately 5.6% of total employment or roughly ~8.7M people.
 
Philippon (a French economist at NYU's Stern School of Business) in the article asserts the optimal size of the financial sector should be about ~2% less.
 
On to some scuffed napkin math. Let's assume 5.6% aggregate workers make up 8% of GDP in finance and if employment numbers shifted down in proportion to ~6% of GDP instead, we're looking at about 4.2% of people employed in finance instead. In real numbers, that would translate to ~6.6M employed in finance rather than ~8.7M and could imply ~2.13M folks being available to allocate to other industries/sectors. There's a lot of assumptions here, but let's continue.
 
Let's assume those ~2.13M folks went into academia/science where each dollar earned spills over to make the economy $5 better off ([positive externality](https://www.economicshelp.org/micro-economic-essays/marketfailure/positive-externality/)). It would then be reasonable to presume we'd likely be better off should this have happened,. But, Collin would we be any closer to flying cars? Who knows. That's anyone's guess. However, Reid Hoffman tweeted about a [little something something](https://twitter.com/reidhoffman/status/1372639338832355330) 8 years after Thiel's quote, so there's that. 🤷
 
What good is an optimistic take if we can't assume the reallocation of talent would have yielded flying car or any other number of scientific breakthroughs for these moonshots? Hope and aspirations are noble and worth believing in. It is definitely enticing to think about. Come on, you have to wonder with all that extra brain power, could progress on one or several fronts could have happened.
 
Wishful thinking? Perhaps.
 
Anyway, there's another problem. Where does the money come from? The private sector? Is this taboo to talk about?
 
If we take a step back and put our "investor" hat on and imagined ourselves as a rational investor presented with where to allocate capital, where would this capital go? Would you place your money on moonshots with potentially a low probability or at best, an uncertain probability of success (implying commercial ROI) and longer time horizon or would you allocate capital to a software company that sounds promising with much lower risk and a shorter time horizon? I'd argue the majority of us would fall into the latter bucket. The analysis begs the question, where could the investments and incentives come for these endeavors then. I believe that's a policy question and if I'm being honest, I imagine meaningful progress here has to involve the state. It wouldn't be the first time technological advancement made strides commercially. [GPS](<https://www.darpa.mil/attachments/(2O10)%20Global%20Nav%20-%20About%20Us%20-%20History%20-%20Resources%20-%2050th%20-%20GPS%20(Approved).pdf>) and [memory foam](https://spinoff.nasa.gov/Spinoff2005/ch_6.html) are two that come to mind immediately.
 
I don't imagine this is thought experiment is deviates much from the real world as the vast majority of venture capital is not dispersed or allocated to high-risk moonshots. Wall Street Journal has graphic illustrating venture capital allocation up to 2018 [here](https://graphics.wsj.com/venture-capital-deals/) showing capital going into software by a substantial margin. That doesn't mean there isn't any venture money flowing into moonshots and "crazy ideas," but they are certainly in the minority.
 
Would this imply public and private partnerships? It alludes to it, but I'm not a policy expert; just someone who may have spent too much time on Wikipedia that one day.
 
Before concluding, I came across [incentive design](https://www.gsb.stanford.edu/faculty-research/centers-initiatives/sil/research/methods/incentive-design). Let that be a topic for another time.

Incentives are fascinating. When, if at all, should we revisit the incentives around us?

Thinking about incentives

<Image
 src="/images/writings/tranquil-scene-02.png"
 width="768"
 height="448"
 alt="Tranquil scene"
 className="my-10 mx-auto"
/>

**"An Ode To Open Source" by Collin Wu**

 
_Software built by those_
 
_Allow ideas to thrive_
 
_We ought to sustain_
 
 
I worry about our open source ecosystem. Open source is the life blood of many,
if not most developers. With the misalignment of incentives, I am afraid of what
might happen should benevolence no longer be enough.
 
Bless all the amazing folks out there that have contributed and got us this far.
 
As a community, we owe them.
 
 

We can [Sponsor](https://github.com/sponsors) and try to get our companies to get more involved and help more. It's the right thing to do.

Standing on the shoulders of giants. Where would we be without open source? How about a haiku?

Writings