mvilim

The two most obvious solutions to the thought experiment presented are either 1) space is absolute in some way (i.e. the classical Newtonian response) or 2) the behavior of space "here" is affected by the by distribution of matter "over there". General relativity gives us a strong argument in favor of (2) by showing that a) many physical principles thought to be absolute are actually relative and b) showing that mass "over there" affects the shape of space "here".

To say anything more concrete requires requires defining the question much more precisely. I believe there is still some disagreement on the interpretation of Mach's principle in light of general relativity. For example, see https://en.wikipedia.org/wiki/Mach's_principle#Variations_in... (and a couple sections above, the 1993 poll of physicists asking: "Is general relativity with appropriate boundary conditions of closure of some kind very Machian?"

I hope that is helpful in some way.

  | However, I've been toying around with the idea
  | of eventually writing a minimal 'vi' clone that
  | you cannot exit. I'm sure there's pent-up demand
  | just waiting for one!

> Why do there seem to be more examples of rapidly-completed major projects in the past than the present?

A large contributing factor is that major projects today are much more complicated than they were in the past. The tools we have built are always advancing, but the size of the human brain is not. As projects become more and more complicated, they require a larger number of people to collaborate, and that comes with almost unavoidable slowdowns and inefficiencies. The Lockheed P-80 is nowhere near as complex as the F-35. The BART extension might take longer to build than the transcontinental railroad, but there was no networking equipment on that railroad.

It's also important to distinguish between projects that are deep vs. broad (i.e. those solved by new thinking vs. those solved by scaling up). To be fair, most of the examples in the original article are indeed "deep" projects, but, for example, the Empire State Building was constructed quickly partly because there were 3500 people working on it. As technology has advanced, deep projects just get deeper. Although each level of technology builds on the last, there is still complexity added at every level.

http://hyperpolyglot.org/ is a great website with a similar idea.

Sorry, dropped a k on that 42. Should be 42k km. Though there are clearly no calculations here, using the distance from the center of the earth is standard for gravitational calculation. It makes more sense to say that the ISS is 7000km/42000km=1/6th of the distance to a geosynchronous orbit than to say it's 400km/35000km=1/90th.

There are two types of energy at play here: the gravitational potential energy and the kinetic energy of the orbiting object (necessary to maintain an orbit).

As you climb the cable, the force of gravity pulling you back to earth decreases, and the centrifugal force pulling you away from earth increases. The difference between these two is the force you need to provide to climb the cable.

I believe you are correct for tethers much shorter than geosynchronous orbit. Below geosynchronous orbit, the force of gravity is higher than the centrifugal force. Therefore, an object climbing a space elevator will have to provide energy equal to the integral of the difference between the centrifugal force and the gravitational force across the distance traveled. The remaining energy (the remaining gravitational potential and the kinetic energy of the orbit) will be leeched from the orbiting counterweight (requiring the counterweight to have a rocket to maintain orbit, as you suggested)

For tethers that extend beyond geosynchronous orbit, it is possible to for no energy to be removed from the counterweight (instead, all the non-climbing energy will be taken from the rotation of the earth). Imagine that we place a counterweight on a tether beyond geosynchronous orbit. This counterweight and the earth it form an orbiting two body system. The tether will be under tension (the force necessary to keep the counterweight in synchronous orbit) -- let's call that force T. A climber that scales the tether will exert some force T_1 on the counterweight, pulling it towards the earth. However, as long as T_1 is less than T, the counterweight will remain where it is. The force of the table on the earth will become T_2 = T - T_1. In other words, a portion of the force necessary to keep the counterweight in orbit will now be applied by the climber instead of by earth. The energy that the climber must apply is the same as before, but the counterweight is not affected. The remaining energy, by process of elimination, must come from the rotation of the earth.

Geosynchronous orbit is 42 km from the center of the earth while the ISS orbits 7k km from the center of the earth. I expect the experiments are being done at the ISS for convenience rather than from a plan to build a space elevator to the ISS. The article also cites speed and distance numbers that imply reaching a geosynchronous orbit.

To answer your questions more directly: 1) below geosynchronous orbit, yes. 2) No, the ability to extract energy from the earth's rotation is the main advantage. 3) Yes, but for a counterweight beyond geosynchronous orbit, the tension on the tether will pull it vertical.

Five and ten year US bonds have had lost less value than the three year bond in the past 8 months, so that doesn't seem sufficient to explain it (i.e. it makes the difference worse).

That said, I was very loose in my calculations. Without exact knowledge of their holdings and careful calculations, I'm not surprised that the numbers don't fully add up.

Addendum: I say you're "locked into" a bond here because most people don't consider the possibility of selling bonds (i.e. they plan to hold to maturity). However, you can sell most bonds (not directly back to the issuer but to other people). This may make the similarity between funds and ladders clearer. In the scenario 1 example, if you were to sell your bond, it would also be worth ~$99 (using the same argument as in scenario 2). In other words, the fact that you don't think of this as a loss if you don't sell the bond doesn't change the fact that the bond lost value (the comment by ThrustVectoring further down this chain says this well). If you assume the market pricing of interest rates is fair and that the market is perfectly efficient (i.e. no transaction fees, management fees, etc.), then the expected value of holding, rolling, or investing in a bond holding fund is all the same.

I think your key point is this: "If you suspect that rates are still rising when you let your ladder burn down then this can be a good approach." I agree with this statement.

If you disagree with the market pricing of interest rates, then yes, you should do something other than the market (i.e. what the bond fund would do). Letting the ladder burn down (as opposed to continuing to roll, as the fund would) is claiming that the rates will be higher than the market is currently pricing them.

If you agree with the market pricing of bonds, then the ladder is equivalent to the bond fund (because the bond fund is simply managing the ladder for you by proxy).

I looked up VFITX. It looks like they pay distributions (i.e. dividends) that are roughly proportional to the expectation of the interest rate over the average maturity of their holdings, so you need to take this into account when considering "what-if". They have paid approximately 1.4% in dividends during 2018. That makes their total losses around 0.6%.

This doesn't fully explain the underperformance of VFITX compared to a 3 year bond (which should have made 8 mo/12 mo * 2% = 1.3% in interest and lost around 0.7% on rising interest rates), a net gain of 0.6%.

So VFITX underperformed a three year bond by 1.2%. 0.13% of this is their management fee (0.2% * 8 mo/12 mo). I'm not able to explain the last 1% of difference.

However, in theory, a bond fund loses just as much value on an interest rate rise as the bonds it is holding lose. In my example above, the bond is worth ~$99 after the increase to a 3% rate, just like the fund. The only difference between the bond and the fund is the choice of when to liquidate or roll.

It's possible that VFITX got unlucky on the timing of their bond rolling (see cousin comment).

I don't think this has anything to do with how long you hold the fund. In essence, the original comment was using bond ladders as a proxy for holding bonds till expiration and using bond funds as a proxy for always liquidating your bonds and reinvesting at the new rate on any rate change. The question is really about holding vs liquidating bonds, not funds vs ladders (which theoretically could hold or liquidate, depending on their implementation). If the market is fairly priced, then there is no expected value difference between holding and liquidating.

In the example I gave above, the value of the fund in a year is still $102 (independent of whether they hold the bonds to maturity or whether they sell at the fair market value and reinvest at the higher rate). In your example, buying and holding a treasury would only be better than VGSH if the market on average underestimated the future interest rate over that time period (so that as VGSH rolled (i.e. liquidated and reinvested) its bonds at an average rate of less than 2%). This has less to do with holding vs liquidating than it has to do with fair pricing of the interest rate. The main difference between holding to maturity and rolling the bonds is this: if you hold to maturity you make a single large bet on the interest rate; if you roll your bonds, you make several smaller bets on the interest rate.

Yes, as you say, holding a bond instead of rolling it can lead to a different return (when the market expectation of the future rate is wrong). But for most people this is irrelevant, as they won't be better at valuing interest rates than the rest of the market.

No, bond ladders are not strictly better than a bond fund. In theory, they are equivalent. In a bond fund, you simply see your loss on rising interest rates more directly.

Scenario 1 (holding bonds to maturity, i.e. bond ladder):

Let's imagine you invest in a $100 1yr bond at a 2% rate. You will be paid $102 in a year's time. Immediately after you buy the bond, the rate goes to 3%. You are locked into the bond, so you can't switch to the higher rate (i.e. you've lost out on a potential $1).

Scenario 2 (bond funds, ignoring reinvestment):

Instead imagine that you invest $100 in a fund that currently holds 1yr bonds at a 2% rate. You expect to be able to sell this fund in a year's time for $102. Now the rate changes to 3%. You are not locked into the fund, but the fund is locked into the bonds that they bought. If you can sell your shares in the fund for $100, you could then buy the new 3% rate bonds directly (i.e. you have avoided the loss due to the interest rate change). This would be a risk-free arbitrage between the fund and the new bonds. The price of the fund needs to drop to ~$99 to be "fair" (to be precise, it's 1.02/1.03, not exactly 99). If you sell at ~$99 and buy new 3% bonds directly, you will receive $102 in a year's time, just like scenario 1.

In short, the bond fund loses value because you maintain the optionality to withdraw whenever you want (and invest at higher rates if rates go up). The expected value between bond funds and bond ladders is still the same. In essence, the difference is between holding bonds to maturity and having the possibility of selling them, which doesn't change the expected value.