## San Diego – 5 day itinerary

Where To Stay: Hotel Republic. It is in the Financial District (downtown), walking distance to the Marina, Amtrak, Aaharn and Karl Strauss Brewing Company.

Where to buy tickets: Go City pass or Costco.

Transportation: Recommend to take Uber and not rent a car since there is \$50 valet parking charge at hotel per day.

Day 1: Arrive at hotel. Buy groceries from Ralph’s nearby and head to Coronado island in the evening (Hotel Del Coronado). Coronado is the happening place in San Diego. More happening than Downtown San Diego itself. And Hotel Del Coronado is a place to visit. Eat at Miguel’s Cocina near Hotel Del Coronado.

Day 2: San Diego Zoo. Or do the Safari Park instead if you have already been to some zoo couple of times. The Zoo comes up as the top attraction of San Diego. Its not bad but comparable to Woodland Park Zoo (Seattle) so can be easily substituted for something else like the Safari. They have lot of monkeys but oddly there were no gorillas. The best exhibit I found was that of Asian Leopards. They have at least 4 of them and they were very active. You do feel a sense of guilt watching the animals in captivity (esp. the birds which are meant to soar in the skies). Dinner at Aaharn. Aaharn is the best place for budget conscious. The food is good and it cost only \$20 for 2 people. Rest of the places were 3x expensive. If you are staying at Hotel Republic you could eat at Aaharn throughout your trip.

Day 3: La Jolla Cove. Start at the children’s pool and walk to La Jolla Cove and the Cave Store. Check out the cave and then head over to Salk Institute. Have lunch at Salk Cafeteria (good food and very cheap) and then go to the Gliderport. Do paragliding there. It is costly (\$175 + \$100 for photos and video) but worth it if you have never done it before. Also the best views of the ocean are from here. Then explore UCSD campus nearby. Dinner at Karl Strauss.

Day 4: Sea World. There are 2 main roller coaster rides – Electric Eel and Manta. Both are lot of fun. Then there is Tidal Twister, Journey to Atlantis and Shipwreck Alley which are fun as well. If you have been to another Sea World then might want to substitute with Legoland. Stroll around the marina in the evening.

Day 5: Check out from hotel. USS Midway. Amazing experience. They have dozens of fighter and bomber planes plus you can take a tour of the ship all the way from the bridge to the engine room. You can see the dining hall, admiral’s desk, kitchen, laundry, radio room, conference rooms, mess, supply room, pretty much everything. They have interesting talks where they explain crew in yellow jackets direct the planes, the crew in red jacket checks ammunition, white jacket checks safety and so on. They have a place where you can park your luggage in case you are taking flight back home in the afternoon.

Gaslamp Quarter is supposed to be an attraction but I found it passable.

## Decoding the algorithm behind Levels.fyi

I have been quite impressed with Levels.fyi website which shows a mapping of career levels between companies. E.g., what does a level 66 in Microsoft map to in Uber? How does it do it? How would I do it? Let’s say we have data from users when they switch jobs that tells us the level of the person in company A and what level the person joined in company B. So this would e.g., give us a table of the form:

So to get a mapping between Microsoft and Uber, for each level `x` in Microsoft:

• filter data and select rows where `From = Microsoft`, `From_Level = x`, `To = Uber`
• and average the `To_Level` column of rows from previous step

That gives mapping of level `x` in Microsoft to Uber. Call it `M(Msft,x,Uber) = M(from,level,to)`

This will not work. To see why, consider the fact that when people switch they usually accept a lateral level or better yet level up. Rarely do they level down. So when we run the above algorithm, we might get a table that looks like (assuming people aggresively level up when they switch):

and if we re-run the algorithm, but switch the roles of Microsoft and Uber i.e., we compute `M(Uber,x,Msft)` we might get a mapping that looks like:

Clearly this is wrong. It implies level 63 at Microsoft = level 66 at Microsoft. For a correct mapping, we require

`M(Uber, M(Msft,x,Uber), Msft) = x`

How to find such a `M`? Well, the solution is simple. Plot all the points where people have switched between Microsoft and Uber on a 2D graph and fit a straight line through them. One might be tempted to do fancy things like clustering to handle non-linearity but it will only make things worse. Hint: Try making a scatter plot where candidates constantly level up. How will you cluster?

Levels.fyi goes beyond this: it actually allows one to select more than two companies and instantly see the mapping between levels. How could this be possible? Well, the answer is simple. In practice it does none of the above. In reality, all levels are mapped to compensation and using compensation as a common hidden variable, it is very easy to get a mapping of levels between arbitrarily selected companies. So in the end, level is nothing but a proxy for money. There you have it. In fact, the table `From, From_Level, To, To_Level` doesn’t even exist. When levels.fyi collects data, their form only records compensation and level at current company, not the levels when a person switches from company A to B.

## Roth vs Traditional 401k – final take

This is my final take on Roth vs. Traditional 401k in which I extend the previous model to include two new variables:

• a different tax rate $t_2$ for money withdrawn from 401k (the expectation is that you will be in a lower tax bracket during retirement) and
• a variable $e$ to denote the expenses in a year. These expenses need to be deducted from the amount that is invested in the ordinary non-tax sheltered account.

with these two variables, the new calculations for Roth vs. traditional are as follows:

Roth 401k

Total = $Roth = (1+r)^N c + (p - c - e - f(p))(1 + r')^N$

where:
$f(x)$ is a function that computes tax on $x$, and
$r' = r(1 - t_1)$ is the reduced rate of return that money in non-tax sheltered account earns
$t_1$ will be the marginal tax rate (bracket)

Total = $Trad = (1+r)^N c (1 - t_2) + (p - c - e - f(p-c))(1 + r')^N$

where:
$t_2$ = expected tax rate at time of withdrawal in retirement

Let’s see what we get if we subtract the two:

$D = Roth - Trad = (1+r)^N c t_2 - (f(p) - f(p-c))(1 + r')^N$
Now recall $f$ is simply the function which computes tax, so $f(p) - f(p-c) = t_1 c$ giving
$D = (1+r)^N c t_2 - (1 + r')^N t_1 c$
simplifying:
$D = ((1+r)^N t_2 - (1 + r')^N t_1) c$
For $D > 0$ (i.e., better to invest in Roth), we get a simple formula
$(1+r)^N t_2 > (1 + r')^N t_1$
This looks like a linear relationship in $t_1$ and $t_2$ but isn’t since $r'$ is a function of $t_1$. The variables $p,c,e$ have cancelled out and we see that the factors that influence whether you should choose Roth vs. Traditional 401k are:

• your current tax bracket $t_1$
• your expected tax bracket during retirement $t_2$
• expected rate of return on investment $r$
• time to retirement $N$

We can write a small function that gives us the breakeven point when both Roth and Traditional will give same return:

Let’s see what it gives:

Plot of breakeven point vs. N (# of years till retirement) with $r=0.08$ and two different values of $t_1$

Enough math. Can I get it in English please? Investing in Roth makes sense if you are young (i.e., N ↑) or in a low tax bracket ($t_1$ ↓). For most people, both these events happen at the same time. To use the graph above, calculate the # of years you have till retirement (x-axis) and your expected tax bracket in retirement (y-axis). That should give you a point on the graph. If that point is above the curve, you are better off investing in a Roth 401k.

Conclusion: Go Roth when you are young and switch to Traditional 401k once you cross 40-45 years of age. For most people that represents mid-point of their career. Thus, in other words, the conclusion is to split evenly between Roth and Traditional 401k. Choose Roth for first-half of your career and Traditional for the second half.

of course, again all this is just bookish exercise for fun. Code is here.

## Roth vs Traditional 401k – take two

There is a subtle bug in my original post on Roth vs. Traditional 401k. The bug being that in Roth 401k, we pay taxes upfront but we still get to invest full contribution amount that grows tax-free. The bug is so subtle that let’s do another analysis that will make it clear. Let

$p$ = principal amount = salary earned in a year = \$100,000 as example
$c$ = contribution amount to 401k = \$19,000 for 2019 whether it be roth or traditional
$r$ = rate of return on investment = 0.08 as example
$t$ = tax rate = 0.35 as example
$N$ = # of years money is invested

Roth 401k
We start with $p$. $c$ goes into 401k account. That leaves us with $p-c$ in ordinary account. Next we pay tax on the full $p$ which further reduces it to $(1-t)p-c$. Call this $A$. This amount can be invested just like we invest the money in a 401k. The only difference is that in ordinary account we will have to pay tax on earnings every year. I leave it as an exercise for reader to prove that the annual tax incurred in the ordinary account basically has the effect of reducing $r$ by a factor of $1-t$ so that at end of $N$ years, $A$ invested in ordinary non-tax sheltered account will grow as $(1+r(1-t))^N A$. The money in 401k grows as $(1+r)^N c$ and can be withdrawn tax free. So at the end we have

Total = $(1+r)^N c + (1+r(1-t))^N ((1-t)p-c)$

We start with $p$. $c$ goes into 401k account. That leaves us with $p-c$ in ordinary account. Next we pay tax on only $p-c$ which reduces it to $(1-t)(p-c)$. This becomes the new $A$. This amount can be invested just like we did earlier. In case of traditional 401k, the money in 401k will grow to $(1+r)^N c$ but we will have to pay tax on this at time of withdrawal. So at the end we have

Total = $(1+r)^N c (1-t) + (1+r(1-t))^N (1-t)(p-c)$

The total amount we end up with is not the same in the two cases. I wrote a small script to compute the two totals

when I run this script:

so Roth seems to be better. But beware, this is just bookish exercise that assumes $t$ to be same in case of retirement vs. not. In reality what is expected is that in retirement your tax rate should be lower than the tax rate when you are earning. In that case traditional 401k might turn out to be better.

Let $p$ be amount invested over $N$ years. $r$ = rate of return. $t$ = tax rate.

Roth 401k
You pay taxes upfront. That reduces $p$ to $(1-t)p$. After $N$ years this becomes $(1+r)^N(1-t)p$ which you can withdraw tax free.

You don’t pay any taxes on $p$. After $N$ years the amount becomes $(1+r)^Np$. Now when you withdraw it, you pay tax and so the net amount becomes $(1+r)^Np(1-t)$ which is same as earlier.

Of course, the catch is the assumption that $t$ remains same in both cases.

## Understanding Docker Volumes

Docker volumes are a complicated beast. They can be created using the `docker volume create` command or in the docker-compose.yaml file under the volumes section. E.g.:

What this does is create persistent storage on the host that 1. does not get deleted when a docker container stops and exits and 2. that can be used to share data amongst containers.

To see a list of volumes on your machine, run:
“`
\$ docker volume ls
“`

To get details of a volume, run (to give an example):

The volumes are not created as regular directories on the filesystem that can be accessed using familiar unix commands. E.g., if you try to list the mountpoint in above:

In fact there is no `/var/lib/docker`. To “get” to the volume requires some steps taken from https://forums.docker.com/t/host-path-of-volume/12277/6:

1. First (on the mac) run `\$ screen ~/Library/Containers/com.docker.docker/Data/vms/0/tty`. This should open an absolutely blank screen. `~/Library/Containers/com.docker.docker/Data/vms/0/tty` itself is a link to `/dev/ttys000`
“`
\$ ls -al ~/Library/Containers/com.docker.docker/Data/vms/0/tty
lrwxr-xr-x 1 sjain68 staff 12 Nov 5 09:03 /Users/sjain68/Library/Containers/com.docker.docker/Data/vms/0/tty -> /dev/ttys000
“`
2. Now ls the mountpoint you found earlier
3. To exit the screen type `Ctrl+A` followed by `:quit`. DO NOT type `exit` as it will mess you up. https://stackoverflow.com/a/2308595/147530

the `tty` is not a file. It is a device.
“`
\$ ls -al /dev/ttys000
crw–w—- 1 sjain68 tty 16, 0 Nov 5 11:13 /dev/ttys000
“`