ChrisLomont

Ha- I came here to say this - I've solved them this way for decades whenever I need one, since the derivation when I'm doodling is often quicker than finding it (or if I'm out somewhere and internet access is difficult).

Note you can use this trick for all sorts of sums, not just powers. After some experience you realize lots of sums are polynomials in the size, so just guess a polynomial without the coefficients, and plug in a few items to get the coefficients. Once you have a polynomial, you can prove the result by induction.

So, for example, summing terms of form k(k+4) from k=1 to n may be hard to look up, but you can guess the result is a polynomial of degree one more than the terms (so here, a cubic), do the generic trick, obtain the sum n(n+1)(2n+13)/6, then prove it via induction.

You can do generic items too, like sum (k+a)(k+b) to get abn + n(n+1)(3(a+b)+2n+1)/6.

It's a good technique.

Or just use Mathematica :)

SSDs could still do it for speed and to write less pages, making the drive last longer, and simply report the uncompressed space as used. They already do all sorts of tricks on pages such as moving them logically, having more internally than they report to use as pages wear out, and so on.

Given that, it's good sense to compress if at all possible simply to make the drive live longer.

And guess what - I just googled, tons of hits, and this has been done for a long time :)

So it makes sense, is done, and is important for modern SSD behavior.

That paper showed a minimum of 26 states, not a maximum. Later papers have increased this significantly.

[1] for example increased the number 10-fold. Papers like [2] have pushed this complexity per synapse into a much higher level of complexity (so much they don't even put a number on it).

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5247597/

[2] https://www.nature.com/articles/s41598-020-64874-9

Sorry for any confusion - what I wrote was "FM does not guarantee most mortgages" in reply to the OP claiming FM guaranteeing mortgages is subsidizing the housing market.

(And I ignored that FM is not the Federal Govt for now...)

From the stats of conforming mortgages being 40% of mortgages and the FM only buying 60% of those, FM is at most guaranteeing (to investors, for a fee) around 24% of mortgages. That's well under 51%, right?

So FM not guaranteeing most mortgages is true, and it's not even close.

>Do you think they don't attempt to keep the house prices from crashing ? (also known as getting more affordable).

Also known as wrecking tax base for police, schools, local and state economies.... This is a terrible idea - deliberately crashing any asset class, especially one underpinning the majority of local services.

Property taxes account for as much as 63% of state revenue (NH) to as little as 17% (DE and AL, both of which offset this loss by other specialized taxes). Over the US around 35% of state revenues are property tax.

For most states your desire would destroy the economy vastly worse than the 2008 recession or COVID, neither of which tanked such a huge amount of revenue used for services. Good idea there.

> 1) monetary policy

Also done because it affects all aspects of the economy, from manufacturing, to employment, to R&D, to medicine. Claiming this is done for housing is shortsighted. Such monetary policy is decorrelated from housing prices (which you can check in Excel if you like). So to change monetary policy simply to drive housing prices down is a blunt hammer that will also lessen employment, lessen investment in productive areas of the economy, lessen trade by making exports more expensive, etc.

>2) Subsidizing mortgages (Fannie mae, Freddie mac) - allows people to borrow more and so spend more

No, it does not make me able to afford more loan - that is determined by my income. It provides more liquidity for the market, lowering prices. If there was less liquidity, then money would be harder to get, making borrowing more expensive, not less expensive. If you look at research on what people borrow, the term is Ability to Pay (ATP) as the driving factor, which is based on income, not on Fannie providing liquidity. And if you read more research, you'll find that the increased liquidity lowers prices significantly. You have this completely backwards.

> 3) Zoning

Done to industrial plants being mixed with housing. Here's a paper [2] showing that the major driving cost of housing is the marginal cost of physical construction costs, not zoning. There are very few places where zoning is much of a restriction (mostly places where land is super scarce, which is not the majority of the US).

>4) Bailing out banks involved in real estate

The "bailouts" were loans to provide liquidity, repaid with interest, profiting the taxpayer [1]. Many banks were forced to take these loans against their will to prevent signaling to the market vulnerable banks, to lessen bank run issues [2]. This was the correct govt action to prevent further harm. I think you seriously misunderstand what the "bailouts" were or what they affected.

So on this point your belief is vastly removed from reality. Spend some time reading on the details of TARP and you'll learn banks paid taxpayers, not the other way around (and note taxpayers did not even fund TARP, the Fed did, who was paid back with interest - not a cent was raised in increased taxes).

> 6) Mortgage interest relief for home owners etc etc

This is done to encourage home ownership, not to make prices high or low (note mortgage interest deduction has existed through many boom and bust cycles of housing prices). A good place to check your claim is looking pre and post the recent big change in mortgage deduction laws, and again, there are decent econ papers studying the question. Such papers are vastly more accurate than your opinion.

[1] https://projects.propublica.org/bailout/

[2] http://archive.boston.com/business/articles/2009/05/15/first...

[3] https://www.nber.org/papers/w8835

That's a list of how long until the landlord can file an eviction, not how long an eviction takes.

"Thus, the eviction process can take from five weeks to three months, assuming there are no delays. If there are delays, the process can take as much as a year."

[1] https://www.findlaw.com/realestate/landlord-tenant-law/how-l...

>You will have put money into the property to keep its value up

You're ignoring what was written: if the building has value 0, then it is not maintained to keep the value up. Of you kept the value up, then it would not have an effective price of 0.

Of course most people put money into properties exactly to keep value up.

>also writing off all of those expenses

Writing off expenses does not make them free - you are still paying for them - out of otherwise profit. It just means you get taxed on net profit instead of taxed on property gross income. But you are still losing money.

Writing off expenses is not some free money giveaway.

The point was to illustrate that OP ignored costs involved for landlords in the thought experiment.

>Hedge funds have been buying houses at scale since the great recession.

Zillow tried that and lost over a billion dollars - I'd expect lots of those purchases are not the money makers you think they are.

>Which increases faster than incomes.

Not for the same size houses - the median house now is many times the size of a median house from 1950, and a few times the size of a median house from 1970. If you buy the same house previous generations bought, you'd find prices relatively the same.

>Hence the way each generation has a declining rate of home ownership.

That's not what historical data shows [1,2], going all the way back to 1900. Each generation has had higher ownership rates at equal points in life than each previous one, except perhaps a recent one due to the 2008 crash, but they're catching back up again.

Certainly there is no way you can claim each generation declines and see the same data FRED and Census post.

For example, FRED shows that Q2, 2022, at 65.8% is higher than all of history except the decade before the crash, and it is trending up again.

[1] https://fred.stlouisfed.org/series/RHORUSQ156N

[2] https://www2.census.gov/programs-surveys/decennial/tables/ti...

Where do you think some of your 401k returns come from?

Are you claiming zero money was spent on those properties for 30 years? I don't think that claim would stand on it's face.

Over 30 years all sorts of things would break, pipes, leaks, batteries corroding and leaking out, animals move in, windows broken, doors removed....

Detroit ruins show what zero money put into a building for 30 years looks like - gutted shells.

Show me an ad for a rentable place that has had zero money spent on the building for any maintenance for 30 years and I'll believe you.

Factors also depend on the age of the house and your location - harsher climates are much worse on various house factors.

A new house will have much less costs to maintain over 25 years than a 50 years old house.

Having owned a few houses (both relatively new), and having gfs with houses and seeing the stuff they've done, and with helping my mom and sister with their house decisions and fixing, the list above is not far off.

State Farm says to budget 1-4% of the value of a house for annual upkeep costs. You're significantly below that it sounds.

>> FM does not guarantee most mortgages,

>What? Of course Fannie and Freddie guarantee the MBS they issue

Yes, they guarantee the MBS they issue, which is on a minority of all loans. The fact remains they do NOT guarantee most mortgages. They guarantee conforming loans, which are around 40% of all mortgage loans. And of all conforming loans, they only end up buying ~60% of them. So they at most guarantee around 24% of all mortgages, which is certainly not most mortgages.

>Alice, who ....

Ignoring the other side where landlords write stuff off and renters get tax breaks. On the ownership side, you're also missing lots of tax changes.

So not identical.

Also, the govt has an interest in property ownership as they have solid evidence that people owning property in a region make them less more stable. So there's very good reason to provide tax incentives for policy reasons. It's been shown that tax incentives, dollar for dollar, are pretty good incentives compared to most other forms of government spending to affect policy.

>The IRS already taxes tons of benefits based on the imputed income, even if no cash changes hand.

And they have tons the other way too - all because they desire to affect outcomes. So that they can do it is not really strong evidence to if they should do it, unless you address all the reasons they desire to do it.

>Not if the supply of housing is completely inelastic.

Which it is not [1]. "most areas that are widely regarded as supply-inelastic are, in fact, severely land-constrained by their topography" which is not most of the country.

[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1193422

>I don't think this is true.

They do guarantee some loans, as I wrote above. The marketing blurb you copies cleverly does not state they will guarantee any mortgage loan.

If they did, the housing crisis would not have been such a crisis - the crisis happened when so many investors realized the loans they bought could crash and cause them massive losses - precisely because FM does NOT guarantee all loans.

They guarantee certain loans (conforming loans), and charge a fee to investors for this when they purchase MBS from Fannie Mae. Conforming loans make up under 40% of all mortgage loans. Of all conforming loans made, Freddie and Fannie end up purchasing about 60% of those.

It may be that they stopped buying loans they deem too risky, but that didn't use to be the case.

>Everyone (with shoes) is counting on their shoes increasing in value. So the government becomes focused on raising the prices of everyone's shoes

That is not how reality works. Prices go up because people are paying them - it has nothing to do with government. A seller wants the highest price, no matter what the govt or local markets do, and a buyer wants the lowest price, no matter what govt or local markets do. Each is competing against other sellers and buyers. At no point is the govt telling a seller they're too low or a buyer they're not high enough. If either side dislikes the deal, they walk.

It has nothing to do with being an asset class - the causality is the other way. Houses are valuable, are a significant amount of money for most people, and increase in value because, if nothing else, inflation - thus they're an asset. So is holding cash (which actually deflates in value, yet is an asset), so are bonds, stocks, annuities, pensions, and on and on.

As to the shoe example - here's more what happens:

People would all love it for their cars to increase in value, but in reality they do not. The govt is not making this market out of magic to satisfy people's desires - houses increase in value at slightly above inflation because the market values them so.

By your reasoning, govt is magically making prices go up, but the market would not simply follow along.

And, if the govt were magically making prices go up against market wishes, they're doing a terrible job at it - housing only increases around what other assets do - and that's the market doing it.

People have tried using govt or other forces to misprice markets, but that never lasts very long before wise investors pull the rug out and crash it.

History has a lot of examples of people both trying to fake high prices for force low prices by law and losing out to the market. The market commands vastly more resources than any govt to put things in check.

>There was a slight slump in rentals after the financial crisis, not before

And a significant decline in mortgages over that time, likely due to mortgage law changes as a result of the crash. Making it slightly harder to get a mortgage would, over time, move people from mortgages to rentals, which is exactly what the data shows, right?

UK added Basel capital rules, the affordability test, and changed capital ceilings in banks, among other changes. Academic papers list these as being major drives in declines in UK mortgage rates. Those people rent instead.

All with no need for speculators to drive the market up - the laws changed.

>Social rentals, which you are bizarrely conflating with private rentals

Ah, so now we're only taking a subset of renters. Good idea.

>To claim that you need to spend money equal to the tax-assessed value of the building over the course of 30 years to maintain equal value is slightly less ridiculous, but still not exactly reasonable.

No one wrote that either. You're reading what you want to argue into what is written yet again.

> which would be 30% of the property value over 30 years

Ignoring increasing property value, compound interest, opportunity cost, that plenty of places put this between 1 and 4%, and that pretty much all places indicate the rate increases as the property ages, and that this rate is for owners whereas tenants are statistically worse on property, then sure.

For example, State Farm [1] recommends between 1% and 4%, which would vastly increase your estimate. And tenants are statistically worse on property than owners

In reality it's a far larger cost over 30 years than 30% of the original price.

[1] https://www.statefarm.com/simple-insights/residence/how-to-b...

>Both Fannie and Freddie buy mortgages

Yes, I said as much. The OP claimed they guaranteed mortgages, which they do not.

I'm decently aware of the MBS market - I developed MBS pricing algorithms in the late 90s/early 00s for putting houses in tranches after a friend at a mortgage company asked for help with algorithms. Turns out the problem was NP-hard (a lattice based linear programming problem if I recall), but good heuristics from the literature and some special sauce outperformed their current (at that time) pricing.

Around the time the whole market blew up I was considering going to hedge funds, and was working out details of how all the math, science, and computer algos work to prepare for interviewing. After the market crash, I moved on more into scientific and R&D computing. But I still read papers in the area out of curiosity.

But the fact is the market is not "guaranteed" in any sense - which is likely good as 2008 showed.

>“ An asset class is a grouping of investments that exhibit similar characteristics and are subject to the same laws and regulations.”

Yes, I got that. Housing has been such for well over 100 years, right?

It is not treated as a service or utility because, well it is neither of those things at all.

Even if you somehow forced it into such a market, the value would still likely be the same cost to a homeowner, since there is not going to be some free lunch here. People willing to pay $X to live at Y will continue to be willing to do that. Services and utilities do not mean free or low cost.

>treat or normal clothing as an asset class

Because it is cheap, it wears out, and goes to zero value. You really don't want the value of your house to be zero, meaning it has no utility to anyone, including you.

Bingo - I'm surprised so many didn't understand the thread flow and jumped on this....

And there was a housing crash in there and decent growth in population over that time.

Next, instead of picking a window wrapping the biggest housing bust in a century, pick various decades and see how normal volatility behaves - and you might find this variability not uncommon.

In fact, from your own source, Figure 1 - the percent of rented properties is, well, nearly constant over the entire window (31% rented in 2007, 37% rented in 2017). And somewhere in there mortgage laws got significantly tighter - no need for pesky investors to be the cause of less mortgages.

So go figure, right? Lots of reasons and complexity in there.

>Are you really in good faith trying to argue that nobody will rent a house that is 30+ years old?

Nope, pointing out that in order to keep the house rentable, the landlord has in put money into over all those years, which the OP left out.

A house that has had no money spent on for 30 years would not be rentable, right?

So depreciation is not a free ride.

>is being treated as an asset class

It always has been and likely always will be an assert class - it can be sold later so it's an asset.

For well over 100 years the inflation adjusted price of new housing has been a quite similar rate per sq foot, despite the quality and safety having increased many fold over that time.

>Those will also get snapped up by investors.

Investors buy around 10-20% (depending on quarter) of all new properties (and likely because they paid to build most of that share).

That's a far cry from 100%.

>Fannie Mae guaranteeing mortgages

FM does not guarantee most mortgages, only certain govt types like FHA and VA loans, which the govt decided to back in order to help low income people get loans (otherwise the rates would be even higher for them).

FM buys up a lot of mortgages and sells them to investors, then turns around and puts the money back into productive use.

>taxing home owners on the imputed value of rent

What does this mean? You want to tax homeowners as if they paid themselves rent? (Which even then is net zero, so no tax...)

If you want people to pay income tax on the imputed rental value (which is likely not even legal - they are not getting an income from ownership - and courts have held income tax must be on sources of income), then you will increase the cost of home ownership, putting even further out of reach for most people.

>In those cases subsidies don't result in expanded supply, only increased prices.

Yet many places subsidies do result in new housing.....

As long as the owner puts significant money into the property over time to fight depreciation. Entropy applies to houses after all.

>you pay no income tax on your rental income

And are losing value on the property, which is the point of depreciation.

>~30 years later, you've deprecated it down to an effective value of $0

An no one will now rent, since your building has an effective value of $0 since it has become crap.

All throughout your list you ignore all the costs involved in being a landlord. Have any friends that have tried it? (I do). Did they become silly rich? Or did they quit because it is a major problem to actually make it very profitable versus other uses of capital and time? I'm a decently saavy investor (in many things), and have watched multiple friends start up rental properties, only to stop once it became clear that tenants destroy things, costs to maintain properties are volatile and astronomical, the work required is significant, and so on.

I have done the math on real estate investing many times, and each time have decided the returns are not worth it.

>The net result is that rental properties generate a ton of income for the owners

If it were so profitable, then tons of capital currently being spent on other uses (tech, medical, finance) would instead go into buying up more housing. But the fact is that being a landlord is not very profitable, so capital doesn't flood into that market - it is still mostly elsewhere.

Historically, housing has performed quite similar to the stock market for returns - as it should be. If housing were a better investment, money would flow in until they balanced. If housing is too poor an investment by screwing with taxes, then money will flow out into other more productive places. And if money flows out, people wanting housing will then have to pay even higher prices for less stock.

Yep.

>Aliasing can be eliminated by low-pass filtering (blurring) the input signal before sampling it.

Nope. I have a PhD in math, and have been doing filtering stuff for decades. You do not eliminate aliasing, you push the error out of the visible spectrum - end of story.

The naive, physically impossible undergrad textbooks might say differently, just like they'd teach Newton as gravity and ignore relativity, or teach the ideal gas law and ignore that real gasses are vastly more complex in behavior.

This is Wikipedia level knowledge: from the low-pass filter page [1]:

"However, the ideal filter is impossible to realize without also having signals of infinite extent in time, and so generally needs to be approximated for real ongoing signals, because the sinc function's support region extends to all past and future times."

So no ideal filter, sorry. That means leakage, which happens in every part of engineering (and is forced by physics, despite you not wanting to believe it). Ideal filters are math, not physics.

And this level is vastly below what is done in industry, what theory (and physics) forces onto real world filtering.

Once you discretize the signal, even after filtering, you have introduce lots of noise in lots of frequency ranges. The simple reason is that you are forced to perturb real sample values (which would require infinitely precise measurements) to the discrete ones your sensor records. These perturbations do not fit your frequency requirements. Don't believe it? Take a photo, apply your "ideal" low pass filter, then fit the resulting image using sin and cos waves of frequency no higher than than your filter - and you'll see it's impossible. You can only approximate it - and that is empirical proof you can do at home.

Another entire level that undergrad level understandings miss is that pretty much zero of the theorems you think apply actually do - because pretty much every one uses infinite precision samples (Nyquist, for example), infinite support reconstruction (physically impossible), and so on. In practice all of these things leave noise in various parts of frequency spectrums.

So, still want to argue that filters would somehow remove aliasing issues? Especially over a sensor with the number of samples and precision that a modern Sony sensor has?

>you are experiencing alias-free sound and image processing all day long

You are confusing Nyquist with reality - and ignoring that Nyquist doesn't even apply to audio (or video) - it's only an approximation to what is really happening. As an approximation it's useful, but the requirements of the theorem are not met in reality and the reconstruction is not met in reality.

Don't believe me? Go look at the proof for the Nyquist theorem, and pay attention to all the requirements that no physical device can meet. it's the frictionless spherical cow of audio processing. One glaring area it fails is the need for the infinite support sinc filter - which again is why real engineering is not so simplistic.

[1] https://en.wikipedia.org/wiki/Low-pass_filter

>They do need to push other images from where the sensor would be :).

Yes, taking a new photo. However, a photo of a photo is going to show artifacts in the frequency spectrum that should not be difficult to detect.

So they cannot edit a picture, even trying to feed it back into the sensor. And. if the signing is built into the die of the sensor, it would take incredible resources to even attempt to feed new data into the sensor grid itself, tech vastly beyond anyone but a nation state.

>I think having having which people may treat ad evidence which is trivial to fake is worse than something which people won't treat as evidence

So you're against police body cams, because everyday people might be faking all the bad police interactions? Because all cameras I've looked into would be easier to tamper with than one designed with signed images that's done well.

>it’s very plausible Apple invests more R&D into custom silicon and/or security in a year than these companies make in total revenue from selling cameras.

Why would you compare all of Apple to the subset of Sony that is cameras? That's a dishonest comparison, especially if you're going to complain about apples to oranges comparisons. Why not Apple camera revenue to Sony camera revenue?

And both have very little to do with the cost to make a secure chip, which either can easily afford if desired. Apple's not spending a significant amount of their budget on the security components, after all, are they?

Certainly Sony makes enough revenue and spends enough on R&D to develop state of the art technology, including security hardware.

>One hopes that Sony learned from PS3

You really think they learned nothing since the PS3?

What in that makes you think there are no aliasing artifacts? Yes, you can take a movie of a movie, and you introduce artifacts that simple frequency analysis will find. There's no reason ILM would even try to remove this for such an application - they simply want pretty visuals, not mathematically indistinguishable from reality digital compositing.

Take a photo. It's not a grid of values. You already screwed with high frequency components. Take a photo of that - you changed these again. It's not hard to detect this. There's an entire field for detecting forensically altered things, and no current tech goes undetected, certainly not stuff simply made for movies.

Or provide some link, paper, or serious scientific claim that ILM has magically removed all aliasing from images, which would, well, simply violate physics. What they actually do is try to move aliasing to less visible portions of a frequency spectrum - but those signals are still there and detectable.