The first decade

I once saw a video (Ted talk, maybe?) about the power of doubling. In the example, the speaker emphasized what it means for something to double repeatedly. He spoke about our oil usage. It doubles roughly every decade, and due to its exponential growth, it means that every decade we use more oil than we'd used in all of history before that.

But, I'm not here to talk about oil. This same concept can be applied to retirement savings. Assume you stash away the same amount of money every year (this is not an entirely valid assumption for a number of reasons and we'll come back to it) and earn a 7% return each year. These assumptions are generally reasonable. The 7% is particularly noteworthy because it's just about the rate needed to double in a decade. This got me thinking: are the assets contributed to a retirement in the first decade going to trump those contributed in the following 3? If so, this is a profound realization.

To double-check, I threw together some Excel tables to test the above and see where the cutoff is (in years). Here's the table, assuming constant contributions of $10,000 per year and constant returns over a 40-year period:

Rate (%)	Final Total	Cutoff
5	1.28M	12
6	1.65M	11
7	2.15M	10
8	2.81M	9
9	3.69M	8
10	4.88M	7

In other words, the first decade is as important as the last 3. If your returns are higher, the effect is exaggerated, but even at a relatively modest 5 percent return the first 12 years net out to the same as the last 18. Of course the effect is reduced if the savings is over less than 40 years, and increased if it's longer.

Now lets revisit the assumptions ...

I used the assumption that the contribution would be the same each year. This is technically and practically unlikely in many cases. Technically, because roughly 2 of every 3 years the contribution limit rises $500. In practice this makes little difference (running the same calculations with this adjustment moves the cutoff from 10 to 11 years at 7%, for example).

The in-practice assumption is the hard one. Most people's earnings increase over time, and with that, so does their ability to save for retirement. Many (due to salary) are forced to choose between "life now" vs "life later" (for example, someone making 30k will not be able to stash $18k in a retirement account). The above illustrates the great power of compounding growth, which should give people more incentive to consider the "life later" bucket.

For anyone who can afford to, it's just as important to save max for the first decade as it is to save max for the next 3. If you can, do it.

Battery-operated flight

A quick followup on solar-powered flight. A comment came up that "battery-operated flight was a possibility because the charge density of battery tech will get there".


I think it's going to take discovering some Star Trek energy crystal flux magic. A current, say, 787 uses about 4 terrajoules of energy on its flight. The rumored next iteration of the Tesla Model S stores 90kW.hr (~= 300 megajoules) in a ~1000lb battery (see: http://my.teslamotors.com/.../forum/forums/model-s-battery-0), which is pretty consistent with this claim that a typical Li-ion battery can store 150W.hr per 1kg.To store the required energy would take around 15000 batteries, weighing 15 million lbs. The corresponding kerosene weighs under 30,000 lbs. That means the same energy requires 500 times more weight in storage. This is the gap that must be closed to a large degree.

 

The Engineer's trap

I'm smart, see? If I just sit down and think really hard, I'll derive the right answer.

This works, sometimes. For some people better than others. But, not always for anyone. In engineering (and many other disciplines), we can't predict the future. Sure, we can have very high confidence that a particular thing will work, functionally. However, we can't inherently predict human reaction. Will people like this interface? Will people enjoy this car design? Will people like having the cup holders in the doors? And so on.

There are an amazing number of smart people being held back by wasting time arguing over the unpredictable. At the core of this must be the desire to be right, to say "I called it!". But, getting things right is more likely through trial and iteration and being able to recognize failed attempts quickly (this is at the heart of the agile fail-fast engineering methodology).

Use your smarts. Apply them in areas where they are more reliable. Instead of foreseeing the future, spend your time thinking about how you know that you're right, or at least on the right track.

2030: A mini ice age climate reprieve

Articles have been going around touting a possible "mini ice age" coming in 2030. The premise is that scientists have predicted a significant drop in "sun activity" (which I think means the number of spots, which are essentially tides of fire), leading to a condition known as the Maunder Minimum, which will therefore lead to significant drops of temperature on Earth, as evidenced by the rare freezing of the Thames river in the late 1600s which coincided with the last Maunder Minimum.

It doesn't help that news outlets are titling their articles with hyperbolae like "the sun will 'go to sleep' in 2030" or "the sun will become inactive" and so on. Climate skeptics have already rallied around this, pointing out things like "the Sun is also part of the climate" and "no wonder they renamed it from warming to change", and so on. Are they right? As usual, they are not.

For one, the freezing of the Thames river was a local condition. While it's true that didn't happen often and didn't happen again after, the flow of the river was altered (sped up) by the replacement of structures in the water about a century later. In other words, we removed the conditions under which the river could freeze. Summers were not any cooler (which we'd expect if the sun is emitting significantly less energy), nor were overall temperatures affected elsewhere in the world. Furthermore, the Maunder Minimum purportedly at fault started 50 years before the Thames froze. So, either it was unrelated, or it took 50 years for the effects to catch up. Either way, we're not gonna see an ice age in 2030 as a result of this.

Suppose for a second that global temperatures will drop significantly as a result of reduced sun activity. What then? if we continue to blanket the Earth in greenhouse gases, we'll roast that much more when the sun becomes "active" again. If we truly believe temperatures will drop, it's even more incentive to get our clean air acts together and use that as a boost towards mitigating climate change damage.

Whose baby is it?

Scenario:

Girl "G" has a brother "Br" who is married to a pregnant girl "PG". G's boyfriend "BF" hypothesizes that G's baby "Ba" was not produced by communion with Br, but rather with an unknown 3rd party, "P". To prove Ba's origin, BF would like to compare Ba's DNA with G's. What can we deduce?

 

Assumptions  **:

1. PG is not related to G, meaning they are no nearer than 6th cousins and can therefore be expected to share less DNA than, say, 4th cousins (chosen because there's a range of sharing published). Thus, PG and G have at most 0.5% common DNA

2. Br is related to G as full sibling and is therefore expected to share 50% DNA. The exact amount may vary significantly, but he should certainly be no further in sharing than a 1st cousin, whose low end of sharing is 7%.

** - reference: 23andme.com's table. Also pasted at the end of the entry.

 

So, what's in the baby?

If the baby is a product of Br and PG, we'd expect to see half each of 50% and less than 0.5%, which should yield something around 25% (also called out in the niece/nephew section). A lower bound can be established by using the 1st cousin range, from that we should see half each of 7% and 0.5%, for a total of ~4% shared DNA. Using the 1st cousin as a crosscheck (because they also have half a family tree that is totally unrelated) we should see no lower than 7% aggregate. The latter is the more correct number, really, because it's already tested for realistic distributions of gene passing.

 

If the baby is a product of P and PG, we'd expect to see half each of less than 0.5% each, for a total of less than 0.5% DNA sharing.

Interpreting the results:

If the sharing is:

1. Greater than 7%, it is highly probable that Br is the father. I think in practice this number would be quite a bit higher (we'd expect it to be around 25%, typically). The edge-case is if P is significantly related to Br, such as Br's parent, uncle, or even grandparent.

2. Less than 0.5%, it is highly probably that Br is not the father.

3. Between 0.5% and 7%, we have a curious case on our hands. Either P or PG are more related to Br than expected. Choice of options depends highly on state of residence.

 

 

 

 

 

Solar-powered flight

I just found out about the Solar Impulse project. It's a solar-powered plane, essentially the Tesla's brethren for the sky. Pretty cool stuff! The goal of the project is to demonstrate the viability of solar.

The last leg of the flight traveled from Japan to Hawaii, a distance of about 5000 miles. No stops, no fuel. Just sun. The plane has batteries to store energy for night flights. This is quite practical because the Japan-Hawaii leg took 5 days. Non-stop.

I think there are two major sets of reactions to this:
1. Holy shit, the future is here, and yeah it's slow now but tech gets better!!!
2. 5 days? Fuck that. Is Honey Boo Boo back on?

There's not much sense in talking to set 2 because they won't care about any of this until it's a real product they can buy. Group 1, however, is interesting to me because we can actually quantify what the concrete technical challenges are and assess the viability of overcoming them.

For viability purposes, let's say that a solar-powered craft would need to reach the same customer scenario as a current fuel-powered plane. That is, a cruising speed in the 530-580mph range and the ability to carry hundreds of passengers. How much energy does that take? I'll use the Boeing 787 as my example since it's the most modern fuel-efficient passenger plane. Looking at the 787-9 specifications, we see that it can transport 408 passengers a distance of 9550 miles using 33384 gallons of fuel at a speed of 567mph. We also should know how much energy is stored in a gallon of fuel. Using the two listed options for "jet fuel", I've opted to just call it 120kBTU per gallon.

Time of travel = 9550 miles / 567 mph = 16.8 hours = ~6E4 seconds.
Energy used = 33384 gallons * 120kBTU per gallon * 1055 J per BTU = ~4.2E12 J
Power = 4.2E12 J / 6E4 s = 7E7 J/s = 70 MW.

How much surface area is needed to collect 70MW? In a sunny place like Tucson, AZ, peak solar energy (mid-day) reaches 1000-1100 watts per square meter. A more realistic average over the Earth, over 24 hours, is 164 watts. We can adjust this for daytime averages by doubling it since the night portion contributes practically zero to this aggregate. So, let's say a typical daytime produces 325 watts, with shorter term highs around 1000W. This gives us a factor of 3 bounding, which should be adequate for this study. It's also important to point out that, per the same source, only 8% of solar energy is reflected back to space by the atmosphere, meaning that going higher up doesn't appreciably increase the available solar power.

Based on the range of incoming solar rates and the power requirements, it would take about 70,000 - 200,000 square meters of cells, operating at perfect efficiency. To put this in perspective, a football field is just shy of 5000 square meters. In other words, even on a bright bright day, it would take wings the size of 7 football fields. And for the average day we're looking at about 20 fields each. This seems intractable, even with "improving tech". The biggest improvement is probably the efficiency of the solar cells, and we've already allowed for that.

The other way to slice this is to look at the per-pound requirements and see how much we win by reducing airplane weight.

Power per pound = 70MW / 557k lbs ~= 125 W per pound.

In other words, I could, in an ideal world, attach a newborn to a square meter cell and send them flying around Arizona. Scaling this up to a typical adult requires some assumptions about their size and luggage and stuff, but let's call it 200 pounds. I'm being optimistic about human sizes by the time this hypothetical solar future arrives. The incremental solar area to carry a human is therefore 25-70 square meters. That's about the size of a one-bedroom apartment. The real lesson here is that we can potentially gain a lot by reducing airplane weight. First, we no longer need to carry 25000 lbs of fuel. However, we do need to carry batteries. Let's say, for the sake of the optimistic argument, that we can make the batteries arbitrarily small. We may also be able to make the wings lighter since they no longer need to support all that fuel. Not sure what kinds of savings that gets us. I'm also not sure if we can significantly reduce the weight of the fuselage. So, not much savings there on a 500,000 pound plane.

For the sake of the absolutely optimistic argument, suppose we can make the weight of the airplane zero. To transport 400 typical adults and bags, we'd need around 10-30,000 square meters of wing. That's 1-3 football fields each. And remember, they have to be perfectly efficient. And weigh nothing. And the passengers are sitting inside an ideal, weightless bubble.

Overall, the idea of solar for mass air travel seems far-fetched, simply because the energy density of solar is not high enough.